Friday, January 18, 2008

New York Times about reincarnation in cosmology

Dennis Overbye
had an entertaining article in the New York Times about some cutting edge cosmology. Its scientific content is bizarre but I think that Overbye faithfully reproduces the actual discussions between theoretical cosmologists - including the most famous ones - and the ideas that they are currently thinking about. Yes, it seems that many of them are losing their minds.

Below, in this essay originally posted on January 16th, I will show that even though the silliness has many forms, most of it is a result of one very concrete flawed assumption about the priors.

First of all, the article talks about Boltzmann's brains.

Recall that Boltzmann half-jokingly argued a century ago that if the Universe exists for an infinite period of time, it is likely that all finite-volume configurations of matter are likely to be repeated infinitely many times (unless the matter density decreases too quickly). The configurations include your brain that spontaneously emerges, with the usual memory and its content, from the middle of some galactic gas. It is unlikely but if you wait for an infinite amount of time, such things do occur.

Some people have seriously claimed that it is thus infinitely more likely that your brain in its current state that you experience didn't occur as a result of an ordered evolution starting from the Big Bang and continuing with human evolution and with love affairs of your parents. Instead, it is more conceivable for it to be a random fluctuation emerging from a complete chaos. Such a brain without its proper context and history is referred to as Boltzmann's brain or a freaky observer.

But are we Boltzmann's brains?

Needless to say, the argument above is completely wrong and I think that every sane person must know that it is wrong. How did we end up with the statement that Boltzmann's brains are more likely than those that have evolved from the Big Bang? Well, we have obtained this answer because we have assumed it from the very beginning. We have assumed a particular "Bayesian prior" making configurations that appear many times much more likely.

Sensible vs absurd priors

However, such a prior is completely irrational. An event or an explanation doesn't become more likely just because it is repeated many times in a hypothetical universe or multiverse. While Joseph Goebbels or the champions of global warming alarmism can make the gullible people think that a statement is more likely if it is repeated 100 times, the actual likelihood doesn't change.

Balanced priors

Once again: we must repeat it many times to make it true. ;-) If a theory predicts an observed event to be repeated many times, it doesn't make the theory more likely than if it predicts one copy of such an event. We only observe the event once and the theories that predict it at least once pass while the theories that predict that the observed phenomenon shouldn't exist fail. But no theories "pass trillions of times".

Why? I could simply say that probabilities can't exceed one. But we may be more detailed. Let me talk in terms of Bayesian inference that is a kind of useful framework for these qualitative discussions. Bayesian inference is a process to refine our idea about the perceived probabilities of different hypotheses. How do we refine them? First, we start with a prior probability: our idea what the probabilities should a priori be. The prior is the most controversial part of the Bayesian inference. But a correct prior assigns comparable probabilities to qualitatively different explanations and theories.

If one hypothesis may come in a quadrillion of forms while another hypothesis is essentially unique, you shouldn't treat the forms as equally good. You shouldn't think that the theory with a quadrillion of forms is a priori much more likely while the unique theory is nearly hopeless to start with. After all, you could always design quintillions of modifications and deformations of any hypothesis to give it a stronger voice. Such a procedure must obviously be forbidden unless we want the degeneracy to inflate and our reasoning to get out of control.

Wrong "proportional" priors lead to dozens of myths

Nevertheless, the mistake above is what many people are doing all the time. For example, the mistake leads some people to believe many kinds of myths, including the myth that
  • a lie repeated 100 times becomes the truth. This is the conclusion of the zealous people who promote the "consensus science" where "scientists" repeat the same sentences after each other, convinced that it makes them more likely. If two arguments are not independent at all, they must be counted as one argument
  • the most likely arrangement of the Universe at any moment, including its birth, is a highest-entropy state. This conclusion blatantly contradicts the second law of thermodynamics according to which the entropy in the past should be, on the contrary, small. The conclusion is a result of an irrational preference of high-entropy states, something that can be dynamically justified in the case of predictions for the future (as we explain below) but something that is absolutely unjustified and flawed for statements about the past
  • we must be typical observers. Clearly, there is no reason why we should be typical observers. A theory that predicts that we are much more typical observers is not much more likely. After all, the best theory should predict that we are insect because insect on Earth is more numerous than mammals. Hartle and Srednicki gave a cool example why this "democratic reasoning" is absurd: it would make a theory that predicts trillions of exotic extraterrestrial organisms virtually falsified - because such a theory would "predict" that we should be them but we are not - even before you observe whether these extraterrestrial forms of life exists. Such a reasoning is logically wrong. A theory simply cannot become more likely or less likely just because it predicts a statement whose validity has not yet been empirically verified (in this case, the existence of extraterrestrial life of some kind) - no Bayesian inference can be made in this case - while the believers in "typicality" irrationally think that the theory without those "Jovian creatures" becomes much more likely
  • a class of string-theoretical vacua with a very large number of elements is much more likely to describe the Universe than a class with a small number of elements that are either unique or almost unique.
As you can see, most of the diseases of the contemporary intellectual world, from global warming and other types of "consensus science" to the anthropic principle to Boltzmann's brains to reincarnation, have a common root. This common root is very silly and it violates all rules of logical inference as well as common sense. But it is very widespread.

Sean Carroll and the cosmology of an egg

Sean Carroll is quoted as saying his favorite childish comment that when he is breaking an egg, he is doing cosmology. I think that the mistake in his reasoning has been explained in so many complementary ways and so clearly, most recently in my Myths about the arrow of time, that even kindergarten kids should begin to get it. Sean Carroll doesn't.

The weird statements that we should be typical; we should be Boltzmann's brains; we should be or shouldn't be reincarnated (a new discovery of Andrei Linde to be discussed below); we should have a higher entropy in the past than what we have today, and so on - all of these statements are simply examples of a wrong choice of priors or a wrong logical inference. People end up with these strange things as a result of a sloppy thinking that assumes that some probabilities are proportional to something even though there is absolutely no rational reason for such a proportionality law.

Neither of the correct answers to these questions depends on any details of your cosmological model. The second law of thermodynamics and the breaking of an egg is a result of general statistical features of a large number of microscopic objects such as atoms and it has nothing whatsoever to do with cosmology. In fact, macroscopic quantities inside an egg are almost exactly uncorrelated with any details about the egg a nanosecond earlier: all patterns are being destroyed very quickly. The independence of an egg's fate on the details of the Big Bang 13.7 billion years earlier is expo-expo-exponentially accurate.

After Sean Carroll argues that he is doing cosmology by breaking an egg, Jeff Harvey of University of Chicago gives an apt reply. He says that this is the difference between cosmologists and particle physicists. Why? Because when particle physicists like Harvey are breaking an egg, they are not doing cosmology but preparing a breakfast.

I am usually preparing a dinner when I am breaking an egg but it is enough for me to be in the same universality class as Jeff Harvey. The properties of an egg including the thermodynamical ones are based on the behavior of atoms and ensembles of atoms. They can be (and, in fact, they have been) derived from local physics but not from cosmology. The predictions of these derivations have been successfully verified and all features of the assumptions behind these derivations may be seen to be irrelevant because the result - for the strength of time-reversal-symmetry-violating processes - is much more robust.

For example, the assumption of "molecular chaos" is just a matter of convenience that simplifies our calculations. Other assumptions about the microscopic structure of your material in the initial state lead to results that are practically indistringuishable from others after a tiny fraction of a second.

Andrei Linde and reincarnation

The most revolutionary new idea along these lines is due to Andrei Linde and Overbye dedicates the last paragraphs to this idea. Linde thinks that the computations of the likelihood of cosmological models will be dramatically influenced by the question whether you have been reincarnated. He argues that many cosmologists are not brave enough to talk about this important physical question. ;-)

Well, unlike others, I am surely brave enough to talk about these things but I am less certain that Andrei Linde will be satisfied with my correct answers.

If I understand well what he wants to argue, he probably wants to say that a human being that has been or will be reincarnated many times is either much more typical or much less typical and the probabilities associated with him or her (or the universe where he occurs) should dramatically change or drop. I don't even know which way his argument is supposed to go but it is wrong in both cases.

Kucinich for president

Instead of full-fledged reincarnation of soul, let me talk about something more graspable, namely identical DNA codes. Imagine that Dennis Kucinich has such a special attractor DNA code that it keeps on repeating many times. The Earth has seen thousands of such identical Kuciniches and it will probably witness many more. So far so good.

You want to calculate something about Kucinich, for example whether he will be elected the U.S. president. Some people could say that because the Kucinich DNA is repeated many times, it is just much more likely that a person with the Kucinich DNA becomes the U.S. president than a person with DNA that doesn't like to be reincarnated. And no person with the Kucinich DNA has been elected so far so he is almost certainly the one. Hillary has therefore no chance because she hasn't been cloned in the history.

Is it true? Is the likelihood that Kucinich is gonna be elected close to 99.99%? I hope not!

If you actually look how the real world works, bizarre coincidences such as the existence of thousands of Kuciniches in the history is completely irrelevant for the election process. The president will actually be chosen by the voters and their odds don't reflect the repetition of the Kucinich DNA in the history. They depend on entirely different things which is why the chances of Kucinich are virtually identical to the chances of all other similar folks, even those dwarf-morons who don't suffer from reincarnation.

Even the identical nature of particles in quantum physics has physical consequences only because of subtleties of quantum physics. For example, scattering amplitudes are obtained by summing over all histories. If we are not allowed to sum over all histories, e.g. in classical physics, we can't really make particles identical.

If someone changed Kucinich's reincarnation into a major political question, it could indeed influence the elections. Kucinich would win some votes of (superstitious) voters and lose some other votes of (equally crazy) voters but these changes wouldn't follow from some exotic counting of reincarnated souls or DNA codes. They would be caused by confusion and superstition of confused souls and minds of American citizens - both reincarnated as well as (the most typical) non-reincarnated. ;-)

Even if reincarnation were true in some sense, it simply doesn't control elections or any other physical phenomena that we normally care about. Politics has been separated from reincarnation long before the state was separated from the church. And physical phenomena at different length scales are also mostly separated from each other: that's why nuclear physics doesn't depend on biology and breaking of eggs doesn't depend on cosmology. Saying anything else is an extraordinary - because apparently manifestly wrong - statement that would require extraordinary evidence.

Humanrightism and democracy

The people who build on typicality, democracy between observers, and similar flawed concepts simply don't understand why seemingly similar things hold in the cases where they hold and why they don't hold elsewhere.

For example, we can show that a body of gas tends to evolve towards the most typical states of highest entropy. But why is it so? It is because there is an actual mechanism that makes this happen: the evolution itself. If the gas evolves for a long time, it chaotically tries all configurations with the same values of conserved quantities and spends roughly the same time in each of them, as a detailed analysis of the evolution implies. The most generic ones will thus dominate in the future. The process is called thermalization.

But this argument certainly can't be applied to the distant past or the beginning of the Cosmos because the beginning of the Cosmos didn't chaotically evolve from something else. There was no thermalization before the Big Bang, almost by definition. The typical chaotic configurations are only obtained in the future because there is a mechanism that makes microstates "equally powerful" in an ensemble: a random evolution that takes a long enough time to kill any initial patterns and easy-to-see correlations.

Analogously, some people assume that each observer (or each stationary point in the landscape) should have the same "voice" in some decisions and calculations of probability, in analogy with a democratic society. But why do most people have the same rights in our society? Because we have written down some laws that are being, at least partially, enforced. This is what allows various majorities to control the main policies in various countries. If the laws were not enforced, there would be no physically meaningful equality. In fact, some of us remember that various people who are considered equal today were not considered equal in the past. The conventions, laws, and constitutions have changed.

In the future, progressive politicians can make the voices of bugs equal to the voices of humans and insect will control the immigration policy across the world. We are not yet there and it is legal to spray out mosquitos whose immigration is not convenient enough for our human minority. Thanks God.

Analogously, there is no actual mechanism that makes the "voice" of a terrestrial human being (or a flux vacuum) be equally loud as a "voice" of a hypothetical citizen of Jupiter (or a heterotic vacuum) which is why all arguments and calculations based on the assumption that terrestrials and Jovians are equal (or individual flux vacua are equally likely as individual heterotic vacua) are just unjustifiable, stupid, insane fantasies. In physics papers, they are just bad science. No such interplanetary or interuniversal thermalization has been seen or demonstrated. Most likely, it cannot exist.

People are only equal and people only have their human rights if there exists a framework that enforces these principles. There exist almost no rules of this kind that you could rely upon in Iran. You might be dreaming about them and think that they are good but they are not true in the real world. And there exist no rules whatsoever that would defend your rights on Jupiter. Because these mechanisms don't exist, you shouldn't be thinking like if you assume that they do exist.

In politics, the active defense of the idea that human rights exist even without mechanisms to enforce them is referred to as humanrightism. It is incompatible with realistic politics of a country in the real world. A country can only promise those rights to the individuals that it is able to enforce. By the way, it costs some money and effort.


I think that if someone offers you some bizarre statements such as those that depend on our typicality, statements that the arrow of time was directed in the opposite direction 5 minutes ago when the eggs were unbreaking, that the reincarnated people are very politically powerful or, on the contrary, hopeless politicians etc., you should ask the person to tell you how he calculated the odds.

In principle, the person should be able to present his or her argument in the framework of the Bayesian inference. He should tell you what his priors are - i.e. to reveal his assumptions - and what observations he has used for the logical inference.

If his Bayesian priors are such that the probability of "almost certainly correct" or "sane" or "reasonable" alternatives are exponentially suppressed, you may tell the person that he is only ending up with bizarre answers because he is already assuming them and excluding the correct answers from the very beginning.

Sean Carroll thinks that the arrow of time should be the opposite what it was 5 minutes ago because he irrationally overhypes high-entropy configurations in the past in his priors which is simply irrational and wrong. High-entropy states in the past are not more likely and there is no sensible reason to think that they are. Retrodictions follow different rules than predictions. Andrei Linde might overhype or suppress the role of reincarnated people, and so forth.

Once you convince the person to adopt sensible priors - that give each qualitatively different hypothesis a comparable chance to live - you should also make sure that the Bayesian inference is correct and follows Bayes' formula. The refined probabilities will never depend on the number how many times an event or a person or a brain or a similar stringy background is repeated. The Bayesian inference simply doesn't allow you to do such things.

Equally importantly, the Bayesian inference can only be made if you actually have some new (direct or indirect observational) evidence that can be compared to your hypotheses, not just a new calculation of the predicted number of Jovian creatures - a number whose correct value in the real world can't actually be measured at this moment. It is impossible to decide which among two otherwise equally robust and consistent theories is more likely without comparing them to some empirical evidence.

Restoring sane conclusions

Once you agree about this basic logic, all the absurdities discussed in Overbye's article and elsewhere will simply go away. The entropy in the past was much smaller than it is today. This statement may be shown by many observations that are consistent with this hypothesis, making it increasingly likely - via the logical inference - that the hypothesis is correct.

Also, the hypothetical reincarnated people won't be discriminated against but they won't have special rights either.

You will be able to see that we are almost certainly not Boltzmann's brains. How can I show it? Well, the theory that we are Boltzmann's brains predicts that the individual events in our memory shouldn't seem to fit together: they are probably chaotic. The theory predicts that the past as reconstructed from our freaky memory doesn't make much sense. On the other hand, the hypothesis that our brains have evolved from a rather ordered evolution predicts that up to some mistakes of the brain, our memory should make sense.

And it mostly does.

If you compare the predictions with reality and make one step of Bayesian inference, you will see that the hypothesis assuming an ordered evolution becomes more likely than it was a priori while the freaky theory becomes less likely (since the conditional probability of order given the assumed freakiness is small). Because you can make many observations of this kind that are more or less independent, you can show that the probability that we are freaky observers is smaller than any reasonably positive number you can think of. There is actually a lot of evidence that we are not freaky observers.

There is no evidence that we are freaky observers: the only way how to argue that we are freaky observers is to choose priors that assume that we are freaky observers and all justifications of such priors are irrational, based on non-existent and wrong proportionality laws. Laws that someone wants to believe because of some bizarre metaphysical reasons but laws that haven't been successful in science.

You will also see that neither of these conclusions depends on any details of your cosmological models as long as the cosmological model is consistent with the present as we observe it and the cosmologists who want to study cosmology by breaking eggs or talking to their deceased relatives are simply being dumb, at least at this particular moment. Once again, you will see that physical phenomena at different scales are largely separated from each other. Breaking eggs is about condensed matter physics whose effective laws may be determined by a careful research of molecular physics but whose features are unaffected by climatology or cosmology.

The information about breaking eggs won't actually help you to decide about the type of the cosmic inflation used in our Universe or anything of the sort. When treated properly, every good enough cosmological model predicts that eggs break and they don't unbreak. They pass (P=1) and none of them passes "trillions of times more". The breaking eggs won't tell you whether you have been reincarnated and messages from your other cloned souls won't inform you about the radius of extra dimensions. And most - but not quite all - other things that follow from common sense will be confirmed by rigorous calculations, too.

And that's the memo.


  1. Highly ordered (low entropy) thick soups in causal contact are not yet conducive to the emergence and multiplicity of design: The attractor for consciousness is design and not sensory depriving chaos.
    Highly disordered (high entropy) thin soups are feeble with design being washed out. Design could not even be created as a "strange attractor" in such a thin soup because any occurence is only a single (non-design building) low level isolated random fluctuation.

    "In the mysterious way the scales of the hidden monster flash iridescently from near impenetrable darkness."

  2. On Loschmidt’s paradox:

    The problem with Loschmidt’s paradox is that it fails to take into account the uncertainty principle in the assumption that the laws of motion are time reversible.

    In a collision between atoms, let’s imagine that two atoms collide and scatter elastically. In that interaction we initially see the electrons of the respective atoms in some configuration surrounding the nucleus. After the collision, those electrons reconfigure into some new arrangement based on the new momentums of the atoms in question.

    Now in some regards, this new arrangement represents a record of the collision and its outcome. If we lived in deterministic world, when we reversed time and watched the collision in reverse, we would expect to see the new arrangement of electrons return to the old arrangement after the atoms recollide (this is the flaw in Loschmidt’s paradox).

    In reality there is always a chance that an electron will randomly change its orbit while moving backward in time before we see the atoms recollide, thereby upsetting the record of the original “time forward” collision, and thus producing a new result as we move backward in time.

    At an individual particle level, it would be very difficult to predict when and if a collision between two particles would be affected by the random transition of an electron, but as we notch our scale up and include more and more particles, the net effect of random changes in electron orbits can not be ignored.

    Thus Boltzmann was largely correct in the conception of molecular chaos. The motion of single particle undergoing several collisions will eventually become uncorrelated with earlier collisions due to random transitions of its electron configuration.

    However, once again, we shouldn’t expect all of the correlations to ever completely vanish, and thus there will always be some non-zero record of initial conditions and intervening states.