Alma record. (Alma, Mich.) 1878-1928, 1889-03-15
THE FOURTH DIMENSION.
A Curious Theory Which Ends
Where IL Began.

wneTe IL Deg
Most IHople know that space--propor
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 10 end, across from side
TO side, and up and down from top 10
bottom, or from bottom TO top-and
then, when you know the shape OF its
circumference, you know all about IT.
II has pleased different persons, chiefly
mathematicians, TO speculate upon the
characteristics of space with only two
dimensions and Of space with four di-
mansions. The human mind is SO made
that il cannot imagine anything about
four dimensional space, except by an
ingenious artitice based upon IA tire
mendous and entirely irrational AS
sumption. The assumption is that four
dimensional space, If there is any,
bears the same relation 10 proper space
as proper space would bear 10 two di-
mensional space il there were any IL
is not very dificult 10 imagine space
with only two dimensions, though il 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 10 morality OF some OF
the theories of dimension hitherto
principally studied in relation to phys
zeal phenomena.
Space in two dimensions would he
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 iu-
/ 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 ii TO be. and that there
| fore il did not exist. Suppose they had
! something they wanted TO keep, and
| they made ring about il, they would
assert il TO be absolutely inclosed, just
as we should assert thing TO be abso-
! lutely inclosed which was shut up in a
hollow sphere. and they would assert
with absolute confidence that if the
substance OF the ring was opaque no
one could see what was inside it., and
also that no one could possibly take the
! inclosed substance away without break
] ing the ring. But If a thrco-dimen-
! siOnal person came upon the scene he
would see merely a ring and some
thing mysteriously suspended in the
! middle Of it, and he would be able
/ 10 take il away without touching
! the ring, which to the two dimensional
! people, when the ring was opeAcd
and the contents found to be gone, would
appear miraculous monstrous and con
| trary TO nature. This idea being es-
! tabished, and the arbitrary assumption
! 2:3::3:4: being firmly made, it is plausi-
! bly, alleged that il we inclosed an on
/ ject in a box, rashly confident that. as
| long as the box remained shut, the
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
! be taken out Of the box at all, and there
| came along four dimensional
| person, that person would see
the thing lying in the box,
would wonder why it did not fall out
in some fourth direction which we can
not imagine, would take hold OF il
without touching the box, and would
walk away with it. Another illustra-
tion of the theoretical possibilities OF
dimensions is that what we call "a
solid thing-that is, a thing in three
! dimensions it intercepts light,
casts a shadow which has only two di-
mansions and has no thickness. SINH
larly, it is argued, when light fell upon
thing OF four dimensions, it would
cast sh adow OF three Dimensions or
course, these speculations need not
stop at four dimensions. They gener-
ally do, even among mathematicians,
because il is complicated enough TO
speculate about one unintelligible d.
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 its own account
may read a pretty and quite easy dis
cussion Of it in a little book called
''Flatland, published not long ago
Saturday Review.