Twisty Little Universes, All Alike

When we left our story, we were stuck in the unfortunate position of living somewhere in a multiverse without any a priori way to figure out where we live. What might we do?

One thing we can do is let the dreaded anthropic principle rears its head. At its most basic essence, the anthropic principle is the statement that we exist. This is data, and we can draw conclusions from this data. The most famous examples of this are Hoyle’s prediction of a particular nuclear resonance based on the need for enough carbon in the universe for us to exist and Weinberg’s bound on the cosmological constant based on the existence of galaxies. Using our existence as data is completely uncontroversial. What is controversial is the underlying philosophy. Put simply, the existence of a multiverse may represent the end of one of the dreams of physics: that we can compute every physical quantity from first principles — as the solution to some mathematical equation, for example. If there is a multiverse and a distribution of parameters, then some things are just random and have no fundamental explanation.

In this context, one can take the anthropic principle to be an inversion of the usual data/inference model of science. Instead of our existence being data we use to draw inferences, we instead consider the need for observers as a theoretical basis for explaining data we have already collected.

The primary tendency is to use this as an explanation for many “coincidences” that occur in nature. Take the classic example of the orbit of the Earth. If you vary it too much, you find that life (as we know it) could not exist. You could argue that it is a incredible coincidence that we happen to live in a zone so remarkably amenable to life, but, of course, there are plenty of planets in the universe, and life only develops on those that can sustain it. There’s no point in trying to predict the radius of Earth’s orbit from first principles; we live here because we can live here.

The danger of this is that if we can’t actually observe the other universes, one may give up on understanding coincidences that actually have fundamental explanations. For example, as I understand it, the existence of Hoyle’s resonance follows from some details of nuclear physics. Would this have been found if everyone had instead ascribed it to some particular facet of the multiverse? Invocation of the anthropic principle in this manner represents the end of science. It could very well be correct, but how does one know when one should close a door?

Beyond this problematic sort of “retrodiction”, many people would like the anthropic principle to lead towards some semblance of predictivity. The key to this is the principle of mediocrity, sometimes called the Copernican principle. This goes beyond the anthropic principle (which is essentially tautological) and deep into the philosophical swamp. What it states is that we are not special. Given some broad class of, well, things of which we are a member, we should be an “average” member of that class. Needless to say, it’s quite hard to turn this into a precise statement.

Still, we do similar things every day. Let’s say that there is a drug that has side effects in 5% of users. What is the probability that if you were to take it, you would experience side effects? To answer this question, one needs to delve into what one means by probability. In the philosophy known as “frequentism”, one does or imagines doing an experiment a number of times, and the probability of something occurring is the percentage of times it occurs. We can apply that to this situation, and we see that the probability is either 100% or 0% — we don’t know which. There’s only one of you, after all, and you’ll either have side effects or you won’t.

A lot of people find this situation unsatisfactory. It seems reasonable that one could assign a value of 5% to the probability that you will experience side effects. To get to that conclusion, you can drop the frequentist philosophy of probability and replace it with the idea that probability expresses the degree of one’s belief in a proposition. Or, to make it more grounded, probability represents the odds that one would take to make a bet on the proposition. This is called Bayesian probability. You begin with the “prior probability”, in this case 5%, and as you learn more information, there are rules, “Bayes’s Theorem”, about how you adjust the odds. You start with the assumption that you are a generic person and give yourself a probability of 5%, and as you learn more, the number changes.

So, at last we’ve arrived at a situation where we might be able to assign some probabilities. I find this extremely odd, myself. While we might not be able to actually predict anything, we find ourself able to take bets. Has anyone called Vegas?

I’m not much of a gambler myself, but before you dismiss this entire situation as completely crazy and unscientific, quantum mechanics rears its ugly head again. As I’m sure most of the readers of this blog are aware, quantum mechanics does not give exact predictions; instead it gives a probability distribution of outcomes. Most of the time, this isn’t a problem as experiments are repeatable, and we can examine the distribution of the results. Still, there are some philosophical issues. We’re not going to last forever, so we can’t do a given experiment an infinite number of times. In any finite number of experiments, there is no guarantee that the resulting distribution will look like the one predicted by theory. So, can we ever say that anything is falsified?

I’ll leave that one for the philosophers of science because we’ve got an even bigger problem. In the previous situation, we could at least repeat out experiment. The theory of inflation, on the other hand, is a theory of the origin of the universe, and so far we’ve only been able to do that experiment once. What inflation tells us is that the fluctuations in the cosmic microwave background radiation are, in fact, quantum mechanical in nature. The rapid expansion of inflation takes quantum fluctuations and blows them up so that they are spread against the sky. One can predict the spectrum of those fluctuations from the theory and compare it to what we observe and find remarkable agreement. But the fluctuations are truly quantum mechanical in nature and, thus, we can only really speak of various probabilities. This uncertainty is called “cosmic variance” (perhaps you’ve heard of it?), and is more than just an academic question. While the agreement of theory with experiment is remarkably good in general, there are two data points which don’t fit the model very well. Are they the result of cosmic variance? Are they indicative of some aspect of the physics we don’t understand? How much would you bet on it?

At this point, my head starts to hurt, but even if we accept this Bayesian principle of mediocrity, we’re still not be out of the woods. There are ugly implementation details and confounding paradoxes that come out of this. These will be the subject of the final post in this series.

The posts in this series are:
The Multiverse: An Apology
The Lay of the Landscape
Twisty Little Universes, All Alike
Alone in the Multiverse

Comments

  1. #1 Arun
    August 21, 2007

    In this context, one can take the anthropic principle to be an inversion of the usual data/inference model of science. Instead of our existence being data we use to draw inferences, we instead consider the need for observers as a theoretical basis for explaining data we have already collected.

    In what sense is this an explanation?

    The only way I can admit this as an explanation is that the need for observers helps us isolate the one solution in the multiverse equation that we should be paying attention to; we do not then have an explanation of why that verse and no other, but we have arrived at a complete description of a potentially infinite number of facts using only a finite number of facts as input.

  2. #2 Uncle Al
    August 21, 2007

    Casinos invest in statistics, players seek fluctuations, and the IRS skims vigorish from overall cashflow. None of that specifies structure. Symmetries define the universe, broken symmetries fuel details, large scale/strong field events are remarkably irrelevant to pond scum’s introspection.

    Grab a magnifier and blunt dissect a human brain. When you finally arrive at the wax slab you will have a mammoth pile of data and no understanding of what constitutes awareness. An axiomatic system is no better than its weakest postulate. You cannot find a maximum on a flat surface – you need a better surface not a better technique.

  3. #3 Aaron Bergman
    August 21, 2007

    In what sense is this an explanation?

    It’s a matter of definition, unfortunately. You get to decide what you accept as a valid explanation. It’s often useful to drop the multiverse and its associated baggage when considering these issues. Is the need for an observers an “explanation” of the distance of the earth from the sun?

    Or, if you don’t like that, is the need for observers an “explanation” for the fact that the distance of the earth to the sum is within the narrow range that admits life?

    Or does that not need explanation?

  4. #4 Neil B.
    August 21, 2007

    I wish scientists wouldn’t use the phrase “dreaded” to describe the anthropic principle, because philosophical assumptions are ultimately unavoidable. The anthropic question came about because: many of the constants in the universe would have prevented life from thriving if they’d been only a little different. Really, why a fine structure constant (dimensionless) of around 1/137, instead of the logically cleaner value of say, one? Why should the way “the” world is, happen to support our existence within a narrow range? In any case, how can a particular manner and set of properties possibly be inherently more likely to “exist” when that term is not an ordinary predicate holding inherent logical connections to particular ways for “existing” things to be? This is not just metaphysics, because it goes into thinking about how to construct the universe from the ground up if that’s what you’re trying to do, even in part.

    Is our own universe just one among other universes? If there’s a range of possible ways to be, then we would be very rare but of course must “find ourselves” here wherever that is. Perhaps, but there are many ironies. Such universes are so far unobserved and may be literally unobservable, barring some sort of extra-dimensional collision or etc. Also, where does it stop? If universes can have “other laws of physics” then why not ones that aren’t lawful looking at all, that more resemble magical fantasy realms, the Warner Brother’s Cartoons, or heavens and hells… BTW the most useful probability approach is to think: If I did turn out to be in the group of x%, what else would I expect? It’s like saying, given I’ve already gotten this hand of cards so far, what are the chances of getting other cards? I will explain the “dreadful” implications later.

    The most stunning point to make, that I still don’t find widely appreciated is this:
    There is, serious as a heart attack, no genuinely logical way to define “existence” above and beyond logical description. IOW, no way to define “matter” aside from the structural descriptions of it, other than appeal (ironically) to metaphysical issues like the realness of our experience, etc. Now you might say, no big deal, since you can imagine just thinking of “the universe” as being pure mathematics/structure (which is evasive since it leaves out experiential qualities, but I digress.) The trouble then is, you have to admit all the other “descriptions” (not just “simulations”) as being equally pseudo-real as well, like it or not (modal realism.) That’s what Max Tegmark says he believes in, roughly. Then, you’ve got a mess on your hands.

    Here’s the problem: All possible worlds really means all possible descriptions. If so, one has a vanishing Bayesian probability of finding oneself in a world that continues to be lawful instead of one of the infinitely more that were like this up to this point and then begin to diverge. Why? Because of all the changes from then on to different laws and variations and distortions of laws that can be described, and indeed the entirety of what behavior can be described after that point which certainly includes a gigantic set of chaotic futures, etc. It’s like once your in the world of “already came up heads 100 times in a row” or similar, then even so it’s not likely the subsequent flips will continue to be orderly.

    Hence, I think there really needs to be a manager of some sort, to ensure placement in effect of observers like us in a world that really has laws, since logical possibility is just too inclusive. Think of that as you wish. (Not to mention, our having experiences etc., but that gets into consciousness issues and I am just making the argument relating to physical conditions and our being here.)

    A thinker can’t really pretend to engage this issue unless basically conversant in issues like modal realism and Bayesian back-engineering of the chances of being in such and such straits now versus the conditions of the future, etc. Such questions can’t just be blown off by appeal to “rationality” or “science” because they concern the fundamentals of framing the issue. If you want to explain why things are like they are, what would you hang it on?

  5. #5 Aaron Bergman
    August 21, 2007

    You’re getting ahead of me. Modal Realism rears its head tomorrow.

  6. #6 island
    August 21, 2007

    One thing we can do is let the dreaded anthropic principle rears its head. At its most basic essence, the anthropic principle is the statement that we exist.

    Aaron, this statement cannot be correct unless you asuume that the multiverse exists, because you cannot lose the strong significance of the evidence, without willfully ignoring much of it.

    On one hand, you have a lot of very pointed phyisics for what is very likely an “entropic” anthropic principle, and you also have the observed universe.

    On the other, you have an anthropic principle and unproven speculation about worlds that may or may not be relevant.

    They don’t weigh the same, so your statement is misrepresentative of the *basic essence* of the observation in a manner that has the effect of downplaying the significance of the evidence, like neodarwinians and anticentrists do.

  7. #7 Coin
    August 21, 2007

    many people would like the anthropic principle to lead towards some semblance of predictivity. The key to this is the principle of mediocrity… What it states is that we are not special. Given some broad class of, well, things of which we are a member, we should be an “average” member of that class. Needless to say, it’s quite hard to turn this into a precise statement.

    See, I just don’t get how this principle can be valid. Okay, so we assume that if there’s some class of universes that admit observers, that we’re an average member of that class. Why can we assume this? What if we’re not?

    The way I look at it is, let’s say there are exactly a hundred universes which have conditions which can produce observers, and ninety-nine of them are mediocre, and one of them is bizarrely special in some way. And let’s say you visit each of these universes, find an observer inside that universe, and explain the anthropic Principle of Mediocrity to them. This argument is going to be just as convincing to the observer in the exceptional universe as it is to the observers in the mediocre ones! By assuming a mediocre universe, you’ve come up with a rubric which will be accurate for most universes, but which is also, for some sentient observer somewhere, guaranteed to fail.

    A comparison is made here to quantum physics, which predicts probabilities of outcomes rather than specific outcomes and therefore sets you up for a situation where each experiment has a probability of failure. But the trick there is that you expect the failures– you set up your experiments such that you get both mediocrity and exceptions, and you know how to deal with each. Particle accelerator people can run their experiments and expect that there’s a certain probability of “exceptions” with each trial, meaning that they can expect a mediocre result and also expect occasional n-sigma deviations. What they don’t do is sit down and say “well, we’ve got this theory, and there’s a 75% chance that it’s true and a 25% chance that the whole thing’s bunk”.

    The same goes for any other science that involves probability: frequentism can tell us there’s a 5% chance of side effects for such and such a drug because they never run a drug trial with just one person. Similarly, if you do call Vegas, what you’ll find is that they never bet the entire casino on a single bet– they run as many trials as possible, they expect that they’ll win some and also that they’ll lose some, and their business model is based around knowing the probability with which successes will outnumber failures. If you call Vegas and ask them what they think about your anthropic-universe bet they won’t even know what to do with it, because banking your livelihood on a single trial is simply not what casinos do– it’s what gamblers do. This is why generally speaking casinos are very rich and gamblers are not.

    Or, if you don’t like that, is the need for observers an “explanation” for the fact that the distance of the earth to the sum is within the narrow range that admits life?

    I don’t think it is, no, because we don’t have any guarantee that the narrow range that admits earth life is the only range where life itself can exist. Maybe somewhere in the universe there’s life that lives in liquid methane oceans, and it’s going to have a separate band where it would be able to survive.

    I mean, I would tend to explain the presence of the earth in the admits-life range by suggesting that the chief reason the admits-life range we perceive is where it is in the first place is that when life arose on this planet it adapted to the circumstances of the planet on which it found itself.

  8. #8 Arun
    August 21, 2007

    Aaron,
    I don’t think what an explanation is is a matter of definition.

    It’s often useful to drop the multiverse and its associated baggage when considering these issues.

    Good idea!

    Is the need for an observers an “explanation” of the distance of the earth from the sun?

    No, it is most certainly not an explanation. It is merely the statement that “Given that there is life on earth, the earth must be in a orbit in the habitable zone around the sun”. It is about as non-explanatory as saying that “Since we don’t know of any English-speaking extraterrestrials, the person writing this sentence must be an earthling.”

    Or, if you don’t like that, is the need for observers an “explanation” for the fact that the distance of the earth to the sum is within the narrow range that admits life?

    Likewise, no.
    In general, “A requires B, and A (exists)” is not an explanation for B.

    Let’s look at a simplified version of Olber’s paradox:
    “The dark night sky requires an expanding universe and the night sky is dark” is not an explanation of the expanding universe. “Why is the universe expanding?” – “Because of Olber’s paradox!” “??????!!!!!????? I thought it had something to do with the dynamics of General Relativity.”

    Or does that not need explanation?

    Something that is closer to an explanation would come from a general theory (say) that described formation of star and planets from interstellar clouds, and (say) showed some statistical correlation between the mass and radius of the initial cloud and the masses of the final star and the amount of material that condensed into planets. Perhaps radiation pressure from the forming star acts differently on different atoms and causes a deficit of light elements near the star, and so rocky planets form near the star.

    Thus (e.g.) we might come to know under what initial conditions an earth-like planet is likely to form. That would constitute more of an explanation than the previous suggestions.

  9. #9 island
    August 22, 2007

    I don’t think it is, no, because we don’t have any guarantee that the narrow range that admits earth life is the only range where life itself can exist. Maybe somewhere in the universe there’s life that lives in liquid methane oceans, and it’s going to have a separate band where it would be able to survive.

    I mean, I would tend to explain the presence of the earth in the admits-life range by suggesting that the chief reason the admits-life range we perceive is where it is in the first place is that when life arose on this planet it adapted to the circumstances of the planet on which it found itself.

    You’re way off the mark here. I’m accused of repeating points that I’ve already made, and yet, nobody does a damned thing to stop them from needing to be made.

    There are very good scientific reasons why carbon based life is the only expected form of life, and you should learn what they are.

    For example, it is a known fact that carbon chains and molecules form more readily than the next most plausible form of life that we have ever been able to imagine, which is silicon based life. This occurs even when the ratio of silicon to carbon is 10:1 in favor of silicon… like it is here on Earth!

    Also, the “narrow range” of the Goldilocks Enigma is balanced between diametrically-opposing cumulatively-runaway tendencies that are all simultaneously in effect to produce intergalactic, galactic, and solar habitable zones, all the way down the the local ecobalance that enables ***practical*** conditions for life to adapt.

    The way that you talk we should expect to find life “adapting” to conditions on the moon… yeah… right.

    You should read this, for starters:

    http://evolutionarydesign.blogspot.com/2007/02/goldilocks-enigma-again.html

  10. #11 Aaron Bergman
    August 22, 2007

    Hi Arun,

    I tend to think that there is some content in the statement that the reason Earth is in the orbital regime that permits life like us is that there are tons and tons of planets and we naturally have developed in the context of our environment.

    Whether or not that’s an explanation seems to me to be a definitional question that I’m not interested in. It’s clearly different than your Olber’s paradox example, and is trying to address a different sort of question. Perhaps you would find the “explanatory” aspect of it in the observation of a broad class of similar entities?

    You might worry, however, that these can never be more than “possible explanations” as it is possible that there is some underlying physical principle yet to be discovered. I think that this is true, and sometimes you just have to live with it.

  11. #12 island
    August 22, 2007

    Jim Clarage, seems conveniently unaware that the contributions of people like, James Lovelock and Lynn Marguilis, who have connected biological evolutionary theory to our local goldilocks enigma.

    Maybe that’s because the majority and their most outspoken neodarwinian critics are predispositioned away from higher purpose in nature because of the relentless pressure from creationists?

    Nah, could’n be that, but they sure don’t mind using it to bail on first principles and causality when it is convenient to do so… to this very same end!

    “The cosmological model of eternal inflation and the transition from chance to biological evolution in the history of life: The possibility of chance emergence of the replication and translation systems, and the protein superfolds.”

    http://arxiv.org/pdf/q-bio/0701023
    “Evolution of life on earth was governed, primarily, by natural selection, with major contribution of other evolutionary processes, such as neutral variation, exaptation, and gene duplication. However, for biological evolution to take off, a certain minimal degree of complexity is required such that a replicating genome encodes means for its own replication with sufficient rate and fidelity. In all existing life forms, this is achieved by dedicated proteins, polymerases (replicases), that are produced by the elaborate translation system. However, evolution of the coupled system of replication and translation does not appear possible without pre-existing efficient replication; hence a chicken-egg type paradox.

    I argue that the many-worlds-in-one version of the cosmological model of eternal inflation implies that emergence of replication and translation, as well as the major protein folds, by chance alone, as opposed to biological evolution, is a realistic possibility and could provide for the onset of biological evolution.”

    Give me a freaking break… because I have now seen every possible form of lame irresponsible rationale that is humanly possible intentionally abused to avoid the most apparent implication that the information is ***INHERENT***.

    Arun, do not ever believe that neodarwinians are motivated by anything other than a culture war.

  12. #13 Arun
    August 22, 2007

    Aaron, if you see explanatory content in that and you’re typical of today’s particle physicists, then while we’re into opinions, I’m in full agreement with Peter Woit, that particle physics is well on the road to pseudo-science. I cannot in good conscience support any politician who wastes taxpayer money on funding this nonsense.

    Good luck!

  13. #14 Arun
    August 22, 2007

    Island,
    Quoting from arxiv as though what is there is necessarily makes scientific sense is simply wrong.

    Secondly, Koonin is not talking about the string theory landscape.

    According to Garriga and Vilenkin, “there are infinitely many O-regions where Al Gore is President and – yes – Elvis is still alive.”

    This is not the landscape.

  14. #15 Aaron Bergman
    August 22, 2007

    I cannot in good conscience support any politician who wastes taxpayer money on funding this nonsense.

    I refer you back to the apology at the beginning of this thing.

    My personal opinion is that it may be true that some physical constants may be the way they are because of random chance, but that we should operate as if they weren’t to not foreclose any possibility.

  15. #16 Jonathan Vos Post
    August 23, 2007

    #14: It took me a minute that you were writing about Eugene V. Koonin, National Center for Biotechnology Information, National Library of Medicine, National Institutes of Health, Bethesda, MD 20894, USA; while I was thnking of Steven E. Koonin. Chief Scientist, BP p.l.c. (world’s second largest independent oil company) and Professor of Theoretical Physics and Former Provost, California Institute of Technology.

    It was the latter Koonin with whom I went to high school and college, and who wrote me one of the two best letters of recommendations I ever received. The college to whom he wrote failed to renew my contract, the Dean saying, according to his secretary, “well, that’s just one man’s opinion.”

  16. #17 island
    August 23, 2007

    Aaron, you’re right, but nothing that you’ve said changes anything that I said, because my point, unfortunately, as usual, is about non-scientific dogma that is killing this science.

    The anthropic principle was originally put forth by Brandon Carter as a “Line of [cosmological] reasoning against, (“conscious and subconscious, anticentrist dogma”), exagerated subserviance to the Copernican Principle” that leads directly to these kind of absurdities by ideologically predispositioned scientists. This is the rule, not the exception.

    And Aaron, I promise to get out of your hair as soon as I make my important but only indirectly relevant points.

  17. #18 island
    August 23, 2007

    whoops… that should have read:

    Arun, you’re right…

    And Aaron, I promise…

    sorry, guys.

  18. #19 Count Iblis
    August 23, 2007

    “There’s only one of you, after all, and you’ll either have side effects or you won’t.”

    But in the multiverse there are an infinite number of copies of you. The observations of the copies will be distributed according to a probability distribution. So, the probability distribution can be interpreted in the usual frequentist way… :)

  19. #20 Neil B.
    August 23, 2007

    As I was saying elsewhere, I think what matters most for scientific prediction is this, not the observers inside the universe: The chance that a universe having a collection of properties also has other properties as well (for example, 10% chance of additional property X based on how many universe “sproutings” that already have the first properties, would also carry X.) That leads to real predictions and possible tests, albeit probabilistic in nature.