The Delta independent., 1889-03-12
THE FOURTH DIMENSION.
A Curious Theory Which Ends
Where 1t Began.

A Curious Theory Which Ends
Where 1t Began.
Most people know that atspace-proper
space, that is, such as we live in-has
three dimensions. Any given piece OF
space you can measure in three ways
along from end to end, across from side
to side, and up and down from top to
bottom, or from bottom to top-and
then, when you know the shape Of its
circumference, you know all about It
It has pleased different persons, chiefly
mathematicians, to speculate upon the
characteristics of space with only two
dimensions and of space with four di-
mensions. The human mind is so made
that it cannot imagine anything about
four dimensional space, except by an
ingenious artifice based upon tre-
| mendous and entirely irrational as
sumption. The assumption is that four
| dimensional space, if there is any,
bears the same relation to proper space
as proper space would bear to two di-
mensional space if there were any. 1t
is not very difficult to imagine space
with only two dimensions, though it is
not so easy as it looks. The following
| suggestions are commonplace to per-
| sons skilled in some branches of math-
| ematics, but may be useful in enabling
those whose learning lies in other di-
rections, and who have not previously
devoted their attention to the subject,
to grasp the Importance Of the analog-
ical extension to morality OF some of
the theories of dimension hitherto
| principally studied in relation to phys
ical phenomena.
Space in two dimensions would be
| space in which nothing had any thick
ness, in which motion might be along
or across, or toward any point Of the
compass, but never up or down. To
the inhabitants of such space the words
up and down, high and low, deep and
shallow, thick, thin, level and so forth,
would have no meaning. They would
not be able to think Of any such ideas.
They would say, or the impulsive ones
| among them would, that space was in
finite because you could go infinitely
| far east, west, north, south, or as the
case might be, but that If thing was
neither east, west, north nor south of
where they were Con the same leveD,
it was nowhere, because there was no
where else for it to be. and that there
fore it did not exist Suppose they had
something they wanted to keep, and
they made ring about it, they would
assert 1t to be absolutely inclosed, just
rs we should assert a thing TO be abso-
lutely inclosed which was shut up in a
hollow sphere, and they would assert
with absolute confidence that II the
substance OF the ring was Opaque no
one could see what was inside it, and
also that no one could possibly take tho
inclosed substance away without break
| ing the ring. But II three-dimen-
sional person came upon the scene he
would see merely a ring and some
thing mysteriously suspended in tho
middle Of 1t, and he would be able
to take 1t away without touching
the ring, which 70 tho two dimensional
people, when the ring was opened
and the contents found to be gone. would
appear miraculous; monstrous and con-
trary to nature. This idea being es-
tablished, and the arbitrary assumption
2:S::3:4: being firmly made, 1t is plausi-
bly, alleged that II we inclosed an oo-
jecS in box, rashly confident that. rs
long as the box remained shut, tho
object since it could not be removed
either up or down, or forward or back
ward, or to the right or left, or in any
mixture Of those directions. could not
De tithen OUT OF the DON Ut nll, ana tner0
came along four dimensional
person, that person would 500
the thing lying in tho box.
would wonder why it did not fall out
in some fourth direction which we can
not imagine, would take hold OF II
without touching the box, and would
walk away with it. Another illustra-
tion OF the theoretical possibilities Of
dimensions is that what we call
solid thing-that is. thing in three
dimensions-when 1t intercepts light,
casts a shadow which has only two di-
mensions and has no thickness SINH
larly, 1t is argued, when light fell upon
n thing Of four dimensions, 1t would
cast a sh adow OF three dimensions. or
course, these speculations need not
stop at four dimensions They gener-
ally do, even among mathematicians.
because 1t is complicated enough to
speculate about one unintelligible di-
rection; but that is no reason why
there should not exist space OF many
other varieties. and perhaps there does.
Anybody interested in this sort
Of thing on It's own account
may read a pretty and quite easy dis
cussion of it in n little book called
"Flatland," published not long ago
SATURDAY. Review