Bismarck daily tribune. [volume] (Bismarck, Dakota [N.D.]) 1881-1916, 1902-01-29
"a HARD PROPOSITION
SCIENTIFIC EXPLANATION COF THE
FOURTH DIMENSION.

To the Lay Mind 1t Would Appear as
Though This Measure of Space
Through Stone Wallis. g.
Suppose a world consisting of q
boundless fat plane to de inhabited
by reasoning beings who can move
about at pleasure on the plane, but are
not. able to turn their heads up or
down or even to see or think of such
terms as above them and below them,
and things around them can be push
ed Or pulled about in any direction, but
cannot be lifted from the plane. Peo-
pie and things a pass around each
other, but cannot step Yer anything.
These jewellers in "fatland" could con-
struct a plane geometry which would
be exactly like ours III being based on
the aXioms of Euclid. Two parallel
straight lines would never meet, though
continued indefinitely.
But suppose that the surface on
which these beings live, instead of be-
ing an infinitely extended plane, is
really the surface of an immense globe
like the earth on which we live. 1t
needs no knowledge of geometry, but
only an examination of any globular
DbJect-an apple, for eXample-to show
that if we draw a line as straight as
possible on a sphere and parallel to it
draw a small piece Of a second line.
and continue this in as straight a line
as we can, the two lines will meet
when we proceed in either direction
one-quarter of the way around the
sphere. For our "fatland" people these
lines would both be perfectly straight
because the only curvature would be
in the direction downward, which they
could never either perceive or discover.
TO explain bypergeometry proper we
must first set forth what a fourth di-
OF space means and show how
natural the way by which it may be
We continue our analo-
gy from ~''1aland." In this supposed
land let US make a cross-two straight
lines intersecting at right angles. The
inhabitants Of this land understand
the cross perfectly and conceive of it
just as we do. But let us ask them to
draw a third line intersecting the same
point and perpendicular to both the
other lines. They would at once pro-
this absurd and impossible. 1t
Is equally absurd and impossible to us
II we require the third line to be
araWn on the paper. But we would re-
ply, IF you allow US to leave the paper
Dr. fat surface, then we can solve the
problem BY simply drawing the third
inc through the paper perpendicular
its Surface" |
Now, to pursue the analogy, suppose |
hat after we have drawn three mutu- !
lily perpendicular lines some being
rom another sphere proposes to us the !
iraWing Of a fourth line through the
'ame point perpendicular to all three
u the lines already there. We should
nsWer him in the same way that. the
inhabitants Of "datland" answered u.s.;
The problem is impossible. You can
draw any such line in space as we
understand it" If our visitor conceived
# the fourth dimension, he would re-
ply to US as we replied to the "fat- !
land" people: 'The problem is absurd
Ind impossible if you confne your line
o space as you understand it. But for !
there is a fourth dimension in
space. Draw your line through that di-
nension, and the problem will be solv-
I'd. This is perfectly simple to me; it is
impossible to you solely because your
conceptions do not admit of more than
:hree dimensions"
Surprising the Inhabitants Of flat.
and" to be intellectual beings as vel
ire, it would be interesting to them to
told what dwellers of space in three |
could do. Let us pursue the
analogy by showing what jewellers in
four dimensions might do. Place a
1weller Of "fatland" inside a circle
drawn on his plane and ask him to
step outside of it without breaking
through it. He would go all around,
and, finding every inch of it closed. he