Subject: Re: 3 Flatland Questions

From: [email-masked] (Thomas Banchoff)

Dear Leo,
        Here are a few brief responses to your questions:

>Number #1 Is Flatland one continous infinite plane expanding in all directions,
> or is it a finite surface with finite boundaries?  In either situation there w
>ould seem to be serious consequences of the pull of "gravity " towards the sout
>herly direction.

        Abbott keeps it flat and local, but the general question about possible shapes of other two-dimensional universes is quite a good one.
>
> Number #2 How do the inhabitants of Flatland prevent themselves from walking i
>n circles? Shouldn't everything they see just be a series of lines of varying b
>rightness? Obviously, they can hear as well and voice identification would help
> them to distinguish between landmark and person, but in a crowded place or ope
>n marketplace wouldn't voices become jumbled and confusion become unbearable?
>
        If you grow up in such a possibly confusing atmosphere, I guess you might learn to cope.  A flea market or a pep rally might seem unbearably confusing to an outsider, but people manage.  There are problems of course, and it will be interesting to consider them to see which ones are peculiar to which dimensions.

>Number #3 If women must rotate at all times when in public, would not they seri
>ously throw off everyone elses sense of direction?
 
        It isn't so much rotation as gentle undulation, which could actually help with the navigation problem, I suspect.

        Prof. B.