Luke Muehlhauser interviews me about philosophical progress

I’m shipping out today to sunny Rio de Janeiro, where I’ll be giving a weeklong course about BosonSampling, at the invitation of Ernesto Galvão.  Then it’s on to Pennsylvania (where I’ll celebrate Christmas Eve with old family friends), Israel (where I’ll drop off Dana and Lily with Dana’s family in Tel Aviv, then lecture at the Jerusalem Winter School in Theoretical Physics), Puerto Rico (where I’ll speak at the FQXi conference on Physics of Information), back to Israel, and then New York before returning to Boston at the beginning of February.  Given this travel schedule, it’s possible that blogging will be even lighter than usual for the next month and a half (or not—we’ll see).

In the meantime, however, I’ve got the equivalent of at least five new blog posts to tide over Shtetl-Optimized fans.  Luke Muehlhauser, the Executive Director of the Machine Intelligence Research Institute (formerly the Singularity Institute for Artificial Intelligence), did an in-depth interview with me about “philosophical progress,” in which he prodded me to expand on certain comments in Why Philosophers Should Care About Computational Complexity and The Ghost in the Quantum Turing Machine.  Here are (abridged versions of) Luke’s five questions:

1. Why are you so interested in philosophy? And what is the social value of philosophy, from your perspective?

2. What are some of your favorite examples of illuminating Q-primes [i.e., scientifically-addressable pieces of big philosophical questions] that were solved within your own field, theoretical computer science?

3. Do you wish philosophy-the-field would be reformed in certain ways? Would you like to see more crosstalk between disciplines about philosophical issues? Do you think that, as Clark Glymour suggested, philosophy departments should be defunded unless they produce work that is directly useful to other fields … ?

4. Suppose a mathematically and analytically skilled student wanted to make progress, in roughly the way you describe, on the Big Questions of philosophy. What would you recommend they study? What should they read to be inspired? What skills should they develop? Where should they go to study?

5. Which object-level thinking tactics … do you use in your own theoretical (especially philosophical) research?  Are there tactics you suspect might be helpful, which you haven’t yet used much yourself?

For the answers—or at least my answers—click here!

PS. In case you missed it before, Quantum Computing Since Democritus was chosen by Scientific American blogger Jennifer Ouellette (via the “Time Lord,” Sean Carroll) as the top physics book of 2013.  Woohoo!!

77 Responses to “Luke Muehlhauser interviews me about philosophical progress”

  1. Rahul Says:

    Nice interview! I was intrigued by this quote:

    “But there were also scientists like Einstein, Schrodinger, Godel, Turing, or Bell, who not only read lots of philosophy but (I would say) used it as a sort of springboard into science — in their cases, a wildly successful one.”

    No doubt, say, Einstein was deeply interested & contributed to philosophy; but did he really use it as a springboard into science? I’m just curious how this springboard worked. Can anyone elaborate?

    I always somehow saw their Philosophy as an “effect” or a postscript once they realized the implications of their science which is why the springboard analogy is very interesting.

  2. rrtucci Says:

    Einstein used philosophy to decide that God does not play dice with the universe, and to work on a TOE (without QM because of philosophical concerns) when the tools for a TOE were not available and it was futile but philosphically fascinating to work on this.

  3. John Sidles Says:

    Scott Aaronson remarks  “But there were also scientists like Einstein, Schrodinger, Godel, Turing, or Bell, who not only read lots of philosophy but (I would say) used it as a sort of springboard into science … in their cases, a wildly successful one.”

    Like Rahul (#1), this (as it seems to me) is a fine observation.

    John von Neumann’s brother Michael — also a scientist/engineer (whom I knew in graduate school) — assured me that (John) von Neumann pursued, not philosophy, but history, specifically Roman history, to much the same purpose.

    E.g., when it came time to choose scientific leaders for the US missile-and-space program, von Neumann’s political worldview\[\text{Pax Romana} \Rightarrow \text{Pax Americana}\] was crafted (according to brother Michael) with a foresighted view toward immediate appreciation and broad-based public confidence.

    The trust so cultivated played a crucial role in von Neumann’s ascension to trusted science-and-technology leader (a “wildly successful” leader in Scott’s phrase) of the TeaPot Committee of 1953 that launched America’s space program.

    The contrast of von Neumann’s carefully-crafted history-guided readily-trusted public persona with that of his friend (and fellow Hungarian) Leo Szilard … whose scathing parodies relentlessly hectored politicians, generals, and even his fellow scientists … could scarcely be more striking.

    Conclusion The well-considered appreciation of philosophy and/or history can provide a powerful springboard both to individual innovation *and* public understanding. So choose your favorite philosophers and historians wisely!

  4. Bram Cohen Says:

    Hey Scott, what do you make of Heisenberg’s more, ahem, obscure writings?

    Also, in your ‘name the higher number’ essay, it seems like you skipped over a step, specifically the one talking about ‘The number of steps which the iteration process defined in Goodstein’s Theorem takes on 111111′, although maybe that violates the ground rules by not using any standard mathematical notation.

  5. Peli Grietzer Says:

    ‘By far the most important disease, I’d say, is the obsession with interpreting and reinterpreting the old masters, rather than moving beyond them.’

    I think this might be a specifically Berkeley thing? There’s relativelhy little history or textual analysis in contemporary analytic philosophy, especially after the undergrad level. If you check out the Philosopher’s Annual about 5% of the papers have to do with an old master: http://www.pgrim.org/philosophersannual/past.html

  6. Luke Muehlhauser Says:

    Peli,

    The judges for the Philosopher’s Annual are unusually heavy in formal philosophy. A more representative sample of contemporary analytic philosophy might be found in the top-ranked philosophy journals (http://is.gd/KfAdoz): Philosophical Review, Journal of Philosophy, Nous, Mind, and Philosophy & Phenomenological Research.

    Those journals still publish quite a fair number of backwards-facing papers. E.g. see the book reviews in the latest issue of Philosophical Review. But in my experience, they are still much better than lower-ranking journals, which seem to publish even more papers of the history/text-analysis sort.

  7. Scott Says:

    Rahul #1 and rrtucci #2: Well, Einstein was also heavily influenced by Ernst Mach’s positivist philosophy when he formulated special relativity (although Mach’s ideas were arguably more of a hindrance than a help when going from SR to GR). Einstein was also a huge fan of Spinoza throughout his life.

    Regarding “God playing dice,” I’d say that Bohr was at least as “philosophical” as Einstein was—have you read any of his writings about complementarity (or tried to)? :-) Personally, I’d say that neither Bohr nor Einstein really understood entanglement or decoherence in a modern way. You might say that Bohr and Heisenberg got closer to what we now know to be the truth about QM (i.e., that local hidden-variable theories can’t work, and the probabilities in QM can’t have an ordinary ignorance interpretation like in QM). But on the other hand, Einstein and Schrödinger were clearer in realizing that you couldn’t restrict QM to “microscopic phenomena” only using nothing but mountains of verbiage about complementarity—that once you adopted QM consistently, there would be no inherent limit to the size or spatial range of superpositions. Both sides were sort of groping toward points that Everett and Bell would make a lot sharper in the 50s and 60s.

    As for the other scientists I mentioned, Gödel spent vast amounts of time studying Leibniz. He was also peripherally involved with the Vienna Circle in the 20s and 30s, and Rebecca Goldstein makes a good case that his work on the incompleteness theorem was probably partly a reaction against the views he heard there equating truth with provability. Turing was heavily influenced as a teenager by the popular philosophical lectures of Arthur Eddington, and (as I learned recently) was also studying Descartes around the time he wrote “Computing machinery and intelligence.” Schrödinger wrote a book about philosophy (Mind and Matter), something that interested him throughout his life. Bell’s Speakable and Unspeakable in Quantum Mechanics is full of remarks of a philosophical nature, though I admit that I don’t have direct knowledge about which philosophers he read (anyone want to fill us in?).

  8. Scott Says:

    Peli #5: I did my undergrad at Cornell and grad school at Berkeley. I freely admit that the small sample of philosophy I’ve been exposed to might be unrepresentative, and I apologize if I made unwarranted generalizations.

    But just to clarify what I meant, here’s something that was striking to me. In science, not even the undergrad curriculum is based around reading and discussing the classics. Personally, I actually think we could do more of that: there’s plenty to gain from reading Galileo or Einstein or Turing in the original. But normally, scientists just take for granted that GR (for example) can be wrenched totally free from Einstein’s words and persona, and that a modern GR textbook is going to be clearer, more direct, more up-to-date, freer from misconceptions, etc. than Einstein’s original papers were. Is the same thing taken for granted in philosophy, about the possibility of (let’s say) wrenching Wittgenstein’s ideas totally free from his words and persona?

  9. Scott Says:

    Bram #4: I haven’t read much of Heisenberg, but from the little I have, I think most of what I said about Bohr in #6 would also apply. Bohr and Heisenberg both had the properties of

    (1) putting way more stress on “wave/particle complementarity” and the uncertainty principle than we’d put today,

    (2) bizarrely, saying almost nothing about the aspects of QM we do see as central today, like entanglement, the enormous size of Hilbert space, or amplitudes being complex-valued analogues of probabilities,

    (3) repeatedly, seeming to walk right up to the cusp of saying that consciousness is implicated in wavefunction collapse, reality is created by our perceptions, and various other “insane” things, but then never saying those things, and

    (4) generally, being a lot more ponderous and obscure than not only their successors, but even contemporaries like Schrödinger and Dirac.

    Regarding the Big Numbers essay: yes, you’re absolutely right, and I apologize! When I wrote the essay, as a 17-year-old back in 1998, I knew of Goodstein’s theorem but didn’t understand it and didn’t know how it fit in with the other things, so I just omitted it. I’m thinking of writing a followup to that essay (or maybe even expanding it into a popular book) someday. If and when I’ll do, I’ll be certain to discuss Goodstein and its generalizations. It’s true that, in the biggest-number contest as I defined it, the Goodstein sequence would be blown out of the water by the Busy Beaver sequence. On the other hand, as Eliezer Yudkowsky recently pointed out to me, if we changed the rules of the big number contest, so that you had to specify your number via a procedure that you could prove halted, then Goodstein and its generalizations into large-cardinal axioms and higher ordinals would be the way to go.

  10. Bram Cohen Says:

    Scott #8: I’ve heard complaints that some of Grothendieck’s works gets similar treatment, but that might just because they aren’t taught at the undergraduate level and are so difficult and voluminous.

    Scott #9: I agree with Eliezer on the rules. I probably should have pointed that out years ago, but I hadn’t read your biggest number essay in a long time and just assumed Goodstein’s was in there.

    On the high end there’s another interesting phenomenon – Ever more powerful Busy Beavers correspond to ever larger numbers, and it seems like they should be able to correspond to LCAs as well, but isn’t clear what that would even mean.

  11. wolfgang Says:

    @Scott #9

    >> Bohr and Heisenberg both had the properties of
    >> putting way more stress on “wave/particle
    >> complementarity” and the uncertainty principle
    >> than we’d put today

    I am not sure what you mean by that.
    We understand the propagation e.g. of electrons in a crystal or e.g. absorption / emission of photons thanks to the work of Heisenberg et al. and nothing has changed about the uncertainty principle in recent decades as far as I know.

    Physics is not a debate club where we put more or less stress on some facts …

  12. Lubos Motl Says:

    Hi Scott, if you manage to raise your IQ by 50 points for a few hours, you may be able to read a text

    http://motls.blogspot.com/2013/12/for-uncertainty-principle-against.html?m=1

    explaining why you’re an anti-quantum, philosophically brainwashed crank and liar, to put it mildly. Enjoy.

    Luboš

  13. Rahul Says:

    As an aside, Feynman absolutely hated these philosophers of his day, didn’t he? Just to balance the scales. I’m curious, were there other top-notch scientists that made public their disdain of philosophy?

    Another point: The philosophical debates I find fascinating are mostly science-ey. Ergo a lot of the best philosophy in this are seems to have been practiced by non-philosophers (e.g physicists, or mathematicians)

    Who are the best non-science-ey modern philosophers? Is there still post-1950 non-physical-law work that’s a major advance? Or has the bulk of it been finished by Hume et al long ago?

  14. John Sidles Says:

    Rahul asks  “I’m curious, were there other top-notch scientists that made public their disdain of philosophy”

    —–
    An oft-quoted scientists criticizes philosophers:

    Ed Wilson  “Much of the history of modern philosophy, from Descartes and Kant forward, consists of failed models of the brain.

    Ouch … oh wait, our brains make us say that.

    —–

    Philosophers punch back:

    Sidney Morgenbesser (to B.F. Skinner):  “So, you’re telling me it’s wrong to anthropomorphise humans?

    Right now the scientists are ahead on points, but (as it seems to me) the philosophers are pretty likely to win in the end.

  15. Scott Says:

    wolfgang #11:

      We understand the propagation e.g. of electrons in a crystal or e.g. absorption / emission of photons thanks to the work of Heisenberg et al. and nothing has changed about the uncertainty principle in recent decades as far as I know.

      Physics is not a debate club where we put more or less stress on some facts …

    Err, all the physicists I actually know—like all the scientists I know—are exceedingly interested in debating, not only which claims are true or false, but which ones are more or less interesting, important, or fundamental. I can’t think of a single counterexample—indeed, the people who say things like “physics is not a debate club” tend to be among the most enthusiastic of the debaters. ;-)

    You’re absolutely right that there’s been no revision to the uncertainty principle since it was discovered in the 1920s. How could there have been? It’s a simple theorem provable from the axioms of quantum mechanics, and of course those axioms have withstood every test.

    And yes, of course Bohr and Heisenberg made titanic contributions to quantum mechanics (as did Schrödinger, Einstein, Dirac, and a few others).

    In the comment you quoted, I meant nothing more or less than the following: from my perspective, if you’re teaching QM, then the pedagogically best thing to do is to start with the core idea, which I would say is the replacement of probabilities by complex numbers called amplitudes that can destructively interfere with each other. In Quantum Computing Since Democritus, I lay out a detailed argument that, once you make that single “design choice,” the other central aspects of QM—unitary evolution, the Born rule, tensor products, entanglement, mixed states—fall out more-or-less inevitably.

    As for the uncertainty principle, it’s one particular fact that you can prove about this wonderful framework that generalizes probability theory. It tells you that, if you have two “complementary” measurement bases B1 and B2, then for any state |ψ⟩, the product of your uncertainty (suitably defined) about the outcome of applying B1 to |ψ⟩ and your uncertainty about the outcome of applying B2 to |ψ⟩ must be at least some constant. It’s an interesting and important fact, but it’s not at all surprising once you’ve understood more basic facts about how Hilbert space works, and I’m not sure whether it’s more important than all sorts of other facts provable from the axioms of QM, like (let’s say) the Bell inequality, the Kochen-Specker Theorem, or the fact that ~√N steps are necessary and sufficient for searching a list of N possibilities.

  16. Scott Says:

    Everyone:

    There’s something perspective-inducing about flying south for eleven hours, the last few of them over the cloud cover of the Amazon rainforest, then descending into Rio de Janiero (my first time in Brazil), with lush green all around and oddly-shaped mountains peeking out of the mist—and then turning on my phone and being immediately greeted with a fresh screed by Lubos Motl, calling me “an anti-quantum, philosophically brainwashed crank and liar.”

    I’m too tired to respond at length to Lubos’s “arguments.” I’ll simply state for the record that:

    (1) If X was obvious to people in the 1920s, and it’s obvious to us today that X implies Y, it doesn’t follow that Y was obvious to people in the 1920s. I’ll leave it as an exercise for the reader to list counterexamples.

    (2) Lubos’s characterization of me as a “hardcore Marxist,” and of Karl Marx as my “objective materialist hero,” reveal embarrassing deficiencies in Lubos’s fact-checking operation. My true heroes have always been Engels, Lenin, and Trotsky.

  17. John Sidles Says:

    Scott Aaronson asserts: “There’s been no revision to the uncertainty principle since it was discovered in the 1920s. How could there have been? It’s a simple theorem provable from the axioms of quantum mechanics, and of course those axioms have withstood every test.”

    LOL … Scott, that statement immediately went into my database of Great Truths (truths whose opposite also is a great truth). Let us us reflect upon it.

    Observation  The Peano Axioms (1889) have “withstood every test” for the past 124 years. Yet needless to say, the post-Peano ZFC axioms have turned out to yield more general, more useful, more beautiful mathematical theorems and understanding than the (rigorously consistent but practically too-narrow) Peano Axioms ever did.

    Great Claim I: The axioms (of Hilbert-QM) have withstood every mathematical test  This claim is manifestly a Great Claim, in that Hilbert-QM fails (mathematically) to provide finite descriptions of gauge-field dynamics, and any description at all of gravitational dynamics. Distressingly, these are the only dynamical systems that Nature provides, and this striking lack of quantum dynamical diversity is a key reason why BQP computing/BosonSampling technologies are so very difficult — perhaps impossible? — to scale. So this claim is both right and wrong: it’s a Great Claim.

    Great Claim II: The axioms (of Hilbert-QM) have withstood every practical test  This claim is manifestly a Great Claim, in that quantum information theory predicts that Hilbert-QM dynamics is generically in EXP, whereas one full century of practical experience plainly shows us that that Nature’s quantum dynamics is generically in PTIME. So this claim too is both right and wrong: it’s another Great Claim.

    These reflections lead us to

    Yet Another Great Claim (following Ed Wilson)  “Much of the history of modern quantum mechanics, from Heisenberg and Schroedinger forward, consists of finding plausible excuses for relaxing the axioms of Hilbert-space dynamics.”

    Open Problems  A strategically crucial class of 21st century open problems (as it seems to me and many) is to find better answers to the questions: “What new arenas for thermodynamical flows can provide a more mathematically natural, pedagogically synoptic, and physically extensible explanation of the panoply of dynamical analysis methods that we are already vigorously embracing? And for how many more doublings can Moore’s Law progress in PTIME quantum-dynamical simulation be sustained?

    Aye, Shtetl Optimized lassies and laddies, *these* are philosophical bones have plenty of the nourishing meat of physical applications upon them, and hopefully too, plenty of the tasty marrow of fundamental mathematical insights within them!

  18. Rahul Says:

    Scott:

    Yeah, sorry you have to endure those ad hominems.

    OTOH, in hindsight, ironically are we falling into the same trap as philosophers? Perhaps it’s futile trying to speculate which of the long dead wise men of science understood how much of these theories? It’s a futile exercise.

  19. Sid Says:

    Great interview. I really liked your answer to the final question. In particular I quite liked point #3 in that answer, where cautioned against “throwing an arsenal of theory at it”. You echoed Paul Halmos:

    “What mathematics is really all about is solving concrete problems. Hilbert once said (but I can’t remember where) that the best way to understand a theory is to find, and then to study, a prototypal concrete example of that theory, a root example that illustrates everything that can happen. The biggest fault of many students, even good ones, is that although they might be able to spout correct statements of theorems, and remember correct proofs, they cannot give examples, construct counterexamples, and solve special problems”

  20. roland Says:

    Even though Lubos clearly is an idiot, the last segment about Heisenberg’s half-statements about consciousness and it’s implicated in wavefunction collapse is compelling.

  21. Sid Says:

    Also, to reply to Lubos, if I were you, I’d use the variant of the “why ain’t you rich argument”, that is: “why don’t you have tenure at MIT”.

    I know you are above that. But just saying.

  22. wolfgang Says:

    @Scott

    >> exceedingly interested in debating
    ok, then let’s debate this 8-)

    As you explain in the interview, you follow the tradition of analytic philosophy (Wittgenstein-Carnap), emphasizing formalism over substance.
    In other words, you seem to think that math is more fundamental than physics, which clearly is a mistake.

    It was always the case that math follows the developments in physics (see eg Newton vs Leibniz) and the same happened with quantum theory.
    Bohr, Heisenberg etc. found the important physical principles and later the mathematicians (von Neumann) found the best mathematical formulation.
    This repeated when Feynman used wave/particle duality to introduce the path integral (and mathemarticians still struggle to formalize it).

    But it is a major mistake to think that the mathematical formalism is more fundamental than the physics imho.
    “Establishing the axioms of QM” and deriving various theorems may seem more fundamental to you now now and perhaps there are better ways to teach QM than in 1930s, but this does not change the importance of Bohr, Heisenberg et al.

    Btw it is no coincidence that Einstein, Heisenberg et al. rejected the conclusions of the Vienna circle, i.e. the founding fathers of the analytical philosophy you seem to follow…

  23. J Says:

    I remember my sister reading Shakespeare where she was 21. However, I doubt if there is another person in the world who would have thought of writing about big numbers in their late teen years for just class credit.

  24. Scott Says:

    wolfgang #22: I don’t know where you got the idea that I “follow the tradition” of Wittgenstein, Carnap, or other philosophers involved with the Vienna Circle. I didn’t say that in the interview, and I don’t agree with it. For one thing, I greatly prefer Russell over Wittgenstein, because he was a clearer writer, and funnier. :-) For another, Vienna-Circle philosophy strikes me as the kind where you first decide that all non-empirical statements are meaningless (even Fermat’s Last Theorem is “just a tautology,” like 2+3=5), then spend your whole career making non-empirical statements. Myself, I prefer just to get on with the science-ing!

    As for your case that math “always” follows developments in physics, it relies entirely on a careful choice of examples. Complex numbers were discovered by mathematicians centuries before their application to physics. Riemannian geometry preceded Einstein, linear algebra preceded Heisenberg, and Lie groups preceded Yang, Mills, and Gell-Mann. Steven Weinberg once described mathematicians’ ability to anticipate developments in physics as “uncanny.”

  25. John Sidles Says:

    Scott Aaronson asserts a (20th century) Great Claim  “If you’re teaching QM, then the pedagogically best thing to do is to start with the core idea, which I would say is the replacement of probabilities by complex numbers called amplitudes that can destructively interfere with each other.”

    To which a dual (21st century) Great Claim is

    The Church of the Blown-Up Hilbert Space  “If you’re learning QM, then the pedagogically best thing to do is to start with the core idea, which is the computational unravelling of symplectomorphic flows on classical systems \(\{M,g,\omega\}\) — such that the thermodynamical Four Laws are respected — and then restrict that core idea to (low-dimension) varietal manifolds \(M\) whose \(g\) and \(\omega\) comprise a compatible triple \(\{g,\omega,J\}\), such that the generic blow-up of \(M\) is a (large-dimension) Hilbert Space, and the complex structure \(J\) ensures that unravelled trajectories dynamically interfere with each other.”

    This alternative curriculum studies a world that concretely models Gil Kalai’s Quantum Postulates … and has plenty of practical applications too.

    Aram Harrow asked me if these ideas were written-up anywhere. The answer (of course) is “yes” … but (as remarked in #17) the early 21st century reading list is neither concise nor entirely consistent in its pedagogy.

    Presumably by the middle of the 21st century, the core curriculum will be shorter and so will the individual books!

  26. wolfgang Says:

    >> Myself, I prefer just to get on with the science-ing!
    Great!

    >> Riemannian geometry preceded Einstein
    But it goes back to Gauss, who began with physics intuition and actually triangulated the peaks of real mountains …

    Einstein is of course a great example of what I was talking about: He was immensely productive when his research was guided by fundamental physical principles and he got lost when he unfortunately decided to rely on math (and philosophy) alone.

  27. Hal Swyers Says:

    I think philosophy is still important, but that our approaches to answer some of these questions could use a refresh. Now I’m sure some (#12) would argue the nonsense of these sorts of things as it were, but we can borrow some items from the development of statistical mechanics and information theory to at least re-ask some traditional topics of philosophy.

    In the article below one can use basic combinatorics and terminology from statistical mechanics to look at question of ultimate deities vs nature. It isn’t to hard to reach a conclusion that such things are probably undecidable, unless on chooses to maximize some sort of “entropy of judgement” which you can define fairly readily. In which case nature wins.

    Just a fun exercise to tease the mind. I only post in hopes of creating some more discussion.

    http://thefurloff.com/2013/12/15/philosophy-reduces-to-statistical-mechanics/

  28. Lubos Motl Says:

    “My true heroes have always been Engels, Lenin, and Trotsky.”

    Excellent, Scott, but nothing whatsoever changes about my arguments if you replace Marx with these three “heroic” equivalents. All of them were wrong about the society; all of them were wrong about the foundations of physics, too. Get used to it.

  29. Bram Cohen Says:

    Umm, Lubos, Scott was being sarcastic about Engels, Lenin, and Trotsky, and I suspect he said that knowing full well that the sarcasm would go right over your head.

    The indicator of his sarcasm was that he’d just said that he isn’t a follower of Marx. Since Engels and Marx are nearly identical in terms of the history of thought, one couldn’t be a follower of one but not the other.

  30. Scott Says:

    wolfgang #26:

      But it goes back to Gauss, who began with physics intuition and actually triangulated the peaks of real mountains …

    Sorry dude, but you don’t get to claim the Prince of Mathematicians as a physicist! :-) Gauss was primarily a mathematician, but one whose curiosity and abilities were so wide-ranging that they spilled over into physics, astronomy, and other fields (and was neither the first nor the last such mathematician).

      Einstein is of course a great example of what I was talking about: He was immensely productive when his research was guided by fundamental physical principles and he got lost when he unfortunately decided to rely on math (and philosophy) alone.

    So if I understand correctly, you get to classify physics research after the fact as “guided by physical principles” if it succeeds, or as “math and philosophy” if it fails? ;-)

    From what I know about it, I don’t think Einstein’s failed work on a unified field theory was any more “mathematical” than his immensely successful work on GR was. The problem wasn’t that he was using math, but simply that he was no longer using the right math—e.g., he didn’t realize that to get further in his program, one would have to incorporate the strong and weak nuclear forces, and that the right way to do that was using non-abelian gauge theory. But I’ve always thought we should give poor old Al a break: after the failure of his last few decades of research to revolutionize physics, he was left “merely” having done so 3 or 4 times, more than anyone else since Newton.

  31. wolfgang Says:

    Scott,

    >> Gauss
    when he triangulated the mountain peaks he was obviously a physicist and my point is that it was natural in this situation to ask if the angles add up to pi/2
    This was not even a question within the dominant philosophy (Kant) and math (Euclid) at the time.

    >>poor old Al
    The problem was not that his unified theory was more or less mathematical than GR … the problem was that he had no fundamental physical principle, like he did with GR (equivalence principle), to follow.

  32. wolfgang Says:

    sorry, above should be pi not pi/2 (obviously I am not a mathematician 8-)

  33. John Sidles Says:

    Mathematicians (more than scientists?) commonly expression Wittgenstein-style philosophical sentiments; for example:

    Saunders Mac Lane (1970)  “Mathematical ideas do not live fully until they are presented clearly, and we never quite achieve that ultimate clarity.”

    ———

    Saunders Mac Lane (1986)  “Analysis is full of ingenious changes of coordinates, clever substitutions, and astute manipulations. In some of these cases, one can find a conceptual background. When so, the ideas so revealed help us understand what’s what. We submit that this aim of understanding is a vital aspect of mathematics.”

    “It has taken me over fifty years to understand the derivation of Hamilton’s equations … the point of this cautionary tale is the difficulty in getting to the bottom of it all.”

    ———

    Vladimir Arnold (1990)  “Every mathematician knows that it is impossible to undertand any elementary course in thermodynamics.”

    ———

    David Mumford (1988)  In twenty years of giving colloquium talks about algebraic geometry to audiences of mostly non-algebraic geometrs, I have learned only too well that algebraic geometry is not so easily accessible, nor are its basic definitions universally known.

    It may be of some interest to recall how hard it was for algebraic geometers, even knowing the phenomena of the field very well, to find a satisfactory language in which to communicate to each other. At the time these notes were written, the field was just emerging from a twenty-year period in which every researcher used his own definitions and terminology, in which the “foundations” of the subject had been described in at least half a dozen different mathematical “languages.” … There was a general realization that not all the phenomena could be clearly expressed, and a frustration at sacrificing the suggestive geometric terminology of the previous generation.

    ———

    Bill Thurston (2010)  “Mathematics is commonly thought to be the pursuit of universal truths, of patterns that are not anchored to any single fixed concept. But on a deeper level the goal of mathematics is to develop enhanced ways for humans to see and think about the world. Mathematics is a transforming journey, and progress in it can better be measured by changes in how we think than by the external truths we discover.”

    “As I read, I stop and ask ‘What’s the author trying to say? What is the author really thinking?’”

    “Studying mathematics transforms our minds.”

    Open Question  If “studying mathematics transforms our minds” (in Thurston’s broad sense), and “philosophy is the study of minds and their languages” (in the Wittgenstein’s broad sense), then in what concrete senses (if any) do advances in philosophy amount to anything more than advances in mathematics?

  34. Scott Says:

    wolfgang #31: For someone whose stated position is that “physics is not a debate club,” you’re doing an amazing amount of semantic acrobatics here!

    Gauss, who the entire world knows as a mathematician, went out to the hills with his lanterns and protractors, guided by his understanding of mathematics to make a measurement that no physicist (under whose purview such things would normally fall) had enough imagination to perform at that time. Yet in your telling, this somehow turns into an intellectual victory for physics over math! How? Because Gauss, by the very act of doing something that you like, became a physicist while doing that thing. Likewise, the question he asked “was not even a question within the dominant philosophy (Kant) and math (Euclid) at the time”—with no mention of the dominant physics at the time (Newton), and no acknowledgment that math had moved beyond Euclid decades before physics moved beyond Newton.

    Now as for the equivalence principle: when you get down to it, the EP is a relatively (har, har) abstract mathematical statement, about a symmetry of the equations of physics under a certain kind of transformation (changing an acceleration to a gravitational force or vice versa). As far as I can see, the only thing that justifies you in calling the EP a “fundamental physical principle,” rather than a mathematical guess, is this: the EP turned out to be right.

    But if so, then the advice that you and many others are so eager to give physicists—namely, “rely on fundamental physical principles rather than abstract mathematics”—basically boils down to, “make the mathematical guesses that will turn out to be right, rather than the guesses that will turn out to be wrong.” Which, I suppose, is not completely useless advice, but not particularly useful either! :-)

  35. wolfgang Says:

    Scott,

    this debate actualy confirms that indeed you are arguing in the spirit of analytical philosophy as I initially suspected, much more interested in semantic details than the truth 8-)

    So let me give you direct proof of the superiority of physics:
    1) I guess we can both agree that the standard model (SM) describes physics of every day life, including human beings and their brains.
    1b) In fact a simplified approximation (low-energy, quasi-classical) is probably sufficient, lets call it RSM (reduced standard model). Imagine it as a fancy version of molecular dynamics (John Sidles might be able to fill in the details).

    2) It follows that all mathematicians and their results are described by RSM-math. Every theorem you mathematicians could ever proof can be derived by simulating a mathematician (or a group of them) using RSM-math.

    3) However, it is clear that the fundamental theory FT (perhaps a variant of superstring theory?) of physics is not contained in RSM. Actually it must be the other way around, RSM is a subset of FT.

    4) We can assume that given enough time physicists will discover and understand that fundamental theory FT.

    5) So why can physicists do in 4) what mathematicians cannot? The reason is that experiments beyond RSM and beyond SM will reveal the fundamental principles of FT.

  36. Lubos Motl Says:

    Bram Cohen #29,
    he may have tried to pretend to be sarcastic but I know very well that the content is damn serious.

    You’re also completely wrong that Marx and Engels were identical – one may understand the lack of resolution of people happily unexposed such as yourself. But be sure that all of us who lived in a regime promoting similar ideas as well as people like Scott who are fans of those things can distinguish these men well.

    You’re right that they’re indistinguishable at the level of the remote debate about quantum mechanics. All of them were wrong.

    Cheers
    LM

  37. Lubos Motl Says:

    Scott #34,

    in your bizarre reply to Wolfgang and elsewhere, you are completely confused about the difference between maths and physics.

    Gauss may be known as a mathematician and you may be used to say he was just a mathematician. But that can’t change anything about the fact that he was working as a physicist while he was doing experimental physics – to some extent, one could even say “geophysics”. By your inertia of using the word “mathematician” in these contexts, you are only showing how sloppy or misguided you are about rather fundamental issues – as sloppy and misguided as an average drunk homeless man on Mass Ave.

    Mathematics is simply not doing measurements, especially not measurements of continuous variables.

    Euclidean geometry is counted as a branch of maths today – after it was “cleared” of the empirical and heuristic “flavor” that the mathematicians learned to despise – but of course that it was founded as the oldest branch of physics, one that studies the relative positions of various solid bodies. Be sure that everyone who understands and cares about the distinction between maths and natural science knows it very well. See e.g. Einstein’s quotes about geometry as the oldest branch of physics here:

    http://books.google.cz/books?id=H5rm7MjrYDkC&pg=PA195&lpg=PA195&dq=einstein+geometry+oldest+branch+of+physics&source=bl&ots=tp2o2VPGZe&sig=KmwY3-P574Icrvl_eAY06NL7Od0&hl=cs&sa=X&ei=26muUvTPC4OnhAe2qIDABA&ved=0CC8Q6AEwAA#v=onepage&q=einstein%20geometry%20oldest%20branch%20of%20physics&f=false

    It is also unbelievably confused for you to say that the equivalence principle is a “mathematical principle”. Mathematics is solely the enterprise of deciding whether some propositions logically follow (can be proven or disproven) from some assumptions i.e. axioms. The equivalence principle is a statement about accelerated motion and gravitational forces in the real world. It has always said that the real world phenomena obey some properties. If you erase the “real world” from the equivalence principle, nothing is left. The mathematical “part” of the principle is completely trivial. What is true or false about it may be decided immediately.

    It’s an important principle only because it says something about the physical phenomena. The statement is true which makes it even more important. To some extent, we may include wrong or falsified statements about Nature as “physical principles”, too. But they still deal with properties of the Universe around us (or its extensions or generalizations) but the point is that they are about “what someone may observe and measure”, not about abstract things that may be proven just on the paper.

    I feel that you might be knowing the difference between maths and physics but you may be deliberately obscuring this difference in order to suggest that you also know something about physics – even though you don’t.

    Incidentally, your list of “things more important than the uncertainty principle” is breathtakingly uninformed. The uncertainty principle is a major summary of all the key novelties of quantum mechanics. All quantum, non-classical phenomena exist because of a nonzero hbar. The constant always has some interpretation in terms of a minimal uncertainty or a commutator of observables that used to commute in classical physics – or some more mathematical assertions involving hbar but as long as we connect them with physics, with observable phenomena, it’s always about the uncertainty etc. Hbar and the uncertainty principle are what is turning classical physics into quantum mechanics.

    On the other hand, some speed of a random quantum algorithm is an engineering detail of a very minor importance – if included as a “law of physics”, it would surely fail to make it into the top 10,000 most important laws in physics. I find it totally staggering is someone suggests that they’re comparably important – but you seem willing to even say that the uncertainty principle is *less* important.

    It is also remarkably stupid for you to say that the uncertainty principle is equally or less important than Bell’s theorem. Bell’s theorem is a trivial theorem that has been known not to belong to modern physics for 90 years – because it is just an inequality proven for a class of theories that demonstrably *don’t* describe the real world as they lack the key principles and subtleties to do so (postulates of quantum mechanics). Bell’s theorem may be important for those who keep on trying to deny that classical physics has been over for almost 90 years and the quantum revolution can’t be undone. So these folks care about every new “hit” and this one from the 1960s was just another one and they still talk about it only because it is fashionable. But those who actually follow or study physics have known that the theories discussed in Bell’s theorem have nothing to do with the real world since the 1920s. The world isn’t classical – it contradicts the assumptions of “realism” made in Bell’s theorem.

    Cheers
    LM

  38. Rahul Says:

    My question to Lubos & Scott & Wolfgang is why does it matter? Maybe Gauss was a math guy maybe he was a physicist. Maybe he was half of each with bits of philosophy thrown in. Why try so hard and bin him into pigeonholes?

    So also about whether Heisenberg really understood QM as we did now, or whether he didn’t! Can we ever settle this and even if we do how have we progressed in our knowledge?

    Aren’t these fairly academic & meaningless debates. Come on guys, let’s try to be better than philosophers: let’s forget the people & discuss their ideas. Let’s debate what *we* think about stuff not what other scientists of yore may or may not have.

  39. Scott Says:

    Rahul: Dude, I’m not the one who keeps bringing this up! I’m happy to adopt the commonsense position that math and physics are both great, and to give the historical figures a rest and move on (as I said repeatedly in the interview that started this exchange).

    Unfortunately, Lubos and Wolfgang both take the “maximalist” position that math is completely inferior / subservient to physics, and is pulled along by the latter to the extent it does anything worthwhile. And incredibly, they’re using Gauss as their example: the mathematician who did the farsighted physics that physicists didn’t or wouldn’t becomes, ipso facto, a physicist proving the inferiority of math! Given such an absurdity, what’s there for me to do but to argue with them? Someone (two people, actually) are wrong on the Internet. :-)

  40. Scott Says:

    Bram #29:

      Umm, Lubos, Scott was being sarcastic about Engels, Lenin, and Trotsky, and I suspect he said that knowing full well that the sarcasm would go right over your head.

    LOL! It’s now confirmed that it did. Lubos is really, genuinely incapable of comprehending, either the science-fiction silliness of claiming that Karl Marx is my hero, or the way that that silliness left me no choice but to “agree and amplify” in response. (What else was I supposed to do, issue a stone-faced denial? “I am not, nor have I ever been, a member of any Communist organization. I firmly believe in the American system of free enterprise. And as for the writings of Karl Marx, I find them even more ponderous than the writings of Bohr and Heisenberg…” ;-) )

    Last night, someone suggested to me that it was mean to use sarcasm on someone who I knew had a cognitive disability that would prevent him from understanding it. In response, I promised to be more sensitive to the special needs of the guy who’d just called me a “brainwashed crank and liar” with a low IQ (the latest in eight years of insults and invective).

  41. Lubos Motl Says:

    Dear Scott,

    I haven’t said a word about the superiority or inferiority of maths or physics whatsoever. And I haven’t seen Wolfgang having done it, either.

    Maths and physics aren’t separated by one’s being superior and the other’s being inferior. They’re separated by physics’ being the learning of the truths about Nature around us; while mathematics studies the validity of propositions about abstract objects that are being invented by humans and studied regardless of their relationship with the real world – this independence of the messy real world is needed for maths to be rigorous.

    But in a sharp contradiction with your mud, they are separated! People used to study all of them together and many people still do so today – but they may recognize that they are doing two things, even if relationships between many things on both sides exist.

    It’s just your dogmatism to present Gauss as a “pure mathematician and nothing else”. Even if you open e.g. Wikipedia

    https://en.wikipedia.org/wiki/Carl_Gauss

    you will learn that he was also a “physical scientist” who also studied “astronomy, electrostatics, geophysics, optics”, among other things. He cared what the experiments with lens, charges, mountains etc. actually reveal. If someone doesn’t care about it, he is not doing physics. If someone thinks that an estimate for a speed of an algorithm is more important than the cornerstone principle of modern physics, the uncertainty principle, he is clearly not studying the world as a physicist.

    Cheers, LM

  42. Scott Says:

    wolfgang #35:

      So let me give you direct proof of the superiority of physics … all mathematicians and their results are described by RSM-math. Every theorem you mathematicians could ever proof can be derived by simulating a mathematician (or a group of them) using RSM-math. However, it is clear that the fundamental theory FT (perhaps a variant of superstring theory?) of physics is not contained in RSM. Actually it must be the other way around, RSM is a subset of FT. We can assume that given enough time physicists will discover and understand that fundamental theory FT.

    I can’t believe that’s actually the ground on which you want to conduct this argument! (Maybe I, too, am slightly sarcasm-challenged.)

    If it is, then the real victor is not only math, but theoretical computer science. Unless you agree with Roger Penrose, the theory FT is simulable by a Turing machine—some fixed machine M, with some finite (probably not too large) number of states, out of the whole infinity of Turing machines on offer in Platonic heaven. Furthermore, that M is presumably not itself simulable in the physical universe, by the time/space hierarchy theorems.

  43. Amir Safavi-Naeini Says:

    This is starting to be painful. Please stop. Lets get back to science or math or CS or “da good shit” or whatever you want to call it.

  44. wolfgang Says:

    @Scott #42

    Let’s face it.
    Mathematicians are just RSM multi-particle states.
    Complicated, yes, but low-energy 8-)

    How should we learn from them anything interesting about the high-energy physics of the FT?

  45. wolfgang Says:

    Scott,

    I found this on wikipedia, which you may find interesting, because it tells us what Gauss himself thought about math 8-)

    “Though Gauss had up to that point been financially supported by his stipend from the Duke, he doubted the security of this arrangement, and also did not believe pure mathematics to be important enough to deserve support. Thus he sought a position in astronomy…”

    I rest my case …

  46. Raoul Ohio Says:

    1. It seems Lubos either thinks he is being funny, or truly enjoys being obnoxious. In either case, it obscures some good points he makes; e.g.

    “Maths and physics aren’t separated by one’s being superior and the other’s being inferior. They’re separated by physics’ being the learning of the truths about Nature around us; while mathematics studies the validity of propositions about abstract objects that are being invented by humans and studied regardless of their relationship with the real world – this independence of the messy real world is needed for maths to be rigorous.”

    That might not be the entire story, but I (proud owner of degrees in math, in physics, and in applied math) won’t argue with it.

    2. Of the early “Superheros of Math and Physics” (say: Archimedes, Newton, Leibniz, Gauss, Euler, LaPlace, Riemann, Einstein, …, ?), is it known who considered themselves to be a mathematician, and who a physicist? My guess is that most would have considered it to be a dumb question.

  47. Rahul Says:

    I rest my case …

    Whew….Finally. :)

  48. John Sidles Says:

    wolfgang asserts (comment #46) “Gauss doubted the security of this arrangement [royal support for pure mathematics] thus he sought a position in astronomy.”

    Gauss’ focus upon astronomy was prudent given the obvious-to-everyone crucial strategic role of celestial navigation in Gauss’ pre-chronometer era.

    Here is a hilarious, linked-to-literature, verbatim quote to somewhat the same effect:

    The Herschel Partnership,
    as Viewed by Caroline

    by Michael Hoskin (2003)

    William Hershel writes in 1785 to King George III:

    “In a letter which Sir J. [Joseph] Banks laid before his Majesty, I have mentioned that it would require 12 or 15 hundred pounds to construct a 40-ft telescope, and that moreover the annual expenses attending the same instrument would amount to 150 or 200 pounds.

    As it was impossible to say exactly what some might be sufficient to finish so grand a work, I now find that many of the parts take up so much more time and labour of workmen, and more materials than I apprehended they would have taken, and that consequently my first estimate of the total expence will fall short of the real amount.”

    [historian Hoskin comments] “Not for the last time in the history of astronomy, an astronomer seeking support had been modest in his initial demands, knowing that the funding body, confronted later with a choice between writing off all the money spent so far or coughing up more, would cough up.”

    Shades of Charles Babbage & Ada Lovelace / controlled thermonuclear fusion / gravity wave detection / quantum computing …

    The more things change, the more they stay the same!

  49. Jay Says:

    Nice interview!

    > Last night, someone suggested to me that it was mean to use sarcasm on someone who I knew had a cognitive disability that would prevent him from understanding it.

    I vote her/him for the best piece of irony of this thread! :-)

  50. Jordan Says:

    Lubos, you might be a perfectly reasonable gentleman in other contexts, but you have behaved here as a sophomoric turd. Scott is being a very big person to even dignify what you are saying with a response. Scott and the other readers of this blog deserve more respect. You yourself deserve better than to have your ideas overlooked as a result of you not carrying yourself with dignity. You can take my post as a challenge and respond with more invective, snark, or denials, or you can learn something and grow as a person. I’m offering you an opportunity to apologize to everyone here for how you have behaved.

    Whatever function “Scott Aaronson” fulfills in your psyche, it’s clear that you feel disappointed. Who you are actually disappointed in, I will not bother to speculate about. What I will say is that nobody is perfect and you would do well to be more forgiving and kinder to those who fail to live up to your expectations.

    Spirited debate and the sharing of ideas can be a fun experience. Everyone is here to learn and to think and to enjoy themselves. Most of us are having fun here. This isn’t an arena for you to prove your worth, Lubos. Please relax and enjoy the festivities. Have a drink, have some snacks. It will be okay.

    Scott is very generous to maintain this blog and to engage with random people on the internet. I have learned an enormous amount from this blog and deeply appreciate that Scott does this. If you don’t like him, put on your big boy pants and kept it to yourself, nobody cares. You’re perfectly welcome to debate and share your views, and you might even be taken seriously if you would stop gratuitously engaging in ad hominem attacks (which in addition to being oafish and bizarrely out of place, are not even clever). I don’t care if personally attacking Scott makes you feel better about yourself in some perverse way, you’re being an odious and boorish nuisance and a bully. And a bore. Knock it off.

  51. Jordan Says:

    Scott, hope you have a great time in Brazil!

  52. Joshua Zelinsky Says:

    The disagreement over who is a physicist or a mathematician reflects to some extent that the boundary between them can be extremely difficult to distinguish. Mathematician and physicist may not be natural categories. The Gauss example is particularly interesting because his early work was almost completely what would normally be called math. But the last 20 years of his life his work was almost completely in the physics category http://en.wikipedia.org/wiki/Gauss#Later_years_and_death_.281831.E2.80.931855.29

    To some extent arguing over whether Gauss was a physicist or a mathematician has some similarity over arguing over what Einstein’s religious views were. Einstein’s views changed over time which is part of why there are so many dueling quotes. In a similar fashion, what Gauss was depends on when in his life one is looking. However, it does seem fair to say that he was overall more in the mathematician camp than the physicist camp. At minimum, while Gauss was a first rate physicist, he was a zeroth rate mathematician.

  53. Scott Says:

    Jordan #51:

      Scott, hope you have a great time in Brazil!

    Thanks!! Just went up Sugarloaf today, and have been stuffing my face with the mashed acai sweetened with guarana that they sell at juice stands (as soon as I tasted it, I felt like I’d have to make up in one week for a whole lifetime of not eating it).

  54. Scott Says:

    Joshua #52:

      At minimum, while Gauss was a first rate physicist, he was a zeroth rate mathematician.

    Thank you for that zeroth-rate distillation of what I’d been trying to say far less felicitously, which caused me a surprising amount of amusement at the end of a long and exhausting day.

  55. edmeasure Says:

    Instructing Lubos in etiquette is futile.

  56. Olav Says:

    Interesting interview! A couple of brief remarks:

    (1) I think it’s fair to say that contemporary philosophy is largely ahistorical. That is, most articles in most of the top journals mostly contain citations of articles written in the past couple of decades, and most departments have an ahistorical focus (Cornell is an exception).

    (2) My own main interest is in the philosophy of science (I’m a graduate student in philosophy). However, I still think the history of philosophy is very important and valuable. True, the history of philosophy is not that important for the purposes of understanding the empirical world; but I hardly think understanding the empirical world is the only business of philosophy. One of the valuable things that comes from studying the history of philosophy (and I could mention others) is that it forces you to come to grips with very alien ways of viewing the world. This makes you aware of just how contingent your own way of seeing the world is. For example, today we take the conceptual distinction between the mind and the body for granted (I’m not saying that everybody thinks there is a mind distinct from the body — I’m just saying that the conceptual distinction is taken for granted). However, if you read Aristotle, you won’t find any such distinction. Aristotle does talk of “body” and “soul,” but these terms mean something completely different to him than they do to us.

  57. Sid Says:

    Olav #56:

    I think you make an important point in (2). I especially like your example about the historical recentness of the mind-body duality.

    I hadn’t even realized how ingrained this worldview is in me and what consequences that has until I read these fantastic essays by Kevin Simler reviewing Julian Jaynes’ book on the Origin of Consciousness:

    http://www.meltingasphalt.com/mr-jaynes-wild-ride/
    http://www.meltingasphalt.com/accepting-deviant-minds/

  58. John SIdles Says:

    Lubos Motl asserts (uncompromisingly) “Mathematics is solely the enterprise of deciding whether some propositions logically follow (can be proven or disproven) from some assumptions i.e. axioms.”

    Certainly this assertion has plenty of historical precedent. And yet, if we call to mind the philosophical progression:

    (1)  early Wittgenstein
    (of the Tractatus), then

    (2)  late Wittgenstein
    (of the Investigations), then

    (3)  post-Wittgenstein
    (the PostModernism of Derrida, Foucalt and Lacan)

    we appreciate that these philosophical themes are recapitulated in the mathematical literature

    (1)  traditional mathematical formalism
    (per Jaffe and Quinn Theoretical Mathematics, arXiv:math/9307227 [math.HO]), then

    (2)  early Thurston informalism
    (of On Proof and Progress, arXiv:math/9404236 [math.HO]), then

    (3)  late Thurston informalism
    (of What’s a mathematician to do? and Thinking and explaining)

    Conclusion  It is well to keep in mind that (as it seems to me) philosophy and mathematics alike would be grievously impoverished if everyone agreed in these matters (no matter what that agreement was), and that is why all of the above works are recommended — to young researchers especially — despite their obvious mutual incompatibility.

    Recommended Reading  Bill Thurston in his last decade of life wrote introductions to many fine mathematical textbooks, and those introductions and textbooks are (as they seem to me) uniformly worth reading and reflecting upon.

  59. John SIdles Says:

    JAS provided links to Bill Thurston’s (highest-rated) MathOverflow answer What’s a mathematician to do?, and his (also highest-rated) MathOverflow question Thinking and explaining.

    A typo in the latter link now has been corrected.

    Thurston’s foreword to Princeton University Press’ The Best Writing on Mathematics 2010 — a collection that includes considerable philosophical material — is recommended too (Amazon’s “Look Inside”/Table of Contents feature shows it).

    Conclusion  There’s plenty of nourishing mathematical meat on these philosophical bones.

  60. John Merryman Says:

    Might there be some dichotomy between math and physics, or science and philosophy? Say top down (math, philosophy?), versus bottom up(physics, science?).
    We need to edit the signals from the noise, yet all noise is signal at some frequency and amplitude. Physics and science seem to be about sorting through all the input, while math is the emergent algorithms and philosophy is the general conclusions.
    ?
    One thought I keep trying to push is that if we think of time, not as a passage or measure from prior to succeeding events, but the process by which these events come into being and dissolve, ie. not of the present moving from past to future, but the changing configuration of what is, turning future into past. For example, not the earth moving along some flow or dimension from yesterday to tomorrow, but tomorrow becoming yesterday because the earth rotates.
    This would make the concept of time much more dynamic and not just a static, scalar measure, which would tie it to thermodynamics, in which time is the linear structure within the non-linear dynamic. The timeline of the emergent entity within the dynamic context.
    We exist as particular points of perspective within this sea of activity and so experience it as a series of encounters and our brains function by sequences of thoughts, yet metabolically, non-linear thermodynamics is more elemental.
    One could say that time is to temperature what frequency is to amplitude.
    So the reason clocks run at different rates is simply because all actions are their own clocks. If time were a vector from past to future, than the faster clock would logically get to the future more rapidly, but the opposite is true, they age/burn/process quicker and so recede into the past faster.
    So rather than thinking in a normal, linear cause and effect manner and trying to figure how to go from a determined past, into a probabilistic future and ending up in multiworlds, or a consciousness generated reality(we do pick the signal, but not create the noise), it is a process of letting nature decide, with probabilities preceding actualities. There are ten potential winners before a race, but only one actual winner after it.
    We still see the sun moving east to west, even though we now know it’s the earth spinning west to east.

  61. Hal Swyers Says:

    I would make the case that all languages are reducible to some form of mathematics. The goal of early theorists in computation seemed more about reducing everything into some type of computation, and to a large extent they have succeeded. http://thefurloff.com/2013/12/18/we-are-natural-mathematicians/

  62. Rahul Says:

    Olav says:

    “One of the valuable things that comes from studying the history of philosophy (and I could mention others) ”

    Can you please? Not being snarky.

    Genuinely curious especially since you major in it.

  63. Jordan Says:

    I’m also curious what, if anything, of recent philosophy (from say, within the past 50 years) might be of interest to math and science people? I think Scott made a compelling case that science did more for philosophy in the 20th century than philosophy ever could have done on its own from the confines of the armchair or the coffee shop (and that in general, philosophers too-little appreciate the many gifts conferred from outside of philosophy-the-field). Turning the tables, are there any recent ideas *endogenous* to philosophy-the-field that science people underappreciate?

  64. Jay Says:

    Philosophical zombies?

  65. Vitruvius Says:

    I’ll take Metaphysical Quantum Ontic Pancomputationalism for a thousand, Alex. I don’t know if it’s correct or not, but it’s way more fun at symposia (in the classical sense).

  66. J Says:

    Joshua#52 and Scott#54

    Gauss as 0th rate mathematician says who?

    Someone who settled a 2000 year old puzzle on constructing regular polygons and who showed the fundamental theorem of arithmetic and showed a composition law for quadratic forms even before a group notion was formalized. The last is an idea that one hardly understood until dirchlet came along with a kindergarden approach and which became standard until Manjul’s masterstroke after 150 years clarifed Gauss’ approach and generalized in great detail and which may very well be a seed for a 21st century Field’s medal for Manjul. In a way Gauss was a different class of mathematician when compared to Euler(who no doubt was a great mathematician but also a very great programmer). If Ramanujan is to Euler then Grothendieck is to Gauss. The nature of mathematics changed in the 19th century and sowed the seeds for the revolution by Grothendieck. So in all ways Gauss was a very great first rate mathematician.

  67. Scott Says:

    J #67: ROTFL! I guess it isn’t math humor if it isn’t lost on someone. But here’s a hint: 2nd rate is to 1st rate as 1st rate is to what?

  68. Fred Says:

    Too bad most discussions here degenerate into “physicists” vs “mathematicians”… esp considering that “engineers” are the ones who matter in the end! :P

  69. John Sidles Says:

    Fred says “Too bad most discussions here degenerate into “physicists” vs “mathematicians””

    Fred, one effective remedy is to read the “Foreword” and/or “Preface” to pretty much any well-respected book by any well-respected philosopher / mathematician / scientist / engineer. You will find that nowadays it’s increasingly difficult to guess the author’s profession from the preface.

    As a test, try to guess the profession — philosopher, mathematician, scientists, or engineer — that is associated to this Preface:

    “As a graduate student working in [redacted] I encountered deep irritation caused by the work I was doing, something quite fundamental that I did not understand.

    Certain elementary notions that are accepted as starting points for work in [redacted] somehow had no fundamental foundation, no verifiable root. My inclination was to mine [redacted] vertically, and here was a subject whose tunnels were dug horizontally.

    I now appreciate more clearly where my question was headed: Yes it does head downward, and it goes very deep. What is less clear is that there is a path in that direction understood by anyone very well.

    Here one must face those notorious issues of interpretation that stimulate much confusion and contention but few definite answers.

    Hint: the (sole!) author of this textbook is the person who invented the one-word answer to the crossword-puzzle clue “process associated to BOSONSAMPLING mysteries”

        “_ n _ _ v _ _ _ i _ _”

    British spelling please.

    Bonus Question: Name the profession (different book, different profession, and no fair Googling!)

    We have been particularly anxious to introduce the pioneers to whom we owe so much, and from whom we can still draw useful inspiration. They were human beings not so different from ourselves, and perhaps some of our readers will be inspired to make similar contributions.

    However, it is always the youngest generation of professionals who see the future most clearly and who must build on their imperfect inheritance.

    Each new book depends for its success on many more individuals than those whose names appear on the title page. The most obvious debt is certainly to the hard-working and gifted students who have collectively taught us much more than we have taught them.

    Best Wishes for Happy Holidays are extended to all Shtetl Optimized readers and their families!

  70. A Says:

    #69 lol I see we have a DWave spy here…

  71. J Says:

    Scott#68
    Oh God! (Slapping my head there)

    Fred#69
    Engineering is very hard and very good engineers have an intuition that is very rounded and schooling, academics and higher mathematics does not help much in practical on the field thinking. In that way capability wise Engineers > physicists > mathematicians > computer science (no wonder you have had old stars like Lefschetz, Dwork, Bott etc who were formerly engineers) even though the philosophical impact has probably an inverted ordering.

  72. asdf Says:

    https://web.archive.org/web/20120118185542/http://borcherds.wordpress.com/2007/05/26/my-dad-has-more-money-than-yours/

    That reminded me of your big numbers article (or maybe it was the other way around) a while back.

  73. Ninguem Says:

    It’s spelled Rio de Janeiro.

  74. Scott Says:

    Ninguem #73: (gasp) Sorry! Fixed.

  75. John Sidles Says:

    Dick Lipton and Ken Regan nominated Colin McLarty’s What does it take to prove Fermat’s Last Theorem? Grothendieck and the logic of number theory as a candidate for “What Is Best Result Of The Year?” … the point of interest being that Colin McLarty is a bonafide philosopher … whose mathematical insights regarding algebraic geometry have (as it seems to me) appreciable relevance to the practical challenges of efficient BosonSampling simulations.

  76. Raoul Ohio Says:

    TCS Update:

    Turing pardoned!

    http://www.smh.com.au/world/alan-turing-who-broke-engima-code-in-world-war-ii-pardoned-by-queen-over-conviction-for-homosexuality-20131224-2zvfw.html

  77. Scott Says:

    Rahul Ohio #74: Lucky him! :-D

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