I had to write lots of answers at the Physics Stack Exchange to win the "legendary badge" which I just did – but John Rennie already did so two years ago! ;-)
Meanwhile, Eric Worrall at Anthony Watts' blog told us that Elon Musk is 99.9999999999% certain that he lives in Matrix. His reason? People play 3D games so they must be characters from games, too. Holy cow. Musk has three extra theories that support his picture: all of us will be killed by CO2, all of us will be killed by asteroids, and he is being watched by the extraterrestrial aliens. Clearly, billions of dollars aren't enough for a good psychiatrist in the U.S.
But I want to say something about the ideas that were flowing between Roger Penrose and Scott Aaronson, see Aaronson's blog on it. These men are very smart. Penrose has found lots of deep things in mathematical physics as well as lots of ingeniously playful things in recreational mathematics, among other things. And of course, many of us would love to live at his age, let alone be at least as intellectually capable as Penrose is.
Scott Aaronson wanted to undergo a chemical castration to improve his feminist credentials. He's a nut but he also has the ability to pretend sanity.
In these discussions about Gödel, consciousness, gravity, quantum mechanics, and computation, I think that Aaronson is vastly more often right than Penrose. And some things that Penrose says look really embarrassing.
First, let me begin with the claim in which Penrose is more right. I think that just like your humble correspondent, Penrose says that Gödel's incompleteness theorem (the consistency of a strong enough axiomatic system cannot be proven within the same system) is just a bureaucratic restriction boiling down to the axiomatic system's ban on self-referring contradictions. But you may always use a slightly broader system of tools to think and decide what the answer actually is. In particular, I believe that we do know that the ZF and GB set theory are consistent axiomatic systems. We know that you can't actually construct a proof of a contradiction. I think it's totally plausible that all "natural enough" propositions may be either proven or disproven.
But what about all the other things? Take microtubules, a topic that Penrose's colleague and crazy physician Mr Hameroff is particularly obsessed with. OK, there's some building block of a cell. But why would you repeat this word all the time while pretending that it's something fundamental? Cells and organisms have many other components and emergent structures but all these things are technicalities.
Let us look at five topics identified as Aaronson as points where he disagrees with Penrose.
First, Penrose apparently believes in some kind of creationism (or whatever is supposed to be his alternative explanation) because he thinks that the natural selection would never produce (the skills for) the mathematical reasoning because the mathematical reasoning is useless for the survival. Holy crap. Needless to say, a similar argument against evolution has been used by creationists many times – they just replaced "mathematical reasoning" by another thing that was supposed "not to evolve according to Darwin's theory".
All these complaints are just rubbish.
To be clever enough is damn useful for hunting, agriculture, and other activities that were deciding about the survival for quite some time. You can trick an animal, catch it, and eat it. I hope that I don't have to spend an hour by explanations why a brain might be useful in a practical life. ;-) And once the organisms or humans get clever enough for similar practical purposes, they automatically have the ability to use their brain for goals that aren't clearly linked to survival.
It's just like the coitus and masturbation. Organisms including humans have evolved some building blocks that allow them to participate in the coitus (I am using Sheldon's notation) which is helpful for reproduction. But the same building blocks automatically make masturbation possible, too. While seemingly useless, masturbation may be considered a training for the coitus or anything else. At any rate, it's clearly possible even if it weren't the original goal.
Nature has produced many such seemingly useless things as an unavoidable byproduct of things that are useful. For example, why haven't gays gone extinct? Has Nature produced gays in order to improve the fashion design? No, male gays are an unavoidable consequence of some genes that make their female relatives more fertile. Tons of effects like that – coupling a "useless" and "useful" things into almost inseparable packages – exist in Nature.
So some of the people simply have good enough brains to do mathematics or physics. Sometimes, an upward fluctuation helps. In many cases, the upward fluctuation is simply due to a larger brain.
Second, Penrose says that Gödel's incompleteness is an artificial restriction that can be overcome by working just a little bit outside the formal box. I have already said that I agree with him on this point. I think that Aaronson's counter-arguments are missing the point. The thing that allows us to see whether a Gödel-like proposition is ultimately right or wrong isn't some biological character of our brains or some mysterious animated religious power but simply our will to think outside the box. Smart and especially sufficiently independently thinking computers could do it as well.
Third, Penrose says that the laws of physics may be simulated arbitrarily accurately by a classical Turing machine. Well, he clearly denies the qualitative difference between classical and quantum mechanics here and other things. But I don't really understand why he's saying such things at all so I don't know what I should focus on. While I disagree with Aaronson's "certainty" that \(P\neq NP\), I agree that certain problems are "easier" to solve in some way than other ways. For example, certain problems are easier to solve with quantum computers than classical ones. That's enough to see that the good enough classical algorithms don't simply "simulate" the quantum one. They just work along totally different rules and use different tricks. It's absolutely silly for Penrose and others to try to deny that these two situations – and many other pairs of situations and problems – are completely inequivalent. This Penrose attitude that "all problems are equivalent" means that the speaker is either totally wrong or the statement is meant to be almost totally vacuous. There are lots of equivalences but once you say that "all problems are equivalent", you have clearly gone too far in your quest for unification.
I also agree with Aaronson that the mystery of consciousness – if there is one – has nothing to do with "hardware upgrades" of our brain. The possibly mysterious part is only hiding in the problems that seem strictly separated from all the hardware technicalities. As I said many times, when we explain quantum mechanics and the fundamental role that the observer and his observations play in it, we are not planning to explain some technicalities in the inner workings of the brain. The important thing is that the observer knows the results of some observations. This knowing is a "logical circumstance" which is subjective in character (i.e. not really provable from outside) and independent of the technical details about "how he made himself aware of something" etc. We may perhaps say that the consciousness is mysterious but if we overwhelm this discussion by some technicalities about microtubules or millions of other things, we just won't solve anything.
Fourth, Penrose is simply denying the basic postulates of quantum mechanics while Aaronson isn't. Penrose keeps on talking about things such as the "gravitationally induced collapse of the wave function". I just find this unusually misguided. Take an astronaut. He may vomit in the spaceship because the liquids in his stomach aren't sitting where they should because the Earth's gravity is missing. But otherwise the astronaut clearly lives and works just fine.
What is the effect of gravity? The effect of gravity is just some self-interaction of the brain with itself. Newton's constant \(G\) is about \(6.67\times 10^{-11}\) in SI units, so a kilogram at a meter separation gives forces such as \(10^{-10}\) newtons per whole brain. This is absolutely undetectable and beaten by all the other effects. Because the surface of the brain is comparable to a squared meter, we also have the pressure \(10^{-10}\) pascals and so on. All these pressures are negligible relatively to the surface tension and other things that matter in the brain.
So how could the gravitational force decide about anything that is important? It's clearly parameterically negligible due to the small value of \(G\). If you talk about something that isn't scaling like \(G\), it's not gravity that you're talking about. You shouldn't use this word. You should use a different word for your idea, mostly like "bullšit".
Despite the flawless record of quantum mechanics since its birth in 1925, Penrose expects brutal violations of it at every point. A subset of his crazy attitudes is reflected in his opinions about "quantum gravity". He believes that the term "quantum gravity" is already wrong (this is an idea by which he clashes not only with string theorists but even with subpar scientists such as the loop quantum gravitists) because the task shouldn't be to make gravity compatible with quantum mechanics. Instead, Penrose believes, people should study "gravitized quantum mechanics". Wow. The phrase means that quantum mechanics has to be modified and "bend" to serve the main overlord, gravity, which is known exactly, Penrose implicitly suggests.
Aaronson talks about his being conservative. I am conservative but I wouldn't use conservatism as the main reason why Penrose's views are absolutely wrong. The main reasons why he's wrong were actually found in the recent 60 years or so, relatively recently. We just know that field theories aren't exact. The omission of higher-derivative e.g. \(R^2\) terms in Einstein's equations isn't a deep exact fact or some "beauty". They may be neglected because their coefficients are expected to be small enough not to affect the long-distance experiments much. Einstein's GR is an effective theory. We know that even QED etc. were effective theories. But GR is even "more effective" than QED because it's not even renormalizable. So it must be "as effective as" Fermi's four-fermion interaction. We know that it must be interpreted with a grain of salt. Einstein's simple equations cannot be believed to be exact.
On the other hand, quantum mechanics has to be exact. At the end, its general formalism is just a unique complex generalization of the probability calculus. There's nothing to adjust here. An adjustment means a logical inconsistency. Quantum mechanics requires linearity of the Hilbert space and the operators on it (observables), Hermiticity of observables, unitarity of transformation operators, the collapse into eigenstates, and other things. It makes some things "undeformable" but it also gives us some freedom – what the Hamiltonian, S-matrix, or the "algebra of observables" could be.
That's the freedom that gravity and everything else simply have to use in order to adapt to the general rules of QM. In 2016, to believe that the postulates of quantum mechanics should be deformed to resemble the gravitational image is just utterly unreasonable.
Fifth, Aaronson wants to be conservative in biochemistry and neuroscience. More precisely, he wants to lick the rectum of the "consensus". That's not exactly a deep or correct explanation but the main point is right: Penrose is an amateur in biochemistry and neuroscience and his would-be far-reaching, seemingly technical proposals in those fields are bound to be wrong according to the actual state-of-the-art research in these disciplines. It's little bit like the case of Nathan Myhrvold and asteroids. Myhrvold just doesn't have the same "base of knowledge" that virtually every asteroid expert has. So he is willing to say than the diameter (or radius – he can't quite distinguish the two words) of a particular asteroid is 600 km for some obscure reasons he just decided to trust even though every asteroid expert was taught quite some detailed reasons to be sure that the radius is 20 km, for example.
It may happen than an outsider finds something important but if an outsider decides to build a personal industry of correcting thousands of technical details, you may be sure that almost all of his "corrections" will be wrong. It just doesn't work like that. If you want to be able to do lots of the mundane industry in a field, you simply have to become an expert who is really spending time with it and learns a lot of not really fundamental facts as well. It is not enough to be clever; you have to "live" in that field. I would never claim to be more right than the specialized experts about hundreds of technicalities in a field that I haven't been trained in.
They have touched lots of the memes about Laplace's demons, Boltzmann's brains, multiverse (it was suddenly said that Penrose wants to believe some form of the many world interpretation – this particular would-be philosophy looks like a very different thing than his highly idiosyncratic gravitationally collapsed delusions about QM), but I think that none of the things had the desirable depth to deserve a meaningful reply.
I want to store these numerous topics for more specialized blog posts because Aaronson's hodgepodge looks long but, due to the high number of topics, superficial, too. But generally, it's interesting to see how the human society in general and the scientific community in particular is capable of so much progress even though some of its greatest drivers have so unreasonable views about such a huge majority of topics, including topics that are directly related to the discipline where they have made deep contributions.
Meanwhile, Eric Worrall at Anthony Watts' blog told us that Elon Musk is 99.9999999999% certain that he lives in Matrix. His reason? People play 3D games so they must be characters from games, too. Holy cow. Musk has three extra theories that support his picture: all of us will be killed by CO2, all of us will be killed by asteroids, and he is being watched by the extraterrestrial aliens. Clearly, billions of dollars aren't enough for a good psychiatrist in the U.S.
But I want to say something about the ideas that were flowing between Roger Penrose and Scott Aaronson, see Aaronson's blog on it. These men are very smart. Penrose has found lots of deep things in mathematical physics as well as lots of ingeniously playful things in recreational mathematics, among other things. And of course, many of us would love to live at his age, let alone be at least as intellectually capable as Penrose is.
Scott Aaronson wanted to undergo a chemical castration to improve his feminist credentials. He's a nut but he also has the ability to pretend sanity.
In these discussions about Gödel, consciousness, gravity, quantum mechanics, and computation, I think that Aaronson is vastly more often right than Penrose. And some things that Penrose says look really embarrassing.
First, let me begin with the claim in which Penrose is more right. I think that just like your humble correspondent, Penrose says that Gödel's incompleteness theorem (the consistency of a strong enough axiomatic system cannot be proven within the same system) is just a bureaucratic restriction boiling down to the axiomatic system's ban on self-referring contradictions. But you may always use a slightly broader system of tools to think and decide what the answer actually is. In particular, I believe that we do know that the ZF and GB set theory are consistent axiomatic systems. We know that you can't actually construct a proof of a contradiction. I think it's totally plausible that all "natural enough" propositions may be either proven or disproven.
But what about all the other things? Take microtubules, a topic that Penrose's colleague and crazy physician Mr Hameroff is particularly obsessed with. OK, there's some building block of a cell. But why would you repeat this word all the time while pretending that it's something fundamental? Cells and organisms have many other components and emergent structures but all these things are technicalities.
Let us look at five topics identified as Aaronson as points where he disagrees with Penrose.
First, Penrose apparently believes in some kind of creationism (or whatever is supposed to be his alternative explanation) because he thinks that the natural selection would never produce (the skills for) the mathematical reasoning because the mathematical reasoning is useless for the survival. Holy crap. Needless to say, a similar argument against evolution has been used by creationists many times – they just replaced "mathematical reasoning" by another thing that was supposed "not to evolve according to Darwin's theory".
All these complaints are just rubbish.
To be clever enough is damn useful for hunting, agriculture, and other activities that were deciding about the survival for quite some time. You can trick an animal, catch it, and eat it. I hope that I don't have to spend an hour by explanations why a brain might be useful in a practical life. ;-) And once the organisms or humans get clever enough for similar practical purposes, they automatically have the ability to use their brain for goals that aren't clearly linked to survival.
It's just like the coitus and masturbation. Organisms including humans have evolved some building blocks that allow them to participate in the coitus (I am using Sheldon's notation) which is helpful for reproduction. But the same building blocks automatically make masturbation possible, too. While seemingly useless, masturbation may be considered a training for the coitus or anything else. At any rate, it's clearly possible even if it weren't the original goal.
Nature has produced many such seemingly useless things as an unavoidable byproduct of things that are useful. For example, why haven't gays gone extinct? Has Nature produced gays in order to improve the fashion design? No, male gays are an unavoidable consequence of some genes that make their female relatives more fertile. Tons of effects like that – coupling a "useless" and "useful" things into almost inseparable packages – exist in Nature.
So some of the people simply have good enough brains to do mathematics or physics. Sometimes, an upward fluctuation helps. In many cases, the upward fluctuation is simply due to a larger brain.
Second, Penrose says that Gödel's incompleteness is an artificial restriction that can be overcome by working just a little bit outside the formal box. I have already said that I agree with him on this point. I think that Aaronson's counter-arguments are missing the point. The thing that allows us to see whether a Gödel-like proposition is ultimately right or wrong isn't some biological character of our brains or some mysterious animated religious power but simply our will to think outside the box. Smart and especially sufficiently independently thinking computers could do it as well.
Third, Penrose says that the laws of physics may be simulated arbitrarily accurately by a classical Turing machine. Well, he clearly denies the qualitative difference between classical and quantum mechanics here and other things. But I don't really understand why he's saying such things at all so I don't know what I should focus on. While I disagree with Aaronson's "certainty" that \(P\neq NP\), I agree that certain problems are "easier" to solve in some way than other ways. For example, certain problems are easier to solve with quantum computers than classical ones. That's enough to see that the good enough classical algorithms don't simply "simulate" the quantum one. They just work along totally different rules and use different tricks. It's absolutely silly for Penrose and others to try to deny that these two situations – and many other pairs of situations and problems – are completely inequivalent. This Penrose attitude that "all problems are equivalent" means that the speaker is either totally wrong or the statement is meant to be almost totally vacuous. There are lots of equivalences but once you say that "all problems are equivalent", you have clearly gone too far in your quest for unification.
I also agree with Aaronson that the mystery of consciousness – if there is one – has nothing to do with "hardware upgrades" of our brain. The possibly mysterious part is only hiding in the problems that seem strictly separated from all the hardware technicalities. As I said many times, when we explain quantum mechanics and the fundamental role that the observer and his observations play in it, we are not planning to explain some technicalities in the inner workings of the brain. The important thing is that the observer knows the results of some observations. This knowing is a "logical circumstance" which is subjective in character (i.e. not really provable from outside) and independent of the technical details about "how he made himself aware of something" etc. We may perhaps say that the consciousness is mysterious but if we overwhelm this discussion by some technicalities about microtubules or millions of other things, we just won't solve anything.
Fourth, Penrose is simply denying the basic postulates of quantum mechanics while Aaronson isn't. Penrose keeps on talking about things such as the "gravitationally induced collapse of the wave function". I just find this unusually misguided. Take an astronaut. He may vomit in the spaceship because the liquids in his stomach aren't sitting where they should because the Earth's gravity is missing. But otherwise the astronaut clearly lives and works just fine.
What is the effect of gravity? The effect of gravity is just some self-interaction of the brain with itself. Newton's constant \(G\) is about \(6.67\times 10^{-11}\) in SI units, so a kilogram at a meter separation gives forces such as \(10^{-10}\) newtons per whole brain. This is absolutely undetectable and beaten by all the other effects. Because the surface of the brain is comparable to a squared meter, we also have the pressure \(10^{-10}\) pascals and so on. All these pressures are negligible relatively to the surface tension and other things that matter in the brain.
So how could the gravitational force decide about anything that is important? It's clearly parameterically negligible due to the small value of \(G\). If you talk about something that isn't scaling like \(G\), it's not gravity that you're talking about. You shouldn't use this word. You should use a different word for your idea, mostly like "bullšit".
Despite the flawless record of quantum mechanics since its birth in 1925, Penrose expects brutal violations of it at every point. A subset of his crazy attitudes is reflected in his opinions about "quantum gravity". He believes that the term "quantum gravity" is already wrong (this is an idea by which he clashes not only with string theorists but even with subpar scientists such as the loop quantum gravitists) because the task shouldn't be to make gravity compatible with quantum mechanics. Instead, Penrose believes, people should study "gravitized quantum mechanics". Wow. The phrase means that quantum mechanics has to be modified and "bend" to serve the main overlord, gravity, which is known exactly, Penrose implicitly suggests.
Aaronson talks about his being conservative. I am conservative but I wouldn't use conservatism as the main reason why Penrose's views are absolutely wrong. The main reasons why he's wrong were actually found in the recent 60 years or so, relatively recently. We just know that field theories aren't exact. The omission of higher-derivative e.g. \(R^2\) terms in Einstein's equations isn't a deep exact fact or some "beauty". They may be neglected because their coefficients are expected to be small enough not to affect the long-distance experiments much. Einstein's GR is an effective theory. We know that even QED etc. were effective theories. But GR is even "more effective" than QED because it's not even renormalizable. So it must be "as effective as" Fermi's four-fermion interaction. We know that it must be interpreted with a grain of salt. Einstein's simple equations cannot be believed to be exact.
On the other hand, quantum mechanics has to be exact. At the end, its general formalism is just a unique complex generalization of the probability calculus. There's nothing to adjust here. An adjustment means a logical inconsistency. Quantum mechanics requires linearity of the Hilbert space and the operators on it (observables), Hermiticity of observables, unitarity of transformation operators, the collapse into eigenstates, and other things. It makes some things "undeformable" but it also gives us some freedom – what the Hamiltonian, S-matrix, or the "algebra of observables" could be.
That's the freedom that gravity and everything else simply have to use in order to adapt to the general rules of QM. In 2016, to believe that the postulates of quantum mechanics should be deformed to resemble the gravitational image is just utterly unreasonable.
Fifth, Aaronson wants to be conservative in biochemistry and neuroscience. More precisely, he wants to lick the rectum of the "consensus". That's not exactly a deep or correct explanation but the main point is right: Penrose is an amateur in biochemistry and neuroscience and his would-be far-reaching, seemingly technical proposals in those fields are bound to be wrong according to the actual state-of-the-art research in these disciplines. It's little bit like the case of Nathan Myhrvold and asteroids. Myhrvold just doesn't have the same "base of knowledge" that virtually every asteroid expert has. So he is willing to say than the diameter (or radius – he can't quite distinguish the two words) of a particular asteroid is 600 km for some obscure reasons he just decided to trust even though every asteroid expert was taught quite some detailed reasons to be sure that the radius is 20 km, for example.
It may happen than an outsider finds something important but if an outsider decides to build a personal industry of correcting thousands of technical details, you may be sure that almost all of his "corrections" will be wrong. It just doesn't work like that. If you want to be able to do lots of the mundane industry in a field, you simply have to become an expert who is really spending time with it and learns a lot of not really fundamental facts as well. It is not enough to be clever; you have to "live" in that field. I would never claim to be more right than the specialized experts about hundreds of technicalities in a field that I haven't been trained in.
They have touched lots of the memes about Laplace's demons, Boltzmann's brains, multiverse (it was suddenly said that Penrose wants to believe some form of the many world interpretation – this particular would-be philosophy looks like a very different thing than his highly idiosyncratic gravitationally collapsed delusions about QM), but I think that none of the things had the desirable depth to deserve a meaningful reply.
I want to store these numerous topics for more specialized blog posts because Aaronson's hodgepodge looks long but, due to the high number of topics, superficial, too. But generally, it's interesting to see how the human society in general and the scientific community in particular is capable of so much progress even though some of its greatest drivers have so unreasonable views about such a huge majority of topics, including topics that are directly related to the discipline where they have made deep contributions.
Penrose debates Aaronson
![Penrose debates Aaronson]()
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June 03, 2016
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