Capitolo 70
"And what can be the nature of the Figure that I am to mould out
from this motion that you are pleased to denote from the word ` direct upward?'
I suppose it is describable in the language of Flatland."
Sphere. Oh, certainly. It is every plain and simple, and in severe
agreement with Analogy--only, you don't have by the way, to speak of the
you result as being a Figure, but as a Solid. But I will describe him/it to you.
Or rather not me but Analogy.
We started with a solo Point that clearly--a Point being himself/herself/itself--
it Only has an end point.
A Point produces a Line with final Colons.
A Line produces a Plaza with Four end point.
You can now give him the answer to Your his/her own question: 1, 2,
4, are evidently in to Proceed Geometric. Which is the next number?
ME. Otto.
Sphere. Precisely. The one Plaza produces a Some thing-that-you-
Do-not-as-still-know-a-name-for-but-that-we-call-a-cube with Otto
End point. Is you/he/she now convinced?
ME. And it has this Creature it sides, as what you call
"End point?"
Sphere. Clearly; and all second Analogy. But, by the way,
what you call what We call sides. You would call them SOLIDS.
ME. And how much solids or sides want appertain to this Being that
I am to produce from the motion of mine in in a direction "direct upward",
and what do you call a Cube?
Sphere. How can you/he/she ask? And You a mathematician! The side of anything
it is always, if I can say this way me, a Dimension behind the thing. Accordingly,
as there any Dimension is behind to a Point, a Point has 0 sides; a Line,
if I can say this way me, it has 2 sides (for the points of a Line you/he/she can have called
from courtesy, his/her sides); a Plaza has 4 sides; 0, 2, 4; what a Progress
Does make her call that?
ME. Arithmetician.
Sphere. And which is the next number?
ME. You are.
Sphere. Precisely. Then you see you answered to Your his/her own question.
The Cube that you will produce will be limited from you are in general,
that is to say, you are of Your insides. Does he/she now see him/it eh entirely?