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I found a paper by Diederik Aerts about composite concepts recognition which in spite of the mouthful of the title (General Quantum Modeling of Combining Concepts: A Quantum Field Model in Fock Space) hints at a very simple and always overlooked fact: We do not use any "obvious" logic in our actual appraisal of category membership.

Following several previous papers of his own about the use of quantum logic instead of classical (boolean) logic this one sum up the whole of his ideas on the matter and demonstrates a stunning adequacy to experimental results from cognitive psychologist James Hampton.

To quickly highlight the main point, it amounts to have the concepts somehow warp their "expected" combination (conjunctive or disjunctive) depending on the instance member to be tested for.
To this purpose Diederik Aerts deploys the full gear of Quantum Field Theory with excellent results, however...
Beside being quite an overkill this monstrous apparatus is still in need of a little help from the experimenter in the form of "appropriately choosen" quantum angles which parametrize the sought for quantum interferences.
With such finely hand tuned values Aerts quantum model of concepts combination gets an astounding zero discrepancy with respect to almost all experimental measurements of human responses.

Not only is it highly suspicious to have a "perfect match" with psychological experiments necessarily subject to measurement errors but, alas, a few unruly sample cases refuse to bow to the quantum model dictums no matter the choice of the "quantum angles", what a pity!

This otherwise outstanding piece of work suffers from a common disease, trying to forcefully shoehorn the reality into a whimsical model instead of trying to unravel more cogent causes for the observations.
From both the succesful cases (even if a bit cheated) and the failing ones it should be obvious that:

Whenever concepts are combined in a composite query they interact in intricate "non classical" ways.
Quantum logic as such isn't the perfect match to model this interaction.

Why the heck would it have to be?
Like the Platonic Solids were to match the planets orbits?

That was by itself an excellent enlightening exercise in new concepts formation, but now would somebody please give us the actual model of concepts interactions which show up in Hampton's experiments?

Submitted by Kevembuangga [/html]

KevembuanggaonThursday 06 November 2008 - 19:42:35

comment: 3

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Aleks @ 22 Nov : 22:38
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Jean-Luc, I've looked at previous Aerts' papers, and liked them... But I wonder, given the abundant work applying Bayesian statistics to this issue (see http://web.mit.edu/cocosci/josh.html - he appears to be the centroid), can Aerts do something that Bayesian probability can't?

Kevembuangga @ 23 Nov : 07:02
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can Aerts do something that Bayesian probability can't?

Most certainly, even if inadvertently (

) , Aerts work exposes the inadequacy of common (mis)conceptions about semantics which bayesian statistics are happily sharing.
The "problem" isn't where it appears to be (more accurate or refined predictions) but in the inherent vagueness of human made concepts which we nevertheless manage to make good use of even in mathematics.

What is a "beautiful" or "interesting" theorem?
Yet, all mathematicians rely on such clues for their daily work.
Whenever we will be able to formalize the transition from "interesting bits of knowledge" toward formal proofs or programs, that will be it (AI...)

[ edited 23 Nov : 07:11 ]

Caledonian @ 25 Apr : 18:26
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"What is a "beautiful" or "interesting" theorem?"

Have you read Wolfram's A New Kind of Science? Among other things, he discusses what properties of theorems seem to be associated with our judgments of "being interesting" or "usefulness" in the context of logical operations.

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