Sound to me like the proponents of this argument should read Husserl. He seems to demonstrate pretty clearly that the only way to ascribe the status of 'timeless, necessary truths' to mathematics is to confine math to itself. Attempts to relate it to material reality operate on another, lower and questionable level.

By  Chuckie K, at Sunday, November 21, 2010 4:28:00 pm  

Hmm. If material reality regularly and predictably behaves in ways that conform to Mathematics, except when it doesn't, and if Mathematics is a domain of timeless necessary truth, then... material reality is regularly and predictably governed by timeless necessary truths, except when it isn't.

I think the AIG Busted guy would deny the existence of "except when it doesn't" cases, but I'm not sure on what grounds.

By  Phil, at Sunday, November 21, 2010 5:08:00 pm  

I think what they're saying is that to exist as an implication of a TOE is to exist, full stop. The universe is a mathematical object, which from the inside is material reality.

By  Ken, at Sunday, November 21, 2010 8:35:00 pm  

I found this pretty late at night and shall think about the hypothesis. I have read a bit about the Mathematical Universe idea, namely a paper by cosmologist Max Tegmark. I'm almost certain that Spinoza would reject Tegmark's version.

More to the point, the formulation you give is riddled with problems. For starters, there is no consencus about what it means to call an equation or a system of equations 'necessary.' So nobody knows what a necessary
system of physically applied equations is. My own opinion
is that the notion is empty. More tomorrow, I hope.

By  George Berger, at Monday, November 22, 2010 1:06:00 am  

I think what they're saying is that to exist as an implication of a TOE is to exist, full stop.

In that case they've reinvented the ontological proof for the existence of God, which probably wasn't their intention. But they've got a more fundamental problem. From AIG Busted:

Imagine that you "invent" your own universe. You write down the physical laws of your imaginary universe, and you work out the equations* to figure out how it would evolve over time. Eventually your equations** show that your universe develops planets and life at some point in its history. Further equations*** prove that intelligent, humanoid creatures would evolve in this universe. Working even more equations**** reveals that a pair of these humanoids are having a conversation about their universe, wondering why it exists.

I'll let you have the equations* that set up the imaginary universe, and even (at a stretch) the equations** that show there's something called 'life' in this universe. But the third and fourth sets of equations are unimaginable. This is part of the point of my previous comment: if we knew that everything in the universe functioned with mathematical regularity, then we'd know that the universe instantiated a mathematical model. But we don't. We can assume it does, but then we're assuming a good part of our conclusion. (And it's no use saying that this is an imaginary scenario - I could just as easily imagine that I could set up an imaginary universe using prayers or spells.)

By  Phil, at Monday, November 22, 2010 9:11:00 am  

Mind is biology. Biology is chemistry. Chemistry is physics. Physics being math. Mind perceives math, thus the universe exists physically. Erase the "baggage" and all that's left is math.

More here, 'The mathematical universe: the map that is the territory': http://lesswrong.com/lw/1zt/the_map_that_is_the_territory

By  Alexander Kruel, at Monday, November 22, 2010 11:38:00 am  

Some interesting stuff:

"There is something almost mystical about this: any sequence of digits, for example, randomly conceived in the mind, must correspond to a sequence of digits in the unknowable expansion of Pi (in that realm over 10^1000 digits into the expansion), based on the laws of probability." — Garth Kroeker, Irrational Numbers Metaphor

The Unreasonable Effectiveness of Mathematics http://www-lecb.ncifcrf.gov/~toms/Hamming.unreasonable.html

The Unreasonable Effectiveness of Mathematics in the Natural Sciences http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

Is mathematics invented or discovered? http://www.thebigquestions.com/2010/01/12/jellyfish-math/

Nature by Numbers http://www.vimeo.com/9953368

The Universes of Max Tegmark http://space.mit.edu/home/tegmark/home.html

By  Alexander Kruel, at Monday, November 22, 2010 12:21:00 pm  

Hmmm. One of the (many) problems with this to my mind is:

1) I observe the universe
2) I work out a mathematical model that describes my observations
3) I then turn everything on its head by deciding, auite inexplicably, that the universe abides by the mathematical model (rather than the other way round)
4) I form a belief (similar to a 'religious belief', rather than a 'factual belief') that my model predicts that I exist, without any causal link being provable.

As a previous poster said, it's the ontological argument all over again, and doesn't prove a thing.

By  Anonymous, at Monday, November 22, 2010 12:57:00 pm  

Here is a sense of 'necessary' that I would accept. Suppose that purely philosophical principles guarantee that there must be exactly one universe, and that everything in it can be truly described by exactly one set of equations. Then I'd call that set necessary, and each equation in it derivatively necessary. This would appeal to Spinoza, who argued philosophically for the first clause of my second sentence, and whose faith in science would be captured by the rest. It is a mathematical naturalism but not Tegmark's hypothesis.

By  George Berger, at Monday, November 22, 2010 1:19:00 pm  

@Ken--Your statement shows how far the Hypothesis goes beyond a traditional philosophical notion. Russell, Schlick, Weyl, and Eddington held that almost all we can know about reality is its mathematical/logical structure. For we have no sensory insight into most of matter (whatever that means), but we can develop testable structural theories. Some are provisionally confirmed, others are not. Russell & Schlick then argued that introspection of our sensations is a second mode of knowing (Russell) or describing (Schlick) our material brains but nothing else. The Hypothesis rejects this argument.

By  George Berger, at Tuesday, November 23, 2010 9:56:00 am  

I didn't understand TOE at all until I read Egan's Distress,but Diaspora is the book I can't stop reading over and over, and every time Kozuch Theory leaves me pondering for hours.

By  David Page, at Tuesday, November 23, 2010 5:14:00 pm  

David - I must check out Distress, but the canonical Egan for this particular stuff is the short story 'Dust' and the novel Permutation City.

Phil: I think the AIG Busted guy would deny the existence of "except when it doesn't" cases, but I'm not sure on what grounds.

I'm not sure on what grounds you affirm them! Or why you don't think that everything in the universe does 'function with mathematical regularity'. Nor do I understand why you think the 'further equations' are unimaginable. These all look to me like straightforward consequences of physicalism and determinism, and these are as well supported as any generalization from known facts can be, in that we have never, ever found a single exception.

By  Ken, at Tuesday, November 23, 2010 9:23:00 pm  

@Ken--You are right about Permutation City, It ia an attempt to see what lives would feel like and seem like "to" purely virtual beings that are mathematical structures. Tegmark (the only person I've read on the Hypothesis) refers to this Egan book in almost everything he has written. His intent is not clear to me, but the above is my construal. The book is so demanding that I plan to re-read it.

By  George Berger, at Wednesday, November 24, 2010 12:07:00 am  

@Ken - I had some difficulty with Permutation City ,but then iv'e only read it once and usually need two or more reads to fully grasp plot and premise,will have to read Dust though thx for the pointer..

By  David Page, at Saturday, November 27, 2010 10:38:00 am  

I was being a bit frivolous when I used the theological term 'necessary being', which may have been a bit misleading. I don't think the people I cite are recreating something like the ontological argument.

In fact - and this is strictly my own take, I don't know if anyone else has put this forward - Tegmark's mathematical universe actually excludes, if not the existence of God, at least divine intervention. Here's how.

Suppose, as Tegmark does, that you are in a universe which exists in (handwave) 'mathematical space', and that everything that happens in it is a logical consequence of the fundamental equations of the TOE. so what is from within the universe experienced as a history in time with cause-and-effect is (from outside) a timeless mathematical structure of logical consequences: IF this THEN that, on and on and on. Causation is implication, if you like.

Now, one of the standard arguments against - or at least expressions of incredulity about - miracles and other supposed divine interventions is 'God can't break his own rules'. This has always struck me as a very weak argument, and I was surprised to find that Spinoza seems to argue for something like it. The Christian materialist Donald Mackie countered it in his book The Clockwork Image by drawing the analogy of a sim (though he didn't use that exact expression, as it wasn't around when he wrote). It's perfectly possible for the programmer to create a sim with self-consistent rules, which from a POV within the sim seem to indicate a completely closed causal system and (for that matter) a history going back to the Big Bang or whatever, whereas in fact the programmer set the whole thing up this morning. And of course the programmer can (in principle) intervene in the sim any time she or he chooses, without in any way being inconsistent. Hence Mackie had no problem in principle with miracles (or with creation of apparent age, I suspect).

But the mathematical universe is not a sim. To return to the theological question: all but a handful of theologians would agree that omnipotence does not mean that the omnipotent being can perform logical impossibilities. As C. S. Lewis put it, a meaningless sentence does not acquire meaning by preceding it with the words 'God can' or 'Can God ... ?'

But if not even God can create four-sided triangle, not even God can stop a logical implication from following from its premisses. So not even God can intervene in a mathematical universe. This is what I think Spinoza may have been getting at.

I trust this clears up any remaining confusion on the matter.

By  Ken, at Saturday, November 27, 2010 4:55:00 pm  

@Ken

http://lesswrong.com/lw/uk/beyond_the_reach_of_god/

By  Alexander Kruel, at Saturday, November 27, 2010 6:59:00 pm  

XiXiDu: that's an interesting article, and very much to the point. (But as fine person you are, couldn't you at least embed the link to it, and save us all a second?)

My main disagreement with it is this:

The obvious example of a horror so great that God cannot tolerate it, is death - true death, mind-annihilation. I don't think that even Buddhism allows that. So long as there is a God in the classic sense - full-blown, ontologically fundamental, the God - we can rest assured that no sufficiently awful event will ever, ever happen. There is no soul anywhere that need fear true annihilation; God will prevent it.

The possibility of true annihilation, mind-annihilation, is the best good news humanity ever got, and may the name of our saviour Epicurus be forever blessed for proclaiming it! And the idea that there is a God who will prevent that and keep some (most?) minds conscious in eternal agony is without a doubt the most horrifying idea that has ever occurred to humanity.

For more on how I feel about this, see my short SF story: A Tulip for Lucretius.

By  Ken, at Saturday, November 27, 2010 8:26:00 pm  

Ken. You touch on one of the main open issues with the Hypothesis. Tegmark admits that he can only try to point in the right direction. He holds that in a structure described by the correct TOE there are no intial conditions. This is a difficult idea that I cannot explicate. To try though, note that the relations described by the TOE are not logical relations, just as the relations between the sides of a square are not logical relations but items described by geometrical axioms that can be consistently denied and hence are mathematical but not logical.

If this is right, then by analogy the TOE is a theory whose subject-matter is not logic, but the class of its models. These are Tegmark's structures. In them, causation might be a species of relation, but the latter are not logical relations like implication. So I think it is wrong to say, "causation is implication." More below.

By  George Berger, at Saturday, November 27, 2010 8:39:00 pm  

Now, if one admits an analogue to such causation in a timeless mathematical structure (as I think Tegmark does), then what replaces our normal physical notion of a temporally initial condition? Tegmark's answer is, "Nothing." A structure's conscious inhabitants might describe it in temporal terms (need they?). They mistake certain sets of abstract, atemporal, structural items for groups of temporal physical events whose occurances are intial causal conditions for other such groups. Ontologically they are wrong but (if they lack the Hypothesis) do not know it. They misdescribe their atemporal structure sub speciae temporalis, as Spinoza might say. Many physicists and philosophers now reject the idea that "time flows," and so does Tegmark. They owe us a detailed account of this misperception. J. McT. E. McTaggart's brilliant attempt made this clear before 1910. Tegmark (on his own, I guess) sees that this is a problem about (among other things) initial conditions and admits ignorance. Nobody knows how to accurately formulate the issue, let alone provide a satisfactory account.

By  George Berger, at Saturday, November 27, 2010 9:23:00 pm  

@Ken

I sent you an e-mail titled 'Re: A Tulip for Lucretius'. It includes something I'd rather not link to in public. Interested in your opinion if you have enough time. No worries if not.

Thanks for your great fiction, the short-story was an awesome read.

By  Alexander Kruel, at Sunday, November 28, 2010 3:04:00 pm  

As long as the answer is '42', it all makes sense.
By the way, just learned about you in an old Vernor Vinge reference, ordered all 4 of your Fall revolution books, and have nearly finished all of them and am on what I am guessing is the
4th, 'The Sky Road'.
Wow. I am completely impressed and look forward to reading the rest of your work over here in the heart of the Empire, Texas.
best regards and good luck with that white stuff falling on you.

By  Anonymous, at Monday, November 29, 2010 5:00:00 pm  

Many thanks, Anon.

By  Ken, at Monday, November 29, 2010 5:20:00 pm  

George: re time - you got me on that one.

By  Ken, at Monday, November 29, 2010 5:21:00 pm  

straightforward consequences of physicalism and determinism, and these are as well supported as any generalization from known facts can be

Once a Calvinist, eh?

PS The long delay before this comment and the glib flippancy of the comment itself are in fact related, inasmuch as I've been trying to formulate something better for the last week. This morning I gave up, or gave in.

By  Phil, at Tuesday, November 30, 2010 7:58:00 am  

Phil - yes. You've hit the nail on the head.

I must admit that reading Lorraine Boettner's The Reformed Doctrine of Predestination at the age of fourteen or so left its mark. But what impressed me most in the book wasn't the theology, which passed me by completely because of my total depravity, but the argument that Calvinism was the only (Christian) doctrine compatible with physics. A close second was Boettner's post-millenarian contention that the future of humanity was probably vaster and longer and better than our wildest dreams, and many many times greater than the gloomy dispensationalist notion that it was all about to end Real Soon Now could accommodate. This was very reassuring to a kid who'd just read the Foundation trilogy, which as you'll recall opens in about 12,000 A.D.

Some time about 1987 A.D. I discussed determinism with Francis Mulhearn in our Islington local, and we were both amused to discover that as a result of our respective religious educations, neither of us could get our heads around the other's take on the issue. To Francis, free will seemed just intuitively obvious and determinism unimaginable, whereas to me ...

By  Ken, at Tuesday, November 30, 2010 8:24:00 pm