A "concept" could be said to be computable iff there is a procedure that enumerates all instances of said concept... (That is, we can try to equate a concept with a language L of strings) In that vein, I think triangle is pretty much computable as is every concept in geometry. They do cover all essential aspects of geometry in computable analysis, by the way.
However, it is much easier to talk about computable numbers and computable functions as they have a more rigorous definition.
Modulo this technical talk, yes, when counting we can represent "1" exactly, but not so, perhaps, when we are drawing, it remains more of a mental idealization. This is especially easy to see if we consider that counting itself is a mental operation.
It boils down to a central issue in philosophy of computation. Simulating 2+2=4 *is* addition. Simulating rain is not rain.
However, it is much easier to talk about computable numbers and computable functions as they have a more rigorous definition.
Modulo this technical talk, yes, when counting we can represent "1" exactly, but not so, perhaps, when we are drawing, it remains more of a mental idealization. This is especially easy to see if we consider that counting itself is a mental operation.
It boils down to a central issue in philosophy of computation. Simulating 2+2=4 *is* addition. Simulating rain is not rain.
BTW, quantum logic is weird. I never fully understood quantum information theory either... should go back and study a bit too, I recommend studying quantum computation as well. Just for the WTF factor. :)
Apart from that I was in a very interesting conference on Evidence Based Medicine today, will comment on that soon also.
Apart from that I was in a very interesting conference on Evidence Based Medicine today, will comment on that soon also.
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