The Providence news. (Providence [R.I.]) 1891-1906, 1902-01-29
The Fourth Dimension.

In Harper's for January Prof Simon
,Newcomb In his article on THE Fairy
land OF Geometry gives this explanation
or what the fourth dimension really Is:
Suppose a world consisting OF a bound
less nat plane TO be inhabited by reason
ing beings who can move about at pleas
ure on the plane. but are nO1 dbh to turn
their heads up or down. or even 10 see
or think OF such terms as above them and
below them. and things round them can
pc pushed or pulled about In any direc-
ton bat cannot be lifted from The plane.
People and things can pass around each
other, but cannot step over anything.
These dvellerS in fiat land could con-
struct a plain geometry which would be
exactly like ours I'm being based on the
axiom OF Euclid. Two parallel straight
lines would never m7et, though continued
But suppose that the surface on which
these beings live, instead of being an in
nnitely extended plane is really the sur
face OF an immense globe. like the earth
on which We live. II needs no knowledge
or geometry. but only an examine ton of
any giobular obtect-an apple. for ex-
ample--to show that N we draw a line as
straight as possible on sphere, add par
ailel 10 IL draw "A small piece OF n second
line. and 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 NAT land people these lines would
both be perfectly straight, because the
only curvature would be In the direction
downward. which they could never either
perceive or discover
ITO explain hyperReomctry proper we
must first set forth what a fourth dimen-
sion OF space means, and show how nat
ural the way by which II may be APP
preached. We continue our analogy from
fiat land In this supposed land let us
make cross--two straight lines inter
secting at right angles. The Inhabitants
St cS THIS and spS % Ss Gros m we c
But let ~ ask them to draw a third line,
fntrrrcrtTrE tfr- rari- r,oirrt; sffa-t-sf--
pendicular 10 both the other lines. They
would AZ once pronounce this absurd and
impossible. II is equally absurd and inn
possible 10 us II we require the third line
10 be drawn on the psper. But We should
reply. II you allow us 20 leave the paper
on fiat surface. than we can solve the
problem by simply drawing the third line
through, the paper perpendicular TO its
Now, 10 pursue the analogy. suppose
that, after we have drawn three mutually
perpendicular lines. some being from am
OF a fourth line through tire sans point
perpe ndlCular to all three OF the lines al
ready there. We should answer him In
land answered Us: The problem is inn
possible. You cannot draw any such line
in space as we understand it. III our
visitor conceived Of the fourth dimension,
he would reply 90 us % we replied 20 the
fiat land people; The problem is alb
surd and impossible n you confne your
line TO space az you understand Il But
space Draw YOUR line through that di-
mension. and the problem Will be solved.
This is perfectly simple to mo; II IL i'm
possible 10 you. solely because your con-
centions do not admit OF more than three
dimensions
''supposlng the inhabitants of nat
land To be intellectual beings as we are,
IT would be interesting 20 them TO be
told what dwellers Of space IN three d.
mensions could do. Let us pursue the
analogy by showing what dwellers in
four dimensions might do. Place
dweller OF fat land inslde circle
drawn on his plane. and ark him 70 step
outside OF IL without breaking through
every inch Of Il closfd he would say II
was irnncssihle from the very nature OF
The conditions Bat we would reply
that is because Of your limited Soncep-
tions We cap step over II.
" 'cfep over it, he would eNclalfn. 4
do not know what that means. can
PASS around anything ~ there is way
omen. but I cannot irnarine what you
mean by stoppinR over It,
"But we should simply step over the
line and rcappear on the other side. SO,
~ we coninc a being able % move In
fourth dimension IN the walls of a dun
geon, OF which the sides, the floor and
tho ceiling were all inspenctrable Ire
any part of the buildRg. just as easily
as we could stcp over circle drawn on
the rlane without touching H.. Tie would
sirnuly disaprenr from our view like
spirit and perhans reeppear the next
moment outside the prison. To do this,
NJ would oNly have 10 make "A little eN-
cursion in the fourth dimension"