52 ms·

The Simple Truth about Physics

82 points by aluket 7y ago

imglorp 7y ago
Heard an interesting idea about the overlap of information theory and physics in one of Sean Carroll's recent podcast discussions. They blew past it but I think it bears its own subject. The idea goes like this. If you want to talk about simplicity, beauty, or elegance of a physical law--maybe because you think that's more likely to be correct than a complicated law--then we've already got tools like Kolmogorov complexity to talk about such laws.
- deleted 7y ago
  [deleted]
- btrettel 7y ago
  This seems to be the particular podcast: https://www.preposterousuniverse.com/podcast/2019/12/09/76-ned-hall-on-possible-worlds-and-the-laws-of-nature/ https://www.preposterousuniverse.com/podcast/2019/12/09/76-n...
- salty_biscuits 7y ago
  I think it would be something like the bayesian information criteria or minimum description length.
- ssivark 7y ago
  Is Kolmogorov complexity an actual tool, or just a concept with a name which is very difficult to compute/measure/etc and use practically?
stabbles 7y ago
Of course there is no guarantee truths about the universe are simple. Newtonian mechanics is extremely simple, yet it is only true as a limiting case of relativistic mechanics, which is not as simple. Maybe relativistic mechanics is only true as a limiting case of an even more complex theory, et cetera. What we should value is not simplicity, but power of explanation.
- tbabb 7y ago
  Each additional unchecked assumption that is added to a theory is another opportunity to be wrong. These probabilities of failure, however small, are compounded with multiplication, so the probability of failure rises exponentially with the number of unchecked assumptions. (10 assumptions each with 95% chance of correctness have only a collective 59% chance of being right— .95^10 = .59). To maximize the chance of choosing a model which corresponds to reality, we must involve as few unchecked assumptions as possible when deciding between theories that agree with the data; and this matters more than any particular assumption having a relatively high chance of being right, because of this exponential sensitivity. So if we want theories that are correct, yes, we should value simplicity.
  - klyrs 7y ago
    > So if we want theories that are correct, yes, we should value simplicity. I'm reminded of a problem I was given on a math exam: a hand-drawn polynomial on a 5x5 grid, where the curve intersected the grid in 5 points. "Find the equation of this cubic polynomial." The given integral points weren't possible for any cubic; if the function was a polynomial, it was a quartic at a minimum. Sadly, my teacher was not trying to trick us. Simplicity, itself, was an unchecked assumption which rendered correctness impossible.
  - vladf 7y ago
    I don't understand how we can reason with "probabilities of failure" about such fundamental things such as laws of physics. Under the frequentist interpretation of probability, 95% of having a "correct assumption" means that as you observe iid experiments of this assumption, the long-run average of them will have 95/100 of such experiments exhibit the assumption as true. But "experiment" here isn't a physics experiment, it's a _universe_ in which this assumption could be true. We're in some _fixed_ universe. This assumption holds in ours with probability 0 or 1 (we don't know which). So, I think the 95% you're referring to here is a Bayesian belief level. This is coherent in that it doesn't require some ambient set of multiple universes to meaningfully describe what is meant by "probability", but the prior required for this interpretation is a bit of weird beast. That is, we have some prior over the space of all possible assumptions for models of physics and update our beliefs based on evidence (we can collect evidence from our single universe multiple times and update our beliefs in a coherent way). In the limit of evidence, this prior matters less, but constants matter here! How much evidence do we need before we can be confident the "belief levels" we're throwing around aren't that subjective anymore? We don't really have a good sense for what the structure over this space of "assumptions of physical models" is, so we can't really answer this question. Within specific settings for statistical learning theory, we find that simple models generalize well. But that's an implication: _if_ you have a class of simple models and it fits the data well, _then_ you'll generalize well. When it comes to answering the question, "Which theories generalize well?", such analysis is incomplete.
tus88 7y ago
Well we will soon be approaching a CENTURY without any significant advances in physics or our understanding of the universe...no wonder they are desperate.
- kurthr 7y ago
  I'd say that fuse/splitting the atom counts as a significant advancement in physics whether weapons or power generation. Next, I'd say solid state transistor physics (not to mention Lasers, LEDs, OLEDs) also count as significant advances. I guess we're APPROACHING a century, but we're no where near it yet... maybe another 30 years? If we're talking about understanding the universe, strong/weak force (also Neutrinos have mass), dark matter/energy (and Cosmic Microwave Background), gravitational waves (and black holes) all seem pretty significant and happened after 1920. What has happened is that the advances have gotten harder to explain and more ubiquitous in their effects. So maybe it feels like there's not advancement, because we're soaking in Moore's law and post WW2 economic growth?
  - tus88 7y ago
    Your talking about applications not theory. And the new theories you mention (dark energy/matter) are right at the heart of the current crisis in physics.
    - kurthr 7y ago
      None of those issues were even known of 100 years ago. We barely had the photo-electric effect much less the Copenhagen interpretation (1925) and they weren't fully accepted. Even so theory isn't much (see Strings) without application and experiment. Nobel prizes are given for things that have consequences rather than just seem interesting.
      - tus88 7y ago
        General relativity - 1915 Schrodinger equation - 1925 Theory is good when it explains observations, no application necessary. The latter is mostly engineering challenge, how do we refine uranium for example.
montalbano 7y ago
This doesn't just apply to physics. All scientists should strive for parsimony. In other words Occam's Razor: "It is futile to do with more things that which can be done with fewer", where things in scientific theories can be considered assumptions. Parsimony, along with falsifiability, are the two most important features of any reasonable scientific theory. We need to teach more philosphy of science at all levels of science education. I was quite surprised to read that a physics post-doc would openly seek to complicate their models just for the sake of appearance.
- TheOtherHobbes 7y ago
  Occam's razor only applies if your model actually solves the problem it claims to solve. Plenty of beautiful, elegant, parsimonious, wonderful, understated, aesthetically pleasing models in physics turned out to be complete bunk when confronted with real data.
  - montalbano 7y ago
    Agreed, that's why i mention falsifiability along with parsimony.
- perl4ever 7y ago
  Bode's law vs...what exactly do we believe now explains the positions of the planets?
improbable22 7y ago
Half the article is about the social observation that making your work unnecessarily complicated is, too often, a way to impress people. Especially those, like funding agencies, who try to judge without understanding it. Many will be impressed to see you flexing large calculational muscles, even if they can't quite see why. The other half appears to be an advert for the author's paper https://arxiv.org/abs/1910.13608 https://arxiv.org/abs/1910.13608 which advocates a particular measure they call "explanatory depth". It's not immediately obvious (to me) how this works, or how it relates to other bayesian & information-based measures. But it seems worth a look.
deepnotderp 7y ago
The formalism for this is Kolmogorov Complexity and Occam's Razor. I also believe that we also value Sophistication, which is at least a partial driver of the interest in string theory, with less free parameters.

82 points by aluket 7y ago

Heard an interesting idea about the overlap of information theory and physics in one of Sean Carroll's recent podcast discussions. They blew past it but I think it bears its own subject. The idea goes like this. If you want to talk about simplicity, beauty, or elegance of a physical law--maybe because you think that's more likely to be correct than a complicated law--then we've already got tools like Kolmogorov complexity to talk about such laws.

deleted 7y ago
[deleted]
btrettel 7y ago
This seems to be the particular podcast: https://www.preposterousuniverse.com/podcast/2019/12/09/76-ned-hall-on-possible-worlds-and-the-laws-of-nature/ https://www.preposterousuniverse.com/podcast/2019/12/09/76-n...
salty_biscuits 7y ago
I think it would be something like the bayesian information criteria or minimum description length.
ssivark 7y ago
Is Kolmogorov complexity an actual tool, or just a concept with a name which is very difficult to compute/measure/etc and use practically?

stabbles 7y ago

Of course there is no guarantee truths about the universe are simple. Newtonian mechanics is extremely simple, yet it is only true as a limiting case of relativistic mechanics, which is not as simple. Maybe relativistic mechanics is only true as a limiting case of an even more complex theory, et cetera. What we should value is not simplicity, but power of explanation.

tbabb 7y ago
Each additional unchecked assumption that is added to a theory is another opportunity to be wrong. These probabilities of failure, however small, are compounded with multiplication, so the probability of failure rises exponentially with the number of unchecked assumptions. (10 assumptions each with 95% chance of correctness have only a collective 59% chance of being right— .95^10 = .59). To maximize the chance of choosing a model which corresponds to reality, we must involve as few unchecked assumptions as possible when deciding between theories that agree with the data; and this matters more than any particular assumption having a relatively high chance of being right, because of this exponential sensitivity. So if we want theories that are correct, yes, we should value simplicity.
- klyrs 7y ago
  > So if we want theories that are correct, yes, we should value simplicity. I'm reminded of a problem I was given on a math exam: a hand-drawn polynomial on a 5x5 grid, where the curve intersected the grid in 5 points. "Find the equation of this cubic polynomial." The given integral points weren't possible for any cubic; if the function was a polynomial, it was a quartic at a minimum. Sadly, my teacher was not trying to trick us. Simplicity, itself, was an unchecked assumption which rendered correctness impossible.
- vladf 7y ago
  I don't understand how we can reason with "probabilities of failure" about such fundamental things such as laws of physics. Under the frequentist interpretation of probability, 95% of having a "correct assumption" means that as you observe iid experiments of this assumption, the long-run average of them will have 95/100 of such experiments exhibit the assumption as true. But "experiment" here isn't a physics experiment, it's a _universe_ in which this assumption could be true. We're in some _fixed_ universe. This assumption holds in ours with probability 0 or 1 (we don't know which). So, I think the 95% you're referring to here is a Bayesian belief level. This is coherent in that it doesn't require some ambient set of multiple universes to meaningfully describe what is meant by "probability", but the prior required for this interpretation is a bit of weird beast. That is, we have some prior over the space of all possible assumptions for models of physics and update our beliefs based on evidence (we can collect evidence from our single universe multiple times and update our beliefs in a coherent way). In the limit of evidence, this prior matters less, but constants matter here! How much evidence do we need before we can be confident the "belief levels" we're throwing around aren't that subjective anymore? We don't really have a good sense for what the structure over this space of "assumptions of physical models" is, so we can't really answer this question. Within specific settings for statistical learning theory, we find that simple models generalize well. But that's an implication: _if_ you have a class of simple models and it fits the data well, _then_ you'll generalize well. When it comes to answering the question, "Which theories generalize well?", such analysis is incomplete.

tus88 7y ago

Well we will soon be approaching a CENTURY without any significant advances in physics or our understanding of the universe...no wonder they are desperate.

kurthr 7y ago
I'd say that fuse/splitting the atom counts as a significant advancement in physics whether weapons or power generation. Next, I'd say solid state transistor physics (not to mention Lasers, LEDs, OLEDs) also count as significant advances. I guess we're APPROACHING a century, but we're no where near it yet... maybe another 30 years? If we're talking about understanding the universe, strong/weak force (also Neutrinos have mass), dark matter/energy (and Cosmic Microwave Background), gravitational waves (and black holes) all seem pretty significant and happened after 1920. What has happened is that the advances have gotten harder to explain and more ubiquitous in their effects. So maybe it feels like there's not advancement, because we're soaking in Moore's law and post WW2 economic growth?
- tus88 7y ago
  Your talking about applications not theory. And the new theories you mention (dark energy/matter) are right at the heart of the current crisis in physics.
  - kurthr 7y ago
    None of those issues were even known of 100 years ago. We barely had the photo-electric effect much less the Copenhagen interpretation (1925) and they weren't fully accepted. Even so theory isn't much (see Strings) without application and experiment. Nobel prizes are given for things that have consequences rather than just seem interesting.
    - tus88 7y ago
      General relativity - 1915 Schrodinger equation - 1925 Theory is good when it explains observations, no application necessary. The latter is mostly engineering challenge, how do we refine uranium for example.

montalbano 7y ago

This doesn't just apply to physics. All scientists should strive for parsimony. In other words Occam's Razor: "It is futile to do with more things that which can be done with fewer", where things in scientific theories can be considered assumptions. Parsimony, along with falsifiability, are the two most important features of any reasonable scientific theory. We need to teach more philosphy of science at all levels of science education. I was quite surprised to read that a physics post-doc would openly seek to complicate their models just for the sake of appearance.

TheOtherHobbes 7y ago
Occam's razor only applies if your model actually solves the problem it claims to solve. Plenty of beautiful, elegant, parsimonious, wonderful, understated, aesthetically pleasing models in physics turned out to be complete bunk when confronted with real data.
- montalbano 7y ago
  Agreed, that's why i mention falsifiability along with parsimony.
perl4ever 7y ago
Bode's law vs...what exactly do we believe now explains the positions of the planets?

improbable22 7y ago

Half the article is about the social observation that making your work unnecessarily complicated is, too often, a way to impress people. Especially those, like funding agencies, who try to judge without understanding it. Many will be impressed to see you flexing large calculational muscles, even if they can't quite see why. The other half appears to be an advert for the author's paper https://arxiv.org/abs/1910.13608 https://arxiv.org/abs/1910.13608 which advocates a particular measure they call "explanatory depth". It's not immediately obvious (to me) how this works, or how it relates to other bayesian & information-based measures. But it seems worth a look.

deepnotderp 7y ago

The formalism for this is Kolmogorov Complexity and Occam's Razor. I also believe that we also value Sophistication, which is at least a partial driver of the interest in string theory, with less free parameters.