I’ve been very busy with practical AI matters over the last 6 months so the following (crazy?) ideas have been parked in a folder. That’s a bit boring, so I thought I’d throw it out there to see what people think…
While working on computing a Cumulative Prospect Theory model of investor behaviour a couple of years ago I came across the work of Pothos and Busemeyer (2009) where they argue that quantum probability provides a better model of human decision making, rather than taking the Prospect Theory type of approach by Kahneman, Tversky and co. That just struck me as quirky at the time: why on earth would humans implement something as exotic as quantum logic/probability? They don’t actually think that the brain is operating in the quantum regime do they, or is it computing the quantum probabilities from essentially classical computations? Surely not? I decided to pass.
Then about a year ago I was reading up on search and classification systems when I came across a book by Dominic Widdows in which he introduces quantum logic (and quantum probability) as a useful generalisation of classical logic for this domain. Still being somewhat averse to things either quantum or logic I was naturally a bit sceptical about the utility of learning more about this. It’s not that I disagree with either of these areas, the problem is that they are huge monsters that don’t seem too relevant to what interests me… and so I save my meagre mental powers for other endeavours. Nevertheless, Widdows provided some interesting arguments for why this idea might deserve a closer look, and somehow I took the bait.
What I discovered is that, while classical logic can be seen as a special limiting case of quantum logic, or conversely that quantum logic is a “softened” classical logic, there is quite a bit more subtlety to it than that. For example, Busemeyer and Trueblood (2009) argue that quantum inference can be seen as a generalisation of Bayesian inference, the two coinciding only when compatible measures are involved and thus we have a single Boolean algebra of events. Busemeyer, Wang and Townsend (2006) argue that this often isn’t the case in intelligent agents when one type of judgement interferes with another. That’s interesting, but what got me even curious was when I found Pitowsky (2003) in which he shows that the rules of rational betting imply all the main features of quantum probability. Surely that can’t just be a quirk? Piotrowski and Sladkowski (2002) even argue that we can use it to provide a solution of Newcomb’s paradox. Is something really going on here?
What really caught my interest, however, was when I picked up the book “A New Approach to Quantum Logic” by Engesser, Gabbay and Lehmann (2007 – if you google a bit there is a mostly complete draft online, but hey, it’s also pretty cheap to by). In this they discuss the dynamic and holistic aspects of quantum logic, roughly, the way in which it can describe partially observable complex systems that evolve over time and that have a kind of strong global consistency guarantee. Moreover, it is non-monotonic, self-referentially sound, complete and has so called No Windows Theorems which imply that it’s, in some sense, a completely self-contained logical entity. As far as the authors are aware, and they are experts in the area so I’ll take their word for it, this is unique.
At least to me this seems like the kind of system you’d want if you were looking for a foundation for a recursively self-improving artificial intelligence. Perhaps it’s not the way to try to build the first human level artificial intelligence, but if you were super intelligent and really knew what you were doing, maybe this is what you should be looking at…
Now let’s step back get really wild for a moment. If quantum probability/logic is the right way to build a fully self-referential and consistent, recursively self-improving super-intelligence, and it’s also the fundamental mathematical structure of the physical world… surely that can’t be a coincidence.
So, got any plans to port AIXI? And then maybe book some time on a D-Wave box…
Could AIXI be converted, or just Solomonoff induction to start with… that’s a good question. I don’t know that answer. There has been some work on quantum algorithmic information theory, but from what Vitanyi told me it doesn’t come out very mathematically clean.
At least to me this seems like the kind of system you’d want if you were looking for a foundation for a recursively self-improving artificial intelligence.
Does Jürgen know about that?
Anyway, that sounds quite interesting but I guess I’m in the same “quircky” state that you were… I’d have liked more details as to what this logic can do that classical bayesianism cannot
But hey, you give the references.
From the sound of it, it seems even more difficult to compute, isn’t it?
My guess would be yes.
If you came to be interested in quantum logic I had a blog post a while a go which contains references to such material: Almost right…
I would trust Diederik Aerts much more than Dominic Widdows on this topic, I have been very disappointed by Widdows’ book “Geometry and Meaning”.
I quite like Widdow’s book… it has it own quirky kind of style. But yes, it only just scratches the surface of the topic. Aerts and Gabora are the people to read.
Let me state my opinion of this stuff: it’s crap. It’ll be bad karma for me, scorning it so unconditionally; but immersing oneself in these ideas about an origin outside of physics for the peculiar features of quantum probability will be intellectually fatal for anyone who actually wants to achieve clarity and understanding regarding quantum mechanics, decision theory, and the nature of probability.
van Rijsbergen’s book, The Geometry of Information Retrieval, is an example of quantum-inspired AI-relevant techniques which is *not* crap, because he’s not trying to *explain* quantum mechanics as due to a particular epistemic situation (this is Aerts’s sin, in particular, but more on that presently). van Rijsbergen is just taking some features of the quantum formalism and employing them to represent interactivity.
So I’m not against people using Hilbert spaces in decision theory, etc. Where this stuff goes off the rails is in the attempt to *explain* the peculiarities of quantum mechanics – complex probability amplitudes, complementary observables. There are at least two ways in which people go wrong here. The first is to say that ‘quantum probability is noncommutative probability theory’, as if that was an explanation, rather than a description. The second is to say that ‘quantum probability’ or ‘noncommutative probability’ is the appropriate form of probability theory to use when you have some form of interactivity or reflexivity in the relationship between observer and observed. Aerts is by the far most prominent advocate of this position, so he must be held most responsible for the existence of this newest way to abuse quantum mechanics.
Where it gets really bad is when people assume the validity of the Aertsian derivation of QM, and then dub other things as ‘quantum’ because they share the (not quantum at all) properties of Aerts’s toy models. Thus we are now hearing about quantum psychology and quantum sociology… All such studies ought to be purged entirely of references to quantum mechanics, and described and re-named in terms of their actual logical and mathematical content. Whatever they’re doing, it’s definitely not quantum mechanics.
In what I’ve seen of Aert’s papers he has never tried to construct an explanation of quantum mechanics. Rather, he’s argued that the mathematics used in quantum mechanics could be applicable to domains outside of physics, in particular the modelling of mental concepts.
However, I haven’t read all of his work, so could you kindly point me to the paper and section where I can find him trying to construct an explanation of quantum mechanics?
Thanks!
Aerts has written dozens of papers on that subject. It’s how he got started.
http://www.vub.ac.be/CLEA/aerts/publications/subject.html
It was only later, having concluded that he had figured out where QM comes from, that he branched out to other subjects like cognitive science, and started talking about “quantum effects” there.
As a cognitive scientist you may not especially care whether this is correct as an explanation of QM, if it is providing you with interesting new perspectives on cognition. But from a physics perspective, Aerts’s explanation of QM is one more bogus approach to the subject in a world already crowded with bogus explanations of QM, and this particular explanation appears to be playing a foundational role in the self-understanding of a new school of thought in psychology and artificial intelligence.
Someone really, really needs to save “Quantum Interaction” from itself, by producing a description of what the field is about and what its signature postulates are, in a language completely purged of references to quantum mechanics and physics in general.
Hm, well, the list of nice features which you give is obviously not enough in itself to really point to a solution for self-improving AI… like Laurent said, it would be nice to hear a more specific description of what it can do that classical Bayes can’t.
Besides that, well… it would be more intuitively appealing to have a story that said “we set up these requirements and… oh look, we get quantum logic!” (starting from independently motivated requirements for a logic for general intelligence).
I believe Bruno Marchal has done some work deriving quantum logic from self-reference considerations, though (similar to the way you can get intuitionistic logic within classical logic when you consider the provability predicate…). So, maybe.