Re: Did prime numbers evolve?


On Apr 16, 1:25 pm, d...@xxxxxxxxxxxxxxxxxxxxxxxxx (DK) wrote:
...
Bottom line is, prime numbers "exist" no more than
such things as negative or complex numbers or infinity
do. All are inseparable from the way our mind functions.

I was with you, at least in part, until the last sentence.

I think I can easily separate numbers from the way our minds
function.

We don't have access to other minds and can't compare our
concepts to theirs. But we do know about electronic computers.
A calculator, for example, peforms arithmetic in a totally
different way from the way our minds function. We can understand
it. After all, we designed it. But how many people perform
subtraction by addition of two's complements, or perform floating
point operations with separate operations on fixed length
mantissa and exponent, or determine signs by "extending" the most
significant binary digit to the left for up to 16, 32 or 64
binary places, or perform any mathematical operation by first
converting numbers to binary representation?

And yet calculators not only do all that, they come up with the
same exact answers that humans do - and faster and more reliably
too.

A computer program may find prime numbers in a completely
different way from the way we do. It might use the sieve of
Eratosthenes, or might use trial and error, or might use a
different algorithm. But again, it gets the same set of prime
numbers that we do. And that's not an accident of evolution.

I argue that the electronic calculator produces the same answers
that the human calculator does, not because it mimics the way our
minds function, or because it "thinks" of or represents numbers
the way we do, but because both we and the calculators execute
functions derived from the fundamental properties of numbers.

I argue that the notion of cardinal numbers is central to the
understanding of reality, and that any intelligent mind, human or
not, would develop a notion of cardinal numbers and would see the
same set of properties and derive the same set of prime numbers
that we do. They might speak of un deux trois, uno dos tres, ein
zwei drei, ee er san, or one two three. They might use base 2,
10, 16, or the funny Roman system. But the properties of the
numbers are identical. They might use calculators, abacuses, or
pencil and paper for performing calculations, but the end results
are the same. II + II = IV no matter how the mind functions or
what tricks it uses to perform the addition.

I argue that, although number is an abstraction, it is an
accurate and non-arbitrary abstraction from material existence.

I argue that humans have not evolved an arbitrary notion of
numbers that is idiosyncratic to us. Rather we have evolved to
the point that we can understand the actually existent objective
realities of which numbers are accurate abstractions.

So I think we can argue about your first sentence. We can argue
that "material existence" and "abstraction" mean two different
things. But I don't think we can argue that numbers and their
properties are inseparable from the way that our minds function.
They seem completely separable and non-subjective to me.

Alan

.

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