6 ms·

There's no relevant physics without mathematics, one has to work out the math before trying to answer the 'why' questions. There are no short cuts. (Note: I'm a

by tca 16y ago

There's no relevant physics without mathematics, one has to work out the math before trying to answer the 'why' questions. There are no short cuts. (Note: I'm also a theoretical physicist :) )

Confusion 16y ago
The math follows from the basic assumptions made about nature. Assume translational, rotational and time invariance, add the finite speed of light and some less obvious assumptions and all of classical physics (for those non-phycisists: this includes special and general relativity) follows. Assume charged fundamental particles and EM follows. Assume quantized fundamental units and quantum mechanics follows. Lots of relevant physics can be described and shown with hardly any mathematics at all. The idea that nature is mathematical in essence is a notion that primarily physicists entertain. They mistake intelligence for knowledge and philosophers, that have actual knowledge of the philosophical problems involved, know better. The idea that nature is mathematical in essence, and that we have discovered this fundamental essence, is both hubris and usually utterly devoid of any philosophical sophistication.
- tca 16y ago
  You could invert the phrase and still make a lot of sense: 'Nature follows from the basic mathematical assumptions.' But you are quite right: Philosophers know better, could know...
  - Confusion 16y ago
    You could invert the phrase and still make a lot of sense: 'Nature follows from the basic mathematical assumptions. It's not just that. It's also that a lot of physics can readily be explained and understood without mathematics. It's just that with mathematics, it's easier to demonstrate the consequences. It's important to remember that Einstein got at relativity by understanding the right assumption to be made. Just to be clear on this: I fully agree that in advanced physics, you sometimes you have to blindly 'do the math' and can determine the physical interpretation of the result only afterwards. However, that doesn't mean that there is no physics without mathematics, it doesn't mean that there isn't a lot of physics that can be understood without mathematics and it certainly doesn't mean nature is mathematical in essence. Hell, it isn't even physical in essence, unless you can reduce our minds to physics. The notion that 'nature is mathematical in essence' is not logically seperated from assumptions about the object/subject and mind/matter dualities (and about whether they are dualities in the first place) that I doubt most of the phycisists espousing these notions are willing to support, because they are rather incompatible with other parts of their worldview.
    - pwhelan 16y ago
      I like what you say, but I am conflicted. As I understood it, math is the language that physics uses for us to understand/manipulate reality. Just as one understand "coffee" without the word coffee, one can understand projectile motion without understanding derivatives -- however in the absence of a language to describe it, the concept remains difficult to build upon. I do not understand about it not being logically separated from assumptions about dualities (Platonic forms?) and their respective worldview. Could you explain more please.
      - lmkg 16y ago
        Some guy by the name of Hartry Field claims to have successfully generated a logical axiomitization of Newtonian mechanics, without using math, only qualitative concepts like "betweenness."[1] Math can extend this model and is consistent with it, but it's not necessary in principle. Of course, this does not mean that you don't need math in practice, in the same way that continuations are the only control structure you need in principle but in practice you use loops and function calls and switches or whatever. What it does mean, from a philosophical view, is that math isn't necessary the quintessential 'language of the universe' that we thought it was. As far as advanced mathematical physics goes, our problem is that we stop being able to easily understand what the math represents when you go deep enough. A first derivative is understandable as velocity, the second as acceleration, and multiplying that by mass to get force has some intuitive notion. If you look in the middle of a bunch of scribblings, it's possible to put the equation into words and it will make sense and have a physical interpretation. Special relativity and the beginnings of quantum mechanics came about because we had intuitive concepts, and were able to fit math around them. In modern physics, the math has come first, and the intuition later or not at all. Quantum phenomena still have competing interpretations (probability fields, many-worlds), which may not even be mutually exclusive. Once we figure out what in the hell is going on, the math may prove to be unnecessary, but right now the math is all we have to go on, and we sort of have to treat it like a literal truth in order to get anything done. [1] http://en.wikipedia.org/wiki/Philosophy_of_mathematics#Fictionalism http://en.wikipedia.org/wiki/Philosophy_of_mathematics#Ficti...
        16y ago
  - jayruy 16y ago
    > 'Nature follows from the basic mathematical assumptions.' This statement is more treacherous than you give it credit for. If we understood all those mathematical assumptions, wouldn't that be the death of free will? One might make the statement that mathematics is the act of discovering god's laws, but godel makes even that statement treacherous because he proves god's laws can never be consistent. my understanding of the modern philisophical take on mathematics is that it's just the invention of useful tools for manipulating logical entities, which can seem rather pedestrian to the layman - but will never deter a true mathematician
- RevRal 16y ago
  This XKCD strip comes to mind: http://xkcd.com/435/ http://xkcd.com/435/ . I don't think anyone is actually saying nature is math. In that strip you can see that the line continues rightward, though I don't know if that was intentional. Math is just symbols that happen to have congruence with something deeper in reality. They're representations that can effectively substitute. Math just inherently works to explain nature and physics. And as far as philosophers, well I wouldn't say it's far-fetched to call someone like Stephen Hawking a philosopher. The danger is the philosophers who misunderstand, or who ignore the advancements in mathematics and scientific knowledge we've been making.
  - Confusion 16y ago
    Math is just symbols that happen to have congruence with\ something deeper in reality. In which you already sidestep an enormous debate about whether such a thing as 'a deeper reality' exists. Nietzsche's 'God is dead' doesn't apply to the Christian God or Gods in general: it applies to every absolutist philosophy. Wittgenstein's work on the limits of language may have consequences for even what thoughts can possibly make sense. Their whole lineage, including people like Heidegger, Davidson and Rorty, is completely ignored by such an implicit, seemingly innocent, assumption. The danger is the philosophers who misunderstand, or who ignore the advancements in mathematics and scientific knowledge we've been making. Philosophers tend to have a pretty good understanding of the meaning of physics. It is taught to them at length, because of the importance of the scientific advances you refer to. It's certainly not the other way around. The fact is that most intelligent people are mostly unaware of the last 150 years of philosophy. The time before that is all they hear about, because it is pretty easy to explain. After that, it gets hard. However, those folks, among each other, just keep repeating the debates of back then, without realizing the advancements that have already been made. It's a damn shame. Even when you have progressed as little as I have, just to understanding how complicated these dualities are, discussing the Cartesian mind/matter duality with them over and over again gets like teaching yet another kid to integrate. They may be top-notch phycisists, but they simply don't know philosophy.
    - RevRal 16y ago
      To a very large degree, I agree with what you say. If we go any further I think it would amount to nit picking.
- Jun8 16y ago
  "The math follows from the basic assumptions made about nature." I disagree. Most physicists have expressed great surprise that math, which has nothing to do with the physical world, is so good in explaining it.
deleted 16y ago
[deleted]

by tca 16y ago

There's no relevant physics without mathematics, one has to work out the math before trying to answer the 'why' questions. There are no short cuts. (Note: I'm also a theoretical physicist :) )

Confusion 16y ago

The math follows from the basic assumptions made about nature. Assume translational, rotational and time invariance, add the finite speed of light and some less obvious assumptions and all of classical physics (for those non-phycisists: this includes special and general relativity) follows. Assume charged fundamental particles and EM follows. Assume quantized fundamental units and quantum mechanics follows. Lots of relevant physics can be described and shown with hardly any mathematics at all. The idea that nature is mathematical in essence is a notion that primarily physicists entertain. They mistake intelligence for knowledge and philosophers, that have actual knowledge of the philosophical problems involved, know better. The idea that nature is mathematical in essence, and that we have discovered this fundamental essence, is both hubris and usually utterly devoid of any philosophical sophistication.

tca 16y ago
You could invert the phrase and still make a lot of sense: 'Nature follows from the basic mathematical assumptions.' But you are quite right: Philosophers know better, could know...
- Confusion 16y ago
  You could invert the phrase and still make a lot of sense: 'Nature follows from the basic mathematical assumptions. It's not just that. It's also that a lot of physics can readily be explained and understood without mathematics. It's just that with mathematics, it's easier to demonstrate the consequences. It's important to remember that Einstein got at relativity by understanding the right assumption to be made. Just to be clear on this: I fully agree that in advanced physics, you sometimes you have to blindly 'do the math' and can determine the physical interpretation of the result only afterwards. However, that doesn't mean that there is no physics without mathematics, it doesn't mean that there isn't a lot of physics that can be understood without mathematics and it certainly doesn't mean nature is mathematical in essence. Hell, it isn't even physical in essence, unless you can reduce our minds to physics. The notion that 'nature is mathematical in essence' is not logically seperated from assumptions about the object/subject and mind/matter dualities (and about whether they are dualities in the first place) that I doubt most of the phycisists espousing these notions are willing to support, because they are rather incompatible with other parts of their worldview.
  - pwhelan 16y ago
    I like what you say, but I am conflicted. As I understood it, math is the language that physics uses for us to understand/manipulate reality. Just as one understand "coffee" without the word coffee, one can understand projectile motion without understanding derivatives -- however in the absence of a language to describe it, the concept remains difficult to build upon. I do not understand about it not being logically separated from assumptions about dualities (Platonic forms?) and their respective worldview. Could you explain more please.
    - lmkg 16y ago
      Some guy by the name of Hartry Field claims to have successfully generated a logical axiomitization of Newtonian mechanics, without using math, only qualitative concepts like "betweenness."[1] Math can extend this model and is consistent with it, but it's not necessary in principle. Of course, this does not mean that you don't need math in practice, in the same way that continuations are the only control structure you need in principle but in practice you use loops and function calls and switches or whatever. What it does mean, from a philosophical view, is that math isn't necessary the quintessential 'language of the universe' that we thought it was. As far as advanced mathematical physics goes, our problem is that we stop being able to easily understand what the math represents when you go deep enough. A first derivative is understandable as velocity, the second as acceleration, and multiplying that by mass to get force has some intuitive notion. If you look in the middle of a bunch of scribblings, it's possible to put the equation into words and it will make sense and have a physical interpretation. Special relativity and the beginnings of quantum mechanics came about because we had intuitive concepts, and were able to fit math around them. In modern physics, the math has come first, and the intuition later or not at all. Quantum phenomena still have competing interpretations (probability fields, many-worlds), which may not even be mutually exclusive. Once we figure out what in the hell is going on, the math may prove to be unnecessary, but right now the math is all we have to go on, and we sort of have to treat it like a literal truth in order to get anything done. [1] http://en.wikipedia.org/wiki/Philosophy_of_mathematics#Fictionalism http://en.wikipedia.org/wiki/Philosophy_of_mathematics#Ficti...
      - 16y ago
- jayruy 16y ago
  > 'Nature follows from the basic mathematical assumptions.' This statement is more treacherous than you give it credit for. If we understood all those mathematical assumptions, wouldn't that be the death of free will? One might make the statement that mathematics is the act of discovering god's laws, but godel makes even that statement treacherous because he proves god's laws can never be consistent. my understanding of the modern philisophical take on mathematics is that it's just the invention of useful tools for manipulating logical entities, which can seem rather pedestrian to the layman - but will never deter a true mathematician
RevRal 16y ago
This XKCD strip comes to mind: http://xkcd.com/435/ http://xkcd.com/435/ . I don't think anyone is actually saying nature is math. In that strip you can see that the line continues rightward, though I don't know if that was intentional. Math is just symbols that happen to have congruence with something deeper in reality. They're representations that can effectively substitute. Math just inherently works to explain nature and physics. And as far as philosophers, well I wouldn't say it's far-fetched to call someone like Stephen Hawking a philosopher. The danger is the philosophers who misunderstand, or who ignore the advancements in mathematics and scientific knowledge we've been making.
- Confusion 16y ago
  Math is just symbols that happen to have congruence with\ something deeper in reality. In which you already sidestep an enormous debate about whether such a thing as 'a deeper reality' exists. Nietzsche's 'God is dead' doesn't apply to the Christian God or Gods in general: it applies to every absolutist philosophy. Wittgenstein's work on the limits of language may have consequences for even what thoughts can possibly make sense. Their whole lineage, including people like Heidegger, Davidson and Rorty, is completely ignored by such an implicit, seemingly innocent, assumption. The danger is the philosophers who misunderstand, or who ignore the advancements in mathematics and scientific knowledge we've been making. Philosophers tend to have a pretty good understanding of the meaning of physics. It is taught to them at length, because of the importance of the scientific advances you refer to. It's certainly not the other way around. The fact is that most intelligent people are mostly unaware of the last 150 years of philosophy. The time before that is all they hear about, because it is pretty easy to explain. After that, it gets hard. However, those folks, among each other, just keep repeating the debates of back then, without realizing the advancements that have already been made. It's a damn shame. Even when you have progressed as little as I have, just to understanding how complicated these dualities are, discussing the Cartesian mind/matter duality with them over and over again gets like teaching yet another kid to integrate. They may be top-notch phycisists, but they simply don't know philosophy.
  - RevRal 16y ago
    To a very large degree, I agree with what you say. If we go any further I think it would amount to nit picking.
Jun8 16y ago
"The math follows from the basic assumptions made about nature." I disagree. Most physicists have expressed great surprise that math, which has nothing to do with the physical world, is so good in explaining it.

deleted 16y ago

[deleted]