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June 6, 2008

Urban Myths in Contemporary Cosmology

Posted by Urs Schreiber

Here is something that disturbs me.

For the bulk of human history, cosmology has been myth telling. Serious progress towards a science of cosmology was made when Einstein’s differential geometric theory of gravity was matched with the observation of the cosmic microwave radiation and the observation of Hubble’s law. With the advent of modern sattelite based refinements of such measurements, such as notably WMAP, cosmology has become an exact science. People therefore often speak of the present as the golden age of cosmology.

In this golden age of exact science cosmology, having overcome the age of myths, are we wary of urban myths within the scientific community?

Among some cosmologists the story of the Boltzmann brain is being retold frequently. Influential proponents are Alexander Vilenkin and Andrei Linde.

Vilenkin calls “Boltzmann brains” freak observers:

Alexander Vilenkin
Freak observers and the measure of the multiverse
arXiv:hep-th/0611271

Andrei Linde,
Sinks in the Landscape, Boltzmann Brains, and the Cosmological Constant Problem
arXiv:hep-th/0611043

(“Boltzmann brains” are spelled “Boltzmann branes” on p. 3 of that. One finds the typo the other way around, too.)

Richard Gott III voices the opinion that Boltzmann Brains–I’d Rather See Than Be One.

According to Sean Carroll # the term has been introduced into the scientific literature by

Andreas Albrecht, Lorenzo Sorbo
Can the universe afford inflation?
arXiv:hep-th/0405270

In section C of this article the authors make the following claim:

The most likely fluctuation consistent with everything you know is simply your brain (complete with “memories” of the Hubble Deep fields,WMAP data, etc) fluctuating briefly out of chaos and then immediately equilibrating back into chaos again.

No further details are provided there, nor is a justification given. Is this statement self-evident? Is it even clear what the terms mean? Is no quantitative scientific scrutinization necessary? Is this statement supposed to qualify as a scientific statement?

The only proof given in the above article is a reference to the book

J. Barrow and F. Tipler,
The anthropic cosmological principle
Oxford University Press (1986)

F. Tipler has otherwise written books such as The physics of immortality and The physics of Christianity. According to Wikipedia #, George Ellis has actually read these books and found that the myths they tell are a “masterpiece in pseudoscience”.

A version of the argument which is usually cited is on the first two pages of section 6 of

Lisa Dyson, Matthew Kleban, Leonard Susskind
Disturbing Implications of a Cosmological Constant
arXiv:hep-th/0208013

Two numbers are mentioned there in support of the claim. The first number, N 1N_1, is taken to be the entropy of a given macrostate. The second number, N 2<<N 1N_2 \lt\lt N_1 to be the entropy of the macrostate it evolved from under time evolution. It is pointed out that this means that there are more microstates for the macrostate which did not time evolve from a low entropy macrostate than vice versa.

As far as I can tell, this is a version of the elementary standard thermodynamic textbook observation which says that picking any given macrostate its entropy will with high probability increase both in the future and in the past.


I am not a professional cosmologist. I have looked around through the literature, followed public discussions and talked in person to (a small sample of) active professional cosmologists. In all these places those who accepted the above statement did so with no further justification than the ones given above.

I do not accept the Boltzmann brain story as a scientific truth. For two reasons: first because I do not accept it as a well-defined scientific statement. And second, I don’t even think as a vague plausibility argument it is sensible.

This is why I don’t think the statement makes sense as a scientific statement:

- We have only a very vague understanding of thermodynamics in general relativity There is no accepted well-formed framework which would allow one to make good scientific sense of entropy and probability “of the universe”. For instance it is unclear which level of coarse-graining is assumed for the definition of entropy here, while on the other hand this is conceivably very relavant for the argument.

- The implicit assumption that we, as inhabitants of this world, are bound to perceive around us the “most typical situation” is neither well defined nor supported by logic. Certainly not by published logic.

(But this principle of mediocracy is propagating through the community of contemporary “theoretical cosmology”. )

- There is no concept of what matter configuration counts as an “observer” and which does not.


This is why I think the statement is wrong even as a plausibility argument:

A well-established scientific theory from two centuries ago explained well which complex structures can be expected to arise in an abundance much higher than suggested by their proportion among all equally weighted configurations: this theory is Darwinian evolution and it refers to self-replicating systems.

Based on this theory I would tend to say that I expect, if I were forced to do so, that the “typical observer in a universe” is a self-replicating system which is a descendant of a very small self-replicating system which arose from some local equilibrium through a comparatively small fluctuation.

And I even have circumstancial experimental support for this statement: by all what we know, the observers that we observe all arose from what must have been a coincidence (=”fluctuation”) by which a bunch of nucleotides suddenly came into an arrangement which lead to self-replication (possibly as described by the RNA world hypothesis).

I find it self-evident that the probability that an observer (a “brain” if you insist) evolves from such a comparatively tiny fluctionation by Darwinian evolution is orders of orders of orders of magnitudes higher than that the observer arises directly by a fluctuation.


But I promise I will not write a scientific article about this argument. My problem is rather: if I am wrong and Boltzmann-brainiology is right: can you prove it to me?

Is there more of an argument than I have summarized above (Albrecht-Sorbo and Dyson-Kleban-Susskind)?

Is the question in reach of exact science?

I find this comparison useful:

When Zeno formulated Zeno’s paradox of Achilles and the tortoise he was not doing exact science. Still, there was some value to the argument. It was finally resolved as a non-paradox many hundred years later in an exact way by the conception of differential calculus, which made the notions appearing in the argument precise and thereby amenable to rational discourse.

Posted at June 6, 2008 6:12 AM UTC

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Re: Urban Myths in Contemporary Cosmology

“My problem is rather: if I am wrong and Boltzmann-brainiology is right: can you prove it to me?”

This is like asking if a religion is wrong an other right. According to their own arguments, no one can, since it comes down to just waiting too long for one to show up. It’s like waiting the second coming of Jesus.

Posted by: Daniel de Franša MTd2 on June 6, 2008 1:11 PM | Permalink | Reply to this

Re: Urban Myths in Contemporary Cosmology

So are there any indications as to what gave Zeno’s argument its value? And are these indications lacking in Boltzmann brain discussions?

It’s intriguing how ‘metaphysical’ reflection can have indirect effects down the line. It’s plausible that the astrological idea that heavenly bodies could affect us on Earth played a role in working out the cause of the tides.

Closer to our times, after all that reflection about possible worlds, what if the modal logic that emerged with it, and its extension to dynamic/temporal logic, is merely a useful tool in computer science?

I share your sense, Urs, that this particular line of enquiry is likely to be unproductive, however indirectly. Even though Zeno’s paradox suggests it may take centuries for such value to emerge, so that we can never be certain of valuelessness, a plausible ‘what if’ history could have had the paradox resolved much more quickly. And, in any case, that kind of thinking was having its effect in producing brilliant work such as the quadrature of the parabola.

Posted by: David Corfield on June 6, 2008 1:25 PM | Permalink | Reply to this

Re: Urban Myths in Contemporary Cosmology

Daivd wrote:

what if the modal logic that emerged with it, and its extension to dynamic/temporal logic, is merely a useful tool in computer science?

We have Aristotle trying to formalise concepts like necessity and people like Avicenna and scholastic philosophers pushing the ideas further (partly motivated by the ontological argument, I believe). I get the impression that mathematicians looked down on modal logic and then suddenly a philosopher, Kripke, makes a connection with the far-out idea of many worlds and the whole thing becomes respectable mathematics. And then, as if by magic, through a Curry-Howard-like isomorphism, modal logics like S4 turn out to be exactly what you need to formally describe things like partially evaluating computer programs while you compile them. This is an amazing journey for a concept to take and it really shows how you can’t tell, a priori, where an idea might lead, or even what you should be reading to get good ideas for use in a particular field.

Posted by: Dan Piponi on June 6, 2008 6:27 PM | Permalink | Reply to this

Re: Urban Myths in Contemporary Cosmology

David asks:

So are there any indications as to what gave Zeno’s argument its value?

You will know more about the history of Zeno’s paradox than I do. All I meant to say is that Zeno’s argument is an interesting, albeit wrong, argument, which is thought provoking. It requires quite a bit of sophistication (well, we teach it in school today, but it took mankind a while to figure it out) to resolve it:

as we know, the resolution is:

- the concept that Zeno was lacking was that of a convering series (an infinite converging sum).

- the wrong assumption that Zeno made was that every series (namely of time intervals spent by Achilles chasing the tortoise) with non-vanishing entries has to diverge.

This is wrong. I don’t blame it on Zeno, but I point it out as an example that there are plenty of arguments which may sound sophisticated and may sound right, but are based on hidden false assumptions and indeed wrong.

And that science/math happens only when we stick to those arguments where we have reasonable control over the assumptions and the meaning of the terms involved.

There are, and of course have been in history, plenty of interesting open questions which one might long to answer in a scientific manner, but which are simply out of reach for exact science.

Another famous such paradox is Fermi’s paradox (which is actually closely related to brainimania).

Or speculations about consciousness. I can imagine that one day in the far future, mankind understands the phenomenon of consciousness on a much deeper, scientific, level than we do today, possibly figuring out how it is related to quantum cosmology (as some contemporary cosmologists suggest). But we are certainly not there yet and can’t reason about it within exact science.

Which is not to say that it is not fun, and even useful, to wonder about this and exchange arguments about it while, say, sitting around a camp fire. But not in articles that come with the appearance of scientific papers.

And are these indications lacking in Boltzmann brain discussions?

I find the Boltzmann brain argument itself weird. I do see some value, in the above campfire-sense, in the general discussion about the meaning and relevance of life-in-the-cosmos. It can certainly be fun and thought-provoking. But for it to come closer to science, even to speculative science, the proponents should put more effort into trying to scrutinize their arguments. And maybe those of their leading figures.

Posted by: Urs Schreiber on June 6, 2008 6:43 PM | Permalink | Reply to this

Re: Urban Myths in Contemporary Cosmology

David wrote:

So are there any indications as to what gave Zeno’s argument its value? And are these indications lacking in Boltzmann brain discussions?

The value of a paradox or puzzle depends to some extent on how intelligently one responds to it. If the modern theory of the continuum was a response to Zeno’s paradox — I don’t know if it really was — then we’d have to say this paradox was very useful. But, we’d also have to admit there was a lot of ‘added value’ in the intelligent response to the puzzle.

The Boltzmann brain puzzle could prove useful if it led to intelligent reflections about the thermodynamics of life, the arrow of time, etc. But it seems often people use it to carry out some variant of the following argument:

“If the universe lasts forever, it will suffer a heat death and eventually the number of brains arising from vacuum fluctuations — so-called ‘Boltzmann brains’ — will exceed the number of brains that arise the usual way, through evolution. So, if the universe lasts forever, it’s most likely that I am a Boltzmann brain. But that’s absurd! Therefore, the universe must not last forever.”

This is silly, because if the argument leading up to But that’s absurd! were really ironclad, we couldn’t just declare it absurd out of some feeling of emotional revulsion, and then conclude that the premise — the long-lived universe — must be false.

After all, lots of physics arguments do lead to conclusions that seem absurd: nothing moves faster than light, every particle has an antiparticle that can annihilate it, etc. But when these arguments are solid, the absurd conclusions have an interesting way of being true.

Of course, there’s a good chance that the argument leading up to But that’s absurd! is not actually solid. So, people should find a hole in it.

In short: one would need to examine the whole puzzle in a disciplined way to get something really interesting out of it. I haven’t seen people doing that. On the other hand, I haven’t looked very hard — since I have more interesting things to think about.

Posted by: John Baez on June 6, 2008 7:55 PM | Permalink | Reply to this

Re: Urban Myths in Contemporary Cosmology

On typicality, imagine (for the sake of argument) that we have two theories of cosmology, theory A and theory B, where we initially have no reason to prefer one over the other.

Now suppose that (somehow) we’re able to extract the following (somewhat fanciful) predictions: theory A implies that in the entire history of the universe, there will be 1050 observers* of class 1 and 105000 observers of class 2, while theory B implies that in the entire history of the universe, there will be 105000 observers of class 1 and 1050 observers of class 2.

* We define “observers” as any creature or system able to do astronomy and ponder the results. (Yeah, I told you it was fanciful to think we could count them as a consequence of a cosmological theory, but suppose we could.)

We then decide to make use of the fact that human beings are very definitely class 2 observers, not class 1. Does this fact, and the predictions of the two theories, give us a good reason to believe that theory A is true?

I would claim that it doesn’t. The sole observation we have is that at least about 1010 class 2 observers exist. Both theory A and theory B imply this fact with certainty. So Bayes’s theorem leaves our prior 50% probability for each of them entirely unchanged. The fact that an observer selected at random from the pool of all observers would be more likely to be class 2 under theory A is irrelevant; nobody has to “select us at random” before we’re allowed to make an observation.

Posted by: Greg Egan on June 6, 2008 2:31 PM | Permalink | Reply to this

Re: Urban Myths in Contemporary Cosmology

You say that the sole observation we have is that some number of class 2 observers exist - however, this is not the case. I additionally have the observation that I am a class 2 observer.

Consider the following situation - the dictator has just decided to round up 100 citizens (including me) and shoot some of them for fun. However, to make it exciting, he has announced that he won’t kill all of them - he’ll flip a coin, and if it comes up heads then he’ll have 90 of the citizens (chosen randomly from this group) shot while the rest are fired at with blanks, but if it comes up tails, he’ll have only 10 shot while the rest are fired at with blanks. Now the day of the execution comes, and the prisoners are taken before the firing squad and fired at. After the bullets and blanks are fired, I realize that I’ve survived, and I can see a few of the other prisoners who have also survived (it’s a large field that we’re in, so I can’t tell what’s gone on beyond the couple people closest to me).

If you were right that the only information we have is the number of class 2 observers, then the only information I have is that at least a few people have survived, so I have no evidence whether the coin came up heads or tails. Yet intuitively, it seems that I have somewhat strong evidence that the coin came up tails (because otherwise I would probably be dead).

Posted by: Kenny Easwaran on June 7, 2008 8:25 AM | Permalink | Reply to this

Re: Urban Myths in Contemporary Cosmology

Kenny, in your example you get to experience a pre-execution state, in which you are waiting around to be randomly allocated into one of the states victim or survivor, with either p v=0.9p_v=0.9 and p s=0.1p_s=0.1 or vice versa. But in my example, I have no experience of a pre-life disembodied existence in which I was waiting around to be allocated at random into the body of a class 1 or class 2 observer.

We could make your example less violent, and repeatable, by changing it to a paintball game with either 90% red paint and 10% blue, or vice versa. Then (just by witnessing your own shooting, and no others) you could certainly make money over time by betting that the majority paint colour was the one that you were hit with.

But short of reincarnation in multiple universes, what’s the equivalent in cosmology? Maybe we could assume that there is a multiverse, consisting of many universes obeying theory A and many universes obeying theory B. Then if someone states explicitly that what they want is a strategy that – if adopted by all observers in the multiverse – will maximise the number of observers across the multiverse who correctly guess the theory that applies to their universe … well, then I can’t deny that a good strategy for doing that would be to guess the theory that implies you belong to the majority class.

But is such a strategy really what cosmology is, or ought to be? Why is the weight 1 per observer? Maybe it would be more “scientific” to weight observers by their lifespans? Or the number of “mental events” they experience? I’m being facetious, but my point is, why should we care about this pan-multiverse weighted average of correct guesses at all? What if someone comes up with a theory that we think is very unlikely, but if it were true it would multiply the number of human-like observers in the universe to which it applies by 10 100000010^1000000? Should we say “yes, we’ll act as if we have a good reason to believe that this theory applies to our universe” because, even if we’re wrong, we’ve followed a strategy that – if also followed by everyone else in the multiverse – will lead to a vast number of human-like observers being correct, overall?

Posted by: Greg Egan on June 7, 2008 12:03 PM | Permalink | Reply to this

Re: Urban Myths in Contemporary Cosmology

Greg, are you a halfer or a thirder? Sounds like you’re a halfer.

Posted by: Dan Piponi on June 10, 2008 2:42 AM | Permalink | Reply to this

Re: Urban Myths in Contemporary Cosmology

Dan, experiments like this just make me think that concepts like “credence” are ill-defined. If there was some future monetary reward, or other consequence, based on a global sum of correct guesses of heads or tails upon each waking, then I would choose a strategy to maximise the expectation value for that reward. But in the absence of any such globalising mechanism, it’s not clear to me what “credence” means (or if it can be defined, why we should care about it).

Posted by: Greg Egan on June 10, 2008 5:13 AM | Permalink | Reply to this

Re: Urban Myths in Contemporary Cosmology

Hadn’t spotted these comments when I posted my comment below, otherwise I’d’ve posted it as a (shorter) reply to these. As I said, I’ve only been half-following this discussion.

Posted by: Andrew Stacey on June 10, 2008 12:25 PM | Permalink | Reply to this

Re: Urban Myths in Contemporary Cosmology

Thanks for the reference, Andrew! I agree with Groisman completely.

This example, and Groisman’s approach in general, does make it even clearer to me that we shouldn’t be surprised that there can be some counter-intuitive consequences of cosmological theories involving different numbers of observers … without those numbers of observers actually influencing the likelihood of the theory being the correct description of the universe. Sleeping Beauty can make money by betting on Tails, but we shouldn’t let that sway us into imagining that the coin isn’t fair.

Posted by: Greg Egan on June 10, 2008 3:03 PM | Permalink | Reply to this

Re: Urban Myths in Contemporary Cosmology

Thanks for figuring out a good argument against this Boltzmann brain baloney, Urs. I’ve always considered the subject a waste of time — and its popularity, a sign of the decadence that’s infected certain quarters of theoretical physics. But I guess it won’t go away until someone thinks clearly about it.

In an ideal world, this one blog entry is all you write about the subject. Other people jump in and develop your argument. Others fight back, but the subject will be clarified without your needing to spend more time on it. You can keep doing serious physics.

But the following scenario seems more in tune with the tenor of the times:

You publish a paper on this topic and do everything possible to stir up controversy about it. You get interviewed by New Scientist, Scientific American and other magazines. They photograph you next to this statue of Boltzmann, with the caption “Who Has More Brains?”

A media furor ensues. Fox News runs a retraction saying that you, not Garrett Lisi, are the next Einstein. Other physicists become upset, claiming that they are the next Einstein. The issue is finally settled on a new reality show: a physics version of American Idol called Who’s the Next Einstein?. You make millions, give up physics and become a laid-back surfer dude.

Posted by: John Baez on June 6, 2008 4:02 PM | Permalink | Reply to this

Re: Urban Myths in Contemporary Cosmology

Urs wrote:

“Boltzmann brains” are spelled “Boltzmann branes” on p. 3 of that. One finds the typo the other way around, too.)

This reminds of a story I heard about Witten. As you know, mathematicians regard Witten as a genius who vastly surpasses normal human abilities. For example, my friend the Italian mathematician Cotta–Ramusino was beaten by Witten in a game of Scrabble… in Italian. Anyway, once Witten was lecturing to an audience of mathematicians, who were desperately struggling to follow what he was saying. He said a bit about 2-branes and 5-branes in string theory, which didn’t make much sense to them… but then he tried to reassure them, saying something that sounded like:

“Luckily, for today’s talk we will only need two brains”.

Posted by: John Baez on June 6, 2008 4:24 PM | Permalink | Reply to this

Re: Urban Myths in Contemporary Cosmology

“Luckily, for today’s talk we will only need two brains”.

That’s a fun story.

You may not have heard of him, but Prof. Dr. Abdul Nachtigaller has seven brains, five of which are visible here:

Nachtigaller, head of the Night School, had been working on extracting energy from pure darkness long before the concept of dark energy became popular in cosmology. There is a measure of darkness named after him, one Nachtigall, which is precisely the amount of darkness in one closed fridge. Hence 400 Nachtigall is the amount of darkness in 400 fridges.

Nachtigaller invented the Nachtigalloskop with which he was the first to see the dark energy between the stars. He was the first to point out that, while starlight reaching us from far away stars is very old, the darkness between the stars is much older still. In his wine cellar he keeps darkness in bottles of almost 5 billion years of age.

He is not being cited much, though. Not yet.

“Knowledge”, bellowed Professor Nachtigaller in the classroom, widening his eyes until they were large as saucers, “Knowledge is night!” That was one doctrine of Eyedetic Philosophy, a subject which was taught only at the Night School.

Professor Nachtigaller often said things like that, probably to disconcert us. There was a method behind these apparently meaningless assertions: before one realized that they were completely stupid, one had already thought in all kinds of directions. And that was exactly what Professor Nachtigaller wanted: we were supposed to learn how to think, and in as many directions as possible.

(from: Walter Moers: Die 13 1/2 Leben des Käpt’n Blaubär)

Posted by: Urs Schreiber on June 7, 2008 12:07 AM | Permalink | Reply to this

Re: Urban Myths in Contemporary Cosmology

A paradox is always the result of a gap in our knowledge. The Boltzmann brain paradox is much more about the lack of a real theory on complexity rather than some cosmological insight.

Posted by: Paul on June 6, 2008 11:59 PM | Permalink | Reply to this

Theophysics; Re: Urban Myths in Contemporary Cosmology

The theory, that our universe is a random fluctuation of order in a great ocean of chaos, leads to stranger notions, which is why we mention Boltzmann Brains.

Just imagine two Universes: one with only a single galaxy in an ocean of chaos, and one with just Earth, and everyone hallucinating that they see other galaxies.

Clearly, the latter is much more probable as a result of a random fluctuation.

Really, these are not probability/cosmology arguments. They are
philosophical games akin to Bertrand Russell’s notion, which created a
back-and-forth among theologians that still continues in the Creationist bizarro world.

Reverend Canon Brian Hebblethwaite, for example, preached against Bertrand Russell’s projection of Gosse’s concept:

Bertrand Russell wrote, in The Analysis of Mind: “there is no logical
impossibility in the hypothesis that the world sprang into being five minutes ago, exactly as it then was, with a population that ‘remembered’ a wholly unreal past.”

But that, like much of what Russell wrote and said, is nonsense. ‘Human beings’, posited in being five minutes ago with built-in ‘memory’ traces, would not be human beings. The suggestion is logically incoherent.[Reverend Canon Brian
Hebblethwaite, In Defence of Christianity, 6 March 2005]

The basis for Hebblethwaite’s objection, however, is the presumption of a God that would not deceive us about our very humanity. But this takes us back to the more radically skeptical Descartes, who
considered that Satan might very well be deceiving us about our very humanity, and feeding false sense impressions into our minds.

Again, this is, in my opinion, NOT science at all, but some sort of
Theophysics and Theomathematics.

Those of us who consider ourselves rational (whether we are or not) might well realize the theological and philosophical context in which some others argue, regardless of whether they speak or write in deep Scientism (the trappings and vocabulary of science, without the substance).

Posted by: Jonathan Vos Post on June 7, 2008 5:07 PM | Permalink | Reply to this

Re: Theophysics; Re: Urban Myths in Contemporary Cosmology

Clearly, the latter is much more probable as a result of a random fluctuation.

Sorry to say so, but it is these “clearly”-arguments which worry me.

In the above entry I gave an argument in which I came to the opposite conclusion. In fact, I feel “clearly” the conclusion you come to is weird.

Do we have a means to clarify the situation using solid reasoning?

Posted by: Urs Schreiber on June 8, 2008 10:22 PM | Permalink | Reply to this

Re: Theophysics; Re: Urban Myths in Contemporary Cosmology

Urs, I don’t have any solid calculations of entropy to contribute, but one argument the BB fans make that I’m not sure you address directly is that in the current epoch where stars are burning, self-replicating life can make use of that huge disequilibrium to grow – whereas in some far-future epoch after the universe has been reduced to a bath of thermal radiation, a replicator that arises by itself will have nothing to exploit, in order to grow. A few molecules of RNA alone certainly comprise a small fluctuation, but without any stars around (or maybe some smaller energy source) that RNA can’t do anything.

So the general BB argument is that ordinary Darwinian life will dominate the early epoch of the universe, but in a cosmological model with an infinite future, the kind of fluctuations that give rise to “freak” observers with no history will involve smaller deviations from equilibrium than those that provide a complete “sensible” Darwinian history full of ancestors.

Posted by: Greg Egan on June 9, 2008 1:45 AM | Permalink | Reply to this

Re: Theophysics; Re: Urban Myths in Contemporary Cosmology

Greg,

thanks for the reply.

Methinks my argument applies locally just as well, i.e. to every single fluctuation in that heat bath.

I am thinking: as soon as we have some state away from equilibrium, its relaxation to equilibrium can potentially drive evolution of self-replicators. For that the initial fluctuation that produces the non-equilibrium state, if you wish, need not be highly organized itself, it only needs to provide the context for the proverbial self-organization.

If I’d have to imagine an ever-lasting gravitational heat bath and estimate the fluctuations away from equilibrium, I’d imagine it much more likely that “suddenly” due to simple density fluctuations a local non-equlibrium state arises which can drive tiny self-replicators to evolve to conciousness, than that these concious descendants pop out into existance from the heat bath directly.

To me, personally, the former feels “unlikely” whereas the latter seems “weird”.

There was a time, two or three decades back, when, my impression is, the typical cosmological thinker would have agreed with me on that estimate (but of course I can’t know for sure), a time when books such as The self-organizing universe were written and read. At that time, at least, these speculations were motivated by concrete experimental and theoretical insights into what became called “dissipative structures”.

While I am aware that the development of these approaches remained imperfect, this general idea has always struck me as by far the best general explanation for “life” and “conciousness” from fundamental physical law which we have.

Posted by: Urs Schreiber on June 9, 2008 4:01 AM | Permalink | Reply to this

Re: Theophysics; Re: Urban Myths in Contemporary Cosmology

Ah, I think I understand your argument better now. Although our own particular history as Darwinian life involved a truly massive deviation from equilibrium, in the form of the Big Bang, star formation, etc., you’re suggesting that the advantages of self-replication will dominate over a much broader range of situations. Just because we rely on the sun, it doesn’t mean Darwinian replication needs such a huge disequilibrium.

Ultimately, I see this as a fascinating question in its own right – but not one that can be used to reach conclusions about cosmology, because I don’t think we’re entitled to assume that we are typical.

Posted by: Greg Egan on June 9, 2008 4:18 AM | Permalink | Reply to this

Re: Theophysics; Re: Urban Myths in Contemporary Cosmology

but not one that can be used to reach conclusions about cosmology, because I don’t think we’re entitled to assume that we are typical.

I don’t know if “we” are typical. But I guess what I am arguing is that this “self-organization in dissipative structures relaxing fluctuations” is typical. And probable.

It’s a (different) interesting question whether such Darwinian evolution in turn produces “typical” results.

The only thing I know about this is that it’s striking how the same ecological niches on different continents and in different times, on Earth, are, again and again, populated by their “typical” inhabitants.

But I don’t know how that little observation scales to the vast deSitter cosmology that we are talking about.

Posted by: Urs Schreiber on June 9, 2008 4:51 AM | Permalink | Reply to this

Re: Theophysics; Re: Urban Myths in Contemporary Cosmology

I think I agree with your intuition here, though I’m not able to quantify any of this.

There is one aspect of the BB argument that is independent of these issues, though; rather than debating whether far-future life will be “freakish” or “Darwinian”, if we accept an infinite or extremely long future in which observers of any kind are present – so long as they can make observations that show them that they are not living in the early universe – then “typicality” is not a matter of being a Boltzmann brain or a Darwinian brain, but simply whether you are living in the early universe or the later universe.

The way the BB fans use probability, they would then argue that the universe is very unlikely to have this very long extended future, because then a “typical” observer would live in the far future … making us “atypical” because we live in the early universe. I guess that’s really just a variant of the infamous Doomsday argument, applied to the universe as a whole: the universe is unlikely to last very long, otherwise it would be “unlikely” for us to find ourselves so near the beginning. That’s where I think they’re simply misusing probability: we are not a random selection of observers taken from the entire history of the universe.

Posted by: Greg Egan on June 9, 2008 5:20 AM | Permalink | Reply to this

Re: Theophysics; Re: Urban Myths in Contemporary Cosmology

Greg, I am enjoying this conversation with you. By accident I came across something that made me get back to this summary of some of the BB-reasoning you had given:

but in a cosmological model with an infinite future, the kind of fluctuations that give rise to “freak” observers with no history will involve smaller deviations from equilibrium than those that provide a complete “sensible” Darwinian history full of ancestors.

Remarkably, Sean Carroll and Jennifer Chen, in their article Does Inflation Provide Natural Initial Conditions for the Universe? which is being referred to in popular articles tell a story in which the most likely thing to start off as a fluctuation from a deSitter heat bath is — an inflationary big bang such as ours.

I suppose that this is clearly so (??)

Posted by: Urs Schreiber on June 9, 2008 5:47 PM | Permalink | Reply to this

From the ambiplasma future; Re: Theophysics; Re: Urban Myths in Contemporary Cosmology

“Just imagine two Universes: one with only a single galaxy in an ocean of chaos, and one with just Earth, and everyone hallucinating that they see other galaxies.”

“Clearly, the latter is much more probable as a result of a random fluctuation.”

Let me clarify “clearly.”

Just imagine two Universes:
(1) one with only a single galaxy in an ocean of chaos, and
(2) one with just Earth, and everyone hallucinating that they see other galaxies.”

(1) has roughly a billion times more planets in the non-chaos island within the cosmic ocean of chaos than does (2).

Hence, among all possible states, (1) is much less likely to have emerged from heat-death than (2). hence, in the late universe (after all the cheap oil has been burned, I mean after the stars are rarer because the age of stellar birth has long passed) we are much more likely to be denizens of a single real planet in (2), with false sense impressions and false memories making it appear that we are in (1).

Nor did my example ever assume that we were in the early universe. To the contrary, I was the first to publish that we were likely to be simulations in the era when all black holes have evaporated away to Hawking radiation, and are running in a very cold very dilute ambiplasma (electron-positron) computer.

So the probability that are “clear” to me arise from enumeration in the space of all possible simulated universes, modulo indistinguishability by obervers (humans for sure, maybe fruit flies, but I’ve yet to see a convincing argument that an amoeba cannot be a Copenhagen interpretation observer).

I agree with Greg Egan that at no time (before conception, after death) are we waiting around for equidistributed bodies to be built into which we incarnate/reincarnate.

Posted by: Jonathan Vos Post on June 9, 2008 5:25 PM | Permalink | Reply to this

Re: From the ambiplasma future; Re: Theophysics; Re: Urban Myths in Contemporary Cosmology

Hence […] (1) is much less likely to have emerged from heat-death than (2).

Is it?

Can you tell me how you obtain the probability for a given hallucination to materialize from a heat bath?

Posted by: Urs Schreiber on June 9, 2008 5:57 PM | Permalink | Reply to this

Embedding; Re: From the ambiplasma future; Re: Theophysics; Re: Urban Myths in Contemporary Cosmology

With all due respect, Urs Schreiber, I think it reasonable to make this levels/nesting assumption.

Default:

Hallucinations are embedded in brains.

Brains are embedded in bodies.

Bodies are embedded in planets (at what we perceive to be the early era of the universe when life is mostly on planets).

Planets are mostly embedded in solar systems.

Solar systems are mostly embedded in galaxies.

Galaxies are mostly embedded in cluster of galaxies.

Clusters are mostly embdedded in superclusters.

Non-default:

skip one or more levels, fool the oberver with false sense-data and/or false memories, embed everything in a simulation which may have Egan-like weirdnesses of lazy computation or non-sequential execution.

It is naive to map hallucinations to reality. That’s what Literature and Art are about.

Enumerations (and hence entropy) depend strongly on the structure of the nesting, even before we go all recursive and intentionally confuse the picture.

Posted by: Jonathan Vos Post on June 9, 2008 6:26 PM | Permalink | Reply to this

Re: Urban Myths in Contemporary Cosmology

Greg and Urs:I think you’re making great progress! Greg raised what seemed to me a fatal objection, and Urs escaped it with Houdini-esque ease, and then Greg agreed.

The other issue Greg raises — whether we can draw sensible conclusions from assuming we are ‘typical observers’ — seems really difficult and frustrating. For one thing, we have to decide who counts as an observer. That might be so difficult that it vitiates the whole argument.

Does a fruit fly count as an observer? If so, should I be shocked that I’m not a fruit fly, since there are so many more of those?

Well, presumably I wouldn’t be blogging now if I were a fruit fly — so given that fact about myself, it’s not so improbable that I’m human.

But if I get to use facts like that, it’s also not improbable that I’m a left-handed expert on nn-categories whose cousin is a folk singer.

And lest you think that fruit flies are too stupid to count as ‘observers’, don’t forget that there could be far-future observers who think we’re too stupid to count as observers.

Posted by: John Baez on June 9, 2008 8:03 AM | Permalink | Reply to this

Re: Urban Myths in Contemporary Cosmology

For one thing, we have to decide who counts as an observer.

Whether we have to decide this may depend on what we are hoping to achieve. But it is certainly fun to think about this.

Something about feedback loops will have to enter in this thinking. Fruit flies I’d possibly want to count as observers. The subtle boundary, might be a bit below fruit flies, for instance when it comes to plants that turn their leaves towards the sun.

Do they observe the sun? One tends to think, in this case, that this phenomenon is nothing but some cleverly arranged biochemical feedback loop within the plant.

But the same qualitative statement should be true for a fruit fly searching for fruit. Or for a mathematician putting a paper on the arXiv…

Then again, maybe something should count as an observer only if it recognizes itself when looking into a mirror. That would exclude fruit flies, as far as I know.

Posted by: Urs Schreiber on June 9, 2008 12:57 PM | Permalink | Reply to this

Re: Urban Myths in Contemporary Cosmology

Or for a mathematician putting a paper on the arXiv…

Indeed!

Posted by: Bruce Bartlett on June 9, 2008 2:13 PM | Permalink | Reply to this

Re: Urban Myths in Contemporary Cosmology

I might have mentioned this before, but there’s a very nice discussion of some of these issues in a short paper called “Are We Typical?” by Hartle and Srednicki. Sean Carroll mentioned this on his blog a while back, and I’ve been plugging it ever since.

A related notion that some people keep invoking is a vague “Copernican principle”, any violation of which is supposed to be very backward-looking and unscientific. The only “Copernican principle” I’d consider worth defending would be one that avoids coincidences, rather than one that assumes typicality. For example, if we came up with a cosmological model which only fitted our observations if our galaxy happened to lie at Geometrically Special Point A in the model (and nothing in the model favoured galaxy formation at Special Point A; that the Milky Way was there, rather than an intergalactic void, was just down to luck) … then that would violate the Copernican Principle.

But a theory that merely implies that there probably are – or will be, or have been – any number of creatures doing astronomy who happen to differ wildly from us in various ways doesn’t require a coincidence. And the idea that we should be surprised not to belong to some majority class – either known (like JB’s fruit flies) or just hypothesised (like future observers), strikes me as utterly bizarre. There was no “me” floating outside spacetime prior to my birth, waiting to be incarnated in a body chosen at random from all living creatures throughout history (or all observers, or whatever). If that preincarnation fantasy was true, then no doubt we could use it to extract some kind of probabilistic information about the future … but since it’s not, we can’t.

Posted by: Greg Egan on June 9, 2008 1:07 PM | Permalink | Reply to this

Re: Urban Myths in Contemporary Cosmology

Greg wrote:

I might have mentioned this before, but there’s a very nice discussion of some of these issues in a short paper called “Are We Typical?” by Hartle and Srednicki.

Thanks, that’s interesting. I’m glad some smart people have thought hard about this ‘principle of typicality’. I think this relieves me of the need to ponder it further, for now!

Posted by: John Baez on June 10, 2008 8:16 AM | Permalink | Reply to this

Re: Urban Myths in Contemporary Cosmology

John wrote:

The other issue Greg raises — whether we can draw sensible conclusions from assuming we are ‘typical observers’ — seems really difficult and frustrating. For one thing, we have to decide who counts as an observer. That might be so difficult that it vitiates the whole argument.

Urs wrote:

Whether we have to decide this may depend on what we are hoping to achieve. But it is certainly fun to think about this.

I meant we have to decide this if we adopt a Principle of Typicality saying:

“We are likely to be typical observers, so we should question any theory that leads to the conclusion that we are atypical”.

This principle seems to underlie arguments like the one in this abstract, which predicts that the universe will decay in billions of years.

I’m suspicious of the Principle of Typicality. I want to undercut it! So, I’m arguing that this principle only makes precise sense after we define what counts as an observer. After all: the more things count as observers, the less typical observers we are.

And, I think it’s hard to precisely define what counts as an observer — and also strange that the choice of this definition should affect our opinion on whether the universe will decay.

I think this all this casts doubt on the Principle of Typicality.

Posted by: John Baez on June 9, 2008 6:51 PM | Permalink | Reply to this

Gott paradox?Re: Urban Myths in Contemporary Cosmology

The glaring flaw in the ultra-Copernican Principle of Typicality is the application of it uniformly to space and time, without probing the assumptions.

Hence J. Richard Gott III’s strange notion that we are at a “typical” time, and that the likely future age of anything (the USA, human species, planet, cosmos) can be calculated from typicality.

I objected vigorously to that when he published. I extracted responses directly from, for instance, Dr. Gregory Benford, and sent an article to Analog Science Fiction/Science Fact magazine. The article was not bought, but the quotes from Benford, Brin, et al that I’d sent were sprinkled randomly through succeeding issues of the magazine.

Gott is smart. He knows lots of cosmology. But to say that his argument is naive in terms of probability theory is, to me, an understatement.

What is an observer? This is also not to be swept under the rug; I agree with John Baez on that.

The Coperhagen versus von Neumann versus multiverse theories grapple with this, but talk past each other, in no real debate.

To oversimplify, QM dropped the classical notion of observer, but kept classical space and time. SR then GR dropped classical space and time but kept the classical observer.

That QM and GR do not fit together is the scandal underlying the crisis in physics and cosmology.

Recent observations and analysis by Benjamin Wandelt indicate (just below the level where they announce “detection” in the forthcoming Phys Rev Letters but instead say “evidence for”) “non-gaussianity” in the CMB. This may be the start of the collapse of Alan Guth’s “inflation” – the unifying principle of Cosmology since Big Bang. That is, inflation matches CMB data nicely to first order, but seems to badly miss on 2nd order.

So are there two inflaton fields? Doe Steinhardt’s ekpyrotic model fit the data better (it also can’t explain the nongaussianity and polarization data)?

There is a genuine crisis here of theory and of data.

I feel strongly that the Boltzmann brains nonsense distracts from awareness of, let alone resolution of, the crisis.

Posted by: Jonathan Vos Post on June 9, 2008 7:22 PM | Permalink | Reply to this

Re: Urban Myths in Contemporary Cosmology

Jonathan wrote:

Recent observations and analysis by Benjamin Wandelt indicate (just below the level where they announce “detection” in the forthcoming Phys Rev Letters but instead say “evidence for”) “non-gaussianity” in the CMB.

Interesting! I hadn’t heard of that. This paper by Yadav and Wandelt claims ‘detection’:

Their abstract finishes with: “We conclude that the WMAP 3-year data disfavors canonical single field slow-roll inflation.”

But, I see this paper was submitted to Phys. Rev. Lett. Did the referees force them to change ‘detection’ to ‘evidence’?

This may be the start of the collapse of Alan Guth’s “inflation” – the unifying principle of Cosmology since Big Bang.

That would be very exciting, though in some ways sad, because after the Standard Model, inflation was the only new ‘fundamental law’ formulated by a theoretical physicist that wound up correctly predicting experimental results. We’ve mainly just seen:

  • theories that make predictions that are shown wrong, like the grand unified theories that predict proton decay at a rate above what’s observed,
  • theories that don’t yet make predictions we can test, like string theory and loop quantum gravity,
  • unexpected results from experimental or observational astrophysics — like neutrino oscillations, dark matter and dark energy.

Even inflation is a bit ad hoc for a ‘fundamental law’, since it involves an ‘inflaton field’ which is not part of the Standard Model or any overarching formalism. If inflation is right, presumably physics needs to grow a good deal to accomodate it. If it’s slightly wrong, physics may need to grow even more. I guess we’re in for a show either way.

I feel strongly that the Boltzmann brains nonsense distracts from awareness of, let alone resolution of, the crisis.

Awareness, yes. Resolution? I’m not sure. The question is whether the people interested in Boltzmann brains would help or hinder serious work on cosmology, were they to become involved.

Posted by: John Baez on June 10, 2008 7:35 PM | Permalink | Reply to this

Re: Urban Myths in Contemporary Cosmology

John wrote:

This principle seems to underlie arguments like the one in this abstract, which predicts that the universe will decay in billions of years.

Beyond all the legitimate points people are raising about the vagueness of the concept of “observer” and the difficulty of computing the probability for complex systems like observers to arise in various ways … for me, what kills these arguments stone dead is simply the claim that we can distinguish between two theories based solely on their different predictions about the future.

When we do a simple probabilistic experiment here and now – say, prepare a meson in some state and look at its decay products – then even though we only see one outcome, in a sense we assume that our experiment had “access” to the entire probability distribution for all possible outcomes. Quantum mechanics invites us to think of that distribution as being available in its totality, locally.

Now, we could also imagine stepping out of spacetime and looking at the massive data set consisting of all meson decays in the history of the universe whose initial conditions agreed with our experiment. That data set would also give us the same probability distribution as the one we probed with our particular experiment. But we would be getting things completely backwards to think that our own particular experiment somehow involved access to that whole-of-spacetime data set. Because of the simplicity of the experiment, we could think that way and still get correct answers, but nonetheless any idea that we were “sampling” all meson decays in the history of the universe would be mistaken.

When we do something more complex, like count the number of “observers”, however defined, in a certain region of spacetime, the correct predictions for that number will involve a horrendously complex set of calculations, but even if we can make all kinds of simplifying assumptions and get sensible estimates … the bottom line is, all legitimate calculations are about sampling probability distributions to which we have access either because they are part of the laws of physics everywhere in spacetime, or because the relevant data lies in our causal past. Just as with the meson experiment, we’d be mistaken to think we’re somehow sampling data from the whole of spacetime – only in this case, the conceptual mistake won’t yield the right answer, it will yield nonsense.

Sometimes people try to circumvent these basic considerations of causality by summing over all observers and showing that a strategy of assuming typicality gives a global advantage. Well, of course the totality of obervers will contain information about their complete distribution throughout spacetime! And if every creature in the universe assumes they are typical, any majority that actually is typical will then contribute to a large global average of correct guesses. But … so what? This is an uninteresting tautology. It is not science.

Posted by: Greg Egan on June 10, 2008 4:14 AM | Permalink | Reply to this

Re: Urban Myths in Contemporary Cosmology

Wasn’t the whole point of decoherence the premise that we could now safely remove ‘the human observer’ from the equation and we don’t have to worry about this sort of thing.

Lubos wrote a nice series of articles on the arrow of time and Boltzmann brains and I find myself largely agreeing with him as its more or less the sort of viewpoint the establishment has.

It’s become fashionable again to question this, for whatever reason, but its pretty much old hat.

Posted by: Haelfix on June 10, 2008 12:21 AM | Permalink | Reply to this

Re: Urban Myths in Contemporary Cosmology

Wasn’t the whole point of decoherence the premise that we could now safely remove ‘the human observer’ from the equation and we don’t have to worry about this sort of thing.

I don’t think these anthropic arguments are related to quantum mechanical issues of what counts as an observer or a measurement. Although the specific cosmological theories like inflation rely on QM, the actual anthropic issues can be factored out and discussed in a purely classical context.

Posted by: Greg Egan on June 10, 2008 5:57 AM | Permalink | Reply to this

From the arXiv today

I’ve only been half-following this discussion so I apologise if this is completely off-topic but in my half-baked (Boltzmann) brain it seems vaguely connected.

On the arXiv today is an article on the Sleeping Beauty problem. The basic premise is that Sleeping Beauty is put to sleep on Sunday. She is told that while she is asleep a fair coin will be flipped. If it lands heads, she will be woken on Monday. If it lands tails, she will be woken on Monday, then put back to sleep and reawoken on Tuesday. Moreover, she will be given a drug that makes her forget the fact that she was woken on the Monday. Upon awakening she will be asked: ‘What do you think is the probability that the coin landed heads?’

There are two answers: one half, since the coin is fair and nothing has occurred to change her belief in that. One third, since on a long series of trials she is more likely to be woken up after a Tail than a Head.

You can read the article to see the resolution. I know too little about the issues involved to assess whether it answers all the apparent questions but it seems fine to me.

The connection, if there is one, would be to the question: ‘Am I a Boltzman brain?’. I’m not sure that one can line up the problems exactly, but the general principle seems to be: ‘Equal probability of events does not equate to equal probability that I am currently observing a particular event.’.

PS While we’re blowing urban myths out of the water, can we please get rid of the ‘In an infinite universe, anything is possible.’ one. It seems to be resurfacing as ‘In an infinite number of universes, there’s one where I’m currently typing this on a computer running Windows’. I hope that that example is sufficient to destroy it completely.

PPS Also from the arXiv today. Imagine my disappointment when I actually read the article Smooth Loops and Fiber Bundles: Theory of Principal Q-bundles. Not that it doesn’t look like an interesting article, of course.

Posted by: Andrew Stacey on June 10, 2008 8:39 AM | Permalink | Reply to this

Re: From the arXiv today

Andrew Stacey wrote:

While we’re blowing urban myths out of the water, can we please get rid of the ‘In an infinite universe, anything is possible.’ one. It seems to be resurfacing as ‘In an infinite number of universes, there’s one where I’m currently typing this on a computer running Windows’.

Over the past year, I’ve spent altogether too many late nights and early mornings sleeplessly fretting over the question, “Is there a universe in which a counterpart of me is a Windows user?”

Maybe this happens to other people, too: you’re reading something nicely modest and technical which is at least tangentially related to your own work, you click the author’s name to see what else they’ve posted to the arXiv lately, you check the “cited by” page, and then you’re trying to tread water in the sea of speculations on the ill-defined and the untestable.

(I suspect that, if your view of probability is closer to, e.g., Fuchs and Peres than to Doering and Isham, many of these myth-flavoured questions are simply ill-posed. What’s the point of asking, “What are the potential consequences to me of my experimental intervention into this phenomenon?” if the phenomenon in question is, by definition, inaccessible?)

Posted by: Blake Stacey on July 3, 2011 4:37 PM | Permalink | Reply to this

Re: From the arXiv today

I suspect that, if your view of probability is closer to, e.g., Fuchs and Peres than to Doering and Isham, many of these myth-flavoured questions are simply ill-posed.

Clearly many of these questions are ill-posed, which is part of the reason why the above entry starts with the words “Here is something that disturbs me.”

But I am not following what you are suggestiong Doering and Isham’s “views” have to do with this.

In the article that you point to they wish to identitfy a topos whose internal truth values may be identified with elements in [0,1][0,1], such as to be able to say “a probability is the same as a truth value in this topos”. For whatever that’s worth (I haven’t studied their article in detail), this at least involves a desire for formal reasoning.

I find the disturbing aspect of “these myth-flavoured questions” is the lack of interest in any formal reasoning. Hence in science. It’s all about good fireplace stories, instead.

Posted by: Urs Schreiber on July 4, 2011 6:31 PM | Permalink | Reply to this

Re: From the arXiv today

I could have been clearer. Doering and Isham are concerned that what they call an “instrumentalist” position is no good for doing cosmology (pp. 2-3); Fuchs and Peres disagree. (For a statement by Peres alone, see arXiv:quant-ph/9711003, p. 9.) I bet the actual topos-theoretic work can be divorced from these motivational issues, though.

Posted by: Blake Stacey on July 4, 2011 7:09 PM | Permalink | Reply to this

Re: From the arXiv today

I could have been clearer. Doering and Isham are concerned that what they call an “instrumentalist” position is no good for doing cosmology (pp. 2-3); Fuchs and Peres disagree.

Oh, I see, I had skipped over the intro.

I bet the actual topos-theoretic work can be divorced from these motivational issues, though.

Yes, I think so, too.

I have recently said something related elsewhere: this kind of investigation might benefit from having 1. less chat and 2. more theorems.

To be convincing in these matters, it may help to let more proven facts speak more for themselves. So I guess we agree.

Posted by: Urs Schreiber on July 4, 2011 7:39 PM | Permalink | Reply to this

Re: From the arXiv today

An argument like, “Your promising-looking calculations are problematic because they’re sensitive to details of trans-Planckian physics” (cf. Brandenberger, arXiv:1103.2271) looks to me much more scientifically fruitful than one about how many Boltzmann brains we think are flying about spacetime.

I’ve been trying to understand a bit of cosmology, because — well, honestly — some of the “campfire” discussions conjure up the bleakest scenarios I can imagine, and it’s hard not to think about them. Sometimes, I feel like a character in a story co-authored by Greg Egan and Jorge Luis Borges, fretting over not just the Eternal Return but the Eternal Return with variations … not exactly the most productive frame of mind for thinking about stochastic Petri nets, Rényi entropy or anything else for which we could hope to make progress!

The more I learn, though, the more I wonder if I should rather be unhappy over the scientific process, instead of the conclusions. Take, for example, Linde and Noorbala’s recent article (arXiv:1006.2170) on the “measure problem” in eternally inflationary cosmology. As they say,

The main problem here is that in an eternally inflating universe the total volume occupied by all, even absolutely rare types of the “universes,” is indefinitely large. Therefore comparison of different types of vacua involves comparison of infinities. As emphasized already in the first papers on the probability measure in eternal inflation [6–8], such a comparison is inherently ambiguous and depends on the choice of the cutoff, which is required to regularize the infinities.

A bit later, when discussing candidate measures:

Out of all of these measures, the original proper time cutoff measure P(ϕ,t)P(\phi,t) is the simplest. However, this measure suffers from the youngness problem [14], which was especially clearly formulated in [15]: This measure exponentially rewards parts of the universe staying as long as possible at the highest values of energy density. As a result, this measure exponentially favors life appearing in the parts of the universe with an extremely large temperature, which contradicts the observational data.

Again, we’re back to assuming typicality. And then on we go with the Boltzmann-brain business … We have an “inherently ambiguous” situation, and the means people have taken to address it make no sense to me. Every “solution” looks like an elaborate contrivance which does nothing but reproduce the starting point.

Posted by: Blake Stacey on July 6, 2011 9:27 PM | Permalink | Reply to this

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