The Dickinson press., 1902-03-22
A HARD PROPOSITION

A HARD PROPOSITION
SCIENTIFIC EXPLANATION OF THE
FOURTH DIMENSION.
To the Lay Mind 1t Would Appear as
Though This Measure Of Space
Were the Ability to Disappear
Through Stone Walls.
Suppose a world consisting Of a
boundless fiat 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,
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 can pass around each
other, but cannot step over anything.
These dwellers in "fatland" 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
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. It
needs no knowledge of geometry, but
bnly an examination of any globular
object-an apple, for example-to show
that II we draw line as straight as
possible on sphere and parallel to It
draw q small piece of second line,
ond continue this in as straight 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 hypergeometry proper we
must first set forth what a fourth di-
mension Of space means and show how
natural the way by which it may be
approached. We continue our analo-
gy from "fatland." 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 third line intersecting the same
point and perpendicular to both the
other lines. They would at once pro-
nounce this absurd and impossible. It
Is equally absurd and impossible to us
# we require the third line to be
drawn on the paper. But we would re-
ply, IF you allow US to leave the paper
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 tho
drawing Of fourth line through the
same point perpendicular to all three
OF the lines already there. We shout:
answer him in the same way that the
inhabitants Of "fatland" answered u:
"The problem is impossible. You ear.
not draw any such line in space ae
understand it." If our visitor conc.
Of the fourth dimension, he wo,5:
ply to us as we replied to til
land" people: "The problem is
and impossible If you confine
to space as you understand ii
me there Is fourth dino ~.
space. Draw your line through &.
mension, and the problem will Ic NJ.
ed. This is perfectly simple to me: j:
impossible to you solely because yc
conceptions do not admit Of more til.
three dimensions"
Supposing the inhabitants of ..E::t.
land" to be intellectual beings as 81,
are, 1t would be interesting to them 10
be told what dwellers of space in three
dimensions could do. Let us pursue the
analogy by showing Wat dwellers iaA
four dimensions might do. Place "a
dweller. of "flatland" inside a circle
drawn on his plane and ask him to
step outside Of it without breaking
through 1t. He would go all around,
and, finding every inch Of it closed. he
would say 1t was impossible from the
very nature Of the conditions. "But."
we would reply, "that is because or
your limited conceptions. We can step
over it."
"step over itp' he would exclaim. II
DO not know what that means can
pass around anything If there is way
open. but cannot imagine what you
mean by stepping over it."
But we should simply step over. the
line and reappear on the other side.
So If we confine being able to move
In a fourth dimension in the walls Of D
dungeon of which the sides, the floor
and the ceiling were all impenetrable
be would step outside of it without
touching any part Of the building Just
as easily as we could step over a cir.
Gle drawn on the plane without touch.
Ing 1t. He would simply disappear
from our view like spirit and perhaps
the next moment outside the
prison. To do this he would have to
make little excursion in the fourth
dimension. II Professor Simon Newcomb
ID Harper's Magazine.
HIS Thoughtiessness.
He-Ah, those days Of our young
love! You remember that afternoon
you promised to meet me ant, didn't
come? How raved!
She-Just like man! And there vas
!. suffering agonies, trying on that
dress you liked so much.-Life.
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