1. I think this would have been easier for me to draw - > I don't really understand how, from looking at a > shape straight on, the square could tell it's degree > of social refinement. Because it seems possible that, > beyond the widest forward faces that reflected light, > there could have been a lot of smooth faces that were not > seen. Are all the sides of all the Shapes except Isosceles > exactly the same size? I mean,could there be a tear-dropped > Shape that had a really sharp angle but also had a really smooth > and refined, almost spherical end as well?
It seems that the authorities in Flatland try very hard to make sure that individuals all have equal sides, since that makes it much easlier to deal with the beings that one encounters. An irregular shape such as you suggest would require a full examination before anyone would be comfortable knowing its characteristics. It's much easier to discernthe shape of a figure that it regular--once you understand the neighborhood of a point, or of two adjacent points, you can infer all the rest.
2. Couldn't two members of the Isosceles class stick together front-end > to back end and form a square? that would be within the size limits > of the Shapes and also fool the other shapes into thinking there was > more sophistication there then actually is?
Such collusion appears a despicable exercise. How could any being consider such a fundamentally disturbing plan?/P>
3. If an Isosceles has a .5 degree angle, then its' other angles are very >wide, almost 90, apiece. Could't it just face the other way in its' > everyday travels and make people think it was a square? Or at least, > an Isosceles very high on the social ladder to becoming an Equilateral?
Presumably individuals in Flatland move around a lot, so it would be difficult for an isosceles to fool anyone. He would have to concentrate on facing exactly the same way all the time with respect to the person he was triying to deceive, whidh might be possible if there were only one or two beings around. Even two could see that there was something fishy about an individual always trying to face in a certain direction.
p.s. I really liked the part of class where we did the exercises in groups! > we should do more of that drawing and thinking challenge kind of thing > -it is fun.
Let's try some more. I agree it can be fun, and productive. Prof. B.