The Lambertville record. [volume] (Lambertville, N.J.) 1872-1968, 1902-01-29
t. HARD PROPOSITION
SCIENTIFIC EXPLANATION OF THE
FOURTH DIMENSION.
To the Lay Mind IL Would Appear as
Though This Measure of space
Were the Ability to Disappear
Through Stone Walls.


Were the Ability to Disappear
Through Stone walls.
Suppose world consisting Of a
boundless FIAT plane to be inhabited
by reasoning beings who can move
about ut 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 "fiatland" 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. IL
needs no knowledge of geometry, but
only TN examination of any globular
object-an apple, for example-to show
that IL we draw line as straight as
possible ON a sphere and parallel to 1t
draw small piece of second line,
and 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 "hatland' 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 fourth d.
mension of space means and show how
natural the way by which It may BIO
approached. We continue our analo-
gy from "datland." In this supposed
land let US make Il cross-two straight
lines intersecting ut 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 at once pro-
nounce this absurd and impossible. 1t
is equally absurd and impossible to us
IL 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 fat 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 bein,
from another sphere proposes to us til,
drawing Of a fourth line through tn
same point perpendicular to all thre
of the lines already there. We shout
answer him IN the same way that til
inhabitants of "hatland" answered u
@'Tne problem Is impossible. You car
not draw any such line In space as W
understand it," II our visitor conceive
of the fourth dimension, he would re
ply to us as we replied to the "Hat
land" people: "rhe problem is absur,
and impossible IL you confine your lin
to space as you understand II. But TO
me there is fourth dimension fl
space. Draw your line through that di
mens.ou. and the problem will be solv
ed. This Is perfectly simple to me; 1t 1.
impossible TO you solely because your
conceptions do not admit of more than
| three dimensions"
Surprising the Inhabitants of FIAT.
land" to be intellectual beings as we
are, 1t would be interesting to them to
be told what jewellers of space in three
dimensions could do. Let us pursue the
analogy by showing what jewellers in
four dimensions might do. Place a
dweller of "Hatland' inside circle
drawn on his plane and ask him TO
step outside OF 1t without breaking
through 1t. He would go all around,
and, finding every inch of 1t closed, he
would say 1t was impossible from the
very nature OF the conditions But"
we would reply, that is because OF
your limited conceptions. We can step
over It."
step over It'll" he would exclaim. IL
do not know what that means can
p"D' "icuhu ouJ suinB IL theic IN u why
open. but l 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 con0ne being able to move
In fourth dimension In the walls Of a
dungeon of which the sides, the floor
and the ceiling were all impenetrable
he would step outside Of 1t 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
reappear the next moment outside the
prison. To do this lie would have to
make n little excursion In the fourth
| Observation-Disclosures Simon Eewcomb
In Harper's Magazine.