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The Relation Between Mathematics and Physics by Paul Dirac (1939)

170 points · 85 comments · rramadass

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rramadass · 1789355830 · focus · HN ↗
Also see Relationship between Mathematics and Physics - <a href="https://en.wikipedia.org/wiki/Relationship_between_mathematics_and_physics" rel="nofollow">https://en.wikipedia.org/wiki/Relationship_between_mathemati...
wolfi1 · 1789631105 · focus · HN ↗
there is a quote from Pauli about Dirac : 'There is no God and Dirac is his prophet' Heisenberg and Dirac had different opinions on the existence of a god and Pauli, asked for his opinion, had the former to say
1. Tazerenix · 1789636055 · focus · HN ↗
  There's a quote Atiyah has about spin geometry which he heard from his advisor Hodge, who had an office next to Dirac at Cambridge.
  Only two people understand spinors: God, and Dirac. And Dirac's dead.
general_reveal · 1789632157 · focus · HN ↗
[dead]
1. n4r9 · 1789634153 · focus · HN ↗
  This is probably a reference to Hume's problem of induction, i.e. that observing a regularity in the past cannot justify assuming that it will hold in the future. It's vaguely related to the article, but talking about "time windows" and "Mathers" muddles the point.
  1. general_reveal · 1789634390 · focus · HN ↗
    Is it vaguely related? He wondered why measuring anything even works. Why wouldn’t the measurement disappear, thus making all this measuring pointless? Because, apparently the measurement(s) are true each time-step, and it will be true for that time, until it’s not true. Why it reasonably works well for us? Well, God , I guess. Same way the Sun doesn’t burn our skin off (God, I guess, but some have issues with that).
    Sorry, I had to critique that immediately because I could already see that other paragraph I quoted coming, as in, this author probably worships Math, Science, and those that do it, certainly not God, because he was unable to characterize the phenomena of it as related to God.
    n4r9 · 1789634689 · focus · HN ↗
    Yes, vaguely related. He's not wondering why measurement itself works, but why mathematical reasoning applies so effectively to the measurement results.
    I think it's valid to be surprised that all observations of a physical phenomena up until this point have obeyed a (relatively) simple mathematical relationship, without even thinking about predicting the future.
    GoblinSlayer · 1789639659 · focus · HN ↗
    Measurement works because universe moves in a simple way. As Hume indicates, you need very complex motion for irregularity, maybe even sentient, but sentient universe is fairy tale.
    pixl97 · 1789665713 · focus · HN ↗
    > but sentient universe is fairy tale.
    Ehhhhh.... this is actually a much bigger claim than you realize and to immediately dismiss it leads to some problematic issues in the continuum of reality.
    Without a rigorous falsifiable definition of sentient at all scales it can apply at best the problem is undefined. Are brains sentient? Are neurons sentient? Are the actual algorithms these structures run sentient? Without those answers we can really only say "The universe is probably not sentient".
    Also, you are the universe experiencing itself.
    lioeters · 1789668130 · focus · HN ↗
    A sentient universe that is not quite mature nor aware of itself declares conclusively: "A sentient universe is fairy tale."
    GoblinSlayer · 1789679744 · focus · HN ↗
    For a regularity to be broken, the phenomenon causing this regularity should be sentient to break the regularity in an intelligently chosen way. It doesn't matter how sentient are neurons, they don't affect anything and might as well be absent. See <a href="https://en.wikipedia.org/wiki/Discovery_of_neptune" rel="nofollow">https://en.wikipedia.org/wiki/Discovery_of_neptune - what neurons did there?
    general_reveal · 1789681636 · focus · HN ↗
    In other words, if I write this for loop:
    For (i=0; i< math.random; i++)
    This stability, as anarchic as it is with that randomness, still within reach of our finite mine to understand that it isn’t totally random, however instantaneous to our mind, such explicit and confined loop, why should such a thing ever be unpredictable?
    Some will argue that simple .randomnesss() is the thing that mindfucks you. But plenty are gifted to not be perturbed by randomness, that even in the noise they can seek out a truth.
    Hah. Yeah, why would magic emerge out of a clear cut predictable system, like the for loop I defined above, which to the naive will seem infinitely impossible to predict because I increased the domain to randomness.
    Somewhere here, God laughs. I write jokes for the divine, I never thought that’d be me, hah!
    GoblinSlayer · 1789686060 · focus · HN ↗
    Trading sacrifices for a good hunt is kinda useless now.
    rramadass · 1789706687 · focus · HN ↗
    This is just meaningless twaddle.
    Read the chapter on "Chance" in Poincare's "Science and Method" linked to here - <a href="https://news.ycombinator.com/item?id=49743377">https://news.ycombinator.com/item?id=49743377
    Randomness/Chance itself is amenable to laws by which we can estimate its bounds. In one sense everything is chance since the deterministic laws themselves operate within approximation bounds. When the approximation bound in the effect is similar in magnitude to that in the cause and both are very small, we call it "deterministic" whereas when the approximation bound in the effect is much larger than that in the cause for no discernible reason we say "chance" is operating.
    n4r9 · 1789723712 · focus · HN ↗
    Could you cite your reference to Hume here? I'm not aware of him talking about complexity in relation to regularity in this manner.
    GoblinSlayer · 1789725199 · focus · HN ↗
    Chicken and farmer.
    n4r9 · 1789726564 · focus · HN ↗
    I don't see what that has to do with simple vs complex motion.
    GoblinSlayer · 1789806305 · focus · HN ↗
    The chicken has a problem with prediction of future because of intelligent behavior of the farmer.
    n4r9 · 1789830329 · focus · HN ↗
    I wonder if you're reading too far into one example. Hume's original example was of the sun rising every day - nothing to do with sentience or arguably even complexity. The chicken/farmer example is one that Russell came up with to make it easier to imagine.
    otabdeveloper4 · 1789640550 · focus · HN ↗
    > Math, Science, ..., certainly not God
    Pretty much everyone worships some sort of God. (The exceptions are non-self-aware people living moment-to-moment.)
    What people argue about is the degree of personality and autonomy that God possesses.
    pixl97 · 1789665753 · focus · HN ↗
    Are you talking about god as being, or god as a concept?
    otabdeveloper4 · 1789748353 · focus · HN ↗
    It's capital-G God. Also the question is circular because how you define what a "being" is is dependent on your concept of God.
    n4r9 · 1789754983 · focus · HN ↗
    I'm pretty sure that I don't worship some sort of God, unless perhaps you substantially dilute the meaning of the word "worship".
2. lolakutty · 1789634364 · focus · HN ↗
  >There is no logical reason why the second method should be possible at all,
  One reason I can think of is if we consider that some regularity in the physical behavior is required for consciousness to evolve and so consciousness only forms in such worlds.
3. rramadass · 1789641024 · focus · HN ↗
  Later down in the essay, Dirac himself answers this;
  With this kind of cosmological picture one is led to suppose that there was a beginning of time, and that it is meaningless to inquire into what happened before then. One can get a rough idea of the geometrical relationships this involves by imagining the present to be the surface of a sphere, going into the past to be going in towards the centre of the sphere, and going into the future to be going outwards. There is then no limit to how far one may go into the future, but there is a limit to how far one can go into the past, corresponding to when one has reached the centre of the sphere. The beginning of time provides a natural origin from which to measure the time of any event. The result is usually called the epoch of that event. Thus the present epoch is 2 x 109 years [actually 2x10^9].
  One further point in connection with the new cosmology is worthy of note. At the beginning of time the laws of Nature were probably very different from what they are now. Thus we should consider the laws of Nature as continually changing with the epoch, instead of as holding uniformly throughout space-time. This idea was first put forward by Milne, who worked it out on the assumptions that the universe at a given epoch is roughly everywhere uniform and spherically symmetrical. I find these assumptions not very satisfying, because the local departures from uniformity are so great and are of such essential importance for our world of life that it seems unlikely there should be a principle of uniformity overlying them. Further, as we already have the laws of Nature depending on the epoch, we should expect them also to depend on position in space, in order to preserve the beautiful idea of the theory of relativity there is fundamental similarity between space and time. This goes more drastically against Milne's assumptions than a mere lack of uniformity in the distribution of matter.
  Show respect to Mathematicians/Physicists/etc. many of whom had studied Philosophy and i dare say had a better understanding/insight of it than mere academic Philosophers. Why? Because they don't go off into la-la land but try very hard to have both observed evidence and a mathematical model of it match cleanly via a Theory.
  For your edification, read first Meditations on First Philosophy by Rene Descartes followed by "Physics and Philosophy by Werner Heisenberg".
  1. pixl97 · 1789666364 · focus · HN ↗
    The difference between science and woo is science makes falsifiable predictions.
    I mean, go back 500 years. Tell everyone that everything is actually make of fields (no not the kind you grow things in). These fields manifest waves that carry certain amounts of energy. Those bits of energy build larger structures that are still so incredibly tiny the human imagination fails. But then you take those larger structures in a pattern and it builds atoms. Those atoms are actually 99.9999999% nothing but empty space end fields of force and electricity. This is why you don't pass thru things. Oh yea, these tiny empty things connect to each other in predictable ways creating molecules that are the basis of life. Just a tiny speck of them contains quadrillions of these molecules, crazy tiny.
    [The people you are talking to]: Get the wood, we're burning this witch.
    undershirt · 1789670966 · focus · HN ↗
    We cant even verify if these fields are real though. It is an ordered mythology for making predictions that work. If I have a machine that can reproduce the footprints of an animal no one has ever seen, I have not discovered that animal. (This is personally a more powerful analogy than saying "the map is not the territory" which gets at the same point.)
    pixl97 · 1789671467 · focus · HN ↗
    >We cant even verify if these fields are real though
    We can perform casual experiments that are falsifiable against them. This is the scientific definition of real within a probabilistic framework.
    undershirt · 1789673613 · focus · HN ↗
    Sure. Just making sure people understand that the "scientific definition of real" is based on a metaphysical assumption that real = works. It is very hard to remember this since philosophy of science is not taught school.
    GoblinSlayer · 1789682536 · focus · HN ↗
    Did you verify that we can't verify?
    undershirt · 1789688631 · focus · HN ↗
    I think so. Are you familiar with epistemology and how assumptions can be formally justified?
    GoblinSlayer · 1789724796 · focus · HN ↗
    Are you familiar with fallibilism? Aristotle justified geocentrism too. Who's to say your justification is correct for real this time?
    undershirt · 1789749674 · focus · HN ↗
    Fallibilism seems to smuggle a claim of certainty about how we can't be certain about anything, which leads to a performative contradiction when brought up in an argument where people are trying to arrive at certainty.
    GoblinSlayer · 1789806220 · focus · HN ↗
    If you don't like such skepticism, then it should be okay to believe in fields. Where do you draw a line, how much skepticism is enough? Does radio exist? You can't see it, just like other fields.
    undershirt · 1789832123 · focus · HN ↗
    I was only addressing your argument. If fallibilism leads to a contradiction then it doesn't work to undermine all agnostic arguments against the actual reality of fields.
    My warning is that science becomes something like a 'scientism' religion when "real" is used as shorthand for "effective abstraction". Science has philosophical boundaries that isn't part of the science curriculum.
    GoblinSlayer · 1789986943 · focus · HN ↗
    It was your argument that you verified that we can't verify. But if we can't verify, then how could you verify? Fallibilism doesn't lead to a contradiction, it only rejects infallibility. If you think agnosticism helps you prove your infallibility, prove it. Also radio demonstrates that your approach is unworkable.
4. rramadass · 1789665410 · focus · HN ↗
  Read my other comment here first which answers your first part - <a href="https://news.ycombinator.com/item?id=49738762">https://news.ycombinator.com/item?id=49738762
  > Thorough worshipping of Math and “Mathers”, like as if they are a gift from God
  "There is no God and Dirac is his Prophet" -- Wolfgang Pauli.
  > Again, let’s stick with Hume, you’re the shit until you’re not.
  BS. Hume's ideas of Mathematics and their usage in Science were laughable (they predated modern mathematics and physics). The mathematics used in a theory has tremendous predictive power and does not depend on "miracles". So we know where it works and where it does not.
  > Einstein went to death not understanding Physics as he wanted to.
  No, that is not quite true. Einstein perfectly understood quantum physics/mechanics but considered it incomplete and philosophically abhorrent.
  > God loves that essay Hume wrote, truly. It’s all fun and games until God mindfucks your understanding.
  Nonsense.
VorpalWay · 1789633486 · focus · HN ↗
Shouldn't this have a "(1939)" suffix on the title according to HN rules? ;)
1. sigmoid10 · 1789635944 · focus · HN ↗
  Should it though? I don't see such a rule.
  <a href="https://news.ycombinator.com/newsguidelines.html">https://news.ycombinator.com/newsguidelines.html
  1. baxtr · 1789638944 · focus · HN ↗
    unwritten rules
    sigmoid10 · 1789714307 · focus · HN ↗
    Why should anyone know or care about it then? This is not a static platform with a static userbase.
    baxtr · 1789722530 · focus · HN ↗
    another unwritten rule: don't take everything too serious that you read here ;)
    sigmoid10 · 1789751590 · focus · HN ↗
    Then let's make up another rule while we're at it: Don't use smileys to change the meaning of your statements.
  2. delichon · 1789645138 · focus · HN ↗
    Kaffee: Corporal, would you turn to the page in this book that says where the mess hall is, please? Barnes: Lieutenant Kaffee, that’s not in the book, sir. Kaffee: You mean to say in all your time at Gitmo you’ve never had a meal?
    sigmoid10 · 1789714432 · focus · HN ↗
    Your quote should give proper attribution according to the rules.
2. ape4 · 1789646372 · focus · HN ↗
  If an article is a few years old then it could be out-of-date. But if an article is almost 100 years old then its classic.
3. [deleted] · 1789657199 · focus · HN ↗
  [deleted]
jdw64 · 1789636728 · focus · HN ↗
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GoblinSlayer · 1789637250 · focus · HN ↗
>but as time goes on it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which Nature has chosen
This is quantifiable, right? Should be possible to measure how many mathematicians favor ideas like turbulence, macroscopic quantum physics, anthropic principle, analog geometry, finitism. I think, mathematics doesn't really try to match physics yet.
1. huurtehoog · 1789648350 · focus · HN ↗
  I think this passage is more about the fact that mathematics is a form of symbolic computation people create and it is weirdly congruent to the physical measurements and models of reality. Not that mathematicians find certain models and objects used in physical models in a favorable way. What favor even means here?
  It is quantifiable: several mathematical objects and categories people invented to do symbolic computation in letters and published papers is somehow very useful to model and understand data from physical measurements of reality.
  I highly recommend reading the "Unreasonable effectiveness of mathematics" essay by Wigner:
  <a href="https://www.hep.upenn.edu/~johnda/Papers/wignerUnreasonableEffectiveness.pdf" rel="nofollow">https://www.hep.upenn.edu/~johnda/Papers/wignerUnreasonableE...
  1. GoblinSlayer · 1789677405 · focus · HN ↗
    I don't see unreasonable effectiveness of mathematics. On one hand, it's a self fulfilling prophecy: if your math doesn't work, just make different math, and so on until it works (gravity was invented, like, 4 times), so it's as effective as logic. On the other hand, it's fundamentally approximation limited by precision, so for any model we know when it breaks. And it's basically unworkable for chaotic or exponentially complex phenomena.
    podocarp · 1789690076 · focus · HN ↗
    You're just claiming it's effective. We know it's effective. But there's no reason it should be effective. It's primarily because philosophy has not caught up and we still can't explain the foundations of mathematics and causality. These things seem to be baked into our very nature. It is possible to image an alien race with different conceptions of logic and causality that are just unable however hard they try to formulate either proper mathematics or proper physical laws from mathematics. (Take for example the Pythagoreans who could not believe irrational numbers existed, so the famous cube root of 2 was fake news to them. They could never build their little cubic altar to whomever.)
    GoblinSlayer · 1789723253 · focus · HN ↗
    Mathematics can model simple parts of physics, because mathematics is simple and can do simple things, like a puddle fits in the hole. It doesn't model complicated parts of physics, because it can't to complicated things, because mathematics is invented by humies and thus limited by humie cognitive abilities.
    huurtehoog · 1789730107 · focus · HN ↗
    > Mathematics can model simple parts of physics, because mathematics is simple and can do simple things, like a puddle fits in the hole. It doesn't model complicated parts of physics, because it can't to complicated things,
    You ought to learn some advanced mathematics to avoid making such absurd claims as "mathematics is too simple to model complex physics"
    Pray tell what parts of physics are too complicated for mathematics
    lioeters · 1789752259 · focus · HN ↗
    It's a waste of time arguing with someone who can utter such a nonsensical statement, that mathematics "can't do complicated things", that physics is "complicated", and therefore mathematics can't model physics. With such sloppy thinking and ignorance of the subject, they feel confident to post numerous comments in public exhibiting their embarrassing intellect. Many such cases.
    GoblinSlayer · 1789803522 · focus · HN ↗
    Chaos and exponential complexity.
2. DonaldFisk · 1789648777 · focus · HN ↗
  In favour of Dirac's point, and not known at the time he gave the talk, the standard model of particle physics is based on the symmetry groups U(1), SU(2), and SU(3), so Lie groups (which mathematicians find interesting) appear to have been chosen by nature.
3. empath75 · 1789651647 · focus · HN ↗
  I sort of have this suspicion that the kinds of phenomena that we can even apprehend are pretty closely related to what we can reason about mathematically, and the reason that math seems to work so well to model behavior that we understand says more about how our brain works than how the universe works.
  If a phenomenon isn’t model-able by relatively simple math it doesn’t even look like a phenomenon to us, it looks like a chaotic mess.
  Which is to say that unless something has mathematical coherence it is more or less invisible to our experience.
  1. sigbottle · 1789655130 · focus · HN ↗
    Well there are counting arguments to say that a higher level intelligence that somehow achieves say, 100000× brain efficiency of humans, still can't do that much more work than humans, if humans found the "best abstraction". Think about computability for example - that means you could feasibly solve problem instances of n+20 relative to what a human can solve.
    Of course, I think putting numbers to wishy washy meta-quantities like "how efficiently does a certain conceptual scheme help you" are super loaded and hard to properly talk about (incommensurability). I've been toying with trying to make a repository of all the possible "moves" one can make in this kind of abstract analysis - constrain the problem statement, argue something like "the system is what it does", dissolving, etc. but even that seems hard
  2. axionbraid · 1789662389 · focus · HN ↗
    [dead]
  3. rramadass · 1789663649 · focus · HN ↗
    In case you haven't read it; see "Science and Method by Henri Poincare" - <a href="https://archive.org/details/sciencemethod00poinuoft" rel="nofollow">https://archive.org/details/sciencemethod00poinuoft
    Here is a summary - <a href="https://thetelos.org/science-and-method-science-et-methode-henri-poincare/" rel="nofollow">https://thetelos.org/science-and-method-science-et-methode-h...
    Here is a video discussion - <a href="https://www.youtube.com/watch?v=sQ-t8-igDZo" rel="nofollow">https://www.youtube.com/watch?v=sQ-t8-igDZo
    The thesis is that Science is made for efficiency and hence does not include everything (which is infinite). It only looks for a hierarchy of interesting facts and focusing on simple foundational recurring phenomena from nature. It then uses the language of Mathematics to economize and impose order on the complexity to make it tractable.
    Finally, our subconscious prefers aesthetic attributes and hence we often find/create harmony/symmetry/beauty in our mathematical products.
    podocarp · 1789690677 · focus · HN ↗
    Perhaps symmetry is overrated and it is not the beauty that works, but it's economy. If something is symmetric depending on how symmetrical you can remove half or more of the required work during calculation. It is also useful to work in abstractions where it does not related to the system 1:1 but is some transformed representation (e.g. phase space). And it may be useful when you find a way to transform it to some easily solvable (symmetrical?) state, solve it there, and reverse the transform. Think of working in Cartesian and polar coordinates. Just a change in coordinate representations can improve your quality of life immediately on some problems with different symmetry. There's no intrinsic reason other than its much simpler on one than the other. Beauty doesn't have to come in. If it's round it's round. If it's square it's square.
    So I think symmetry might just be one of the tricks that keep working and keeps on giving back and so we love it and call it "beautiful".
taaha47 · 1789637505 · focus · HN ↗
"I would like to put forward a suggestion as to how such a scheme might be realized. If we express the present epoch, 2 x 109 years, in terms of a unit of time defined by the atomic constants, we get a number of the order 1039, which characterizes the present in an absolute sense. Might it not be that all present events correspond to properties of this large number, and, more generally, that the whole history of the universe corresponds to properties of the whole sequence of natural numbers? At first sight it would seem that the universe is far too complex for such a correspondence to be possible. But I think this objection cannot be maintained, since a number of the order 1039 is excessively complicated, just because it is so enormous. We have a brief way of writing it down, but this should not blind us to the fact that it must have excessivly complicated properties."
this cannot be an early hint to the result made by chaitin; Chaitin’s Incompleteness Theorem?
1. rramadass · 1789639713 · focus · HN ↗
  Related;
  From Heisenberg to Goedel via Chaitin - <a href="https://arxiv.org/abs/quant-ph/0402197" rel="nofollow">https://arxiv.org/abs/quant-ph/0402197
2. rramadass · 1789640279 · focus · HN ↗
  Just to clarify; The term "2 x 109" is actually "2 x 10^9" or 2 billion years which was considered the present epoch i.e. accepted age of the universe at that time.
  Dirac large numbers hypothesis - <a href="https://en.wikipedia.org/wiki/Dirac_large_numbers_hypothesis" rel="nofollow">https://en.wikipedia.org/wiki/Dirac_large_numbers_hypothesis
  1. DonaldFisk · 1789642534 · focus · HN ↗
    Correct (but now we know it should be somewhat higher than that), and 1039 should be 10^39, one of Dirac's Large Numbers, the size of the observable universe in atomic units, and also the ratio of electromagnetic to gravitational forces in the hydrogen atom.
    rramadass · 1789644503 · focus · HN ↗
    Right. Added the wikipedia link to Dirac's LNH above.
    Also found this; The fundamental constants and their variation: observational status and theoretical motivations - <a href="https://arxiv.org/abs/hep-ph/0205340" rel="nofollow">https://arxiv.org/abs/hep-ph/0205340
Xmd5a · 1789639646 · focus · HN ↗
> The dominating idea in this application of mathematics to physics is that the equations representing the laws of motion should be of a simple form. The whole success of the scheme is due to the fact that equations of simple form do seem to work. The physicist is thus provided with a principle of simplicity, which he can use as an instrument of research.
<a href="https://arxiv.org/abs/math-ph/0009007" rel="nofollow">https://arxiv.org/abs/math-ph/0009007
> Occam's Razor as a Formal Basis for a Physical Theory
> We introduce the principle of Occam's Razor in a form which can be used as a basis for economical formulations of physics. This allows us to explain the general structure of the Lagrangian for a composite physical system, as well as some other artificial postulates behind the variational formulations of physical laws. As an example, we derive Hamilton's principle of stationary action together with the Lagrangians for the cases of Newtonian mechanics, relativistic mechanics and a relativistic particle in an external gravitational field.
anthk · 1789639863 · focus · HN ↗
Now dive down into Math with Penrose and David Bohm with the implicate order.
1. rramadass · 1789645209 · focus · HN ↗
  Quite independently of the Mathematics, Bohm's ideas of "Implicate and Explicate Order" are very interesting and comprehensible by the layman at a high-level - <a href="https://en.wikipedia.org/wiki/Implicate_and_explicate_order" rel="nofollow">https://en.wikipedia.org/wiki/Implicate_and_explicate_order
  In particular, students of Hindu Philosophical Schools will find lots of parallels here. Bohm was heavily influenced by Jiddu Krishnamurti which inspired his take on quantum theory.
  Bohm also wrote a great book, "Quantum Theory" based on the Copenhagen Interpretation which contains separate parts on "Physical Formulation" and "Mathematical Formulation" of quantum theory.
  1. lioeters · 1789661794 · focus · HN ↗
    Great answer.
thisisauserid · 1789640633 · focus · HN ↗
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3lambda · 1789650848 · focus · HN ↗
Given its strength in mathematics, it seems likely that AI should be of great help with discovering new physics. We just need to teach it to ask interesting questions.
1. jbmchuck · 1789651621 · focus · HN ↗
  How does this comment relate to the article?
  1. JimmyBuckets · 1789652771 · focus · HN ↗
    Dirac comments that he thinks a potential path to the discovery of new physics is to start with a mathematical domain and work outwards from there, guided by mathematical beauty. This is what I took OP's comment to be about - of course setting aside questions on an LLMs ability to recognize beauty
    goatlover · 1789662441 · focus · HN ↗
    Superstring theory has been based on the idea of mathematical beauty, but it's run into serious complications when it to empirical results. Science is empirical first and foremost, because we need to verify that theories actually predict the universe we live in.
    pixl97 · 1789666875 · focus · HN ↗
    Actually there are people attempting to find new math via biological entities. Cells and such. The interesting thing here is it is easily falsifiable even though working at these scales is still insanely hard.
    Take the golden rule for example. It's a simple algorithm that shows up everywhere in nature. It represents the least amount of energy needed to assemble all kinds of structures. The gist here is nature finds these algorithms via evolution over billions of years and quadrillions of individual life experiments. We see life finding simple algorithms and platonic maths, how complex of algorithms has it found?
    You no longer have to do an impossible number of experiments, instead you have to tease apart gene expressions to turn them on and off. Now, that is still a monumental task, but it's still doable in a reasonable amount of time.
  2. [deleted] · 1789656780 · focus · HN ↗
    [deleted]
voxleone · 1789655697 · focus · HN ↗
There's this little pet project of mine, the Functional Universe [0]. It explores a direction suggested by Dirac: treating mathematical structure and transformation not merely as a language for describing physical reality, but as potentially constitutive of it. FU models physical reality in terms of functional state evolution, with an emphasis on composition, aggregation, and transitions. In that sense, I think there's an interesting point of contact with Dirac's emphasis on transformations: Dirac points toward transformations as fundamental mathematical structures from which physics might be derived; FU asks what happens if physical reality itself is formulated in terms of transitions and their composition.
[0] <a href="https://voxleone.github.io/FunctionalUniverse/" rel="nofollow">https://voxleone.github.io/FunctionalUniverse/
1. [deleted] · 1789657258 · focus · HN ↗
  [deleted]
2. lioeters · 1789661396 · focus · HN ↗
  Curious, in this model, is there any discussion on whether the mathematical structures underlying space-time are continuous or discrete?
  1. lerp-io · 1789664343 · focus · HN ↗
    universe is continuous / cant be proven otherwise but any measurement or simulation of it is discrete by nature same reason pi is computed infinitely computed and reason why calculus exists and why math exists at all to try and explain continuity of nature even if all of it is perceived discretely.
    pixl97 · 1789665331 · focus · HN ↗
    The question is what exactly is continuous. The quantum fields themselves? And we have no evidence the the quantum fields are discrete quantum states themselves, but the particles they produce appear otherwise.
    It's always possible that continuous maths are a side effect of this field. Of course, the causality could be revered.
    podocarp · 1789691123 · focus · HN ↗
    It is an interesting discussion you bring up but will take much more than a comment to talk about. There is a divide between mathematics and physics regarding numbers. Real numbers have supposedly infinite precision, and arbitrary size, which are not true in our physical universe. Indeed infinities have given physicists quite some headaches. It's a bit of a dark art as to where you can and cannot just use infinity willy nilly and many have expressed distaste to it. Also at some point you have to talk about computability, like are these infinite precision and magnitudes even real if nothing in the universe even gets close, what is omega to the omega, statements dream up by the utterly deranged?
    I remember there being a talk or some article about this but can't find it anymore, but it is an interesting thing.
    GoblinSlayer · 1789724233 · focus · HN ↗
    Only infinite magnitude causes problems in physics, infinite precision doesn't. Real numbers have infinite number of digits only in digital model of numbers, so their infinite size is a modelling artifact.
    lerp-io · 1789721191 · focus · HN ↗
    if you think of universe as minecraft lattice (which is arguably best way to think of it and explain all of physics currently in existence in intuitive level) then yea, it can be like eg a spin lattice discrete at some plank length from which field perturbations as particles emerge..look up spin lattice from <a href="https://arxiv.org/abs/hep-th/0507118" rel="nofollow">https://arxiv.org/abs/hep-th/0507118 so basically bringing back idea of quantum ether cuz explaining empty space with waves without some underlying structure doesn't really make sense anyway since all other waves have mediums in nature.
    GoblinSlayer · 1789723660 · focus · HN ↗
    The underlying structure is the quantum field, it looks empty to particles just like steel looks empty to sound.
3. pixl97 · 1789665117 · focus · HN ↗
  I think Michael Levin is also doing work around platonic math being a thing that exists moreso than an actual concept. His work is related to biologies discovery of algorithms, the complexity levels of simple algorithms, and n-order effects that life is finding way to exploit for computational purposes.
  While not being deeply familiar with the work but I think the short of it is that life has found algorithms at many different orders that we've not discovered them yet, and by 'running' these different algorithms it turns many P problems into NP problems.
  The interesting thing about it is you can make falsifiable tests around this and do actual science around it.
4. podocarp · 1789690816 · focus · HN ↗
  Btw it's unredable on mobile because the table of contents box blocks the actual contents
[deleted] · 1789657141 · focus · HN ↗
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sahil50 · 1789666756 · focus · HN ↗
[dead]
jimbokun · 1789667116 · focus · HN ↗
Did Dirac’s prediction that studying “beautiful” mathematics would lead to breakthroughs in the understanding of Physics pan out?
1. lacker · 1789670512 · focus · HN ↗
  Yes, quite well in fact. This lecture was in 1939. In the 50's, Lie groups (previously just a pure, beautiful mathematics) were used in particle physics. Gell-Mann used SU(3) to predict some new particles before anyone observed them.
  And then similar stuff happened later in quantum mechanics, with gauge theory, but I understand that only at a handwavy level. I think overall the "standard model" is a perfect example of what Dirac predicted.
  Whether this still holds up in the past 40 years is another question. I don't have a great example from my lifetime.
  1. GoblinSlayer · 1789675742 · focus · HN ↗
    The standard model is completely accidental, no? Also hierarchy problem.
  2. skew-aberration · 1789724345 · focus · HN ↗
    Also a layman but I have a different read of it.
    1) Dirac actually developed big parts of Lie Theory and its application in relativistic particle physics, without using the mathematical formalisms at all (until later on).
    His work was subsumed/beautified by mathematicians after the fact (30s), an 'optimization' really which helped to extend and understand it further, not to discover it. The Gell-Mann prediction mirrors Dirac's own positron (non)prediction closely but was done without Lie formalisms.
    The applications of Lie theory in relativistic fields theories began even earlier, with the Noether/Klein/Hilbert/Einstein collaboration in 1910s.
    2) Continuous symmetries are a convenience and not essential to particle physics IMHO.
    e.g. It's obvious we can swap positive and negative charge and get the same physics. That's a discrete symmetry. But in gauge theories the symmetry is not +ve <-> -ve, but rather the continuous rotation of the unit circle in a complex plane. electron becomes proton via complex numbers. It doesn't mean there's a complex electron with +-ie charge, but it does work better with relativistic Lagrangian fields theories where phase changes are continuous and frame dependent. Noether's methodology of using an invariant action integral leverages the Lie theory very effectively, but there are other ways to skin that cat though.
    3) Beauty is in the eye of the beholder, but I doubt the standard model and the perturbative methods (renormalization, etc) underpinning it would be to Dirac's liking.
viamiraia · 1789677150 · focus · HN ↗
as an example of this, pretend probability is a velocity: <a href="https://www.mathpages.com/home/kmath216/kmath216.htm" rel="nofollow">https://www.mathpages.com/home/kmath216/kmath216.htm
going beyond that page, think about beta distributions (and dirichlets). they are probability distributions about probabilities. try recentering the beta distribution between -1 and 1 first (representing c).
going even further, recall the bernoulli-binomial-beta connection. treat the recentered beta distribution's parameters as bernoulli trials. try placing them in a light cone. let me know what interesting things you find :)
nikisweeting · 1789726287 · focus · HN ↗
For those into deriving the laws of physics from pure math and game-of-life style iteration of simple rules, checkout the Wolfram Physics Project: <a href="https://www.wolframphysics.org/" rel="nofollow">https://www.wolframphysics.org/
<a href="https://github.com/pirate/wolfram-gauge-physics" rel="nofollow">https://github.com/pirate/wolfram-gauge-physics

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