G-d and Pi

[ZackMartin]

While PI has an infinite non-repeating decimal expansion, it can be written in a finite form - there are many infinite series that converge to PI for which we can give a finite formula to calculate each element of the series.

PI, while a transcendental irrational number, is still a computable number. Wouldn't an uncomputable number, such as a Chaitin's constant, be a better analogy for God? For an uncomputable number, no such finite form can be provided, so in a sense uncomputable numbers are "more" "infinite" than computable ones are.

Uncomputable numbers - we can prove they exist, but we can also prove we can't know what they are - a bit like God maybe?

But while Chaitin's constants are uncomputable numbers, they are still definable numbers - wouldn't an undefinable number be an even better analogy for God? Undefinable numbers, we can prove they exist, but we can't even talk about them as individuals. The undefinable numbers are so much more grander than the definable numbers, since not only can we not talk about them as individuals, there are infinitely more of them than there are of the definable numbers

To be a bit more technically accurate: Numbers that are not first order definable we cannot talk about with first order logic, but we can talk about them with second order logic; but then there are numbers we can't talk about with second order logic either. But we can also talk about numbers definable by mathematical texts (using any natural language and any formal notation which might be devised), although unlike "nth order definability", this is a notion impossible to formalise. Since the set of all possible finite mathematical texts is countable, whereas the set of all reals is uncountable, it follows that almost all real numbers cannot be defined uniquely by any mathematical text. Such numbers are truly beyond all human knowledge. The vast majority of all real numbers are so beyond human knowledge it is impossible for us to even discuss them, except as one gigantic unimaginably infinite amorphous mass. Could this be a sign of God's presence in mathematics? Could this infinity of inherently unknowable numbers somehow be God?

Then again, as much as I enjoy mathematics, and even will dabble in a bit of Cantorian mathematical mysticism like the above (Georg Cantor once described the transfinite hierarchies as heaven - heaven for pure mathematicians, that is), God is so much greater than any mere number could ever be. So other times I think analogising God to a number is slightly silly. And then I remember that I am an ultrafinitist, and a believer in a finite deity, so I don't believe in any of this stuff anyway But even while not believing in it, I can understand at least in part why some mathematicians find these ideas so alluring and seductive.

[JimL]

To nit-pick, the presence of matter, distorting space in its vicinity, should change pi.

I reflect that there's matter even in the vacuum, due to the quantum flux, so it should be the case that pi is never pi anywhere.

Anyone any idea what happens to pi at and below the Planck length (1.616199×10⁻³⁵ metres)?

David

It probably gets even more irrational.

[lao tzu]

To nit-pick, the presence of matter, distorting space in its vicinity, should change pi.

Pi does not measure any physical feature of any universe.

[David Hayward]

Pi does not measure any physical feature of any universe.

Just as well.

David

[Tanakh Keeper]

I think he'd make a great atheist if he's not already.

I'd always thought that Judaism is closer to the beliefs of atheists than to christians.

Pi's {sic} existence comes before the universe, and has no conceivable ending.

That might make Gerry happy.

[lao tzu]

"Sic" is used following uncorrected text that contains an error, TK. When amending for clarity, enclose in brackets:

[Pi's] existence ...

[headheart]

I'd always thought that Judaism is closer to the beliefs of atheists than to christians.

I think it is in some sense and especially based on my experience of interacting in the music industry. I think that the idea of a religious Jew varies from person to person. Most don't continue holding to their religion in much the same way a religious Christian and other would once they get done with a few years at University some even sooner, some never get bitten by the madness of religion. I mean over the years I have had a rich and varied experience of life and so far I think that most wear the cloak of religion as a heavy disguise.


Heavy Disguise by Strawbs

Crowded afternoon and there's not enough room in the city today
The people assembled to hear what resembled evangelists say
Some came just to see them for a laugh
Others to be free
Fools must pretend to be wise
We've a faith that we use as a heavy disguise.

Tears from the crowd with men crying aloud or just ringing their hands
The love in their hearts at this joining of people from far away lands
I'd so many questions I could ask
I wanted to be free
Fools must pretend to be wise
We've a faith that we use as a heavy disguise.

Cheers from the crowd for a much-loved constituent lately arrived
Here's to the soul of the man who takes toll for just staying alive
Can't ignore the feeling in the air
Glad that I was there
Fools must pretend to be wise
We've a faith that we use as a heavy disguise.

Evening drew on with a change of opinion from left wing and right
And North accused South who were left little doubt that they needed to fight
I cannot begin to understand
The suffering tonight
Fools must pretend to be wise
We've a faith that we use as a heavy disguise.

Peace,
Eric