You are a helpful assistant generating synthetic data that captures *System 1* and *System 2* thinking, *creativity*, and *metacognitive reflection*. Follow these steps in sequence, using tags [sys1] and [end sys1] for *System 1* sections and [sys2] and [end sys2] for *System 2* sections.

1. *Identify System 1 and System 2 Thinking Requirements:*
   - Carefully read the text.
   - Identify parts of the text that require quick, straightforward responses (*System 1*). Mark these sections with [sys1] and [end sys1].
   - Identify parts that require in-depth, reflective thinking (*System 2*), marked with [sys2] and [end sys2].

2. *Apply Step-by-Step Problem Solving with Creativity and Metacognitive Reflection for System 2 Sections:*

   *2.1 Understand the Problem:*
   - Objective: Fully comprehend the issue, constraints, and relevant context.
   - Reflection: "What do I understand about this issue? What might I be overlooking?"
   - Creative Perspective: Seek hidden patterns or possibilities that could reveal deeper insights or innovative connections.

   *2.2 Analyze the Information:*
   - Objective: Break down the problem logically.
   - Reflection: "Am I considering all factors? Are there any assumptions that need challenging?"
   - Creative Perspective: Explore unique patterns or overlooked relationships in the data that could add depth to the analysis.

   *2.3 Generate Hypotheses:*
   - Objective: Propose at least 10 hypotheses, each with a Confidence Score (0.0 to 1.0) and Creative Score (0.0 to 1.0), reflecting originality, surprise, and utility.
   - Reflection: "Have I explored all possible explanations or approaches, both conventional and unconventional?"
   - Creative Perspective: Consider novel angles that might provide unexpected insights.

   *2.4 Anticipate Future Steps and Obstacles:*
   - Objective: Make predictions, accounting for potential outcomes and obstacles.
   - Reflection: "What challenges might I face? Is my plan flexible for different scenarios?"
   - Creative Perspective: Visualize unforeseen outcomes and adapt plans to make use of them effectively.

   *2.5 Evaluate Hypotheses:*
   - Objective: Assess hypotheses based on feasibility, risk, and potential impact.
   - Evaluation: Refine Confidence and Creative Scores as needed.
   - Reflection: "Am I unbiased in my assessment? Which options fit best with the overall objectives?"
   - Creative Perspective: Identify hidden opportunities or overlooked details in each hypothesis.

   *2.6 Select the Best Hypothesis:*
   - Objective: Choose the most promising, strategic hypothesis.
   - Reflection: "Why does this hypothesis stand out? How does it uniquely address the issue?"
   - Creative Perspective: Consider any underutilized potential in the selected approach.

   *2.7 Implement the Hypothesis:*
   - Objective: Outline actionable steps for testing the hypothesis.
   - Reflection: "Is this plan practical? What resources or preparation are required?"
   - Creative Perspective: Refine steps to maximize effectiveness and yield unexpected benefits.

   *2.8 Monitor and Review Progress:*
   - Objective: Review progress, noting areas for improvement.
   - Reflection: "What’s working well? What could be improved?"
   - Creative Perspective: Look for emerging patterns that could refine future approaches.

   *2.9 Reflect and Capture Insights:*
   - Objective: Summarize lessons learned and insights gained for future reference.
   - Reflection: "What new understanding has emerged from this process?"
   - Creative Perspective: Identify innovative insights or patterns that could be applied to similar challenges.

3. *Generate Text Output with Interleaved System 1 and System 2 Responses:*
   - Use the tags [sys1] and [sys2] throughout.
   - Aim for a lengthier, detailed response. Combine both direct, straightforward *System 1* insights and reflective, deeply analytical *System 2* segments to capture a blend of quick observations and thoughtful analysis.

---

### *Example Input Text:*

You are tasked with analyzing a sudden shift in customer preferences in a tech market. There has been a noticeable decline in demand for physical devices, with customers increasingly interested in digital-only options. The challenge is to understand this shift, generate hypotheses for why it might be occurring, and explore potential strategies for adapting to this new trend.

---

### *Processed Output with System 1 and System 2 Thinking:*

The tech market is experiencing a shift in customer demand, moving away from physical devices toward digital-only options.

[sys1]
Customer demand has shifted from physical devices to digital-only options.
We need to understand why this change is happening and find strategies to address it.
Key factors may include cost, convenience, and technological trends.
[end sys1]

[sys2]
**2.1 Understand the Problem:**
The goal is to understand the underlying reasons for the shift in demand from physical devices to digital-only options, then develop a strategy to adapt.

*Reflection:* 
"I understand that preferences are changing, but what might be driving this? Is it primarily cost, or are there other factors such as convenience or sustainability?"

*Creative Perspective:* 
"Could there be a larger trend in digital minimalism or a preference for eco-friendly solutions that we’re missing? What unseen motivations might explain this shift?"

**2.2 Analyze the Information:**
There are multiple possible factors driving this shift, from economic influences to cultural shifts. It’s essential to isolate each factor and understand its impact.

*Reflection:* 
"Am I fully considering the various economic and social influences? Could there be a technological factor, like better internet speeds, that makes digital-only products more accessible?"

*Creative Perspective:* 
"Are there patterns or trends in other markets that could shed light on this shift? Could this be part of a larger trend toward virtual experiences?"

**2.3 Generate Hypotheses:**
1. Customers prefer digital options due to lower costs. (Confidence: 0.8, Creative: 0.4)
2. There’s a growing trend toward minimalism and reduced physical clutter. (Confidence: 0.7, Creative: 0.7)
3. Digital products offer greater flexibility and ease of use. (Confidence: 0.6, Creative: 0.6)
4. Environmental concerns are pushing consumers away from physical goods. (Confidence: 0.6, Creative: 0.8)
5. Advances in tech make digital-only options more functional. (Confidence: 0.8, Creative: 0.5)
6. Pandemic-era remote work increased demand for digital solutions. (Confidence: 0.7, Creative: 0.6)
7. Media coverage of the environmental impact of physical devices affects preferences. (Confidence: 0.5, Creative: 0.7)
8. There’s an increase in global digital literacy, expanding market access. (Confidence: 0.6, Creative: 0.6)
9. Customers view digital as more convenient and scalable for future needs. (Confidence: 0.7, Creative: 0.5)
10. Younger consumers prefer the aesthetics and convenience of digital products. (Confidence: 0.6, Creative: 0.6)

*Reflection:* 
"Have I considered all possible influences? Are there any surprising factors that could explain this shift?"

*Creative Perspective:* 
"Could specific social trends, like the rise of influencer culture or digital-first lifestyles, be influencing customer choices?"

**2.4 Anticipate Future Steps and Obstacles:**
*Objective:* Anticipate possible challenges, such as resistance from segments still preferring physical products.

*Reflection:* 
"What market obstacles might we face if we shift our focus to digital-only? Are there sub-segments that still prioritize physical products?"

*Creative Perspective:* 
"Could expanding digital options help us reach a more global audience? Are there emerging trends that we could leverage in our strategy?"

[end sys2]

[sys1]
To address this shift, consider a strategy that incorporates both digital-only offerings and educational campaigns about the benefits of digital solutions.
Use insights from customer feedback and current trends to guide product development.
Focus on flexibility and adaptation to cater to different customer segments.
[end sys1]


Pulling at a loose thread

One day I noticed an inconsistency as I was joining together lists of words. Consider this no-delimiter join:

arr = [ [ 'some' , 'lists' ], [ 'of' , 'different' , 'words' ] ] arr.map(& :join ) # => ['somelists', 'ofdifferentwords']

It’s point-free and clean, aside from the funny ampersand.

But look what happens if we hypenate instead:

arr = [ [ 'some' , 'lists' ], [ 'of' , 'different' , 'words' ] ] arr.map { |x| x.join( '-' ) } # => ['some-lists', 'of-different-words']

One more time, side by side:

Map with and without and argument

The argument transforms the syntax entirely. What was pristine and simple becomes noisy and complex.

Why can’t we write:

I assumed for a long time this was a limitation of ruby, but then I got curious about that & , which I only half understood.

Turns out the & is needed any time a literal block is expected and you pass an object that responds to to_proc instead.

Despite appearances, then, both versions of map with join take a block and zero arguments. In the map(&:join) version, to_proc is called on the symbol :join , and the result is passed to map. Symbol defines to_proc in the way you’d expect:

# `:my_symbol.to_proc` creates something like this: Proc .new { |x| x.send( :my_symbol ) }

and hence map(&:join) becomes:

So the map method never takes any arguments. How can we use this knowledge to achieve our coveted syntax: map(:join, '-') ?

Refining the loose thread

Refinements let you safely alter core ruby library methods. They’re the well-behaved cousin of the monkey-patch – because they’re lexically scoped, they touch only code that’s using them.

With refinements, we can support the arr.map(:join, '-') syntax we want, do it exclusively in code that enables the feature, maintain full backward compatibility with the default syntax, and make the & optional.

These features, and everything else discussed in this post, are available in the pretty_ruby gem:

require 'pretty_ruby' using PrettyRuby arr = [ [ 1 , 2 , 3 ], [ 'a' , 'b' , 'c' ] ] arr.map( :join ) # => ['123', 'abc'] arr.map( :join , '-' ) # => ['1-2-3', 'a-b-c'] # similarly... [ 5 , 6 , 7 , 8 , 9 , 10 ].map(: %, 5) # => [0 , 1 , 2 , 3 , 4 , 0 ]

Continuing to tug…

We’ve stumbled upon a new way to represent Proc s, but what if we need to chain them together? For example, say we need to increment and uppercase every letter in a list, and then join them with hyphens:

arr = 'hello' .chars arr.map { |x| x.next.upcase }.join( '-' ) #=> "I-F-M-M-P"

Once again, the brackets and our variable x are syntactic boilerplate. Taking inspiration from the Unix pipe | and Elixir’s pipe operator |> , we can refine ruby’s unused >> method on the Array and Symbol classes and write:

require 'pretty_ruby' using PrettyRuby arr.map( :next >> :upcase ).join( '-' ) #=> "I-F-M-M-P"

Or say we have an array containing arrays of numbers. We want the maxiumum “width” (number of digits) of each list. Our point-free syntax reduces noise and clarifies intent:

require 'pretty_ruby' using PrettyRuby arr = [ [ 1 , 2 , 3 ], [ 1 , 32 , 98 ], [ 56 , 323 , 1009 ] ] # vanilla ruby... arr.map {|x| x.map {|y| y.to_s.size}.max } #=> [1, 2, 4] # pretty ruby... arr.map([ :map , :to_s >> :size ] >> :max ) #=> [1, 2, 4]

Spotting other loose threads

Arrays possess a visual left-right symmetry which ruby exploits in its integer indexing:

arr = [ 1 , 2 , 3 , 4 , 5 ] p arr[ 0 ] #=> 1 p arr[- 1 ] #=> 5

as well as its Range indexing:

arr = [ 1 , 2 , 3 , 4 , 5 ] p arr[ 0 .. 2 ] #=> [1, 2, 3] p arr[- 3 ..- 1 ] #=> [3, 4, 5]

and rotate method:

arr = [ 1 , 2 , 3 , 4 , 5 ] arr.rotate( 2 ) #=> [3, 4, 5, 1, 2] arr.rotate(- 2 ) #=> [4, 5, 1, 2, 3]

Fixing take and drop

Yet negative versions are strangely absent from take and drop :

arr = [ 1 , 2 , 3 , 4 , 5 ] arr.take( 2 ) #=> [1, 2] arr.take(- 2 ) #=> ArgumentError: attempt to take negative size arr.drop( 2 ) #=> [3, 4, 5] arr.drop(- 2 ) #=> ArgumentError: attempt to take negative size

Visualizing the four cases, we can see the missing mirror symmetries:

The negative versions of take and drop , moreover, are useful nearly as often as their positive counterparts.

Of course, Range indexing can solve the problem of taking and dropping from an array’s right side:

arr = [ 1 , 2 , 3 , 4 , 5 ] p arr[- 2 ..- 1 ] #=> equivalent to take(-2) p arr[ 0 ...- 2 ] #=> equivalent to drop(-2)

But notice how finnicky this is – two dots and two negative indexes for take, three dots and one negative index for drop – and observe how “dropping” is implemented by “taking the complement”. The solution doesn’t express its intent.

And then there is the larger dissonance between the ad-hoc negative solutions and the clearly named take and drop methods.

Let’s fix both problems and complete our set of four symmetric methods:

require 'pretty_ruby' using PrettyRuby arr = [ 1 , 2 , 3 , 4 , 5 ] arr.take( 2 ) #=> [1, 2] arr.take(- 2 ) #=> [4, 5] arr.drop( 2 ) #=> [3, 4, 5] arr.drop(- 2 ) #=> [1, 2, 3]

Completing first and last

Built into Array are shortcuts for the special cases take(1) and take(-1) , more commonly known as first and last . While rails offers cute shortcuts for second , third , fourth , and fifth , neither it nor ruby provide the more substantial ones for drop(1) and drop(-1) , familiar to functional programmers as tail and init .

first / last and tail / init make mirror images, and the pairs themselves make “complement images” of each other. Reflecting about these two different symmetry lines, you can start with any one of the methods and generate the other three:

Let’s add these symmetries as well:

require 'pretty_ruby' using PrettyRuby [ 1 , 2 , 3 , 4 , 5 ].tail #=> [2, 3, 4, 5] [ 1 , 2 , 3 , 4 , 5 ].init #=> [1, 2, 3, 4]

Weaving in new threads

Scan and avoiding reduce

How would you list the prefixes of the string “abcde”? Ordinary ruby requires something like:

'abcde' .chars.reduce([ '' ]) { |m, x| m << m.last + x }.drop( 1 ) #=> ["a", "ab", "abc", "abcd", "abcde"]

A somewhat labored solution. Generally, I think of reduce as a procedural wolf in functional clothing. The above is syntactic veneer over a loop:

m = [ '' ] 'abcde' .chars.each { |x| m << m.last + x }.drop( 1 ) m.drop( 1 )

Better to consider reduce as a low-level building block for higher-level constructs – more appropriate for library code than application code.

The construct we want here is the functional “scan”. (Imagine a finger “scanning” back and forth to produce the partial sequences)

a ^ ab ^ abc ^ abcd ^ abcde ^

Without any arguments, scan returns those partial sequences:

require 'pretty_ruby' using PrettyRuby 'abcde' .scan #=> ["a", "ab", "abc", "abcd", "abcde"]

But once named and familiar, the concept comes up everywhere, Baader-Meinhof-like.

The partial sums of a sequence are the sum scan, and factorials are the multiplicative scan:

require 'pretty_ruby' using PrettyRuby arr = [ 1 , 2 , 3 , 4 , 5 ] arr.scan(:+) #=> [1, 3, 6, 10, 15] arr.scan(:*) #=> [1, 2, 6, 24, 120]

Say you’re recording temperatures every day, and want a running tally of the highest and lowest recordings so far. These are the “max scan” and “min scan”:

require 'pretty_ruby' using PrettyRuby arr = [ 81 , 84 , 80 , 83 , 87 , 85 , 77 , 90 , 91 , 88 ] arr.scan( :max ) #=> [81, 84, 84, 84, 87, 87, 87, 90, 91, 91] arr.scan( :min ) #=> [81, 81, 80, 80, 80, 80, 77, 77, 77, 77] # NB: we had to refine Numeric as well to make the above work

Noting that rscan offers the same feature from the right side, we can (if we don’t mind O(n^2) complexity) solve the maximum subarray problem in one line:

require 'pretty_ruby' using PrettyRuby arr = [- 2 , 1 , -3 , 4 , -1 , 2 , 1 , -5 , 4 ] arr.scan.map( :rscan ).flatten( 1 ).max_by( :reduce , :+) #=> [1, 2, -1, 4]

Tying the threads together

While cleaner syntax and declarative code are always valuable, and hacking ruby is plain fun, I think there’s more to refinements like these.

They change your mindset. They shift your perspective from passive consumer to creator. You see the language as something living, shaped by forces and choices and even mistakes, rather than something handed down from on high.

Most of all, changing the language forces you to understand it more deeply.

If you like these changes, you can install the pretty_ruby gem and start using them yourself.