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Post by abacus9900 on Sept 17, 2010 12:21:32 GMT 1
You can't really think that maths is done for its own sake can you? If you do you are very naive. Nonsense. Why do you think Cantor did his work on transfinite arithmetic? Why do people do mathematical puzzles, such as sudoku, if not for their own sake? Mathematicians do Maths because it is beautiful and because it is interesting - any practical applications are nice, but that is not the motivating factor. I would be just as interested in Maths (and Science) even if it was completely useless. Cantor was expected to produce useful theorems. If maths was mainly left to amateurs we would not have had the developments we have had.
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Post by eamonnshute on Sept 17, 2010 14:10:21 GMT 1
Cantor was expected to produce useful theorems. No he wasn't. Where did you get that idea from? Why do you think Cantor worked on transfinite arithmetic if not for its own sake? Do you really think it was expected to be useful? The fact that there are amateurs proves that maths is done for its own sake. The word amateur is derived from the Latin for "love".As for professionals, the only difference is that they are paid to do it, it doesn't mean that their work is intended to have practical applications, and it says nothing about the motivation of mathematicians in choosing that occupation over others.
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Post by abacus9900 on Sept 17, 2010 14:56:53 GMT 1
You can't really think that maths is done for its own sake can you? If you do you are very naive. Nonsense. Why do you think Cantor did his work on transfinite arithmetic? Why do people do mathematical puzzles, such as sudoku, if not for their own sake? Mathematicians do Maths because it is beautiful and because it is interesting - any practical applications are nice, but that is not the motivating factor. I would be just as interested in Maths (and Science) even if it was completely useless. Cantor was no amateur - he teached maths. Anyway, how STA can say a function used in the context of a computer algorithm is not maths is quite beyond me.
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Post by speakertoanimals on Sept 17, 2010 15:11:56 GMT 1
The definition of a function in maths is one thing, the definition of a function in terms of a particular programming langugage is another thing entirely! All of which arose from the definition someone gave as the output of a function changing, which is something that may appear on particular programming languages, but doesn't appear in the mathematical definition of a function.
So, for a function (maths), we could have a vector, and a function on the space of vectors which returns a NUMBER (such as the length of the vector). If you wanted to normalise vectors in your code, you might write something that took the vector, computed the function that is length, then returned the normalised vector. Which is really two things -- the function which takes you from a vector to a number, then the scaling operation applied to a vector using the output of the first function. You could write that as a function that given a vector, returns the corresponding normalised vector, which could be seen as a particular case where the output of the function changes the input -- but that is not generallyn the case, either form mathematical functions, or for functions in programming.
I never said programming didn't involve maths, just that it is a different discipline, and terms differ between disciplines, as well as between different programming languages.
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Post by abacus9900 on Sept 17, 2010 15:46:34 GMT 1
Oh, so you're backpedaling now.
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Post by abacus9900 on Sept 18, 2010 8:44:54 GMT 1
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Post by speakertoanimals on Sept 20, 2010 12:26:16 GMT 1
Just to remind the hard of thinking -- I never said functions in computing didn't involve maths, I just said that the definition of a function someone gave from computing disagreed with the maths one, in that the output of the function was described as CHANGING the input. That was the phrase I was objecting to, whilst pointing out that the output of a function can be of a totally different sort to the input, so you can have a vector as input to a function, but a number as output (for example, the length of the vector). You can use that output to change the input (such as producing a unit vector), but that is not the same as the definition of a function itself.
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Post by abacus9900 on Sept 20, 2010 14:44:45 GMT 1
I'm sorry, but this type of operation is as valid as any other mathematical one, so to deny it has any part to play in the redefinition of what a function is seems a little perverse to me.
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Post by speakertoanimals on Sept 20, 2010 19:25:35 GMT 1
It is a mathematical operation, BUT it doesn't alter the fact that it is about what you may or may not do with the output of a function, not about the definition of a function itself.
You can't just say -- it's all maths, so all equally valid, when the sole object in giving one particular part of maths, because it crops up over and over again, a specific name, and a very general definition, is that it is GENERAL. Arguing that something which only applies in particular cases should be included in the definition just removes the whole point of the process.
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