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That seems to be the same thing as representing sqrt(2) as sqrt(2).
by kaibee 8y ago
That seems to be the same thing as representing sqrt(2) as sqrt(2).
- lisper 8y agoYes, exactly my point.
- mcguire 8y agoYes, sort of. You can "compute" sqrt(2) by the geometric construction of a unit square and "drawing" the diagonal. You cannot do it physically, because marks on paper are not geometric primitives: points are not 0-dimensional; when drawn with a pencil, they have a physical size. A line on paper is not 1-dimensional, etc. But on the other hand, all physical computers are actually equivalent to finite state machines: they don't have infinite (or, unbounded) storage. I'm halfway through the video, and they are discussing this: the fundamental limit of Turing machines, etc., is that they cannot do an infinite (or unbounded) amount of work in a finite number of steps. As a result, geometric constructions a la Euclid are not computable.