The free lance. (Fredericksburg, Va.) 1885-1926, 1902-02-20

4 Ill A 4 ~
~, ,....,re az space
I'M, - D,sappcar
-
Suppose "oriu 'oi'S'S''''7 "
boundleSs Hat plane to be lnhaoi'eu
by reasoning beings who can move
obout nj pleasure ON the plane. but are
NOT able to turn their heads up or
3.,,.,, al, cvon ia SEQ or think of such
..,.....,. t,,.,,, ,,,l holo,v them
~ as ...... H.. ,,,.,,.
ana '"''-S "'''''''' ''''' 80
ed or pulled ABOUT III any "'''''''''' '"'
cannot DC ihteu lr"h 'n' pane W
pie and things can pass around each
other, but cannot step over anything.
These jewellers in "hai.and couid con
struct a plauc geometry which would
Ice exactly Ike ours in being based ON
the aNioms of Euclid. Two pardhei
straight lines would never meet, though
continued indefinitely.
But suppose chat the surface on
which these beings live. instead of lee
mg an infinitely extended plane. is
really the surface of an immense globe
like the earth on which we live. lt
needs no Knowledge of geometry, but
only an examination OF any globuar
obicct-an apple. Tor cXample-to show
that IL we draw line as straight as
possible on a sphere aud parallel to II
draw a small piece OF second me-
and continue this i'm as straight line
as We eau. the two lines will meet
when we proceed in either direction
one-quarter Of the way around the
sphere. For our "hatland' people these
lines would both be perfectly sralsn'
because the only curvature would be
in the direction downward. which they
could never either perceive or discover
To explain hyperseomelry proper we
must first set forth what lour'h III
mension OF space means ana s"o" ~"
| natural the way d! when IL may "0
| approached. We continue our """'o,
gy from 'haiiahu. IN 'uiS SuPPoSV"
land let US make cFosS-1"o s'I",si'
lines interSecunS ak r,-"I "hS'vS' Nv
inhabitants OF ms iahd unu'rS'a'i''
! the cross perfectly ana CONCEIVE Vi II
just as we GO. hu' let uS "SN 'ii'il ~
ara" 'u''" '''i' ~ ',''7 t..A ,ro
| point ana peII'""'0" '"' ~ 'o'"
other mes "'S "'u'u "' o'''V P'T
nounce TINS absurd ana i'llosS,''ie' -
is equally anSurd ana luil 'HS'''o ~ u'
II we require 'he .uIu i'ne ~ '0
drawn on the paper hu' " - "oulu ~.
| ply II you aio" us u ''"'' '"V p"p.l
OF nat surface 'heh we can s'i'e ."1
problem by SIMPLY uI""l"F '"e 'i'''
line through the paper P'il'''"' u'"'
to It's surface
Now, 10 pursue the ahNlos|' suppose
that afIer we nave drawn lhree nlu'u-
ally perpendicular INES some peins
from another sphere proposes 10 US tue
drawing OF a touflh IIhe through the
same point perpendicular 10 IN 'llee
OF the lines already there' we Shouiu
answer him IN the same way tnat the
inhabitants OF "hatland' answered u.s.
The problem is impossible. You can
not draw any such line IN space as we
understand II. II our VISITOR conceived
Of the fourth dimension. he would re-
ply TO US as we replied to the nat
land" people: THE problem is absurd
and impossible If you conine your line
to space as you understand II. hut TOT
me there is fourth dimension III
space. Draw your line through that Oil
mensiOn, and the problem VIII be SOW
ed. This IS perfectly simple 10 me- IL is
impossible to YOU solely because youi
conceptions 90 not ADMIT OF more IMAM
three dimensions.
Supposing the inhabitants OF nat
land' TO be intellectual beings as We
are 1t would De interesting 10 then u
be tod what dweiiers OF space III 'hret
dimensions could 90. Let Us pursue 'he
analogy by showing what dWellers IL
four dimensions might DO. race q
dweller Of "Gatland' inside a circle
drawn on his plane and ask him tc
step outside Of ii without breaking
through it. He would 20 all around
and, finding every inch Of it closed. he
would say il was impossible from The
very nature Of The conditions. but,
we would reply, that is because Cl