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I thought this article had an interesting take on philosophy of science. Sharing it cause I hadn’t run across this perspective before.

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    EDIT: Vented way too hard here and I apologize for that.

    Although the shape is a physical phenomenon, scientists don’t even attempt to study it.

    That’s not what “studying physical phenomena” means.

    The most obvious example is symmetry of location. This means that if one performs the same experiment in two different places, the results should be the same.

    That’s not what ‘symmetry of location’ means. In physics, it means the laws of physics won’t change in respect to location. The experiment will still be different at different locations, aka it’s an experiment.

    Symmetry of time means that the outcomes of experiments should not depend on when the experiment took place.

    See above.

    In contrast, if her experiments failed to be symmetric, she would ignore them.

    No, she’d ask “why”.

    He postulated that the laws of physics should be the same even if the experimenter is moving close to the speed of light.

    That’s not what he said. He said that if you’re not accelerating, light still moves at c with respect to you.

    Whether or not a computer will halt for a given input can be seen as a physical question and yet we learned from Alan Turing that this question cannot be answered.

    That’s not what the halting problem means.

    Einstein was the first to understand that symmetry was the defining characteristic of physics.

    Lagrange and Hamilton beat him by a century.

    A little after Einstein showed the vital importance of symmetry for the scientific endeavor, Emmy Noether proved a powerful theorem that established a connection between symmetry and conservation laws

    Noether’s theorem (arguably one of the most groundbreaking theorems in mathematical physics) has nothing to do with Einstein’s work, and probably wasn’t influenced by it at all.

    Whatever has symmetry will have a law of nature. The rest is not part of science.

    What

    The physicist must be a sieve and study those phenomena that possess symmetry and allow those that do not possess symmetry to slip through her fingers.

    What

    All phenomena seem to come from these theories, even those that do not seem to have symmetry.

    “Emergent behavior” is a thing in physics.

    Determining the winner of an election is too complicated for the scientist to deal with, but the results of the election are generated by laws of physics that are part of science.

    There are types of science aside from physics.

    We postulated that, for the most part, the universe is chaotic and there is not so much structure in it. We, however, focus only on the small amount of structure that there is.

    Emergent behavior is a thing in physics.

    Similarly, one who believes in the multiverse believes that most of the multiverse lacks the structure to form intelligent life.

    That’s only a property in common in an extremely nebulous analogy way.

    The new system that one develops has less structure (i.e. fewer axioms) than the starting system.

    That’s not what axioms are.

    The quaternions show up in physics but are not a major player.

    Because we found much better ways of writing equations without them.

    Rather than looking at the real numbers as central and the octonions as strange larger number systems, think of the octonions as fundamental and all the other number systems as just special subsets of octonions. The only number system that really exists is the octonions.

    That’s not how “fundamental number systems” work.

    Take, for example, any group

    Good job explaining complex numbers like I’ve never heard of them before but drop in groups like I’m familiar with the mathematical definition of a group.

    We simply select those parts that satisfy the axiom and ignore (“bracket out”) those that do not.

    That’s not what axiom means.

    Notice that the mathematics for a subset chosen to satisfy an axiom is easier than the mathematics for the whole set.

    That isn’t necessarily true. It depends on the subset you pick and what you’re trying to do.

    These two bracketing operations work hand in hand.

    No they don’t. His argument involves taking a complex mathematical base and simplifying it, versus simple physical principles that get insanely complicated when you introduce emergent behavior.

    The job of physics is to formulate a function from the collection of observed physical phenomena to mathematical structure

    No, it’s to make predictions. Mathematics is incredibly useful to that, but we don’t need to mathify everything in physics to understand things.

    When physicists started working with quantum mechanics they realized that the totally ordered real numbers are too restrictive for their needs. They required a number system with fewer axioms. They found the complex numbers.

    Physicists were using complex numbers well before quantum physics came along.

    In quantum mechanics it is known that for some systems, if we first measure X and then Y, we will get different results than first measuring Y and then measuring X. In order to describe this situation mathematically, one needed to leave the nice world of commutativity. They required the larger class of structures where commutativity is not assumed.

    I don’t have an example off the top of my head but I’d be pretty surprised if we weren’t using noncommutativity well before this.

    When Boltzmann and Gibbs started talking about statistical mechanics, they realized that laws they were coming up with were no longer deterministic. Outcomes of experiments no longer either happen (p(X) = 1) or do not happen (p(X) = 0). Rather, with statistical mechanics one needs probability theory.

    HAVE YOU HEARD OF EMERGENT BEHAVIOR BEFORE

    In order to describe more phenomena, we will need larger and larger classes of mathematical structures and hence fewer and fewer axioms.

    It depends on what you’re doing, really. Statistical Mechanics is all about distributions, but the same doesn’t hold for GR. And GR has hyperbolic geometry which SM doesn’t need. Oh, and please stop saying axioms when you mean properties.

    One possible conclusion would be that if we look at the universe in totality and not bracket any subset of phenomena, the mathematics we would need would have no axioms at all.

    Gah!

    Total lawlessness! The mathematics are just plain sets without structure.

    This isn’t even wrong! We’ve somehow gone from “Math is hard and physics has a lot of math” to “physics isn’t real”! How does this even happen?!

    It is only the way we look at the universe that gives us the illusion of structure.

    Am I being pranked? Is this a prank article?

    Noson S. Yanofsky has a Ph.D. in mathematics from The Graduate Center of The City University of New York.

    You should know better than this. Stop using the word axiom.

    In conclusion, I am very sad now.

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      I think your rant is just fine; a lot of the stuff you quoted from the article is complete BS.

      Scott Aaronson (I think?) has a good article that I can’t seem to find where he talks about this weird argument that “science can’t predict the election outcome, therefore it’s incomplete”. The answer here is that, in fact, physics does predict the election outcome, we just know from computational complexity and chaos theory that we can’t practically follow through with making that prediction.

      The rest of this article is insanely hand-wavy or just plain incorrect. It reads like an acid-inspired hippy talking about cosmic vibrations, except replace “vibrations” with “symmetry”. You covered most of the objections I have.

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      I thought this was a great introduction to contemporary metaphysics. If you read this and didn’t freak out like hwayne but actually found it interesting and thought-provoking, I recommend taking a look at Deleuze’s writings.

      Deleuze was probably the greatest metaphysician in recent memory. Heidegger said that Nietzsche’s statement that “god is dead and we have killed him” means the end of metaphysics. But Deleuze’s response was simple: if the old metaphysics was wrong, we should build a new one. This new metaphysics that Deleuze started building incorporates 20C mathematics and physics, nonlinear dynamics and chaos theory, probability and self-organizing systems, computability and Turing’s ideas on ordinal logics, and lots of graph theory (e.g. the “rhizome” concept from Capitalism and Schizophrenia).

      Contemporary metaphysics is very similar to yet much more thorough than this article, but it is all very interesting. If it sounds interesting to you then I recommend exercising the priciple of charity and picking up some of Deleuze’s early work, Nietzsche and Philosophy is a good one to start with. Difference and Repetition is where the metaphysics gets really developed.

      Edit: What is Philosophy? by Deleuze and Guattari is another good book to start with. Also I added links.

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        Okay, now that I’m a bit more coherent I’d like to address one of the big things that bothers me about his argument. He says “the universe lacks structure” and everything seems so ordered (to some definition of order) because we ignore all of the messy parts of physics. The problem is that his argument is based on the idea that the fewer axioms properties the system has, the harder it is to understand. But for the vast majority of physics research, the opposite is true: the basics are, for the most part, pretty easy to model. The problems start not when you take stuff away, but when you add it.

        The archetypical example is the N-body problem. Given two masses exerting gravitational pull on each other, how do they move over time? Not only is there a perfect analytic solution, you could assign deriving it as a high-school homework problem. How about three masses? Turns out a solution is impossible. But that change isn’t driven by any sort of fundamental shift in physics. It’s the same laws of physics in both situations. Adding that extra body just makes things too complicated to handle.

        Obviously there are exceptions, and fairly big ones. But when we say that the universe seems ordered, what we mean is that everything obeys our current understanding of physics. A few things don’t, not because they have different physics but because there are gaps in our understanding. And many, many things do but are incomprehensible to us, because even a few particles give rise to complex emergent behavior, let alone untold nonillions.

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          The problems start not when you take stuff away, but when you add it.

          If that’s true couldn’t it be possible to just invert this argument and come up with a similar conclusion? For example, the universe has a high amount of complexity (stuff added to it) but “physics” is our limited, simplified understanding of this greater complexity (such that physics arises insofar as we subtract complexity that is truly present in reality).

          Edit/disclaimer: I don’t have a strong opinion either way. I just think this is interesting to think about :)

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            The idea isn’t that “we ignore the messy parts of physics.” It is this: we introduce structure in the very act of interpreting our observations of the universe. Interpretation in science necessarily involves partitioning the world into smaller parts - the science of chemistry only studies interactions between chemicals, for example. And in chemistry there is a certain structure to how things work that isn’t as prevalent in e.g. particle physics. We could use physics to do all of our chemistry, but that would be difficult, so we use this higher level of abstraction to interpret chemical interactions because it allows us a more convenient structure. The point is that, by creating chemical formulas and partitioning chemistry from physics, we have introduced structure into the world by way of our interpretation. This is generally true: the world is chaotic, we introduce orderly structure in our interpretations because it is easier for us to understand and make predictions with.