Past Hypothesis Taxonomy

Let me try an experiment: using a blog post to develop a taxonomy.  Here I'll try to develop a list/taxonomy of (at least semi-coherent) answers to the question I posed yesterday: why is it harder to formally predict pasts, versus futures (from presents)? Mostly these are explanations of the "past hypothesis", but I'm trying to stay open-minded toward a wide range of explanations.

I'll start with a list of answers, and then add more and group them as I read comments, think, etc.  I'll feel free to edit the post from here on:

  • Extremely unlikely:
    • Reality isn't different; we just ask different future vs. past questions.
    • An outside "God" intervened to make our past different.
    • We live after a big local ebb (i.e., fluctuation) in matter.
  • Rather unlikely:
    • Quantum measurement has a local time asymmetry that makes big effects.
    • A weak local time asymmetry in matter accumulates to big effects.
    • A past ebb in spacetime shape (e.g., inflation) forced a big matter ebb.
    • All spacetime boundaries satisfy a law-like "low entropy" condition.
  • Unlikely:
    • Our expanding cosmos violates one-to-one state mappings across time.
    • Past and future have different spacetime law-like boundary conditions.
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  • http://timtyler.org/ Tim Tyler

    There’s no evidence for physics being temporally asymmetric. The laws of physics as we know them have exhibited microscopic reversibility for hundreds of years – assuming that you ignore the Copenhagen crackpottery. The observed macroscopic temporal asymmetry is explained perfectly well by standard statistical mechanics – plus a low-entropy distant past. Find any evidence for asymmetry and the Nobel prize for physics is yours.

  • James D. Miller

    There are significantly greater benefits to predicting the future than the past, thus we have put much more effort into it. This asymmetry of effort is the reason why we now have a better relative ability to predict the future.

  • http://amckenz.googlepages.com Andy McKenzie

    Interesting. One answer that you should probably *avoid* is to attribute the difference to the cognitive architecture of the scientists who designed the system. Although it is common to characterize humans as “prediction-making machines”, most of the behavioral tests to measure this ability (on a micro scale) have shown that predictions are no more accurate than retrodictions. (See http://repositories.cdlib.org/postprints/2520/ and doi:10.1016/j.cogpsych.2008.09.002 for references.) I only mention this because that was my first instinct.

  • mjgeddes

    Robin said:

    mjgeddes, tim is right; high entropy states can be very simply indicated.

    Ignore ‘states’ and focus on ‘the laws of physics’ themselves. Robin stated:

    Past and future have different spacetime law-like boundary conditions

    If

    (1) The laws of physics are not independent of the boundary conditions,

    and if

    (2) Laws of physics that are ‘simple’ are associated with different boundary conditions for past/future

    then from (1),(2) and

    (3) Occam’s razor, the simple has higher probablity than the complex

    it follows that

    (4) Simplest Laws of physics most probable, and thus most probable to see maximal difference between past and future boundary conditions

    further since:

    (5) “Among several patterns classified as “comparable” by some subjective observer, the subjectively most beautiful is the one with the simplest (shortest) description, given the observer’s particular method for encoding and memorizing it.” (Schmidhuber)

    Reference:
    http://www.idsia.ch/~juergen/beauty.html

    it follows that

    (6) The laws of physics (being the simplest) encode maximal ‘beauty’ , and from (1)-(15), laws of physics setting boundary conditions for past and future, it follows that

    (7) The notion of beauty is objectively real and consitutes a universal terminal value.

    As to Yudkowsky, three words: ‘I got him’ 😀

  • David

    I disagree with Tim in that I don’t think a low-entropy distant past is necessary for statistical mechanics to hold.

    Instead of dealing with the distant past perhaps we can discuss the infinitessimal past. Stealing an example from L.K. Nash, imagine the universe is a box of 1000 coins, and we start out with all the coins set to heads. This can only happen one out of 10^301 ways, the lowest entropy possible. The box shakes, but only a few coins flip each time. After a while we observe the distribution of coins as 900 heads, 100 tails. This can happen 10^140 ways. Still later we observe the distribution at 700/300. This can happen 10^264 different ways. Entropy is increasing. Eventually we expect the distribution to stabilize around 500/500, which can happen 10^299 different ways.

    Imagine that with no knowledge of the distribution prior to 700/300 we try to predict a prior state. In an attempt to measure a rate of change we observe a future state as quickly as technology will allow and see 698/302. Well, 698/302 is 5 times more likely to occur than 700/300. It is easier to predict the future because in the future the assembly will be in a state that is much more likely. It is harder to predict the past, even the infinitessimal past, because any estimate more distant from the predominant configuration is much less likely to be the correct one.

    You may say that coins are not atoms and so forth but I tell you that as you increase N and degrees of freedom this effect only becomes more pronounced.

  • JGWeissman

    Consider two blocks of the same mass of the same type of metal. Suppose one has a temperature of 10 degrees, and the other a temperature of 20 degress. These temperatures correspond to many different states of the blocks at a deeper, but harder to compute, level, characterized by average energy of the particles. Now, bring the two blocks together, and wait for them to achieve thermal equilibrium. Statistical mechanics predicts that the combined system would have a temperature of 15 degrees, which corresponds to many states of the particles of the combined system, the one that actually occurs should in principal be derivable from the actual initial states of the two blocks.

    Now suppose, that instead, the blocks each individually had temperatures of 15 degrees before they were brought together. Statistical mechanics predicts the same combined temperature of 15 degrees, but this should correspond to a different state of the particals than in the first case.

    So, why do you believe that a model that gives up all the information about the differences of the two system, to just label both as 15 degrees, should be able to distinguish them? It would have to distinguish them to give different predictions about the pasts, let alone the correct ones.

    The information that was lost is that unlike the vast majority of combine 15 degrees states, which came from earlier 15 degrees states, the particular state at the end of the first example came from a state that corresponds to one box being 10 degrees and the other being 20 degrees, and running the laws of physics in reverse is like starting with a very unusual state of 15 degrees that happens to evolve into a state corresponding to one box being 10 degrees and the other 20 degrees, which statistical mechanics cannot handle because all it knows about is average energy.

    In summary, running the statistical mechanics backwards in time is likely to find situations that seem contrived to violate the assumptions which justify the approximations in the model. Statistical mechanics is the use of non-time-reversable approximations on time-reversable physics. There is no reason to expect the model to be time reversible.

  • Matt Simpson

    @James: Interesting. Your hypothesis requires that predicting the past to should be significantly (or at least somewhat) different from predicting the future. This naturally leads to another question: what is so different about predicting the past? Pretty close to where Robin started.

  • http://timtyler.org/ Tim Tyler

    Re: I disagree with Tim in that I don’t think a low-entropy distant past is necessary for statistical mechanics to hold.

    That is not what I said. My assertion was that a low-entropy distant past plus statistical mechanics were a reasonable and complete explanation for macroscopic temporal asymmetry in a reversible universe.

  • David

    Statistical mechanics is not explicitly “non-time-reversable.” The best prediction of the past state of a system at equilibrium is the equilibrium state. It doesn’t matter if you use classical thermodynamics or account for quantized microstates, without additional information you can say nothing extraordinary about the past.

  • David

    Tim, OK, but I think my example shows that low-entropy distant past is not required even for your last assertion.

  • http://timtyler.org/ Tim Tyler

    Re: why is it harder to formally predict pasts, versus futures (from presents)?

    It probably isn’t.

    There are lots of situations where it is easier to predict the future than the past. For example, if you follow a water molecule down a stream, the future is predictable (the ocean) whereas the past is not (raindrops almost anywhere could have produced the same outcome).

    However, there are also lots of situations where it is easier to predict the past than the future. For example, ink diffusing into water, or a glass pane cracking – or in general, any situation where the previous history leaves “traces” in the present.

    I have little idea how to count the relative frequency of occurrence of these types of outcome – but my guess would be that the latter situation is much more common. The past leaves historical traces, not the future – and diffusion phenomena in gas and liquids (where it is easier to predict the past than the future) are ubiquitous.

    So: the premise seems to be faulty.

  • http://profile.typepad.com/6p010537043dce970c Wei Dai

    I think the answer is implicit in Solomonoff Induction. Consider all possible universes with a time dimension and one-to-one state mappings across time. Each such universe that has low Kolmogorov complexity overall, and hence high measure, likely has a low-entropy state at some time coordinate (with that coordinate also having low Kolmogorov complexity). On one or both sides of that entropy minimum (depending on whether it occurs at a temporal boundary), you’ll see regions with arrows of time pointing away from the entropy minimum. It’s likely that we live in such a region, which explains the “past hypothesis”.

    However, I don’t know if this argument has be formalized anywhere, nor have I done a detailed calculation myself.

  • http://timtyler.org/ Tim Tyler

    @Wei: I discussed that on the last thread:

    “High thermodynamic entropy start conditions – looking similar to the heat death – could probably be specified extremely compactly. Similarly, a PRNG can produce an awful lot of what looks like noise with an extremely small internal state.”

    “Informational entropy is one thing, and thermodynamic entropy is another. It may be quite possible to specify a heat-death-like state highly concisely if you are using a Turing machine for the specification.”

    Do you have a substantial disagreement?

    There are other (anthropic) reasons for considering a “bang” hypothesis – it takes a lot of negentropy to drive 4 billion years of evolution and produce intelligent agents.

  • ShardPhoenix

    I think I agree with JGWeissman: it’s basically the same reason why you can’t rewind a replay from a Real Time Strategy game (a limitation often bemoaned on gaming forums) – there’s more than one way to get here from there and you don’t know where you started because that’s what you’re trying to predict. With physics it’s because you’re losing information when you talk about macrostates, leading to the same effect.

  • ShardPhoenix

    And if you’re thinking this is an issue even on a micro level (I’m not sure it is), then I think that would be purely psycological – we tend to view the future as mutable/probabilistic and the past as fixed, so there is a higher standard of accuracy for retrodictions than for predictions. In other words, if a retrodiction is contradicted by further evidence it’s just wrong, whereas if a prediction is thrown off by some unlikely event, you say “well, my prediction was still right, I can’t be expected to predict these unlikely events…”

  • http://profile.typepad.com/6p010537043dce970c Wei Dai

    “High thermodynamic entropy start conditions – looking similar to the heat death – could probably be specified extremely compactly. Similarly, a PRNG can produce an awful lot of what looks like noise with an extremely small internal state.”

    Tim, I do not disagree with this statement. And such a universe has both low Kolmogorov complexity and presence of observers, in the form of Boltzmann brains. However, these Boltzmann brains only occur at spacetime coordinates that have high Kolmogorov complexity. So things should work out if we let the prior probability of the hypothesis “I’m at coordinate c in universe u” to be 1/2^(K(u)+K(c)).

  • ScentOfViolets

    why is it harder to formally predict pasts, versus futures (from presents)?

    This question is not well-posed. Some attention needs to be addressed as to what constitutes a particular system, what sort of observations are allowed, and what sort of past and present times are under consideration. Absent external influences, for example, the orbital elements of the major planets can be predicted with great accuracy either forwards or backwards in time by some years or centuries. Otoh, in a prepared sample of carbon-14/silicon-28, it is possible to predict rather greater accuracy which atoms were once radioactive as opposed to which atoms will decay over the next month.

  • http://profile.typepad.com/halfinney Hal Finney

    In addition to Wei’s proposal for measure of Boltzmann and other brains, which I have been a big fan of for many years, I think there are other grounds for arguing against Tim’s claim that seemingly high entropy states can be specified nearly as compactly as low entropy ones,.

    First, “nearly” may cover a lot of ground. A program to fill memory with zeros is almost certainly shorter than one that runs a pseudo-random generator and fills memory with pseudo-random bits. How much shorter? I would bet dozens to hundreds of bits. A widely used probability measure is the reciprocal of two to the power of program length, hence these universes would be at least billions of times less common, and possibly astronomically less common.

    A related issue is that the smallest pseudo-random generators are going to have relatively short repetition periods. This will produce a periodic universe (one that repeats every N spatial units). This could further rule out the smallest pseudo-random generators.

  • http://profile.typepad.com/halfinney Hal Finney

    Another proposal I have seen is that both the past and future will have low entropy boundary conditions. This requires a “big crunch” scenario, which currently has evidence against it, but physics seems to regularly change its opinion on such matters. In this scenario time would run backwards when the universe starts to contract. Here is an amusing paper proposing that there may be patches of time-reversed matter lying around, remnants of the future contracting phase.

  • http://profile.typepad.com/robinhanson Robin Hanson

    Hal, the “expanding cosmos violates one-to-one state mappings” might imply entropy reduction with contraction. But wouldn’t that also imply entropy reduction approaching a black hole singularity?

    Wei, I’m not following you at all. It sounds like you are saying a huge matter fluctuation is likely, which goes against all ordinary physical calculations of likelihood.

  • http://profile.typepad.com/6p010537043dce970c Wei Dai

    Robin, you don’t list Algorithmic Information Theory among your many interests, nor have I found a sample of your writing that mentions AIT (or Kolmogorov complexity, or Solomonoff induction). So I don’t know whether the reason you’re not following me is that you’re not familiar with the basic concepts of this field, or that I haven’t explained clearly enough how I’m using them.

    If it’s the former, this site links to a number of introductory material. If it’s the latter, Hal’s exposition might help.

    It sounds like you are saying a huge matter fluctuation is likely, which goes against all ordinary physical calculations of likelihood.

    I thought the point of this blog post was that ordinary physical calculations of likelihood are giving wrong predictions, and you’re looking for alternatives?

  • Mike

    Robin’s “taxonomy” seems about right to me.

  • http://profile.typepad.com/robinhanson Robin Hanson

    Wei, I read Cover and Thomas long ago, and understand universal priors over bit strings. I don’t understand your intended mapping between big strings and physical universes.

  • ScentOfViolets

    Given the, er, incomplete specifications in each of the proposed ‘solutions’, this bit from Scott Aaronson on why Time is Different from Space:

    So from my perspective, it’s not surprising that time and space are treated differently in relativity. Whatever else the laws of physics do, presumably they have to differentiate time from space somehow—since otherwise, how could polynomial time be weaker than polynomial space?

    But you might wonder: is reusability really the key property of space that isn’t shared by time—or is it merely one of several differences, or a byproduct of some other, more fundamental difference? Can we adduce evidence for the computer scientist’s view of the space/time distinction—the view that sees reusability as central? What could such evidence even consist of? Isn’t it all just a question of definition at best, or metaphysics at worst?

    On the contrary, I’ll argue that the computer scientist’s view of the space/time distinction actually leads to something like a prediction, and that this prediction can be checked, not by experiment but mathematically. If reusability really is the key difference, then if we change the laws of physics so as to make time reusable—keeping everything else the same insofar as we can—polynomial time ought to collapse with polynomial space. In other words, the set of computational problems that are efficiently solvable ought to become PSPACE. By contrast, if reusability is not the key difference, then changing the laws of physics in this way might well give some complexity class other than PSPACE.

    But what do we even mean by changing the laws of physics so as to “make time reusable”? The first answer that suggests itself is simply to define a “time-traveling Turing machine,” which can move not only left and right on its work tape, but also backwards and forwards in time. If we do this, then we’ve made time into another space dimension by definition, so it’s not at all surprising if we end up being able to solve exactly the PSPACE problems.

    But wait: if time is reusable, then “when” does it get reused? Should we think of some “secondary” time parameter that inexorably marches forward, even as the Turing machine scuttles back and forth in the “original” time? But if so, then why can’t the Turing machine also go backwards in the secondary time? Then we could introduce a tertiary time parameter to count out the Turing machine’s movements in the secondary time, and so on forever.

    But this is stupid. What the endless proliferation of times is telling us is that we haven’t really made time reusable. Instead, we’ve simply redefined the time dimension to be yet another space dimension, and then snuck in a new time dimension that behaves in the same boring, conventional way as the old time dimension. We then perform the sleight-of-hand of letting an exponential amount of the secondary time elapse, even as we restrict the “original” time to be polynomially bounded. The trivial, uninformative result is then that we can solve PSPACE problems in “polynomial time.”

    Iow, if it were possible to travel backwards in time, regressions to previous lower-entropic states would be unremarkable. Thus, the question comes down to whether or not time is really ‘different’ from space.

    It is 🙂

  • http://profile.typepad.com/6p010537043dce970c Wei Dai

    Robin, I did not have a specific mapping in mind when I wrote my comment, and my explanation of the arrow of time should work for any reasonable mapping between bit strings and physical universes. But for concreteness, let’s map each physical universe to its description in the language of a formal set theory (in other words, use set theory to specify a mathematical structure that’s isomorphic to the physical universe), then encode that description as a bit string.

  • http://timtyler.org/ Tim Tyler

    To give some indication of how simple a PRNG can be, here’s Wolfram’s Rule 30:

    http://upload.wikimedia.org/wikipedia/commons/2/2e/Rule_30_2000Generations.gif

    This is a simple deterministic system that fills the universe with random noise, from a single bit seed. The system exhibits indefinite heat-death-like behaviour, with no analog of the second law. If you look at the space of CAs, such behaviour is common – with most systems lying one side or the other of “the edge of chaos” – and thus either exihibiting trivial, boring behaviour, or noise.

  • http://profile.typepad.com/robinhanson Robin Hanson

    Wei, I don’t know what a “reasonable” map between bit strings and physical universes would be, nor can I see any correlation between a universe with a low entropy part and having a shorter description in some formal language. So I’m really lost interpreting your proposal.

  • http://profile.typepad.com/6p010537043dce970c Wei Dai

    Robin, if a universe has a low-entropy state at some time coordinate (with that time coordinate also having a short description), you can give a short description of this universe by describing the low-entropy state, the time coordinate at which it occurs, and the function for mapping states across time.

  • http://profile.typepad.com/robinhanson Robin Hanson

    Wei, why is a description of a low entropy state shorter than for other states?

  • mitchell porter

    Robin currently lists 9 explanations. Three rely on a “local time asymmetry” (here I include the one about state mappings). Two say we live after “a big local ebb” in matter entropy. Two talk about space-time boundary conditions. One appeals to magic (God), one to semantics (different questions).

    So, reorganizing on the basis of type of explanation, I’d propose classifying as follows:

    1. This Is All Just One Big Fluctuation, High Entropy Is The Norm
    2. The Big Bang Was Low-Entropy For Some Special Reason
    3. There Is A Local Dynamical Asymmetry Which Decreases Entropy If You Work Backwards
    4. Other

    (1) is Boltzmann’s original idea, but people think the universe is unnecessarily large to be a fluctuation – why not have only one galaxy, or only one solar system? (2) has some defenders, but no-one is able to say *why* it was low entropy, except to say it’s a basic law or an act of God. (3) sounds like it could explain the difference, except it doesn’t explain why the past started *that* low in entropy. Why couldn’t, why shouldn’t, a universe with this posited time-asymmetric dynamics still start in a high-entropy state?

    Inflation comes up in these discussions, but I read that inflation itself requires unusual initial conditions.

    Under the original post, Robin asked how someone could hope that string theory provides the answer. The hope is that string cosmology will somehow determine the initial conditions. However, at this time I only see people translating ideas from pre-string quantum cosmology into the string context, but no specifically stringy considerations that can decide between them. I suppose that if a particular choice of cosmic initial conditions happened to favor a long-term string ground state that resembles the physics we observe, that would be regarded as a strong post-hoc reason for believing that this is the right choice. But we would still be lacking an explanation for it.

  • http://profile.typepad.com/6p010537043dce970c Wei Dai

    Robin, the relationship between entropy and description length is a basic result of Algorithmic Information Theory. See section 7.3 of Cover and Thomas if you still have it handy (or view it at http://www.amazon.com/Elements-Information-Theory-Thomas-Cover/dp/0471062596#reader). Informally, a lower-entropy state exhibits more regularities (think of ice crystals vs. liquid water), which can be compressed into a shorter description.

  • http://profile.typepad.com/robinhanson Robin Hanson

    Wei, that section only discusses bit strings, not physical universes. Some low entropy states may exhibit regularities, but most may not.

    Mitchell, your summary is reasonable.

  • ScentOfViolets

    The hope is that string cosmology will somehow determine the initial conditions.

    Um, not exactly. There are also competing theories that look ‘the same’ for sufficiently diverse definitions of ‘same’. One possibility is that time is not a first-order presupposition, but rather an emergent phenomena. Another one is that travel backwards in time is impossible.

  • http://profile.typepad.com/6p010537043dce970c Wei Dai

    Robin, you’re right, that section in Cover and Thomas doesn’t quite show what I need. Instead, try section 6, “Algorithmic Entropy and Thermodynamics”, of C.H. Bennett’s The Thermodynamics of Computation – A Review, or Chapter 8, “Physics, Information, and Computation”, of Li and Vitanyi’s An Introduction to Kolmogorov Complexity and Its Applications.

  • http://profile.typepad.com/robinhanson Robin Hanson

    Wei, Bennett says that to specify a state, you can specify a macrostate, and then specify the exact state within it. For lower entropy macrostates, it may take less to specify the exact state within, but it takes more to specify the macrostate itself. Relative to equilibrium distribution expectations, this doesn’t make it easier to describe such states. Yes, if you have non-equilibrium expectations that make low entropy macrostates more likely, you can take advantage of this to create shorter descriptions of exact states within such macrostates. But the whole question here was explaining why such expectations make sense; you can’t assume them and then think you’ve proved why they make sense.

  • mjgeddes

    I gotta guess that quantum mechanics is involved in the solution here Robin. Complex things are built from simple things – a general principle? – if so the universe at the beginning was in the simplest possible state. What is the simplest state of a QM wave function? Maximal coherence surely? So decoherence is associated with increasingly complex quantum branching…think an ever more complex branching tree in many-worlds, needs more info to specify. Decoherence represents info loss in a particular observer branch, and thus increasing entropy. And, it is more complex to specify.

    Any way, its important to get this solved. I’m damn sure there’s a whopping rebuttal of all of Yudkowsky’s ideas at the end of this, and if I find out I’m right about my radical postulates (Bayes just a special case of something more general like analogy formation, beauty a universal terminal value etc etc) I’ll be trumpeting for all eternity by golly.

  • http://profile.typepad.com/6p010537043dce970c Wei Dai

    Wei, Bennett says that to specify a state, you can specify a macrostate, and then specify the exact state within it.

    Yes.

    For lower entropy macrostates, it may take less to specify the exact state within, but it takes more to specify the macrostate itself. Relative to equilibrium distribution expectations, this doesn’t make it easier to describe such states.

    You’re not supposed to specify a macrostate relative to the equilibrium distribution, but rather specify it as a computer program, relative to a universal Turing machine. One page 938 in Bennett’s paper, there’s a paragraph that goes “We needs to say in more detail what it means to describe a distribution [i.e. macrostate] … a Monte Carlo program for sampling some distribution q not too different from p”. Consider such a program for sampling the low-entropy initial macrostate proposed by the inflation hypothesis. It may be somewhat longer than the program for sampling the equilibrium distribution, but surely that’s more than made-up by the vastly smaller number of bits needed to specify a microstate within the low-entropy macrostate.

    Yes, if you have non-equilibrium expectations that make low entropy macrostates more likely, you can take advantage of this to create shorter descriptions of exact states within such macrostates. But the whole question here was explaining why such expectations make sense; you can’t assume them and then think you’ve proved why they make sense.

    The idea is, some states are more likely than others because they have shorter descriptions relative to a universal Turing machine. You’re right that this deviates from equilibrium expectations, but having this kind of prior seems to work, in the sense of giving sensible predictions, whereas equilibrium expectations give nonsensical predictions, as you’ve observed. If you need further motivations, there’s the appeal to Occam’s Razor and Schmidhuber’s suggestion that reality is directly structured to favor universes described by short programs. I consider the question of “why does the universal prior make sense?” to be still open, but it clearly makes more sense than equilibrium expectations.

  • http://profile.typepad.com/robinhanson Robin Hanson

    Wei, if your claim is that there is a universal prior over bit strings, and a mapping from bit strings to physical states such that some low entropy states have high probability, I can accept it. But if your claim is more like that all priors and all mappings make all low entropy states have high probability, you need to do much more than outline an example of one prior, one mapping, and one state.

  • http://profile.typepad.com/6p010537043dce970c Wei Dai

    Wei, if your claim is that there is a universal prior over bit strings, and a mapping from bit strings to physical states such that some low entropy states have high probability, I can accept it. But if your claim is more like that all priors and all mappings make all low entropy states have high probability, you need to do much more than outline an example of one prior, one mapping, and one state.

    Robin, this one example is sufficient to explain the “past hypothesis”. If you give even a small weight to this particular prior in your actual prior, then your posterior belief, conditioned on your current observations, will be that with high probability you are in a universe at a time coordinate with lower entropy in one direction, and higher entropy in the other.

    But my argument applies to any mapping that can be transformed into the particular one I proposed by a short computer program, which should cover all “reasonable” mappings. It also applies to any low-entropy state that can be sampled by short Monte Carlo programs, which should cover most low-entropy states that physicists might consider.

  • http://profile.typepad.com/robinhanson Robin Hanson

    Wei, we already believe the past was low entropy. I won’t just take your word regarding your “reasonable” and “most” claims.

  • http://profile.typepad.com/6p010537043dce970c Wei Dai

    Robin, do you have a counterexample of a low-entropy state that a physicist has considered, but can’t be sampled by a short Monte Carlo program, or a mapping between bit strings and physical states that you consider reasonable, but can’t be transformed into the one I gave by a short program?

  • http://profile.typepad.com/robinhanson Robin Hanson

    Wei, your area is not my focus, so I’m not going to take the time to prove a counter-example, or even to figure out what you mean precisely enough to know what to you would count as a count-example. It is up to the proponents of such claims to offer arguments in their favor.

  • http://profile.typepad.com/6p010537043dce970c Wei Dai

    Robin, looking for counter-examples is a useful technique for understanding and judging claims that are not backed by formal arguments, which I admitted are not available. You don’t have to prove to my satisfaction any counter-examples you might find. Feel free to state them informally, or just use them to privately update your own beliefs. And as far as I can tell, the claims under discussion are already stated in simple language that doesn’t require any specific focus to understand.