The reference to 'nothing' meant that nothing came before the Big Bang was one of the possible choices, making the Big Bang the thing that is infinite. Whatever you arrive at, if nothing came before it, that thing is infinite. Even if we try to characterize what came before the Big Bang as 'nothing' that nothing is something, a void of white or darkness or just 'nothing' but that inself is a characteristic making it infinite, because it had to be. Essentially, everything comes from something, except that which was there at the beginning. — GigoloJoe

Say what? Nothing has no properties. It's not infinite (in whatever respect you're thinking of that) or anything else.

'i disagree, at its base all math is, is a numerical model of reality.'


I think you should read the Turing-Wittgenstein debates on the issue. Turing had a view similar to yours, as do I, but Wittgenstein thought it was just a convention. Neither argument is easy to defeat - it comes down to personal preference.

My belief about Pi is its defined as the ratio of a circle's circumference to its diameter. As a logical system defined by Hilbert it has a precise meaning in that system. Are logical systems eternal or only exist once discovered? Well I will let posters here discuss the issue - on one side you have Penrose - on the other Poincare and Wittgenstein.

An illumining issue to discuss in this regard is the logical principle behind Cantors diagonal argument which can be used to prove some very counter intuitive things - even Godel's Theorem. That really brings the issues with infinity to the fore.

Regarding is the universe infinite and the infinite regress argument it uses the concept of before ie of time. The modern view is the big bang was the birth of space-time. Is the concept of before valid in an era when time itself did not exist?

Thanks
Bill

The modern view is the big bang was the birth of space-time. Is the concept of before valid in an era when time itself did not exist? — Bill Hobba

Pre anything is a valid concept, as long as the "anything " exists, and that anything can certainly be space time.

My belief about Pi is its defined as the ratio of a circle's circumference to its diameter. A — Bill Hobba

The ratio of a circle to its diameter existed before it was observed, named and quantified. The ratio was not invented it was observed.

Say what? Nothing has no properties.

It is an absence.

The ratio of a circle to its diameter existed before it was observed, named and quantified. The ratio was not invented it was observed. — Rank Amateur

Where did it exist? And what else might exist in the same realm? The baby Jesus? The Flying Spaghetti Monster? Captain Ahab?

I have trouble with Platonism.

By the way FWIW, $\pi$ is defined these days as the smallest positive zero of the sin function; which itself is defined by an infinite series or else in terms of the complex exponential. No circles are harmed or even involved.

go throw a rock in a pond

↪fishfry go throw a rock in a pond — Rank Amateur

That's your heartfelt defense of mathematical Platonism? I've seen better. Try these for a start.

https://www.iep.utm.edu/mathplat/

https://plato.stanford.edu/entries/platonism-mathematics/

Can you frame a coherent argument in support of your claim that $\pi$ has some sort (what sort?) of existence prior to the existence of any mind?

I wasn't being nasty, I was pointing out circles exist in nature, and the ratio of the circumstances to the diameters of these circles exist in nature.

↪fishfry I wasn't being nasty, I was pointing out circles exist in nature, and the ratio of the circumstances to the diameters of these circles exist in nature. — Rank Amateur

Ah. Ok! But those aren't circles. There aren't any idealized circles in nature. Mathematical abstractions are idealized versions of things in nature. Mathematical circles are inspired by circle-like things in nature, but the circle-like things aren't mathematical circles. I confess I'm surprised to have to be continually explaining this point, which I thought was universally agreed to. If you could freeze a moment in time and carefully measure the circumference and diameter of a circle of water in a pond, you would not get $\pi$ for two reasons:

1) The water's made of molecules, the molecules are made of atoms, the atoms are made of quarks and gluons and such, and the quarks and gluons themselves are just probability waves. You couldn't find a circle if you tried; and

2) All physical measurement is approximate. A physical measurement consists of some number that's the output of a physical apparatus; along with some error bars; along with a probability distribution that tells you how likely it is that the number you got is within the error bars of the "true" value, if there even is such a thing. So even if there was a perfect circle in the world (which of course there isn't) you could not measure it to arbitrary precision.

I recall writing these exact words just a day or two ago here. All physical measurement is approximate.

It's worth noting that the most accurate physical measurement we know of, something or other about the electron in quantum chromodynamics, is good to 12 decimal places. That's plenty good for a physical theory, but not very precise for a mathematical real number.

ok sure.

↪fishfry ok sure. — Rank Amateur

Ok. And yet ... $\pi$ is forced on us. A crude measurement of the ripple circles will give us a couple of decimal places. Archimedes calculated $\pi$ to three decimal places using mathematical reasoning.

I'm not denying the out-there-ness of $\pi$. I'm a Platonist on weekends. But to me the case isn't as obvious as it is to others. Sure, we don't have any choice in whether 5 is prime. So it's out there. But where is it? Was it there before the Big Bang? Platonism is not as obvious as some think. How do we know that math and logic aren't qualities of our own minds and not so much of the world? Just as a bat thinks the world is full of informative sounds. We are very human-centric in these matters and I wonder if someday we'll get past that.

There is a profound difference between a physical drawing, and an abstract, idealized geometric shape. You can't draw a mathematical circle with a pencil and paper. Nor could you ever make a physical measurement of any irrational number. Do you understand that? I'm asking just to make sure we're not talking past each other on this essential point. — fishfry

And you cannot ever make a physical measurement of a natural number like 2. As I've said earlier, every physical measurement is obviously an approximation. Naturally every drawing is too. Do you understand that? I guess you do, so I assume you do understand the abstract theoretical nature of mathematics, hence I'm not sure what where the disagreement is here.

I'm not denying the out-there-ness of ππ. I'm a Platonist on weekends. But to me the case isn't as obvious as it is to others. Sure, we don't have any choice in whether 5 is prime. So it's out there. But where is it? Was it there before the Big Bang? Platonism is not as obvious as some think. How do we know that math and logic aren't qualities of our own minds and not so much of the world? Just as a bat thinks the world is full of informative sounds. We are very human-centric in these matters and I wonder if someday we'll get past that. — fishfry

If Platonism is the problem, I think this is a different question, which is more a metaphysical one.