Danish lit star Helle Helle, Marianne Faithfull and Jim Al-Khalili on Quantum Biology El Reg bookworm Mark Diston reviews the latest releases from the publishing world. Helle Helle proves a master of understatement while Marianne Faithfull's recollections seem large than life. And talking of life, scientists Jim Al-Khalili and Johnjoe McFadden shed light on the latest thinking on its mysteries. This Should be …
The story moves on to genetics, where one Per-Olov Lowdin is quoted as saying: “The genetic code that makes life possible is inevitably a quantum code.”
Evidently not. You can write the code down on paper, then reconstruct the molecule from scratch. So it's a classical code.
It is suggested a tad unscientifically that: “Quantum weirdness could be playing a role in the mutations that drive evolution.”
I recommend Greg Egan's "Teranesia" for an exploration of that kind of idea. It's unlikely though. High parallelism and random feelers through the search space are good enough. Moreover, one would need to find out what function releated to "driving evolution" would be computed more efficiently via a quantum computer than via bog-standard classical one. Things always go south once has to get the classical bits out of the quantum system, with additional randomness introduced. The complexity BQP is well-defined nowadays, have at it!
The book goes on to describe the work of Roger Penrose, who theorised that the human mind is a quantum computer.
Not that shot again. Penrose also things we think by logical deduction and that Gödel's incompleteness theorem somehow applies. Please!
“Perhaps death represents the severing of the living organism’s connection with the orderly quantum realm, leaving it powerless to resist the randomising forces of thermodynamics.”
What the hell am I even reading? Death represents the randomization of large hierarchy of processes that were going off the rails a bit before death. As for the "quantum realm" (what is that?) being "orderly", I think a famous cat, possibly gassed, has something to say about that.
You misrepresent Penrose's argument. He certainly doesn't claim that we 'think by logical deduction' (although obviously we can), quite the opposite. He points out that if (as some strong AI proponents claim) the mind is simply an algorithmic process, equivalent to a Turing machine, it would be impossible for us to understand Gödel's incompleteness theorem, which we (some of us, anyway) clearly do. Therefore, the mind cannot be completely equivalent to an algorithm, no matter how complex.
He speculates that some type of quantum process could be involved, though he freely admits that he can't demonstrate a physical mechanism that would operate at body temperature ('more research is needed into this topic') - perhaps the work examined by the authors is taking us closer to establishing the feasibility of such a process.
it would be impossible for us to understand Gödel's incompleteness theorem
I will cite directly from Jimbo's bag of stuff:
The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an "effective procedure" (e.g., a computer program, but it could be any sort of algorithm) is capable of proving all truths about the relations of the natural numbers (arithmetic). For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that such a system cannot demonstrate its own consistency.
Part 1) Axiomatic system cannot actually prove all theorems in natural number theory. Note that in real mathematics, we are not encountering many of those for some reason and the one Gödel provided had a self-referential relationship, and it can evidently be proved OUTSIDE of the given axiomatic system.
No minds are involved unless minds are theorem provers working on number theory described by first-order-logic only. Which ain't the case.
Part 2) The second incompleteness theorem, an extension of the first, shows that such a system cannot demonstrate its own consistency.
Consistency of axiomatic systems is not a great concern of the real world. And consistency can be proved outside of the system. See also: Gentzen's consistency proof.
That argument was just Hollywood-level bad and pop science from the get-go. Let it rest.
You need to face up to the fact that Sir Roger Penrose may be slightly cleverer than you are (he's certainly cleverer than I am, but some may consider that to be not much of a hurdle). He isn't challenging the truth of Gödel's theorem or claiming that it somehow undermines all of mathematics. He's just pointing out that the fact that we can understand it (and, specifically, see that Gödel statements must be true, even though they can't be proved algortihmically) contradicts any claim that human intelligence is ultimately derived from algorithmic computation.
As you're familiar with Gentzen's theorem, you may well be aware of the related theorem due to Goodstein (1944), which was proved by showing it to be equivalent to a Gödel statement in higher order arithmetic. (I've pinched this from Penrose's The Large, the Small and the Human Mind.)
Sir Roger Penrose may be extremely clever but I suspect he is answering the wrong question. I think I'll wait till the psychologists and the neurologists explain how the brain works in detail, because I'm not sure I fully understand what "derived from algorithmic computation" means in this context, whereas philosophy of science 101 explains quite clearly that we cannot construct a model of the world without induction as well as deduction - and we have no idea of how induction works at the neurone level.
"...Gödel statements must be true, even though they can't be proved algortihmically."
It depends on what you mean by 'algorithmically'. Any set of logical operations to input data can be translated as an algorithm. Same thing regarding logical tests and philosophical arguments like 'reductio ad absurdum'. What is exactly the part of the process a machine can't perform?.
I can understand K.Gödel using such a limited definition for algorithm, as IT was an emerging field back then, but this argument seems to have aged poorly.
What Gödel is saying (oversimplifying horrendously) is that for any* system of logic and a finite set of axioms, there will always be true statements that cannot be 'proved' using only the rules of the system. Of course, you can trivially program a computer to print "Gödel's theorem is true" (just as you can to print 'Hello world') but you can't program the computer to justify that statement.
Turing (and independently, earlier, Church) proved the Church-Turing Theorem on computable numbers. He used a version of Cantor's diagonal argument to demonstrate the ultimate limitations of a 'Turing machine' (a purely theoretical construct he invented for this purpose). If you haven't already, I recommend reading "Gödel, Escher. Bach" by Hofstadter - an astonishing book.
* sufficiently complex - i.e. powerful enough to encompass standard arithmetic
I have several issues with that reasoning. The biggest one is that, even if a 'brain' can't be directly programmed, it can be simulated. Given enough processing power and enough knowledge about the way brains work, a human brain could be simulated, loaded with a set of -probably synthetic- memories and knowledge, and put to work on this kind of problems, and solve them. Even if we lack the technology necessary for this, it still works as a thought experiment.
Claiming that humans can solve a kind of logical problems that no computer can ever solve is, in my opinion, the same as saying that there is some 'magical sauce' in the human brain that prevents it from being understood.
Evidence of souls, Midiclorians or similar entities is really scarce, so there must be some other factor at play.
You know, I've always wondered if Turing's works would be different had he known the concept of 'fractal dimensions' from chaos theory.
You must accept (because the mathematics is watertight and getting on for a century old) that there are fundamental limits to what a computer (Turing machine) can do. If the human mind is capable of such things, then it can't be simulated on a computer, no matter how powerful and how clever the programmer. It might (pure speculation) be possible to emulate the mind on a quantum computer, which is not subject to the same limitations.
Penrose has explicitly said that he is not claiming that there must be something non-physical about human consciousness. He accepts that it may one day be possible to emulate the human mind with a machine - but it is not possible to do it with a Turing machine, something more powerful would be needed.
Rather than try to remember Alt+0246, I just type Godel into Google (other search engines are available, apparently), which corrects it to Gödel, which I can then paste into the edit box. If you use Chrome (other browsers, blah, blah) it autocorrects to the correct spelling - same with Düsseldorf.
That's what I mean by fiddly. A little unobtrusive half-size umlaut key for those occasions would be the thing. I've got a pause/break key - never use that, or the scrl/lck, or the mail button, or the web home button. Lot of junk on keyboards could be replaced by an umlaut. I bet the Germans have special umlaut keys. I bet even the Austrians have them eh ?
"Note that in real mathematics, we are not encountering many of those for some reason and the one Gödel provided had a self-referential relationship, and it can evidently be proved OUTSIDE of the given axiomatic system."
This is precisely the problem that non-mathematicians have trying to understand something incredibly subtle like completeness and consistency of axiomatic systems.
Gödel's theorem essentially states that in any "useful" system (although there are plenty of useful systems that are not "useful") there are things that you can say about the system that you cannot prove within that system. In particular, the statement "this system is consistent" is one of them.
You can always prove any statement, including "this system is consistent", from outside the system, by creating an axiomatic system, together with the axiom "the previous system is consistent". Well, job's a good 'un. No, of course, because your new system is also "useful", and so cannot itself be proved to be consistent without inventing another system to contain it.
Why doesn't this matter? Once you know there's a certain level of granularity you are not allowed to ask difficult questions about (remind anyone of quantum theory, as an aside?) you stop asking these questions. That's the only reason it's not of concern to the real world: because we know we won't be able to do it.
Why does it matter? Because if you want to start programming computers to do things, one of those things is to check that arguments are sound, and produce automated theorem checkers (like the inappropriately named Coq). Also, if you want to say that the human brain is just a very complicated computer, well, computers have rules they have to follow. In particular, all of our computers are Turing machines; they cannot just bullshit results. So one of two things is true: other humans and I are lying when we say we understand Gödel's theorem; or humans are not Turing machines, so cannot be emulated on a computer. They can be simulated to a high degree of accuracy, for example a third of the time just by looking asleep, but not emulated completely.
"well, computers have rules they have to follow"
Just like human brains. In the case of brains it's a set of biological (genetic, chemical, physical, etc.) rules. Those rules can be 'emulated' or even 'simulated' in a 'normal' computer. The 'entity' resulting from such a simulation should show the same kind of behaviour as a human brain.
"there are things that you can say about the system that you cannot prove within that system. In particular, the statement "this system is consistent" is one of them."
That's true both for human brains and for computers. No human brain can say about itself 'this system is consistent' without lots of external data. Actually, no human KNOWS whether human brains are consistent or not. :-)
"Just like human brains. In the case of brains it's a set of biological (genetic, chemical, physical, etc.) rules. Those rules can be 'emulated' or even 'simulated' in a 'normal' computer. The 'entity' resulting from such a simulation should show the same kind of behaviour as a human brain."
Assertion without proof. If you want to prove that a human brain can be simulated by computer, you have to prove that a human brain is equivalent to one, namely a Turing machine. This isn't some woolly philosophy exercise about complicated algorithms. This is a mathematical statement. In particular, you need to be able to explain how human brains can (allegedly) understand paradoxes, and statements like Goedel's theorems, or how I can consider uncomputable numbers, inaccessible cardinals, the class of all ordinals, non-standard models, etc. All these juicy mathematical constructs that look very bad from the standpoint of Turing machines.
Godel's provability theorem can possibly lead to a test as to whether the mind is quantum, but it is one approach only, and based on nothing but abstract argument.
The 1998 paper from Penrose and Hameroff had some real physical mechanisms and predictions in there*. What I liked best about Penrose is that he starts by acknowledging that the brain "behaves like" a quantum computer, leading to the suspicion that it might be...
I can't possibly do justice to the material starred below, in this post, so I just recommend a look for those interested. I'll leave you with a recent quote from Hameroff
After 20 years of skeptical criticism, "the evidence now clearly supports Orch OR," continue Hameroff and Penrose. "Our new paper updates the evidence, clarifies Orch OR quantum bits, or "qubits," as helical pathways in microtubule lattices, rebuts critics, and reviews 20 testable predictions of Orch OR published in 1998 – of these, six are confirmed and none refuted.
*see http://phys.org/news/2014-01-discovery-quantum-vibrations-microtubules-corroborates.html#jCp
also http://www.quantumconsciousness.org/penrose-hameroff/quantumcomputation.html
I'm not sure it's accurate to say this is the first layman's book on quantum biology. McFadden's earlier book "Quantum Evolution" surely counts (there may be others). That book was a rather fanciful and unscientific exposition, although interesting.
But what's all the fuss about quantum mechanics and biology? Self evidently QM influences biology. Without it atoms and molecules wouldn't be stable (the entire world wouldn't exist). The quantum de-localisation of electrons makes much of chemistry (hence biology) possible. Of course reaction pathways follow the routes that QM allows even when they're classically forbidden: QM was invented to explain the behaviour of atoms after all.
What's more contentious is whether the more "spooky" quantum effects can survive and be observed at a macroscopic scale. McFadden's first book was full of such claims, but little of it convinced me. As this subject advances, it seems to be leaving these wilder claims behind and focusing on more mundane aspects of QM that amount to - well, little more than normal chemistry to be honest. If the macroscopic consequences of QM in biology are so remarkable, then so, also are other simple facts, like the existence of solids and liquids, electrical conductivity and countless other phenomena we take for granted.
Penrose's conjecture certainly retains the essence of "spooky quantum action" and deserves more study than it's been getting, but apart from that, I say "meh" to quantum biology.
"Scientists were very dubious as to whether these phenomena were active in the “warm and wet” conditions of living cells, but it turns out that on a minute scale, particles within living cells obey the same principals as those in non-living molecules."
This seems to me to be not just a sweeping statement but a wrong statement. Chemical reactions at the molecular level are quantum processes, dependent on stuff like quantized energy levels in electrons and ions. This applies to cell chemistry as much as inorganic chemistry. Another immediately obvious quantum effect is vision, depending on the corpuscular nature of light.
That's an interesting point...
I'm not one to say the brain is a specific way (quantum or classical, logical or random, knowable or unknowable) but I'm not keep to rule out any system as being "classical only" until fully known.
We don't know everything about the brain and it's functions. One thing is for certain, cellular activity is on the atomic scale. Is it on the quantum scale within a cell? As my thoughts are effected by my physical makeup, my cells and their reaction, could it be effected on the quantum level?
Even without, it's hard to copy/read/grab a moving target, and the brain is very much a plastic thing.
Even had the Oxford comma not been omitted, it still would have come across as sounding as though those three people were discussing quantum biology (whatever that is).
I was intrigued, as I'd never heard of Ms. Faithfull being involved in scientific endeavors outside of pharmacology.
Perhaps "Danish lit star Helle Helle, Marianne Faithfull, and Jim Al-Khalili and Johnjoe McFadden on Quantum Biology" would have been slightly less misleading.
" He's just pointing out that the fact that we can understand it (and, specifically, see that Gödel statements must be true, even though they can't be proved algortihmically) contradicts any claim that human intelligence is ultimately derived from algorithmic computation."
Ah, so that's what it's about. Sorry I flogged my Godel book on Amazon now. Got a tenner for it though.
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