cierdan said:
I thought that was what you were saying when you said that just because it is useful doesn't mean that natural selection would favour them.
While that's true, that in no way means that natural selection
wouldn't favour them (once again you have twisted my words... do you do it out of malice or ignorance?). As far as I know, wheels have never evolved, and hence there's no way of knowing what selective pressure would do.
What YOU are failing to realize is that NOT ALL series of mutations are equally likely to occur. It is also true that some classes of series of mutations are more likely to occur than others. Series of mutations producing wings or wheels OR ANY OTHER THING OF THAT NATURE fall under a class of series of mutations where it is astronomically unlikely that ANY MEMBER of that class will occur.
And I suppose you have proof for this? You say it as though it is fact, yet determining the probability of a mutation occuring is rather tricky. The best we can do is approximate, or make educated guesses (hypotheses). So to ask you a less rhetorical question: What makes you think that wings or wheels are less likely to evolve than other things?
Incidentally, Yom's link presented a few educated guesses. I suppose yours as to the opposite question addresses it more adequately?
There are many theories in mathematics which are NOT TESTABLE.
Maths is based on axioms, NOT theories. A theory is something that deals with the physical world that can be tested. Maths does NOT deal with the Physical world, and Physics uses maths as a TOOL to express the physical world on paper. Maths deals with axioms, which, in a mathematical context, are simply assumptions, e.g. 1+1=2.
Depending on how you define "science" maths can be a science or not. If you define science as purely empirical, and dealing only with the physical world, end purely employing scientific method, then maths is not a science. If you think that mathematical axioms are inherent properties of the universe, then maths is indeed a science to be discovered (a rigourous proof of a theorem being equivalent to scientific method). If you are indeed interested in my opinion on this issue, and are not merely being asinine, I think that whether or not maths is a science depends on the context, which is loosely based on the two alternative definitions of science I described above.
I'd like to add also that Science does NOT depend on maths in the empirical sense. For example, one could easily test the hypothesis: "In the northern hemisphere, the sun rises in the east and sets in the west", which is a valid scientific hypothesis, without using any maths, just empirical evidence. This would be an example of where maths is not a science. Quantum Mechanics can equivalently be described and provide predictions without using maths (indeed, its postulates are not inherently mathematical, as one would expect from a physical theory, though the formalism is mathematical, as one would expect from Physics).
(Incidentally, Popper's definition of a theory is one I do not agree with - it does not encapsulate the true underlying meaning of a theory but rather it's mere appearance. It's an empirical definition rather than an axiomatic one

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EDIT: I don't wish to debate this any further in this thread. If you want to, you can start a new thread. But since you asked what my opinion was, I assume you don't wish to debate it.