Re: The Very Very First Sentence

Philippe Caquant wrote:

>Thank you, it was quite interesting reading it. It
>remembers me very much of George Gamow's book, 'One,
>two, three... infinite', which I read when I was in my
>teens and was stolen from me some day, or maybe
>disappeared in 4th dimension. (But it looks like we
>can make it appear again by the power of Amazon and a
>few bucks).
>
>Gamow of course wrote no romance, but mathematical
>vulgarization. He also uses very much Analogy to make
>us understand for instance what could be an
>'hypercube', which Abbott called an extra-cube I
>think.
>
>At the moment, my concern is not so much about
>hypothetical 2-dimensional beings (looks like the
>Cards in Carroll's Alice), but about language
>primitives we need, we being 'normal' 3-d people, to
>describe a 2- (or less) -d world. So I'm not trying to
>fancy about 2d living beings, because nobody ever saw
>any one (let's except some actresses out of charity):
>I think of a 2d-world as a purely geometrical one, and
>that is quite well known to everybody who learned a
>little of geometry at school. (NB: there is also
>3d-geometry, of course). The question is: what
>concepts, and what words, do we need to describe such
>a word, or rather: which ones do we NOT need ?
>
>
Well, first, we need to ignore 'forwards' and 'backwards'   We only have
up, down, left(or west, perhaps), and right(or east). I really cant
think of anything else.

Incidentally, surely, just as we can project 3D things into 2D space(in
drawings), we can  project 4D things into 3D space - so, we can create a
sculpture of a hypercube.  If we were very clever, we could construct it
so we can rotate it in 4D space(not through actual  4D rotation, of
course, but through mechanical morphing).  A hypercube, from whatever
the 4-D equivalent of 'the top' is, looks a lot like a cube within
another cube.  Though very exactly proportioned.

It ought also be possible to fold the net of a hypercube, in 4D space,
again, using clever mechanics.