Comments on: The Higgs, Boltzmann Brains, and Monkeys Typing Hamlet

By: Lyudmil Antonov

Lyudmil Antonov — Mon, 19 Nov 2012 14:42:59 +0000

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.

By: Jim Abbott

Jim Abbott — Fri, 16 Nov 2012 03:06:22 +0000

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

By: Amir Aczel

Amir Aczel — Fri, 09 Nov 2012 19:19:56 +0000

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.

By: Warren Criswell

Warren Criswell — Tue, 06 Nov 2012 17:43:36 +0000

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.

By: Ray Montgomery

Ray Montgomery — Mon, 05 Nov 2012 17:19:56 +0000

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.

By: Warren Criswell

Warren Criswell — Mon, 05 Nov 2012 00:31:31 +0000

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

By: Darryl Schmidt

Darryl Schmidt — Sun, 04 Nov 2012 18:28:32 +0000

A fish.

By: tamurphy

tamurphy — Sun, 04 Nov 2012 17:54:43 +0000

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

By: Amir Aczel

Amir Aczel — Sun, 04 Nov 2012 16:46:22 +0000

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

By: tamurphy

tamurphy — Sun, 04 Nov 2012 16:06:33 +0000

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.