I finally went over and read Sparky's screed about pi. It was hilarious. Apparently he hasn't heard that the modern definitions of pi don't require ideal circles or other fanciful ideas... other than accepting the idea that infinite series with certain properties converge. And if he rejects that then he's gonna have to throw out calculus too.
Pi can't be possibly be removed from the geometry of circles which generated AND DEFINES the ratio which IS pi. I would like to have the Lite Bright of Eschaton to point out to me anywhere where the definition of pi is unrelated to circles. I suspect, but haven't checked that the simple thinker can't navigate the difference between definition and means of calculating, but I haven't got the time to check that out, just now.
As to the circles of plane geometry being a fanciful idea, you'd have to throw out a hell of a lot more math if you gave up plane geometry, including but not only including, calculus. Huge swaths of post-Cartesian mathematics takes the ideal forms of plane geometry and the conclusions drawn from them as being far more than merely fanciful. Not to mention classical physics and, perhaps even more so, chemistry. It is the ideal figure which produced the MATHEMATICAL CONSTANT pi. I seem to recall a great deal of speculation as to why it seems to turn up over and over again in so many contexts is related to its embodiment in the form of a circle, though I'm not that well versed in that area of speculation. Or is there some nifty-new-notion as to why that might be the case which doesn't deal with old-hat like plane geometry.
I love how they go several bubbles out of level when you point out that science is entirely dependent on imaginary entities. Here's an old post I did pointing out that the only things we have that we can actually and absolutely prove anything about are imaginary entities.
But the matter of what a proof is and what "to prove something" means is seldom considered. The common belief that this thing called a "proof" provides an objective and unambiguous certainty that "a truth" provided by the proof is a complete and entirely reliable "thing" or condition of being or historical event, complete with its retinue of supporting and related "things"(quite often in themselves not "proven") and associated aspects of reality. It is quite often and wrongly asserted that science provides proof of this or that. Which is a claim made on their behalf that scientists careful with their claims and language - or, more often, forced to by rigorous debate opponents - will openly disclaim. Oh, so often, their disclaimer is revealed to be disingenuous as soon as it's issued because they continue in encouraging the habit of thought that holds that science issues proof of stuff. I will mention in passing that I have never read or encountered an ideologically campaigning atheist-scientist who doesn't talk out of both sides of their mouth on that point.
Really careful scientists will admit that mathematicians are the ones who are in the business of providing proofs, and the even more careful will point out that it is prudent to make that claim only about pure mathematics, in which the objects "proved" are abstract entities that exist only in the minds of those with sufficient learning in mathematics to contain those entities. Which could reasonably lead someone who was either being extremely precise about the denotation of the words, or who wanted to give materialists a hard time, to say that this prime desideratum of theirs, "proof," would seem to be only available when dealing with imaginary objects and their imaginary properties. And when the materialist or "physicalist" or, almost always, rather emotional atheist, hears that and associates it with the actual object of their attack, they don't like the implications and often get really pissy.
Jesus, if I'm remembering correctly in this hour before I'm supposed to be at work, didn't provide a logical "proof" of God or what he was saying. He advised people to consult their own experience of life and events around them, to see the signs of the time. In doing that he was being honest about something hardly anyone in the "proof" business is honest about. "Proof" is a matter of being persuaded that all of those things allegedly provided by a proof in my second paragraph, proof is, in the words of the atheist and mathematician and scientist, Joseph Weizenbaum, a matter of human psychology and persuasion.
On that personal and willful act relies everything that we hold should be believed to be true and that belief should have a real effect in changing the behavior and thinking and feeling of the person who is persuaded. "Proof" "a proof" is something that is done or experienced by a person and people, its existence happens only in human minds, it is something we pretend has some independent, allegedly objective existence, when its complete reliance on us and our most subjective experience is one of the most obvious aspects of "proof". Prove that there is a proof that exists outside of human thought. Prove that any proof that isn't the product of human thought and relies for its very existence on a subjective and willful act of individual persuasion. If you can't do that then this objective, independent proof thing must be a delusion, by the very claims you make for proof and what the absence of such a proof insures. Those who make proof the object of cult like devotion and search are the ones who are the most dishonest about what proof actually is, especially its dependence on subjective thought,that it has no real and objective existence independent of that subjective thought and it is also not unrelated to human desires and subject to human self-deception.
Proof is entirely a matter of persuasion, no matter how rigorous the proof is, in the end a person has to accept the proof and, as some of the most rigorous application of proof in the past century "proved" no matter how rigorous a stickler for proof that you hold yourself to be, your proof depends on things that can't be proven, that can't even enter into this business of proof. The hero of materialists and atheists, Bertrand Russell, had to rather bitterly accept that was true, after years of some of the most rigorous thinking on the topic ever undertaken, he had to reluctantly accept it was true. And at the same time he had to gloomily and bitterly accept that was also the direction that physics, the subject that dealt most rigorously with his ultimate reality, the material universe, was headed in the same direction. Perhaps it was due to his habits of thought gained from being a mathematician that made him accept that when even so many of the physicists don't seem to be able to accept what their very science shows about the relationship of human minds and the subjects it studies. When you want to press those issues, nothing that we can say about the physical universe isn't entirely reliant on our subjective will and experience because we use our minds to even perceive the objects physics deals with and there is no absolute proof available of any of it.
The law uses the word "proof" as in "a case being proved beyond a reasonable doubt" or some such construction. The looseness with which legal "proof" is accepted is best shown by those convicted of murders and executed only, later, to have someone else confess or shown to have committed the murder. If you want to see how confident you should be in that brand of "proof" look at how prosecutors and judges who are in the dirty business of killing people that way resist looking at the quality of their proof when their actions are questioned. If you want to really look at the con job that "proof" often contains in a real life context, look at the things that someone like Antonin Scalia has said which proves how sleazy and dishonest this proof stuff can be in the hands of a sleazy and dishonest person with power. A proof that is held to be worthy of the greatest of respect and given the power to kill people can be as dishonest as that. In the hands of physicists and other scientists, those have ever more power to get us all killed than Scalia could dream of in his most megalomaniac imaginings. Such is the power and the quality of what proof provides when it is removed from the teachings of such folk as Jesus, held to be exempt from those by virtue of their higher proofyness, or something. Allowing that exemption is both illogical and insane.
No, even in this business of proof, you're stuck with making a choice on the basis of will and in the absence of the comfort that comes with a real instead of your merely imagined absolute and totally reliable truth. You're stuck with that because that's all it is, despite all imaginary assertions to the contrary.
Update: I should be out the door but it occurred to me that the question I asked yesterday, why shouldn't scientists predict that they're going to find "alien" life in the next 28 seconds as opposed to their predicted two decades, is a good illustration. Predictions of something with an expiration date of 28 seconds can be subjected to reality and stand the chance of being debunked in rather real time as opposed to that imagined world twenty years from now. By then the budget for the project they are promoting will have been spent in the lost and forgotten past, even as their almost promised results are unachieved and, likely, forgotten. I doubt that any of them still alive and working at NASA will be the ones to bring it up. They don't want to do a truth test of their sciency assertions quite on that short a time scale. The one going into six figures, not very urgent when you're asking for an appropriation in this congress. What they expect to do with these aliens they predict they are going to find might be a question to ask. As I've asked before, what if the aliens are 1. smarter than us, 2. fervently religious? What if they think our science is extremely dangerous Plutonium Age delusion? That going to impress the high and sciency?
Update: An unpublished comment says, " I never realized before that there really isn't any way to know if we are actually living in The Matrix." Apparently that's supposed to make what I said above officially stupid. I am only very vaguely aware of this "Matrix" that is referred to in the comment, since I haven't gone to see a movie in, literally more than two decades and don't do the lowest of filmed sci-fi. But if the idea that we are all in a matrix is stupid then he unwittingly agrees with me about contemporary cosmology since a kind of"matrix" universe is all the rage just now. I mean, it's published in freakin' Nature! But, then, everything he says is unwitting. About that hologram stuff, I doubt it and I doubt it will last five years. Which would seem to be about as long as any scheme of cosmology lasts these days.