Mathematics; discovered or invented?

[davidm]

I agree with Bee (Sabine H.) that beauty can lead people astray. Our neural networks are wired to appreciate symmetry and other particular mathematical qualities that give pleasure, but that doesn't mean fundamental physics couldn't be a sloppy mess in some respects.

As an aside, Bee and Don Lincoln recently had quite the exchange on her blog. Bee takes no prisoners! :-D

Maybe you could invite her to contribute to the Expert Notes section.

[-1-]

Math: invention. Only it has been invented more than once, and the inventions are congruent.

The reason we communicate with aliens with simple math: we assume math is a universal invention. Symbolic language is random, but symbolic math is not random. You can represent all the integers with numbers of dots, and therefore you can make up a series leaving out integers, a series which form all the prime integers in an interval. This has the power of communicating to a different world that we (or they, if they send this message to us) are capable of discerning what a prime number is. This will communicate that we are at least somewhat intelligent.

Communicating that Hamlet, the Danish prince went mad over the murder of his father by his stepfather, is a bit more difficult to transmit, because symbolic languages are random in their expressions. By expressions I mean, the phoneme chains have no logical connection to the meaning of the word they form covers.

Now, putting the series of equations that Newton created, that is, finding the derivative function of f(x) = X^2, is not as easily done as listing all primes within an interval.

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It is true that one stone and one stone anywhere in the universe will form the sum of two stones. "Two", as such, is not a natural constant, however; it takes a mind to conceptualize what two means, and nature, known nature, outside of man, has no concept of numbers. This is an empirical finding; but a priori, numbers are an invention to EXPRESS quantities of stuffs. They are no more than a form of communicable expressions. Then it follows that only those use numbers, who need to communicate quantities; and outside a sentient organization there is no need to express anything. The universe operated prior to man's appearance quite well without communication.

If we accept that math is a tool of expression, then we can conclude that math is an invention, not a discovery.

[hyksos]

I agree with Bee (Sabine H.) that beauty can lead people astray. Our neural networks are wired to appreciate symmetry and other particular mathematical qualities that give pleasure, but that doesn't mean fundamental physics couldn't be a sloppy mess in some respects.

As an aside, Bee and Don Lincoln recently had quite the exchange on her blog. Bee takes no prisoners! :-D

Maybe you could invite her to contribute to the Expert Notes section.