The Daily Ardmoreite. [volume] (Ardmore, Okla.) 1893-current, 1902-02-03
A HARD PROPOSITION
scirNTiFIc EXCLAMATION or T-E
FcURTr DIMENSION

eli .NfHIre n IT NI.4 .'..- N-
boull'es Cat plane f9 o. Inhabited
b. rc1 a9ulas le.es who c-u move
about at pleasure 1a tls plane bot are
not able o. tlru t.er beads W or
down o- even tY s.e 1- tl.la of slc-
terms as above t..u aal below them.
and things 1l.laI .lel clu ic push
cd ~ p4.ied aaol. .a any direction. ..lt
cannot bc lifted fr3l tLe l.ae feo
pie and fLuss lu pass ar... each
other. llt cannot step rser ... 'uG
There dWo,I.ls I'D "Gr-alI could COB.
strucl a plane geometry which would
b. exactly IKE ours .l being based on
the aziOms o. Euclid Two parallel
straight lines would never meet though
continued indefinitely.
But suppose that tie surface On
which these beings 1--we. Instead ~ De.
Ing an infinitely extended plane. is
really the surface 0f an Immense globe
Ike the earth on which We I've. u
needs no knowledge ~ geometry. but
only an examination % any gi0bular
objcct-an apple. for eEampie-tO show
that u we draw o. line o. straight 90
possible on a sphere and parallel 70 30
draw a small piece o. @ second line,
ond continue this in as straight line
a. we can. the two lines viii meet
when we proceed in either direction
one-quarter of the Fay around the
sphere. For our "nat.and' people these
lines wouid JOih b. perfectly straight
because the only curvature would be
In the direction downward. which they
could never either perceive or discover.
TO explain hypergc. mrf.g proper we
must FIRST set forth what % fourth d.
mensiOn Of space means and show bow
natural the way Ly which g. may be
approached Wo continue olr auai0-
gy from "fatilrI." Do this supposed
land let Us make % cross-iWo straight
lines intcrsectug 90 uzit angles The
inhabitants a this land understand
the cross perfectly and conceive Of %
Just ns we DO. But lst us aas them %
draw third line intersccung the same
point and perpendicular % bO,h the
other lines. They would at once pro
nounce this absurd aud impossible. IL
81 equally absurd and impossible 20 Us
10 we require the third line 10 be
drawn on the paper But we would re
ply. III you allow US 20 leave the paper
or fat surface. then we con solve the
problem by simply drawing thn third
line through the paper pcrpcldicular
10 It's surface"
Now. 10 pursue the analogy. suppose
thnt after we have drawn three mutu-
ally perpendicular lines some being
from another sphere proposes TO us the
drawing of a fourth line through tho
same point perpendicular 20 all three
OF the lines already there. We should
answer him IN the same way that the
Inhabitants OF "nntland" answered us.
'"Ihc problem IS impossible You can
not draw any such line iu space as we
understand IT," II our visitor conceived
Df The fourth dimension. hc would re-
ply 10 us as we replied 60 the "nat.
lnnd' people: "Thc problem ls absurd
ana Impossible if you cOugue your line
10 space as you understand IT, But fur
me there IS a fourth dimension In
space. Draw your limo through that di.
mcus.ou, and the problem viii bc soly.
cd. This II perfectly simple 10 me; il Is
Impossible 10 you solely because your
conceptions do not admit OF more than
thlrc dimensions"
SuppOsing the inhabitants OF Dat
land 20 be intellectual beings as w
arc. IL would be interesting to them "a
be told what dwcllers Of space IN three
dimensions could do. Let MS pursue the
analogy By showing what dwellers iu
four dimensions might do. Place a
dwcller OF "natand" inside clrcl,
drawn on his plane and ask him "a
step outside or It without breaking
through a. lie would 20 all around
and, finding every inch Of II closed. b,
would say II was impossible from the
very nature Of the conditions. But"
we would reply. that IL because Of
your limited conceptions. We can stcI
over H."
"S'cp over H." ne would oxclaim. Il
do not know what that means. can
pass around anything II there is way
open but ! cannot imagine what you
mean 10y stepping over It,"
nut we hhould simply step over the
line and rcappear on the other side.
30 " we cOnnnc being able 90 move
in fourth dimension I'm the walls Of n
dungeon OF which the sides. the floor
ana the ceiling were an impeuetrablc
be would step outside OF II 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 IT, He would simply disappear
from our view like a spirit and perhaps
rcappear the next moment outside the
prison. To DO this he would have To
make a little excursion IN the fourth
Observation-Disclosures simon Newcomb
~ llarper's Magazine.
- His Maiden Name.
IL Is said that at certain seasons I'm
Scotland when the fishing IL not very