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What is this idea that making the math prettier or more elegant is not important? That's like saying a new algorithm isn't important; new math or models make pr

What is this idea that making the math prettier or more elegant is not important? That's like saying a new algorithm isn't important; new math or models make problems potentially tractable that aren't now. All of our math is an attempt to represent things or ideas. The most important thing I learned in my physics education was how to read math as a metaphor for putting together things I understand into a picture of a thing I don't understand. But I don't think anyone serious thinks that their math is "true", such an assertion just makes no sense. The point of it is to find new ways to approach the evidence to see if it gives some different metaphor that wasn't obvious before. I don't know enough modern physics to have an opinion on whether this is the case for cosmology or string theory, but I do know that in recent history just formulating a problem slightly differently can suddenly make the solution fit in the same framework as a known simpler problem. Not unlike things I read all the time about algorithm research at all, right? Teaching and understanding models is predicated highly on metaphor, it's much easier to explain for instance that MRI works via a quantum effect that has the same math as a harmonic oscillator than it is to just... dive in. The model isn't the universe, but humans live by metaphor and so the model is important. Which is perhaps not the point you were trying to make; I don't know enough modern physics to know whether a critique of these new areas as purely fantastical is justified, but it's also pretty fantastical to think of a particle in a box as if it were like a weight on a spring. Who am I to say that something about this approach can't make a currently intractable, approximate, or computational impossible problem solvable with time?

kensai 10y ago
Very insightful comment, thanks for sharing!
hyperbovine 10y ago
There are people whose job it is to make pretty math, they are called "mathematicians" ;-) So much of early physics, be it thermodynamics, electromagnetics, classical mechanics, is genuinely beautiful and elegant. I can see why quantum physicists would strive for that ideal as well. But at the end of the day I agree that physics should favor creating testable predictive models over developing untestable, elegant ones.
- megalodon 10y ago
  I'm sure most theoretical physicists would call themselves mathematicians. I don't agree physics should favour creating testable predictive models, because who are we to say what's testable in the future? Take the theory of relativity, for example. Would you have stopped Einstein et al from researching it, just because it wasn't testable at the time? In my opinion, physics is and has always been about answering the big questions, the how's, the why's of our existence. That new technology sometimes comes out of it is a bonus, not the ultimate goal.
  - ankurdhama 10y ago
    If that is so then why don't we just accept the religious answers to these big questions? Some supernatural entity is in the control of everything that's the answer and we are done. The goal of any science should be to answer questions such that those answers can help us solve the problem humanity faces and not just make us feel proud sitting in our chairs that we know answers.
    - megalodon 10y ago
      I think you are generalising my comment quite a bit, it was just a reaction to the poster above. We are never "done", that's kind of the point I was trying to convey. I completely agree that we should use science to help us deal with our current problems. Once we understand more about our world and ourselves, we will automatically get better at solving them. I'm just against the whole short-term, instant results way of thinking.
    - deleted 10y ago
      [deleted]
  - tolkienfan 10y ago
    Although difficult to test, there were features that were in theory testable! AFAIK this is currently not true with ST
dogma1138 10y ago
I didn't say that math is not important, but you can also dig yourself into a hole with it, there are quite a few competing theories all of which have a strong mathematical basis because you develop the math to explain your model of reality especially when you cannot gain sufficient evidence from experimentation. The overall point was which I might not have expressed fully is that there is in my opinion too much bias in the field of theoretical physics, and to paraphrase Brian Greene again we took a giant leap and probably skipped a few steps and no one seems to want to look back and see if we missed something. I think one of my favorite quotes that somewhat describes this view is by Rudolf Peierls: “In recent years the debate on these ideas has reopened, and there are some who question what they call ‘the Copenhagen interpretation’ of quantum mechanics’ - as if there existed more than one possible interpretation of quantum mechanics.” And I think that this view is antithetical to the advancement of current physics, and sadly this bias is instituted even unintentionally in most new physics students especially those who take physics as part of their degree in CompSci/Engineering.
- neltnerb 10y ago
  I totally get your point, that getting stuck in a framework can make it harder to get out of said framework, but I also have every reason to think that the experts in the field (which may well include you) are aware of this trap and spend a huge amount of time trying to get out of it. But I'd also expect that people making new theories be intimately familiar with the current ones, right? It would be silly to expect someone to come up with hamiltonian mechanics for the first time without having ever been exposed to newtonian mechanics, even though both give the same answers to every problem. Yeah, thinking outside the box is always super hard, but you have to at least deeply understand the box before you can know enough to replace it. I definitely don't understand this particular box, but I feel it's reasonable to assume that those that do are trying their darndest to escape it -- if for no other reason than fame if successful.
richardw 10y ago
It might but we've been generating many imaginary solutions without a lot of take-home benefit for a while now. ST has had an extraordinary run given how useless it's been, especially since it's sucked up money and time that might have been better spent on real science.
d13 10y ago
The danger with math is that it can prove its own truths based on its own internal rules, so there's a temptation to believe that whatever you can describe mathematically describes something that actually exists in the real world. But until you've tested it experimentally, you don't know whether you're describing a total fantasy world, like The Lord of the Rings, or something actually real, but boring, like an apple. Just because you've proven with mathematical certainly the existence of hobbits doesn't mean you'll actually find any.
- Tyr42 10y ago
  > The danger with math is that it can prove its own truths based on its own internal rules... Actually, there's a theorem about that ;) Godel's Incompleteness theorem. I would describe the problem more like: The new model matches the old model in almost everything (because we've observed a lot). But the math works out quite nicely if itty bitty particles behave this way when exploded at super high temperatures. We have a hard time watching those particles explode, so it's not really tested. Either way it works out, it's not really going to matter for anyone who doesn't explode tiny particles.
  - Myrmornis 10y ago
    Given that GP was discussing publicly, on a technical internet forum, the relationship between mathematical provability and truth/existence, don't you think it likely that GP was aware of Gödel's Incompleteness theorem? My concern is that the "actually", and the smiley face, seems, to me, very patronizing. I really don't mean to be attacking you for a small point of etiquette, and I also acknowledge that the main purpose of this thread (the nature of reality) is a bit more important, but I do make this point sincerely. This is something I find a real problem when discussing things with software engineers. I personally hate the feeling of being patronized in public, or of someone replying in public with the implication that I was not aware of something which I am perfectly well aware of. I'm not claiming that the GP is an expert on the Incompleteness Theorem, and I'm certainly not, but that "actually", and the smiley, sound and look awful. We should assume that others are competent and knowledgable on the subjects they talk about until given evidence to the contrary.
loki49152 10y ago
Actually, many people believe that math is "true", and in many cases they believe that math is more real than the physical universe. The position is called Platonism, in its older form, though Kant has his own spin on the idea.
- tolkienfan 10y ago
  But there are many incompatible mathematical systems, and only at most one of them could describe the actual universe.
tolkienfan 10y ago
As I understand ST, by choosing particular parameters you can make it predict (more or less) anything. If so, what does it mean for it to have made a prediction?

kensai 10y ago

Very insightful comment, thanks for sharing!

hyperbovine 10y ago

There are people whose job it is to make pretty math, they are called "mathematicians" ;-) So much of early physics, be it thermodynamics, electromagnetics, classical mechanics, is genuinely beautiful and elegant. I can see why quantum physicists would strive for that ideal as well. But at the end of the day I agree that physics should favor creating testable predictive models over developing untestable, elegant ones.

megalodon 10y ago
I'm sure most theoretical physicists would call themselves mathematicians. I don't agree physics should favour creating testable predictive models, because who are we to say what's testable in the future? Take the theory of relativity, for example. Would you have stopped Einstein et al from researching it, just because it wasn't testable at the time? In my opinion, physics is and has always been about answering the big questions, the how's, the why's of our existence. That new technology sometimes comes out of it is a bonus, not the ultimate goal.
- ankurdhama 10y ago
  If that is so then why don't we just accept the religious answers to these big questions? Some supernatural entity is in the control of everything that's the answer and we are done. The goal of any science should be to answer questions such that those answers can help us solve the problem humanity faces and not just make us feel proud sitting in our chairs that we know answers.
  - megalodon 10y ago
    I think you are generalising my comment quite a bit, it was just a reaction to the poster above. We are never "done", that's kind of the point I was trying to convey. I completely agree that we should use science to help us deal with our current problems. Once we understand more about our world and ourselves, we will automatically get better at solving them. I'm just against the whole short-term, instant results way of thinking.
  - deleted 10y ago
    [deleted]
- tolkienfan 10y ago
  Although difficult to test, there were features that were in theory testable! AFAIK this is currently not true with ST

dogma1138 10y ago

I didn't say that math is not important, but you can also dig yourself into a hole with it, there are quite a few competing theories all of which have a strong mathematical basis because you develop the math to explain your model of reality especially when you cannot gain sufficient evidence from experimentation. The overall point was which I might not have expressed fully is that there is in my opinion too much bias in the field of theoretical physics, and to paraphrase Brian Greene again we took a giant leap and probably skipped a few steps and no one seems to want to look back and see if we missed something. I think one of my favorite quotes that somewhat describes this view is by Rudolf Peierls: “In recent years the debate on these ideas has reopened, and there are some who question what they call ‘the Copenhagen interpretation’ of quantum mechanics’ - as if there existed more than one possible interpretation of quantum mechanics.” And I think that this view is antithetical to the advancement of current physics, and sadly this bias is instituted even unintentionally in most new physics students especially those who take physics as part of their degree in CompSci/Engineering.

neltnerb 10y ago
I totally get your point, that getting stuck in a framework can make it harder to get out of said framework, but I also have every reason to think that the experts in the field (which may well include you) are aware of this trap and spend a huge amount of time trying to get out of it. But I'd also expect that people making new theories be intimately familiar with the current ones, right? It would be silly to expect someone to come up with hamiltonian mechanics for the first time without having ever been exposed to newtonian mechanics, even though both give the same answers to every problem. Yeah, thinking outside the box is always super hard, but you have to at least deeply understand the box before you can know enough to replace it. I definitely don't understand this particular box, but I feel it's reasonable to assume that those that do are trying their darndest to escape it -- if for no other reason than fame if successful.

richardw 10y ago

It might but we've been generating many imaginary solutions without a lot of take-home benefit for a while now. ST has had an extraordinary run given how useless it's been, especially since it's sucked up money and time that might have been better spent on real science.

d13 10y ago

The danger with math is that it can prove its own truths based on its own internal rules, so there's a temptation to believe that whatever you can describe mathematically describes something that actually exists in the real world. But until you've tested it experimentally, you don't know whether you're describing a total fantasy world, like The Lord of the Rings, or something actually real, but boring, like an apple. Just because you've proven with mathematical certainly the existence of hobbits doesn't mean you'll actually find any.

Tyr42 10y ago
> The danger with math is that it can prove its own truths based on its own internal rules... Actually, there's a theorem about that ;) Godel's Incompleteness theorem. I would describe the problem more like: The new model matches the old model in almost everything (because we've observed a lot). But the math works out quite nicely if itty bitty particles behave this way when exploded at super high temperatures. We have a hard time watching those particles explode, so it's not really tested. Either way it works out, it's not really going to matter for anyone who doesn't explode tiny particles.
- Myrmornis 10y ago
  Given that GP was discussing publicly, on a technical internet forum, the relationship between mathematical provability and truth/existence, don't you think it likely that GP was aware of Gödel's Incompleteness theorem? My concern is that the "actually", and the smiley face, seems, to me, very patronizing. I really don't mean to be attacking you for a small point of etiquette, and I also acknowledge that the main purpose of this thread (the nature of reality) is a bit more important, but I do make this point sincerely. This is something I find a real problem when discussing things with software engineers. I personally hate the feeling of being patronized in public, or of someone replying in public with the implication that I was not aware of something which I am perfectly well aware of. I'm not claiming that the GP is an expert on the Incompleteness Theorem, and I'm certainly not, but that "actually", and the smiley, sound and look awful. We should assume that others are competent and knowledgable on the subjects they talk about until given evidence to the contrary.

loki49152 10y ago

Actually, many people believe that math is "true", and in many cases they believe that math is more real than the physical universe. The position is called Platonism, in its older form, though Kant has his own spin on the idea.

tolkienfan 10y ago
But there are many incompatible mathematical systems, and only at most one of them could describe the actual universe.

tolkienfan 10y ago

As I understand ST, by choosing particular parameters you can make it predict (more or less) anything. If so, what does it mean for it to have made a prediction?