Self-Indication Solves Time-Asymmetry

This seems a deep insight simple enough to explain in a blog post (and so I’m probably not the first to see it):  the self-indication approach to indexical uncertainty solves the time-asymmetry question in physics!  To explain this, I must first explain time-asymmetry and indexical uncertainty.

A deep question in physics is time asymmetry – why doesn’t stuff happen as often "backwards" in time?  We have no idea about the tiny CP-violation in particle physics, but all the other time asymmetries are thought to arise from a very-low early-universe entropy.  The most popular explanation for this is inflation, especially eternal inflation, which says that any small space-time region satisfying certain conditions is connected to infinitely many large time-asymmetric regions much like what we see around us.  Alas, the chance that any small region satisfies these inflation conditions is extremely small.  As a recent paper puts it:

Initial conditions which give the big bang a thermodynamic arrow of time must necessarily be low entropy and therefore "rare." There is no way the initial conditions can be typical, or there would be no arrow of time, and this fact must apply to inflation and prevent it from representing "completely generic" initial conditions.  … If you can regard the big bang as a fluctuation in a larger system it must be an exceedingly rare one to account for the observed thermodynamic arrow of time.

So the question of time-asymmetry reduces to this: why does the universe have enough independently variable small regions that at least one of them gives eternal inflation?  That is: why is the universe so big?

Indexical reasoning is about where we are in space-time.  Even if we knew everything about what will happen where and when in the universe, we could still be uncertain about where/when we are in that universe. To reason about this form of uncertainty we need something equivalent to a prior which says where/when we should expect to find ourselves, if we knew the least possible about that topic.  This indexical prior over locations in a universe must be combined with a prior over possible universes to give a total prior over where we might find ourselves. 

For a particular universe, if we would have been equally likely to find ourselves as any of the observer-moments (e.g., "me now") in that universe, then we should expect to find ourselves in the parts of that universe with the most such moments.  Among humans on Earth, for example, you should expect to find yourself in the eras and nations containing the most people.  The self-indication approach to indexical uncertainty says that this same reasoning also applies to possible universes: not only should you expect more to find yourself in universes that are more likely to exist, but you should in addition expect more to find yourself in universes that have many slots for creatures like you.  For example, you should expect to be in a populous era in a big nation in a big long-lasting universe.  (This approach favors thirders in the sleeping beauty problem.)

The self-indication approach says that if very large universes are at all possible, you should think yourself very likely to be in one.  In the limit, if there is a non-zero probability of situations where the universe has infinitely many slots for creatures like you, you should be almost certain you are in that sort of situation.  This may seem arrogant, and Nick Bostrom argues it is unreasonably presumptuous.  Nevertheless, it does handily answer the key time-asymmetry question: why is the universe so big?   (And it is more presumptuous than being sure to be in an infinite, vs. finite, part of an infinite universe?)   

That is, given self-indication we should expect to be in a finite-probability universe with nearly the max possible number of observer-moment slots.  Such universes seem large enough to have at least one inflation origin, which then implies at least one (and perhaps infinitely many) large regions of time-asymmetry like what we see around us.  And if, as it seems, most observer-moments in such universes are in such regions, then we have explained why we see what we see.

I found the self-indication approach pretty persuasive on theoretical grounds before, and now I’m all the more sold.  If that is presumptuous, so be it – I bite bullets.  But do I contradict myself?

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  • http://www.hopeanon.typepad.com Hopefully Anonymous

    Sounds plausible. I encourage you to post this on the arXive forums, too.

  • Lake

    Indexical reasoning allows you to say: given we’re in a universe at all, we would expect to be in a big universe. But that doesn’t tell us why this particular universe is big – it just suggests that it *is* big. What am I missing here?

  • http://acceleratingfuture.com/steven steven

    But is the extra size enough to compensate for the extra improbability? If so, then yes, it sounds plausible. I don’t think even Nick Bostrom would object to applying self-indication to really-existing worlds, just to possible but nonexistent ones.

  • Tim Tyler

    We have no idea about the tiny CP-violation in particle physics, but all the other time asymmetries are thought to arise from a very-low early-universe entropy.

    Nooo! CPT symmetry is not an asymmetry – and it is easy to explain. The universe is reversible – and it’s symmetric under t => -t. Asking why you need to reverse parity and charge when you reverse time is like asking why you need to reverse momenta when you reverse time. You don’t – the simplest explanation is parity, charge and momentum are time-dependent dynamical phenomena – i.e. they reverse themselves automatically on t => -t. Details are on my web site.

    Also: “why is the universe so big?” has a simple anthropic answer – if you accept the premises that it necessarily started small, and that it takes at least 4 billion years to evolve something like us.

    Similarly: “why doesn’t stuff happen as often “backwards” in time” has a simple anthropic answer – if you accept the premise that dissipative structures like living organisms need sustained entropy-gradients to support their continued evolution.

    The idea that low-entropy conditions are “rare” is an odd one in this context. A better way of looking at is is that low-entropy initial conditions have an extremely short description – and are therefore preferred by Occam’s razor.

    Lastly: “inflation” has a technical meaning in physics which is quite different from “expansion”. This essay muddles those concepts together – in a way which would probably make most physicists squirm.

  • http://hanson.gmu.edu Robin Hanson

    Tim, I don’t see how I confused “inflation” with “expansion” (a word I never used.)

  • http://www.cmp.uea.ac.uk/~jrk Richard Kennaway

    That is, given self-indication we should expect to be in a finite-probability universe with nearly the max possible number of observer-moment slots.

    This runs straight into Fermi’s paradox. If we are in a populous universe, then where are all the aliens?

  • Tim Tyler

    Put it this way: it seems pretty debatable that the the most popular explanation for a low-entropy early universe and the resulting time asymmetry has anything to do with inflation. Any-old explosion in a reversible universe will produce something akin to the second law of thermodynamics; any old bomb can produce an explosion – and the bang has to have been big, if it must leave entropy gradients big enough to support life four billion years later. From that perspective, inflation seems more like an implementation detail.

  • Constant

    Tim – how about stuff like this:

    The authors show that inflation explains the “small entropy problem” posed by Penrose as well as the well known “large entropy problem”. They also show that inflation which is generic in the expansion phase of the Universe is unstable in the collapse phase. This suggests that inflation might also provide an explanation to the question of the direction of the arrow of time.

  • http://brokensymmetry.typepad.com Michael F. Martin

    I’m not sure I buy into the many universe theories, but within that framework, I think you’re really onto something here. Please say more about this!

  • http://cosmicvariance.com/ Sean Carroll

    Hi Robin–

    I think your mistake is in the penultimate paragraph. Sure, given SIA, the universe should be as big as possible, and therefore have plenty of inflationary trajectories. But if you focus on patches of universe like ours today (big, low density, etc), standard counting would suggest that only an infinitesimal fraction of them came from low-entropy inflationary beginnings. That is, given a patch with something like our current medium-entropy configuration, it is overwhelmingly likely to have come from a high-entropy past as well as evolving toward a high-entropy future.

    See e.g.:

    Page
    Price
    Hollands and Wald
    Carroll and Chen

    or just

    this blog post.

    Which is not to say the problem can’t be solved, but it’s not so easy.

  • Tim Tyler

    A controversial cryptic-teaser abstract. My guess is that there is probably a paywall involved.

  • Constant

    Tim – Then how about this? The journal is prominent, the scientist is well known, and it’s from 1983, showing the possibility of a connection between inflation and time’s arrow has been getting air time since soon after inflation was first proposed.

    The recently proposed inflationary Universe scenario explains several of the mysteries of modern cosmology. I argue here that it also provides a natural explanation for the origin of time asymmetry (‘time’s arrow’) in the Universe. The new feature which inflation injects into this long-standing problem is the temporary dominance of the cosmological term in the gravitational field equations, which acts as a sort of repulsive gravity. This term generates huge quantities of energy and radiation (or matter) entropy, while drastically reducing the entropy density of the gravitational field. It thus establishes a large gap between the radiation entropy and the gravitational entropy, which gravity is now trying to close.

  • http://www.garbett.org Shawn Garbett

    Borders on Anthropic reasoning. Interesting.

  • http://profile.typekey.com/Psy-Kosh/ Psy-Kosh

    What about the whole Boltzman Brain problem?

    It would be far more likely to find myself in any particular single “big” universe than a particular “small” universe, (That is, one that has many slots for “me” vs one that has few) but wouldn’t there be many many more “small” worlds or other small local formations of order, sufficient to cause me to expect to find myself in one of those?

    Why am I not a Boltzman brain?

  • Tim Tyler

    Isn’t that the guy who wrote: “The Mind of God”? The origin of time asymmetry is the low-entropy state in big bang. Sure, inflation has something to do with that, but almost any large explosion would do more-or-less equally well. Set off a nuclear weapon and suddenly you see an arrow of time.

  • http://uncommon-priors.com Paul Gowder

    I was thinking exactly what Shawn said — Susskind would be happy to hear this!

  • Jim

    Perhaps I’m missing something, as this is radically outside of my field, but this explanation seems to border on circular reasoning to me.
    These things exist because it’s the most probable way for me to exist. What I mean is, I’m unsure of what this actually explicates other than an anthropic explanation – beyond the fancier words and the far greater ability to observe and test, how is this significantly superior to Descartes.
    But then again, I’m a social scientist and may be missing something. 😉

  • http://brokensymmetry.typepad.com Michael F. Martin

    Assuming energy conservation, is it true that lowest entropy states will also be highest in symmetry? Then isn’t Robin just saying that increasing entropy requires time asymmetry when energy is conserved?

  • http://occludedsun.wordpress.com Caledonian

    Why am I not a Boltzman brain?

    You are. You just don’t understand what being a Boltzmann brain implies.

  • Garbun

    I have a question for everybody:

    Suppose that a civilisation has already (or will have) reached the state where it can produce trillions of trillions of sentient minds, whatever their substrate. According to the self-indication principle, shouldn’t we be one of them instead of belonging to the human race, which has “only” billions of beings ?

    It’s something close to the Fermi paradox and the Bostrom’s computer simulation’s argument.

    Note that the time has logically no influence on that problem, because even if that kind of super-civilisation does not exist yet – but WILL exist – then we should have been born in the future.

    That implies that either we have been very very unlucky (one chance over x, with x being how many times the super-civilisation is bigger than ours in terms of number of souls); either that kind of super-civilisation has never and will never exist.

    Any thought on that ?

  • Tim Tyler

    Similarly, the odds are billions to one that you are the oldest guy on the planet. It’s a rare job – but someone has got to be doing it.

  • http://profile.typekey.com/Psy-Kosh/ Psy-Kosh

    Caledonian: Perhaps I ought be more precise.

    Why is it that I seem to percieve more order, more structure than is needed for me to exist for, well, a brief interval?

  • http://occludedsun.wordpress.com Caledonian

    Why is it that I seem to percieve more order, more structure than is needed for me to exist for, well, a brief interval?

    Because 1) the perception of the order and structure requires more than a brief interval, 2) your wondering why you perceive so much order and structure takes even longer, and 3) any duration of existence, no matter how brief, is ‘continued’ in other sections of the Many Worlds.

    If you have not already, you should read “The Library of Babel”. How long is the longest text contained by the Library?

  • http://profile.typekey.com/Psy-Kosh/ Psy-Kosh

    Caledonian, consider it this way:

    I notce that I’m not seeing the walls dissolve, I notice that I’m not actually floating in the middle of space and dying of decompression, I notice that my brain has encoded in it a memory of me, say, making the bed this morning and by golly, that seems to coincide with what I observe now, specifically that my bed is made.

    All of these things seem to be an excess of order, way more than is needed to instantiate me for a bit of time.

    So I remain confused on the whole Boltzman Brains issue. Clearly there’s something I’m not understanding here, something is missing in my model of the world, and (at least) in my model of Robin Hanson’s model of the world as depicted here.

  • http://occludedsun.wordpress.com Caledonian

    I notce that I’m not seeing the walls dissolve, I notice that I’m not actually floating in the middle of space and dying of decompression,

    Although ‘normal’ human bodies are a subset of the possible Boltzmann Brains that encode the algorithm that constitutes your mind, they are an insignificantly tiny fraction of the total possibilities.

    You’re making several errors: you’re assuming that the Brains that are running your consciousness are actual brains, and you’re confusing what happens to the Brain with what your consciousness experiences.

    Does it matter to an implementation of Conway’s Game of Life whether it’s being run on a Mac or an Apple or a PC or a Cray? If you compute T1 to T2 for a pattern, end the program, and fifty years later run the program to compute T2 to T10,000 for that pattern, do you think the pattern knows the difference?

  • http://hanson.gmu.edu Robin Hanson

    Sean: [Regarding] patches of universe like ours today … standard counting would suggest that only an infinitesimal fraction of them came from low-entropy inflationary beginnings. That is, given a patch with something like our current medium-entropy configuration, it is overwhelmingly likely to have come from a high-entropy past as well as evolving toward a high-entropy future.

    The recent paper I cite above argues that counting correctly does say patches like ours are more likely to have come from inflation, though they and I admit it isn’t entirely clear. Similarly others argue that a correct counting makes ordinary brains more common than Boltzman brains, though this also isn’t entirely clear. But yes the pre-inflation past would be high-entropy in any case.

  • mjgeddes

    Good interesting first attempt at an answer Robin, but it’s more likely that the time asymmetry can only be explained by….universal terminal values…built into the structure of the universe.

    Tim said:

    ‘A better way of looking at is is that low-entropy initial conditions have an extremely short description – and are therefore preferred by Occam’s razor.’

    But of course this merely pushes the question back to accounting for Occam’s razor again. Occam’s razor only works because for every knowledge domain there are associated *aesthetic principles* (built-in design principles- not neccesserily human) which provide appropriate initial constraints.

    Even at this early stage of theorizing, I am very confident if there are universal terminal values, the objective morality is likely very closely associated with the creation of beauty. Now that all readers know, get out there and make some good art! 😉

    “…Copernicus’ aesthetic objections to [equants] provided one essential motive for his rejection of the Ptolemaic system….”

    – Thomas Kuhn, The Copernican Revolution

    “All of us had been trained by Kelly Johnson and believed fanatically in his insistence that an airplane that looked beautiful would fly the same way.”

    – Ben Rich, Skunk Works

    “Beauty is the first test: there is no permanent place in this world for ugly mathematics.”

    – G. H. Hardy, A Mathematician’s Apology

    Paul Graham: Taste For Makers

  • http://profile.typekey.com/Psy-Kosh/ Psy-Kosh

    Caledonian: You’re right in that what I’m fundamentally implemented on isn’t so much a concern. The issue is that _WHATEVER THAT MAY BE_ seems to contain/encode more order than, at least at a surface glance, would seem to be justifiable with merely anthropic type arguments. ie, whatever it is that’s encoding me seems to be encoding rather more regularity and so on then is necessary to just encode, well, a few minutes of me.

    Maybe you’re seeing some obvious thing here that I’m missing, but, well, if so, then there’s something I’m missing. I remain confused on this issue.

    Robin: That paper you mention, does it explain about proper counting solving the Boltzman Brain problem, or do you mean that’s something that others have done entirely separately. If so, if you happen to know the basic idea, well, what is the basic idea about that? Thanks.

  • http://occludedsun.wordpress.com Caledonian

    Similarly others argue that a correct counting makes ordinary brains more common than Boltzman brains, though this also isn’t entirely clear.

    Since ‘ordinary’ brains are a subset of Boltzmann brains, that would have to be a truly extraordinary redefinition of ‘correct’.

    whatever it is that’s encoding me seems to be encoding rather more regularity and so on then is necessary to just encode, well, a few minutes of me.

    The order you perceive is a property of you, the information processed by your algorithm. Not the environment running the algorithm.

    The walks through Libraryspace that do not preserve the illusion of continuity far, far outnumber those that do. But in worlds where that continuity is not preserved, either you do not exist at all or you do not perceive the discontinuity. The more properties of the algorithm that aren’t preserved in ‘switching’ from one instance to another, the less likely it is that the two fit the criteria for a valid continuity.

  • Diversity

    Nice reasoning, but are you sure that time assymetry always holds in this universe? Teleporting even individual photons, even accross the Danube, seems to cast some doubt on that.

  • http://www.iphonefreak.com frelkins

    @mjgeddes

    For your allusion to Copernicus, cite the source directly – he begins with beauty and with art in his introduction. It is so nicely written I take the liberty of quoting the opening in full:

    “Among the many various literary and artistic pursuits which invigorate men’s minds, the strongest affection and utmost zeal should, I think, promote the studies concerned with the most beautiful objects, most deserving to be known. This is the nature of the discipline which deals with the universe’s divine revolutions, the asters’ motions, sizes, distances, risings and settings, as well as the causes of the other phenomena in the sky, and which, in short, explains its whole appearance.

    What indeed is more beautiful than heaven, which of course contains all things of beauty? This is proclaimed by its very names [in Latin], caelum and mundus, the latter denoting purity and ornament, the former a carving. On account of heaven’s transcendent perfection most philosophers have called it a visible god. If then the value of the arts is judged by the subject matter which they treat, that art will be by far the foremost which is labeled astronomy by some, astrology by others, but by many of the ancients, the consummation of mathematics.

    Unquestionably the summit of the liberal arts and most worthy of a free man, it is supported by almost all the branches of mathematics. Arithmetic, geometry, optics, surveying, mechanics and whatever others there are all contribute to it.”

    – N. Copernicus, De revolutionibus, Introduction, Book One

    This preoccupation with the beauty and elegance in science is not a solely a Western phenomenon, it can also be found in Abhinavagupta and in Buddhist natural philosophy as well.

    Note also that Copernicus is interesting in that he begins to separate science from what was then called “natural philosophy,” when he later says:

    “However, since different hypotheses are sometimes offered for one and the same motion (for example, eccentricity and an epicycle for the sun’s motion), the astronomer will take as his first choice that hypothesis which is the easiest to grasp. The philosopher will perhaps rather seek the semblance of the truth.”

    What is the difference to Copernicus between the practitioner of this new science – astronomy – which he distinguishes from its Medieval name “astrology” – and the philosopher? Yet even as Copernicus struggles to create science, he insists on retaining beauty!

    Thus I ask you mjgeddes, would you agree that Robin’s foray above meets Copernicus’ criteria of being both “beautiful” and “easy to grasp,” despite being perhaps unexpected?

  • http://www.soulphysics.org Bryan

    Here’s how I understand your argument.

    1. There is a high probability that the Universe is very large.
    2. If the Universe is very large, then there is a high probability that we are in a low-entropy region.
    3. Any low-entropy region will lead to an asymmetry in time.

    This is interesting, but it’s sure a lot of extra machinery for this kind of claim. The claim you’re interested in would be the past-hypothesis: the initial conditions of the Universe pick out a low-entropy state. Why not simply posit this as a fact about the Universe, instead of going through the exercise of (1) and (2)? Here’s two reasons why it’s worth considering:

    First: there is no probability space in which (1) makes sense; and
    Second: (2) seems to be false.

    No matter what interpretation of probability you adopt, defining a probability measure on the “space of possible Universes” will be completely meaningless. This suggests there is no meaningful way to precisely state (1), if one has any empiricist scruples. And if the Universe is infinite, as our best models now suggest, then the probability that you’ll end up in any finite region is 0. So (2) would simply be false. I suspect there are no bullets to be bitten here, before these problems are worked out more carefully.

    Thanks for the interesting post!
    Bryan

  • http://dao.complexitystudies.org/ Günther Greindl

    @Caledonian

    I tend to agree with you. Have you perchance read Greg Egan’s “Permutation City”? The “dust theory” of that book – patterns finding themselves (which is what you are essentially saying) – is very intriguing, and the more I’ve been thinking about all the metaphysical problems involved in “traditional” theories, the more I find a “dust theory” attractive.

    Cheers,
    Günther

  • Tim Tyler

    The pre-inflation past would be high-entropy in any case.

    I’d assign a rather low probability to that. Physics is thought to be reversible – and the idea has stood up well over the centuries. For an early entropy decrease, you’d need irreversible physics – or enormous spans of time. I am not currently aware of any evidence favouring irreversible physics – and I don’t think you can argue that the universe is likely to have started in an arbitrary state, and then stumbled upon a low-entropy zone by chance – since that hypothesis would not predict the incredibly-low entropy beginning we seem to see. Also, complex initial conditions would themselves need explaining in the face of Occam’s razor.

  • http://evolutionarydesign.blogspot.com/ island

    This sounds like the same bogus unobservable crackpot hype that Sean Carroll is pushing.

    I’ve got a better idea for you to chew on after the LHC finds nothing and people start to get really desperate when the funding for crackpot research goes away:

    http://www.lns.cornell.edu/spr/2006-02/msg0073320.html

    • http://timtyler.org/ Tim Tyler

      It *is* the same stuff Sean Carroll is on about. Remember this is a world where Rupert Sheldrake and Roger Penrose find audiences.

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