South Bend news-times. (South Bend, Ind.) 1913-1938, 1918-03-31

arises. in spite of your knowledge
that a point in a material sense, is
nothing, an image of an infinitely
minute something, which as you
continue to think about it, assumes
a spherical shape. a sphere i'm
measurably small.
Now, imagine a series of points
lying i'm a row, and you perceive
that they suggest a line. A mathe-
NAUTICAL line has no breadth, be
cause il is made up Of points having
no size, but which, since they have
position, may be placed in line. A
little thought will show you that the
line is, in itself, as materially nom
existent as a point, but it involves
the idea Of length. and that is some
thing of which we have experimental
knowledge Thus the line furnishes
us our first dimension" which is
called length" and we know by
experience. that every material
thing has length.
Now, if you move a line sideways,
or if you place an infinite number
of parallel lines side by side, you
get a plane, which by another di-
mension that experience tells US all
bodies possess, viz. breadth. 4
plane. with no thickness whatever
possesses the two dimensions of
length and breadth. There re-
mains one more step 10 take, which
is to life the plane up. keeping it
IL
ton, or else to superpose one above
another as infinite number Of par
allel planes. In this way you will
introduce a third dimension, thick
ness, and thus at last you get a
body complete in all its dimensions;
in other words, a solid body.
Every material body must have
these three dimensions. and it can
at least so our experience, based
on the operations of our physical
senses, tells us-have no more than
three dimensions. We live in a
three-dimensional world. This world
of the senses is represented mathe-
matically by the axioms and deduc-
tons of Euclid's geometry.
Now, notwithstanding the doubts
and inquiries of few philosophers
and mathematician. it was less
than a 100 years ago that Euclid s
geometry, which had stood with the
solidity Of a pyramid for more than
1000 years. began 10 be shaken TO
its foundations, not by forces that
could destroy il. but by forces cap
able Of building up rivals 10 it, and
of ousting it from the exclusive pos
session Of the field that il had held.
There came between 1890 and
1860 three wonderful mathematic-
ians-Lobatchew q Russian. who
had a face like NapOleon's; Bolyai,
a Hunga rian. who, when a sub
lieutenant in the army, accepted the
simultaneously challenges of Is
brother officers. on condition that he
should be allowed TO play his violin
between each successive duel and
won every fight. and Riemann, a
German. who had the fine pointed
nose of a critical thinker-and these
three men, all working in ignorance
Of what the others were doing,
proved TO a world Of 1900 million
people. Of whom only one in 100
million paid any attention. that
Euclid's time-honored geometry was
/ but one particular case Of a three
fold mathematical whole. or one
face Of a kind of three-faced Janus,
I and that each and every one Of these
three kinds or forms Of geometry
was. apparently. equally sound.
Thus what is called non Euclid
/ ian geometry was born. and the
thought Of a fourth dimension is "a
child Of non Euclidian geometry.
but only one among A possibly il
hmitable family OF similar children.
whose playground is "n-dimension-
al space"
This brings Us 10 the specie ques-
ton that l set out 10 answer. J. e,
( why some people associate the fourth
dimension with ghosts.
Recall how a solid body is built
ND on three axes. or along three d.
mansions. and then see If you can
get a clear idea OF another dimen-
sion that a body could have in ad-
dition 10 length, breadth, and thick
ness. Don't mislead yourself by
deceptive interpretations of those
three terms. BY careful thinking
you can satisfy yourself that they
cover all the possible fundamental
directions in which a solid can eX-
tend in order TO NIL the space that il
| occupies.
Now, TO follow the method Used
- - .,,r,,,-,o,S ur-star ~ thai