The Higgs, Boltzmann Brains, and Monkeys Typing Hamlet

By Amir Aczel | October 31, 2012 4:14 pm

Amir D. Aczel writes often about physics and cosmology. His book about the discovery of the Higgs boson, Present at the Creation: Discovering the Higgs Boson, is published in paperback by Broadway Books in November 2012. 

If somebody told you that there are angels floating in space, observing our world and forming their impressions of our everyday reality, you would think that this person is nuts—a religious fanatic with an active imagination, and certainly not a scientist. Scientists, as we all know, are rational beings who believe only in what nature reveals to us through experimentation and observation, coupled with theory that is never divorced from the physical measurements they make. The link between the two remains tightly regulated through the strict rules of the scientific method.

So how do you explain the bizarre fact that, for about five years now, some of the world’s most prominent physicists have been describing a scenario—which they seem to truly believe may be real—in which, instead of the Biblical angels, space is permeated by disembodied brains?

These compact, conscious observers, called “Boltzmann brains,” cruise the vastness of intergalactic space, and beyond it, to the infinite “multiverse” that some scientists believe exists outside the reaches of the universe we observe through our telescopes and satellites. Their consciousness makes the Boltzmann brains recreate our reality. They imagine life such as the one you and I believe we are experiencing here on Earth, to the point that these brains in space may think that they are living on a planet like ours, that they may even be us. Some recent physics papers and commentaries have even explored the possible limits on the number of Boltzmann brains in the universe as compared with “real” brains, in an effort to estimate the probability that we are real rather than Boltzmann entities.

Brain MRI. Image from Nevit Dilmen/Wikimedia commons

Brain MRI. Image from Nevit Dilmen found at Wikimedia commons

This idea, to any reasonable observer, would seem like something beyond “The Matrix,” beyond the surrealism depicted by a Dali painting, beyond the wildest imaginable work of science fiction. And yet, the physicists and cosmologists who have been contemplating and advocating such a bizarre picture of reality are among the most renowned and include names such Alan Guth of MIT, Leonard Susskind of Stanford, and Sean Carroll of Caltech (who writes a blog for this magazine; his blog post on this very idea can be found here).

So, what is a “Boltzmann brain”?

Ludwig Eduard Boltzmann (1844-1906) was an Austrian physicist who pioneered statistical mechanics and derived the famous equation for the entropy (or degree of disorder) of a system: S = k log W, where S is entropy, k is Boltzmann’s constant, log is the natural logarithm, and W is  the frequency of occurrence of a macrostate of the system (such as pressure or temperature). The second law of thermodynamics implies that the entropy—the degree of randomness, or disorder—of any closed system never decreases (and generally increases).

To better understand randomness and entropy—and to get a feel for why entropy naturally increases—think of a child’s room that is neat and orderly at the beginning. Then the children come in and play, and afterwards you always find complete chaos: the electric train tracks are strewn all over the carpet, there is a toy truck upside down, a couple of dolls have been randomly thrown on the floor, and a chair is lying on its side. Then the child’s mother comes into the room and expends energy (perhaps 20 calories, equivalent to running on your treadmill for 2 minutes) to restore order to the room. Energy and entropy are indeed related concepts—as we see here through the fact that investing energy can bring back order to the system and thus reduce its entropy. So a high-entropy state is “normal,” while creating order is something that requires concentrated, directed energy. This is an important observation.

Boltzmann wondered why our observed universe seems so orderly rather than completely random, as one might expect as the “natural” state of the universe. He obviously was never stuck in rush-hour traffic in Manhattan, or downtown Taipei or Tel Aviv. And he hypothesized that perhaps our portion of the universe is just a statistical fluke: an aberration within a wider universe in which randomness reigns supreme. So a Boltzmann brain, named after him, is a brain–a conscious observer–that materializes out of the disorderly universe purely by chance (a very, very small chance, I must emphasize) in the same way that, as Boltzmann had suggested, our entire universe may have emerged out of a wider chaotic multiverse purely through a random event. As Andrei Linde of Stanford put it in an interview with the New York Times: “It’s cheaper” to create just a disembodied brain than it is to make a universe.

But is it, really?

Connecting to the Higgs boson

I will come back to this question shortly, but first I want to talk about the Higgs boson. What does it take to “create” a single subatomic particle, a Higgs boson? If you’ve followed the story of the search for the Higgs, which culminated with great excitement in a press conference at CERN, near Geneva, Switzerland, on July 4th of this year when the Higgs discovery was announced, then you know a few things. You know that it takes expending an energy that is equivalent to the entire electric power consumption of a city the size of Geneva, running continuously for several years in a highly concentrated way—many trillions of protons are accelerated to close to the speed of light and then directed very precisely to crash into other protons—just to create a few Higgs bosons.

And the Higgs is highly ephemeral: it lives for a tiny fraction of a second–something like 0.0000000000000000000007 seconds. Then it decays into other particles. The reason that the Higgs lives for only such a minuscule fraction of a second is the celebrated Heisenberg’s Uncertainty Principle. According to this principle, there is a quantum-mechanical constraint on the product of time and energy. Since the Higgs has a mass that is equivalent to an energy of 125.3 GeV (billion electron volts), it can only live for a very small fraction of a second. (A muon, on the other hand, can live much longer—for 2.2 millionths of a second—because its mass-energy is much smaller.)

Now back to the Boltzmann brains: The proponents of cosmic inflation, Alan Guth (who first proposed the theory in 1980) and Andrei Linde and Alex Vilenkin (who both independently argued that inflation is eternal), have come to the conclusion that the multiverse must exist because the inflationary process undergoes quantum fluctuations. So even though the inflation that worked its magic on our universe ironing out any primeval “kinks” to create the “flat,” or mathematically Euclidean universe we see today seemed to come to a stop, it never did. It just went elsewhere. It is now doing its trick on infinitely many other universes. These three physicists (together with Andrea de Simone of MIT, Mahdiyar Noorbala of Stanford, and Michael P. Salem of Tufts) recently wrote an article that attempted to set some bounds on the number of Boltzmann brains in the multiverse and the spacetime volume of the multiverse.

But the existence of both Boltzmann brains and an infinite multiverse rely on probability theory within the context of the deep mathematical concept of infinity. And physicists have traditionally had a very uneasy relationship with infinity. At least eight extremely gifted individuals have been awarded Nobel Prizes in physics for the great achievement of removing infinities from physical theories! These are Richard Feynman, Julian Schwinger, and Sin-Itiro Tomonaga; Gerardus ‘t Hooft and Martinus Veltman; and Frank Wilczek, David Gross, and H. David Politzer. Infinity has until recently been the scourge of theoretical physics, and the people mentioned above have established various quantum field theories–essential to modern physics–by ingenious and painstaking work of making infinite answers (which physicists consider completely nonsensical) disappear from calculations. This task is called “renormalizing a theory.”

But now, after Linde and Vilenkin have argued that inflation must be eternal (and string theory and the “many worlds” approach also imply the existence of other universes), infinity has wiggled its way into physics in a seemingly positive way. But infinity is a nasty, unwieldy idea. There is good reason to try to purge it from physical theories.

Infinity and beyond

Let me explain what I mean using the most familiar example I know: monkeys typing Hamlet. Monkeys don’t type Hamlet, or anything, really. But suppose a monkey sits in front of a computer keyboard forever. The minute you talk about forever, anything at all is possible. The first trillion-trillion-gazillion attempts lead to nothing: just garbage of letters being typed randomly. Then, by chance, the monkey types: “Act one, Scene 1: Elsinore. A platform before the castle. Enter Barnardo and Francisco, two Sentinels.” But then the monkey continues: “gsdft rhdfsrax uurlwtsc bzdw…” and you wait another googolplex of years, and you get back the real sentence above, plus–instead of the nonsense–“Barnardo: Who’s there?” and then back to garbage. Of course, in between, the monkey also types the first sentence as I have it, except that “Elsinore” is typed as “Elsibore”–so no cigar; and so on, pretty much forever.

The play has about 30,000 words, and if we assume an average of 5 letters per word, we have about 150,000 characters that the monkey needs to get right and in sequence. So the probability of getting it correctly the first time (leaving out spaces and punctuation, and special characters, which would make it even more difficult) is one divided by 26 raised to the power 150,000, which is a number very, very close to zero–but not identically zero. So, theoretically, as you “go to infinity,” it will happen, but in reality you would have to wait an exceptionally long period of time (given any rate at which the monkey types), which could very well be “forever.”*

And there are theorems in the theory of probability where an event (a recurrence of a state, such as in a random walk or a Markov chain) will occur infinitely often–however, the waiting time for even the first recurrence can be proved to be infinite! This means that, yes, something can happen infinitely many times, but for it to occur the first time, you have to wait until “forever.” How does this fact affect “infinity” considerations in the practical realm of physics?

Mathematicians can talk about actual infinity (in addition to the potential infinities, appearing as limits in the calculus) because, to them, it has no application in the real world. What, in the real world, is truly infinite? The example I am showing you here demonstrates yes, if you “go to infinity”–whatever that means in the real world–you can “prove” almost anything you like! The monkey typing forever, meaning producing infinitely many replications of 26 characters, will theoretically produce not only the whole of Hamlet–in fact, the monkey will do it infinitely many times!–but also every piece of writing ever created in history, including all the works in the lost great library of Alexandria, as well as Virgil, Dante, Hemingway, Jane Austen, Salman Rushdie, and the U.S. Constitution; and every letter any person in history has ever written to another person, or would have written, or might write, or could write, or will ever write; and every possible grocery list, and every possible presidential election speech. You can see just how preposterous all of this becomes when you try to apply an abstract mathematical concept to the real world. And by the theorem I’ve alluded to, it may take “forever” for these things to happen.

Back to Boltzmann

But if you travel forever in the multiverse, will you encounter a single Boltzmann brain?

The argument made by Linde (in the New York Times link above) and by Carroll (in his “Cosmic Variance” blog) as well as by other proponents of the infinite multiverse and its Boltzmann brains is that the probability of producing–purely by chance, through quantum fluctuations, in infinite space and time–a disembodied brain is higher than the probability of producing an entire universe.

But this is not true. A brain requires a body to support it, and a world to feed it and house it and protect it, and–from everything we know so far from science–it needs 13.7 billion years of an expanding universe, galaxy and star formation, including many millions of years of fusion in stars to create and spread around the iron and carbon and oxygen and other essentials needed to start and maintain life on a hospitable planet, and to set evolution in motion, in order to create a conscious, thinking, self-aware brain.

You might say that we don’t really need a human brain–it can be a computer. It would have to be a very advanced computer–one with consciousness, which is something we haven’t been able to make so far. But even so, it would still require the silicon chips, and the rare-earth metals, and the integrated circuits, and all the right electronic connections, and a power source, and everything would have to be put together in a precisely-specified way: or else it won’t work.

Wait to infinity and these ingredients will all just materialize in the right way through a “quantum fluctuation”? I think not. The case of a Boltzmann brain is unmeasurably more complicated, and astronomically more demanding probabilistically, than that of a simple sequence of 150,000 characters to be typed in the right order. It is, in fact–because of the requirements of something like our world to support a human or a computer brain–an event of probability zero. It cannot happen by itself even “at infinity.”

If you are not convinced, let’s go back to the Higgs boson (I brought it up for a reason). I hope I’ve convinced you that even a single subatomic particle–to make it appear as a particle, rather than the field associated with the particle (the Higgs field permeates everything)–requires immense amounts of highly directed energy. Multiply that by an unimaginably large factor to create even a few atoms to be placed in the right spots (all of this happening by chance, through some “quantum fluctuation,” as these physicists describe it) and you still have a fantastically long way to go to make an actual brain. My contention is that even infinity won’t help you here, since the probability of a quantum fluctuation producing a complex entity such as a brain is zero. Ask yourself: What is the probability that a Large Hadron Collider would materialize out of the void, all by itself, with all its required highly concentrated energy, to produce even one particle? And for a brain we need an extremely ordered array of many particles.

Recall that the Higgs lives for a very short time because of its mass. Suppose even that a Boltzmann brain can be small enough to be a quantum object, created through a quantum fluctuation in the vacuum. Its mass alone would cause a big problem. And here I come to the crux of my argument: By the Heisenberg Uncertainty Principle, this brain will live a lifetime that is far, far shorter than the tiny lifetime of a Higgs boson. (You can think about it another way: How long does a quantum fluctuation in the vacuum last? An exceptionally short flash.) If this brain lives for such a short period of time, no signal can travel between two parts of it for long enough to create a single thought–let alone imagine the entire known life and history of the world, so as to make it indistinguishable from a “real” brain.

And if the Boltzmann brain is not a quantum object–meaning that it is a large entity that has suddenly “grown” to a macro size starting from a quantum variation in the vacuum of space–then to create it would require a process that is indistinguishable from cosmic inflation (because cosmic inflation following the Big Bang is the only process we know of by which a quantum fluctuation has resulted in the creation of a macro object). And in such a case you would have a whole universe–not just a single brain.

So even infinite time and infinite space and infinitely many worlds (if they exist) won’t work here. A brain just can’t materialize by itself in the vast emptiness of space out of a random “quantum fluctuation in the vacuum”–no matter what. But here is as close to a brain in space as we can get:

A picture of Felix Baumgartner as he jumps fro

Felix Baumgartner jumps from the stratosphere. Credit: Red Bull

So I’m sorry to disappoint you: You certainly don’t live in a “Matrix.” What you are observing is a real universe, with its good and its bad, and with its conscious beings marveling at the riddle of existence. We are the consciousness of the universe (even though there may be others, in other civilizations). We evolved on this planet and developed self-aware, conscious brains and, in a sense, through us the universe as a whole gained consciousness and self-awareness. I think this is a profound enough idea so that we don’t really need to contemplate the dubious existence of Boltzmann brains floating around. But if you want, we can next discuss how many angels can dance on the head of a pin.

* Note: To a first-order approximation using the geometric distribution, the mean time to occurrence is infinite. (If there is interest, I can elaborate on this in the Comments.)

  • wilzard

    There is no amount of evidence, logic, reason, maths, or slaps in the face that will make someone who believes in these things abandon their belief, no matter how silly they look.

  • John Berenberg

    Interesting. But the only part on which I feel qualified to comment is the heading on the final section, which has a typo: Back to Blotzmann.

  • http://amirdaczel.com Amir Aczel

    Hi John: This is embarrassing! My brain will never be a Blotzmann brain… I’ll let the editor know!!
    Many thanks!
    :)

  • Tony

    Another very minor typo in the second section: log is the common base-10 logarithm while ln is the natural base-e logarithm. Other than that, great thought-provoking article.

  • Steve Wenner

    “you would have to wait an exceptionally long period of time … , which could very well be ‘forever.’”

    I don’t understand that comment; although the mean time to occurrence is infinite, any individual instance is certainly finite! On your more general point about the odds of a Boltzmann brain spontaneously forming, you may be right that the most likely way to spontaneously create a brain is to first create a universe; but, aren’t there other, perhaps less likely, ways to create a brain and sustain it for a significant period of time? And the main point about Boltzmann brains is not that any old brain is formed, but that my personal brain is exactly duplicated, which is certainly much less likely than the formation of a universe! Of course it is unlikely to happen quickly, but if a quantum fluctuation can create anything, then it seems to me that it would eventually create my brain and, with a bit more luck, keep it in good shape long enough for it to contemplate Boltzmann brains.

    I admit that the whole concept of Boltzmann brains is not particularly profound and other mysteries of existence are far more interesting; but, you haven’t convinced me that there is a fundamental fallacy in the concept.

  • William von Witt

    That was a lot of fun :) some mental exercise with infinities and I laughed at the end. Given the area of my thesis was to do with branes and space time, homophonic but different again. Now I have to read the papers that inspired this and I have lots of work to do…

  • http://www.pheromones.com James V. Kohl

    Bottom-up biology or top-down physics?

    The epigenetic effects of nutrient chemicals and pheromones on intracellular signaling, intermolecular changes, and stochastic gene expression occur in the context of “biological embedding” or adaptive evolution. However, the epigenetic effects on adaptive evolution are not theoretical and need involve no physicists in attempts to explain cause and effect.

    Is it best to embrace the actual biological complexity of the cell and of all organisms before attempting to embrace the theoretical complexity of the universe in which all organisms exist? The alternative to this bottom-up approach to understanding the biology of our behavior, is to start from the top down and first decipher the complexity of the universe.

  • Sverre Munthe

    I don’t pretend to know much about quantum mechanics, or even having any firm grip on the subject, but I do have fantasy in abundance. :)

    I fell that, to rule out any possibilities in the universe, as long as they follow the basic rules of our universe, is pointless. Science has yet to finsh mapping all the particles (every time I read or watch anything, it seems new things have been predicted), and we still have the strings, vibrations and dimensions. And why focus on metal and minerals, couldn’t it be possible to create a brain with gasses, electromagnetism, or by other means?

    The evolution of science is increasing exponentialy, and, yet, we can not see an end to this. I bet you, nature still have a few tricks up it’s sleeve. ;)

  • Carol N

    James – Yes and No. Given the vast number of extant primate brains x infinite time x itchy curiosity there really is enough space to support an uncalculatable number of ideas. And I think that’s the basic premise of the essay. Embrassing the Blotzman Brain is only one option of multi-mega gazillions. Aren’t we lucky?

  • Jerry Chase

    Fred Hoyle posited the idea of intelligence within interstellar gas clouds in his story “The Black Cloud” a number of years ago. He also considered the universe to be steady state instead of expanding, but was a great scientist and astronomer none the less.

    The concept you were expanding upon is the idea of small infinities vs. large infinities, which is a theoretical math axiom. It is interesting, but has little to do with proving or disproving determinism, which is the ultimate conundrum of people stuck within the confines of a purely Euclidean and Newtonian universe, and the real backbone of the article.

    A few years back, philosophers “proved” that there was no free will, based on the concept of every action having an equal and opposite reaction as well as other conservation of energy concepts, since they could not see structures in the brain that were small enough to engage any quantum change (microtubules were ruled out for some reason I have forgotten . If they are correct, I was destined to make this response, had no free will in doing so, and am REALLY good at deceiving myself and others. You are equally good at this, and Calvinism was as good a scientific theory of existence as any.

    While we are at it, remember that it was also “proven” that man could not fly.

    Boltzmann brain type speculations answer lots of questions better than some of the traditional theories and I feel that any rush to judgment is premature. Without such speculations, we are right back at determinism, in which case we can just relax and have a drink until our time comes.

    Briefly contemplate the navel of the universe as we know it. At some point, the three commonly described length, width, and breadth began and expanded along with a fourth axis of time. Multiverse ruminations can be simply ascribed to a fifth axis – probability. A (large) infinite number of universes are not required, only enough to cover deviations from an ideal probability. Chances of us living in the most probable universe are… probable (although I have no idea how reality shows and a giant mouse taking over Star Wars can ever be “probable”).

    Also keep in mind that string or M theory seems to work best with a NUMBER of dimensions, many of which are supposedly recursive and of little import. Perhaps… just perhaps…, some of those dimensions might be a little more important than suspected, but in ways our math hasn’t yet grasped. Stranger things have happened.

    Further… explain away (with a straight face) the Casimer effect WITHOUT an underlying substrate of an alternate dimension from which particles mysteriously appear momentarily, only to disappear. Perhaps not all dimensions began at the big bang, but that Hoyle was partially correct, that the big bang created dimensions WITHIN a static universe of alternative dimensions. If so, contemplating the navel of the universe might not be as important as exploring the attributes of the turtle it rode in on. :-)

  • Charles Barr

    “If this brain lives for such a short period of time, no signal can travel between two parts of it for long enough to create a single thought” – but if a human brain is faithfully produced, it likely will already be somewhere in mid-thought, possibly spending its infinitesimal lifetime wondering where it put the keys.

  • Patrick W

    Interesting article, but I think your insistence on physical manifestation of the brain as we know it (biological, computer, etc) puts an unnecessary constraint on the argument. A computer really is the collection of bits in a non-random, useful order representing data and instructions. This can occur at many levels — for example, one could call DNA a “computer” in that it contains data and instructions to make proteins. It is not too much of a stretch to imagine a “brain” consisting of subatomic particles in different states representing data and instructions. Given that entanglement shows subatomic particles can be linked even though separated in space suddenly makes the idea of one or more Boltzmann brains somewhat plausible.

  • lepton

    Since the Higgs has a mass that is equivalent to an energy of 125.3 GeV (billion electron volts), it can only live for a very small fraction of a second. (A muon, on the other hand, can live much longer—for 2.2 millionths of a second—because its mass-energy is much smaller.)

    Proton is 0.938 GeV, but it lives very long, shouldn’t there be other mechanisms to decide (half) life of a particle?

  • John W

    And yet, in less than 14 billion years, on a tiny collection of stardust orbiting an ordinary star, billions of consciousness have emerged to produce all of humanity’s enduring creativity – mostly in a few thousand years.

  • http://perceptualcosmology.com tamurphy

    Thanks for this nicely presented loosening of the bonds of finite understanding.

    As I get it, the impossibility of anything would appear to be a function of time, which is itself an artifact of macroscopic brains evolving within relativistic universes. Underlying all that higher order stuff is an atemporal quantum realm of random fluctuations—eternal inflation of everything possible within the boundless potential of nothing in particular.

    So, with respect to this timeless substrate, which of itself is nothing but pure possibility, every event from big-bang to present discussion is eternally now.

    In this context, recent speculations about the universe being a simulation within some meta-universe appears not only feasible but probable.

  • http://amirdaczel.com Amir Aczel

    Tamurphy: “…to present discussion is eternally now” reminds me of something I read just a few days ago. Dante’s highest point in heaven (in the Divine Comedy, vol.iii, Paradiso) is a point at which all time is the present and all locations are “here.” Pretty cool idea for a non-math or physics guy who lived 700 years ago!
    :)

  • September Amyx

    Well, I know I’ll sound like a crazy person, but here goes.
    A. I’ve been aware all my life of being watched by people I can’t see. So now you’ve given me a fairly good reason why this may actually be so!
    B. I have observed, over the course of 20 years on 3 different occasions, animals that had recently passed (as one that died seconds, one that died minutes, and one that died hours ago). Just go with me on this.
    C. I’ve felt and heard people who had passed a few minutes ago, someone who had passed within the hour which I felt for several hours until his body was discovered, and heard someone who had passed years ago yelling my name excitedly. Just go with me on this as well, OK?
    D. I had a couple of dreams that were very odd, not repetitive but yet the same set of circumstances in which my Dad was showing me he was alive after all. I knew it was real because he was standing there, yet at he same time I was thinking “but we buried him” or “the doctors said he died” or “he’s been gone all these years, he must be dead, why am I thinking or seeing he’s alive?” Go with me…
    E. Then I was taken for a visit to see my husband while asleep. I ‘woke’ up and realized I was positioned next to a ‘river’ that had no bottom, was very wide, and consisted of blue ‘ffff!zz!!zzz!!’ energy (not water) which I knew I would never survive if I tried to cross it. I was standing, but unable to move sideways or backwards, in what I could say is the feeling you’d get if you were a sandwich in a vending maching. It felt mechanical and round. l was standing where I could be found at ‘X’ spot. Across the river I could see this man, and he was standing on the bank with his hands clasped behind his back, looking up at the night sky in a supremely complacent “I could stand watching the stars forever” way. Observing him I felt/knew, that this man had been around and around this universe(s) so many times he knew every nook and cranny, and was able to guide anyone to any spot in the universe. I hear voices but can’t see anyone coming from my left , but then suddenly two people came around a bend in the path. My husband came striding resolutely into view, and there was this ‘clerical’ guy with him who’s saying, “Now you know we don’t have much time (time?!). You’re the ONLY one in the universe with the skills to (do the mission or job that needs to be done.) I thought, ‘come on, honey, you’re not buying this are you. The ONLY person with suitable skills? In the entire universe?!’ The ‘feeling’ regarding them was that my husband had accidentally figured out something about the operations of that place, and the guy wasn’t pleased at all. I’m feeling like my husband had been polite and patient, and while he was waiting he observed the interactions. He saw a little crack of opportunity that he determinedly pursued, and found they couldn’t refuse his request. He was walking with an air of intense satisfaction, as if he had strategically won something, and he just wanted to get his prize. As they reach the ‘gatekeeper’ (*facepalm-groaning* I know it’s cheesy but that’s what he was!), the gatekeeper turned towards me while raising his arm. As soon as his arm was eye level with me, all of a sudden I had this overwheming sensation of bodily warmth and energy blanketing me, and his vitality was so strong I could smell it, it was the smell he had in his late 30’s. I had totally forgotten how good he smelled. The feelings it aroused were so intense I woke up. I could remember that smell for several months afterwards.
    I’m thinking that we are not the exception to chaos, that the universe(s) are pretty much orderly, and they even have an orderly system of interaction with and within each other. And time is linear there too. And we STILL have jobs to do???!!!

  • Matt

    For the paragraph before “Back to Boltmann” about infinite monkeys producing all possible works, this idea is sort of explored in the Jorge Luis Borges short story The Library of Babel. Might be of interest to someone.

    Thanks for the thought provoking post!

  • http://perceptualcosmology.com tamurphy

    Amir Aczel: “Dante’s highest point in heaven…is a point at which all time is the present and all locations are “here.”

    Amazing. Thanks for that illuminating reference.

  • http://perceptualcosmology.com tamurphy

    Amir, I must tell you that my eldest brother, Patrick Murphy, who’s a Jesuit priest, just recently mentioned in a letter that Dante is one of his all-time favorite authors. I listened to your interview on NPR’s Science Friday, and was struck by the similarities between Teilhard de Chardin’s life and that of my brother, who at 80 is still travelling for Food for the Poor.

    I’m pleased to have become aware of you and your excellent work.

  • http://amirdaczel.com Amir Aczel

    Hi Tamurphy, Thanks for this!! It cheers me up! The Teilhard book was the most interesting I’ve ever written–I followed him from France to Rome to China (no Horn of Africa, though, with all these pirates…). I am curious about your brother’s life. Take care, Amir

  • http://perceptualcosmology.com tamurphy

    My brother is an exceedingly brilliant and erudite person who has essentially shunned the communal academic life common to Jesuits in favor of service to the poor and the downtrodden. His iconoclastic course has put him at odds with the establishment, while endearing him to thousands. I’d be pleased to put you in touch with him if you’ll send me a private email. All the best to you, Tom

  • Darryl Schmidt

    A fish.

  • http://www.warrencriswell.com Warren Criswell

    Thanks for this, Amir. At last a physicist agrees with me about Boltzmann’s brains! I just read Sean Carrol’s “From Eternity to Here” and could not understand why he (and Boltzmann and everybody else apparently except you and me) thinks it’s statistically more likely for a random fluctuation to produce a brain than a universe. As you say, it seems like you would need a universe, infinite or not, in order to get the brain. Carroll seems uncertain as to which comes first, the chicken or the egg.

    We may well live in a multiverse, but it seems to me the many worlds theory arises as way to intuit that which is unintuitable. All of our rational thinking is based on our bodily experiences in the world we perceive, as the cognitive scientist George Lakoff demonstrates in “The Embodied Mind” and his other great books. Our languages, both verbal and mathematical, are based on metaphors for these experiences. (For instance, “based on” comes from the base of a pot or whatever.) We have no experience with an object being in two places at the same time (entanglement), or being a wave or a particle depending on whether we look at it or not, or knowing how fast something is going or where it is but not both at any given time, or something going backwards in time and other quantum craziness, so we can’t picture these things. They don’t make sense, because we have no senses for them, so in order to rationalize them we come up with concepts like an infinite number of universes to take care of the infinite paths a particle might take. But maybe, speaking of monkeys typing Hamlet, ” There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy.”

    I mean, maybe it IS possible, at least at the quantum level, for an object to be in two places at the same time– in the same universe. No matter how hard we try to be objective, I guess it’s impossible for us to escape our own subjectivity. OK, I need to read your book on entanglement–and I intend to do so after this excellent article. But I’m thinking that Max Muller was right when he said that time and space are determined by the self. “We might say that there is no There without a Here, no Then without a Now, and that both Here and Now depend on us as recipients, as measurers, as perceivers.” I would like to ask you if any of this makes sense– but now that sounds like an ironic pun! lol.
    Warren

  • Ray Montgomery

    Very interesting article and discussion.
    I must protest, though, the rather condescending statement “Scientists, as we all know, are rational beings who believe only in what nature reveals to us…”. In reality, there are many well-regarded and accomplished scientists in many fields who also believe in God. To pretend that they do not exist shows a great disrespect or ignorance.
    The supposed conflict between God and science is only a product of our ignorance and labeling of groups. Please do not paint all believers as non-scientific. Sure, there are some who deny science, but all the ones I know do not.

  • http://www.warrencriswell.com Warren Criswell

    PS. I just received your book “Entanglement” and read your J.B.S. Haldane quote at the beginning: “My own suspicion is that the universe is not only queerer than we suppose, but queerer than we CAN suppose.” That was my point in the above diatribe.

  • http://amirdaczel.com Amir Aczel

    Thanks for all your comments!! Ray, I meant no disrespect to religious scientists. In fact, I spent several years researching the life of one of the most prominent religious scientists of the last century: Pierre Teilhard de Chardin (a devout Jesuit priest); and in my latest book, “Present at the Creation: Discovering the Higgs Boson,” I quote extensively Jacob Bekenstein (of “Bekenstein-Hawking radiation” fame), who is a devout Orthodox Jew who has shed light on cosmology and black holes in particular. Sorry it came out with a wrong implication–absolutely unintended. Thanks again, everyone, for your very thoughtful comments. I need to think now of some more arguments why a “brain alone” is not easier to make than a whole universe…food for thought.

  • Jim Abbott

    Amir:
    In the late 60’s I was working in the Physics Dept. at UCLA setting up demonstrations for the lecturer and running short films to illustrate this and that of physics. I remember a short film illustrating Brownian motion. An air table with oscillating wire sides contained about a dozen pucks painted white and another dozen painted black. They were on separate sides of the table. The air was turned on and the wires set in motion. As expected, the pucks began to bounce around off the walls and also off of each other. After less than a minute the whole table was evenly mixed with black and white bouncing pucks. Then all of a sudden out of all that randomness, the black and white pucks migrated back to separate sides. The film stopped the action for a couple of seconds and the title came up, “The chance of this happening again in this is very nearly zero or less than a bunch of monkeys typing Hamlet.” At least I got to see entropy reverse to order and then revert to entropy. The film was produced by Encyclopedia Britainica. I don’t they they would stoop to trickery.

    I very much enjoyed your article even though it took most of a day to get my mind around it. Thanks, i rmn & etc…

    Jim Abbott

  • http://www.lyudmilantonov.blogspot.com Lyudmil Antonov

    Although the conclusion is right: the probability that Boltzman brains arise by chance alone is zero, the author only skims the surface and does not prove rigorously why it is so.
    The monkeys-type-Hamlet example is usually given in connection with the (second) Borel-Cantelli lemma which states:

    Let (Omega,A, P) be a probability space, and { An}n≥1 a sequence of events.
    (a) If Sum∞:n=1 P( An) converges, then P(lim sup An) = 0.
    (b) If the events An are independent and Sum∞n=1 P( An) diverges (i.e., Sum∞n=1 P( An)=∞), then P(lim sup An) = 1.

    We see that for condition b) (the second lemma) to be fulfilled, not only the sum of probabilities must diverge, but the events must be independent which clearly is not the case.

  • caywen

    I’m not sure I understand the author’s argument. I’m reading that the probability is just about 0, which is basically 0? I thought 0 is 0, and everything else is not.

    The only 0-probability thing I can think of is one of a logical contradictive scenario. I’m not getting where the contradiction of a spontaneous formation of a large piece of matter is.

  • bax

    emerging properties! these come right from bolztmann’s theory and ultimately can rationally explain order and thereby the brain.

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The Crux

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About Amir Aczel

Amir D. Aczel studied mathematics and physics at the University of California at Berkeley, where he was fortunate to meet quantum pioneer Werner Heisenberg. He also holds a Ph.D. in mathematical statistics. Aczel is a Guggenheim Fellow, a Sloan Foundation Fellow, and was a visiting scholar at Harvard in 2005-2007. He is the author of 18 critically acclaimed books on mathematics and science, several of which have been international bestsellers, including Fermat's Last Theorem, which was nominated for a Los Angeles Times Book Award in 1996 and translated into 31 languages. In his latest book, "Why Science Does Not Disprove God," Aczel takes issue with cosmologist Lawrence M. Krauss's theory that the universe emerged out of sheer "nothingness," countering the arguments using results from physics, cosmology, and the abstract mathematics of set theory.

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