The Indianapolis journal. [volume] (Indianapolis [Ind.]) 1867-1904, 1901-12-29
THE FOURTH DIMENSION.
Prof. NewcOmb's Explanation of What
1t Really is.
January Harper.

January Harper.
Suppose a world consisting of bound
less 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
pushed or pulled about in any direction
but cannot be lifted from the plane. People
and things can pass around each other
but cannot step over anything These
jewellers in Maitland could construct a
plain geometry which would be exactly like
ours in being based on the aXioms of
Euclid. Two parallel straight lines would
Eever meet, though continued indefinitely.
But suppose that the surface on which
these beings live, instead of being an in
finitcly 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 Object-an apple, for eXample-tO
show that if draw line straight
as possible on a sphere, and parallel TO it
draw a small piece or a second line, and
continue this in as straight a line as we
can, the two lines will meet when we pro-
coed either direction one-quarter of the
way around the sphere. For our falkland
people these lines would both be perfectly
straight, because the only curvature would
be in the direction downwards, which they
could never either perceive or discover.
ITO explain hypergeometry proper we
must first set forth what a fourth dimen-
sion of space means, and show how natural
the way by which it may be approached
we CONTINUES our analogy from Maitland
In this supposed land let us make a cross
two straight lines intersecting al right
angles. The inhabitants of this land un-
derstand the cross perfectly, and conceive
of it just as we do. But let us ask them
TO draw third line interSectng in the
same point, and perpendicular to both the
other lines. They would at once pronounce
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 should reply 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 it's surface
Now. to pursue the analogy, suppose
that, after we have drawn three mutually
perpendicular lines, some being from an
of a fourth line through the same point.
perpendicular to all three Of the lines al
ready there. We should answer him i'm the
same way that the inhabitants of fiat
land answered us: The problem is impos-
sible. You cannot draw any such line in
space as we understand it If our visitor
conceived of the fourth dimension he would
reply TO us as we replied to the falkland
people: The problem is absurd and i'm
possible If you confine your line TO space
you understand it, But for me there is
a fourth dimension, and the problem will
be solved. This is perfectly simple to me:
it is impossible to you solely because your
conceptions do not admit of more than
three dimensions
Suppose the inhabitants of 'hat-land' to
be intellectual beings are, it would
be interesting to them to be told what
jewellers in space in three dimensions could
do. Let us pursue the analogy by show
ing what jewellers in four dimensions might
do. Place a dweller of falkland inside a
circle drawn on his plane, and ask him
to step outside of it without brea king
through it. He would go all around. and
finding every inch of il closed, he would
say it was impossible from the very nature
of the conditions. But we would reply,
that is because of your limited concep-
tons. We can step over it,
Step over it! he would exclaim. L do
not know what that means. 1 can pass
around anything if there is a way open,
but | cannot imagine what you mean by
stepping over it.
But We should simply step over the line
and reapDear on the other side. So, if we
confine a 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, ne would step out
side of it without touching any part of the
building, just as we could step over a circle
drawn on the plane without touching it.
He would simply disappear from our view
like a spirit, and perhaps reappear the
next moment outside the prison. To do
this he would only have to make a little
excursion in TIE fourth dimension