God and Mathematics

Yes "modelling" in "common-sense" terms fails, and thus the more precise and abstracted mathematical models we have produced work better. And in a large part I think it is because mathematics is an abstract way of dealing with fundamental concepts in a precise way. (And we see something similar in mathematics - the mathematics of infinity is also very strange to us).To me it suggests only that our mental capabilities are more geared to dealing with the physics of everyday existence. To deal with these other situations where the rules are very different we need to resort to the mental tools we have created - just as physical tools expand our physical capabilities.

As I remember it I got to induction at A level - but I did take O Level earlier and go on to Further Mathematics with a few others.And JohnDM's posts make me think that he is skipping on the medication he should be taking. So I'm not sure that it is really something to smile about.

quote:

---

To me it suggests only that our mental capabilities are more geared to dealing with the physics of everyday existence. To deal with these other situations where the rules are very different we need to resort to the mental tools we have created - just as physical tools expand our physical capabilities.

---

Very well put.

Yes, it was my first day of sixth form, first day of A-level. I took further in parallel with normal A-level. Oh, now those were the days... O-level maths JMB syllabus B with calculus... great days...You do realise now that a single A-level "mathematician" will leave without having met a complex number...Now, talking of A-level, I am now way way behind with my exam marking

Just start trying to think of the physical teleological continuum in tramps of Cantor's continuum hypothesis at the juncture of the empirics of artifical and natural selection and surely it will be God that gave the pure math that Kant KNEW Hume did not format and led Russel to form the opinion subjectively that that something certain was findable. Uncertainity however is not this freely willable application of e-numbers. The sublime math vs dynamics ARE biological even if physicists such as Dirac only found this beauty in the equations.This message has been edited by Brad McFall, 07-14-2005 09:58 PM

Why should this be? This is the core of the "unreasonable effectiveness". Exactly, so why is the mathematics we have constructed with these mental capabilities so unbelievably appropriate for areas of physics of which we have absolutely no experience, and had even less inkling... But why on earth should the tools work? I don't expect my rather extensive toolkit to enable me to perform nuclear manipulations... even miniturising my toolkit would not work becasue we have entered an entirely new realm of existence and rules.

Yeah, I know it I think know where you are coming from, and if so, I would agree with those ideas. There's lots on this, check out for example Misner, Thorne, and Wheeler "Gravitation" pages 1121-1122.If anyone is interested in GR and is not scared, then the referenced book is awesome and is written by some great guys. Wheeler of course is simply a legend. Can you believe he was Feynman's supervisor and he's still alive!! I'm not sure when he last was at a conference but it wasn't that long ago...If you want something slightly thinner and less likely to collapse into a black hole then try Ray D'Inverno's "Introduction to General Relativity". Both books are highly geometric, which is good.

Of course, there is one thing I have been conveniently glossing over in this entire discussion which I think raises issues in both camps...GR in no way represents reality !!!It has absolutely no dynamics. It is (usually) a four dimensional theory, and describes four dimensional universes... there is absolutely no sense of our own existence as three dimensional beings travelling through time. Time in GR is just another dimension. People are (borrowing from Pratchett) just 4-dimensional carrot shaped objects. GR gives a God's-eye view on the universe (oops, sidelined is going to get arsey again )Now how did our ever improving toolbox of mathematics make such an enormous blunder But this is the biggest question in theoretical physics in my mind: what the hell are we about? It's not so much a question of the arrow of time... it's how is there an arrow at all? Nothing gives us any clue as to why conscious existence as we experience it is an ordered sequence of space-like hypersurfaces traversing our universe.GR is the most accurate theory ever devised, yet has absolutely no room for consciousness...GR and QM remind me of Moorcock's gods of law and chaos: static stagnation vs raging anarchy

I'd say that the effectiveness comes largely from the fact that the concepts inolved really are fundamental enought that they "work" ath the level of ordinary experience, at relativistic level and to a great extent event the quantum level.That the concepts are dealt with in an abstract way, divorced from most of the expectations of ordinary experience also helps (e.g. the development of non-Euclidean geometry).I think your comemnt on your father's toolkit is really extending the metaphor rather too far. Why should it be surprising that an extremely versatile and generally useful tool should have applications in areas that were not anticipated by the designer ?

I don't think we're going to get much further with this particular line. I'm going to cop out with the following:I understand completely why you think as you do, I used to myself. Not to imply that I have evolved beyond you, I've just changed my mind BUT, I would say that things that have changed my mind are only apparent from the privalidged viewpoint of having spent years in the fields of fundemental physics. You would not even pick this up from GR, QFT or string graduate textbooks as they cannot possibly do justice to the subjects. My attempts at explaining why I think as I do are pathetic, but I am at a loss. I'm very proud of the fact that I can explain GR, black holes and string theory to anyone over a pint (well, usually 3 ) But to get to the level of appreciation I have, I think you have to get immersed in the subject.I will make a statement and will try to back it up if I can find enough quotes:

quote:

---

the number of mathematicians/physicists with Platonistic leanings is massively biased towards those in fundemental physics.

---

Not that this is even suggestive that my viewpoint is correct, it merely backs up my assertion that you really do need to be immersed in this subject to appreciate what I'm sayying... which is incredibly frustrating.Now, how's that for a cop-out...?

Just to clarify exactly what I am failing to express:IMO as I have delved deeper into fundemental physics through Special and General Relativity, Quantum Field Theory, String Theory, and many other areas of Qunatum Gravity (pre-geometry, algebraic structures, spin-networks, formal approaches, etc) I have been convinced that the nature of mathematics has changed. It is no longer a tool, it is now the guiding hand. I find it hard to believe that mathematics is merely a conscious construct. Physics is revealing itself as essentially mathematics incarnate, that the physical world IS the Platonic Realm observed at a level of immense complexity. Physics is "emergent" from the maths in the sense that biology is emergent from chemistry, and chemistry in its turn is emergent from atomic physics.By the way Paul, it was my toolkit, not my father's. Whatever gave you that idea? But so fails to capture the nature and inter-relationship of mathematics and physics in the areas I'm discussing. I just wish I knew how to convey this effectively.

Brad, why you left out Gladishev eludes me, but I knew I could trust you to one day come up with Cantor, God, Kant, Hume, and Russel, in that order no less, all together in one otherwise completely obscure sentence. But, although it's well-nigh impossible to out-obscure you, it's very easy to outname you, as you can see.Having said that, I would ask you to try and put it in plain English, for us mere mortals of the present?This message has been edited by Parasomnium, 15-Jul-2005 12:48 PM

---

We are all atheists about most of the gods that humanity has ever believed in. Some of us just go one god further. - Richard Dawkins

I'm surprised Noether's theorem hasn't come up in this discussion yet.

I apologise for my litle misreading (mistaking "rather" for "father's" - I was a little hurried and must have skimmed over the unimportant bit of that sentence)From my point of view, the nature of mathematics has certainly changed over time - from the growing generalisations (e.g. complex numbers and non-Euclidean geometries), increasing formalism - and thus abstraction - (e.g. the Hilbert program) and more recently even to embracing a form of experimentalism (e.g. the Mandelbrot set).But I am not convinced that physics is emergent from mathematics in the same way that chemistry is from physics. Not only is there the question of interpretation there is the whole issue of the "Theory of Everything". Under your statement that theory would just be the axioms and operations of mathematics - not even some specialised set chosen to represent our universe. And I find that as implausible as I find the idea that physics does not require some interpetive step to get form the mathematics to the entities the mathematics describes.I would add I think that it is a false dilemma to describe mathematics as "merely" a conscious construct. Mathematics started as a problem-solving tool, abstracting and generalising common elements of problems. Mathematics is a conscious construct in much the same way that language is - and has a similar basis in empirical reality. And Mathematics has been hugely developed, expanded and refined from those beginnings in a way that no physical tool has been.From my point of view you, and the mathematicsl physicists who share your view have fallen into an intellectual trap and are confusing a description with the reality. Yes it is a very good description - better than the natural language descriptions we are used to. Yes, it often deals with things that have to be described rather than perceived (and this brings the story of the blind men and the elephant to mind). It's very understandable why you might fall into that trap.

It would have if the conversation on conserved quantities had developed, but whoever posted that went quiet...I could spend hours dwelling on how symmetry, gauge theory, etc speak to me of a Platonistic view but I think the same problems apply. I can teach these concepts without any problem, but conveying the appreciation is much harder, especially over this medium. Now give me the old 2nd floor lecture room and I can get across anything Perhaps you can have a go... or do you hold different views???