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I
recall with great pleasure a discussion with my mathematician friend
Beppe Pea over a pizza one evening. At that time I had created my Columns
of Thought and I was tormented by the idea that I had always cut my
cubes and parallelepipeds in two spatial dimensions only. The third was
absolute taboo. Untouchable. What excited me was the idea - for instance
- of cutting a wooden cube using the so-called method of the columns of
thought, but from all three dimensions which, until proved otherwise (leaving
aside Einstein's extraordinary space-time reality) are X, Y and Z, so
that a sphere can be seen within.
We had a lengthy discussion about the feasibility of these three
successive cuts and I clearly remember the conclusion we reached - the
third cut would undoubtedly destroy the work already done.
Shortly afterwards I managed to make a column of thought cut in three
dimensions but I reached the conclusion (provisional in the light of
subsequent developments) that it was feasible provided that the drawing
on the three faces of the cube or parallelepiped was not a closed
figure, and that anyway it always touched the four corners of each face.
In
effect, if you look at the column of thought I am talking about from all
three dimensions, you always 'see' an X shape.
Guido Moretti
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