Thread

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

172 points · 84 comments · rramadass

general_reveal · 1789632157 · focus · HN ↗
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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 second 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. Dirac is 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 beautiful and (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.
    [deleted] · 1789668130 · focus · HN ↗
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    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 ↗
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    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 please? I'm not aware of him linking complexity to regularity.
    GoblinSlayer · 1789725199 · focus · HN ↗
    Chicken and farmer.
    n4r9 · 1789726564 · focus · HN ↗
    That's Russell rather than Hume, and I don't see how it links to complexity.
    GoblinSlayer · 1789806305 · focus · HN ↗
    The chicken has a problem with prediction of future because of intelligent behavior of the farmer, i.e. the farm is a conspiracy of sorts.
    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 ↗
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    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 in 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.

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