Evening star. [volume] (Washington, D.C.) 1854-1972, 1908-08-02

ward motion, would be compelled to move always
and, finally, would possess nothing of the quality
known in our three -dimensonal space as " solid y
although, to themselves they would seem solid
enough.
Similarly, if the F1atlanders dwet in houses their
homes would be nothing than open surfaces
inclosed by lines, with swinging lines to take the
place of doors. In order to imprison Flatlander,
it would thus be quite sufficient to draw an un
broken line around him. Not having the power of
upward or downward motion, he could neither step
over it nor burrow beneath it, and to him it would
be fully as impossible stone or iron wall
Now, even if this two-dimensional world
situated in the very midst of the three dimensional
space familiar to us, its people would ordinarily
have conception whatever of the larger space
surrounding them. The latter would be- for all
practical purposes completely outside their universe
and entirely invisible to them. Indeed, upward
and downward" and height" and depth"
being terms that conveyed no meaning to their
minds they would be strongly inclined to deny the
would probably unite to suppress any rash indi-
vidual that might its existence the strength
of some otherwise inexplicable experience: The
only knowledge they could have of it would come
from the intrusion of some nhabitant of the three
dimensional world into the plane on which they
lived. And even then he would seem to them to be
a supernatural being; or, If they dsbeheved IN the
supernatural would sorely perplex them as suggest
ing the need of sweeping changes in their long estab-
lished notions of the universe.
Visiting the Flatlanders
IMAGINE for example, the sensations of Flat
lander at the unexpected appearance OF three
dimensional man in his bed room. He had securely
bo1ed the door before retiring; had made sure that
no midnight marauder could gain entrance. Yet
there before his startled eyes, stood uncouth and
monstrous shape, different from any he ever had
behed before. The three dimensional man would
not it true, be by the astounded Flatlander
in the form familiar to other three dimensonal men
And, at the slightest upward or downward motion,
he would instantly vanish from sight But so long
as he remained on the plane as the Flatlander,
he would be visible and would be recognized as
other than a native of Flatland.
Most perplexing of all would be the question of
how he gained admittance to the house. The Flat
lander, having idea that everything about him
was open overhead, could not possibly appreciate
the fact that the dmensional man had entered
by the simple process of stepping across the lines
that formed the walls of the house and of the bed
room. And matters would not be much clearer to
his limited understanding, if his visitor undertook
to give him concrete demonstration of the proper
ties of the third dimension.
You see," we may fancy the three dimensional
man explaining, II not obliged, like you, to move
always level. l can 60 up or can 60 down;
and being able to go up and down can easily step
over the lines that to you to be SOLID walls and
also can look directly into this room, which you
imagine is all nclosed but which is really open to
the gaze and entrance of every three dimensonal
being The same is true of your cupboards, and
bureaus and everything else in which you store your