Effective Float
Strategies
Frank
Mittelbach

Effective Float Strategies
DocEng Conference 2017, Malta

Introduction
Visualization
Adding Floats
Results

Frank Mittelbach
frank.mittelbach@latex-project.org

Comparisons
The End

LATEX3 Project

September, 2017
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What’s this all about . . .
Effective Float
Strategies
Frank
Mittelbach
Introduction

Pagination with floats

Visualization
Adding Floats
Results
Comparisons
The End

I Last year’s starting point
I Visualizing the generalapproach
I Adding floats to the mix
I Results
I ComparisonsJohn Tenniel, 1870

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Last year’s starting point(text-only case — no floats)
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Pagination with greedy algorithm fails for nearly
100% of the cases
Idea: use dynamic programming approach (e.g.,
Knuth/Plass) for pagination

Adding Floats
Results

Doable . . . Complexity is

ComparisonsI

The EndI

O(n) for fixed spread structureO(n2 ) otherwise

But . . .
I
Ithere is not enough flexibility in a pageThus: most of the time optimizing runs out of options

Add enough flexibility . . . throughI
I

spread height variations (run them long or short)paragraph variations (format to different heights)
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Last year’s starting point(text-only case — no floats)
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Pagination with greedy algorithm fails for nearly
100% of the cases
Idea: use dynamic programming approach (e.g.,
Knuth/Plass) for pagination

Adding Floats
Results

Doable . . . Complexity is

ComparisonsI

The EndI

O(n) for fixed spread structureO(n2 ) otherwise

But . . .
I
Ithere is not enough flexibility in a pageThus: most of the time optimizing runs out of options

Add enough flexibility . . . throughI
I

spread height variations (run them long or short)paragraph variations (format to different heights)
(

:

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)

Last year’s starting point(text-only case — no floats)
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Pagination with greedy algorithm fails for nearly
100% of the cases
Idea: use dynamic programming approach (e.g.,
Knuth/Plass) for pagination

Adding Floats
Results

Doable . . . Complexity is

ComparisonsI

The EndI

O(n) for fixed spread structureO(n2 ) otherwise

But . . .
I
Ithere is not enough flexibility in a pageThus: most of the time optimizing runs out of options

Add enough flexibility . . . throughI
I

spread height variations (run them long or short)paragraph variations (format to different heights)
(

:

:

)

Last year’s starting point(text-only case — no floats)
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Pagination with greedy algorithm fails for nearly
100% of the cases
Idea: use dynamic programming approach (e.g.,
Knuth/Plass) for pagination

Adding Floats
Results

Doable . . . Complexity is

ComparisonsI

The EndI

O(n) for fixed spread structureO(n2 ) otherwise

But . . .
I
Ithere is not enough flexibility in a pageThus: most of the time optimizing runs out of options

Add enough flexibility . . . throughI
I

spread height variations (run them long or short)paragraph variations (format to different heights)
(

:

:

)

Last year’s starting point(text-only case — no floats)
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Pagination with greedy algorithm fails for nearly
100% of the cases
Idea: use dynamic programming approach (e.g.,
Knuth/Plass) for pagination

Adding Floats
Results

Doable . . . Complexity is

ComparisonsI

The EndI

O(n) for fixed spread structureO(n2 ) otherwise

But . . .
I
Ithere is not enough flexibility in a pageThus: most of the time optimizing runs out of options

Add enough flexibility . . . throughI
I

spread height variations (run them long or short)paragraph variations (format to different heights)
(

:

:

)

Last year’s starting point(text-only case — no floats)
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Pagination with greedy algorithm fails for nearly
100% of the cases
Idea: use dynamic programming approach (e.g.,
Knuth/Plass) for pagination

Adding Floats
Results

Doable . . . Complexity is

ComparisonsI

The EndI

O(n) for fixed spread structureO(n2 ) otherwise

But . . .
I
Ithere is not enough flexibility in a pageThus: most of the time optimizing runs out of options

Add enough flexibility . . . throughI
I

spread height variations (run them long or short)paragraph variations (format to different heights)
(

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The battlefield
A visualization of the algorithms
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization
Adding Floats
Results
Comparisons
The End

John Tenniel, 1870
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Visualization of the algorithm
The Basics
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization
Adding Floats

0

xxx

xxx

Results
Comparisons
The End

The galley in need of pagination
I Blue bars represent (blocks of) lines
I Breaks happen only between blocks
I Above we mark candidate breaks (active nodes) in red

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Visualization of the algorithm
The Basics
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization
Adding Floats

230 20001

xxx

390 310 340

1

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2

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xxx

Results
Comparisons
The End

Active nodes
I Sliding window into the document
I Add new node when breakpoint can end a page
I Only the best solution (accumulated costs) is used
I Deactivate when too far from current point

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Visualization of the algorithm
The basics
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualizationxxx

Adding Floats

xxx

Results
Comparisons
The EndStep
I Generate a galley from source material . . .

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Visualization of the algorithm
The basics
Effective Float
Strategies
Frank
Mittelbach
Introduction

0

Visualizationxxx

Adding Floats

xxx

Results
Comparisons
The EndStep
I Make active node representing document start . . .

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Visualization of the algorithm
The basics
Effective Float
Strategies
Frank
Mittelbach
Introduction

0

Visualization
Adding Floats
Results
Comparisons
The End6

too close

Step
I Loop through breakpoints and try to make a page . . .

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Visualization of the algorithm
The basics
Effective Float
Strategies
Frank
Mittelbach
Introduction

0

Visualization
Adding Floats
Results
Comparisons
The End6

too close

Step
I Loop through breakpoints and try to make a page . . .

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Visualization of the algorithm
The basics
Effective Float
Strategies
Frank
Mittelbach
Introduction

0

Visualization
Adding Floats
Results
Comparisons
The End6

too close

Step
I Loop through breakpoints and try to make a page . . .

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Visualization of the algorithm
The basics
Effective Float
Strategies
Frank
Mittelbach
Introduction

0

Visualizationxxx

Adding Floats
Results
Comparisons
The End6

still too close

Step
I Loop through breakpoints and try to make a page . . .

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Visualization of the algorithm
The basics
Effective Float
Strategies
Frank
Mittelbach
Introduction

0

Visualizationxxx

Adding Floats
Results
Comparisons

6230

The EndStep
I . . . first success (costs 230) . . .

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Visualization of the algorithm
The basics
Effective Float
Strategies
Frank
Mittelbach
Introduction

230
0

1

Visualizationxxx

Adding Floats
Results
Comparisons

6230

The EndStep
I Make active node representing solution . . .

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Visualization of the algorithm
The basics
Effective Float
Strategies
Frank
Mittelbach
Introduction

230
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Visualizationxxx

Adding Floats
Results
Comparisons

6200

The EndStep
I . . . next success (costs 200) . . .

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Visualization of the algorithm
The basics
Effective Float
Strategies
Frank
Mittelbach
Introduction

230 200
0

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Visualization

1xxx

Adding Floats
Results
Comparisons

6200

The EndStep
I Make active node representing solution . . .

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Visualization of the algorithm
The basics
Effective Float
Strategies
Frank
Mittelbach
Introduction

230 200
0

1

Visualization

1xxx

Adding Floats
Results
Comparisons

6200

The End6
too closeStep
I Try second active node . . . (fail) . . .

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Visualization of the algorithm
The basics
Effective Float
Strategies
Frank
Mittelbach
Introduction

230 200
0

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Visualization

1xxx

Adding Floats
Results
Comparisons6

too far away

The EndStep
I Try making page (fail) . . .

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Visualization of the algorithm
The basics
Effective Float
Strategies
Frank
Mittelbach
Introduction

230 200
0

1

Visualization

1xxx

Adding Floats
Results
Comparisons6

too far away

The End

Step
I Disable active node too far away . . .

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Visualization of the algorithm
The basics
Effective Float
Strategies
Frank
Mittelbach
Introduction

230 200
0

1

Visualization

1xxx

Adding Floats
Results
Comparisons6

too far away

The End6

Step
I Try next active node (fail) . . .

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Visualization of the algorithm
The basics
Effective Float
Strategies
Frank
Mittelbach

230 200

Introduction

1

Visualizationxxx

Adding Floats

1xxx

Results
Comparisons

6

The End

too close

Step
I Other active nodes will fail too, so try next breaks . . .

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Visualization of the algorithm
The basics
Effective Float
Strategies
Frank
Mittelbach

230 200

Introduction

1

Visualizationxxx

Adding Floats

1xxx

Results
Comparisons

6

The Endstill too close

Step
I Continue trying . . .

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Visualization of the algorithm
The basics
Effective Float
Strategies
Frank
Mittelbach

230 200

Introduction

1

Visualizationxxx

Adding Floats

1xxx

Results
Comparisons

6

The Endstill too close

Step
I Continue trying . . .

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Visualization of the algorithm
The basics
Effective Float
Strategies
Frank
Mittelbach

230 200

Introduction

1

Visualizationxxx

Adding Floats

1xxx

Results
Comparisons

6

The End160

Step
I . . . success (costs 160) . . .

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Visualization of the algorithm
The basics
Effective Float
Strategies
Frank
Mittelbach

230 200

Introduction

1

Visualization

1xxx

Adding Floats

xxx

Results
Comparisons

6 6

The End

160
200

Step
I . . . alternative solution (costs 200) . . .

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Visualization of the algorithm
The basics
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

230 200

390

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Adding Floats

xxx

Results
Comparisons

6 6

The End

160
200

Step
I Make active node for best solution . . .

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Visualization of the algorithm
The basics
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

230 200

390

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Adding Floats

1xxx

Results
Comparisons

6

The End100

Step
I Next break with solution (costs 100) . . .

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Visualization of the algorithm
The basics
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

230 200

390

1

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Adding Floats

xxx

Results
Comparisons

6 6

The End

100
110

Step
I . . . alternative solution (cost 110) . . .

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Visualization of the algorithm
The basics
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

230 200

390 310

1

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Adding Floats

2xxx

Results
Comparisons

6 6

The End

100
110

Step
I Second solution is best overall, make active node . . .

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Visualization of the algorithm
The basics
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

230 200

390 310

1

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Adding Floats

2xxx

Results
Comparisons

6 6

The End100
110

6
too closeStep
I Try next active node to make third page (fail) . . .

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Visualization of the algorithm
The basics
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

230 200

390 3101

2xxx

Adding Floats

1

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Results
Comparisons

6

The Endtoo far away now

Step
I Try next break with first active node . . .

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Visualization of the algorithm
The basics
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

230 200

390 3101

2xxx

Adding Floats

1

2

xxx

Results
Comparisons

6

The Endtoo far away now

Step
I . . . disable active node (too far away) . . .

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Visualization of the algorithm
The basics
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

230 200

390 310

1

2

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Adding Floats

2xxx

Results
Comparisons

6 6

The End140

Step
I Try next active node (success, costs 140) . . .

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Visualization of the algorithm
The basics
Effective Float
Strategies
Frank
Mittelbach

230 200

Introduction

1

Visualization

1xxx

Adding Floats

390 310 340
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Results
Comparisons

6 6

The End140

Step
I Make new active node for solution . . .

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Visualization of the algorithm
The basics
Effective Float
Strategies
Frank
Mittelbach

230 200

Introduction

1

Visualization

1xxx

Adding Floats

390 310 340
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Comparisons

6 6

The End6
140
too close

Step
I Look at active nodes ending second page (fail) . . .

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Visualization of the algorithm
The basics
Effective Float
Strategies
Frank
Mittelbach

200

Introduction

390 310 340

1Visualizationxxx

Adding Floats

2

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Comparisons
The EndStep
I . . . continue with next break . . .

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Visualization of the algorithm
Complexity
Effective Float
Strategies
Frank
Mittelbach
Introduction

230 200
0

1

Visualizationxxx

Adding Floats

390 310 340

1

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2

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Comparisons
The EndComplexity
I Loop through all n breakpointsIand try making pages back to each active node

I Thus the complexity isI

O(n × haverage length of active listi)

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Visualization of the algorithm
Pages have identical heights
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

660

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Adding Floats
Results
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The End

In later parts of the document . . .
I active nodes for different pages may get close together

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Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

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Adding Floats
Results

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The EndStep
I One candidate solution . . .

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Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

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Adding Floats
Results

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I Another candidate solution . . .

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Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

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The End200

Step
I And as page height is identical this one competes too . . .

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Introduction
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The End200

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I So we only need to remember the best of them . . .

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Mittelbach
Introduction
Visualization

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The EndStep
I . . . and make one active node for it . . .

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Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

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too far away

The EndStep
I And . . .

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Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

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too far away

The EndStep
I And so . . .

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Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

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The EndStep
I And so on . . .

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Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

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The End160

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I And so on with . . .

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The End160
too close

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I And so on with all . . .

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Frank
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Introduction
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The End160
too close

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I And so on with all further . . .

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Frank
Mittelbach
Introduction
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I And so on with all further breaks . . .

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Introduction
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too far away

The EndStep
I And so on with all further breaks . . .

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Introduction
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too far away

The EndStep
I And so on with all further breaks . . .

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Introduction
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The EndStep
I And so on with all further breaks . . .

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Introduction
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The End

too close

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I And so on with all further breaks . . .

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too close

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I And so on with all further breaks . . .

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The EndStep
I And so on with all further breaks . . . (total of 4)

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The EndDifferent page heights are the more complex situation
I as we will have more active nodes to deal with . . .

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Frank
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Introduction
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The EndStep
I Trying to build page 6 (success) . . .

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Introduction
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The EndStep
I . . . an alternative (slightly higher costs) . . .

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Introduction
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I but overall better . . .

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I We can also make page 7 end here . . .

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I . . . thus we make another active node . . .

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Frank
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Introduction
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too far away

The EndStep
I Try next break . . .

(

:

:

)

Visualization of the algorithm
Pages have different heights
1030

Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

660

580

830

7
700

5

5

6

6

xxx

xxx

Adding Floats
Results

6
Comparisons

too far away

The EndStep
I First active node no longer reachable, thus disable . . .

(

:

:

)

Visualization of the algorithm
Pages have different heights
1030

Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

660

580

830

7
700

5

5

6

6

xxx

xxx

Adding Floats
Results

6

6Comparisons

100

The EndStep
I Next one is possible (costs 100) . . .

(

:

:

)

Visualization of the algorithm
Pages have different heights
1030

Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

660

580

830

7
700 680

5

5

6

6

xxx

6

xxx

Adding Floats
Results

6

6Comparisons

100

The EndStep
I . . . thus another solution for page 6 . . .

(

:

:

)

Visualization of the algorithm
Pages have different heights
1030

Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

660

580

830

7
700 680

5

5

6

6

xxx

6

xxx

Adding Floats
Results6

6

6Comparisons

100

The End160

Step
I A candidate for page 7 (costs 160) . . .

(

:

:

)

Visualization of the algorithm
Pages have different heights
1030

Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

660

580

830

7
700 680

5

5

6

6

xxx

6

xxx

Adding Floats
Results

6

6

6

6

Comparisons

100

The End160
too close

Step
I In fact the only one (as this one is too short), so . . .

(

:

:

)

Visualization of the algorithm
Pages have different heights
1030 990

Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

660

580

830

7
7
700 680

5

5

6

6

xxx

6

xxx

Adding Floats
Results

6

6

6

6

Comparisons

100

The End160
too closeStep
I . . . make yet another active node . . .

(

:

:

)

Visualization of the algorithm
Pages have different heights
1030 990

Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

660

580

830

7
7
700 680

5

5

6

6

xxx

6

xxx

Adding Floats
Results

6

6

6

6

Comparisons

100

The End160
too close

Step
I Ending page 8 here doesn’t work . . .

(

:

:

)

Visualization of the algorithm
Pages have different heights
1030 990

Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

580

830

7
7
700 680

5

6

6

xxx

6

xxx

Adding Floats
Results

6
Comparisons

too far away

The EndStep
I Next break is too far from first active node . . .

(

:

:

)

Visualization of the algorithm
Pages have different heights
1030 990

Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

580

830

7
7
700 680

5

6

6

xxx

6

xxx

Adding Floats
Results

6
Comparisons

too far away

The EndStep
I . . . so we disable it . . .

(

:

:

)

Visualization of the algorithm
Pages have different heights
1030 990

Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

580

830

7
7
700 680

5

6

6

xxx

6

xxx

Adding Floats
Results

6

6Comparisons

145

The EndStep
I But next active node is a candidate for page 7 . . .

(

:

:

)

Visualization of the algorithm
Pages have different heights
1030 990

Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

580

830

7
7
700 680

5

6

6

xxx

6

xxx

Adding Floats
Results6

6

6Comparisons

145

The End

too close

Step
I In fact the only one, so . . .

(

:

:

)

Visualization of the algorithm
Pages have different heights
1030 990

Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

580

830

7
7
700 680

975

5

6

6

7

xxx

6

xxx

Adding Floats
Results6

6

6Comparisons

145

The End

too closeStep
I . . . make yet another active node . . .

(

:

:

)

Visualization of the algorithm
Pages have different heights
1030 990

Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

580

830

7
7
700 680

975

5

6

6

7

xxx

6

xxx

Adding Floats
Results6

6

6Comparisons

145

The End

too close

Step
I Page 8 is not possible from here, so we are done . . .

(

:

:

)

Visualization of the algorithm
Pages have different heights
1030 990

Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

xxx

830

7
7
700 680

975

6

6

7

xxx

6

xxx

Adding Floats
Results
Comparisons
The EndStep
I . . . and so on and so forth . . . (total of 6 in this example)

(

:

:

)

Visualization of the algorithm
Complexity II
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Pages have identical heights (after some page)
I Active list is bounded by a constantI ThusI

O(n × haverage length of active listi) = O(n)Adding Floats
Results
Comparisons
The EndPages have varying heights
I Active list can grow arbitrarily (i.e., O(n))
I Thus we end up withI

O(n × haverage length of active listi) = O(n2 )Spread and paragraph variations
I They add a factor of O(1) to the length of the active list
I Thus the complexity doesn’t change!
(

:

:

)

Visualization of the algorithm
Complexity II
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Pages have identical heights (after some page)
I Active list is bounded by a constantI ThusI

O(n × haverage length of active listi) = O(n)Adding Floats
Results
Comparisons
The EndPages have varying heights
I Active list can grow arbitrarily (i.e., O(n))
I Thus we end up withI

O(n × haverage length of active listi) = O(n2 )Spread and paragraph variations
I They add a factor of O(1) to the length of the active list
I Thus the complexity doesn’t change!
(

:

:

)

Visualization of the algorithm
Complexity II
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Pages have identical heights (after some page)
I Active list is bounded by a constantI ThusI

O(n × haverage length of active listi) = O(n)Adding Floats
Results
Comparisons
The EndPages have varying heights
I Active list can grow arbitrarily (i.e., O(n))
I Thus we end up withI

O(n × haverage length of active listi) = O(n2 )Spread and paragraph variations
I They add a factor of O(1) to the length of the active list
I Thus the complexity doesn’t change!
(

:

:

)

Managing floats
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization
Adding Floats
Results
Comparisons
The End

John Tenniel, 1870

(

:

:

)

Managing floats
A visualization
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization
Adding Floats
Results
Comparisons
The End

660

580

2

2

xxx

xxx

We extend the algorithm at the point where we . . .
I . . . add active nodes for a new spread (here page 3)
(

:

:

)

Managing floats
A visualization
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization
Adding Floats
Results
Comparisons
The End

660

580

2

2

xxx
6

xxx

110

Step
I Trying to build page 3 (success) . . .
(

:

:

)

Managing floats
A visualization
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization
Adding Floats
Results
Comparisons
The End

660

580

2

2

xxx

xxx
6

6

110
120

Step
I . . . an alternative (slightly higher costs) . . .
(

:

:

)

Managing floats
A visualization
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization
Adding Floats
Results
Comparisons
The End

660

580

700

2

2

3

xxx

xxx
6

6

110
120

Step
I but overall better . . . so this ends the spread!
(

:

:

)

Managing floats
A visualization
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization
Adding Floats
Results
Comparisons
The End

660

580

700

2

2

3

xxx

xxx
6

no floats

6

110
120

Now we prepare float placements for the next spreadI . . . this is for the case without floats
(

:

:

)

Managing floats
A visualization
700

Effective Float
Strategies

3
700

Frank
Mittelbach

3700

Introduction
Visualization
Adding Floats
Results
Comparisons
The End

660

580

3
700

2

2

3

float placement B
float placement A
no floats

xxx

xxx
6

..
.

6

110
120

Now we prepare float placements for the next spreadI . . . and for each layout with floats add another node
(

:

:

)

Managing floats
A visualization
700+. . .

Effective Float
Strategies

..
.
3
700+B
float placement B
3
700+A
float placement A
3
700
no floats
3

Frank
Mittelbach
Introduction
Visualization
Adding Floats
Results
Comparisons
The End

660

580

2

2

xxx

xxx

Now we prepare float placements for the next spreadI . . . which may have extra costs associated . . .
(

:

:

)

Managing floats
A visualization
700+. . .

Effective Float
Strategies

..
.
3
700+B
float placement B
3
700+A
float placement A
3
700
no floats
3

Frank
Mittelbach
Introduction
Visualization
Adding Floats
Results
Comparisons
The End

660

580

2

2

xxx
6

xxx

too far awayStep
I . . . then we continue looping . . .
(

:

:

)

Managing floats
A visualization
700+. . .

Effective Float
Strategies

..
.
3
700+B
float placement B
3
700+A
float placement A
3
700
no floats
3

Frank
Mittelbach
Introduction
Visualization
Adding Floats
Results
Comparisons
The End

660

580

2

2

xxx
6

xxx

too far awayStep
I . . . then we continue looping . . .
(

:

:

)

Managing floats
A visualization
700+. . .

Effective Float
Strategies

..
.
3
700+B
float placement B
3
700+A
float placement A
3
700
no floats
3

Frank
Mittelbach
Introduction
Visualization
Adding Floats
Results
Comparisons
The End

660

580

2

2

xxx

xxx

xxx

6
Step
I . . . and so on and so forth . . .
(

:

:

)

Executing the extended algorithm
Main points
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

When ending a spread
I Add new active nodes for each candidate placement
I Add “costs” in case the placement involves a preference rulethat can be determined at this point(e.g., some float regions are preferred over other)

Adding Floats
Results
Comparisons
The End

When seeing a call-out
I Check if any call-out/float relation is violated andif so deactivate the corresponding active node
I If a call-out/float preference rule is triggered we add

the corresponding costs to the active node
When attempting to make a page (or column)
I Make a new active node only if we have seen all required

call-outs (i.e., otherwise the attempt fails)
(

:

:

)

Executing the extended algorithm
Main points
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

When ending a spread
I Add new active nodes for each candidate placement
I Add “costs” in case the placement involves a preference rulethat can be determined at this point(e.g., some float regions are preferred over other)

Adding Floats
Results
Comparisons
The End

When seeing a call-out
I Check if any call-out/float relation is violated andif so deactivate the corresponding active node
I If a call-out/float preference rule is triggered we add

the corresponding costs to the active node
When attempting to make a page (or column)
I Make a new active node only if we have seen all required

call-outs (i.e., otherwise the attempt fails)
(

:

:

)

Executing the extended algorithm
Main points
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

When ending a spread
I Add new active nodes for each candidate placement
I Add “costs” in case the placement involves a preference rulethat can be determined at this point(e.g., some float regions are preferred over other)

Adding Floats
Results
Comparisons
The End

When seeing a call-out
I Check if any call-out/float relation is violated andif so deactivate the corresponding active node
I If a call-out/float preference rule is triggered we add

the corresponding costs to the active node
When attempting to make a page (or column)
I Make a new active node only if we have seen all required

call-outs (i.e., otherwise the attempt fails)
(

:

:

)

Executing the extended algorithm
Main points
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

When ending a spread
I Add new active nodes for each candidate placement
I Add “costs” in case the placement involves a preference rulethat can be determined at this point(e.g., some float regions are preferred over other)

Adding Floats
Results
Comparisons
The End

When seeing a call-out
I Check if any call-out/float relation is violated andif so deactivate the corresponding active node
I If a call-out/float preference rule is triggered we add

the corresponding costs to the active node
When attempting to make a page (or column)
I Make a new active node only if we have seen all required

call-outs (i.e., otherwise the attempt fails)
(

:

:

)

Executing the extended algorithm
Main points
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

When ending a spread
I Add new active nodes for each candidate placement
I Add “costs” in case the placement involves a preference rulethat can be determined at this point(e.g., some float regions are preferred over other)

Adding Floats
Results
Comparisons
The End

When seeing a call-out
I Check if any call-out/float relation is violated andif so deactivate the corresponding active node
I If a call-out/float preference rule is triggered we add

the corresponding costs to the active node
When attempting to make a page (or column)
I Make a new active node only if we have seen all required

call-outs (i.e., otherwise the attempt fails)
(

:

:

)

Executing the extended algorithm
Main points
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

When ending a spread
I Add new active nodes for each candidate placement
I Add “costs” in case the placement involves a preference rulethat can be determined at this point(e.g., some float regions are preferred over other)

Adding Floats
Results
Comparisons
The End

When seeing a call-out
I Check if any call-out/float relation is violated andif so deactivate the corresponding active node
I If a call-out/float preference rule is triggered we add

the corresponding costs to the active node
When attempting to make a page (or column)
I Make a new active node only if we have seen all required

call-outs (i.e., otherwise the attempt fails)
(

:

:

)

Precompute candidate float placements(whenever a spread has ended)
Effective Float
Strategies

Without any restricting rules (the bad case)Frank
Mittelbach

I We know which floats have already been placed

Introduction

I There is only a limited amount of space available

Visualization

I But beyond that: We know nothing!

Adding Floats
Results
Comparisons
The End

Important facts resulting from the above
I Number of placements is O(nc ) for some constant c > 1
I

c is roughly the average the number of floats
that can be placed on a spread

(

:

:

)

Precompute candidate float placements(whenever a spread has ended)
Effective Float
Strategies

Without any restricting rules (the bad case)Frank
Mittelbach

I We know which floats have already been placed

Introduction

I There is only a limited amount of space available

Visualization

I But beyond that: We know nothing!

Adding Floats
Results
Comparisons
The End

Important facts resulting from the above
I Number of placements is O(nc ) for some constant c > 1
I

c is roughly the average the number of floats
that can be placed on a spread

(

:

:

)

Precompute candidate float placements(whenever a spread has ended)
Effective Float
Strategies

Without any restricting rules (the bad case)Frank
Mittelbach

I We know which floats have already been placed

Introduction

I There is only a limited amount of space available

Visualization

I But beyond that: We know nothing!

Adding Floats
Results
Comparisons
The End

Important facts resulting from the above
I Number of placements is O(nc ) for some constant c > 1
I

c is roughly the average the number of floats
that can be placed on a spread

(

:

:

)

Precompute candidate float placements(whenever a spread has ended)
Effective Float
Strategies

Without any restricting rules (the bad case)Frank
Mittelbach

I We know which floats have already been placed

Introduction

I There is only a limited amount of space available

Visualization

I But beyond that: We know nothing!

Adding Floats
Results
Comparisons
The End

Important facts resulting from the above
I Number of placements is O(nc ) for some constant c > 1
I

c is roughly the average the number of floats
that can be placed on a spread

(

:

:

)

Precompute candidate float placements(whenever a spread has ended)
Effective Float
Strategies

Without any restricting rules (the bad case)Frank
Mittelbach

I We know which floats have already been placed

Introduction

I There is only a limited amount of space available

Visualization

I But beyond that: We know nothing!

Adding Floats
Results
Comparisons
The End

Important facts resulting from the above
I Number of placements is O(nc ) for some constant c > 1
I

c is roughly the average the number of floats
that can be placed on a spread

(

:

:

)

Precompute candidate float placements(whenever a spread has ended)
Effective Float
Strategies

Without any restricting rules (the bad case)Frank
Mittelbach

I We know which floats have already been placed

Introduction

I There is only a limited amount of space available

Visualization

I But beyond that: We know nothing!

Adding Floats
Results
Comparisons
The End

Important facts resulting from the above
I Number of placements is O(nc ) for some constant c > 1
I

c is roughly the average the number of floats
that can be placed on a spread

So this will get unmanageable fast!

(

:

:

)

Float rules (structuring the approach)
Different types of rules
Effective Float
Strategies
Frank
Mittelbach
Introduction

Rule types
I Absolute rules: placement not allowed if violated
I Preference rules: placement is (un)favorable

Visualization
Adding Floats
Results
ComparisonsCall-out / float constraints
I Floats are placed in order of their first/main call-out
I

The EndDifferent streams are (usually) independent

I A float must appear after its call-out . . .

same or later column (usual approach)strictly after (fairly restrictive)
I same page or spread or later (difficult with greedy
algorithms; involves reformatting)
I must be placed in their subsection (dangerous)
I must be visible from the call-out (very dangerous)
I
I

(

:

:

)

Float rules (structuring the approach)
Different types of rules
Effective Float
Strategies
Frank
Mittelbach
Introduction

Rule types
I Absolute rules: placement not allowed if violated
I Preference rules: placement is (un)favorable

Visualization
Adding Floats
Results
ComparisonsCall-out / float constraints
I Floats are placed in order of their first/main call-out
I

The EndDifferent streams are (usually) independent

I A float must appear after its call-out . . .

same or later column (usual approach)strictly after (fairly restrictive)
I same page or spread or later (difficult with greedy
algorithms; involves reformatting)
I must be placed in their subsection (dangerous)
I must be visible from the call-out (very dangerous)
I
I

(

:

:

)

Float rules (structuring the approach)
Different types of rules
Effective Float
Strategies
Frank
Mittelbach
Introduction

Rule types
I Absolute rules: placement not allowed if violated
I Preference rules: placement is (un)favorable

Visualization
Adding Floats
Results
ComparisonsCall-out / float constraints
I Floats are placed in order of their first/main call-out
I

The EndDifferent streams are (usually) independent

I A float must appear after its call-out . . .

same or later column (usual approach)strictly after (fairly restrictive)
I same page or spread or later (difficult with greedy
algorithms; involves reformatting)
I must be placed in their subsection (dangerous)
I must be visible from the call-out (very dangerous)
I
I

(

:

:

)

Float rules (structuring the approach)
Different types of rules
Effective Float
Strategies
Frank
Mittelbach
Introduction

Rule types
I Absolute rules: placement not allowed if violated
I Preference rules: placement is (un)favorable

Visualization
Adding Floats
Results
ComparisonsCall-out / float constraints
I Floats are placed in order of their first/main call-out
I

The EndDifferent streams are (usually) independent

I A float must appear after its call-out . . .

same or later column (usual approach)strictly after (fairly restrictive)
I same page or spread or later (difficult with greedy
algorithms; involves reformatting)
I must be placed in their subsection (dangerous)
I must be visible from the call-out (very dangerous)
I
I

(

:

:

)

Float rules (structuring the approach)
Different types of rules
Effective Float
Strategies
Frank
Mittelbach
Introduction

Rule types
I Absolute rules: placement not allowed if violated
I Preference rules: placement is (un)favorable

Visualization
Adding Floats
Results
ComparisonsCall-out / float constraints
I Floats are placed in order of their first/main call-out
I

The EndDifferent streams are (usually) independent

I A float must appear after its call-out . . .

same or later column (usual approach)strictly after (fairly restrictive)
I same page or spread or later (difficult with greedy
algorithms; involves reformatting)
I must be placed in their subsection (dangerous)
I must be visible from the call-out (very dangerous)
I
I

(

:

:

)

Float rules (structuring the approach)
Different types of rules
Effective Float
Strategies
Frank
Mittelbach
Introduction

Rule types
I Absolute rules: placement not allowed if violated
I Preference rules: placement is (un)favorable

Visualization
Adding Floats
Results
ComparisonsCall-out / float constraints
I Floats are placed in order of their first/main call-out
I

The EndDifferent streams are (usually) independent

I A float must appear after its call-out . . .

same or later column (usual approach)strictly after (fairly restrictive)
I same page or spread or later (difficult with greedy
algorithms; involves reformatting)
I must be placed in their subsection (dangerous)
I must be visible from the call-out (very dangerous)
I
I

(

:

:

)

Float rules (structuring the approach)
Different types of rules
Effective Float
Strategies
Frank
Mittelbach
Introduction

Rule types
I Absolute rules: placement not allowed if violated
I Preference rules: placement is (un)favorable

Visualization
Adding Floats
Results
ComparisonsCall-out / float constraints
I Floats are placed in order of their first/main call-out
I

The EndDifferent streams are (usually) independent

I A float must appear after its call-out . . .

same or later column (usual approach)strictly after (fairly restrictive)
I same page or spread or later (difficult with greedy
algorithms; involves reformatting)
I must be placed in their subsection (dangerous)
I must be visible from the call-out (very dangerous)
I
I

(

:

:

)

Float rules (structuring the approach)
Different types of rules
Effective Float
Strategies
Frank
Mittelbach
Introduction

Rule types
I Absolute rules: placement not allowed if violated
I Preference rules: placement is (un)favorable

Visualization
Adding Floats
Results
ComparisonsCall-out / float constraints
I Floats are placed in order of their first/main call-out
I

The EndDifferent streams are (usually) independent

I A float must appear after its call-out . . .

same or later column (usual approach)strictly after (fairly restrictive)
I same page or spread or later (difficult with greedy
algorithms; involves reformatting)
I must be placed in their subsection (dangerous)
I must be visible from the call-out (very dangerous)
I
I

(

:

:

)

Float rules (structuring the approach)
Different types of rules, continued
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Column, page, spread related constraints
I Number of floats
I

Example: no more than x floats on top of column
Example: no more than y floats on spread

I

Example: more than one float per page is discouraged

I

Adding Floats
Results
Comparisons
The EndI Area sizing
I
I

Example: minimum of x% of text required
Example: bottom area must be smaller than . . .

I Area relations
I
I

Example: only top or bottom area can be used
Example: Adjacent areas need visually compatible floats

(

:

:

)

Float rules (structuring the approach)
Different types of rules, continued
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Column, page, spread related constraints
I Number of floats
I

Example: no more than x floats on top of column
Example: no more than y floats on spread

I

Example: more than one float per page is discouraged

I

Adding Floats
Results
Comparisons
The EndI Area sizing
I
I

Example: minimum of x% of text required
Example: bottom area must be smaller than . . .

I Area relations
I
I

Example: only top or bottom area can be used
Example: Adjacent areas need visually compatible floats

(

:

:

)

Float rules (structuring the approach)
Different types of rules, continued
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Column, page, spread related constraints
I Number of floats
I

Example: no more than x floats on top of column
Example: no more than y floats on spread

I

Example: more than one float per page is discouraged

I

Adding Floats
Results
Comparisons
The EndI Area sizing
I
I

Example: minimum of x% of text required
Example: bottom area must be smaller than . . .

I Area relations
I
I

Example: only top or bottom area can be used
Example: Adjacent areas need visually compatible floats

(

:

:

)

Float rules (structuring the approach)
Different types of rules, continued
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Column, page, spread related constraints
I Number of floats
I

Example: no more than x floats on top of column
Example: no more than y floats on spread

I

Example: more than one float per page is discouraged

I

Adding Floats
Results
Comparisons
The EndI Area sizing
I
I

Example: minimum of x% of text required
Example: bottom area must be smaller than . . .

I Area relations
I
I

Example: only top or bottom area can be used
Example: Adjacent areas need visually compatible floats

(

:

:

)

Precompute candidate float placements(whenever a spread has ended)
Effective Float
Strategies
Frank
Mittelbach

Floats are sequenced (the better case)

Introduction

I We know which floats are next in sequence

Visualization

I There is only a limited amount of space available

Adding Floats

I We know if a call-out for a float can appear on

Results
Comparisons

the next spread

The End

Important facts
I Number of placements is bounded by a constant
I Placements can be computed in linear time (and fast)

(

:

:

)

Precompute candidate float placements(whenever a spread has ended)
Effective Float
Strategies
Frank
Mittelbach

Floats are sequenced (the better case)

Introduction

I We know which floats are next in sequence

Visualization

I There is only a limited amount of space available

Adding Floats

I We know if a call-out for a float can appear on

Results
Comparisons

the next spread

The End

Important facts
I Number of placements is bounded by a constant
I Placements can be computed in linear time (and fast)

(

:

:

)

Precompute candidate float placements(whenever a spread has ended)
Effective Float
Strategies
Frank
Mittelbach

Floats are sequenced (the better case)

Introduction

I We know which floats are next in sequence

Visualization

I There is only a limited amount of space available

Adding Floats

I We know if a call-out for a float can appear on

Results
Comparisons

the next spread

The End

Important facts
I Number of placements is bounded by a constant
I Placements can be computed in linear time (and fast)

(

:

:

)

Precompute candidate float placements(whenever a spread has ended)
Effective Float
Strategies
Frank
Mittelbach

Floats are sequenced (the better case)

Introduction

I We know which floats are next in sequence

Visualization

I There is only a limited amount of space available

Adding Floats

I We know if a call-out for a float can appear on

Results
Comparisons

the next spread

The End

Important facts
I Number of placements is bounded by a constant
I Placements can be computed in linear time (and fast)

(

:

:

)

Precompute candidate float placements(whenever a spread has ended)
Effective Float
Strategies
Frank
Mittelbach

Floats are sequenced (the better case)

Introduction

I We know which floats are next in sequence

Visualization

I There is only a limited amount of space available

Adding Floats

I We know if a call-out for a float can appear on

Results
Comparisons

the next spread

The End

Important facts
I Number of placements is bounded by a constant
I Placements can be computed in linear time (and fast)

(

:

:

)

Precompute candidate float placements(whenever a spread has ended)
Effective Float
Strategies
Frank
Mittelbach

Floats are sequenced (the better case)

Introduction

I We know which floats are next in sequence

Visualization

I There is only a limited amount of space available

Adding Floats

I We know if a call-out for a float can appear on

Results
Comparisons

the next spread

The End

Important facts
I Number of placements is bounded by a constant
I Placements can be computed in linear time (and fast)

(

:

:

)

Complexity with sequenced floats
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Assumptions
I Floats are placed sequentially
I Different float streams are independent
I Relation between # of floats and the document length is linear

Adding Floats
Results
Comparisons
The End

The length of the active list
I First float on the next spread may be any of the floats (i.e., thepossibilities are equal to # of floats)
I Number of different candidate solutions with the first float

fixed is bounded by a constant
The overall complexity is therefore
I O(n# of float streams+1 ) if the page height is fixed
I O(n# of float streams+2 ) otherwise
(

:

:

)

Complexity with sequenced floats
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Assumptions
I Floats are placed sequentially
I Different float streams are independent
I Relation between # of floats and the document length is linear

Adding Floats
Results
Comparisons
The End

The length of the active list
I First float on the next spread may be any of the floats (i.e., thepossibilities are equal to # of floats)
I Number of different candidate solutions with the first float

fixed is bounded by a constant
The overall complexity is therefore
I O(n# of float streams+1 ) if the page height is fixed
I O(n# of float streams+2 ) otherwise
(

:

:

)

Complexity with sequenced floats
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Assumptions
I Floats are placed sequentially
I Different float streams are independent
I Relation between # of floats and the document length is linear

Adding Floats
Results
Comparisons
The End

The length of the active list
I First float on the next spread may be any of the floats (i.e., thepossibilities are equal to # of floats)
I Number of different candidate solutions with the first float

fixed is bounded by a constant
The overall complexity is therefore
I O(n# of float streams+1 ) if the page height is fixed
I O(n# of float streams+2 ) otherwise
(

:

:

)

Complexity with sequenced floats
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Assumptions
I Floats are placed sequentially
I Different float streams are independent
I Relation between # of floats and the document length is linear

Adding Floats
Results
Comparisons
The End

The length of the active list
I First float on the next spread may be any of the floats (i.e., thepossibilities are equal to # of floats)
I Number of different candidate solutions with the first float

fixed is bounded by a constant
The overall complexity is therefore
I O(n# of float streams+1 ) if the page height is fixed
I O(n# of float streams+2 ) otherwise
(

:

:

)

Complexity with sequenced floats
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Assumptions
I Floats are placed sequentially
I Different float streams are independent
I Relation between # of floats and the document length is linear

Adding Floats
Results
Comparisons
The End

The length of the active list
I First float on the next spread may be any of the floats (i.e., thepossibilities are equal to # of floats)
I Number of different candidate solutions with the first float

fixed is bounded by a constant
The overall complexity is therefore
I O(n# of float streams+1 ) if the page height is fixed
I O(n# of float streams+2 ) otherwise
(

:

:

)

Complexity with sequenced floats
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Assumptions
I Floats are placed sequentially
I Different float streams are independent
I Relation between # of floats and the document length is linear

Adding Floats
Results
Comparisons
The End

The length of the active list
I First float on the next spread may be any of the floats (i.e., thepossibilities are equal to # of floats)
I Number of different candidate solutions with the first float

fixed is bounded by a constant
The overall complexity is therefore
I O(n# of float streams+1 ) if the page height is fixed
I O(n# of float streams+2 ) otherwise
(

:

:

)

The overall complexity — Anything non-linear is bad news
Effective Float
Strategies

Apply pruning

Frank
Mittelbach

I Require that floats stay close to

their call-out:
I Candidate solutions that
require too many
page-turns are dropped
I (unless floats cannot be
placed earlier)

Introduction
Visualization
Adding Floats
Results
Comparisons
The End

Is this adequate?
I Yes: Users expect to see a float

close to its call-out
John Tenniel, 1870

I Unnecessary page-turns reducereading experience
(

:

:

)

The overall complexity — Anything non-linear is bad news
Effective Float
Strategies

Apply pruning

Frank
Mittelbach

I Require that floats stay close to

their call-out:
I Candidate solutions that
require too many
page-turns are dropped
I (unless floats cannot be
placed earlier)

Introduction
Visualization
Adding Floats
Results
Comparisons
The End

Is this adequate?
I Yes: Users expect to see a float

close to its call-out
John Tenniel, 1870

I Unnecessary page-turns reducereading experience
(

:

:

)

The overall complexity — Anything non-linear is bad news
Effective Float
Strategies

Apply pruning

Frank
Mittelbach

I Require that floats stay close to

their call-out:
I Candidate solutions that
require too many
page-turns are dropped
I (unless floats cannot be
placed earlier)

Introduction
Visualization
Adding Floats
Results
Comparisons
The End

Is this adequate?
I Yes: Users expect to see a float

close to its call-out
John Tenniel, 1870

I Unnecessary page-turns reducereading experience
(

:

:

)

The overall complexity — With pruning applied
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization
Adding Floats
Results

Length of the active list
I First float on next spread must have its call-out close by
I Thus, the number of different possibilities for the

first float is bounded by a constantI Thus, the factor by which the active list can increase isbounded by a constantComparisons
The EndThe overall complexity drops back to
I O(n) if the page height is fixed
I O(n2 ) otherwise

(

:

:

)

The overall complexity — With pruning applied
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization
Adding Floats
Results

Length of the active list
I First float on next spread must have its call-out close by
I Thus, the number of different possibilities for the

first float is bounded by a constantI Thus, the factor by which the active list can increase isbounded by a constantComparisons
The EndThe overall complexity drops back to
I O(n) if the page height is fixed
I O(n2 ) otherwise

(

:

:

)

The overall complexity — With pruning applied
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization
Adding Floats
Results

Length of the active list
I First float on next spread must have its call-out close by
I Thus, the number of different possibilities for the

first float is bounded by a constantI Thus, the factor by which the active list can increase isbounded by a constantComparisons
The EndThe overall complexity drops back to
I O(n) if the page height is fixed
I O(n2 ) otherwise

(

:

:

)

The overall complexity — With pruning applied
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization
Adding Floats
Results

Length of the active list
I First float on next spread must have its call-out close by
I Thus, the number of different possibilities for the

first float is bounded by a constantI Thus, the factor by which the active list can increase isbounded by a constantComparisons
The EndThe overall complexity drops back to
I O(n) if the page height is fixed
I O(n2 ) otherwise

(

:

:

)

The overall complexity — With pruning applied
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization
Adding Floats
Results

Length of the active list
I First float on next spread must have its call-out close by
I Thus, the number of different possibilities for the

first float is bounded by a constantI Thus, the factor by which the active list can increase isbounded by a constantComparisons
The EndThe overall complexity drops back to
I O(n) if the page height is fixed
I O(n2 ) otherwise. . . which is where we want it to be

(

:

:

)

Time and space . . .
or what happens in real life
Effective Float
Strategies“Well, in OUR country,” said
Alice, still panting a little,“you’d generally get tosomewhere else—if you ranvery fast for a long time, as
we’ve been doing.”

Frank
Mittelbach
Introduction
Visualization
Adding Floats
Results
Comparisons
The End

John Tenniel, 1870

“A slow sort of country!” said
the Queen. “Now, HERE,
you see, it takes all therunning YOU can do, to keepin the same place. If you wantto get somewhere else, youmust run at least twice as fast
as that!”
(

:

:

)

The chosen challenge
Effective Float
Strategies

Through the Looking GlassFrank
Mittelbach

I A galley with 2516

breakpoints

Introduction

I 47 pictures to place

Visualization
Adding Floats
Results

The askComparisons

I Layout with 46 lines per

The EndcolumnI No orphans and widows!
I Maximum of one figure

per column
I Favor solutions withJohn Tenniel, 1870

sections at column top
(

:

:

)

Trial results with standard LATEX (i.e., greedy algorithm)
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Always enforced / preferred
I No widows and orphans
I Minimum of 2 text lines after a heading
I Encourage headings at top of columns

Adding Floats
Results
Comparisons
The End

Running time: less than 2 seconds
Results:I

98 text columns
55 good columns (badness < 4000)
1 horrible column (badness 6559)
I 34 infinitly bad columns
I

I

I
I

5 half-empty float columns
Only 1 heading at top of column (out of 9)

Estimated time for fixing: (35 + 5) × 15 min ≈ 10 hours
(

:

:

)

Trial results with standard LATEX (i.e., greedy algorithm)
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Always enforced / preferred
I No widows and orphans
I Minimum of 2 text lines after a heading
I Encourage headings at top of columns

Adding Floats
Results
Comparisons
The End

Running time: less than 2 seconds
Results:I

98 text columns
55 good columns (badness < 4000)
1 horrible column (badness 6559)
I 34 infinitly bad columns
I

I

I
I

5 half-empty float columns
Only 1 heading at top of column (out of 9)

Estimated time for fixing: (35 + 5) × 15 min ≈ 10 hours
(

:

:

)

Trial results with standard LATEX (i.e., greedy algorithm)
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Always enforced / preferred
I No widows and orphans
I Minimum of 2 text lines after a heading
I Encourage headings at top of columns

Adding Floats
Results
Comparisons
The End

Running time: less than 2 seconds
Results:I

98 text columns
55 good columns (badness < 4000)
1 horrible column (badness 6559)
I 34 infinitly bad columns
I

I

I
I

5 half-empty float columns
Only 1 heading at top of column (out of 9)

Estimated time for fixing: (35 + 5) × 15 min ≈ 10 hours
(

:

:

)

Trial results with standard LATEX (i.e., greedy algorithm)
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Always enforced / preferred
I No widows and orphans
I Minimum of 2 text lines after a heading
I Encourage headings at top of columns

Adding Floats
Results
Comparisons
The End

Running time: less than 2 seconds
Results:I

98 text columns
55 good columns (badness < 4000)
1 horrible column (badness 6559)
I 34 infinitly bad columns
I

I

I
I

5 half-empty float columns
Only 1 heading at top of column (out of 9)

Estimated time for fixing: (35 + 5) × 15 min ≈ 10 hours
(

:

:

)

Trial results with global optimization and no restrictions(other than sequencing)
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Always enforced / preferred
I No widows and orphans
I Minimum of 2 text lines after a heading
I Encourage headings at top of columns

Adding Floats
Results
Comparisons

Algorithm
I Include both paragraph and spread variations

The End

(

:

:

)

Trial results with global optimization and no restrictions(other than sequencing)
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Always enforced / preferred
I No widows and orphans
I Minimum of 2 text lines after a heading
I Encourage headings at top of columns

Adding Floats
Results
Comparisons

Algorithm
I Include both paragraph and spread variations

The EndMore than 10 hours processing time

(

:

:

)

Trial results with parameterized objective function(Floats and base algorithm and pruning)
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Always enforced / preferred
I No widows and orphans
I Minimum of 2 text lines after a heading
I Encourage headings at top of columns

Adding Floats
Results

Algorithm

Comparisons

I Just the base algorithm + floats

The End

I Try pruning after x page turns to shorten time necessary

(

:

:

)

Trial results with parameterized objective function(Floats and base algorithm and pruning)
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Always enforced / preferred
I No widows and orphans
I Minimum of 2 text lines after a heading
I Encourage headings at top of columns

Adding Floats
Results

Algorithm

Comparisons

I Just the base algorithm + floats

The End

I Try pruning after x page turns to shorten time necessary

Runs out of options to optimize near the beginning

(

:

:

)

Trial results with parameterized objective function(Floats and variations and pruning)
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Always enforced / preferred
I No widows and orphans
I Minimum of 2 text lines after a heading
I Encourage headings at top of columns

Adding Floats
Results

Restricting allowed page-turns

Comparisons

I Allow 0, 1, 2, 3, . . . turns (per float)

The End

I Costs = expensive / moderate / cheap

Spread length variations
I Disallowed / expensive / moderate / cheap

Paragraph length variations (\looseness)
I Disallowed / allowed (costs based on paragraph quality)
(

:

:

)

Trial results with parameterized objective function(Floats and variations and pruning)
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Always enforced / preferred
I No widows and orphans
I Minimum of 2 text lines after a heading
I Encourage headings at top of columns

Adding Floats
Results

Restricting allowed page-turns

Comparisons

I Allow 0, 1, 2, 3, . . . turns (per float)

The End

I Costs = expensive / moderate / cheap

Spread length variations
I Disallowed / expensive / moderate / cheap

Paragraph length variations (\looseness)
I Disallowed / allowed (costs based on paragraph quality)
(

:

:

)

Trial results with parameterized objective function(Floats and variations and pruning)
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Always enforced / preferred
I No widows and orphans
I Minimum of 2 text lines after a heading
I Encourage headings at top of columns

Adding Floats
Results

Restricting allowed page-turns

Comparisons

I Allow 0, 1, 2, 3, . . . turns (per float)

The End

I Costs = expensive / moderate / cheap

Spread length variations
I Disallowed / expensive / moderate / cheap

Paragraph length variations (\looseness)
I Disallowed / allowed (costs based on paragraph quality)
(

:

:

)

Trial results with parameterized objective function(Floats and paragraph variations)
Effective Float
Strategies
Frank
Mittelbach

I Horizontally: apply pruning after 0, 1, 2, . . . page turns
I Vertically: page turn costs are expensive / moderate / cheap

Introduction

I Champagne bottles indicate 8 or 9 sections placed on column top

Visualization

I Hourglass means this (and later) trials need more than 5 min

Adding Floats
Results
Comparisons
The End

(

:

:

)

Trial results with parameterized objective function(Floats and paragraph variations)
Effective Float
Strategies
Frank
Mittelbach

I Horizontally: apply pruning after 0, 1, 2, . . . page turns
I Vertically: page turn costs are expensive / moderate / cheap

Introduction

I Champagne bottles indicate 8 or 9 sections placed on column top

Visualization

I Hourglass means this (and later) trials need more than 5 min

Adding Floats
Results
Comparisons
The End

(

:

:

)

Trial results with parameterized objective function(Floats and paragraph variations)
Effective Float
Strategies
Frank
Mittelbach

I Horizontally: apply pruning after 0, 1, 2, . . . page turns
I Vertically: page turn costs are expensive / moderate / cheap

Introduction

I Champagne bottles indicate 8 or 9 sections placed on column top

Visualization

I Hourglass means this (and later) trials need more than 5 min

Adding Floats
Results
Comparisons
The End

(

:

:

)

Trial results with parameterized objective function(Floats and paragraph variations)
Effective Float
Strategies
Frank
Mittelbach

I Horizontally: apply pruning after 0, 1, 2, . . . page turns
I Vertically: page turn costs are expensive / moderate / cheap

Introduction

I Champagne bottles indicate 8 or 9 sections placed on column top

Visualization

I Hourglass means this (and later) trials need more than 5 min

Adding Floats
Results
Comparisons
The End

(

:

:

)

Trial results with parameterized objective function(Floats and paragraph variations)
Effective Float
Strategies
Frank
Mittelbach

I Horizontally: apply pruning after 0, 1, 2, . . . page turns
I Vertically: page turn costs are expensive / moderate / cheap

Introduction

I Champagne bottles indicate 8 or 9 sections placed on column top

Visualization

I Hourglass means this (and later) trials need more than 5 min

Adding Floats
Results
Comparisons
The End

(

:

:

)

Trial results with parameterized objective function(Floats and spread variations)
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization
Adding Floats
Results
Comparisons
The End

(

:

:

)

Trial results with parameterized objective function(Floats and all variations)
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization
Adding Floats
Results
Comparisons
The End

(

:

:

)

Summary of results(when using floats)
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Pagination with greedy algorithm still fails for nearly
all cases (i.e., floats do not make things better)
Idea: use dynamic programming approach forpagination with extra flexibility and add floats

Adding Floats
Results

Doable . . . in that case complexity is

ComparisonsI

The End

I

O(n# of float streams+1 ) if the page height is fixedO(n# of float streams+2 ) otherwise

But . . .
I
I

quadratic or cubic growth (or worse) is still too slow
who wants to wait 10+ hours each run?

Apply pruning . . . to cut down the search spaceI
I

this is reasonable as it fits with user expectations
and produces results in acceptable time!
(

:

:

)

Summary of results(when using floats)
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Pagination with greedy algorithm still fails for nearly
all cases (i.e., floats do not make things better)
Idea: use dynamic programming approach forpagination with extra flexibility and add floats

Adding Floats
Results

Doable . . . in that case complexity is

ComparisonsI

The End

I

O(n# of float streams+1 ) if the page height is fixedO(n# of float streams+2 ) otherwise

But . . .
I
I

quadratic or cubic growth (or worse) is still too slow
who wants to wait 10+ hours each run?

Apply pruning . . . to cut down the search spaceI
I

this is reasonable as it fits with user expectations
and produces results in acceptable time!
(

:

:

)

Summary of results(when using floats)
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Pagination with greedy algorithm still fails for nearly
all cases (i.e., floats do not make things better)
Idea: use dynamic programming approach forpagination with extra flexibility and add floats

Adding Floats
Results

Doable . . . in that case complexity is

ComparisonsI

The End

I

O(n# of float streams+1 ) if the page height is fixedO(n# of float streams+2 ) otherwise

But . . .
I
I

quadratic or cubic growth (or worse) is still too slow
who wants to wait 10+ hours each run?

Apply pruning . . . to cut down the search spaceI
I

this is reasonable as it fits with user expectations
and produces results in acceptable time!
(

:

:

)

Summary of results(when using floats)
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Pagination with greedy algorithm still fails for nearly
all cases (i.e., floats do not make things better)
Idea: use dynamic programming approach forpagination with extra flexibility and add floats

Adding Floats
Results

Doable . . . in that case complexity is

ComparisonsI

The End

I

O(n# of float streams+1 ) if the page height is fixedO(n# of float streams+2 ) otherwise

But . . .
I
I

quadratic or cubic growth (or worse) is still too slow
who wants to wait 10+ hours each run?

Apply pruning . . . to cut down the search spaceI
I

this is reasonable as it fits with user expectations
and produces results in acceptable time!
(

:

:

)

Summary of results(when using floats)
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Pagination with greedy algorithm still fails for nearly
all cases (i.e., floats do not make things better)
Idea: use dynamic programming approach forpagination with extra flexibility and add floats

Adding Floats
Results

Doable . . . in that case complexity is

ComparisonsI

The End

I

O(n# of float streams+1 ) if the page height is fixedO(n# of float streams+2 ) otherwise

But . . .
I
I

quadratic or cubic growth (or worse) is still too slow
who wants to wait 10+ hours each run?

Apply pruning . . . to cut down the search spaceI
I

this is reasonable as it fits with user expectations
and produces results in acceptable time!
(

:

:

)

Summary of results(when using floats)
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization

Pagination with greedy algorithm still fails for nearly
all cases (i.e., floats do not make things better)
Idea: use dynamic programming approach forpagination with extra flexibility and add floats

Adding Floats
Results

Doable . . . in that case complexity is

ComparisonsI

The End

I

O(n# of float streams+1 ) if the page height is fixedO(n# of float streams+2 ) otherwise

But . . .
I
I

quadratic or cubic growth (or worse) is still too slow
who wants to wait 10+ hours each run?

Apply pruning . . . to cut down the search spaceI
I

this is reasonable as it fits with user expectations
and produces results in acceptable time!
(

:

:

)

ComparisonsEffective Float
Strategies
Frank
Mittelbach
Introduction
Visualization
Adding Floats
Results
Comparisons
The End

John Tenniel, 1870
(

:

:

)

Comparison – spreads 1 + 2
greedy viz. optimal, 0 turns
Effective Float
Strategies—

THROUGH THE LOOKING-GLASS
By Lewis Carroll
The Millennium Fulcrum Edition 1.7

Introduction
Visualization

1

2

IMG1

Frank
Mittelbach
I. Looking-Glass housegreedyAdding Floats
Results

One thing was certain, that the WHITE kitten had
had nothing to do with it:—it was the black kitten’s
fault entirely. For the white kitten had been having
its face washed by the old cat for the last quarter ofan hour (and bearing it pretty well, considering); so
you see that it COULDN’T have had any hand in themischief.
The way Dinah IMG1
washed her children’s faces was
this: first she held the poor thing down by its ear with
one paw, and then with the other paw she rubbed its
face all over, the wrong way, beginning at the nose:and just now, as I said, she was hard at work on thewhite kitten, which was lying quite still and trying topurr—no doubt feeling that it was all meant for its
good.
But the black kitten had been finished with earlier in the afternoon, and so, while Alice was sitting curled up in a corner of the great arm-chair,half talking to herself and half asleep, the kitten had
been having a grand game of romps with the ball ofworsted Alice had been trying to wind up, and had
been rolling it up and down till it had all come undone
again; and there it was, spread over the hearth-rug,
all knots and tangles, with the kitten running after
its own tail in the middle.
‘Oh, you wicked little thing!’ cried Alice, catching up the kitten, and giving it a little kiss to make—IMG2

it understand that it was in disgrace. ‘Really, Dinah ought to have taught you better manners! YouOUGHT, Dinah, you know you ought!’ she added,
looking reproachfully at the old cat, and speaking inas cross a voice as she could manage—and then she
scrambled back into the arm-chair, taking the kitten and the worsted with her, and began winding up
the ball again. But she didn’t get on very fast, as
she was talking all the time, sometimes to the kitten,
and sometimes to herself. Kitty sat very demurely
on her knee, pretending to watch the progress of thewinding, and now and then putting out one paw andgently touching the ball, as if it would be glad to help,
if it might.
‘Do you know what to-morrow is, Kitty?’ Alicebegan. ‘You’d have guessed if you’d been up in thewindow with me—only Dinah was making you tidy,
so you couldn’t. I was watching the boys getting insticks for the bonfire—and it wants plenty of sticks,
Kitty! Only it got so cold, and it snowed so, they had
to leave off. Never mind, Kitty, we’ll go and see thebonfire to-morrow.’ Here Alice wound two or threeturns of the worsted round the kitten’s neck, justto see how it would look: this led to a scramble, inwhich the ball rolled down upon the floor, and yards
and yards of it got unwound again.
‘Do you know, I was so angry, Kitty,’ Alice wenton as soon as they were comfortably settled again,‘when I saw all the mischief you had been doing, I
was very nearly opening the window, and putting youout into the snow! And you’d have deserved it, you
little mischievous darling! What have you got to say
for yourself? Now don’t interrupt me!’ she went on,
holding up one finger. ‘I’m going to tell you all yourfaults. Number one: you squeaked twice while Dinah was washing your face this morning. Now you
can’t deny it, Kitty: I heard you! What’s that you
say?’ (pretending that the kitten was speaking.) ‘Herpaw went into your eye? Well, that’s YOUR fault,
for keeping your eyes open—if you’d shut them tightup, it wouldn’t have happened. Now don’t make any
more excuses, but listen! Number two: you pulled
Snowdrop away by the tail just as I had put down
the saucer of milk before her! What, you were thirsty,
were you? How do you know she wasn’t thirsty too?

Now for number three: you unwound every bit of theworsted while I wasn’t looking!
‘That’s three faults IMG2
, Kitty, and you’ve not beenpunished for any of them yet. You know I’m saving up all your punishments for Wednesday week—
Suppose they had saved up all MY punishments!’
she went on, talking more to herself than the kitten. ‘What WOULD they do at the end of a year?
I should be sent to prison, I suppose, when the day
came. Or—let me see—suppose each punishment was
to be going without a dinner: then, when the miserable day came, I should have to go without fifty dinners at once! Well, I shouldn’t mind THAT much!
I’d far rather go without them than eat them!
‘Do you hear the snow against the window-panes,
Kitty? How nice and soft it sounds! Just as if some
one was kissing the window all over outside. I wonder
if the snow LOVES the trees and fields, that it kisses
them so gently? And then it covers them up snug, youknow, with a white quilt; and perhaps it says, “Go
to sleep, darlings, till the summer comes again.” And
when they wake up in the summer, Kitty, they dress
themselves all in green, and dance about—whenever
the wind blows—oh, that’s very pretty!’ cried Alice,
dropping the ball of worsted to clap her hands. ‘And

I do so WISH it was true! I’m sure the woods look
sleepy in the autumn, when the leaves are getting
brown.
‘Kitty, can you play chess? Now, don’t smile, mydear, I’m asking it seriously. Because, when we wereplaying just now, you watched just as if you understood it: and when I said “Check!” you purred!
Well, it WAS a nice check, Kitty, and really I might
have won, if it hadn’t been for that nasty Knight,that came wiggling down among my pieces. Kitty,
dear, let’s pretend—’ And here I wish I could tell you
half the things Alice used to say, beginning with her
favourite phrase ‘Let’s pretend.’ She had had quite along argument with her sister only the day before—
all because Alice had begun with ‘Let’s pretend we’rekings and queens;’ and her sister, who liked being
very exact, had argued that they couldn’t, because
there were only two of them, and Alice had been reduced at last to say, ‘Well, YOU can be one of themthen, and I’LL be all the rest.’ And once she had really frightened her old nurse by shouting suddenly inher ear, ‘Nurse! Do let’s pretend that I’m a hungry
hyaena, and you’re a bone.’
But this is taking us away from Alice’s speech to
the kitten. ‘Let’s pretend that you’re the Red Queen,
Kitty! Do you know, I think if you sat up and folded
your arms, you’d look exactly like her. Now do try,
there’s a dear!’ And Alice got the Red Queen off
the table, and set it up before the kitten as a model
for it to imitate: however, the thing didn’t succeed,
principally, Alice said, because the kitten wouldn’t
fold its arms properly. So, to punish it, she held it
up to the Looking-glass, that it might see how sulky
it was—‘and if you’re not good directly,’ she added,‘I’ll put you through into Looking-glass House. How
would you like THAT?’‘Now, if you’ll only attend, Kitty, and not talk somuch, I’ll tell you all my ideas about Looking-glass
House. First, there’s the room you can see throughthe glass—that’s just the same as our drawing room,
only the things go the other way. I can see all of it
when I get upon a chair—all but the bit behind thefireplace. Oh! I do so wish I could see THAT bit! I
want so much to know whether they’ve a fire in thewinter: you never CAN tell, you know, unless ourfire smokes, and then smoke comes up in that room

—

3

IMG3

IMG4

too—but that may be only pretence, just to makeit look as if they had a fire. Well then, the books
are something like our books, only the words go thewrong way; I know that, because I’ve held up one ofour books to the glass, and then they hold up one in
the other room.
‘How would you IMG3
like to live in Looking-glass
House, Kitty? I wonder if they’d give you milkin there? Perhaps Looking-glass milk isn’t good todrink—But oh, Kitty! now we come to the passage. You can just see a little PEEP of the passage in Looking-glass House, if you leave the doorof our drawing-room wide open: and it’s very likeour passage as far as you can see, only you know it
may be quite different on beyond. Oh, Kitty! how
nice it would be if we could only get through into
Looking-glass House! I’m sure it’s got, oh! such
beautiful things in it! Let’s pretend there’s a wayof getting through into it, somehow, Kitty. Let’s pretend the glass has got all soft like gauze, so that we
can get through. Why, it’s turning into a sort of mist
now, I declare! It’ll be easy enough to get through—’
She was up on the chimney-piece while she said this,though she hardly knew how she had got there. And
certainly the glass WAS beginning to melt away, justlike a bright silvery mist.
In another moment IMG4
Alice was through the glass,and had jumped lightly down into the Looking-glass
room. The very first thing she did was to lookwhether there was a fire in the fireplace, and she wasquite pleased to find that there was a real one, blazing away as brightly as the one she had left behind.
‘So I shall be as warm here as I was in the old room,’
thought Alice: ‘warmer, in fact, because there’ll be
no one here to scold me away from the fire. Oh,
what fun it’ll be, when they see me through the glassin here, and can’t get at me!’Then she began looking about, and noticed thatwhat could be seen from the old room was quite common and uninteresting, but that all the rest was asdifferent as possible. For instance, the pictures on
the wall next the fire seemed to be all alive, and thevery clock on the chimney-piece (you know you can
only see the back of it in the Looking-glass) had got
the face of a little old man, and grinned at her.

Comparisons
The End— pagesize change: ≠12.0pt ——THROUGH THE LOOKING-GLASS
By Lewis Carroll
The Millennium Fulcrum Edition 1.7

1
IMG1

2

—

optimal

One thing was certain, that the WHITE kitten had
had nothing to do with it:—it was the black kitten’s
fault entirely. For the white kitten had been having
its face washed by the old cat for the last quarter ofan hour (and bearing it pretty well, considering); so
you see that it COULDN’T have had any hand in themischief.
The way Dinah IMG1
washed her children’s faces was
this: first she held the poor thing down by its ear with
one paw, and then with the other paw she rubbed its
face all over, the wrong way, beginning at the nose:and just now, as I said, she was hard at work on thewhite kitten, which was lying quite still and trying topurr—no doubt feeling that it was all meant for its
good.
But the black kitten had been finished with earlier in the afternoon, and so, while Alice was sitting curled up in a corner of the great arm-chair,half talking to herself and half asleep, the kitten had
been having a grand game of romps with the ball ofworsted Alice had been trying to wind up, and had
been rolling it up and down till it had all come undone
again; and there it was, spread over the hearth-rug,
all knots and tangles, with the kitten running after
its own tail in the middle.
‘Oh, you wicked little thing!’ cried Alice, catching up the kitten, and giving it a little kiss to makeit understand that it was in disgrace. ‘Really, Dinah ought to have taught you better manners! YouOUGHT, Dinah, you know you ought!’ she added,
looking reproachfully at the old cat, and speaking inas cross a voice as she could manage—and then she
scrambled back into the arm-chair, taking the kitten and the worsted with her, and began winding up
the ball again. But she didn’t get on very fast, as
she was talking all the time, sometimes to the kitten,
and sometimes to herself. Kitty sat very demurely
on her knee, pretending to watch the progress of thewinding, and now and then putting out one paw andgently touching the ball, as if it would be glad to help,
if it might.
‘Do you know what to-morrow is, Kitty?’ Alicebegan. ‘You’d have guessed if you’d been up in thewindow with me—only Dinah was making you tidy,
so you couldn’t. I was watching the boys getting insticks for the bonfire—and it wants plenty of sticks,
Kitty! Only it got so cold, and it snowed so, they had
to leave off. Never mind, Kitty, we’ll go and see thebonfire to-morrow.’ Here Alice wound two or threeturns of the worsted round the kitten’s neck, justto see how it would look: this led to a scramble, inwhich the ball rolled down upon the floor, and yards
and yards of it got unwound again.
‘Do you know, I was so angry, Kitty,’ Alice wenton as soon as they were comfortably settled again,‘when I saw all the mischief you had been doing, I
was very nearly opening the window, and putting
you out into the snow! And you’d have deserved
it, you little mischievous darling! What have you
got to say for yourself? Now don’t interrupt me!’she went on, holding up one finger. ‘I’m going totell you all your faults. Number one: you squeaked
twice while Dinah was washing your face this morning. Now you can’t deny it, Kitty: I heard you!
What’s that you say?’ (pretending that the kitten
was speaking.) ‘Her paw went into your eye? Well,that’s YOUR fault, for keeping your eyes open—
if you’d shut them tight up, it wouldn’t have happened. Now don’t make any more excuses, but listen! Number two: you pulled Snowdrop away by thetail just as I had put down the saucer of milk be-— pagesize change: 12.0pt —IMG2

I. Looking-Glass housefore her! What, you were thirsty, were you? How do
you know she wasn’t thirsty too? Now for number
three: you unwound every bit of the worsted while
I wasn’t looking!
‘That’s three faults IMG2
, Kitty, and you’ve not beenpunished for any of them yet. You know I’m saving up all your punishments for Wednesday week—
Suppose they had saved up all MY punishments!’
she went on, talking more to herself than the kitten. ‘What WOULD they do at the end of a year?
I should be sent to prison, I suppose, when the day
came. Or—let me see—suppose each punishment was
to be going without a dinner: then, when the miserable day came, I should have to go without fifty dinners at once! Well, I shouldn’t mind THAT much!
I’d far rather go without them than eat them!
‘Do you hear the snow against the window-panes,
Kitty? How nice and soft it sounds! Just as if some
one was kissing the window all over outside. I wonder
if the snow LOVES the trees and fields, that it kisses
them so gently? And then it covers them up snug, youknow, with a white quilt; and perhaps it says, “Go
to sleep, darlings, till the summer comes again.” And
when they wake up in the summer, Kitty, they dress
themselves all in green, and dance about—whenever
the wind blows—oh, that’s very pretty!’ cried Alice,

dropping the ball of worsted to clap her hands. ‘And
I do so WISH it was true! I’m sure the woods look
sleepy in the autumn, when the leaves are getting
brown.
‘Kitty, can you play chess? Now, don’t smile, mydear, I’m asking it seriously. Because, when we wereplaying just now, you watched just as if you understood it: and when I said “Check!” you purred!
Well, it WAS a nice check, Kitty, and really I might
have won, if it hadn’t been for that nasty Knight,that came wiggling down among my pieces. Kitty,
dear, let’s pretend—’ And here I wish I could tell you
half the things Alice used to say, beginning with her
favourite phrase ‘Let’s pretend.’ She had had quite along argument with her sister only the day before—
all because Alice had begun with ‘Let’s pretend we’rekings and queens;’ and her sister, who liked being
very exact, had argued that they couldn’t, because
there were only two of them, and Alice had been reduced at last to say, ‘Well, YOU can be one of themthen, and I’LL be all the rest.’ And once she had really frightened her old nurse by shouting suddenly inher ear, ‘Nurse! Do let’s pretend that I’m a hungry
hyaena, and you’re a bone.’
But this is taking us away from Alice’s speech to
the kitten. ‘Let’s pretend that you’re the Red Queen,
Kitty! Do you know, I think if you sat up and folded
your arms, you’d look exactly like her. Now do try,
there’s a dear!’ And Alice got the Red Queen off
the table, and set it up before the kitten as a model
for it to imitate: however, the thing didn’t succeed,
principally, Alice said, because the kitten wouldn’t
fold its arms properly. So, to punish it, she held it
up to the Looking-glass, that it might see how sulky
it was—‘and if you’re not good directly,’ she added,‘I’ll put you through into Looking-glass House. How
would you like THAT?’‘Now, if you’ll only attend, Kitty, and not talk somuch, I’ll tell you all my ideas about Looking-glass
House. First, there’s the room you can see throughthe glass—that’s just the same as our drawing room,
only the things go the other way. I can see all of it
when I get upon a chair—all but the bit behind thefireplace. Oh! I do so wish I could see THAT bit! I
want so much to know whether they’ve a fire in thewinter: you never CAN tell, you know, unless ourfire smokes, and then smoke comes up in that room

— pagesize change: 12.0pt —

—

3

IMG3

IMG4

too—but that may be only pretence, just to makeit look as if they had a fire. Well then, the books
are something like our books, only the words go thewrong way; I know that, because I’ve held up one ofour books to the glass, and then they hold up one in
the other room.
‘How would you IMG3
like to live in Looking-glass
House, Kitty? I wonder if they’d give you milkin there? Perhaps Looking-glass milk isn’t good todrink—But oh, Kitty! now we come to the passage. You can just see a little PEEP of the passage in Looking-glass House, if you leave the doorof our drawing-room wide open: and it’s very likeour passage as far as you can see, only you know it
may be quite different on beyond. Oh, Kitty! how
nice it would be if we could only get through into
Looking-glass House! I’m sure it’s got, oh! such
beautiful things in it! Let’s pretend there’s a wayof getting through into it, somehow, Kitty. Let’s pretend the glass has got all soft like gauze, so that we
can get through. Why, it’s turning into a sort of mist
now, I declare! It’ll be easy enough to get through—’
She was up on the chimney-piece while she said this,though she hardly knew how she had got there. And

certainly the glass WAS beginning to melt away, justlike a bright silvery mist.
In another moment IMG4
Alice was through the glass,and had jumped lightly down into the Looking-glass
room. The very first thing she did was to lookwhether there was a fire in the fireplace, and she wasquite pleased to find that there was a real one, blazing away as brightly as the one she had left behind.
‘So I shall be as warm here as I was in the old room,’
thought Alice: ‘warmer, in fact, because there’ll be
no one here to scold me away from the fire. Oh,
what fun it’ll be, when they see me through the glassin here, and can’t get at me!’Then she began looking about, and noticed thatwhat could be seen from the old room was quite common and uninteresting, but that all the rest was asdifferent as possible. For instance, the pictures on
the wall next the fire seemed to be all alive, and thevery clock on the chimney-piece (you know you can
only see the back of it in the Looking-glass) had got
the face of a little old man, and grinned at her.
‘They don’t keep this room so tidy as the other,’
Alice thought to herself, as she noticed several of thechessmen down in the hearth among the cinders: butin another moment, with a little ‘Oh!’ of surprise,

(

:

:

)

Comparison – spreads 3 + 4
greedy viz. optimal, 0 turns
Effective Float
Strategies
4

—

—

IMG5

Frank
Mittelbach‘They don’t keep this room so tidy as the other,’
Alice thought to herself, as she noticed several of thechessmen down in the hearth among the cinders: butin another moment, with a little ‘Oh!’ of surprise,
she was down on her hands and knees watching them.
The chessmen were walking about, two and two!
‘Here are the IMG5Red King and the Red Queen,’ Alice said (in a whisper, for fear of frightening them),‘and there are the White King and the White Queensitting on the edge of the shovel—and here are two
castles walking arm in arm—I don’t think they canhear me,’ she went on, as she put her head closer
down, ‘and I’m nearly sure they can’t see me. I feel
somehow as if I were invisible—’
Here something began squeaking on the table behind Alice, and made her turn her head just in timeto see one of the White Pawns roll over and begin
kicking: she watched it with great curiosity to see
what would happen next.
‘It is the voice of my child!’ the White Queen criedout as she rushed past the King, so violently that she
knocked him over among the cinders. ‘My precious
Lily! My imperial kitten!’ and she began scrambling
wildly up the side of the fender.
‘Imperial fiddlestick!’ said the King, rubbing his
nose, which had been hurt by the fall. He had a rightto be a LITTLE annoyed with the Queen, for he wascovered with ashes from head to foot.
Alice was very anxious to be of use, and, as thepoor little Lily was nearly screaming herself into a

Introduction
Visualization
Adding Floats
Results

IMG6

fit, she hastily picked up the Queen and set her on
the table by the side of her noisy little daughter.
The Queen gasped, and sat down: the rapid journey through the air had quite taken away her breathand for a minute or two she could do nothing but hug
the little Lily in silence. As soon as she had recovered
her breath a little, she called out to the White King,
who was sitting sulkily among the ashes, ‘Mind thevolcano!’‘What volcano?’ said the King, looking up anxiously into the fire, as if he thought that was themost likely place to find one.
‘Blew—me—up,’ IMG6
panted the Queen, who was stilla little out of breath. ‘Mind you come up—the regular way—don’t get blown up!’
Alice watched the White King as he slowly struggled up from bar to bar, till at last she said, ‘Why,
you’ll be hours and hours getting to the table, at that
rate. I’d far better help you, hadn’t I?’ But the King
took no notice of the question: it was quite clear thathe could neither hear her nor see her.
So Alice picked him up very gently, and lifted him
across more slowly than she had lifted the Queen,that she mightn’t take his breath away: but, before
she put him on the table, she thought she might aswell dust him a little, he was so covered with ashes.
She said afterwards that she had never seen in all
her life such a face as the King made, when he foundhimself held in the air by an invisible hand, and being

dusted: he was far too much astonished to cry out,
but his eyes and his mouth went on getting larger
and larger, and rounder and rounder, till her hand
shook so with laughing that she nearly let him drop
upon the floor.
‘Oh! PLEASE don’t make such faces, my dear!’she cried out, quite forgetting that the King couldn’t
hear her. ‘You make me laugh so that I can hardly
hold you! And don’t keep your mouth so wide open!
All the ashes will get into it—there, now I think
you’re tidy enough!’ she added, as she smoothed hishair, and set him upon the table near the Queen.
The King immediately fell flat on his back, and lay
perfectly still: and Alice was a little alarmed at what
she had done, and went round the room to see if she
could find any water to throw over him. However, she
could find nothing but a bottle of ink, and when she
got back with it she found he had recovered, and heand the Queen were talking together in a frightenedwhisper—so low, that Alice could hardly hear what
they said.
The King was saying, ‘I assure, you my dear, I
turned cold to the very ends of my whiskers!’
To which the Queen replied, ‘You haven’t got any
whiskers.’‘The horror of that moment,’ the King went on, ‘Ishall never, NEVER forget!’‘You will, though,’ the Queen said, ‘if you don’t
make a memorandum of it.’
Alice looked on with great interest as the King took
an enormous memorandum-book out of his pocket,
and began writing. A sudden thought struck her,and she took hold of the end of the pencil, whichcame some way over his shoulder, and began writingfor him.
The poor King looked puzzled and unhappy, andstruggled with the pencil for some time without saying anything; but Alice was too strong for him, andat last he panted out, ‘My dear! I really MUST geta thinner pencil. I can’t manage this one a bit; itwrites all manner of things that I don’t intend—’‘What manner of things?’ said the Queen, looking
over the book (in which Alice had put ‘THE WHITEKNIGHT IS SLIDING DOWN THE POKER. HE
BALANCES VERY BADLY’) ‘That’s not a memorandum of YOUR feelings!’

5

6

IMG7

—

—

‘Twas brillig, and the slithy toves
Did gyre and gimble in the wabe;
All mimsy were the borogoves,
And the mome raths outgrabe.
‘Beware the Jabberwock, my son!
The jaws that bite, the claws that catch!
Beware the Jubjub bird, and shun
The frumious Bandersnatch!’
He took his vorpal sword in hand:Long time the manxome foe he sought—
So rested he by the Tumtum tree,
And stood awhile in thought.

IMG8

II. The Garden of Live Flowers

And as in uffish thought he stood,
The Jabberwock, with eyes of flame,
Came whiffling through the tulgey wood,
And burbled as it came!

‘I should see the garden far better,’ said Alice to herself, ‘if I could get to the top of that hill: and here’s apath that leads straight to it—at least, no, it doesn’t
do that—’ (after going a few yards along the path,and turning several sharp corners), ‘but I suppose it
will at last. But how curiously it twists! It’s more
like a corkscrew than a path! Well, THIS turn goes tothe hill, I suppose—no, it doesn’t! This goes straightback to the house! Well then, I’ll try it the otherway.’
And so she did: wandering up and down, and trying turn after turn, but always coming back to thehouse, do what she would. Indeed, once, when she
turned a corner rather more quickly than usual, sheran against it before she could stop herself.
‘It’s no use talking about it,’ Alice said, looking
up at the house and pretending it was arguing withher. ‘I’m NOT going in again yet. I know I shouldhave to get through the Looking-glass again—backinto the old room—and there’d be an end of all myadventures!’So, resolutely turning her back upon the house,
she set out once more down the path, determined tokeep straight on till she got to the hill. For a few
minutes all went on well, and she was just saying, ‘I
really SHALL do it this time—’ when the path gave
a sudden twist and shook itself (as she described itafterwards), and the next moment she found herself
actually walking in at the door.

One, two! One, two! And through andthrough
The vorpal blade went snicker-snack!
He left it dead, and with its headHe went galumphing back.

There was a book lying near Alice on the table,
and while she sat watching the White King (for she
was still a little anxious about him, and had the ink
all ready to throw over him, in case he fainted again),
she turned over the leaves, to find some part that she
could read, ‘—for it’s all in some language I don’tknow,’ she said to herself.
It was like this.

‘And hast thou slain the Jabberwock?
Come to my arms, my beamish boy!
O frabjous day! Callooh! Callay!’
He chortled in his joy.
‘Twas brillig, and the slithy toves
Did gyre and gimble in the wabe;
All mimsy were the borogoves,
And the mome raths outgrabe.

YKCOWREBBAJ
sevot yhtils eht dna,gillirb sawT’ebaw eht ni elbmig dna eryg diD,sevogorob eht erew ysmim llA.ebargtuo shtar emom eht dnA‘It seems IMG8very pretty,’ she said when she had finished it, ‘but it’s RATHER hard to understand!’(You see she didn’t like to confess, even to herself,that she couldn’t make it out at all.) ‘Somehow it
seems to fill my head with ideas—only I don’t exactly know what they are! However, SOMEBODY
killed SOMETHING: that’s clear, at any rate—’‘But oh!’ thought Alice, suddenly jumping up, ‘if I
don’t make haste I shall have to go back through the
Looking-glass, before I’ve seen what the rest of thehouse is like! Let’s have a look at the garden first!’

She puzzled over this for some time, but at last abright thought struck her. ‘Why, it’s a Looking-glass
book, of course! And if I hold it up to a glass, thewords will all go the right way again.’This was IMG7
the poem that Alice read.
JABBERWOCKY

She was out of the room in a moment, and ran down
stairs—or, at least, it wasn’t exactly running, but a
new invention of hers for getting down stairs quickly
and easily, as Alice said to herself. She just kept thetips of her fingers on the hand-rail, and floated gently
down without even touching the stairs with her feet;then she floated on through the hall, and would havegone straight out at the door in the same way, if she
hadn’t caught hold of the door-post. She was getting
a little giddy with so much floating in the air, andwas rather glad to find herself walking again in thenatural way.

7
‘Oh, it’s too bad!’ she cried. ‘I never saw such ahouse for getting in the way! Never!’However, there was the hill full in sight, so there
was nothing to be done but start again. This time
she came upon a large flower-bed, with a border ofdaisies, and a willow-tree growing in the middle.
‘O Tiger-lily,’ said Alice, addressing herself to one
that was waving gracefully about in the wind, ‘I
WISH you could talk!’‘We CAN talk,’ said the Tiger-lily: ‘when there’s
anybody worth talking to.’Alice was so astonished that she could not speak fora minute: it quite seemed to take her breath away. At
length, as the Tiger-lily only went on waving about,she spoke again, in a timid voice—almost in a whisper. ‘And can ALL the flowers talk?’‘As well as YOU can,’ said the Tiger-lily. ‘And agreat deal louder.’‘It isn’t manners for us to begin, you know,’ said
the Rose, ‘and I really was wondering when you’dspeak! Said I to myself, “Her face has got SOME
sense in it, though it’s not a clever one!” Still, you’rethe right colour, and that goes a long way.’‘I don’t care about the colour,’ the Tiger-lily remarked. ‘If only her petals curled up a little more,
she’d be all right.’
Alice didn’t like being criticised, so she began asking questions. ‘Aren’t you sometimes frightened atbeing planted out here, with nobody to take care ofyou?’‘There’s the tree in the middle,’ said the Rose:‘what else is it good for?’‘But what could it do, if any danger came?’ Aliceasked.
‘It says IMG9
“Bough-wough!”’ cried a Daisy: ‘that’s
why its branches are called boughs!’‘Didn’t you know THAT?’ cried another Daisy, andhere they all began shouting together, till the air
seemed quite full of little shrill voices. ‘Silence, every
one of you!’ cried the Tiger-lily, waving itself passionately from side to side, and trembling with excitement. ‘They know I can’t get at them!’ it panted,
bending its quivering head towards Alice, ‘or theywouldn’t dare to do it!’‘Never mind!’ Alice said in a soothing tone, andstooping down to the daisies, who were just beginning

Comparisons
The End4—
she was down on her hands and knees watching them.
The chessmen were walking about, two and two!
‘Here are the IMG5Red King and the Red Queen,’ Alice said (in a whisper, for fear of frightening them),‘and there are the White King and the White Queensitting on the edge of the shovel—and here are two
castles walking arm in arm—I don’t think they canhear me,’ she went on, as she put her head closer
down, ‘and I’m nearly sure they can’t see me. I feel
somehow as if I were invisible—’
Here something began squeaking on the table behind Alice, and made her turn her head just in timeto see one of the White Pawns roll over and begin
kicking: she watched it with great curiosity to see
what would happen next.
‘It is the voice of my child!’ the White Queen criedout as she rushed past the King, so violently that she
knocked him over among the cinders. ‘My precious
Lily! My imperial kitten!’ and she began scrambling
wildly up the side of the fender.
‘Imperial fiddlestick!’ said the King, rubbing his
nose, which had been hurt by the fall. He had a rightto be a LITTLE annoyed with the Queen, for he wascovered with ashes from head to foot.
Alice was very anxious to be of use, and, as thepoor little Lily was nearly screaming herself into afit, she hastily picked up the Queen and set her on
the table by the side of her noisy little daughter.
The Queen gasped, and sat down: the rapid journey through the air had quite taken away her breathand for a minute or two she could do nothing but hug
the little Lily in silence. As soon as she had recovered
her breath a little, she called out to the White King,
who was sitting sulkily among the ashes, ‘Mind thevolcano!’‘What volcano?’ said the King, looking up anxiously into the fire, as if he thought that was themost likely place to find one.
‘Blew—me—up,’ IMG6
panted the Queen, who wasstill a little out of breath. ‘Mind you come up—theregular way—don’t get blown up!’
Alice watched the White King as he slowly struggled up from bar to bar, till at last she said, ‘Why,
you’ll be hours and hours getting to the table, at that
rate. I’d far better help you, hadn’t I?’ But the King
took no notice of the question: it was quite clear thathe could neither hear her nor see her.

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5

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And as in uffish thought he stood,
The Jabberwock, with eyes of flame,
Came whiffling through the tulgey wood,
And burbled as it came!
One, two! One, two! And through andthrough
The vorpal blade went snicker-snack!
He left it dead, and with its headHe went galumphing back.

So Alice picked him up very gently, and lifted him
across more slowly than she had lifted the Queen,that she mightn’t take his breath away: but, before
she put him on the table, she thought she might aswell dust him a little, he was so covered with ashes.
She said afterwards that she had never seen in all
her life such a face as the King made, when he foundhimself held in the air by an invisible hand, and being
dusted: he was far too much astonished to cry out,
but his eyes and his mouth went on getting larger
and larger, and rounder and rounder, till her hand
shook so with laughing that she nearly let him drop
upon the floor.
‘Oh! PLEASE don’t make such faces, my dear!’she cried out, quite forgetting that the King couldn’t
hear her. ‘You make me laugh so that I can hardly
hold you! And don’t keep your mouth so wide open!
All the ashes will get into it—there, now I think
you’re tidy enough!’ she added, as she smoothed hishair, and set him upon the table near the Queen.
The King immediately fell flat on his back, and lay
perfectly still: and Alice was a little alarmed at what
she had done, and went round the room to see if she
could find any water to throw over him. However, she
could find nothing but a bottle of ink, and when she
got back with it she found he had recovered, and heand the Queen were talking together in a frightenedwhisper—so low, that Alice could hardly hear what
they said.
The King was saying, ‘I assure, you my dear, I
turned cold to the very ends of my whiskers!’
To which the Queen replied, ‘You haven’t got any
whiskers.’‘And hast thou slain the Jabberwock?
Come to my arms, my beamish boy!
O frabjous day! Callooh! Callay!’
He chortled in his joy.
‘The horror of that moment,’ the King went on, ‘Ishall never, NEVER forget!’‘You will, though,’ the Queen said, ‘if you don’t
make a memorandum of it.’
Alice looked on with great interest as the King took
sevot yhtils eht dna,gillirb sawT’
an enormous memorandum-book out of his pocket,
ebaw eht ni elbmig dna eryg diD
and began writing. A sudden thought struck her,,sevogorob eht erew ysmim llA
and she took hold of the end of the pencil, which.ebargtuo shtar emom eht dnAcame some way over his shoulder, and began writingfor him.
She puzzled over this for some time, but at last a
The poor King looked puzzled and unhappy, and bright thought struck her. ‘Why, it’s a Looking-glass
struggled with the pencil for some time without say- book, of course! And if I hold it up to a glass, theing anything; but Alice was too strong for him, and words will all go the right way again.’at last he panted out, ‘My dear! I really MUST get
This was IMG7
the poem that Alice read.
a thinner pencil. I can’t manage this one a bit; itwrites all manner of things that I don’t intend—’
JABBERWOCKY‘What manner of things?’ said the Queen, looking‘Twas brillig, and the slithy toves
over the book (in which Alice had put ‘THE WHITE
Did gyre and gimble in the wabe;
KNIGHT IS SLIDING DOWN THE POKER. HE
All mimsy were the borogoves,
BALANCES VERY BADLY’) ‘That’s not a memoAnd the mome raths outgrabe.
randum of YOUR feelings!’
There was a book lying near Alice on the table,‘Beware the Jabberwock, my son!
and while she sat watching the White King (for she
The jaws that bite, the claws that catch!
was still a little anxious about him, and had the ink
Beware the Jubjub bird, and shunall ready to throw over him, in case he fainted again),
The frumious Bandersnatch!’
she turned over the leaves, to find some part that she
could read, ‘—for it’s all in some language I don’t
He took his vorpal sword in hand:
know,’ she said to herself.
Long time the manxome foe he sought—
It was like this.
So rested he by the Tumtum tree,
YKCOWREBBAJ
And stood awhile in thought.

‘Twas brillig, and the slithy toves
Did gyre and gimble in the wabe;
All mimsy were the borogoves,
And the mome raths outgrabe.
‘It seems IMG8very pretty,’ she said when she hadfinished it, ‘but it’s RATHER hard to understand!’(You see she didn’t like to confess, even to herself,that she couldn’t make it out at all.) ‘Somehow it
seems to fill my head with ideas—only I don’t exactly know what they are! However, SOMEBODY
killed SOMETHING: that’s clear, at any rate—’‘But oh!’ thought Alice, suddenly jumping up, ‘if I
don’t make haste I shall have to go back through the
Looking-glass, before I’ve seen what the rest of thehouse is like! Let’s have a look at the garden first!’
She was out of the room in a moment, and ran down
stairs—or, at least, it wasn’t exactly running, but a
new invention of hers for getting down stairs quickly
and easily, as Alice said to herself. She just kept thetips of her fingers on the hand-rail, and floated gently
down without even touching the stairs with her feet;then she floated on through the hall, and would havegone straight out at the door in the same way, if she
hadn’t caught hold of the door-post. She was getting
a little giddy with so much floating in the air, andwas rather glad to find herself walking again in thenatural way.

II. The Garden of Live Flowers‘I should see the garden far better,’ said Alice to herself, ‘if I could get to the top of that hill: and here’s apath that leads straight to it—at least, no, it doesn’t
do that—’ (after going a few yards along the path,and turning several sharp corners), ‘but I suppose it
will at last. But how curiously it twists! It’s more
like a corkscrew than a path! Well, THIS turn goes tothe hill, I suppose—no, it doesn’t! This goes straightback to the house! Well then, I’ll try it the other way.’
And so she did: wandering up and down, and trying turn after turn, but always coming back to thehouse, do what she would. Indeed, once, when she
turned a corner rather more quickly than usual, sheran against it before she could stop herself.
‘It’s no use talking about it,’ Alice said, looking
up at the house and pretending it was arguing withher. ‘I’m NOT going in again yet. I know I should— pagesize change: ≠12.0pt ——have to get through the Looking-glass again—backinto the old room—and there’d be an end of all myadventures!’So, resolutely turning her back upon the house,
she set out once more down the path, determined tokeep straight on till she got to the hill. For a few
minutes all went on well, and she was just saying, ‘I
really SHALL do it this time—’ when the path gave
a sudden twist and shook itself (as she described itafterwards), and the next moment she found herself
actually walking in at the door.
‘Oh, it’s too bad!’ she cried. ‘I never saw such ahouse for getting in the way! Never!’However, there was the hill full in sight, so there
was nothing to be done but start again. This time
she came upon a large flower-bed, with a border ofdaisies, and a willow-tree growing in the middle.
‘O Tiger-lily,’ said Alice, addressing herself to one
that was waving gracefully about in the wind, ‘I
WISH you could talk!’‘We CAN talk,’ said the Tiger-lily: ‘when there’s
anybody worth talking to.’Alice was so astonished that she could not speak fora minute: it quite seemed to take her breath away. At
length, as the Tiger-lily only went on waving about,she spoke again, in a timid voice—almost in a whisper. ‘And can ALL the flowers talk?’‘As well as YOU can,’ said the Tiger-lily. ‘And agreat deal louder.’‘It isn’t manners for us to begin, you know,’ said
the Rose, ‘and I really was wondering when you’dspeak! Said I to myself, “Her face has got SOME
sense in it, though it’s not a clever one!” Still, you’rethe right colour, and that goes a long way.’‘I don’t care about the colour,’ the Tiger-lily remarked. ‘If only her petals curled up a little more,
she’d be all right.’
Alice didn’t like being criticised, so she began asking questions. ‘Aren’t you sometimes frightened atbeing planted out here, with nobody to take care ofyou?’‘There’s the tree in the middle,’ said the Rose:‘what else is it good for?’‘But what could it do, if any danger came?’ Aliceasked.

7
IMG9‘It says IMG9
“Bough-wough!”’ cried a Daisy: ‘that’s
why its branches are called boughs!’‘Didn’t you know THAT?’ cried another Daisy, andhere they all began shouting together, till the air
seemed quite full of little shrill voices. ‘Silence, every
one of you!’ cried the Tiger-lily, waving itself passionately from side to side, and trembling with excitement. ‘They know I can’t get at them!’ it panted,
bending its quivering head towards Alice, ‘or theywouldn’t dare to do it!’‘Never mind!’ Alice said in a soothing tone, andstooping down to the daisies, who were just beginningagain, she whispered, ‘If you don’t hold your tongues,
I’ll pick you!’
There was silence in a moment, and several of thepink daisies turned white.
‘That’s right!’ said the Tiger-lily. ‘The daisies are
worst of all. When one speaks, they all begin together, and it’s enough to make one wither to hear
the way they go on!’‘How is it you can all talk so nicely?’ Alice said,
hoping to get it into a better temper by a compliment.
‘I’ve been in many gardens before, but none of theflowers could talk.’

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Frank
Mittelbach
Introduction

again, she whispered, ‘If you don’t hold your tongues,
I’ll pick you!’
There was silence in a moment, and several of thepink daisies turned white.
‘That’s right!’ said the Tiger-lily. ‘The daisies are
worst of all. When one speaks, they all begin together, and it’s enough to make one wither to hear
the way they go on!’‘How is it you can all talk so nicely?’ Alice said,
hoping to get it into a better temper by a compliment.
‘I’ve been in many gardens before, but none of theflowers could talk.’‘Put your hand down, and feel the ground,’ said
the Tiger-lily. ‘Then you’ll know why.’
Alice did so. ‘It’s very hard,’ she said, ‘but I don’t
see what that has to do with it.’
‘In most gardens,’ the Tiger-lily said, ‘they makethe beds too soft—so that the flowers are always
asleep.’This sounded a very good reason, and Alice wasquite pleased to know it. ‘I never thought of that
before!’ she said.
‘It’s MY opinion that you never think AT ALL,’the Rose said in a rather severe tone.

Visualization
Adding Floats
Results‘I never saw anybody that looked stupider,’ a Violet said, so suddenly, that Alice quite jumped; for it
hadn’t spoken before.
‘Hold YOUR tongue!’ cried the Tiger-lily. ‘As if
YOU ever saw anybody! You keep your head under
the leaves, and snore away there, till you know no
more what’s going on in the world, than if you werea bud!’‘Are there any more people in the garden besides
me?’ Alice said, not choosing to notice the Rose’s
last remark.
‘There’s one other flower in the garden that canmove about like you,’ said the Rose. ‘I wonder how
you do it—’ (‘You’re always wondering,’ said the
Tiger-lily), ‘but she’s more bushy than you are.’‘Is she like me?’ Alice asked eagerly, for thethought crossed her mind, ‘There’s another little girlin the garden, somewhere!’‘Well, she has the same awkward shape as you,’
the Rose said, ‘but she’s redder—and her petals areshorter, I think.’‘Her petals are done up close, almost like a dahlia,’
the Tiger-lily interrupted: ‘not tumbled about anyhow, like yours.’‘But that’s not YOUR fault,’ the Rose added
kindly: ‘you’re beginning to fade, you know—andthen one can’t help one’s petals getting a little untidy.’
Alice didn’t like this idea at all: so, to change thesubject, she asked ‘Does she ever come out here?’‘I daresay you’ll see her soon,’ said the Rose. ‘She’s
one of the thorny kind.’‘Where does she wear the thorns?’ Alice asked withsome curiosity.
‘Why all round her head, of course,’ the Rosereplied. ‘I was wondering YOU hadn’t got some too.
I thought it was the regular rule.’‘She’s coming!’ cried the Larkspur. ‘I hear her
footstep, thump, thump, thump, along the gravelwalk!’
Alice looked IMG10
round eagerly, and found that it was
the Red Queen. ‘She’s grown a good deal!’ washer first remark. She had indeed: when Alice firstfound her in the ashes, she had been only three inches
high—and here she was, half a head taller than Aliceherself!

9

10

IMG10

‘It’s the fresh air that does it,’ said the Rose: ‘wonderfully fine air it is, out here.’‘I think I’ll go and meet her,’ said Alice, for, though
the flowers were interesting enough, she felt that it
would be far grander to have a talk with a real Queen.
‘You can’t possibly do that,’ said the Rose: ‘Ishould advise you to walk the other way.’
This sounded nonsense to Alice, so she said nothing, but set off at once towards the Red Queen. To
her surprise, she lost sight of her in a moment, andfound herself walking in at the front-door again.
A little provoked, she drew back, and after looking
everywhere for the queen (whom she spied out at last,a long way off), she thought she would try the plan,
this time, of walking in the opposite direction.
It succeeded beautifully. She had not been walking
a minute before she found herself face to face with the
Red Queen, and full in sight of the hill she had been
so long aiming at.
‘Where do you come from?’ said the Red Queen.
‘And where are you going? Look up, speak nicely,
and don’t twiddle your fingers all the time.’

—

—

IMG11

Alice attended to all these directions, and explained, as well as she could, that she had lost herway.
‘I don’t know what you mean by YOUR way,’ said
the Queen: ‘all the ways about here belong to ME—
but why did you come out here at all?’ she added ina kinder tone. ‘Curtsey while you’re thinking what
to say, it saves time.’
Alice wondered a little at this, but she was toomuch in awe of the Queen to disbelieve it. ‘I’ll try
it when I go home,’ she thought to herself, ‘the nexttime I’m a little late for dinner.’‘It’s time for you to answer now,’ the Queen said,
looking at her watch: ‘open your mouth a LITTLE wider when you speak, and always say “yourMajesty.”’‘I only wanted to see what the garden was like,your Majesty—’‘That’s right,’ said the Queen, patting her on thehead, which Alice didn’t like at all, ‘though, when you
say “garden,”—I’VE seen gardens, compared withwhich this would be a wilderness.’
Alice didn’t dare to argue the point, but went on:‘—and I thought I’d try and find my way to the topof that hill—’‘When you say “hill,”’ the Queen interrupted, ‘I
could show you hills, in comparison with which you’dcall that a valley.’‘No, I shouldn’t,’ said Alice, surprised into contradicting her at last: ‘a hill CAN’T be a valley, you
know. That would be nonsense—’
The Red Queen shook her head, ‘You may call it“nonsense” if you like,’ she said, ‘but I’VE heard nonsense, compared with which that would be as sensible
as a dictionary!’
Alice curtseyed again, as she was afraid from the
Queen’s tone that she was a LITTLE offended: andthey walked on in silence till they got to the top of
the little hill.
For some minutes Alice stood without speaking,looking out in all directions over the country—and amost curious country it was. There were a numberof tiny little brooks running straight across it fromside to side, and the ground between was divided up
into squares by a number of little green hedges, thatreached from brook to brook.

‘I declare it’s marked out just like a large chessboard!’ Alice said at last. ‘There ought to be somemen moving about somewhere—and so there are!’
She added in a tone of delight, and her heart began to beat quick with excitement as she went on.
‘It’s a great huge game of chess that’s being played—
all over the world—if this IS the world at all, you
know. Oh, what fun it is! How I WISH I was oneof them! I wouldn’t mind being a Pawn IMG11, if only I
might join—though of course I should LIKE to be a
Queen, best.’
She glanced rather shyly at the real Queen as she
said this, but her companion only smiled pleasantly,
and said, ‘That’s easily managed. You can be theWhite Queen’s Pawn, if you like, as Lily’s too young
to play; and you’re in the Second Square to begin
with: when you get to the Eighth Square you’ll be
a Queen—’ Just at this moment, somehow or other,
they began to run.
Alice never could quite make out, in thinking itover afterwards, how it was that they began: all she
remembers is, that they were running hand in hand,
and the Queen went so fast that it was all she could
do to keep up with her: and still the Queen kept
crying ‘Faster! Faster!’ but Alice felt she COULD
NOT go faster, though she had not breath left to say
so.
The most curious part of the thing was, that thetrees and the other things round them never changed
their places at all: however fast they went, they neverseemed to pass anything. ‘I wonder if all the things
move along with us?’ thought poor puzzled Alice.

IMG12

And the Queen seemed to guess her thoughts, for she
cried, ‘Faster! Don’t try to talk!’
Not that Alice had any idea of doing THAT. She
felt as if she would never be able to talk again, she wasgetting so much out of breath: and still the Queen
cried ‘Faster! Faster!’ and dragged her along. ‘Are
we nearly there?’ Alice managed to pant out at last.
‘Nearly IMG12
there!’ the Queen repeated. ‘Why, we
passed it ten minutes ago! Faster!’ And they ran
on for a time in silence, with the wind whistling in
Alice’s ears, and almost blowing her hair off her head,
she fancied.
‘Now! Now!’ cried the Queen. ‘Faster! Faster!’
And they went so fast that at last they seemed toskim through the air, hardly touching the groundwith their feet, till suddenly, just as Alice was getting quite exhausted, they stopped, and she foundherself sitting on the ground, breathless and giddy.
The Queen propped her up against a tree, and said
kindly, ‘You may rest a little now.’
Alice looked round her in great surprise. ‘Why, I
do believe we’ve been under this tree the whole time!
Everything’s just as it was!’‘Of course it is,’ said the Queen, ‘what would you
have it?’‘Well, in OUR country,’ said Alice, still panting alittle, ‘you’d generally get to somewhere else—if you
ran very fast for a long time, as we’ve been doing.’‘A slow sort of country!’ said the Queen. ‘Now,
HERE, you see, it takes all the running YOU cando, to keep in the same place. If you want to getsomewhere else, you must run at least twice as fast
as that!’‘I’d rather not try, please!’ said Alice. ‘I’m quite
content to stay here—only I AM so hot and thirsty!’‘I know what YOU’D like!’ the Queen said goodnaturedly, taking a little box out of her pocket. ‘Havea biscuit?’
Alice thought it would not be civil to say ‘No,’
though it wasn’t at all what she wanted. So she took
it, and ate it as well as she could: and it was VERY
dry; and she thought she had never been so nearlychoked in all her life.
‘While you’re refreshing yourself,’ said the Queen,‘I’ll just take the measurements.’ And she took aribbon out of her pocket, marked in inches, and began
measuring the ground, and sticking little pegs in here
and there.
‘At the end of two yards,’ she said, putting ina peg to mark the distance, ‘I shall give you yourdirections—have another biscuit?’‘No, thank you,’ said Alice: ‘one’s QUITE enough!’‘Thirst quenched, I hope?’ said the Queen.
Alice did not know what to say to this, but luckily
the Queen did not wait for an answer, but went on.
‘At the end of THREE yards I shall repeat them—forfear of your forgetting them. At the end of FOUR, I
shall say good-bye. And at the end of FIVE, I shallgo!’
She had got all the pegs put in by this time, andAlice looked on with great interest as she returnedto the tree, and then began slowly walking down therow.
At the two-yard peg she faced round, and said, ‘Apawn goes two squares in its first move, you know. So
you’ll go VERY quickly through the Third Square—by railway, I should think—and you’ll find yourself in the Fourth Square in no time. Well, THAT
square belongs to Tweedledum and Tweedledee—theFifth is mostly water—the Sixth belongs to Humpty
Dumpty—But you make no remark?’‘I—I didn’t know I had to make one—just then,’Alice faltered out.
‘You SHOULD have said, “It’s extremely kind of
you to tell me all this”—however, we’ll suppose it
said—the Seventh Square is all forest—however, oneof the Knights will show you the way—and in the
Eighth Square we shall be Queens together, and it’s

11
all feasting and fun!’ Alice got up and curtseyed, andsat down again.
At the next peg the Queen turned again, and thistime she said, ‘Speak in French when you can’t thinkof the English for a thing—turn out your toes as you
walk—and remember who you are!’ She did not wait
for Alice to curtsey this time, but walked on quickly
to the next peg, where she turned for a moment tosay ‘good-bye,’ and then hurried on to the last.
How it happened, Alice never knew, but exactly
as she came to the last peg, she was gone. Whether
she vanished into the air, or whether she ran quickly
into the wood (‘and she CAN run very fast!’ thought
Alice), there was no way of guessing, but she wasgone, and Alice began to remember that she was a
Pawn, and that it would soon be time for her to move.

III. Looking-Glass Insects
Of course the first thing to do was to make a grandsurvey of the country she was going to travel through.
‘It’s something very like learning geography,’ thought
Alice, as she stood on tiptoe in hopes of being able
to see a little further. ‘Principal rivers—there ARE
none. Principal mountains—I’m on the only one, but
I don’t think it’s got any name. Principal towns—
why, what ARE those creatures, making honey down
there? They can’t be bees—nobody ever saw bees amile off, you know—’ and for some time she stoodsilent, watching one of them that was bustling about
among the flowers, poking its proboscis into them,‘just as if it was a regular bee,’ thought Alice.
However, this was anything but a regular bee: infact it was an elephant—as Alice soon found out,
though the idea quite took her breath away at first.
‘And what enormous flowers they must be!’ was her
next idea. ‘Something like cottages with the roofs
taken off, and stalks put to them—and what quantities of honey they must make! I think I’ll go down
and—no, I won’t JUST yet,’ she went on, checking
herself just as she was beginning to run down the hill,
and trying to find some excuse for turning shy so suddenly. ‘It’ll never do to go down among them without
a good long branch to brush them away—and what
fun it’ll be when they ask me how I like my walk. I

Comparisons
The End

8—‘Put your hand down, and feel the ground,’ said
the Tiger-lily. ‘Then you’ll know why.’
Alice did so. ‘It’s very hard,’ she said, ‘but I don’t
see what that has to do with it.’
‘In most gardens,’ the Tiger-lily said, ‘they makethe beds too soft—so that the flowers are always
asleep.’This sounded a very good reason, and Alice wasquite pleased to know it. ‘I never thought of that
before!’ she said.
‘It’s MY opinion that you never think AT ALL,’the Rose said in a rather severe tone.
‘I never saw anybody that looked stupider,’ a Violet said, so suddenly, that Alice quite jumped; for it
hadn’t spoken before.
‘Hold YOUR tongue!’ cried the Tiger-lily. ‘As if
YOU ever saw anybody! You keep your head under
the leaves, and snore away there, till you know no
more what’s going on in the world, than if you werea bud!’‘Are there any more people in the garden besides
me?’ Alice said, not choosing to notice the Rose’s
last remark.
‘There’s one other flower in the garden that canmove about like you,’ said the Rose. ‘I wonder how
you do it—’ (‘You’re always wondering,’ said the
Tiger-lily), ‘but she’s more bushy than you are.’‘Is she like me?’ Alice asked eagerly, for thethought crossed her mind, ‘There’s another little girlin the garden, somewhere!’‘Well, she has the same awkward shape as you,’
the Rose said, ‘but she’s redder—and her petals areshorter, I think.’‘Her petals are done up close, almost like a dahlia,’
the Tiger-lily interrupted: ‘not tumbled about anyhow, like yours.’‘But that’s not YOUR fault,’ the Rose added
kindly: ‘you’re beginning to fade, you know—andthen one can’t help one’s petals getting a little untidy.’
Alice didn’t like this idea at all: so, to change thesubject, she asked ‘Does she ever come out here?’‘I daresay you’ll see her soon,’ said the Rose. ‘She’s
one of the thorny kind.’‘Where does she wear the thorns?’ Alice asked withsome curiosity.

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IMG10

‘Why all round her head, of course,’ the Rosereplied. ‘I was wondering YOU hadn’t got some too.
I thought it was the regular rule.’‘She’s coming!’ cried the Larkspur. ‘I hear her
footstep, thump, thump, thump, along the gravelwalk!’
Alice looked IMG10
round eagerly, and found that it was
the Red Queen. ‘She’s grown a good deal!’ washer first remark. She had indeed: when Alice firstfound her in the ashes, she had been only three inches
high—and here she was, half a head taller than Aliceherself!
‘It’s the fresh air that does it,’ said the Rose: ‘wonderfully fine air it is, out here.’‘I think I’ll go and meet her,’ said Alice, for,though the flowers were interesting enough, she feltthat it would be far grander to have a talk witha real Queen.
‘You can’t possibly do that,’ said the Rose: ‘Ishould advise you to walk the other way.’
This sounded nonsense to Alice, so she said nothing, but set off at once towards the Red Queen. To
her surprise, she lost sight of her in a moment, andfound herself walking in at the front-door again.

A little provoked, she drew back, and after looking
everywhere for the queen (whom she spied out at last,a long way off), she thought she would try the plan,
this time, of walking in the opposite direction.
It succeeded beautifully. She had not been walking
a minute before she found herself face to face with the
Red Queen, and full in sight of the hill she had been
so long aiming at.
‘Where do you come from?’ said the Red Queen.
‘And where are you going? Look up, speak nicely,
and don’t twiddle your fingers all the time.’
Alice attended to all these directions, and explained, as well as she could, that she had lost herway.
‘I don’t know what you mean by YOUR way,’ said
the Queen: ‘all the ways about here belong to ME—
but why did you come out here at all?’ she added ina kinder tone. ‘Curtsey while you’re thinking what
to say, it saves time.’
Alice wondered a little at this, but she was toomuch in awe of the Queen to disbelieve it. ‘I’ll try
it when I go home,’ she thought to herself, ‘the nexttime I’m a little late for dinner.’‘It’s time for you to answer now,’ the Queen said,
looking at her watch: ‘open your mouth a LITTLE wider when you speak, and always say “yourMajesty.”’‘I only wanted to see what the garden was like,your Majesty—’‘That’s right,’ said the Queen, patting her on thehead, which Alice didn’t like at all, ‘though, when you
say “garden,”—I’VE seen gardens, compared withwhich this would be a wilderness.’
Alice didn’t dare to argue the point, but went on:‘—and I thought I’d try and find my way to the topof that hill—’‘When you say “hill,”’ the Queen interrupted, ‘I
could show you hills, in comparison with which you’dcall that a valley.’‘No, I shouldn’t,’ said Alice, surprised into contradicting her at last: ‘a hill CAN’T be a valley, you
know. That would be nonsense—’
The Red Queen shook her head, ‘You may call it“nonsense” if you like,’ she said, ‘but I’VE heard nonsense, compared with which that would be as sensible
as a dictionary!’

9
IMG11

Alice curtseyed again, as she was afraid from the
Queen’s tone that she was a LITTLE offended: andthey walked on in silence till they got to the top of
the little hill.
For some minutes Alice stood without speaking,looking out in all directions over the country—and amost curious country it was. There were a numberof tiny little brooks running straight across it fromside to side, and the ground between was divided up
into squares by a number of little green hedges, thatreached from brook to brook.
‘I declare it’s marked out just like a large chessboard!’ Alice said at last. ‘There ought to be somemen moving about somewhere—and so there are!’
She added in a tone of delight, and her heart began to beat quick with excitement as she went on.
‘It’s a great huge game of chess that’s being played—
all over the world—if this IS the world at all, you
know. Oh, what fun it is! How I WISH I was oneof them! I wouldn’t mind being a Pawn IMG11, if only I
might join—though of course I should LIKE to be a
Queen, best.’
She glanced rather shyly at the real Queen as she
said this, but her companion only smiled pleasantly,
and said, ‘That’s easily managed. You can be theWhite Queen’s Pawn, if you like, as Lily’s too young
to play; and you’re in the Second Square to begin
with: when you get to the Eighth Square you’ll be
a Queen—’ Just at this moment, somehow or other,
they began to run.
Alice never could quite make out, in thinking itover afterwards, how it was that they began: all she
remembers is, that they were running hand in hand,
and the Queen went so fast that it was all she could

10—
do to keep up with her: and still the Queen kept
crying ‘Faster! Faster!’ but Alice felt she COULD
NOT go faster, though she had not breath left to say
so.
The most curious part of the thing was, that thetrees and the other things round them never changed
their places at all: however fast they went, they neverseemed to pass anything. ‘I wonder if all the things
move along with us?’ thought poor puzzled Alice.
And the Queen seemed to guess her thoughts, for she
cried, ‘Faster! Don’t try to talk!’
Not that Alice had any idea of doing THAT. She
felt as if she would never be able to talk again,
she was getting so much out of breath: and still
the Queen cried ‘Faster! Faster!’ and dragged heralong. ‘Are we nearly there?’ Alice managed to pantout at last.
‘Nearly IMG12
there!’ the Queen repeated. ‘Why, we
passed it ten minutes ago! Faster!’ And they ran
on for a time in silence, with the wind whistling in
Alice’s ears, and almost blowing her hair off her head,
she fancied.
‘Now! Now!’ cried the Queen. ‘Faster! Faster!’
And they went so fast that at last they seemed toskim through the air, hardly touching the groundwith their feet, till suddenly, just as Alice was getting quite exhausted, they stopped, and she foundherself sitting on the ground, breathless and giddy.
The Queen propped her up against a tree, and said
kindly, ‘You may rest a little now.’
Alice looked round her in great surprise. ‘Why, I
do believe we’ve been under this tree the whole time!
Everything’s just as it was!’‘Of course it is,’ said the Queen, ‘what would you
have it?’‘Well, in OUR country,’ said Alice, still panting alittle, ‘you’d generally get to somewhere else—if you
ran very fast for a long time, as we’ve been doing.’‘A slow sort of country!’ said the Queen. ‘Now,
HERE, you see, it takes all the running YOU cando, to keep in the same place. If you want to getsomewhere else, you must run at least twice as fast
as that!’‘I’d rather not try, please!’ said Alice. ‘I’m quite
content to stay here—only I AM so hot and thirsty!’— pagesize change: ≠12.0pt —‘I know what YOU’D like!’ the Queen said goodnaturedly, taking a little box out of her pocket. ‘Havea biscuit?’
Alice thought it would not be civil to say ‘No,’
though it wasn’t at all what she wanted. So she took
it, and ate it as well as she could: and it was VERY
dry; and she thought she had never been so nearlychoked in all her life.
‘While you’re refreshing yourself,’ said the Queen,‘I’ll just take the measurements.’ And she took aribbon out of her pocket, marked in inches, and began
measuring the ground, and sticking little pegs in here
and there.
‘At the end of two yards,’ she said, putting ina peg to mark the distance, ‘I shall give you yourdirections—have another biscuit?’‘No, thank you,’ said Alice: ‘one’s QUITE enough!’‘Thirst quenched, I hope?’ said the Queen.
Alice did not know what to say to this, but luckily
the Queen did not wait for an answer, but went on.
‘At the end of THREE yards I shall repeat them—forfear of your forgetting them. At the end of FOUR, I
shall say good-bye. And at the end of FIVE, I shallgo!’
She had got all the pegs put in by this time, andAlice looked on with great interest as she returnedto the tree, and then began slowly walking down therow.
At the two-yard peg she faced round, and said, ‘Apawn goes two squares in its first move, you know. So
you’ll go VERY quickly through the Third Square—by railway, I should think—and you’ll find yourself in the Fourth Square in no time. Well, THAT
square belongs to Tweedledum and Tweedledee—theFifth is mostly water—the Sixth belongs to Humpty
Dumpty—But you make no remark?’‘I—I didn’t know I had to make one—just then,’Alice faltered out.
‘You SHOULD have said, “It’s extremely kind of
you to tell me all this”—however, we’ll suppose it
said—the Seventh Square is all forest—however, oneof the Knights will show you the way—and in the
Eighth Square we shall be Queens together, and it’s
all feasting and fun!’ Alice got up and curtseyed, andsat down again.

— pagesize change: ≠12.0pt —

—

11

IMG12
At the next peg the Queen turned again, and thistime she said, ‘Speak in French when you can’t thinkof the English for a thing—turn out your toes as you
walk—and remember who you are!’ She did not wait
for Alice to curtsey this time, but walked on quickly
to the next peg, where she turned for a moment tosay ‘good-bye,’ and then hurried on to the last.
How it happened, Alice never knew, but exactly
as she came to the last peg, she was gone. Whether
she vanished into the air, or whether she ran quickly
into the wood (‘and she CAN run very fast!’ thought
Alice), there was no way of guessing, but she wasgone, and Alice began to remember that she was a “’ (here came the favourite little toss of the head),Pawn, and that it would soon be time for her to move. “‘only it was so dusty and hot, and the elephants
did tease so!”’‘I think I’ll go down the other way,’ she said afIII. Looking-Glass Insects
ter a pause: ‘and perhaps I may visit the elephantslater on. Besides, I do so want to get into the Third
Of course the first thing to do was to make a grand Square!’survey of the country she was going to travel through.
So with this excuse she ran down the hill and‘It’s something very like learning geography,’ thought jumped over the first of the six little brooks.
Alice, as she stood on tiptoe in hopes of being able
to see a little further. ‘Principal rivers—there ARE
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I don’t think it’s got any name. Principal towns—
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why, what ARE those creatures, making honey down
there? They can’t be bees—nobody ever saw bees a‘Tickets, please!’ said the Guard, putting his headmile off, you know—’ and for some time she stood in at the window. In a moment everybody was holdsilent, watching one of them that was bustling about ing out a ticket: they were about the same size as theamong the flowers, poking its proboscis into them, people, and quite seemed to fill the carriage.
‘just as if it was a regular bee,’ thought Alice.
‘Now then! Show your ticket, child!’ the Guard
However, this was anything but a regular bee: in went on, looking angrily at Alice. And a great many
fact it was an elephant—as Alice soon found out, voices all said together (‘like the chorus of a song,’
though the idea quite took her breath away at first. thought Alice), ‘Don’t keep him waiting, child! Why,
‘And what enormous flowers they must be!’ was her his time is worth a thousand pounds a minute!’
next idea. ‘Something like cottages with the roofs‘I’m afraid I haven’t got one,’ Alice said in a frighttaken off, and stalks put to them—and what quan- ened tone: ‘there wasn’t a ticket-office where I cametities of honey they must make! I think I’ll go down from.’ And again the chorus of voices went on. ‘There
and—no, I won’t JUST yet,’ she went on, checking wasn’t room for one where she came from. The land
herself just as she was beginning to run down the there is worth a thousand pounds an inch!’hill, and trying to find some excuse for turning shy‘Don’t make excuses,’ said the Guard: ‘you shouldso suddenly. ‘It’ll never do to go down among them have bought one from the engine-driver.’ And once
without a good long branch to brush them away— more the chorus of voices went on with ‘The man thatand what fun it’ll be when they ask me how I like drives the engine. Why, the smoke alone is worth a
my walk. I shall say—“Oh, I like it well enough— thousand pounds a puff!’

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Comparison – spreads 7 + 8
greedy viz. optimal, 0 turns
Effective Float
Strategies
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‘Tickets, please!’ said the Guard, putting his headin at the window. In a moment everybody was holding out a ticket: they were about the same size as thepeople, and quite seemed to fill the carriage.
‘Now then! Show your ticket, child!’ the Guard
went on, looking angrily at Alice. And a great many
voices all said together (‘like the chorus of a song,’
thought Alice), ‘Don’t keep him waiting, child! Why,
his time is worth a thousand pounds a minute!’‘I’m afraid I haven’t got one,’ Alice said in a frightened tone: ‘there wasn’t a ticket-office where I camefrom.’ And again the chorus of voices went on. ‘There
wasn’t room for one where she came from. The land
there is worth a thousand pounds an inch!’‘Don’t make excuses,’ said the Guard: ‘you shouldhave bought one from the engine-driver.’ And once
more the chorus of voices went on with ‘The man thatdrives the engine. Why, the smoke alone is worth athousand pounds a puff!’
Alice IMG13
thought to herself, ‘Then there’s no use in
speaking.’ The voices didn’t join in this time, as she
hadn’t spoken, but to her great surprise, they all
THOUGHT in chorus (I hope you understand what
THINKING IN CHORUS means—for I must confessthat I don’t), ‘Better say nothing at all. Language isworth a thousand pounds a word!’‘I shall dream about a thousand pounds tonight, I
know I shall!’ thought Alice.
All this time the Guard was looking at her, firstthrough a telescope, then through a microscope, andthen through an opera-glass. At last he said, ‘You’re
travelling the wrong way,’ and shut up the window
and went away.

Introduction
Visualization
Adding Floats
Results—
IMG13

shall say—“Oh, I like it well enough—“’ (here camethe favourite little toss of the head), “‘only it was so
dusty and hot, and the elephants did tease so!”’‘I think I’ll go down the other way,’ she said after a pause: ‘and perhaps I may visit the elephantslater on. Besides, I do so want to get into the Third
Square!’So with this excuse she ran down the hill andjumped over the first of the six little brooks.

Frank
Mittelbach‘So young a child,’ said the gentleman sitting opposite to her (he was dressed in white paper), ‘ought
to know which way she’s going, even if she doesn’tknow her own name!’
A Goat, that was sitting next to the gentleman inwhite, shut his eyes and said in a loud voice, ‘She
ought to know her way to the ticket-office, even if
she doesn’t know her alphabet!’
There was a Beetle sitting next to the Goat (it wasa very queer carriage-full of passengers altogether),and, as the rule seemed to be that they should all
speak in turn, HE went on with ‘She’ll have to go
back from here as luggage!’
Alice couldn’t see who was sitting beyond the Beetle, but a hoarse voice spoke next. ‘Change engines—’
it said, and was obliged to leave off.
‘It sounds like a horse,’ Alice thought to herself.
And an extremely small voice, close to her ear, said,‘You might make a joke on that—something about“horse” and “hoarse,” you know.’
Then a very gentle voice in the distance said, ‘She
must be labelled “Lass, with care,” you know—’
And after that other voices went on (‘What a number of people there are in the carriage!’ thought Alice), saying, ‘She must go by post, as she’s got ahead on her—’ ‘She must be sent as a message by thetelegraph—’ ‘She must draw the train herself the restof the way—’ and so on.
But the gentleman dressed in white paper leaned
forwards and whispered in her ear, ‘Never mind what

they all say, my dear, but take a return-ticket every
time the train stops.’‘Indeed I shan’t!’ Alice said rather impatiently. ‘I
don’t belong to this railway journey at all—I was ina wood just now—and I wish I could get back there.’‘You might make a joke on THAT,’ said the little voice close to her ear: ‘something about “youWOULD if you could,” you know.’‘Don’t tease so,’ said Alice, looking about in vain to
see where the voice came from; ‘if you’re so anxious tohave a joke made, why don’t you make one yourself?’
The little voice sighed deeply: it was VERY unhappy, evidently, and Alice would have said something pitying to comfort it, ‘If it would only sigh likeother people!’ she thought. But this was such a wonderfully small sigh, that she wouldn’t have heard it
at all, if it hadn’t come QUITE close to her ear. The
consequence of this was that it tickled her ear very
much, and quite took off her thoughts from the unhappiness of the poor little creature.
‘I know you are a friend,’ the little voice went on;‘a dear friend, and an old friend. And you won’t hurtme, though I AM an insect.’‘What kind of insect?’ Alice inquired a little anxiously. What she really wanted to know was, whether
it could sting or not, but she thought this wouldn’t
be quite a civil question to ask.
‘What, then you don’t—’ the little voice began,when it was drowned by a shrill scream from theengine, and everybody jumped up in alarm, Aliceamong the rest.
The Horse, who had put his head out of the window, quietly drew it in and said, ‘It’s only a brook
we have to jump over.’ Everybody seemed satisfied
with this, though Alice felt a little nervous at the ideaof trains jumping at all. ‘However, it’ll take us into
the Fourth Square, that’s some comfort!’ she said toherself. In another moment she felt the carriage risestraight up into the air, and in her fright she caught
at the thing nearest to her hand, which happened tobe the Goat’s beard.
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IMG14

But the beard seemed to melt away as she touched
it, and she found herself sitting quietly under a tree—
while the Gnat (for that was the insect she had beentalking to) was balancing itself on a twig just overher head, and fanning her with its wings.
It certainly was a VERY large Gnat: ‘about thesize of a chicken,’ Alice thought. Still, she couldn’t
feel nervous with it, after they had been talking together so long.
‘—then you don’t like all insects?’ the Gnat wenton, as quietly as if nothing had happened.
‘I like them when they can talk,’ Alice said. ‘Noneof them ever talk, where I come from.’‘What sort of insects do you rejoice in, where YOU
come from?’ the Gnat inquired.
‘I don’t REJOICE in insects at all,’ Alice explained, ‘because I’m rather afraid of them—at least
the large kinds. But I can tell you the names of someof them.’‘Of course they answer to their names?’ the Gnat
remarked carelessly.
‘I never knew them to do it.’
‘What’s the use of their having names,’ the Gnat
said, ‘if they won’t answer to them?’‘No use to THEM,’ said Alice; ‘but it’s useful tothe people who name them, I suppose. If not, why
do things have names at all?’‘I can’t say,’ the Gnat replied. ‘Further on, in thewood down there, they’ve got no names—however,go on with your list of insects: you’re wasting time.’‘Well, there’s the Horse-fly,’ Alice began, counting
off the names on her fingers.
‘All right,’ said the Gnat: ‘half way up that bush,
you’ll see a Rocking-horse-fly, if you look. It’s madeentirely of wood, and gets about by swinging itself
from branch to branch.’‘What does it live on?’ Alice asked, with great
curiosity.
‘Sap and sawdust,’ said the Gnat. ‘Go on with thelist.’
Alice IMG14
looked up at the Rocking-horse-fly withgreat interest, and made up her mind that it musthave been just repainted, it looked so bright andsticky; and then she went on.
‘And there’s the Dragon-fly.’‘Look on the branch above your head,’ said theGnat, ‘and there you’ll find a snap-dragon-fly. Its
body is made of plum-pudding, its wings of hollyleaves, and its head is a raisin burning in brandy.’‘And what does it live on?’‘Frumenty and mince pie,’ the Gnat replied; ‘andit makes its nest in a Christmas box.’‘And then there’s the Butterfly,’ Alice went on,
after she had taken a good look at the insect with
its head on fire, and had thought to herself, ‘I wonder if that’s the reason insects are so fond of flying
into candles—because they want to turn into Snapdragon-flies!’‘Crawling at your feet,’ said the Gnat (Alice drew
her feet back in some alarm), ‘you may observe a
Bread-and-Butterfly. Its wings are thin slices of
Bread-and-butter, its body is a crust, and its headis a lump of sugar.’‘And what does IT live on?’‘Weak tea with cream in it.’A new difficulty came into Alice’s head. ‘Supposing
it couldn’t find any?’ she suggested.
‘Then it would die, of course.’‘But that must happen very often,’ Alice remarked
thoughtfully.
‘It always happens,’ said the Gnat.
After IMG16
this, Alice was silent for a minute or two,
pondering. The Gnat amused itself meanwhile byhumming round and round her head: at last it settled
again and remarked, ‘I suppose you don’t want to lose
your name?’‘No, indeed,’ Alice said, a little anxiously.

IMG16‘And yet I don’t know,’ the Gnat went on in acareless tone: ‘only think how convenient it would
be if you could manage to go home without it! For
instance, if the governess wanted to call you to yourlessons, she would call out “come here—,” and there
she would have to leave off, because there wouldn’t be
any name for her to call, and of course you wouldn’t
have to go, you know.’‘That would never do, I’m sure,’ said Alice: ‘thegoverness would never think of excusing me lessons
for that. If she couldn’t remember my name, she’dcall me “Miss!” as the servants do.’‘Well, if she said “Miss,” and didn’t say anything
more,’ the Gnat remarked, ‘of course you’d miss yourlessons. That’s a joke. I wish YOU had made it.’
‘Why do you wish I had made it?’ Alice asked.
‘It’s a very bad one.’
But the Gnat only sighed deeply, while two largetears came rolling down its cheeks.
‘You shouldn’t make jokes,’ Alice said, ‘if it makes
you so unhappy.’
Then came another of those melancholy little sighs,
and this time the poor Gnat really seemed to havesighed itself away, for, when Alice looked up, there
was nothing whatever to be seen on the twig, and, as
she was getting quite chilly with sitting still so long,
she got up and walked on.
She very soon came to an open field, with a woodon the other side of it: it looked much darker than thelast wood, and Alice felt a LITTLE timid about going
into it. However, on second thoughts, she made up
her mind to go on: ‘for I certainly won’t go BACK,’

she thought to herself, and this was the only way to
the Eighth Square.
‘This must be the wood,’ she said thoughtfully
to herself, ‘where things have no names. I wonder what’ll become of MY name when I go in? Ishouldn’t like to lose it at all—because they’d haveto give me another, and it would be almost certain
to be an ugly one. But then the fun would be trying to find the creature that had got my old name!
That’s just like the advertisements, you know, whenpeople lose dogs—“ANSWERS TO THE NAME OF‘DASH:’ HAD ON A BRASS COLLAR”—just fancy
calling everything you met “Alice,” till one of themanswered! Only they wouldn’t answer at all, if they
were wise.’
She was rambling on in this way when she reached
the wood: it looked very cool and shady. ‘Well, at
any rate it’s a great comfort,’ she said as she stepped
under the trees, ‘after being so hot, to get into the—into WHAT?’ she went on, rather surprised at not
being able to think of the word. ‘I mean to get under
the—under the—under THIS, you know!’ putting
her hand on the trunk of the tree. ‘What DOES it
call itself, I wonder? I do believe it’s got no name—why, to be sure it hasn’t!’
She stood silent for a minute, thinking: then she
suddenly began again. ‘Then it really HAS happened, after all! And now, who am I? I WILL remember, if I can! I’m determined to do it!’ But
being determined didn’t help much, and all she could
say, after a great deal of puzzling, was, ‘L, I KNOW
it begins with L!’
Just then a Fawn came wandering by: it looked at
Alice with its large gentle eyes, but didn’t seem at allfrightened. ‘Here then! Here then!’ Alice said, as sheheld out her hand and tried to stroke it; but it only
started back a little, and then stood looking at her
again.
‘What do you call yourself?’ the Fawn said at last.
Such a soft sweet voice it had!
‘I wish I knew!’ thought poor Alice. She answered,rather sadly, ‘Nothing, just now.’‘Think again,’ it said: ‘that won’t do.’Alice thought, but nothing came of it. ‘Please,would you tell me what YOU call yourself?’ she said
timidly. ‘I think that might help a little.’

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‘I’ll IMG17
tell you, if you’ll move a little further on,’ theFawn said. ‘I can’t remember here.’
So they walked on together though the wood, Alicewith her arms clasped lovingly round the soft neck of
the Fawn, till they came out into another open field,
and here the Fawn gave a sudden bound into the air,and shook itself free from Alice’s arms. ‘I’m a Fawn!’
it cried out in a voice of delight, ‘and, dear me! you’rea human child!’ A sudden look of alarm came into its
beautiful brown eyes, and in another moment it had
darted away at full speed.
Alice stood looking after it, almost ready to crywith vexation at having lost her dear little fellowtraveller so suddenly. ‘However, I know my namenow.’ she said, ‘that’s SOME comfort. Alice—
Alice—I won’t forget it again. And now, which ofthese finger-posts ought I to follow, I wonder?’It was not a very difficult question to answer, as
there was only one road through the wood, and thetwo finger-posts both pointed along it. ‘I’ll settle it,’Comparisons
The End

12—
Alice IMG13
thought to herself, ‘Then there’s no use
in speaking.’ The voices didn’t join in this time, as
she hadn’t spoken, but to her great surprise, they all
THOUGHT in chorus (I hope you understand what
THINKING IN CHORUS means—for I must confessthat I don’t), ‘Better say nothing at all. Language isworth a thousand pounds a word!’‘I shall dream about a thousand pounds tonight, I
know I shall!’ thought Alice.
All this time the Guard was looking at her, firstthrough a telescope, then through a microscope, andthen through an opera-glass. At last he said, ‘You’re
travelling the wrong way,’ and shut up the window
and went away.
‘So young a child,’ said the gentleman sitting opposite to her (he was dressed in white paper), ‘ought
to know which way she’s going, even if she doesn’tknow her own name!’
A Goat, that was sitting next to the gentleman inwhite, shut his eyes and said in a loud voice, ‘She
ought to know her way to the ticket-office, even if
she doesn’t know her alphabet!’
There was a Beetle sitting next to the Goat (it wasa very queer carriage-full of passengers altogether),and, as the rule seemed to be that they should all
speak in turn, HE went on with ‘She’ll have to go
back from here as luggage!’
Alice couldn’t see who was sitting beyond the Beetle, but a hoarse voice spoke next. ‘Change engines—’
it said, and was obliged to leave off.
‘It sounds like a horse,’ Alice thought to herself.
And an extremely small voice, close to her ear, said,‘You might make a joke on that—something about“horse” and “hoarse,” you know.’
Then a very gentle voice in the distance said, ‘She
must be labelled “Lass, with care,” you know—’
And after that other voices went on (‘What a number of people there are in the carriage!’ thought Alice), saying, ‘She must go by post, as she’s got ahead on her—’ ‘She must be sent as a message by thetelegraph—’ ‘She must draw the train herself the restof the way—’ and so on.
But the gentleman dressed in white paper leaned
forwards and whispered in her ear, ‘Never mind what
they all say, my dear, but take a return-ticket every
time the train stops.’

—
IMG13

with this, though Alice felt a little nervous at the ideaof trains jumping at all. ‘However, it’ll take us into
the Fourth Square, that’s some comfort!’ she said toherself. In another moment she felt the carriage risestraight up into the air, and in her fright she caught
at the thing nearest to her hand, which happened tobe the Goat’s beard.
**‘Indeed I shan’t!’ Alice said rather impatiently. ‘I
don’t belong to this railway journey at all—I was ina wood just now—and I wish I could get back there.’‘You might make a joke on THAT,’ said the little voice close to her ear: ‘something about “youWOULD if you could,” you know.’‘Don’t tease so,’ said Alice, looking about in vain to
see where the voice came from; ‘if you’re so anxious tohave a joke made, why don’t you make one yourself?’
The little voice sighed deeply: it was VERY unhappy, evidently, and Alice would have said something pitying to comfort it, ‘If it would only sigh likeother people!’ she thought. But this was such a wonderfully small sigh, that she wouldn’t have heard it
at all, if it hadn’t come QUITE close to her ear. The
consequence of this was that it tickled her ear very
much, and quite took off her thoughts from the unhappiness of the poor little creature.
‘I know you are a friend,’ the little voice went on;‘a dear friend, and an old friend. And you won’t hurtme, though I AM an insect.’‘What kind of insect?’ Alice inquired a little anxiously. What she really wanted to know was, whether
it could sting or not, but she thought this wouldn’t
be quite a civil question to ask.
‘What, then you don’t—’ the little voice began,when it was drowned by a shrill scream from theengine, and everybody jumped up in alarm, Aliceamong the rest.
The Horse, who had put his head out of the window, quietly drew it in and said, ‘It’s only a brook
we have to jump over.’ Everybody seemed satisfied

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IMG14

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But the beard seemed to melt away as she touched
it, and she found herself sitting quietly under a tree—
while the Gnat (for that was the insect she had beentalking to) was balancing itself on a twig just overher head, and fanning her with its wings.
It certainly was a VERY large Gnat: ‘about thesize of a chicken,’ Alice thought. Still, she couldn’t
feel nervous with it, after they had been talking together so long.
‘—then you don’t like all insects?’ the Gnat wenton, as quietly as if nothing had happened.
‘I like them when they can talk,’ Alice said. ‘Noneof them ever talk, where I come from.’‘What sort of insects do you rejoice in, where YOU
come from?’ the Gnat inquired.
‘I don’t REJOICE in insects at all,’ Alice explained, ‘because I’m rather afraid of them—at least
the large kinds. But I can tell you the names of someof them.’‘Of course they answer to their names?’ the Gnat
remarked carelessly.
‘I never knew them to do it.’
‘What’s the use of their having names,’ the Gnat
said, ‘if they won’t answer to them?’‘No use to THEM,’ said Alice; ‘but it’s useful tothe people who name them, I suppose. If not, why
do things have names at all?’‘I can’t say,’ the Gnat replied. ‘Further on, in thewood down there, they’ve got no names—however,go on with your list of insects: you’re wasting time.’‘Well, there’s the Horse-fly,’ Alice began, counting
off the names on her fingers.
‘All right,’ said the Gnat: ‘half way up that bush,
you’ll see a Rocking-horse-fly, if you look. It’s madeentirely of wood, and gets about by swinging itself
from branch to branch.’‘What does it live on?’ Alice asked, with great
curiosity.
‘Sap and sawdust,’ said the Gnat. ‘Go on with thelist.’
Alice IMG14
looked up at the Rocking-horse-fly withgreat interest, and made up her mind that it musthave been just repainted, it looked so bright andsticky; and then she went on.
‘And there’s the Dragon-fly.’‘Look on the branch above your head,’ said theGnat, ‘and there you’ll find a snap-dragon-fly. Its
body is made of plum-pudding, its wings of hollyleaves, and its head is a raisin burning in brandy.’‘And what does it live on?’‘Frumenty and mince pie,’ the Gnat replied; ‘andit makes its nest in a Christmas box.’‘And then there’s the Butterfly,’ Alice went on,
after she had taken a good look at the insect with
its head on fire, and had thought to herself, ‘I wonder if that’s the reason insects are so fond of flying
into candles—because they want to turn into Snapdragon-flies!’‘Crawling at your feet,’ said the Gnat (Alice drew
her feet back in some alarm), ‘you may observe a
Bread-and-Butterfly. Its wings are thin slices of
Bread-and-butter, its body is a crust, and its headis a lump of sugar.’‘And what does IT live on?’‘Weak tea with cream in it.’A new difficulty came into Alice’s head. ‘Supposing
it couldn’t find any?’ she suggested.
‘Then it would die, of course.’— pagesize change: ≠12.0pt —IMG16‘But that must happen very often,’ Alice remarked
thoughtfully.
‘It always happens,’ said the Gnat.
After IMG16
this, Alice was silent for a minute or two,
pondering. The Gnat amused itself meanwhile byhumming round and round her head: at last it settled
again and remarked, ‘I suppose you don’t want to lose
your name?’‘No, indeed,’ Alice said, a little anxiously.
‘And yet I don’t know,’ the Gnat went on in acareless tone: ‘only think how convenient it would
be if you could manage to go home without it! For
instance, if the governess wanted to call you to yourlessons, she would call out “come here—,” and there
she would have to leave off, because there wouldn’t be
any name for her to call, and of course you wouldn’t
have to go, you know.’‘That would never do, I’m sure,’ said Alice: ‘thegoverness would never think of excusing me lessons
for that. If she couldn’t remember my name, she’dcall me “Miss!” as the servants do.’‘Well, if she said “Miss,” and didn’t say anything
more,’ the Gnat remarked, ‘of course you’d miss yourlessons. That’s a joke. I wish YOU had made it.’
‘Why do you wish I had made it?’ Alice asked.
‘It’s a very bad one.’
But the Gnat only sighed deeply, while two largetears came rolling down its cheeks.
‘You shouldn’t make jokes,’ Alice said, ‘if it makes
you so unhappy.’
Then came another of those melancholy little sighs,
and this time the poor Gnat really seemed to havesighed itself away, for, when Alice looked up, there
was nothing whatever to be seen on the twig, and, as
she was getting quite chilly with sitting still so long,
she got up and walked on.
She very soon came to an open field, with a woodon the other side of it: it looked much darker than thelast wood, and Alice felt a LITTLE timid about going
into it. However, on second thoughts, she made up
her mind to go on: ‘for I certainly won’t go BACK,’
she thought to herself, and this was the only way to
the Eighth Square.
‘This must be the wood,’ she said thoughtfully
to herself, ‘where things have no names. I wonder what’ll become of MY name when I go in? Ishouldn’t like to lose it at all—because they’d haveto give me another, and it would be almost certain
to be an ugly one. But then the fun would be trying to find the creature that had got my old name!
That’s just like the advertisements, you know, whenpeople lose dogs—“ANSWERS TO THE NAME OF‘DASH:’ HAD ON A BRASS COLLAR”—just fancy
calling everything you met “Alice,” till one of themanswered! Only they wouldn’t answer at all, if they
were wise.’
She was rambling on in this way when she reached
the wood: it looked very cool and shady. ‘Well, at
any rate it’s a great comfort,’ she said as she stepped
under the trees, ‘after being so hot, to get into the—into WHAT?’ she went on, rather surprised at not
being able to think of the word. ‘I mean to get under
the—under the—under THIS, you know!’ putting
her hand on the trunk of the tree. ‘What DOES it
call itself, I wonder? I do believe it’s got no name—why, to be sure it hasn’t!’
She stood silent for a minute, thinking: then she
suddenly began again. ‘Then it really HAS happened, after all! And now, who am I? I WILL remember, if I can! I’m determined to do it!’ But
being determined didn’t help much, and all she could
say, after a great deal of puzzling, was, ‘L, I KNOW
it begins with L!’
Just then a Fawn came wandering by: it looked at
Alice with its large gentle eyes, but didn’t seem at allfrightened. ‘Here then! Here then!’ Alice said, as sheheld out her hand and tried to stroke it; but it only

— pagesize change: ≠12.0pt ——started back a little, and then stood looking at her
again.
‘What do you call yourself?’ the Fawn said at last.
Such a soft sweet voice it had!
‘I wish I knew!’ thought poor Alice. She answered,rather sadly, ‘Nothing, just now.’‘Think again,’ it said: ‘that won’t do.’Alice thought, but nothing came of it. ‘Please,would you tell me what YOU call yourself?’ she said
timidly. ‘I think that might help a little.’‘I’ll IMG17
tell you, if you’ll move a little further on,’the Fawn said. ‘I can’t remember here.’
So they walked on together though the wood, Alicewith her arms clasped lovingly round the soft neck of
the Fawn, till they came out into another open field,
and here the Fawn gave a sudden bound into the air,and shook itself free from Alice’s arms. ‘I’m a Fawn!’
it cried out in a voice of delight, ‘and, dear me! you’rea human child!’ A sudden look of alarm came into its
beautiful brown eyes, and in another moment it had
darted away at full speed.
Alice stood looking after it, almost ready to crywith vexation at having lost her dear little fellowtraveller so suddenly. ‘However, I know my namenow.’ she said, ‘that’s SOME comfort. Alice—
Alice—I won’t forget it again. And now, which ofthese finger-posts ought I to follow, I wonder?’It was not a very difficult question to answer, as
there was only one road through the wood, and thetwo finger-posts both pointed along it. ‘I’ll settle it,’
Alice said to herself, ‘when the road divides and they
point different ways.’
But this did not seem likely to happen. She went
on and on, a long way, but wherever the road divided there were sure to be two finger-posts pointing the same way, one marked ‘TO TWEEDLEDUM’S HOUSE’ and the other ‘TO THE HOUSE
OF TWEEDLEDEE.’‘I do believe,’ said Alice at last, ‘that they live inthe same house! I wonder I never thought of that
before—But I can’t stay there long. I’ll just call andsay “how d’you do?” and ask them the way out of
the wood. If I could only get to the Eighth Square
before it gets dark!’ So she wandered on, talking
to herself as she went, till, on turning a sharp cor-

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ner, she came upon two fat little men, so suddenlythat she could not help starting back, but in another moment she recovered herself, feeling sure thatthey must be.

IV. Tweedledum And Tweedledee
They were standing under a tree, each with an arm
round the other’s neck, and Alice knew which waswhich in a moment, because one of them had ‘DUM’embroidered on his collar, and the other ‘DEE.’ ‘I
suppose they’ve each got “TWEEDLE” round at theback of the collar,’ she said to herself.
They stood so still that she quite forgot they werealive, and she was just looking round to see if theword “TWEEDLE” was written at the back of eachcollar, when she was startled by a voice coming fromthe one marked ‘DUM.’

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Comparison – spreads 1 + 2
optimal, 0 turns viz. optimal, 2 turns
Effective Float
Strategies— pagesize change: ≠12.0pt —Introduction
Visualization

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THROUGH THE LOOKING-GLASS
By Lewis Carroll
The Millennium Fulcrum Edition 1.7

Frank
Mittelbach—

0 turns

Adding Floats
Results

One thing was certain, that the WHITE kitten had
had nothing to do with it:—it was the black kitten’s
fault entirely. For the white kitten had been having
its face washed by the old cat for the last quarter ofan hour (and bearing it pretty well, considering); so
you see that it COULDN’T have had any hand in themischief.
The way Dinah IMG1
washed her children’s faces was
this: first she held the poor thing down by its ear with
one paw, and then with the other paw she rubbed its
face all over, the wrong way, beginning at the nose:and just now, as I said, she was hard at work on thewhite kitten, which was lying quite still and trying topurr—no doubt feeling that it was all meant for its
good.
But the black kitten had been finished with earlier in the afternoon, and so, while Alice was sitting curled up in a corner of the great arm-chair,half talking to herself and half asleep, the kitten had
been having a grand game of romps with the ball ofworsted Alice had been trying to wind up, and had
been rolling it up and down till it had all come undone
again; and there it was, spread over the hearth-rug,
all knots and tangles, with the kitten running after
its own tail in the middle.
‘Oh, you wicked little thing!’ cried Alice, catching up the kitten, and giving it a little kiss to makeit understand that it was in disgrace. ‘Really, Dinah ought to have taught you better manners! YouOUGHT, Dinah, you know you ought!’ she added,
looking reproachfully at the old cat, and speaking inas cross a voice as she could manage—and then she
scrambled back into the arm-chair, taking the kitten and the worsted with her, and began winding up
the ball again. But she didn’t get on very fast, as
she was talking all the time, sometimes to the kitten,
and sometimes to herself. Kitty sat very demurely
on her knee, pretending to watch the progress of the— pagesize change: 12.0pt —— pagesize change: 12.0pt —IMG2

I. Looking-Glass house

winding, and now and then putting out one paw andgently touching the ball, as if it would be glad to help,
if it might.
‘Do you know what to-morrow is, Kitty?’ Alicebegan. ‘You’d have guessed if you’d been up in thewindow with me—only Dinah was making you tidy,
so you couldn’t. I was watching the boys getting insticks for the bonfire—and it wants plenty of sticks,
Kitty! Only it got so cold, and it snowed so, they had
to leave off. Never mind, Kitty, we’ll go and see thebonfire to-morrow.’ Here Alice wound two or threeturns of the worsted round the kitten’s neck, justto see how it would look: this led to a scramble, inwhich the ball rolled down upon the floor, and yards
and yards of it got unwound again.
‘Do you know, I was so angry, Kitty,’ Alice wenton as soon as they were comfortably settled again,‘when I saw all the mischief you had been doing, I
was very nearly opening the window, and putting
you out into the snow! And you’d have deserved
it, you little mischievous darling! What have you
got to say for yourself? Now don’t interrupt me!’she went on, holding up one finger. ‘I’m going totell you all your faults. Number one: you squeaked
twice while Dinah was washing your face this morning. Now you can’t deny it, Kitty: I heard you!
What’s that you say?’ (pretending that the kitten
was speaking.) ‘Her paw went into your eye? Well,that’s YOUR fault, for keeping your eyes open—
if you’d shut them tight up, it wouldn’t have happened. Now don’t make any more excuses, but listen! Number two: you pulled Snowdrop away by thetail just as I had put down the saucer of milk be-fore her! What, you were thirsty, were you? How do
you know she wasn’t thirsty too? Now for number
three: you unwound every bit of the worsted while
I wasn’t looking!
‘That’s three faults IMG2
, Kitty, and you’ve not beenpunished for any of them yet. You know I’m saving up all your punishments for Wednesday week—
Suppose they had saved up all MY punishments!’
she went on, talking more to herself than the kitten. ‘What WOULD they do at the end of a year?
I should be sent to prison, I suppose, when the day
came. Or—let me see—suppose each punishment was
to be going without a dinner: then, when the miserable day came, I should have to go without fifty dinners at once! Well, I shouldn’t mind THAT much!
I’d far rather go without them than eat them!
‘Do you hear the snow against the window-panes,
Kitty? How nice and soft it sounds! Just as if some
one was kissing the window all over outside. I wonder
if the snow LOVES the trees and fields, that it kisses
them so gently? And then it covers them up snug, youknow, with a white quilt; and perhaps it says, “Go
to sleep, darlings, till the summer comes again.” And
when they wake up in the summer, Kitty, they dress
themselves all in green, and dance about—whenever
the wind blows—oh, that’s very pretty!’ cried Alice,

dropping the ball of worsted to clap her hands. ‘And
I do so WISH it was true! I’m sure the woods look
sleepy in the autumn, when the leaves are getting
brown.
‘Kitty, can you play chess? Now, don’t smile, mydear, I’m asking it seriously. Because, when we wereplaying just now, you watched just as if you understood it: and when I said “Check!” you purred!
Well, it WAS a nice check, Kitty, and really I might
have won, if it hadn’t been for that nasty Knight,that came wiggling down among my pieces. Kitty,
dear, let’s pretend—’ And here I wish I could tell you
half the things Alice used to say, beginning with her
favourite phrase ‘Let’s pretend.’ She had had quite along argument with her sister only the day before—
all because Alice had begun with ‘Let’s pretend we’rekings and queens;’ and her sister, who liked being
very exact, had argued that they couldn’t, because
there were only two of them, and Alice had been reduced at last to say, ‘Well, YOU can be one of themthen, and I’LL be all the rest.’ And once she had really frightened her old nurse by shouting suddenly inher ear, ‘Nurse! Do let’s pretend that I’m a hungry
hyaena, and you’re a bone.’
But this is taking us away from Alice’s speech to
the kitten. ‘Let’s pretend that you’re the Red Queen,
Kitty! Do you know, I think if you sat up and folded
your arms, you’d look exactly like her. Now do try,
there’s a dear!’ And Alice got the Red Queen off
the table, and set it up before the kitten as a model
for it to imitate: however, the thing didn’t succeed,
principally, Alice said, because the kitten wouldn’t
fold its arms properly. So, to punish it, she held it
up to the Looking-glass, that it might see how sulky
it was—‘and if you’re not good directly,’ she added,‘I’ll put you through into Looking-glass House. How
would you like THAT?’‘Now, if you’ll only attend, Kitty, and not talk somuch, I’ll tell you all my ideas about Looking-glass
House. First, there’s the room you can see throughthe glass—that’s just the same as our drawing room,
only the things go the other way. I can see all of it
when I get upon a chair—all but the bit behind thefireplace. Oh! I do so wish I could see THAT bit! I
want so much to know whether they’ve a fire in thewinter: you never CAN tell, you know, unless ourfire smokes, and then smoke comes up in that room

—

3

IMG3

IMG4

too—but that may be only pretence, just to makeit look as if they had a fire. Well then, the books
are something like our books, only the words go thewrong way; I know that, because I’ve held up one ofour books to the glass, and then they hold up one in
the other room.
‘How would you IMG3
like to live in Looking-glass
House, Kitty? I wonder if they’d give you milkin there? Perhaps Looking-glass milk isn’t good todrink—But oh, Kitty! now we come to the passage. You can just see a little PEEP of the passage in Looking-glass House, if you leave the doorof our drawing-room wide open: and it’s very likeour passage as far as you can see, only you know it
may be quite different on beyond. Oh, Kitty! how
nice it would be if we could only get through into
Looking-glass House! I’m sure it’s got, oh! such
beautiful things in it! Let’s pretend there’s a wayof getting through into it, somehow, Kitty. Let’s pretend the glass has got all soft like gauze, so that we
can get through. Why, it’s turning into a sort of mist
now, I declare! It’ll be easy enough to get through—’
She was up on the chimney-piece while she said this,though she hardly knew how she had got there. And

certainly the glass WAS beginning to melt away, justlike a bright silvery mist.
In another moment IMG4
Alice was through the glass,and had jumped lightly down into the Looking-glass
room. The very first thing she did was to lookwhether there was a fire in the fireplace, and she wasquite pleased to find that there was a real one, blazing away as brightly as the one she had left behind.
‘So I shall be as warm here as I was in the old room,’
thought Alice: ‘warmer, in fact, because there’ll be
no one here to scold me away from the fire. Oh,
what fun it’ll be, when they see me through the glassin here, and can’t get at me!’Then she began looking about, and noticed thatwhat could be seen from the old room was quite common and uninteresting, but that all the rest was asdifferent as possible. For instance, the pictures on
the wall next the fire seemed to be all alive, and thevery clock on the chimney-piece (you know you can
only see the back of it in the Looking-glass) had got
the face of a little old man, and grinned at her.
‘They don’t keep this room so tidy as the other,’
Alice thought to herself, as she noticed several of thechessmen down in the hearth among the cinders: butin another moment, with a little ‘Oh!’ of surprise,

Comparisons
The End— pagesize change: ≠12.0pt ——THROUGH THE LOOKING-GLASS
By Lewis Carroll
The Millennium Fulcrum Edition 1.7

1
IMG1

2

—

2 turns

One thing was certain, that the WHITE kitten had
had nothing to do with it:—it was the black kitten’s
fault entirely. For the white kitten had been having
its face washed by the old cat for the last quarter ofan hour (and bearing it pretty well, considering); so
you see that it COULDN’T have had any hand in themischief.
The way Dinah IMG1
washed her children’s faces was
this: first she held the poor thing down by its ear with
one paw, and then with the other paw she rubbed its
face all over, the wrong way, beginning at the nose:and just now, as I said, she was hard at work on thewhite kitten, which was lying quite still and trying topurr—no doubt feeling that it was all meant for its
good.
But the black kitten had been finished with earlier in the afternoon, and so, while Alice was sitting curled up in a corner of the great arm-chair,half talking to herself and half asleep, the kitten had
been having a grand game of romps with the ball ofworsted Alice had been trying to wind up, and had
been rolling it up and down till it had all come undone
again; and there it was, spread over the hearth-rug,
all knots and tangles, with the kitten running after
its own tail in the middle.
‘Oh, you wicked little thing!’ cried Alice, catching up the kitten, and giving it a little kiss to makeit understand that it was in disgrace. ‘Really, Dinah ought to have taught you better manners! YouOUGHT, Dinah, you know you ought!’ she added,
looking reproachfully at the old cat, and speaking inas cross a voice as she could manage—and then she
scrambled back into the arm-chair, taking the kitten and the worsted with her, and began winding up
the ball again. But she didn’t get on very fast, as
she was talking all the time, sometimes to the kitten,
and sometimes to herself. Kitty sat very demurely
on her knee, pretending to watch the progress of thewinding, and now and then putting out one paw andgently touching the ball, as if it would be glad to help,
if it might.
‘Do you know what to-morrow is, Kitty?’ Alicebegan. ‘You’d have guessed if you’d been up in thewindow with me—only Dinah was making you tidy,
so you couldn’t. I was watching the boys getting insticks for the bonfire—and it wants plenty of sticks,
Kitty! Only it got so cold, and it snowed so, they had
to leave off. Never mind, Kitty, we’ll go and see thebonfire to-morrow.’ Here Alice wound two or threeturns of the worsted round the kitten’s neck, justto see how it would look: this led to a scramble, inwhich the ball rolled down upon the floor, and yards
and yards of it got unwound again.
‘Do you know, I was so angry, Kitty,’ Alice wenton as soon as they were comfortably settled again,‘when I saw all the mischief you had been doing, I
was very nearly opening the window, and putting
you out into the snow! And you’d have deserved
it, you little mischievous darling! What have you
got to say for yourself? Now don’t interrupt me!’she went on, holding up one finger. ‘I’m going totell you all your faults. Number one: you squeaked
twice while Dinah was washing your face this morning. Now you can’t deny it, Kitty: I heard you!
What’s that you say?’ (pretending that the kitten
was speaking.) ‘Her paw went into your eye? Well,that’s YOUR fault, for keeping your eyes open—
if you’d shut them tight up, it wouldn’t have happened. Now don’t make any more excuses, but listen! Number two: you pulled Snowdrop away by thetail just as I had put down the saucer of milk be-— pagesize change: ≠12.0pt —IMG2

I. Looking-Glass housefore her! What, you were thirsty, were you? How do
you know she wasn’t thirsty too? Now for number
three: you unwound every bit of the worsted while
I wasn’t looking!
‘That’s three faults IMG2
, Kitty, and you’ve not beenpunished for any of them yet. You know I’m saving up all your punishments for Wednesday week—
Suppose they had saved up all MY punishments!’
she went on, talking more to herself than the kitten. ‘What WOULD they do at the end of a year?
I should be sent to prison, I suppose, when the day
came. Or—let me see—suppose each punishment was
to be going without a dinner: then, when the miserable day came, I should have to go without fifty dinners at once! Well, I shouldn’t mind THAT much!
I’d far rather go without them than eat them!
‘Do you hear the snow against the window-panes,
Kitty? How nice and soft it sounds! Just as if some
one was kissing the window all over outside. I wonder
if the snow LOVES the trees and fields, that it kisses
them so gently? And then it covers them up snug, youknow, with a white quilt; and perhaps it says, “Go
to sleep, darlings, till the summer comes again.” And
when they wake up in the summer, Kitty, they dress

themselves all in green, and dance about—whenever
the wind blows—oh, that’s very pretty!’ cried Alice,
dropping the ball of worsted to clap her hands. ‘And
I do so WISH it was true! I’m sure the woods look
sleepy in the autumn, when the leaves are getting
brown.
‘Kitty, can you play chess? Now, don’t smile,
my dear, I’m asking it seriously. Because, when
we were playing just now, you watched just as if
you understood it: and when I said “Check!” youpurred! Well, it WAS a nice check, Kitty, and really I might have won, if it hadn’t been for thatnasty Knight, that came wiggling down among mypieces. Kitty, dear, let’s pretend—’ And here I wish
I could tell you half the things Alice used to say,
beginning with her favourite phrase ‘Let’s pretend.’
She had had quite a long argument with her sister only the day before—all because Alice had begun with ‘Let’s pretend we’re kings and queens;’ andher sister, who liked being very exact, had argued
that they couldn’t, because there were only two ofthem, and Alice had been reduced at last to say,‘Well, YOU can be one of them then, and I’LL be
all the rest.’ And once she had really frightened her
old nurse by shouting suddenly in her ear, ‘Nurse!
Do let’s pretend that I’m a hungry hyaena, andyou’re a bone.’
But this is taking us away from Alice’s speech to
the kitten. ‘Let’s pretend that you’re the Red Queen,
Kitty! Do you know, I think if you sat up and folded
your arms, you’d look exactly like her. Now do try,
there’s a dear!’ And Alice got the Red Queen off
the table, and set it up before the kitten as a model
for it to imitate: however, the thing didn’t succeed,
principally, Alice said, because the kitten wouldn’t
fold its arms properly. So, to punish it, she held it
up to the Looking-glass, that it might see how sulky
it was—‘and if you’re not good directly,’ she added,‘I’ll put you through into Looking-glass House. How
would you like THAT?’‘Now, if you’ll only attend, Kitty, and not talk somuch, I’ll tell you all my ideas about Looking-glass
House. First, there’s the room you can see throughthe glass—that’s just the same as our drawing room,
only the things go the other way. I can see all of it— pagesize change: ≠12.0pt —

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3

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when I get upon a chair—all but the bit behind thefireplace. Oh! I do so wish I could see THAT bit! I
want so much to know whether they’ve a fire in thewinter: you never CAN tell, you know, unless ourfire smokes, and then smoke comes up in that room
too—but that may be only pretence, just to makeit look as if they had a fire. Well then, the books
are something like our books, only the words go thewrong way; I know that, because I’ve held up one ofour books to the glass, and then they hold up one in
the other room.
‘How would you IMG3
like to live in Looking-glass
House, Kitty? I wonder if they’d give you milkin there? Perhaps Looking-glass milk isn’t good todrink—But oh, Kitty! now we come to the passage. You can just see a little PEEP of the passage in Looking-glass House, if you leave the doorof our drawing-room wide open: and it’s very likeour passage as far as you can see, only you know it
may be quite different on beyond. Oh, Kitty! how
nice it would be if we could only get through into
Looking-glass House! I’m sure it’s got, oh! such

beautiful things in it! Let’s pretend there’s a wayof getting through into it, somehow, Kitty. Let’s pretend the glass has got all soft like gauze, so that we
can get through. Why, it’s turning into a sort of mist
now, I declare! It’ll be easy enough to get through—’
She was up on the chimney-piece while she said this,though she hardly knew how she had got there. And
certainly the glass WAS beginning to melt away, justlike a bright silvery mist.
In another moment IMG4
Alice was through the glass,and had jumped lightly down into the Looking-glass
room. The very first thing she did was to lookwhether there was a fire in the fireplace, and she wasquite pleased to find that there was a real one, blazing away as brightly as the one she had left behind.
‘So I shall be as warm here as I was in the old room,’
thought Alice: ‘warmer, in fact, because there’ll be
no one here to scold me away from the fire. Oh,
what fun it’ll be, when they see me through the glassin here, and can’t get at me!’Then she began looking about, and noticed thatwhat could be seen from the old room was quite common and uninteresting, but that all the rest was as

(

:

:

)

Comparison – spreads 3 + 4
optimal, 0 turns viz. optimal, 2 turns
Effective Float
Strategies
4—
she was down on her hands and knees watching them.
The chessmen were walking about, two and two!
‘Here are the IMG5Red King and the Red Queen,’ Alice said (in a whisper, for fear of frightening them),‘and there are the White King and the White Queensitting on the edge of the shovel—and here are two
castles walking arm in arm—I don’t think they canhear me,’ she went on, as she put her head closer
down, ‘and I’m nearly sure they can’t see me. I feel
somehow as if I were invisible—’
Here something began squeaking on the table behind Alice, and made her turn her head just in timeto see one of the White Pawns roll over and begin
kicking: she watched it with great curiosity to see
what would happen next.
‘It is the voice of my child!’ the White Queen criedout as she rushed past the King, so violently that she
knocked him over among the cinders. ‘My precious
Lily! My imperial kitten!’ and she began scrambling
wildly up the side of the fender.
‘Imperial fiddlestick!’ said the King, rubbing his
nose, which had been hurt by the fall. He had a rightto be a LITTLE annoyed with the Queen, for he wascovered with ashes from head to foot.
Alice was very anxious to be of use, and, as thepoor little Lily was nearly screaming herself into afit, she hastily picked up the Queen and set her on
the table by the side of her noisy little daughter.
The Queen gasped, and sat down: the rapid journey through the air had quite taken away her breathand for a minute or two she could do nothing but hug
the little Lily in silence. As soon as she had recovered
her breath a little, she called out to the White King,
who was sitting sulkily among the ashes, ‘Mind thevolcano!’‘What volcano?’ said the King, looking up anxiously into the fire, as if he thought that was themost likely place to find one.
‘Blew—me—up,’ IMG6
panted the Queen, who wasstill a little out of breath. ‘Mind you come up—theregular way—don’t get blown up!’
Alice watched the White King as he slowly struggled up from bar to bar, till at last she said, ‘Why,
you’ll be hours and hours getting to the table, at that
rate. I’d far better help you, hadn’t I?’ But the King
took no notice of the question: it was quite clear thathe could neither hear her nor see her.

Frank
Mittelbach
Introduction
Visualization
Adding Floats
Results— pagesize change: 12.0pt —— pagesize change: 12.0pt —

IMG5

—

5

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IMG7

6

—

— pagesize change: ≠12.0pt —IMG8

And as in uffish thought he stood,
The Jabberwock, with eyes of flame,
Came whiffling through the tulgey wood,
And burbled as it came!
One, two! One, two! And through andthrough
The vorpal blade went snicker-snack!
He left it dead, and with its headHe went galumphing back.

So Alice picked him up very gently, and lifted him
across more slowly than she had lifted the Queen,that she mightn’t take his breath away: but, before
she put him on the table, she thought she might aswell dust him a little, he was so covered with ashes.
She said afterwards that she had never seen in all
her life such a face as the King made, when he foundhimself held in the air by an invisible hand, and being
dusted: he was far too much astonished to cry out,
but his eyes and his mouth went on getting larger
and larger, and rounder and rounder, till her hand
shook so with laughing that she nearly let him drop
upon the floor.
‘Oh! PLEASE don’t make such faces, my dear!’she cried out, quite forgetting that the King couldn’t
hear her. ‘You make me laugh so that I can hardly
hold you! And don’t keep your mouth so wide open!
All the ashes will get into it—there, now I think
you’re tidy enough!’ she added, as she smoothed hishair, and set him upon the table near the Queen.
The King immediately fell flat on his back, and lay
perfectly still: and Alice was a little alarmed at what
she had done, and went round the room to see if she
could find any water to throw over him. However, she
could find nothing but a bottle of ink, and when she
got back with it she found he had recovered, and heand the Queen were talking together in a frightenedwhisper—so low, that Alice could hardly hear what
they said.
The King was saying, ‘I assure, you my dear, I
turned cold to the very ends of my whiskers!’
To which the Queen replied, ‘You haven’t got any
whiskers.’‘And hast thou slain the Jabberwock?
Come to my arms, my beamish boy!
O frabjous day! Callooh! Callay!’
He chortled in his joy.
‘The horror of that moment,’ the King went on, ‘Ishall never, NEVER forget!’‘You will, though,’ the Queen said, ‘if you don’t
make a memorandum of it.’
Alice looked on with great interest as the King took
sevot yhtils eht dna,gillirb sawT’
an enormous memorandum-book out of his pocket,
ebaw eht ni elbmig dna eryg diD
and began writing. A sudden thought struck her,,sevogorob eht erew ysmim llA
and she took hold of the end of the pencil, which.ebargtuo shtar emom eht dnAcame some way over his shoulder, and began writingfor him.
She puzzled over this for some time, but at last a
The poor King looked puzzled and unhappy, and bright thought struck her. ‘Why, it’s a Looking-glass
struggled with the pencil for some time without say- book, of course! And if I hold it up to a glass, theing anything; but Alice was too strong for him, and words will all go the right way again.’at last he panted out, ‘My dear! I really MUST get
This was IMG7
the poem that Alice read.
a thinner pencil. I can’t manage this one a bit; itwrites all manner of things that I don’t intend—’
JABBERWOCKY‘What manner of things?’ said the Queen, looking‘Twas brillig, and the slithy toves
over the book (in which Alice had put ‘THE WHITE
Did gyre and gimble in the wabe;
KNIGHT IS SLIDING DOWN THE POKER. HE
All mimsy were the borogoves,
BALANCES VERY BADLY’) ‘That’s not a memoAnd the mome raths outgrabe.
randum of YOUR feelings!’
There was a book lying near Alice on the table,‘Beware the Jabberwock, my son!
and while she sat watching the White King (for she
The jaws that bite, the claws that catch!
was still a little anxious about him, and had the ink
Beware the Jubjub bird, and shunall ready to throw over him, in case he fainted again),
The frumious Bandersnatch!’
she turned over the leaves, to find some part that she
could read, ‘—for it’s all in some language I don’t
He took his vorpal sword in hand:
know,’ she said to herself.
Long time the manxome foe he sought—
It was like this.
So rested he by the Tumtum tree,
YKCOWREBBAJ
And stood awhile in thought.

‘Twas brillig, and the slithy toves
Did gyre and gimble in the wabe;
All mimsy were the borogoves,
And the mome raths outgrabe.
‘It seems IMG8very pretty,’ she said when she hadfinished it, ‘but it’s RATHER hard to understand!’(You see she didn’t like to confess, even to herself,that she couldn’t make it out at all.) ‘Somehow it
seems to fill my head with ideas—only I don’t exactly know what they are! However, SOMEBODY
killed SOMETHING: that’s clear, at any rate—’‘But oh!’ thought Alice, suddenly jumping up, ‘if I
don’t make haste I shall have to go back through the
Looking-glass, before I’ve seen what the rest of thehouse is like! Let’s have a look at the garden first!’
She was out of the room in a moment, and ran down
stairs—or, at least, it wasn’t exactly running, but a
new invention of hers for getting down stairs quickly
and easily, as Alice said to herself. She just kept thetips of her fingers on the hand-rail, and floated gently
down without even touching the stairs with her feet;then she floated on through the hall, and would havegone straight out at the door in the same way, if she
hadn’t caught hold of the door-post. She was getting
a little giddy with so much floating in the air, andwas rather glad to find herself walking again in thenatural way.

II. The Garden of Live Flowers‘I should see the garden far better,’ said Alice to herself, ‘if I could get to the top of that hill: and here’s apath that leads straight to it—at least, no, it doesn’t
do that—’ (after going a few yards along the path,and turning several sharp corners), ‘but I suppose it
will at last. But how curiously it twists! It’s more
like a corkscrew than a path! Well, THIS turn goes tothe hill, I suppose—no, it doesn’t! This goes straightback to the house! Well then, I’ll try it the other way.’
And so she did: wandering up and down, and trying turn after turn, but always coming back to thehouse, do what she would. Indeed, once, when she
turned a corner rather more quickly than usual, sheran against it before she could stop herself.
‘It’s no use talking about it,’ Alice said, looking
up at the house and pretending it was arguing withher. ‘I’m NOT going in again yet. I know I should— pagesize change: ≠12.0pt ——have to get through the Looking-glass again—backinto the old room—and there’d be an end of all myadventures!’So, resolutely turning her back upon the house,
she set out once more down the path, determined tokeep straight on till she got to the hill. For a few
minutes all went on well, and she was just saying, ‘I
really SHALL do it this time—’ when the path gave
a sudden twist and shook itself (as she described itafterwards), and the next moment she found herself
actually walking in at the door.
‘Oh, it’s too bad!’ she cried. ‘I never saw such ahouse for getting in the way! Never!’However, there was the hill full in sight, so there
was nothing to be done but start again. This time
she came upon a large flower-bed, with a border ofdaisies, and a willow-tree growing in the middle.
‘O Tiger-lily,’ said Alice, addressing herself to one
that was waving gracefully about in the wind, ‘I
WISH you could talk!’‘We CAN talk,’ said the Tiger-lily: ‘when there’s
anybody worth talking to.’Alice was so astonished that she could not speak fora minute: it quite seemed to take her breath away. At
length, as the Tiger-lily only went on waving about,she spoke again, in a timid voice—almost in a whisper. ‘And can ALL the flowers talk?’‘As well as YOU can,’ said the Tiger-lily. ‘And agreat deal louder.’‘It isn’t manners for us to begin, you know,’ said
the Rose, ‘and I really was wondering when you’dspeak! Said I to myself, “Her face has got SOME
sense in it, though it’s not a clever one!” Still, you’rethe right colour, and that goes a long way.’‘I don’t care about the colour,’ the Tiger-lily remarked. ‘If only her petals curled up a little more,
she’d be all right.’
Alice didn’t like being criticised, so she began asking questions. ‘Aren’t you sometimes frightened atbeing planted out here, with nobody to take care ofyou?’‘There’s the tree in the middle,’ said the Rose:‘what else is it good for?’‘But what could it do, if any danger came?’ Aliceasked.

7
IMG9‘It says IMG9
“Bough-wough!”’ cried a Daisy: ‘that’s
why its branches are called boughs!’‘Didn’t you know THAT?’ cried another Daisy, andhere they all began shouting together, till the air
seemed quite full of little shrill voices. ‘Silence, every
one of you!’ cried the Tiger-lily, waving itself passionately from side to side, and trembling with excitement. ‘They know I can’t get at them!’ it panted,
bending its quivering head towards Alice, ‘or theywouldn’t dare to do it!’‘Never mind!’ Alice said in a soothing tone, andstooping down to the daisies, who were just beginningagain, she whispered, ‘If you don’t hold your tongues,
I’ll pick you!’
There was silence in a moment, and several of thepink daisies turned white.
‘That’s right!’ said the Tiger-lily. ‘The daisies are
worst of all. When one speaks, they all begin together, and it’s enough to make one wither to hear
the way they go on!’‘How is it you can all talk so nicely?’ Alice said,
hoping to get it into a better temper by a compliment.
‘I’ve been in many gardens before, but none of theflowers could talk.’Comparisons
The End4—
different as possible. For instance, the pictures on
the wall next the fire seemed to be all alive, and thevery clock on the chimney-piece (you know you can
only see the back of it in the Looking-glass) had got
the face of a little old man, and grinned at her.
‘They don’t keep this room so tidy as the other,’
Alice thought to herself, as she noticed several of
the chessmen down in the hearth among the cinders: but in another moment, with a little ‘Oh!’of surprise, she was down on her hands and knees
watching them. The chessmen were walking about,
two and two!
‘Here are the IMG5Red King and the Red Queen,’ Alice said (in a whisper, for fear of frightening them),‘and there are the White King and the White Queensitting on the edge of the shovel—and here are two
castles walking arm in arm—I don’t think they canhear me,’ she went on, as she put her head closer
down, ‘and I’m nearly sure they can’t see me. I feel
somehow as if I were invisible—’
Here something began squeaking on the table behind Alice, and made her turn her head just in timeto see one of the White Pawns roll over and begin
kicking: she watched it with great curiosity to see
what would happen next.
‘It is the voice of my child!’ the White Queen criedout as she rushed past the King, so violently that she
knocked him over among the cinders. ‘My precious
Lily! My imperial kitten!’ and she began scrambling
wildly up the side of the fender.
‘Imperial fiddlestick!’ said the King, rubbing his
nose, which had been hurt by the fall. He had a rightto be a LITTLE annoyed with the Queen, for he wascovered with ashes from head to foot.
Alice was very anxious to be of use, and, as thepoor little Lily was nearly screaming herself into afit, she hastily picked up the Queen and set her on
the table by the side of her noisy little daughter.
The Queen gasped, and sat down: the rapid journey through the air had quite taken away her breathand for a minute or two she could do nothing but hug
the little Lily in silence. As soon as she had recovered
her breath a little, she called out to the White King,
who was sitting sulkily among the ashes, ‘Mind thevolcano!’— pagesize change: ≠12.0pt —‘What volcano?’ said the King, looking up anxiously into the fire, as if he thought that was themost likely place to find one.
‘Blew—me—up,’ IMG6
panted the Queen, who wasstill a little out of breath. ‘Mind you come up—theregular way—don’t get blown up!’
Alice watched the White King as he slowly struggled up from bar to bar, till at last she said, ‘Why,
you’ll be hours and hours getting to the table, at that
rate. I’d far better help you, hadn’t I?’ But the King
took no notice of the question: it was quite clear thathe could neither hear her nor see her.
So Alice picked him up very gently, and lifted him
across more slowly than she had lifted the Queen,that she mightn’t take his breath away: but, before
she put him on the table, she thought she might aswell dust him a little, he was so covered with ashes.
She said afterwards that she had never seen in all
her life such a face as the King made, when he foundhimself held in the air by an invisible hand, and being
dusted: he was far too much astonished to cry out,
but his eyes and his mouth went on getting larger
and larger, and rounder and rounder, till her hand
shook so with laughing that she nearly let him drop
upon the floor.
‘Oh! PLEASE don’t make such faces, my dear!’she cried out, quite forgetting that the King couldn’t
hear her. ‘You make me laugh so that I can hardly
hold you! And don’t keep your mouth so wide open!
All the ashes will get into it—there, now I think
you’re tidy enough!’ she added, as she smoothed hishair, and set him upon the table near the Queen.
The King immediately fell flat on his back, and lay
perfectly still: and Alice was a little alarmed at what
she had done, and went round the room to see if she
could find any water to throw over him. However, she
could find nothing but a bottle of ink, and when she
got back with it she found he had recovered, and heand the Queen were talking together in a frightenedwhisper—so low, that Alice could hardly hear what
they said.
The King was saying, ‘I assure, you my dear, I
turned cold to the very ends of my whiskers!’
To which the Queen replied, ‘You haven’t got any
whiskers.’— pagesize change: ≠12.0pt —

—

5

IMG5

6

—

— pagesize change: ≠12.0pt —IMG6

sevot yhtils eht dna,gillirb sawT’ebaw eht ni elbmig dna eryg diD,sevogorob eht erew ysmim llA.ebargtuo shtar emom eht dnA

IMG7

She puzzled over this for some time, but at last abright thought struck her. ‘Why, it’s a Looking-glass
book, of course! And if I hold it up to a glass, thewords will all go the right way again.’This was IMG7
the poem that Alice read.
JABBERWOCKY‘The horror of that moment,’ the King went on, ‘Ishall never, NEVER forget!’‘You will, though,’ the Queen said, ‘if you don’t
make a memorandum of it.’
Alice looked on with great interest as the King took
an enormous memorandum-book out of his pocket,
and began writing. A sudden thought struck her,and she took hold of the end of the pencil, whichcame some way over his shoulder, and began writingfor him.
The poor King looked puzzled and unhappy, andstruggled with the pencil for some time without saying anything; but Alice was too strong for him, andat last he panted out, ‘My dear! I really MUST geta thinner pencil. I can’t manage this one a bit; itwrites all manner of things that I don’t intend—’‘What manner of things?’ said the Queen, looking
over the book (in which Alice had put ‘THE WHITEKNIGHT IS SLIDING DOWN THE POKER. HE
BALANCES VERY BADLY’) ‘That’s not a memorandum of YOUR feelings!’
There was a book lying near Alice on the table,
and while she sat watching the White King (for she
was still a little anxious about him, and had the ink
all ready to throw over him, in case he fainted again),
she turned over the leaves, to find some part that she
could read, ‘—for it’s all in some language I don’tknow,’ she said to herself.
It was like this.
YKCOWREBBAJ‘Twas brillig, and the slithy toves
Did gyre and gimble in the wabe;
All mimsy were the borogoves,
And the mome raths outgrabe.
‘Beware the Jabberwock, my son!
The jaws that bite, the claws that catch!
Beware the Jubjub bird, and shun
The frumious Bandersnatch!’
He took his vorpal sword in hand:Long time the manxome foe he sought—
So rested he by the Tumtum tree,
And stood awhile in thought.
And as in uffish thought he stood,
The Jabberwock, with eyes of flame,
Came whiffling through the tulgey wood,
And burbled as it came!
One, two! One, two! And through andthrough
The vorpal blade went snicker-snack!
He left it dead, and with its headHe went galumphing back.
‘And hast thou slain the Jabberwock?
Come to my arms, my beamish boy!
O frabjous day! Callooh! Callay!’
He chortled in his joy.

‘Twas brillig, and the slithy toves
Did gyre and gimble in the wabe;
All mimsy were the borogoves,
And the mome raths outgrabe.
‘It seems IMG8very pretty,’ she said when she hadfinished it, ‘but it’s RATHER hard to understand!’(You see she didn’t like to confess, even to herself,that she couldn’t make it out at all.) ‘Somehow it
seems to fill my head with ideas—only I don’t exactly know what they are! However, SOMEBODY
killed SOMETHING: that’s clear, at any rate—’‘But oh!’ thought Alice, suddenly jumping up, ‘if I
don’t make haste I shall have to go back through the
Looking-glass, before I’ve seen what the rest of thehouse is like! Let’s have a look at the garden first!’
She was out of the room in a moment, and ran down
stairs—or, at least, it wasn’t exactly running, but a
new invention of hers for getting down stairs quickly
and easily, as Alice said to herself. She just kept thetips of her fingers on the hand-rail, and floated gently
down without even touching the stairs with her feet;then she floated on through the hall, and would havegone straight out at the door in the same way, if she
hadn’t caught hold of the door-post. She was getting
a little giddy with so much floating in the air, andwas rather glad to find herself walking again in thenatural way.

II. The Garden of Live Flowers‘I should see the garden far better,’ said Alice to herself, ‘if I could get to the top of that hill: and here’s apath that leads straight to it—at least, no, it doesn’t
do that—’ (after going a few yards along the path,and turning several sharp corners), ‘but I suppose it
will at last. But how curiously it twists! It’s more
like a corkscrew than a path! Well, THIS turn goes tothe hill, I suppose—no, it doesn’t! This goes straightback to the house! Well then, I’ll try it the other way.’
And so she did: wandering up and down, and trying turn after turn, but always coming back to thehouse, do what she would. Indeed, once, when she
turned a corner rather more quickly than usual, sheran against it before she could stop herself.
‘It’s no use talking about it,’ Alice said, looking
up at the house and pretending it was arguing withher. ‘I’m NOT going in again yet. I know I shouldhave to get through the Looking-glass again—backinto the old room—and there’d be an end of all myadventures!’So, resolutely turning her back upon the house,
she set out once more down the path, determined to— pagesize change: ≠12.0pt —

—

7

IMG8

length, as the Tiger-lily only went on waving about,she spoke again, in a timid voice—almost in a whisper. ‘And can ALL the flowers talk?’‘As well as YOU can,’ said the Tiger-lily. ‘And agreat deal louder.’‘It isn’t manners for us to begin, you know,’ said
the Rose, ‘and I really was wondering when you’dspeak! Said I to myself, “Her face has got SOME
sense in it, though it’s not a clever one!” Still, you’rethe right colour, and that goes a long way.’‘I don’t care about the colour,’ the Tiger-lily remarked. ‘If only her petals curled up a little more,
she’d be all right.’
Alice didn’t like being criticised, so she began asking questions. ‘Aren’t you sometimes frightened atbeing planted out here, with nobody to take care ofyou?’‘There’s the tree in the middle,’ said the Rose:‘what else is it good for?’‘But what could it do, if any danger came?’ Aliceasked.
‘It says IMG9
“Bough-wough!”’ cried a Daisy: ‘that’s
why its branches are called boughs!’‘Didn’t you know THAT?’ cried another Daisy, andhere they all began shouting together, till the air
seemed quite full of little shrill voices. ‘Silence, every
keep straight on till she got to the hill. For a few one of you!’ cried the Tiger-lily, waving itself passionminutes all went on well, and she was just saying, ‘I ately from side to side, and trembling with excitereally SHALL do it this time—’ when the path gave ment. ‘They know I can’t get at them!’ it panted,
a sudden twist and shook itself (as she described it bending its quivering head towards Alice, ‘or they
afterwards), and the next moment she found herself wouldn’t dare to do it!’
actually walking in at the door.
‘Never mind!’ Alice said in a soothing tone, and‘Oh, it’s too bad!’ she cried. ‘I never saw such a stooping down to the daisies, who were just beginninghouse for getting in the way! Never!’again, she whispered, ‘If you don’t hold your tongues,
However, there was the hill full in sight, so there I’ll pick you!’was nothing to be done but start again. This time
There was silence in a moment, and several of theshe came upon a large flower-bed, with a border of pink daisies turned white.
daisies, and a willow-tree growing in the middle.
‘That’s right!’ said the Tiger-lily. ‘The daisies are‘O Tiger-lily,’ said Alice, addressing herself to one worst of all. When one speaks, they all begin tothat was waving gracefully about in the wind, ‘I gether, and it’s enough to make one wither to hear
WISH you could talk!’
the way they go on!’‘We CAN talk,’ said the Tiger-lily: ‘when there’s‘How is it you can all talk so nicely?’ Alice said,
anybody worth talking to.’hoping to get it into a better temper by a compliment.
Alice was so astonished that she could not speak for ‘I’ve been in many gardens before, but none of thea minute: it quite seemed to take her breath away. At flowers could talk.’

(

:

:

)

Comparison – spreads 5 + 6
optimal, 0 turns viz. optimal, 2 turns
Effective Float
Strategies
8—‘Put your hand down, and feel the ground,’ said
the Tiger-lily. ‘Then you’ll know why.’
Alice did so. ‘It’s very hard,’ she said, ‘but I don’t
see what that has to do with it.’
‘In most gardens,’ the Tiger-lily said, ‘they makethe beds too soft—so that the flowers are always
asleep.’This sounded a very good reason, and Alice wasquite pleased to know it. ‘I never thought of that
before!’ she said.
‘It’s MY opinion that you never think AT ALL,’the Rose said in a rather severe tone.
‘I never saw anybody that looked stupider,’ a Violet said, so suddenly, that Alice quite jumped; for it
hadn’t spoken before.
‘Hold YOUR tongue!’ cried the Tiger-lily. ‘As if
YOU ever saw anybody! You keep your head under
the leaves, and snore away there, till you know no
more what’s going on in the world, than if you werea bud!’‘Are there any more people in the garden besides
me?’ Alice said, not choosing to notice the Rose’s
last remark.
‘There’s one other flower in the garden that canmove about like you,’ said the Rose. ‘I wonder how
you do it—’ (‘You’re always wondering,’ said the
Tiger-lily), ‘but she’s more bushy than you are.’‘Is she like me?’ Alice asked eagerly, for thethought crossed her mind, ‘There’s another little girlin the garden, somewhere!’‘Well, she has the same awkward shape as you,’
the Rose said, ‘but she’s redder—and her petals areshorter, I think.’‘Her petals are done up close, almost like a dahlia,’
the Tiger-lily interrupted: ‘not tumbled about anyhow, like yours.’‘But that’s not YOUR fault,’ the Rose added
kindly: ‘you’re beginning to fade, you know—andthen one can’t help one’s petals getting a little untidy.’
Alice didn’t like this idea at all: so, to change thesubject, she asked ‘Does she ever come out here?’‘I daresay you’ll see her soon,’ said the Rose. ‘She’s
one of the thorny kind.’‘Where does she wear the thorns?’ Alice asked withsome curiosity.

Frank
Mittelbach
Introduction
Visualization
Adding Floats
Results—
IMG10‘Why all round her head, of course,’ the Rosereplied. ‘I was wondering YOU hadn’t got some too.
I thought it was the regular rule.’‘She’s coming!’ cried the Larkspur. ‘I hear her
footstep, thump, thump, thump, along the gravelwalk!’
Alice looked IMG10
round eagerly, and found that it was
the Red Queen. ‘She’s grown a good deal!’ washer first remark. She had indeed: when Alice firstfound her in the ashes, she had been only three inches
high—and here she was, half a head taller than Aliceherself!
‘It’s the fresh air that does it,’ said the Rose: ‘wonderfully fine air it is, out here.’‘I think I’ll go and meet her,’ said Alice, for,though the flowers were interesting enough, she feltthat it would be far grander to have a talk witha real Queen.
‘You can’t possibly do that,’ said the Rose: ‘Ishould advise you to walk the other way.’
This sounded nonsense to Alice, so she said nothing, but set off at once towards the Red Queen. To
her surprise, she lost sight of her in a moment, andfound herself walking in at the front-door again.

A little provoked, she drew back, and after looking
everywhere for the queen (whom she spied out at last,a long way off), she thought she would try the plan,
this time, of walking in the opposite direction.
It succeeded beautifully. She had not been walking
a minute before she found herself face to face with the
Red Queen, and full in sight of the hill she had been
so long aiming at.
‘Where do you come from?’ said the Red Queen.
‘And where are you going? Look up, speak nicely,
and don’t twiddle your fingers all the time.’
Alice attended to all these directions, and explained, as well as she could, that she had lost herway.
‘I don’t know what you mean by YOUR way,’ said
the Queen: ‘all the ways about here belong to ME—
but why did you come out here at all?’ she added ina kinder tone. ‘Curtsey while you’re thinking what
to say, it saves time.’
Alice wondered a little at this, but she was toomuch in awe of the Queen to disbelieve it. ‘I’ll try
it when I go home,’ she thought to herself, ‘the nexttime I’m a little late for dinner.’‘It’s time for you to answer now,’ the Queen said,
looking at her watch: ‘open your mouth a LITTLE wider when you speak, and always say “yourMajesty.”’‘I only wanted to see what the garden was like,your Majesty—’‘That’s right,’ said the Queen, patting her on thehead, which Alice didn’t like at all, ‘though, when you
say “garden,”—I’VE seen gardens, compared withwhich this would be a wilderness.’
Alice didn’t dare to argue the point, but went on:‘—and I thought I’d try and find my way to the topof that hill—’‘When you say “hill,”’ the Queen interrupted, ‘I
could show you hills, in comparison with which you’dcall that a valley.’‘No, I shouldn’t,’ said Alice, surprised into contradicting her at last: ‘a hill CAN’T be a valley, you
know. That would be nonsense—’
The Red Queen shook her head, ‘You may call it“nonsense” if you like,’ she said, ‘but I’VE heard nonsense, compared with which that would be as sensible
as a dictionary!’

9

10

IMG11

—
do to keep up with her: and still the Queen kept
crying ‘Faster! Faster!’ but Alice felt she COULD
NOT go faster, though she had not breath left to say
so.
The most curious part of the thing was, that thetrees and the other things round them never changed
their places at all: however fast they went, they neverseemed to pass anything. ‘I wonder if all the things
move along with us?’ thought poor puzzled Alice.
And the Queen seemed to guess her thoughts, for she
cried, ‘Faster! Don’t try to talk!’
Not that Alice had any idea of doing THAT. She
felt as if she would never be able to talk again,
she was getting so much out of breath: and still
the Queen cried ‘Faster! Faster!’ and dragged heralong. ‘Are we nearly there?’ Alice managed to pantout at last.
‘Nearly IMG12
there!’ the Queen repeated. ‘Why, we
passed it ten minutes ago! Faster!’ And they ran
on for a time in silence, with the wind whistling in
Alice’s ears, and almost blowing her hair off her head,
she fancied.
‘Now! Now!’ cried the Queen. ‘Faster! Faster!’
And they went so fast that at last they seemed toskim through the air, hardly touching the groundwith their feet, till suddenly, just as Alice was getting quite exhausted, they stopped, and she foundherself sitting on the ground, breathless and giddy.
The Queen propped her up against a tree, and said
kindly, ‘You may rest a little now.’
Alice looked round her in great surprise. ‘Why, I
do believe we’ve been under this tree the whole time!
Everything’s just as it was!’‘Of course it is,’ said the Queen, ‘what would you
have it?’‘Well, in OUR country,’ said Alice, still panting alittle, ‘you’d generally get to somewhere else—if you
ran very fast for a long time, as we’ve been doing.’‘A slow sort of country!’ said the Queen. ‘Now,
HERE, you see, it takes all the running YOU cando, to keep in the same place. If you want to getsomewhere else, you must run at least twice as fast
as that!’‘I’d rather not try, please!’ said Alice. ‘I’m quite
content to stay here—only I AM so hot and thirsty!’

Alice curtseyed again, as she was afraid from the
Queen’s tone that she was a LITTLE offended: andthey walked on in silence till they got to the top of
the little hill.
For some minutes Alice stood without speaking,looking out in all directions over the country—and amost curious country it was. There were a numberof tiny little brooks running straight across it fromside to side, and the ground between was divided up
into squares by a number of little green hedges, thatreached from brook to brook.
‘I declare it’s marked out just like a large chessboard!’ Alice said at last. ‘There ought to be somemen moving about somewhere—and so there are!’
She added in a tone of delight, and her heart began to beat quick with excitement as she went on.
‘It’s a great huge game of chess that’s being played—
all over the world—if this IS the world at all, you
know. Oh, what fun it is! How I WISH I was oneof them! I wouldn’t mind being a Pawn IMG11, if only I
might join—though of course I should LIKE to be a
Queen, best.’
She glanced rather shyly at the real Queen as she
said this, but her companion only smiled pleasantly,
and said, ‘That’s easily managed. You can be theWhite Queen’s Pawn, if you like, as Lily’s too young
to play; and you’re in the Second Square to begin
with: when you get to the Eighth Square you’ll be
a Queen—’ Just at this moment, somehow or other,
they began to run.
Alice never could quite make out, in thinking itover afterwards, how it was that they began: all she
remembers is, that they were running hand in hand,
and the Queen went so fast that it was all she could— pagesize change: ≠12.0pt —‘I know what YOU’D like!’ the Queen said goodnaturedly, taking a little box out of her pocket. ‘Havea biscuit?’
Alice thought it would not be civil to say ‘No,’
though it wasn’t at all what she wanted. So she took
it, and ate it as well as she could: and it was VERY
dry; and she thought she had never been so nearlychoked in all her life.
‘While you’re refreshing yourself,’ said the Queen,‘I’ll just take the measurements.’ And she took aribbon out of her pocket, marked in inches, and began
measuring the ground, and sticking little pegs in here
and there.
‘At the end of two yards,’ she said, putting ina peg to mark the distance, ‘I shall give you yourdirections—have another biscuit?’‘No, thank you,’ said Alice: ‘one’s QUITE enough!’‘Thirst quenched, I hope?’ said the Queen.
Alice did not know what to say to this, but luckily
the Queen did not wait for an answer, but went on.
‘At the end of THREE yards I shall repeat them—forfear of your forgetting them. At the end of FOUR, I
shall say good-bye. And at the end of FIVE, I shallgo!’
She had got all the pegs put in by this time, andAlice looked on with great interest as she returnedto the tree, and then began slowly walking down therow.
At the two-yard peg she faced round, and said, ‘Apawn goes two squares in its first move, you know. So
you’ll go VERY quickly through the Third Square—by railway, I should think—and you’ll find yourself in the Fourth Square in no time. Well, THAT
square belongs to Tweedledum and Tweedledee—theFifth is mostly water—the Sixth belongs to Humpty
Dumpty—But you make no remark?’‘I—I didn’t know I had to make one—just then,’Alice faltered out.
‘You SHOULD have said, “It’s extremely kind of
you to tell me all this”—however, we’ll suppose it
said—the Seventh Square is all forest—however, oneof the Knights will show you the way—and in the
Eighth Square we shall be Queens together, and it’s
all feasting and fun!’ Alice got up and curtseyed, andsat down again.

— pagesize change: ≠12.0pt —

—

11

IMG12
At the next peg the Queen turned again, and thistime she said, ‘Speak in French when you can’t thinkof the English for a thing—turn out your toes as you
walk—and remember who you are!’ She did not wait
for Alice to curtsey this time, but walked on quickly
to the next peg, where she turned for a moment tosay ‘good-bye,’ and then hurried on to the last.
How it happened, Alice never knew, but exactly
as she came to the last peg, she was gone. Whether
she vanished into the air, or whether she ran quickly
into the wood (‘and she CAN run very fast!’ thought
Alice), there was no way of guessing, but she wasgone, and Alice began to remember that she was a “’ (here came the favourite little toss of the head),Pawn, and that it would soon be time for her to move. “‘only it was so dusty and hot, and the elephants
did tease so!”’‘I think I’ll go down the other way,’ she said afIII. Looking-Glass Insects
ter a pause: ‘and perhaps I may visit the elephantslater on. Besides, I do so want to get into the Third
Of course the first thing to do was to make a grand Square!’survey of the country she was going to travel through.
So with this excuse she ran down the hill and‘It’s something very like learning geography,’ thought jumped over the first of the six little brooks.
Alice, as she stood on tiptoe in hopes of being able
to see a little further. ‘Principal rivers—there ARE
*
*
*
*
*
*
*
none. Principal mountains—I’m on the only one, but
*
*
*
*
*
*
I don’t think it’s got any name. Principal towns—
*
*
*
*
*
*
*
why, what ARE those creatures, making honey down
there? They can’t be bees—nobody ever saw bees a‘Tickets, please!’ said the Guard, putting his headmile off, you know—’ and for some time she stood in at the window. In a moment everybody was holdsilent, watching one of them that was bustling about ing out a ticket: they were about the same size as theamong the flowers, poking its proboscis into them, people, and quite seemed to fill the carriage.
‘just as if it was a regular bee,’ thought Alice.
‘Now then! Show your ticket, child!’ the Guard
However, this was anything but a regular bee: in went on, looking angrily at Alice. And a great many
fact it was an elephant—as Alice soon found out, voices all said together (‘like the chorus of a song,’
though the idea quite took her breath away at first. thought Alice), ‘Don’t keep him waiting, child! Why,
‘And what enormous flowers they must be!’ was her his time is worth a thousand pounds a minute!’
next idea. ‘Something like cottages with the roofs‘I’m afraid I haven’t got one,’ Alice said in a frighttaken off, and stalks put to them—and what quan- ened tone: ‘there wasn’t a ticket-office where I cametities of honey they must make! I think I’ll go down from.’ And again the chorus of voices went on. ‘There
and—no, I won’t JUST yet,’ she went on, checking wasn’t room for one where she came from. The land
herself just as she was beginning to run down the there is worth a thousand pounds an inch!’hill, and trying to find some excuse for turning shy‘Don’t make excuses,’ said the Guard: ‘you shouldso suddenly. ‘It’ll never do to go down among them have bought one from the engine-driver.’ And once
without a good long branch to brush them away— more the chorus of voices went on with ‘The man thatand what fun it’ll be when they ask me how I like drives the engine. Why, the smoke alone is worth a
my walk. I shall say—“Oh, I like it well enough— thousand pounds a puff!’

Comparisons
The End

8

—

—

IMG9

‘Put your hand down, and feel the ground,’ said
the Tiger-lily. ‘Then you’ll know why.’
Alice did so. ‘It’s very hard,’ she said, ‘but I don’t
see what that has to do with it.’
‘In most gardens,’ the Tiger-lily said, ‘they makethe beds too soft—so that the flowers are always
asleep.’This sounded a very good reason, and Alice wasquite pleased to know it. ‘I never thought of that
before!’ she said.
‘It’s MY opinion that you never think AT ALL,’the Rose said in a rather severe tone.
‘I never saw anybody that looked stupider,’ a Violet said, so suddenly, that Alice quite jumped; for it
hadn’t spoken before.
‘Hold YOUR tongue!’ cried the Tiger-lily. ‘As if
YOU ever saw anybody! You keep your head under
the leaves, and snore away there, till you know no
more what’s going on in the world, than if you werea bud!’‘Are there any more people in the garden besides
me?’ Alice said, not choosing to notice the Rose’s
last remark.
‘There’s one other flower in the garden that canmove about like you,’ said the Rose. ‘I wonder how

you do it—’ (‘You’re always wondering,’ said the
Tiger-lily), ‘but she’s more bushy than you are.’‘Is she like me?’ Alice asked eagerly, for thethought crossed her mind, ‘There’s another little girlin the garden, somewhere!’‘Well, she has the same awkward shape as you,’
the Rose said, ‘but she’s redder—and her petals areshorter, I think.’‘Her petals are done up close, almost like a dahlia,’
the Tiger-lily interrupted: ‘not tumbled about anyhow, like yours.’‘But that’s not YOUR fault,’ the Rose added
kindly: ‘you’re beginning to fade, you know—andthen one can’t help one’s petals getting a little untidy.’
Alice didn’t like this idea at all: so, to change thesubject, she asked ‘Does she ever come out here?’‘I daresay you’ll see her soon,’ said the Rose. ‘She’s
one of the thorny kind.’‘Where does she wear the thorns?’ Alice asked withsome curiosity.
‘Why all round her head, of course,’ the Rosereplied. ‘I was wondering YOU hadn’t got some too.
I thought it was the regular rule.’‘She’s coming!’ cried the Larkspur. ‘I hear her
footstep, thump, thump, thump, along the gravelwalk!’
Alice looked IMG10
round eagerly, and found that it was
the Red Queen. ‘She’s grown a good deal!’ washer first remark. She had indeed: when Alice firstfound her in the ashes, she had been only three inches
high—and here she was, half a head taller than Aliceherself!
‘It’s the fresh air that does it,’ said the Rose: ‘wonderfully fine air it is, out here.’‘I think I’ll go and meet her,’ said Alice, for, though
the flowers were interesting enough, she felt that it
would be far grander to have a talk with a real Queen.
‘You can’t possibly do that,’ said the Rose: ‘Ishould advise you to walk the other way.’
This sounded nonsense to Alice, so she said nothing, but set off at once towards the Red Queen. To
her surprise, she lost sight of her in a moment, andfound herself walking in at the front-door again.
A little provoked, she drew back, and after looking
everywhere for the queen (whom she spied out at last,

9

IMG10

a long way off), she thought she would try the plan,
this time, of walking in the opposite direction.
It succeeded beautifully. She had not been walking
a minute before she found herself face to face with the
Red Queen, and full in sight of the hill she had been
so long aiming at.
‘Where do you come from?’ said the Red Queen.
‘And where are you going? Look up, speak nicely,
and don’t twiddle your fingers all the time.’
Alice attended to all these directions, and explained, as well as she could, that she had lost herway.
‘I don’t know what you mean by YOUR way,’ said
the Queen: ‘all the ways about here belong to ME—
but why did you come out here at all?’ she added ina kinder tone. ‘Curtsey while you’re thinking what
to say, it saves time.’
Alice wondered a little at this, but she was toomuch in awe of the Queen to disbelieve it. ‘I’ll try
it when I go home,’ she thought to herself, ‘the nexttime I’m a little late for dinner.’‘It’s time for you to answer now,’ the Queen said,
looking at her watch: ‘open your mouth a LITTLE wider when you speak, and always say “yourMajesty.”’‘I only wanted to see what the garden was like,your Majesty—’‘That’s right,’ said the Queen, patting her on thehead, which Alice didn’t like at all, ‘though, when you
say “garden,”—I’VE seen gardens, compared withwhich this would be a wilderness.’
Alice didn’t dare to argue the point, but went on:‘—and I thought I’d try and find my way to the topof that hill—’‘When you say “hill,”’ the Queen interrupted, ‘I
could show you hills, in comparison with which you’dcall that a valley.’‘No, I shouldn’t,’ said Alice, surprised into contradicting her at last: ‘a hill CAN’T be a valley, you
know. That would be nonsense—’
The Red Queen shook her head, ‘You may call it“nonsense” if you like,’ she said, ‘but I’VE heard nonsense, compared with which that would be as sensible
as a dictionary!’
Alice curtseyed again, as she was afraid from the
Queen’s tone that she was a LITTLE offended: andthey walked on in silence till they got to the top of
the little hill.
For some minutes Alice stood without speaking,looking out in all directions over the country—and amost curious country it was. There were a numberof tiny little brooks running straight across it fromside to side, and the ground between was divided up
into squares by a number of little green hedges, thatreached from brook to brook.
‘I declare it’s marked out just like a large chessboard!’ Alice said at last. ‘There ought to be somemen moving about somewhere—and so there are!’
She added in a tone of delight, and her heart began to beat quick with excitement as she went on.
‘It’s a great huge game of chess that’s being played—
all over the world—if this IS the world at all, you
know. Oh, what fun it is! How I WISH I was oneof them! I wouldn’t mind being a Pawn IMG11, if only I
might join—though of course I should LIKE to be a
Queen, best.’
She glanced rather shyly at the real Queen as she
said this, but her companion only smiled pleasantly,
and said, ‘That’s easily managed. You can be theWhite Queen’s Pawn, if you like, as Lily’s too young
to play; and you’re in the Second Square to begin

10—
with: when you get to the Eighth Square you’ll be
a Queen—’ Just at this moment, somehow or other,
they began to run.
Alice never could quite make out, in thinking itover afterwards, how it was that they began: all she
remembers is, that they were running hand in hand,
and the Queen went so fast that it was all she could
do to keep up with her: and still the Queen kept
crying ‘Faster! Faster!’ but Alice felt she COULD
NOT go faster, though she had not breath left to say
so.
The most curious part of the thing was, that thetrees and the other things round them never changed
their places at all: however fast they went, they neverseemed to pass anything. ‘I wonder if all the things
move along with us?’ thought poor puzzled Alice.
And the Queen seemed to guess her thoughts, for she
cried, ‘Faster! Don’t try to talk!’
Not that Alice had any idea of doing THAT. She
felt as if she would never be able to talk again,
she was getting so much out of breath: and still
the Queen cried ‘Faster! Faster!’ and dragged heralong. ‘Are we nearly there?’ Alice managed to pantout at last.
‘Nearly IMG12
there!’ the Queen repeated. ‘Why, we
passed it ten minutes ago! Faster!’ And they ran
on for a time in silence, with the wind whistling in
Alice’s ears, and almost blowing her hair off her head,
she fancied.
‘Now! Now!’ cried the Queen. ‘Faster! Faster!’
And they went so fast that at last they seemed toskim through the air, hardly touching the groundwith their feet, till suddenly, just as Alice was getting quite exhausted, they stopped, and she foundherself sitting on the ground, breathless and giddy.
The Queen propped her up against a tree, and said
kindly, ‘You may rest a little now.’
Alice looked round her in great surprise. ‘Why, I
do believe we’ve been under this tree the whole time!
Everything’s just as it was!’‘Of course it is,’ said the Queen, ‘what would you
have it?’‘Well, in OUR country,’ said Alice, still panting alittle, ‘you’d generally get to somewhere else—if you
ran very fast for a long time, as we’ve been doing.’— pagesize change: ≠12.0pt —IMG11‘A slow sort of country!’ said the Queen. ‘Now,
HERE, you see, it takes all the running YOU cando, to keep in the same place. If you want to getsomewhere else, you must run at least twice as fast
as that!’‘I’d rather not try, please!’ said Alice. ‘I’m quite
content to stay here—only I AM so hot and thirsty!’‘I know what YOU’D like!’ the Queen said goodnaturedly, taking a little box out of her pocket. ‘Havea biscuit?’
Alice thought it would not be civil to say ‘No,’
though it wasn’t at all what she wanted. So she took
it, and ate it as well as she could: and it was VERY
dry; and she thought she had never been so nearlychoked in all her life.
‘While you’re refreshing yourself,’ said the Queen,‘I’ll just take the measurements.’ And she took aribbon out of her pocket, marked in inches, and began
measuring the ground, and sticking little pegs in here
and there.
‘At the end of two yards,’ she said, putting ina peg to mark the distance, ‘I shall give you yourdirections—have another biscuit?’‘No, thank you,’ said Alice: ‘one’s QUITE enough!’‘Thirst quenched, I hope?’ said the Queen.
Alice did not know what to say to this, but luckily
the Queen did not wait for an answer, but went on.
‘At the end of THREE yards I shall repeat them—forfear of your forgetting them. At the end of FOUR, I
shall say good-bye. And at the end of FIVE, I shallgo!’
She had got all the pegs put in by this time, andAlice looked on with great interest as she returned— pagesize change: ≠12.0pt ——11III. Looking-Glass Insects

IMG12

Of course the first thing to do was to make a grandsurvey of the country she was going to travel through.
‘It’s something very like learning geography,’ thought
Alice, as she stood on tiptoe in hopes of being able
to see a little further. ‘Principal rivers—there ARE
none. Principal mountains—I’m on the only one, but
I don’t think it’s got any name. Principal towns—
why, what ARE those creatures, making honey down
there? They can’t be bees—nobody ever saw bees amile off, you know—’ and for some time she stoodsilent, watching one of them that was bustling about
among the flowers, poking its proboscis into them,‘just as if it was a regular bee,’ thought Alice.
However, this was anything but a regular bee: infact it was an elephant—as Alice soon found out,
though the idea quite took her breath away at first.
‘And what enormous flowers they must be!’ was her
next idea. ‘Something like cottages with the roofs
taken off, and stalks put to them—and what quantities of honey they must make! I think I’ll go down
and—no, I won’t JUST yet,’ she went on, checking
herself just as she was beginning to run down thehill, and trying to find some excuse for turning shy
so suddenly. ‘It’ll never do to go down among themwithout a good long branch to brush them away—
and what fun it’ll be when they ask me how I likemy walk. I shall say—“Oh, I like it well enough—“’ (here came the favourite little toss of the head),“‘only it was so dusty and hot, and the elephants
did tease so!”’‘I think I’ll go down the other way,’ she said after a pause: ‘and perhaps I may visit the elephantslater on. Besides, I do so want to get into the Third
Square!’So with this excuse she ran down the hill andjumped over the first of the six little brooks.

to the tree, and then began slowly walking down therow.
At the two-yard peg she faced round, and said, ‘Apawn goes two squares in its first move, you know. So
you’ll go VERY quickly through the Third Square—by railway, I should think—and you’ll find yourself in the Fourth Square in no time. Well, THAT
square belongs to Tweedledum and Tweedledee—theFifth is mostly water—the Sixth belongs to Humpty
Dumpty—But you make no remark?’‘I—I didn’t know I had to make one—just then,’Alice faltered out.
‘You SHOULD have said, “It’s extremely kind of
you to tell me all this”—however, we’ll suppose it
said—the Seventh Square is all forest—however, oneof the Knights will show you the way—and in the
Eighth Square we shall be Queens together, and it’s
all feasting and fun!’ Alice got up and curtseyed, andsat down again.
At the next peg the Queen turned again, and thistime she said, ‘Speak in French when you can’t thinkof the English for a thing—turn out your toes as you
walk—and remember who you are!’ She did not wait
for Alice to curtsey this time, but walked on quickly
to the next peg, where she turned for a moment tosay ‘good-bye,’ and then hurried on to the last.
How it happened, Alice never knew, but exactly
*
*
*
*
*
*
*
as she came to the last peg, she was gone. Whether
*
*
*
*
*
*
she vanished into the air, or whether she ran quickly
*
*
*
*
*
*
*
into the wood (‘and she CAN run very fast!’ thought
Alice), there was no way of guessing, but she wasgone, and Alice began to remember that she was a‘Tickets, please!’ said the Guard, putting his headPawn, and that it would soon be time for her to move. in at the window. In a moment everybody was hold-

(

:

:

)

Comparison – spreads 7 + 8
optimal, 0 turns viz. optimal, 2 turns
Effective Float
Strategies
12—
Alice IMG13
thought to herself, ‘Then there’s no use
in speaking.’ The voices didn’t join in this time, as
she hadn’t spoken, but to her great surprise, they all
THOUGHT in chorus (I hope you understand what
THINKING IN CHORUS means—for I must confessthat I don’t), ‘Better say nothing at all. Language isworth a thousand pounds a word!’‘I shall dream about a thousand pounds tonight, I
know I shall!’ thought Alice.
All this time the Guard was looking at her, firstthrough a telescope, then through a microscope, andthen through an opera-glass. At last he said, ‘You’re
travelling the wrong way,’ and shut up the window
and went away.
‘So young a child,’ said the gentleman sitting opposite to her (he was dressed in white paper), ‘ought
to know which way she’s going, even if she doesn’tknow her own name!’
A Goat, that was sitting next to the gentleman inwhite, shut his eyes and said in a loud voice, ‘She
ought to know her way to the ticket-office, even if
she doesn’t know her alphabet!’
There was a Beetle sitting next to the Goat (it wasa very queer carriage-full of passengers altogether),and, as the rule seemed to be that they should all
speak in turn, HE went on with ‘She’ll have to go
back from here as luggage!’
Alice couldn’t see who was sitting beyond the Beetle, but a hoarse voice spoke next. ‘Change engines—’
it said, and was obliged to leave off.
‘It sounds like a horse,’ Alice thought to herself.
And an extremely small voice, close to her ear, said,‘You might make a joke on that—something about“horse” and “hoarse,” you know.’
Then a very gentle voice in the distance said, ‘She
must be labelled “Lass, with care,” you know—’
And after that other voices went on (‘What a number of people there are in the carriage!’ thought Alice), saying, ‘She must go by post, as she’s got ahead on her—’ ‘She must be sent as a message by thetelegraph—’ ‘She must draw the train herself the restof the way—’ and so on.
But the gentleman dressed in white paper leaned
forwards and whispered in her ear, ‘Never mind what
they all say, my dear, but take a return-ticket every
time the train stops.’

Frank
Mittelbach
Introduction
Visualization
Adding Floats
Results

—
IMG13

*
*

‘Indeed I shan’t!’ Alice said rather impatiently. ‘I
don’t belong to this railway journey at all—I was ina wood just now—and I wish I could get back there.’‘You might make a joke on THAT,’ said the little voice close to her ear: ‘something about “youWOULD if you could,” you know.’‘Don’t tease so,’ said Alice, looking about in vain to
see where the voice came from; ‘if you’re so anxious tohave a joke made, why don’t you make one yourself?’
The little voice sighed deeply: it was VERY unhappy, evidently, and Alice would have said something pitying to comfort it, ‘If it would only sigh likeother people!’ she thought. But this was such a wonderfully small sigh, that she wouldn’t have heard it
at all, if it hadn’t come QUITE close to her ear. The
consequence of this was that it tickled her ear very
much, and quite took off her thoughts from the unhappiness of the poor little creature.
‘I know you are a friend,’ the little voice went on;‘a dear friend, and an old friend. And you won’t hurtme, though I AM an insect.’‘What kind of insect?’ Alice inquired a little anxiously. What she really wanted to know was, whether
it could sting or not, but she thought this wouldn’t
be quite a civil question to ask.
‘What, then you don’t—’ the little voice began,when it was drowned by a shrill scream from theengine, and everybody jumped up in alarm, Aliceamong the rest.
The Horse, who had put his head out of the window, quietly drew it in and said, ‘It’s only a brook
we have to jump over.’ Everybody seemed satisfied

13

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*
*

*

*
*

*

*
*

*

*
*

*

*
*

*

14

IMG14

with this, though Alice felt a little nervous at the ideaof trains jumping at all. ‘However, it’ll take us into
the Fourth Square, that’s some comfort!’ she said toherself. In another moment she felt the carriage risestraight up into the air, and in her fright she caught
at the thing nearest to her hand, which happened tobe the Goat’s beard.

—**

But the beard seemed to melt away as she touched
it, and she found herself sitting quietly under a tree—
while the Gnat (for that was the insect she had beentalking to) was balancing itself on a twig just overher head, and fanning her with its wings.
It certainly was a VERY large Gnat: ‘about thesize of a chicken,’ Alice thought. Still, she couldn’t
feel nervous with it, after they had been talking together so long.
‘—then you don’t like all insects?’ the Gnat wenton, as quietly as if nothing had happened.
‘I like them when they can talk,’ Alice said. ‘Noneof them ever talk, where I come from.’‘What sort of insects do you rejoice in, where YOU
come from?’ the Gnat inquired.
‘I don’t REJOICE in insects at all,’ Alice explained, ‘because I’m rather afraid of them—at least
the large kinds. But I can tell you the names of someof them.’‘Of course they answer to their names?’ the Gnat
remarked carelessly.
‘I never knew them to do it.’
‘What’s the use of their having names,’ the Gnat
said, ‘if they won’t answer to them?’‘No use to THEM,’ said Alice; ‘but it’s useful tothe people who name them, I suppose. If not, why
do things have names at all?’‘I can’t say,’ the Gnat replied. ‘Further on, in thewood down there, they’ve got no names—however,go on with your list of insects: you’re wasting time.’‘Well, there’s the Horse-fly,’ Alice began, counting
off the names on her fingers.
‘All right,’ said the Gnat: ‘half way up that bush,
you’ll see a Rocking-horse-fly, if you look. It’s made— pagesize change: ≠12.0pt —IMG16

entirely of wood, and gets about by swinging itself
from branch to branch.’‘What does it live on?’ Alice asked, with great
curiosity.
‘Sap and sawdust,’ said the Gnat. ‘Go on with thelist.’
Alice IMG14
looked up at the Rocking-horse-fly withgreat interest, and made up her mind that it musthave been just repainted, it looked so bright andsticky; and then she went on.
‘And there’s the Dragon-fly.’‘Look on the branch above your head,’ said theGnat, ‘and there you’ll find a snap-dragon-fly. Its
body is made of plum-pudding, its wings of hollyleaves, and its head is a raisin burning in brandy.’‘And what does it live on?’‘Frumenty and mince pie,’ the Gnat replied; ‘andit makes its nest in a Christmas box.’‘And then there’s the Butterfly,’ Alice went on,
after she had taken a good look at the insect with
its head on fire, and had thought to herself, ‘I wonder if that’s the reason insects are so fond of flying
into candles—because they want to turn into Snapdragon-flies!’‘Crawling at your feet,’ said the Gnat (Alice drew
her feet back in some alarm), ‘you may observe a
Bread-and-Butterfly. Its wings are thin slices of
Bread-and-butter, its body is a crust, and its headis a lump of sugar.’‘And what does IT live on?’‘Weak tea with cream in it.’A new difficulty came into Alice’s head. ‘Supposing
it couldn’t find any?’ she suggested.
‘Then it would die, of course.’‘But that must happen very often,’ Alice remarked
thoughtfully.
‘It always happens,’ said the Gnat.
After IMG16
this, Alice was silent for a minute or two,
pondering. The Gnat amused itself meanwhile byhumming round and round her head: at last it settled
again and remarked, ‘I suppose you don’t want to lose
your name?’‘No, indeed,’ Alice said, a little anxiously.
‘And yet I don’t know,’ the Gnat went on in acareless tone: ‘only think how convenient it would
be if you could manage to go home without it! For
instance, if the governess wanted to call you to yourlessons, she would call out “come here—,” and there
she would have to leave off, because there wouldn’t be
any name for her to call, and of course you wouldn’t
have to go, you know.’‘That would never do, I’m sure,’ said Alice: ‘thegoverness would never think of excusing me lessons
for that. If she couldn’t remember my name, she’dcall me “Miss!” as the servants do.’‘Well, if she said “Miss,” and didn’t say anything
more,’ the Gnat remarked, ‘of course you’d miss yourlessons. That’s a joke. I wish YOU had made it.’
‘Why do you wish I had made it?’ Alice asked.
‘It’s a very bad one.’
But the Gnat only sighed deeply, while two largetears came rolling down its cheeks.
‘You shouldn’t make jokes,’ Alice said, ‘if it makes
you so unhappy.’
Then came another of those melancholy little sighs,
and this time the poor Gnat really seemed to havesighed itself away, for, when Alice looked up, there
was nothing whatever to be seen on the twig, and, as
she was getting quite chilly with sitting still so long,
she got up and walked on.
She very soon came to an open field, with a woodon the other side of it: it looked much darker than thelast wood, and Alice felt a LITTLE timid about going
into it. However, on second thoughts, she made up
her mind to go on: ‘for I certainly won’t go BACK,’
she thought to herself, and this was the only way to
the Eighth Square.
‘This must be the wood,’ she said thoughtfully
to herself, ‘where things have no names. I wonder what’ll become of MY name when I go in? Ishouldn’t like to lose it at all—because they’d haveto give me another, and it would be almost certain
to be an ugly one. But then the fun would be trying to find the creature that had got my old name!
That’s just like the advertisements, you know, whenpeople lose dogs—“ANSWERS TO THE NAME OF‘DASH:’ HAD ON A BRASS COLLAR”—just fancy
calling everything you met “Alice,” till one of themanswered! Only they wouldn’t answer at all, if they
were wise.’
She was rambling on in this way when she reached
the wood: it looked very cool and shady. ‘Well, at
any rate it’s a great comfort,’ she said as she stepped
under the trees, ‘after being so hot, to get into the—into WHAT?’ she went on, rather surprised at not
being able to think of the word. ‘I mean to get under
the—under the—under THIS, you know!’ putting
her hand on the trunk of the tree. ‘What DOES it
call itself, I wonder? I do believe it’s got no name—why, to be sure it hasn’t!’
She stood silent for a minute, thinking: then she
suddenly began again. ‘Then it really HAS happened, after all! And now, who am I? I WILL remember, if I can! I’m determined to do it!’ But
being determined didn’t help much, and all she could
say, after a great deal of puzzling, was, ‘L, I KNOW
it begins with L!’
Just then a Fawn came wandering by: it looked at
Alice with its large gentle eyes, but didn’t seem at allfrightened. ‘Here then! Here then!’ Alice said, as sheheld out her hand and tried to stroke it; but it only

— pagesize change: ≠12.0pt ——started back a little, and then stood looking at her
again.
‘What do you call yourself?’ the Fawn said at last.
Such a soft sweet voice it had!
‘I wish I knew!’ thought poor Alice. She answered,rather sadly, ‘Nothing, just now.’‘Think again,’ it said: ‘that won’t do.’Alice thought, but nothing came of it. ‘Please,would you tell me what YOU call yourself?’ she said
timidly. ‘I think that might help a little.’‘I’ll IMG17
tell you, if you’ll move a little further on,’the Fawn said. ‘I can’t remember here.’
So they walked on together though the wood, Alicewith her arms clasped lovingly round the soft neck of
the Fawn, till they came out into another open field,
and here the Fawn gave a sudden bound into the air,and shook itself free from Alice’s arms. ‘I’m a Fawn!’
it cried out in a voice of delight, ‘and, dear me! you’rea human child!’ A sudden look of alarm came into its
beautiful brown eyes, and in another moment it had
darted away at full speed.
Alice stood looking after it, almost ready to crywith vexation at having lost her dear little fellowtraveller so suddenly. ‘However, I know my namenow.’ she said, ‘that’s SOME comfort. Alice—
Alice—I won’t forget it again. And now, which ofthese finger-posts ought I to follow, I wonder?’It was not a very difficult question to answer, as
there was only one road through the wood, and thetwo finger-posts both pointed along it. ‘I’ll settle it,’
Alice said to herself, ‘when the road divides and they
point different ways.’
But this did not seem likely to happen. She went
on and on, a long way, but wherever the road divided there were sure to be two finger-posts pointing the same way, one marked ‘TO TWEEDLEDUM’S HOUSE’ and the other ‘TO THE HOUSE
OF TWEEDLEDEE.’‘I do believe,’ said Alice at last, ‘that they live inthe same house! I wonder I never thought of that
before—But I can’t stay there long. I’ll just call andsay “how d’you do?” and ask them the way out of
the wood. If I could only get to the Eighth Square
before it gets dark!’ So she wandered on, talking
to herself as she went, till, on turning a sharp cor-

15
IMG17

ner, she came upon two fat little men, so suddenlythat she could not help starting back, but in another moment she recovered herself, feeling sure thatthey must be.

IV. Tweedledum And Tweedledee
They were standing under a tree, each with an arm
round the other’s neck, and Alice knew which waswhich in a moment, because one of them had ‘DUM’embroidered on his collar, and the other ‘DEE.’ ‘I
suppose they’ve each got “TWEEDLE” round at theback of the collar,’ she said to herself.
They stood so still that she quite forgot they werealive, and she was just looking round to see if theword “TWEEDLE” was written at the back of eachcollar, when she was startled by a voice coming fromthe one marked ‘DUM.’

Comparisons
The End12—
ing out a ticket: they were about the same size as thepeople, and quite seemed to fill the carriage.
‘Now then! Show your ticket, child!’ the Guard
went on, looking angrily at Alice. And a great many
voices all said together (‘like the chorus of a song,’
thought Alice), ‘Don’t keep him waiting, child! Why,
his time is worth a thousand pounds a minute!’‘I’m afraid I haven’t got one,’ Alice said in a frightened tone: ‘there wasn’t a ticket-office where I camefrom.’ And again the chorus of voices went on. ‘There
wasn’t room for one where she came from. The land
there is worth a thousand pounds an inch!’‘Don’t make excuses,’ said the Guard: ‘you shouldhave bought one from the engine-driver.’ And once
more the chorus of voices went on with ‘The man thatdrives the engine. Why, the smoke alone is worth athousand pounds a puff!’
Alice IMG13
thought to herself, ‘Then there’s no use
in speaking.’ The voices didn’t join in this time, as
she hadn’t spoken, but to her great surprise, they all
THOUGHT in chorus (I hope you understand what
THINKING IN CHORUS means—for I must confessthat I don’t), ‘Better say nothing at all. Language isworth a thousand pounds a word!’‘I shall dream about a thousand pounds tonight, I
know I shall!’ thought Alice.
All this time the Guard was looking at her, firstthrough a telescope, then through a microscope, andthen through an opera-glass. At last he said, ‘You’re
travelling the wrong way,’ and shut up the window
and went away.
‘So young a child,’ said the gentleman sitting opposite to her (he was dressed in white paper), ‘ought
to know which way she’s going, even if she doesn’tknow her own name!’
A Goat, that was sitting next to the gentleman inwhite, shut his eyes and said in a loud voice, ‘She
ought to know her way to the ticket-office, even if
she doesn’t know her alphabet!’
There was a Beetle sitting next to the Goat (it wasa very queer carriage-full of passengers altogether),and, as the rule seemed to be that they should all
speak in turn, HE went on with ‘She’ll have to go
back from here as luggage!’
Alice couldn’t see who was sitting beyond the Beetle, but a hoarse voice spoke next. ‘Change engines—’
it said, and was obliged to leave off.

— pagesize change: 12.0pt —‘It sounds like a horse,’ Alice thought to herself.
And an extremely small voice, close to her ear, said,‘You might make a joke on that—something about“horse” and “hoarse,” you know.’
Then a very gentle voice in the distance said, ‘She
must be labelled “Lass, with care,” you know—’
And after that other voices went on (‘What a number of people there are in the carriage!’ thought Alice), saying, ‘She must go by post, as she’s got ahead on her—’ ‘She must be sent as a message by thetelegraph—’ ‘She must draw the train herself the restof the way—’ and so on.
But the gentleman dressed in white paper leaned
forwards and whispered in her ear, ‘Never mind what
they all say, my dear, but take a return-ticket every
time the train stops.’‘Indeed I shan’t!’ Alice said rather impatiently. ‘I
don’t belong to this railway journey at all—I was ina wood just now—and I wish I could get back there.’‘You might make a joke on THAT,’ said the little voice close to her ear: ‘something about “youWOULD if you could,” you know.’‘Don’t tease so,’ said Alice, looking about in vain to
see where the voice came from; ‘if you’re so anxious tohave a joke made, why don’t you make one yourself?’
The little voice sighed deeply: it was VERY unhappy, evidently, and Alice would have said something pitying to comfort it, ‘If it would only sigh likeother people!’ she thought. But this was such a wonderfully small sigh, that she wouldn’t have heard it
at all, if it hadn’t come QUITE close to her ear. The
consequence of this was that it tickled her ear very
much, and quite took off her thoughts from the unhappiness of the poor little creature.
‘I know you are a friend,’ the little voice went on;‘a dear friend, and an old friend. And you won’t hurtme, though I AM an insect.’‘What kind of insect?’ Alice inquired a little anxiously. What she really wanted to know was, whether
it could sting or not, but she thought this wouldn’t
be quite a civil question to ask.
‘What, then you don’t—’ the little voice began,when it was drowned by a shrill scream from theengine, and everybody jumped up in alarm, Aliceamong the rest.
The Horse, who had put his head out of the window, quietly drew it in and said, ‘It’s only a brook—— pagesize change: 12.0pt —

13

IMG13

we have to jump over.’ Everybody seemed satisfied
with this, though Alice felt a little nervous at the ideaof trains jumping at all. ‘However, it’ll take us into
the Fourth Square, that’s some comfort!’ she said toherself. In another moment she felt the carriage risestraight up into the air, and in her fright she caught
at the thing nearest to her hand, which happened tobe the Goat’s beard.
*
*

*

*
*

*

*
*

*

*
*

*

*
*

*

*
*

*

*
*

But the beard seemed to melt away as she touched
it, and she found herself sitting quietly under a tree—
while the Gnat (for that was the insect she had beentalking to) was balancing itself on a twig just overher head, and fanning her with its wings.
It certainly was a VERY large Gnat: ‘about thesize of a chicken,’ Alice thought. Still, she couldn’t
feel nervous with it, after they had been talking together so long.
‘—then you don’t like all insects?’ the Gnat wenton, as quietly as if nothing had happened.
‘I like them when they can talk,’ Alice said. ‘Noneof them ever talk, where I come from.’‘What sort of insects do you rejoice in, where YOU
come from?’ the Gnat inquired.
‘I don’t REJOICE in insects at all,’ Alice explained, ‘because I’m rather afraid of them—at least
the large kinds. But I can tell you the names of someof them.’‘Of course they answer to their names?’ the Gnat
remarked carelessly.

‘I never knew them to do it.’
‘What’s the use of their having names,’ the Gnat
said, ‘if they won’t answer to them?’‘No use to THEM,’ said Alice; ‘but it’s useful tothe people who name them, I suppose. If not, why
do things have names at all?’‘I can’t say,’ the Gnat replied. ‘Further on, in thewood down there, they’ve got no names—however,go on with your list of insects: you’re wasting time.’‘Well, there’s the Horse-fly,’ Alice began, counting
off the names on her fingers.
‘All right,’ said the Gnat: ‘half way up that bush,
you’ll see a Rocking-horse-fly, if you look. It’s madeentirely of wood, and gets about by swinging itself
from branch to branch.’‘What does it live on?’ Alice asked, with great
curiosity.
‘Sap and sawdust,’ said the Gnat. ‘Go on with thelist.’
Alice IMG14
looked up at the Rocking-horse-fly withgreat interest, and made up her mind that it musthave been just repainted, it looked so bright andsticky; and then she went on.
‘And there’s the Dragon-fly.’‘Look on the branch above your head,’ said theGnat, ‘and there you’ll find a snap-dragon-fly. Its
body is made of plum-pudding, its wings of hollyleaves, and its head is a raisin burning in brandy.’‘And what does it live on?’‘Frumenty and mince pie,’ the Gnat replied; ‘andit makes its nest in a Christmas box.’‘And then there’s the Butterfly,’ Alice went on,
after she had taken a good look at the insect with
its head on fire, and had thought to herself, ‘I wonder if that’s the reason insects are so fond of flying
into candles—because they want to turn into Snapdragon-flies!’‘Crawling at your feet,’ said the Gnat (Alice drew
her feet back in some alarm), ‘you may observe a
Bread-and-Butterfly. Its wings are thin slices of
Bread-and-butter, its body is a crust, and its headis a lump of sugar.’‘And what does IT live on?’‘Weak tea with cream in it.’A new difficulty came into Alice’s head. ‘Supposing
it couldn’t find any?’ she suggested.
‘Then it would die, of course.’

14—‘But that must happen very often,’ Alice remarked
thoughtfully.
‘It always happens,’ said the Gnat.
After IMG16
this, Alice was silent for a minute or two,
pondering. The Gnat amused itself meanwhile byhumming round and round her head: at last it settled
again and remarked, ‘I suppose you don’t want to lose
your name?’‘No, indeed,’ Alice said, a little anxiously.
‘And yet I don’t know,’ the Gnat went on in acareless tone: ‘only think how convenient it would
be if you could manage to go home without it! For
instance, if the governess wanted to call you to yourlessons, she would call out “come here—,” and there
she would have to leave off, because there wouldn’t be
any name for her to call, and of course you wouldn’t
have to go, you know.’‘That would never do, I’m sure,’ said Alice: ‘thegoverness would never think of excusing me lessons
for that. If she couldn’t remember my name, she’dcall me “Miss!” as the servants do.’‘Well, if she said “Miss,” and didn’t say anything
more,’ the Gnat remarked, ‘of course you’d miss yourlessons. That’s a joke. I wish YOU had made it.’
‘Why do you wish I had made it?’ Alice asked.
‘It’s a very bad one.’
But the Gnat only sighed deeply, while two largetears came rolling down its cheeks.
‘You shouldn’t make jokes,’ Alice said, ‘if it makes
you so unhappy.’
Then came another of those melancholy little sighs,
and this time the poor Gnat really seemed to havesighed itself away, for, when Alice looked up, there
was nothing whatever to be seen on the twig, and, as
she was getting quite chilly with sitting still so long,
she got up and walked on.
She very soon came to an open field, with a woodon the other side of it: it looked much darker than thelast wood, and Alice felt a LITTLE timid about going
into it. However, on second thoughts, she made up
her mind to go on: ‘for I certainly won’t go BACK,’
she thought to herself, and this was the only way to
the Eighth Square.
‘This must be the wood,’ she said thoughtfully
to herself, ‘where things have no names. I wonder what’ll become of MY name when I go in? Ishouldn’t like to lose it at all—because they’d haveto give me another, and it would be almost certain
to be an ugly one. But then the fun would be trying to find the creature that had got my old name!
That’s just like the advertisements, you know, whenpeople lose dogs—“ANSWERS TO THE NAME OF‘DASH:’ HAD ON A BRASS COLLAR”—just fancy
calling everything you met “Alice,” till one of themanswered! Only they wouldn’t answer at all, if they
were wise.’
She was rambling on in this way when she reached
the wood: it looked very cool and shady. ‘Well, at
any rate it’s a great comfort,’ she said as she stepped
under the trees, ‘after being so hot, to get into the—into WHAT?’ she went on, rather surprised at not
being able to think of the word. ‘I mean to get under
the—under the—under THIS, you know!’ putting
her hand on the trunk of the tree. ‘What DOES it
call itself, I wonder? I do believe it’s got no name—why, to be sure it hasn’t!’
She stood silent for a minute, thinking: then she
suddenly began again. ‘Then it really HAS happened, after all! And now, who am I? I WILL remember, if I can! I’m determined to do it!’ But
being determined didn’t help much, and all she could
say, after a great deal of puzzling, was, ‘L, I KNOW
it begins with L!’
Just then a Fawn came wandering by: it looked at
Alice with its large gentle eyes, but didn’t seem at allfrightened. ‘Here then! Here then!’ Alice said, as sheheld out her hand and tried to stroke it; but it only
started back a little, and then stood looking at her
again.
‘What do you call yourself?’ the Fawn said at last.
Such a soft sweet voice it had!
‘I wish I knew!’ thought poor Alice. She answered,rather sadly, ‘Nothing, just now.’‘Think again,’ it said: ‘that won’t do.’Alice thought, but nothing came of it. ‘Please,would you tell me what YOU call yourself?’ she said
timidly. ‘I think that might help a little.’‘I’ll IMG17
tell you, if you’ll move a little further on,’the Fawn said. ‘I can’t remember here.’
So they walked on together though the wood, Alicewith her arms clasped lovingly round the soft neck of
the Fawn, till they came out into another open field,

—

15

IMG14

IMG16

and here the Fawn gave a sudden bound into the air,and shook itself free from Alice’s arms. ‘I’m a Fawn!’
it cried out in a voice of delight, ‘and, dear me! you’rea human child!’ A sudden look of alarm came into its
beautiful brown eyes, and in another moment it had
darted away at full speed.
Alice stood looking after it, almost ready to crywith vexation at having lost her dear little fellowtraveller so suddenly. ‘However, I know my namenow.’ she said, ‘that’s SOME comfort. Alice—
Alice—I won’t forget it again. And now, which ofthese finger-posts ought I to follow, I wonder?’It was not a very difficult question to answer, as
there was only one road through the wood, and thetwo finger-posts both pointed along it. ‘I’ll settle it,’
Alice said to herself, ‘when the road divides and they
point different ways.’
But this did not seem likely to happen. She went
on and on, a long way, but wherever the road divided there were sure to be two finger-posts pointing the same way, one marked ‘TO TWEEDLEDUM’S HOUSE’ and the other ‘TO THE HOUSE
OF TWEEDLEDEE.’‘I do believe,’ said Alice at last, ‘that they live inthe same house! I wonder I never thought of that
before—But I can’t stay there long. I’ll just call andsay “how d’you do?” and ask them the way out of
the wood. If I could only get to the Eighth Square
before it gets dark!’ So she wandered on, talking
to herself as she went, till, on turning a sharp corner, she came upon two fat little men, so suddenlythat she could not help starting back, but in another moment she recovered herself, feeling sure thatthey must be.

IV. Tweedledum And Tweedledee
They were standing under a tree, each with an arm
round the other’s neck, and Alice knew which waswhich in a moment, because one of them had ‘DUM’embroidered on his collar, and the other ‘DEE.’ ‘I
suppose they’ve each got “TWEEDLE” round at theback of the collar,’ she said to herself.
They stood so still that she quite forgot they werealive, and she was just looking round to see if theword “TWEEDLE” was written at the back of eachcollar, when she was startled by a voice coming fromthe one marked ‘DUM.’‘If you think we’re wax-works,’ he said, ‘you ought
to pay, you know. Wax-works weren’t made to belooked at for nothing, nohow!’‘Contrariwise, IMG18’ added the one marked ‘DEE,’ ‘ifyou think we’re alive, you ought to speak.’‘I’m sure I’m very sorry,’ was all Alice could say;for the words of the old song kept ringing through herhead like the ticking of a clock, and she could hardly
help saying them out loud:—‘Tweedledum and Tweedledee Agreed to have abattle; For Tweedledum said Tweedledee Had spoiled
his nice new rattle.
Just then flew down a monstrous crow, As black
as a tar-barrel; Which frightened both the heroes so,
They quite forgot their quarrel.’‘I know what you’re thinking about,’ said Tweedledum: ‘but it isn’t so, nohow.’‘Contrariwise,’ continued Tweedledee, ‘if it was so,
it might be; and if it were so, it would be; but as it
isn’t, it ain’t. That’s logic.’

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Mischief managed!
Effective Float
Strategies
Frank
Mittelbach
Introduction
Visualization
Adding Floats
Results
Comparisons
The End

Hope I was able to reveal something new for you.
Thank you!
John Tenniel, 1870(::)