The citizen. (Frederick City, Md.) 1895-1923, 1902-01-31
HARD PROPOSITION
IENTlFIC EXPLANATION OF The
FOURTH DIMENSION.

10 the Lay Mind Ii Would ApF
Though This Measure OF space
Were the Ability to Disapp
Through stone walls.
Suppose Il world consisting Vi
|oundless fat plane to be lhhapileu
Reasoning beings who can move
bout at pleasure on the plane ou' are
ot able to turn their heads up or
|own or even to see or think OF such
rms as above them and below them,
nd things around them can be push
i or pulled about in any direction, but
|,nnot he lifted from the plane. Peo-
lie and things can pass around each
| her. but cannot step over anything.
hese jewellers in ''fatland' could con-
ruct a plane geometry which would
exactly like ours in being based on
.e axioms of Euclid. Two parallel
raight lines would never meet, though
Lntinued indefinitely.
FBut suppose that the surface on
hich these beings live, instead of be-
z an infinitely extended plane, is
ally the surface of an immense globe
Re the earth on which we live. 1t
,eds no knowledge of geometry, but
lily an examination of any globular
|jject-an apple, for example-to show
at IL we draw a line as straight as
,ssible on Il sphere and parallel to it
|Mw small piece of second line,
Id continue this in as straight line
we can, the two lines will meet
Then we proceed in either direction
of the way around the
here. For our "datland' people these
Ines would both be perfectly straight
|ecause the only curvature would be
Il the direction downward, which they
build never either perceive or discover.
TO explain hypergeometry proper we
ust first set forth what fourth di-
ension of space means and show how
|ltural the way by which it may be
,proached. We continue our analo-
from "fatland." In this supposed
nd let us make Il crosS-two straight
les intersecting at right angles. The
habitants of this land understand
e cross perfectly and conceive of it
st as we do. But let us ask them to
aw a third line intersecting the same
int and perpendicular to both the
her lines. They would at once pro-
unce this absurd and impossible. 1t
equally absurd and impossible to us
we require the third line to be
avn on the paper. But we would re-
y, IF you allow us to leave the paper
! fiat Surface, then we can solve the
oblem by simply drawing the third
e through the paper perpendicular
its Surface
Now, to pursue the analogy. suppose
1t after we have drawn three mutu-
y Perpendicular lines some being
pm another sphere proposes TO us the
awing Of a fourth line through the
|,me point perpendicular to all three
the lines already there. We should
swer him in the same way that the
labitants of "flatland' answered us:
he problem is impossible. You can
draw any such line in space as we
derstand it," If our visitor conceived
the Fourth dimension, he would re-
p to US as we replied to the flat
ido people: The problem is absurd
n impossible if you confne your line
space as you understand it. But for
there is a fourth dimension in
Ice. Draw your line through that di-
nsion, and the problem will be solv-
This is perfectly simple to me; it is
possible 20 you solely because your
lceptions do not admit of more than
ee dimensions
Imposing the inhabitants of fiat
d" to be intellectual beings as we
it would be interesting to them to
told what jewellers of space in three
tensions could do. Let us pursue the
Eflogy by showing what dwellers in
r dimensions might do. Place
eller of "flatland" inside a circle
wn+on his plane and ask him to
, outside of it without breaking
ough it. He would go all around,
finding every inch of it closed, he
lid say it was impossible from the
y nature of the conditions. But"
would reply, that is because of
|Vr limited conceptions. We can step
III tt.
step over it!' he would excIaim. 81
&C not know what that means. I can
saround anything if there is a way
\ EN-. but | cannot imagine what you
10 BY stepping over it."
II ut we should simply step over the
and reappear on the other side.
u we confne a being able to move
IS. fourth dimension in the walls Of a
geon Of which the sides, the floor
the ceiling were all impenetrable
would step outside of it without
thing any part of the building just
sasiiy as we could step over cir
drawn on the plane without touch.
ER It. He would simply disappear
Ekp our view like spirit and perhaps
ppear the next moment outside the
ION. To do this he would have to
ke q little excursion in the fourth
kPnsion Professor Simon Newcomb
Blarper's Magazine.