Akron daily Democrat. [volume] (Akron, Ohio) 1892-1902, 1902-02-03
A HARD PROPOSITION
SCIENTIFIC EXPLANATION or THE
FOURTH DIMENSION.

10 the Iihy Mtnu IL womb Appear a.
Though This Measure of Space
Were the Ability to Disappear
Through stone Walls.
Suppose a world consisting Of a
boundless fat plane to be 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,
cd Or pulled about in any direction, but
cannot be lifted from the plane. Peo
pie and things can pass around each
other, but cannot step over anything
These dwclers in "hatand" could con-
struct plane geometry which would
be exactly like ours In being based on
the axioms of Euclid. Two parallel
straight lines would never meet, though
continued indefinitely.
But suppose that the surface on
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
objcct-an apple, for eXample-to show
possible on sphere and parallel to 1t
draw n small piece of a second line,
and continue this in as straight line
as wo can, the two lines will meet
when we proceed in either direction
oae-Quarter of the way around the
sphere. For our "hatland" people these
lines wolll both bc perfectly straight
because the only curvature would be
In the direction downward, which they
could never either perceive or discover.
To explain hypergeomctry proper we
must first set forth what fourth di-
menslon Of space means and show how
natural the way by which it may be
approached. We continue our nnalo-
gy from "natland" In this supposed
land let us make n cross-two straight
lines intcrsecting at right angles. The
inhabitants Of this land understand
the cross perfectly and conceive of 1t
Just as we do. But let us ask them TO
draw third line intersecting the same
point and perpendicular to both the
other lines. They would Mt once pro-
nounce this absurd and impossible. 1t
Is equally absurd and impossible to us
If we require the third line to be
drawn on the paper. But we would re-
nlv NI "a ollnuy 10 m Ion tho np ~
or fiat surface, then we can solve the
problem by simply drawing the third
line through the paper perpendicular
TO Its surface"
Now. to pursue the analogy, suppose
that after we have drawn three mutu-
ally perpendicular lines some being
from another sphere proposes TO us the
drawing OF fourth line through the
same point perpendicular to all three
or the lines already there. We should
answer him in the same way that the
Inhabitants OF "latland" answered us
''Thc problem is impossible. You can.
not draw any such line in space as we
understand it." If our visitor conceived
OF the fourth dimension, he would re-
ply to US as we replied to the "dat
land" people: The problem is absurd
and impossible IL you coniine your line
to space as you understand II. But fol
me there is fourth dimension ~
space. Draw your line through that di
mension, and the problem will be solv
ed This is perfectly simple to mo; II IL
Impossible to you solely because youi
conceptions do not admit of more thar
three dimensions"
Supposing the Inhabitants OF nat
land" TO be intellectual beings as w
are, 1t would be interesting TO them tt
be told what dwellers Of space in thre'