Off-Topic Discussion

By student request, I’ve created this post as a place for students and listeners in 6.893 to discuss any questions related to philosophy and theoretical computer science that don’t fit into the other posts.

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10 Responses to Off-Topic Discussion

  1. I was wondering if anybody has a take on this wild claim about entropy from a logician friend-of-a-friend. I’m putting the link below, but here’s a slightly edited copy-paste:

    “The assumption that the (entropic/memory) arrow of time we observe is something requiring exceptional explanation is pernicious and wholly unsupported. Yes, if entropy were defined in some principled fashion independent of our notions of what constitute simple and complex properties the argument might be a good one but physicists consistantly fail to remember that entropy is defined arbitrarily in terms of our idea of what physical states are similar. Any physical system is, by definition, in only a single state at any given instant. Roughly speaking the entropy of that system is the (log of the) number of other microscopic configurations producing a similar macroscopic state.

    Now that’s exactly the sort of definition we want for making predictions about the world but it’s no good for evaluating how radically different beings in a radically different universe would perceive their surroundings. Rather than being localized in space we can imagine beings which are localized in spatial frequency or even encoded into the microstates of macroscopically similar (to us) clouds of atoms. Such a being wouldn’t make use of our definition of entropy but instead count up states giving rise to what they perceived as similar.

    So before we go around trying to solve the puzzle of time asymmetry we should first check that it’s really a puzzle. That means answering the following questions:


    Given any configuration of the world can we always (usually?) concoct a notion of ‘macroscopic’ similarity according to which it is low entropy? I suspect the answer here could easily be shown to be yes.


    The laws of physics let us construct Turing machines that transition between macroscopically distinct internal states but what about other notions of similarity. In particular is it reasonable to expect that ‘most’ configurations of matter admit a notion of simplicity that both renders the configuration low in entropy and capable of supporting complex computations.


    Do evolutionary considerations put any further restraints on when we should expect to see complex reasoning beings encoded relative to a given notion of simplicity.

    It’s my hypothesis that ultimate answer will simply be that complex thinking computations can evolve from virtually any configuration of matter but always encoded so that their notion of simplicity renders the initial conditions simple. That is thinking always (and only) should evolve encoded in states that make it feasible to remember the past and predict the future. Otherwise, what would be the point of evolving complex thought.

    To be fair to the physicists this is a fairly deep and subtle point. They simply aren’t taught to think hard about how entropy is defined and whether that definition depends on the initial conditions of our universe. That is why philosophy has something real and meaningful to offer. Unfortunately, as I will observe in my next post analytic philosophy often drifts far from this useful territory and seems terrifyingly bereft of any correction mechanism.”

    • Silas Barta says:

      1 and 2 look isomorphic to the issue of Kolmogorov complexity differences of the same data under different choices of language (natural or computer). Just like in those cases, the answer is that yes, you can always choose a representation so that a given configuration is simple (or a set of configurations is similar). But things change when you scale up and generalize the system to an arbitrarily large set of possible strings/data/configurations to describe, at which point different languages converge asymptotically on what they regard as “simple” or “similar”.

      • Plus, I think since we’re holding the actual laws of fundamental physics (as opposed to initial condtions) constant we only need to consider languages that make the laws of fundamental physics simple, and it seems plausible that all the (minimal) languages that agree on the simplicity of the laws of fundamental physics will agree on what macrophysical states are simple. No?

  2. bobthebayesian says:

    Is it fair game to have a thread on this page related to how a student can do work at the intersection of complexity theory / learning theory and philosophy? I’ve found this course to easily be the most intellectually inspiring thing I’ve done in graduate school, but after speaking with many people in the ToC area at Harvard and in the philosophy department at Harvard, it seems like this domain is utterly closed off to grad students wanting to perhaps write a dissertation in this topical area.

    What steps should a student take to find a way to work in this field during graduate school? Or is such a desire just a pipe dream and one must study only technical aspects until one has built up a portfolio of work that causes other communities to “grant the privilege” to “pontificate” about philosophical matters? It seems like if a young person wants to wax philosophical about these issues, they are squelched and told to leave it as a hobby or else do some “real” work first and produce philosophical musings only in hindsight (or at least this is what it has seemed like to me).

    Advice from those in philosophy programs would be helpful: how did you get into your current adviser / research situation?

    • Scott says:

      First of all, thanks bob! I’m really happy you’ve found the course intellectually inspiring.

      Now, two thoughts about your questions:

      1. For almost any value of X, I suspect it would be much easier to write a thesis about “the philosophy of X” in a philosophy department than in a department of X. That includes X=TCS. In general, and except for a few oddballs, I’ve found it a lot easier to get philosophers interested in domain knowledge than to get domain experts interested in philosophy! 🙂

      2. In my career, I’ve been lucky enough not to feel an unresolvable tension between doing technical things and “pontificating” about their implications for physics and philosophy. But I think a large part of that is that I never saw the technical things as what I “had” to do to to earn the “privilege” of pontificating—rather, I gravitated toward technical questions in quantum computing theory and other fields that I really cared about in and of themselves, and avoided the technical questions that I didn’t care about. The “pontificating” was then largely just an outgrowth of trying to explain my and others’ technical results and their context to a broad audience.

      So, if you want to remain in CS or cognitive science or wherever you currently are, then my sincere advice to you is to find technical questions in your field that you actually like—possibly because of their philosophical implications—and then tackle those technical questions with the best technical tools available, while also thinking about the possible philosophical implications of the answers.

    • bobthebayesian says:

      Scratch that, it was apparently an April Fools joke dated 3 days later..? They got me good. (link).

  3. bobthebayesian says:

    Not sure if this comment will reach many folks, but it seemed like a nice relevant afterthought to some things we discussed in the class.

    Chess analyst Vasik Rajlich had some big news today: solving the King’s Gambit. I know that this doesn’t add much new to the complexity theory aspects of games like chess, but I would say it’s a beautiful result, very much like the recent improvement on the complexity of matrix multiplication, and it certainly will force people to realize the role computation plays as the King’s Gambit is a pretty popular, classical opening. By any human standard it’s a respectable opening, and yet we can conclusively say it is unequivocally bad for White assuming two rational players.

    I wrote up a short blurb about it at my blog.

  4. uksuperiorpapers says:

    I love this… Its time to turn the way children learn and students teach on its bloody head. We are in the age of technology and children are winning at it.

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