Alas, a few years
ago, I should have said "my universe": but now my mind has been
opened to higher views of things.
In such a country, you will perceive at once that it is impossible
that there should be anything of what you call a "solid" kind; but I
dare say you will suppose that we could at least distinguish by sight
the Triangles, Squares, and other figures, moving about as I have
described them. On the contrary, we could see nothing of the kind,
not at least so as to distinguish one figure from another. Nothing
was visible, nor could be visible, to us, except Straight Lines; and
the necessity of this I will speedily demonstrate.
Place a penny on the middle of one of your tables in Space; and
leaning over it, look down upon it. It will appear a circle.
But now, drawling back to the edge of the table, gradually lower
your eye (thus bringing yourself more and more into the condition of
the inhabitants of Flatland), and you will find the penny becoming
more and more oval to your view, and at last when you have placed your
eye exactly on the edge of the table (so that you are, as it were,
actually a Flatlander) the penny will then have ceased to appear oval
at all, and will have become, so far as you can see, a straight line.
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