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28 June 2010

On the nature of reality itself

It's a question we all ask ourselves from time to time: "Why is there anything at all?" What is the nature of reality? Why does our universe even exist in the first place?

A difficult and vexing one - it is perhaps not surprising that many people have plumped for the notion that there is a big old goddy thing who designed it all, and we're grubbing out its eternal plan. As anyone with half a brain immediately recognises, however, this does not address the question - it only moves it back a level, because then we're entitled to ask: "Well, then, why does GOD exist in the first place?"

Some theologians (a term I equate with charlatans, but hey) regard god as a "necessary being", in that there can't NOT be a god. I will not rehearse the arguments here (maybe some day), but suffice it to say that this is simply silly, and simply trying to define one's way around the problem. It's like saying there is a necessarily perfect cabbage from which all other cabbages derive their cabbageness. Forget it - it is not a fruitful line of enquiry.

So let's try another tack. What can exist without the need for gods? Well, mathematics can. God cannot change Pi - if anything, any hypothetical god must be constrained by Pi. There is a *true* answer for the gazillionth digit of Pi, and no way a god can know it except by calculating it.

And similarly, no way to know what the future holds, other than by calculating it, and comparing it against other contrasting options. BUT, if the universe is mathematical (as is very seriously being suggested by some, including me), there is no need for this silliness - god gets cancelled out of the equation altogether.

Confused? Yeah OK, you're forgiven. Try this paper by Max Tegmark, and leave any questions below in the comments.


  1. hey shane, if you say it often enough, you'll start really believing it ;-) hope you're well!

  2. Pi? Hmmmmmmmmm, pi.

  3. My very, very, long holidays have started, so I'll be able to spend lots and lots of my many many free hours considering this paper...

    Gosh it's tough being a teacher. Hope I don't sound like I'm gloating!!!

  4. Sorry about the Stephen Meyer recommendation on W&T...couldn't resist.

    I thought your comeback was very good, mind! Check the reviews on Pharyngula!

  5. Graham, I like to make sure that people are directed to another source of sanity, quite apart from supping at the delicious tit-bits that drop from my table of plenty :-)

  6. Where did you find that paper? Are you familiar with the author? How was the paper received? (did it get published)

    It looks fascinating. I am sure 90% is over my head, but I will give it a read. I have read Wolfram and a few others that may help me glean from that 10%. I must say, prior to reading, I am of the cellular automaton school, so I am curious how this paper affects my naive, self-deceiving-non-physicist/mathematician, lay opinion. ;-)

    Thank you (back after I read it).

  7. Tegmark has also had articles in New Scientist and Scientific American. He is a very well regarded cosmologist. This article hasn't been published as such, but then it's a speculative piece. A hypothesis. Since this article I think he has perhaps wandered away from the concept towards a slightly weirder view which I don't quite understand, where all mathematical objects *are* physical. I'm not sure that's quite the right way round.

    This is interesting territory...

  8. Well, to pick up from elsewhere...

    The problem I have with Tegmark's proposal is that I think of mathematics as derived from the logical/mathematical modes of thinking that are how our brains think about the world, not as existing in of themselves. Pi doesn't exist, as such, it only exists in our mind.

    The core of our disagreement seems to be that I see reality as primary over its description. I consider reality to comprise the model (http://en.wikipedia.org/wiki/Model_theory) that we then describe through mathematics/logic. The same reality can be modeled differently - a spherical surface can be described both through Euclidean 3D and non-Euclidean 2D geometry.

    Given this understanding, the MUH seems implausible. There is no reason the model (reality) will conform precisely to the full range of possibilities allowed by the mental faculties evolution has wrought in us. It is far more likely our faculties are overly-flexible, presenting us with "possibilities" that don't really exist physically so as to allow greater simplicity, flexibility, and applicability in dealing with everyday-life issues.


  9. Shalom, Yair, and thanks for visiting my little blogarooney :-)

    I hope I have not misled - I am not saying that reality is encompassed by any particular model we make of it, but that there are mathematical "truths" that our brains have (whoopee!) evolved to grasp, or at least be *capable* of grasping, and these truths transcend the local conditions of our wee universe.

    To be specific, I think any sentient beings in any universe of *any* spacetime geometry (even if they HAVE spacetime!) will come up with precisely the same value of Pi as we have, because Pi is not a property of the universe - it transcends anything that could be called a universe; the fact that certain rules of our universe converge on Pi is because the mathematics comes first.

    The laws of addition and multiplication etc hold true no matter what the universal architecture. Indeed, we are not even limited by *our* universe's characteristics in imagining how other frameworks may operate.

    When we are constructing a model of how the (this) universe operates, we are nearly always simplifying things - most commonly our models (which are mathematical entities in their own rights) are higher order approximations of what is "really" going on, but what I'm suggesting is that there really is a bottom level at which we hit the "Theory of Everything", and that will be mathematical (and quite possibly unattainable).

    I'm conscious that I am perhaps not explaining this very well!


  10. Seemed like a good explanation to me.

  11. Three points on your last post, Shane -

    First, I didn't want to bring it up but I suspect Godel puts an end to a true TOE. Any prospective TOE will be a finite axiomatic system, and any calculations we make with it will be finite derivations. Godel's incompleteness theorem implies there would be sentences in the theory - descriptions of physical truths - that will be true in the theory (and presumably the world) but not derivable from within the theory. In other words, no theory can be a theory of EVERYTHING. This perhaps won't matter in practice in any perceptible way, so let's move on.

    Second - Certainly the TOE will be mathematical. This, to me, ain't saying much - it's just saying it will be a coherent description. This is not the MUH, however. The MUH says that the right description of reality is not some particular description/TOE, but specifically the most general description we can think of. The question isn't whether the TOE will be mathematical, but rather whether it will be mathematics.

    Third - How did our mathematical faculties evolve? I believe they evolved as they did due to the Boolean nature of classical physics. In other words they capture a feature of physical reality, an order and regularity that can be expressed mathematically - but not the mathematical object itself.

    Yes, the mathematical truths will hold true for any thing we'd want to call "intelligent" or "sentient". But that's not saying much. They still only hold in our minds and minds like ours. Mathematical truths don't hold in the world. They are informationally empty, carrying no information about reality itself. They are merely conceptual frames that reality may, or may not, fit into.

    A quantum sentience, if such a thing would be possible, would function very poorly with our logic, much like a macroscopic sentience that fails to apply classical logic would fail to succeed in our world (because it fails to capture the Boolean nature of classical/macroscopic reality).

    Ultimately, the sum total of all mathematical structures is a combinatorial construct of our logical intuitions. These capture truths about the nature of reality and information processing that, as Kant showed, are required for any intelligence. But there is no further requirement that this massive combinatorial construct will match the structure of reality itself. Only the basic intuitions need be true [and that too in a limited sense], not all their possible combinations.

    Let me end with a hypothetical - can you imagine that only a small world exists, where a single intelligent being is busy thinking? He can imagine alternate reality, but by assumption these do not exist in our hypothetical. Why can he imagine worlds that don't exist? Why can't we?

  12. I won't attempt to engage in mathematical argument - my maths isn't up to it... but it seems to this non-mathematician that יאיר רזק makes some great points, but I realise that my view won't have much validity for mathematicians since it's not expert. Then again how many of the readers and commenters on this blog are?... and I've no doubt they all feel they've an adequately informed opinion on the subject.

    Shane, your suggestion seems to be that Maths is the great uncaused cause or eternal entity, rather than God. Christians have long been ridiculed for maintaining God "just is." It's interesting, to me anyway, that this is the nature of the terminology that the primitive and "silly" Hebrew people of old had/were given to describe their God - their narrative reports regularly that He described himself with the term "I am." (eg 'Tell them I Am has sent you,' and 'I am who I am.'). Those who claim Jesus never claimed to be God in the NT, would seemed to have missed the significance of the multiple ways Jesus describes himself beginning with I AM...

    I find it particularly interesting to see you regard it as plausible that it's OK for a non-personal entity/set of laws such as maths to be "just is." Why should this be valid?

    Perhaps I need to go back to your source document to get an answer to why this is OK for maths but not for another kind of entity/framework ... Will I find the answer in there? And will it be in language that is accessible to a non-mathematician?

  13. Hi Slicer,
    I don't think you need to be overtly mathematical to grasp the MUH (Yair is pretty hot with the maths, incidentally - he comments on Common Sense Atheism ( http://commonsenseatheism.com ) from time to time, and I think he's very insightful. I don't agree with him on this issue though :-)
    Actually, the pedigree of the "groundedness of being" is not based in the Hebrew mythology, but in Greek philosophy, and for mathematics itself being that ground, the chief expositor of that was Plato. However, Plato had a rather different concept of what it meant for mathematical structures to "exist" than we have now, and certainly Platonic biology was *directly* arse-about, as we now know - we don't define a chicken by its relationship to some platonic "ideal chicken"; rather we classify all chickens together, and use *them* to derive the phenotypic range which we (semi-arbitrarily) label as "chickens".

    There is no doubt that mathematics "is" - the question, I suppose is whether it "*just* is", or whether mathematics itself needs a mind to "actualise" it. This, to me, is relatively easy - before humans were around, 2+2 was still 4; Pi was still 3.14159... - these are not arbitrary things, but as Roger Penrose points out, rather solid and objective things in a way that we find it tricky to get our heads around sometimes. Now maths cannot be grounded in a god, because if it *could*, the god could presumably set a value for constants such as Pi, yet we know that that is not possible. Pi is Pi whatever.
    But having a god as a ground of all being strikes me as deeply incoherent - how could it possibly have specific characteristics? It would not be possible for a god to be Yahweh and not Allah or Amun-Re or whatever, or to have a personality, because that would entail making decisions, presumably, yet a ground-god would not have to make decisions - just create new universes for any possible outcomes, a bit like the Everett formulation of quantum theory. So a ground-god would be no different from no god at all.

  14. The point about Pi sounds to me a bit like the schoolyard challenge "Can God make a hill taller than the grass which grows on it?" There are several potential valid answers to that, one of which is that it's a false construct - a play on words.

    I guess it's because I don't know enough about maths that I don't know whether or not that analogy holds for the Pi argument. (I accept that it may not).

    For the same reason I also don't know whether all mathematicians/cosmologists would agree that Pi must always have the same value beyond our observable horizon, or in a multiverse/infinitesimal number of parallel universes. Why is Pi different than other constants in this regard? Is it because a circle is a circle is a circle? (or a sphere is a sphere is a sphere?) Specifically why is its value being set at a fixed value a valid argument against the existence of God?

    I do know that the argument for multiple universes is driven, at least in part, from the Goldilocks observation - the acknowledged improbability of the fundamental constants in the universe being within the narrow and fortuitous ranges that they are and that they all need to be for the universe to exist at all - so the notion has arisen of this one being a "survivor" in a survival of the fittest of potential universes. (I don't discount that possibility but nor do I feel the "need" for it as an explanation as acutely perhaps as those who are of an atheistic disposition and who agree that the constants are finely tuned).

    I still haven't seen the argument laid out coherently why maths has capacity to exist without a cause. I think I get the notion of speculative processes relating to how the universe could 'pop' into existence via quantum behaviour - but I can't see a reason to join the dots between (i) mathematical logic existing before man's arrival on the scene and (ii) it always existing... any more than for rocks...

    Are those speculative quantum cosmological processes "created" by maths, or does the maths merely describe them?

    So.... I've more questions than attempts at answers.

    I guess I take some consolation (in the context of my inability to engage directly in mathematical proofs) from the observation that not all mathematicians agree... including with Penrose.

  15. @Slicer, yes, not everyone agrees with Penrose - I certainly don't agree with his notion of quantum consciousness (and neither does Max Tegmark!). But I do think he is on to something. Mathematical behaviour is actually completely independent of the setup of our universe. Our universe is a system that obeys certain mathematical principles, but those principles hold whether there is a universe there to obey them or not. A lot of people view the universe as a stage with lots of little actors in it, but in physics the universe is an integrated *system* - there is no part of it that is not fundamentally interconnected with the whole. Particles are not little billiard balls on a big table, and you can remove one or add one willy-nilly - the whole shebang is a big old interlocking system where the appearance/disappearance of virtual particles, vacuum point energy etc is all part of how it operates, and like any system, it can be represented mathematically (in principle), which makes it irrelevant whether there is a host system or not. I don't think this is really an issue for mathematicians - more for simple philosophy. But I think Tegmark is on to something.
    As for god changing Pi, no, it is not one of those silly logic arguments. There is a correct answer to what the sixty-zillionth digit of Pi (in base-10, say) is, but no real reason why from our (or god's) vantage point it should be one rather than another. It just *is*, and neither we nor a hypothetical god can change that. Mathematics would appear to have a more fundamental existence than god, therefore.

  16. That's an interesting "therefore" you slipped in at the end of your final sentence. You still haven't made clear to me (I accept it may be a receiver problem rather than a transmitter problem but then again...) a justification for why maths "just is," despite enlarging that concept to state that it's independent of the universe/matter it describes. What is the justification for leaving maths out of the "Theory of Everything?" I understand it as a speculative proposal, even as an aim/desire for it to be objective and independent of the system it's describing - but who's to say it's not actually part of the system - in the same way that an "independent" investigator such as yourself independently studies and describes genetic processes....

  17. It may be that we just cannot "know" reality and never will be able to. Belief in a Theory of Everything is like belief in a God - as if there has to be one or the other...

    this site looks at these questions from a philosophical point of view, http://bit.ly/fcUP1g

    eg. Why Mathematical Solutions Of Zeno's Paradoxes Miss The Point