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> What other conclusions can be drawn if one were to find this explanation appealing? That even if we find a Grand Unified Theory of Everything that fully expl

by brazzy 14y ago

> What other conclusions can be drawn if one were to find this explanation appealing? That even if we find a Grand Unified Theory of Everything that fully explains the physical world, we'll never run out of things to discover. > Are there other explanations of the relationship between math and our reality, that you've found appealing? None that makes sense, given what I know. > Is there a consensus among mathematicians as to what higher-order math, essentially is in pursuit of or should be in pursuit of? The potential for more math. Mathematicians look for theorems and constructs that are "interesting", which basically means that they are neither simple nor random. Prime numbers would be uninteresting if they were regular, but also if they were random. In fact they are neither, there's a multitude of patterns - the Wikipedia category "Classes of prime numbers" has 69 pages in it! > Is it an exercise of random shooting of darts hoping that some "mathematical truth" sticks and corresponds to some observable phenomenon? Yes, but some people don't care where the darts go, while others care about observable phenomena and notice any darts lying near them and start asking around who shot those and what they were doing...

spitx 14y ago
>That even if we find a Grand Unified Theory of Everything that fully explains the physical world, we'll never run out of things to discover. That's odd. In my experience, these detours in these discussions come as a result of how vague this whole terrain is. There is not even a smidgen of agreement on even the basic of agreed things. Can't mathematicians and theorists not agree on what areas of math are most helpful and what areas least helpful in arriving at a Unified Theory? This leads up to the other question of consensus among mathematicians. >The potential for more math. Mathematicians look for theorems and constructs that are "interesting", which basically means that they are neither simple nor random. Isn't there a faction of math people who strive towards a defined, non-abstract direction as opposed to fostering a laissez-faire approach to mathematics scholarship that naturally creates more math so that their area of expertise gets recognition and not to mention substantial purses of money? Is math so poorly funded that all mathematicians lead a hand to mouth existence and therefore collectively as some sort of cabal, have to resort to these self-preservation tactics? Come on. Really?
- brazzy 14y ago
  > Can't mathematicians and theorists not agree on what areas of math are most helpful and what areas least helpful in arriving at a Unified Theory? Not fully, and with good reason (see below). But actually, my point was that the existence of mathematical constructs that do not correspond to any physical reality means that there will be math to do when (and if) all physics has been done. > Isn't there a faction of math people who strive towards a defined, non-abstract direction as opposed to fostering a laissez-faire approach to mathematics scholarship that naturally creates more math so that their area of expertise gets recognition and not to mention substantial purses of money? Yes and no. There is the branch of applied math, and I'm sure they get funding more easily. But there are also mathematicians (cited several times in the comments here) who see math as art and want to do it for its own sake. And it has happened quite often that these "pure" mathematicians came up with enirely new stuff that only afterwards (and without anyone foreseeing it) turned out to be useful in modelling physical processes. Even among mathematicians you sometimes find that you can prove something in one field by using constructs and theorems from an entirely different field that nobody thought was in any way related. I believe Wiles' proof of Fermat's Last Theorem was like that.

by brazzy 14y ago

spitx 14y ago

>That even if we find a Grand Unified Theory of Everything that fully explains the physical world, we'll never run out of things to discover. That's odd. In my experience, these detours in these discussions come as a result of how vague this whole terrain is. There is not even a smidgen of agreement on even the basic of agreed things. Can't mathematicians and theorists not agree on what areas of math are most helpful and what areas least helpful in arriving at a Unified Theory? This leads up to the other question of consensus among mathematicians. >The potential for more math. Mathematicians look for theorems and constructs that are "interesting", which basically means that they are neither simple nor random. Isn't there a faction of math people who strive towards a defined, non-abstract direction as opposed to fostering a laissez-faire approach to mathematics scholarship that naturally creates more math so that their area of expertise gets recognition and not to mention substantial purses of money? Is math so poorly funded that all mathematicians lead a hand to mouth existence and therefore collectively as some sort of cabal, have to resort to these self-preservation tactics? Come on. Really?

brazzy 14y ago
> Can't mathematicians and theorists not agree on what areas of math are most helpful and what areas least helpful in arriving at a Unified Theory? Not fully, and with good reason (see below). But actually, my point was that the existence of mathematical constructs that do not correspond to any physical reality means that there will be math to do when (and if) all physics has been done. > Isn't there a faction of math people who strive towards a defined, non-abstract direction as opposed to fostering a laissez-faire approach to mathematics scholarship that naturally creates more math so that their area of expertise gets recognition and not to mention substantial purses of money? Yes and no. There is the branch of applied math, and I'm sure they get funding more easily. But there are also mathematicians (cited several times in the comments here) who see math as art and want to do it for its own sake. And it has happened quite often that these "pure" mathematicians came up with enirely new stuff that only afterwards (and without anyone foreseeing it) turned out to be useful in modelling physical processes. Even among mathematicians you sometimes find that you can prove something in one field by using constructs and theorems from an entirely different field that nobody thought was in any way related. I believe Wiles' proof of Fermat's Last Theorem was like that.