A Piece of Pi For Dessert During Covid Shutdown

[Aris Marghetis]

Yes, Aris, but it was a great opportunity to post a 5 characters message

Did you know as well that Monty Python is involved in the world record calculation of Pi?

https://en.wikipedia.org/wiki/Chudnovsky_algorithm

Brilliant lol

[Fred Harvey]

Infinity does not exist! The concept is way beyond the understanding of us mortals, which is why no-one here has really solved the fascinating conjectures about number series satisfactorily. If you need a model, imagine a very large circle, that ultimately comes back to the starting point. If by chance you can navigate this circle, by the time you return, things will have changed enough that recognition is impossible. With this model, all the answers to your questions become moot! There is of course a very old joke about this, but do not ignore the truth of which I speak...... As for pi, why would a mathematical constant be so complicated?

[Ed Seedhouse]

Infinity does not exist! The concept is way beyond the understanding of us mortals, which is why no-one here has really solved the fascinating conjectures about number series satisfactorily. If you need a model, imagine a very large circle, that ultimately comes back to the starting point. If by chance you can navigate this circle, by the time you return, things will have changed enough that recognition is impossible. With this model, all the answers to your questions become moot! There is of course a very old joke about this, but do not ignore the truth of which I speak...... As for pi, why would a mathematical constant be so complicated?

Still beating that dead horse, eh Fred?

Infinity is a rigorously defined mathematical object. Mathematical objects do not exist in the physical world but yet somehow strangely they allow us to predict future events in that physical world with astounding accuracy. I think I will ignore the "truth" of which you speak though, since it isn't a truth at all, but meaningless mumbling "full of sound and fury, signifying nothing."

[Pargat Perrer]

Infinity does not exist! The concept is way beyond the understanding of us mortals, which is why no-one here has really solved the fascinating conjectures about number series satisfactorily. If you need a model, imagine a very large circle, that ultimately comes back to the starting point. If by chance you can navigate this circle, by the time you return, things will have changed enough that recognition is impossible. With this model, all the answers to your questions become moot! There is of course a very old joke about this, but do not ignore the truth of which I speak...... As for pi, why would a mathematical constant be so complicated?

Infinity as an absolute does not exist because it is never-ending. But infinity as a concept does exist, which is what I think Ed Seedhouse is saying in his reply to you.

One model to think about is God: does God have (as most Christians would affirm) infinite power, wisdom, knowledge? Let's take knowledge as an example. If God already had infinite knowledge, and we take that to mean that he already knows absolutely everything, not even the tiniest piece of knowledge escapes him at this moment in time (nor at any past moment in time).... then why in the Old Testament was he always getting so wrathful? Why did he have to have Noah build the ark after which he (God) punished humanity with a global flood (and then later promised mankind he would never do that again, as if he had made a terrible mistake)? Or send Moses down the mountain with the 10 Commandments? Or nuke Sodom and Gomorrah? All the sins that mankind was committing, God would have absolute foreknowledge of it all. And yet according to the scriptures, he still got angry! It's really quite a joke on humanity for buying into the story at all, and still even saying God has infinite knowledge!

However, God could be acquiring infinite knowledge, and we can take this to mean his increase in knowledge is never-ending. In that respect, we can better understand our own existence: we would be (one of) the literal AGENTS of his acquiring knowledge. Everything we experience would be getting recorded as part of his infinitely-growing knowledge. And the rest of the universe would be full of other intelligent species that would be having experiences that would be getting recorded. This would go on infinitely into the future to preserve God's infinitely-growing knowledge. He wouldn't have just created us out of loneliness (although that could have been part of it) but as a means to an end: we would be his living, sentient robots acquiring his new knowledge. It would all be getting stored in an infinitely-growing data warehouse which he would be able to access at any time and instantaneously. Again, though, the idea that God would be getting angry at our sinful behavior is still just as humorous and ridiculous, but this time because he really doesn't need to care about it. In fact, our being sinful probably leads to a much greater increase in the knowledge God acquires through us. If we all led perfectly sinless lives, there wouldn't be much happening.

There are two things that support this idea. The first is the theory of infinite parallel universes, with new universes constantly branching off every time a new fork in the road gets created (such as rolling dice, for example). This theory is backed by the latest mathematical research, which almost requires it in order to explain such things as quantum physics.

The second support is that many people who have come back from near-death experiences report not only going over to the other side and seeing their already-dead relatives, but having a life review using a 3D hologram-like machine. These people relate that every little detail of their lives is replayed to them, and they relate experiencing their own feelings again PLUS the feelings of everyone they affected. This jives with the idea that God is infinitely acquiring knowledge through the worlds and the intelligent species he creates.

And if God did indeed create us and everything around us, he could have created Pi with all its complexity to show us that this very idea of infinity CAN exist, not as an absolute, but as never-endingness.

[Garland Best]

Infinity is a rigorously defined mathematical object."

Infinities and infinite series are ... weird. They lead to all sorts of contradictions. As a physicist I hate infinities. As a mathematician, I find them fascinating.

Take the infinite series S = 1 - 1 + 1 - 1 +1 - 1 + 1 ... What does S equal?

If this was a finite series, then the answer would be either zero or one, depending on what term you ended on. But it doesn't end.
I can "prove" that the series equals 1, or that it equals 0 or even that it equals 1/2.

Even weirder, if you accept my proof that the series equals 1/2 (Which in one viewpoint seems logical), I can go on to prove that the series 1 + 2 + 3 + ... equals -1/12!

Strange but true!

[Stephen Humphreys]

When I encounter things like that, Godel's Incompleteness Theorem comes to mind: https://en.wikipedia.org/wiki/G%C3%B...eness_theorems

In mathematics you can't avoid paradoxes, and many of them involve infinity.

[Dilip Panjwani]

And that is why I say that infinity is a flawed concept...at every universal 'black hole', space-time as it existed since the previous universal 'big bang' simply disappears, and the space-time which begins at the next big bang has nothing to do with the previous space-time...

[Ed Seedhouse]

And that is why I say that infinity is a flawed concept...at every universal 'black hole', space-time as it existed since the previous universal 'big bang' simply disappears, and the space-time which begins at the next big bang has nothing to do with the previous space-time...

Lots of concepts involve paradoxes. That doesn't make them flawed. Mathematics can deal just fine with infinities. In fact if you outlaw infinities you also outlaw motion via Zeno's paradox. This is only solved by the fact that math allows you to take the sum of an infinite series. Outlaw infinities and you are left with a proof that motion is impossible.

Before you go saying that some mathematical concept is "flawed" you might best get yourself educated as to what these concepts are actually about.

Also, if you wish to eliminate infinities, please tell me what the largest integer is...

[Peter McKillop]

Still beating that dead horse, eh Fred?

Infinity is a rigorously defined mathematical object. Mathematical objects do not exist in the physical world but yet somehow strangely they allow us to predict future events in that physical world with astounding accuracy. I think I will ignore the "truth" of which you speak though, since it isn't a truth at all, but meaningless mumbling "full of sound and fury, signifying nothing."

Good old Eddie Snidehouse!! Always ready with the mean-spirited, pedantic put-down.

[Ed Seedhouse]

Good old Eddie Snidehouse!! Always ready with the mean-spirited, pedantic put-down.

Ah, now calling me names proves me wrong! Must be a Drumpf supporter.

[Peter McKillop]

Ah, now calling me names proves me wrong! Must be a Drumpf supporter.

I wouldn't mind temporarily supporting Trump if I could be the trapdoor in a gallows.

[Aris Marghetis]

I wouldn't mind temporarily supporting Trump if I could be the trapdoor in a gallows.

I love such dark brilliance, thanks!

[Garland Best]

And that is why I say that infinity is a flawed concept...at every universal 'black hole', space-time as it existed since the previous universal 'big bang' simply disappears, and the space-time which begins at the next big bang has nothing to do with the previous space-time...

Ok, once you start talking about "universal 'black holes'" and previous "universal 'big bang'" you are going off into metaphysics on stuff with no experimental or observation basis, whereas before we are talking about mathematics, a system of absolute logic.

[Bob Armstrong]

My humble observation about this thread (And I am quite interested) - chess players are really missing OTB!!

Bob A

[Dilip Panjwani]

mathematics, a system of absolute logic.

O I love mathematics.
Unfortunately, the logic seems to break down when dealing with the concept of infinity...