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Among the most elementary actions known to us are small displacements
"in space". We have put the quotes, because people have accustomed to imagine
that some entity, called "space" exists as a primary reality, which
creates the possibility of moving from one point of this space to another.
Our analysis turns this notion topsy-turvy. Only actions constitute
observable reality; space is nothing but a product of our imagination
which we construct from small displacements, or shifts, of even smaller
objects called points. If x is such a shift,
then xx -- the action x repeated twice -- is a double shift, which we
would call in our conventional wisdom a shift at the double distance
in the same direction. On the other hand, we may want to represent a
shift x as the result of another shift x' repeated twice: x = x'x'.
It so happens that we can make three different
kinds of shifts, call them x, y, z, none of which can be reduced to
a combination of the other two. At the same time any shift w
can be reduced to a properly chosen combination of shifts x, y, z.
So we say that our space has three dimensions.
Copyright© 1991 Principia Cybernetica -
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