The Tucson citizen., 1902-02-24
A HARD PROPOSITION
SCIENTIFIC EXPLANATION OF THE
FOURTH DIMENSION.

AhFouGh stone Walls.
Suppose n world consisting OF Il
toundless fiat plane to be inhabited
ny reasoning beiuGs who can move
tpout at pleasure on the plane but are
not able TO turn their heads up or
down or even 10 see or think OF such
terms as above them and below them.
ana things around them can he push.
rd Or pulled about In any direction, but
cannot be lifted from the plane. PEG,
PIE ana things can pass around each
other, but cannot step over anything
These dwellers In "tiatland" could con.
struct plane geometry which would
be exactly Ike ours In being based on
the aXioms OF Euclid. Two parallel
straight lines would never meet. though
continued indefinitely.
But suppose that the surface on
which these beings live, instead Of be.
ing an infinitely extended plane. is
really the surface OF an immense globe
Ike the earth on which we live. 1t
needs no knowledge of geometry. but
obJect-an apple, for example-to show
/ that IT we draw Il line as straight as
possible on sphere and parallel to ii
draw small piece of second line.
ond 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
a.
| lines would both be perfectly straight
because the only curvature would be
In the direction downward, which they
could never either perceive or discover.
10 explain hypergeometry proper we
must first set forth what a fourth d.
mension of space means and show how
natural the way by which 1t may be
approached. We continue our analo-
gy from "fatland." In this supposed
land let us make cross-two straight
lines intersecting Mt right angles. The
inhabitants OF this land understand
the cross perfectly and conceive OF II
just as we do. But let us ask them TO
draw third line intersecting the same
point and perpendicular TO both the
other lines. They would at once pro-
nounce this absurd aud impossible. II
10 equally absurd and impossible to us
TX we require the third line to be
drawn on the paper. But we would re-
oily. IF you allow us TO leave the paper |
or fat surface then we can solve the |
problem by simply drawing the third |
line through the paper perpendicular |
TO It's surface"
Now. to pursue the analogy, suppose
that AFTER we have drawn three mutu-
ally perpendicular lines some being
from another sphere proposes TO us the
drawing Of a fourth line through the
same point perpendicular 20 all three
OF the lines already there. We should |
answer him in the same way that the
inhabitants OF "fiatiand" answered Us:
The problem 10 impossible. You can.
not draw any such line I'm space as we
understand IT," II our visitor conceived
or the fourth dimension he would re-.
ply 20 Us rs we replied to the flat.
iand people: "The problem in absurd
and impossible II you coniine your fine
10 space as you understand IT, but for
me there IL fourth dimension in
'psce. Draw your line through that d.
nension. and the problem will be eoly.
I'd. This is perfectly simple to me; IL ia
impossible 10 you solely because your
do not admit OF more than
hree dimensions"
Suppoaing the Inhabitants of "hat,
and" 10 be intellectual beings as we
ire, 1t would be interesting 20 them 10
'e told what dwellers OF space in three
dimensions could do. Let us pursue the
naloey by showing what dwellers in =
our dimensions might do. Place a !,
weller of ''fatland" inside a circle
Tawn on his plane and ask him TO
tep outside OF It without breaking
through It. He would go all around.
nd. finding every inch OF II closed. he .,
rould say Ii was impossible from the :,
cry nature OF the conditions But" i
70 would eepiy. that liz because OF :,
our limited conceptions We can step =,
yer II" -
Step over it!' he would exclaim. IL :,
o not know what that means | can !.
ass around anything IL there is way =,
pen, but ] cannot imagine what you
lean by stepping over it."
But we should simply step over the
ne and reappear on the other side "a
0 II we confine being able TO move =,
fourth dimension In the walls OF 1,
ungeon OF which the sides, the 6oor 90
nd the ceiling were all impenetrabie M
> would step outside OF II without ~
uching any part OF the building just a,
easily as we could step over a cir 40
Q drawn on the plane without touch.
g It. He would simply disappear
ON our view like a spirit and perhaps
appear the next moment outside the e.,
fson. To do this be would have TO
axe a little excursion Ia the fourth ut
mension. PROFESSOR Simon Newcomb
Harper's Magazine gu
HE MRiden Name. co
Il is said that at certain seasons IN he
otiand when the fishing is not very
IRk the fishermen act as caddies and