The Tucson citizen., 1902-02-17
A HARD PROPOSITION
SCIENTIFIC EXPLANATION OF THE
FOURTH DIMENSION.

suppose Il world consisting or q
poundless fiat plane to be inhabited
by reasoning beings who can move
about at pleasure on the plane, but are
not able to turn their heads up or
Gown or even to see or think of such
terms us above them and below them,
and things around them can be push
Fd or pulled about In any direction, but
rannot be lifted from the plane. Peo-
pie and things can pass around each
other. but cannot step over anything.
These dwellers In 'hatland" could con.
struct Il plane geometry which would
be exactly like ours in being based on
the axioms of Euclid. Two parallel
straight lines would never meet, though
continued indefinitely.
But suppose that the surface or
which these beings live. instead Of be
ing an infinitely extended plane. is
really the surface of all immense globe
like the earth on which we live. 1t
needs no knowledge of geometry. but
only an examination OF any globular
object--an apple. for eXample~~to show
that IL we draw line as straight as
possible on sphere and parallel TO 1t
draw a small piece OF n second line
0nd continue this In as straight line
as we can, the two lines will meet
when we proceed in either direction
one-quarter OF the way around the
sphere For our "Gatland" people these
hines would both be perfectly straight
because the only curvature would be
in the direction downward. which they
could never either perceive or discover,
TO explain hypergeometry proper we
must first set forth what fourth d.
mension of space means and show how
natural the way by which Ii may he
approached. We continue our analo.
gy from "fiatIand" In this supposed
land let US make n cross-two straight
lines intersectlng at right angles. The
inhabitants OF this land understand
the cross perfectly and conceive Of II
Just as we do. But let us ask them 10
draw a third line intersecting the same
point and perpendicular 10 both the
other lines They would at once pro.
nounce this absurd and impossible. II
Is equally absurd and impossible 10 us
IL we require the third line 10 lie
drawn on the paper. But we would re.
ply. 'Tf you allow us to leave the paper
or dat surface. then we can solve the
problem by simply drawing the third
line through the paper perpendicular
to its surface"
Now. to pursue the analogy, supposs
/ that after we have drawn three mutu
| ally perpendicular lines some bein,
from another sphere proposes 10 US tn
drawing OF a fourth line through th
same point perpendicular TO all shrc
Of the lines already there. We shout,
answer him In the same way that th+
| Inha bitaDts OF "6atland" answered US
The problem In impossible You can
! not draw any such line I'm space as WI
understand H." If our visitor conceived
Of the fourth dimension. be would re
ply to Us as we replied to the "tiat
land" people: The problem is absurt
and impossible II you contlne your linz
TO space as you understand II. But foi
me there Is fourth dimension II
space. Draw your line through that di
mension. and the problem will be sow
ed. This La perfectly simple TO me: II IL
impossible to you solely because your
conceptions do not admit OF more thar
three dimensions"
Supposing the Inhabitants OF "flat
land" to be intellectual beings as we
are. 1t would be interesting to them &c
be told what jewellers Of space In three
dimensions could do. Let US pursue the
analogy by showing what dweIiers In
four dimensions might do. Place a
dweIler OF "datland" inside circle
drawn on bis plane and ask him &c
step outside OF IL without brea king
through 1t. He would go all around
and finding every inch OF 1t closed. he
would say II was impossible from the
very nature of the conditions. "But.'
we would seply, that Is because OF
your limited conceptions. We can step
over It."
'.Step over it!'' he would exclaim. 81
do not know what that means. ! can
pass around anything II there Is a why
open. but cannot imagine what you
mean by stepping ever It."
But we should simply step over the
line and reappear on the other side.
So if we confine being able to move
In fourth dimension In the walls OF a
dungeon Of which the Sides the floor
and the ceiling were all impenetrable
he would step outside Of 1t without
touching any part Of the building just
as easily as we could step over cir
Gle drawn on the plane without touch
Ing 1t. He would simply disappear
from our view like spirit and perhaps
reappear the next momeat outside the
prison. To do this he would have to
make a little excursion in the fourth
dimension. -Professos Simon Newcomb
In Harper's Magazine.
His AEaideu Name.
1t is said that at certain seasons In
| al, Co Nnt IN