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The Infinity Illusion: New Scientist 17.08.2013.

Over 40 years ago I had a long discussion with a maths teacher about infinity. It culminated in his conceding that the series of whole numbers, although apparently unbounded in both directions, was not an example of true infinity. Now, in 2013, more than 40 years on, could the scientific/mathematical community be moving in that direction? Imagine my elation when I saw, in the New Scientist an article suggesting that some physicists were trying to remove infinity from scientific – and even mathematical – calculations.

Max Tegmark, it seems, regards infinity as “…the ultimate untested assumption.” He says: “All of our problems with inflation and the measure problem come immediately from our assumption of the infinite.”

This must raise the question: How can we test for infinity? Surely such a test would require an infinite amount of information.

Later in the article we are told that “The largest number of informational bits a universe of our size can hold is 10^122.”

Nobel laureate, David Wineland, says: “Certainly we need nothing like that number of bits to record the outcome of experiments.” Is he saying that experimental science has no need for infinity? The article points out that “…even the best device will not measure with infinite accuracy….”.

Raphael Bousso says: “I don’t think anyone likes infinity. It’s not the outcome of any experiment.”

Mathematician Norman Wildberger says of “potential” infinity: “This type of infinity allows us to add 1 to any number without fear of hitting the end of the number line, but is never actually reached itself. That is a long way from accepting “actual” infinity – one that has already been reached and conveniently packaged as a mathematical entity we can manipulate in equations.”

I doubt that Wildberger is, here, criticising Cantor who appears to have achieved precisely that “packaging” in set theory. However, the fact remains that Cantor’s infinities are “mathematical” infinities, and run into problems with “absolute” infinity”.

“For the past decade he [Wildberger] has been working on a new, infinity-free of trigonometry and Euclidian geometry.” He is working to counter the fact that angles are related, via circles, to pi, with its endless digits following the decimal point. I lack the maths to evaluate Wildberger’s work, but Doron Zeilberger say of it: “Everything is made completely rational. It’s a beautiful approach.”

If Wildberger’s approach is revolutionary, surely, Zeilberger’s must be calculated to set the cat among the pigeons.

Zeilberger, it seems, wants, not only to get rid of infinity; he “wants to dispose of potential infinity as well.” Zeilberger believes there is a largest number. “Start at 1 and just keep on counting and eventually you will hit a number you cannot exceed – a kind of speed of light for mathematics.” Zeilberger’s answer to the question as to what happens if you add 1 to this number is that it acts like a computer which has a maximum number it can process. If you add 1 to it, it either gives you an “error” message, or resets the number to zero. Apparently, Zeilberger favours the latter option.

My own feeling about this is that it draws too heavily on the analogy between a computer and the Universe. Who, or what, would generate the “error” message, or reset the number? Zeilberger’s assertion that this largest number is “…so big you could never reach it” seems a bit of a cop out. Consider what he has actually said: “…eventually you will hit a number you cannot exceed” and “…you could never reach it”.

Tegmark points out that “the calculations and simulations that physicists use to check a theory against the hard facts of the world can all be done on a finite computer. “That” he says “already shows that we don’t need the infinite for anything we’re doing.” He continues: “There’s absolutely no evidence whatsoever that nature is doing it any differently, that nature needs to process an infinite amount of information.”

Physicist Seth Lloyd points out that “We have no evidence that the universe behaves as though it were a classical computer, and plenty of evidence that it behaves like a quantum computer.” This reintroduces infinity, because: “If you really wanted to specify the full state of one qubit, it would require an infinite amount of information.”

Obviously, we do not have an infinite amount of anything at our disposal, so the problem seems academic.
Set theorist, Hugh Woodin suggests separating the two issues of physical and mathematical infinities. He says: “It may well be that physics is completely finite, but in that case, our conception of set theory represents the discovery of a truth that is somehow far beyond the physical universe.”

Obviously there is more in this article than I have mentioned here, but hopefully others will read it and raise different points. I have added a few of my own thoughts above, but it would be good to have some other people’s input before risking swamping the subject with my own crackpottery.

Then, I ask, "What is "true" infinity?"

Perhaps it is what I call nothing to everything, 0, to O. That is, G~0~D to GOD, eh?

Bill-S, then you say, "the series of whole numbers, although apparently unbounded in both directions, was not an example of true infinity."

Now, in 2013, more than 40 years on, could the scientific/mathematical community be moving in that direction?

Imagine my elation when I saw, in the New Scientist an article suggesting that some physicists were trying to remove infinity from scientific – and even mathematical – calculations.

Max Tegmark, it seems, regards infinity as “… the ultimate untested assumption.”

Then I say, "Tegmark, go ahead and Test G~0~D to GOD, and see what happens."

He says: “All of our problems with inflation and the measure problem come immediately from our assumption of the infinite.”

OK, Teg: "What do you assume there is?"

This must raise the question: How can we test for infinity? Surely such a test would require an infinite amount of information.

"Right on BillS! Of course it would."

IMO, GOD is just that--Omniscience. In other words, "an infinite amount of information". Also included is an infinite amount of power (Omnipotence) and an infinite amount of presence (Omnipresence). ... [more]

The following also sounds god-like to me, Bill S :

In the same way that is very difficult for us, limited as we are by 4D spacetime, to think about infinity without using terms that are essentially tied to space and time, so it is difficult to express the difference between that which is infinite and that which is unbounded, but finite. I use the term “true” infinity in an attempt to make that distinction.

I suspect that my definition of "cosmos" and your definition of "god" might have a lot in common; but I'm not at all sure that a detailed comparison would lend itself to the advancement of this thread in its intended direction.

Bill-S, you say,Not to worry! As a relativist, I can live with uncertainties--yours, mine et al.

Also, as long as it is okay for me to keep on exploring--that is, with the help of evidence-based science, for new knowledge--I do not have to know everything--what absolutists and theocrats call The Truth. Also, I do not have to be right about everything! This is why I like process philosophy and theology--the kind I read about in the writings of Alfred North Whitehead and the Rev. Charles Hartshorne, the popularizer of Whitehead's work--
https://www.google.ca/search?q=alfred+north+whitehead&ie=utf-8&oe=utf-8&rls=org.mageia:en-US:official&client=firefox-a&gws_rd=cr

http://www-groups.dcs.st-and.ac.uk/history/Mathematicians/Whitehead.html
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BTW, what IS the "intended direction" of the question posed by this thread?

There is an obvious answer Bill S and it obeys all the normal conventions.

There is no infinity because no one has ever been able to show or prove an infinity.

You don't believe pigs can fly because you have never seen one fly so why would you believe in literal infinities ... personally I am backing the flying pig as more likely and that's about the same odds as an intelligent post from PreEarth.

You saw the Big Bang?

Anyway, who says I don't believe pigs can fly?

I for one believe in infinity, but even I'm not sure in what context.

It was a bout of psychedelics, and losing my ego, or id, that manifested this view. I have the notion I experienced it (infinity), but I cannot fully fathom the experience, nor do I wish to go there again, until my body kicks the bucket and I have no use for a conscience.

Sounds like a lot of religious hooey to most, I know. But just like a yokel saying Jesus or Aliens came to him in the night, no amount of convincing will make him say it didn't happen.

It was a frightening thing to wake up in a body again, no longer part of everything, allowed to have my own thought, and my own experiences once again. Versus having all thought and experience at once for what seemed like eternity.

Sure gave me a positive outlook on life from there on out though. Our bodies are great at protecting us from our own minds.

Neo, your comment reminds me of this:

There was a little kid,
Who had a little id,
Right in the middle of his ego.
When he was good,
'twas because he was understood;
But when he was bad, 'twas his libido.
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BTW 1, no fees are charged for Pneuma-analysis and pneumatherapy (hypnosis without the hocus-pocus)--Shy? Just send a PM), anyone.

However, if you feel that this service provides a valuable one: You may send a tax-exempt donation to www.flfcanada.com eh!
BTW 2, is hypnosis nothing but hocus-pocus? Or is it--as I BELIEVE it is--a evidence-based (science-based) fact?

I see the Reverend is still advertising the Reverend...

Anyone who is unprepared to have his/her thread used to prostitute someone else's pet idea, however off topic, or is fazed by having her/his thread debased by petty sniping comments, should not post on SAGG.

S.O.P. for SAGG then. You knew the job was dangerous when you took it.

Max Tegmark says:

"When quantum mechanics was discovered,we realised that classical mechanics was just an approximation. I think another revolution is going to take place, and we'll see that continuous quantum mechanics is itself just an approximation to some deeper theory, which is totally finite."

If a physicist at MIT is seriously making a statement like this, should it not stir some scientific thoughts on a science discussion forum?

There is more than my "pet subject", more than the spelling of God, more than one poster's need to snipe at another, involved here.

Of course, it takes more than one physicist's early suspicions to cause a revolution, but David Hilbert's assertion: "No one shall dispel us from the paradise Cantor has created" could begin to look a little insecure.

Lawrence Krauss argues that “nothingness” is infinite, and that everything can come from that nothingness. This seems very much like an argument for infinity. This is especially so as he also says: “By nothing, I do not mean nothing……”.

Spoken like a g0Od-like process philosopher/theologian unitheist. For those who like big words, make that 'panENtheist'.

I did say see or prove ... doubt you can prove pigs could fly so you would have to see it

Anyhow personally I don't think it was a big bang more like a quiet whimper .. "in space no one can hear you scream"

Nothingness is a ridiculous concept how does one contain nothingness and what are it's boundaries?

Admit it: “Big Bang” has a much more majestic ring to it, notwithstanding the fact that it was originally intended as an insult, than does “Small Silence”, or “Weenie Whimper”.