God and Mathematics

Hey, you started it! No, I don't believe that mathematics will lead anyone to God... in my book, that is all about faith. But that didn't stop Godel, did it?I actually started the thread as a whimsical heresy about God's relationship with mathematics... a discussion really for open minded theists. But it seems to have gone down the Platonist/anti-Platonist route with non-theists. That's fine, I love talking about this stuff...And I don't tolerate quantum psycobabble... or at least only to the level of Penrose. But objective reality is definitely a valid part of the picture... check out post 36. The "holographic principle" is a major on-going piece of work, and is similar.

yeah, that's what i mean.

yes, sure. parts of it are.but parts of it are not fundamental to anything, and have no real use or application. maybe they WILL someday. but in this case the math is being thought up first, and then applicitions are found, not vice versa. mathematicians often take serious offense at the idea that there even SHOULD be applications for their ideas.

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אָרַח

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Physcial descriptions of reality break down and all we are left with is explanation purely in terms of mathematics.

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Actually, I conclude the opposite from this; in fact, it was the metaphysical stresses that this caused which led me to think about all this deeply and to finally reach the conclusions that I have. (I say "finally," but of course the journey is never really done. I will be thinking deeply about this in the future and my opinions are sure to change -- maybe I will eventually reach the opposite conclusions!)If the universe ran according to mathematical laws I would naively expect that the mathematical equations would represent easily comprehensible entities. Perhaps this is too naive. However, at a minimum I would expect that the universe would run according to a set of mathematical theories exactly, with no errors (beyond the errors due to the usual limitations of experiment and observation, of course) -- preferrably a single mathematical theory would form the foundation of how everything works.But because the entities represented by our currently most accurate theories, quantum mechanics and general relativity, are so hard to comprehend, and especially because even these theories are not a complete description of reality, I have no reason to accept that the universe is really following some sort of mathematical program. Perhaps physicists will succeed in coming up with that "single equation" from which all else comes -- this is one of the goals of the current research programs.I am interested in the comment that I cited above. Do you mean that in the end the physical interpretations of our mathematical equations are meaningless and that the "bare" mathematics is all that there is? I have been toying with that idea for a number of years, but I haven't been brave enough to commit to it.Edited to correct awkward phrasing.This message has been edited by Chiroptera, 13-Jul-2005 10:07 PM

Of course they do, which is what makes it all so much fun Altthough I'm sure "Minkowskian" SR and GR produced waves by formally introducing non-Euclidean geometry to physics, Group theory was really the first major example of this that caused ruffles... and ironically this what not in any fundemental way... merely the classification of particles via Isospin into reps of the Lie groups. But this was nothing compared to Yang Mills on SU(3)... which now gives us Quantum ChromoDynamics.And to counter such luddites, we have giants of mathematicians championing mathematical physics such as Attiyah and Donaldson. I'd lay very good money on where they lean in this debate

I can grant that mathematical descriptions are going to be better than analogies like the "rubber sheet". But does that mean that space "is" mathematics ? Or just that the mathematical model is the most comprehensible and accurate description we have available to us ?It seems to me that mathematics - by intent - deals with highly generalisable and very basic concepts. So it isn't a great surprise that we can generate mathematical descriptions that deal very well with those aspects of of physical reality. And since physics is to a large extent building mathematical models then it is very natural for physics to try to describe poorly-understood entities or concepts in mathematical terms.So I suppose it comes down to the question of interpretation. If it is that the universe is mathematics then all concepts should be purely mathematical - there shoud be no need to interpret the model, the model should be complete using only mathematical rather than physical concepts. We shouldn't need a concept of, say, "charge" - we should be able to derive it purely mathematically. I don't believe that that is possible - and if it isn't then there is more to the universe than mathematics.

Yes and no. I agree, they should represent easily comprehensible entities... but I would add that they do! I think you're asking too much if by comprehensible, you mean a layman's approach. If our everyday lives gave us access to the c-scale and the planck-scale, then much more would be comprehensible and obvious. But we have such a narrow viewpoint on the universe that we cannot expect to get any decent understanding without some effort. This is what we're searching for... that is as good a decription of the TOE as any. Again, only becasue we are such narrow sighted creatures. And seriously, GR is not that hard to understand. You don't need tensor calculus to appreciate what it is saying. The tensors are just there for calculating results. And even tensors are not at all hard to understand.QM is a bit more spooky, but once described in mathematical terms, it becomes much more natural as long as you are willing to let go of your day to day expectations. it's a great shame, but you are right... they are not. But they are infinitely closer than anything that came before. It is they that suggest that a TOE is possible. Before GR, physics was literally the sum total of all physical theories at that time... and physicists were happy with that. The general thought was that as soon as this nonesense about the missing ether was cleared up, physics had come to an end. They really thought that everything would be solved with the first decade of the 20th C. It is only by looking at how different GR is as a theory that gives us hope that a TOE can be found. Well, this is getting strong... certainly much more so than simply postulating a possible TOE. But it's certainly the way I lean. I see our reality as an emergent represention of the real "bare" mathematics. It's something I'll espouse, but I think commit is too strong a word for me. Ask God about how committed I am in my Christianity. He'll tell you some tales...

Well, this is certainly true. I'm arguing that we have no physical descriptions of anything any more, unless you are happy to remain at some mid-scale level. Take a particle falling into a black hole. Have you any physical description of a particle? Have you any physical description of a black-hole?I don't think space "is" mathematics... it would be nice, but QM demonstrates that GR is not enough. It would be wonderful if it was, like say in Wheeler's geometrodyanamics, and then, yes, space would be mathemetics - a hausdorf manifold of dimension 4, with a pseudo-Riemannian metric.What I would say is that there are many aspects of the universe that physics is at a loss to explain, other than by giving such an aspect a name... like charge, as you bring it up. Explain charge. I understand it purely mathematically... I don't have any other explanation other than hand-waving and analogy. Again, I have to say that this is traditionally true, but this is certainly not how mathematics appears in fundemental physics. How does "curved space-time" have anything to do with our universe? This is a bizarre mathematical concept, coming from very strange geometry. Why the hell should the universe look this way??? This is not a slight tweak to our Newtonian understanding. This is not a slight improvment to fit the data better. This is "oh, by the way, the universe is NOTHING like you thought... love Albert". And he only saw the tip of the iceberg, never even having the chance to appreciate black holes... sorry, getting carried away Absolutely. Physics is just giving names to emergent behaviour and using mathematics in a loose toolbox-sense to model this emergent behaviour. We should and we do. But the name "charge" is useful for describing the emergent behaviour, and for those who are not savvy with the mathematics. Do we use quantum field theory in chemistry? Do we use atomic physics in biology? We should be able to do all biology from our knowledge of physics. Of course we don't because of complexity, and so we model the emergent behaviour instead. I've just read this statement of yours in a new light. It has a sense of "more than just boring old, bunch of equations, tedious calculations through countless diff eqns, mathematics".Well, that is certainly how I regarded mathematics as an undergrad studying astrophys. However my conversion occured during my final undergrad year, which is what took me out of physics and into mathematical physics. Now I would say"I have seen things you people wouldn't believe. Attack ships on fire..." Mathematics is awe-inspiring... I don't really need there to be anything more. Try a 200 order magnitude zoom on the mandelbrot set (in an interesting region!) to make you realise how small the universe is in comparison.

Very interesting thread... I'm no mathematician so I'll try to discuss what you were getting at to begin with. HERETIC!!! You must BURN!!!j/kI think you're right. I think you answered your own question when you stated that God is not bound by time. If he's not bound by time, when did he create mathematics? It just exists as the underlying framework of this reality. And all reality exists in God.Did God have a choice in creating a universe that bows to mathematics? Its kinda hard to define choice when you aren't bound by time. Can God ever be truly separate from anything that exists if all existence is sustained by Him? This is Panentheism, which I believe is a good model that agrees with scripture. "I am in the Father and the Father is in me." We're all in God, and so is mathematics.

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What I would say is that there are many aspects of the universe that physics is at a loss to explain, other than by giving such an aspect a name... like charge, as you bring it up. Explain charge. I understand it purely mathematically... I don't have any other explanation other than hand-waving and analogy.

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But doesn't this just come down to what I said ? When dealing with things remote from our everyday experiences analogies are often inadequate and the more precise models of mathematics may be the best descriptions we have. The more so since physics is already biased in favour looking for mathematical descriptions.I would add that I don't remember saying anything about "boring old, bunch of equations". I was pointing out the fundamental difference between the abstractions of pure mathematics and the reality of models. Models require interpretation - the terms in the equations need to be related to the aspects of reality that they model. Pure mathematics - in dealing only with mathematical entities - doesn't include that.And - as I said - my background is more in mathematics than it is in physics, and more in pure mathematics than it is in applied. I don't need to be told about the beauty of mathematics, not since the "aha!" moment when I comprehended the elegance of mathematical induction.

Sorry Paul, those comments were not really aimed at you. They were meant in a much more general sense... No, I understand you point. What I am saying is that this distinction is a result of complexity at our level of perception of the universe. Modelling works in the one realm where we know we are not looking at the real reality - way below c and way above h. As we approach one or the other of these, as we get coser to the nature of things, modelling starts to fail, and the mathematics takes over. Especially so when we approach h and c at the same time...Now of course, this is only suggestive. You may be right that we are just failing to model becasue we don't understand yet. What I would claim is that this actual concept of modelling is an emergent concept. In fact, as this is an anonymous board I will take it further into Chiroptera's scenario... Though of course meaningless doesn't imply useless...It's interesting: most here are implying a physical reality with mathematics as an emergent concept from evolved conciousness. My position is that there is a mathematical reality and observed reality is an emergent concept from evolved conciousness.

Ha, that's funny. There once was this 16 yr old, only one in the school taking further mathematics, sitting in his first lesson being shown induction... not so much "aha" as "wtf" BTW, have you checked out JohnDM's posts on the first page You gotta smile

cavediver Yet you pretend that seeing is a human quality that would be a quality of god without the physical requirement of eyes to intract with light.This is not faith this is substituting magical thinking for rationality.You also make the concrete assertion that he transcends physical reality.What does it mean to "transcend" physical reality? You state this as though such was common knowledge and yet,since we really do not yet know what constitutes reality to begin with I do not see how such a statement can be considered anything but an avoidance of the problem .
You assume a god on faith and yet cannot explain the qualities you assume he has except through appeal to ignorance.You claim he interacts with a physical universe yet cannot explain how such a feat would be accomplished most especially since there is no trace of such activity.To have faith in such is to avoid the work of thinking about the subtlties involved in your assertions and how they are not explanations of any value since they clarify nothing.

Err, no. I use the term "see" in a loose context... I believe that God is aware of every aspect of this reality. It has nothing to do with light. He is aware of every photon, every quark... this is part of my definition of what it is to be a god.I must apologise for not having access to the details of God's interaction with the universe. I struggle enough with understanding my own interaction with the universe. Care to give me an area of theism YOU would not consider "magical thinking".Anyway, I am not getting into a debate on theism here. It's OT and an argument that has raged for millenia. You make many assertions on how I think and what I can and cannot explain. I find this offensive.

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physical interpretations of our mathematical equations are meaningless and that the "bare" mathematics is all that there is

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Though of course meaningless doesn't imply useless...

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Indeed.Take a textbook on logic and look at the sections devoted to symbolic logic. Symbolic logic is really a set of rules that allow you to replace a given group of symbols with another group of symbols, without any meaning being attached to the symbols. A proof is simply a given set of symbols, a concluding set of symbols, and a list of the rules that allow you to transform the initial set into the concluding set. This is all modern pure mathematics is; it is really just symbolic logic, just manipulation of symbols. But it would be impossible to be able to figure out the proof of any theorem by simply trying to figure out the correct sequence of manipulation rules; mathematicians can only figure out this set of rules by giving the symbols some meaning, the symbols represent some sort of entities, and the mathematician uses her intuitive knowledge of the "behavior" of these entities to figure out what the proof is.A similar thing could be happening in, say, physics. The universe is what it is, and we don't know nuthin' about it, really. But there are these equations that, when used properly, give very accurate predictions of what we should predict if we run some sort of experiment (or operate some complicated apparatus). But it would be very difficult (and very dry and uninteresting) to set up and solve bare equations; it is much easier to figure out how to solve a problem if we assume that there are these things called "electrons" which have a certain "charge" and "mass", and we use our intuitive understanding how these electrons behave according to quantum mechanics to set up the equations and solve the problem.-

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It's interesting: most here are implying a physical reality with mathematics as an emergent concept from evolved conciousness. My position is that there is a mathematical reality and observed reality is an emergent concept from evolved conciousness.

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Now this is very interesting when you put it like this. In fact, except for the word "mathematics", the second sentence is similar to some ideas I was toying with a few years ago.