God and Mathematics

Hi Yaro, your post was on pretty much the same lines as PaulK's and I replied to his as his was first... no slight intended

maybe so, but they throw some pretty decent keggers.

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אָרַח

I agree, it is fascinating, and math in one sense is hardwired into the fabric of reality. But It is still an abstraction of reality. Maybe it's the rules reality goes by, but I don't think Math is a thing that requires a mirror in some sort of Platonic realm of forms.Besides, dosn't maths tight bond with reality itself beg a bigger question? Namely why does anything exist at all?

I don't really agree with this, Yaro. I think that mathematics is a completely artificial formal system of manipulating symbols that developed the way it has because it mimicked nature. Nature doesn't follow mathematics; mathematics was invented to mimic nature.

well, yaro said math is an abstraction of reality. the rest of the message doesn't exactly agree, but that bit is sort of what you're saying.but i think your analysis is probably the right one. math was invented to mimic of model nature. and it's not perfect, because we can't possibly ever account for all the variables. but to paraphrase sir william of ockham, the small doesn't matter that much. we just need a good approximation.of course, math has gone beyond mimicing nature. for instance, triangle free graphs in cycle space might be rather meaningless to reality. graph theory might apply to electrical engineering occassionally, but hardly all of the time. most of the time, they're dealing with hypothetical sets of rules that don't even apply to reality in the slightest.

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אָרַח

Ya, I just reread it I just sort of thew that last post out my butt, heheheEssentially Im saying what you say. Math is an abstraction of nature. A construct created to mimic nature.And I guess what I was getting at in the last post, was something along the lines of:What can math tell us about reality?Essentialy, assuming the OP's idea that math is an all pervasive quality of the universe, How does that connect us with the purpose for existance? In this case, God.In other words, how does studying mathmatics lead us closer to any sort of transendental understanding.If anything, it seems to me that math leads us to greater understanding about how we, as humans, think.

yes, or rather maybe. but not of a religious nature, i think. i'd look at it like any other science -- it's not ABOUT god, but it's the study of what may or may not be his creation (depending on your belief). also true.

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אָרַח

I'm noot too sure about the "unreasonable effectiveness". At the most basic level mathematics was developed to describe features of the universe - counting, measurement, geometry - and later on probability and statistics. At more advanced levels mathematics has become a sophisticated toolkit and it is not too surprising that we have found uses for the tools it provides.But I really disagree about your example of "frame-dragging". The mathematical model that is the theory predicts certain behaviour Wellm that is the pointof building models. The "frame-dragging" you see in the mathematics is just a part of the model - a mathematical construct - not the actual physical phenomenon. In short to say that the theories are mathematics looks to me like confusing the representation with the reality.

cavediver Really?What exactly about the physical laws makes you think god created them? Can you explain how you place god outside of time and yet can see past present and future.First off how do you see without eyes and second how do prpose god sees the future but does not know it?

Are you asking why I believe in a god at all? That's just faith (short answer )Now, assuming God, why do I think he created the physical laws...?Well, IMO the physical laws are an integral part of our universe, and hence part of creation. I could imagine a created reality that had different laws, or one that was based on continuous divine intervention and "magic". IMO God chose to create a "physical" universe along with laws that made the whole thing logical and self-consistent. Now, there is a question as to how much freedom God had in making the laws for such a "physical" universe...If god is within the physical laws and subject to them, then IMO he is not a god, just some sort of pan-galactic mega-being having fun. This is possible of course, but does not have any place in my faith. First of all, I meant "know the future" in our humanistic sense of premonition or foretelling. God doesn't look into the future, he "sees" all of time as one whole.And I think you're anthropomorphising your concept of god a little too far to ask how does he "see". God transcends physical reality (as He created it!) I do not pretend to understand the metaphysical methodology with which God interacts with His creation, but it certainly doesn't have anything to do with "eyes" This message has been edited by cavediver, 07-13-2005 05:10 AM

Yes, mathematics is a sophisticated toolkit, and we continually find uses for it. The "unreasonable effectiveness" is "why is the universe so ameniable to such detailed mathematical modelling?"But in theoretical physics we have a new phenomenon, which you only start to appreciate once you delve into it... we no longer model with mathematics. We explore mathematics. You have to understand that GR is not a bunch of unrelated mathematical expressions that we pick and choose to mimmick reality. It can be summed up by G=T. Yes, it gives us Newton's gravity in the limit which is what was required. But from that tiny equation also comes: frame dragging, the big bang, expansion of the universe, black holes, perihelion of mercury, galactic lensing, gravity waves... none of these were modelled. They were not known about to model! Why should the universe exhibit all of this bizarre behaviour if the maths is merely a tool to model physical phenomena of which we are aware. Yes, and this confusion is very real amongst theoretical physicists and has been throughout the 20th century... they are extremely confused because the hammer has ripped itself out of the physicist's hand and said "ha, let me show how things really are!". Both GR and QM are forcing the confusion...

I hate to disappoint you, but graph theory is fundemental to quantum field theory That's an easy one. I would've thought you'd try with, say, Galois theory: hmmm, string theory. Group theory: snigger, QM, particles, GR, string theory. Believe me, there is not an area of pure mathematics that is not finding relevance in the universe somewhere. Even Topos theory is being considered in the serach for the ultimate TOE. It was largely due to this discovery of "pure mathematical" concepts in the universe that drove many into a Platonic viewpoint.

Hmmm, try telling nature that... for the past 100 years it seems to have been shouting the opposite at us. The more fundemental we have pushed physics (outwards and inwards), nature has demonstrated itself as more mathematical, not less. And the mathematics has become so much more elegant and natural. Can you believe that many of the major advances in pure mathematics are being made by the theoretical physicists? The universe is giving insight into mathematics that we never had just considering mathematics alone.

As a mathematician I think maths is a human invention that we ascribe far too much meaning to. I think that physics appears to follow maths follows quite straight forwardly from conservation laws.I see nothing surprising or unreasonable about it.

I never said that the theory was an unrelated set of mathematical expressions. Rather it is a sophisticated and highly integrated model. That the model predicts physical consequences that are later found only shows that it is an accurate model.Remembering that firstly much of mathematics was developed to model aspects of the universe it is not too surprising that it is effective. And how can we judge whether it "should" be "more" or "less" effective ? Would mathematics be considered more effective if the universe followed Newtonian mechanics rather than GR ? Or if it were classical rather than Quantum in nature ? If not then how could mathematics be less effective ?