Rich Wilson wrote:


That's one reason why it's 'real', it is not 'just a concept'
and not an invention of the mind.


I could make up a number and argue exactly the same, and it would still be
made up.


Going to regret this but...

Thats the point, pi isn't a "made up number", its a direct result of the
geometry of the universe we live in, it would have the same value at any
place in space, and any race that had the concept of the loci of a
moving point on a plain, and so the concept of a line and a circle,
would arrive at the ratio that is pi.

Just because you could make up numbers does not put them in the same set
as pi and a few others.



Alternatively you might invent something useful that way. For example, by
taking the idea of a square root and applying it to something that you
wouldn't normally apply it to, like -1.

Again, you are looking at it from the wrong side. All you are doing, is
taking the concept of a square root, and applying it to exactly what you
expect to apply it to, that is a number, no more, no less, the fact
that numnber is negative has no meaning to the mathematics, only to your
attempt to expect all matematical concepts to have a analog in what we
regard as reality. There is nothing different between 1+0i (square root
of 1) and 0+1i (square root of -1). They are both just different complex
numbers. It would make more sense if we called complex numbers just
numbers, and numbers with a zero imaginary part simple numbers.

--
Nick