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The logical conclusion is not what you say, but that 36% would not want to play again when they ARE told their first result.

Felicity - I'm glad you started that by stating you aren't a logic expert as you would have come across a bit foolish otherwise!

It says, "Next, you ask if these objects belong to the combined category 'home furnishings or furniture'." So it's a new question. If the people can't get out of the rut of the answering the first question, then it does show that they are not logical. I don't think the researchers are to blame.

Two comments here.

Programming computers to reproduce reasoning patterns that are a little vague is exactly what we've been trying to do, with considerable success. If we say "computers can't be intuitive", then we have to start restricting the definition of intuitive to keep up with technological progress, which seems like the tail wagging the dog to me.

I agree that probability rules in many cases, but not all probability is classical in the sense of the Kolmogorov axioms. Andrei Khrennikov's recent book "Ubiquitous Quantum Structure" gives an excellent introduction on this topic.

If we restate one of the experiments we may notice an alternative explanation.

Instead of saying that players weren't told the result of the first game we might say that players were given a choice between one game or two from the outset.

One game has a worst-case outcome of losing $100 and best case of gaining $200. Two games has a worst-case outcome of losing $200 and a best case of gaining $400.

Thus, choosing to play only one game protects you against the possibility of losing $200.

This is the same logic as somebody who buys one lottery ticket when he has enough money in his wallet to buy two. He's prepared to make a small loss but wants to keep enough money for the bus fare home.

Absolutely right. The Busemeyer et al paper, "A Quantum Theoretical Explanation for Probability Judgment Errors" is probably the best exploration to date that shows how accurate the vector space projections are for predicting the observed outcomes.

http://mypage.iu.edu/~jbusemey/quantum/PJudge6.pdf

As a differential geometer by training I think of quantum mechanics as entirely linear, but I see what you mean by non-linear in this case!

The words 'emperor', 'new', and 'clothes' spring to mind. How a very simple abstract mathematical structure will explain human thinking, as opposed to an explanation based on neurophysiology, psychology, and sociology is beyond me. On the other hand, such a simple-minded notion can very easily generate a research fashion bubble full of papers, conferences, hot air, and researchers either too shallow-thinking or too unprincipled to resist the temptation of joining in. This article is far too naive and uncritical to point this out, of course

Congratulations for the many interesting comments. I add some reflections that respond to different aspects mentioned in the comments. Most of all with respect to the question 'why exactly using quantum structures (logic, probability) to model human reasoning?', because this is indeed one of the intriguing questions that immediately pop up. Dominic Widdows reacted already in part to it, hence what follows is complementary to his reactions. Let me first tell you that in the first phases of this investigation my thoughts where that the specific quantum formalism would only play a limited role in all this, and most of all we needed to look for general non-Kolmogorovian and non-Boolean structures to model human thought. In the course of the investigations however at different times I was stumbled by the sheer power of the quantum formalism itself to model human thought, hence now I do believe that something deeper is touched upon than merely coping with non-Kolmogorovian and non-Boolean structures.

- Quantum theory is in some way a double layer mathematical theory. Calculations are done on the deeper layer of a complex vectors space, and then at the end of the calculation when contact is made with experiment, the deeper layer is squared (by taking literally the square of the absolute value of the complex numbers involved) to give rise to probabilities that can be compared with relative frequencies of outcomes of experiments. But not only calculations are done on this deeper underlying mathematical layer, for example, also when two or more systems are combined, this combining is done on the deeper layer, and this is what gives rise to the existence of the weird quantum phenomenon of entanglement. Recently we have proved that exactly this same entanglement exists when in human reasoning (very simple) concepts are combined (see: http://arxiv.org/abs/1104.1322), which shows that 'the deep layer is also present in human reasoning'. In fact, before finding the explicit appearance of entanglement there were other signs in this direction, and in http://uk.arxiv.org/abs/0810.5332 an attempt is made to describe what we have called 'the quantum conceptual mode of human thought', which resembles in some sense intuitive thought. A technically more difficult article goes further into this (http://uk.arxiv.org/abs/0805.3850). Hence, at the actual stage of investigation, I do believe that more than just capturing the fuzziness of human thought is at stake. If this is true, it means that the Quantum Cognition approach to model human thought is definitely more powerful than, for example, the fuzzy set approach (with fuzzy logics), which indeed only captures the fuzzy aspect of human thought.

- A second possible reason, for me personally as a physicist at least, of why the quantum formalism works well in modeling human thought, is much more speculative, but worth mentioning. This second reason is not investigated within the Quantum Cognition community, since its focus is not on 'cognition' but on 'quantum physics' itself. So I work on it as a quantum physicist, alone at the moment (its too speculative still to engage young researchers in it at this stage), and mostly in elaborating a new type of interpretation of quantum theory itself. In this new interpretation quantum particles are seen as conceptual entities carrying conceptual information. This investigation is at this moment in a purely explorative phase, and for those interested there are three published articles (http://uk.arxiv.org/abs/1004.2530, http://uk.arxiv.org/abs/1004.2531, http://uk.arxiv.org/abs/1005.3767). If this new interpretation is true, it would mean that the quantum formalism works so well to model human thought, "because" also microphysics quantum dynamics is a conceptual interaction process. Hence, the mathematics of the deep structure of a cognitive process would appear in both cases naturally.

I absolutely agree. One clear (classical!) fallacy to avoid is the deduction "quantum is not classical, this thing is not classical, therefore it's quantum". Even when we're careful to avoid this. our measurable experimental results so far only really say that in some cases, an obviously quantum-like model is faster and more effective than Boolean / Kolmogorovian models. Which doesn't say that the quantum-like model is uniquely the best, just that it may be pointing us in the right direction.

I do agree that most practical measuring impossibilities boil down to contraints on resources. Quantum theory does pose limits on measurability, but in most practical cases in (say) linguistics we run into unmeasurable quantities long before for a host of other reasons.

Thanks for the links as well. Much to ponder.

For you, probability and complimentarity seem key. The Bohr account of complimentarity does not seem to contradict classical logic. My issue is with the implicit neo-Bayesian dogma together with a confusion between logic referring to reason and logic referring to computation. Criticise classical computation by all means (I do it all the time) but do not (inadvertently) disparage the key to good reasoning. (First sentance of article!) Comments welcome on my blog.

That test if flawed from the start:

If you're asked to put yellow in one of two groups, "white" or "black", you'd probably put on "white". " 2 choices, you choose the best one...

After, if you're asked to put yellow in the "Black or White" or in "Other", you'd probably choose "Other".

This are independent tests, the only thing in common are the names.

Also, a tall chihuahua is still a tall dog, like a fat chihuahua is a fat dog independently of the average size or mass of a particular dog race.

What matters is the apparent proportion of all the body, compared to an initial idea of what a (general) dog should be.

Michael, you've misread the article. It doesn't say that Furniture is a larger category than Home Furnishings. It says:

quote

Next, you ask if these objects belong to the combined category "home furnishings or furniture". Obviously, if "ashtray" or "painting" belongs in home furnishings, then it certainly belongs in the bigger, more inclusive combined category too.

unquote

Good question. I don't think there's a clear answer yet, partly because it's not clear what kind of classical logic develops in living creatures and what it's used for. For example, in today's terms Boolean logic is based most clearly on logical connectives, while Aristotelean logic is based most clearly on quantifiers, which makes computational implementations quite different. Such considerations are more on the "artificial" side of "artificial intelligence", but it certainly affects what sorts of "intelligence" we can model to date.

Lots of mathematical logic exists independently of any resource-bound implementation, whereas living creatures are always making decisions with finite resources in terms of information, time, and effort available. We don't survive by "proving" that a situation is dangerous, we survive be making a snap decision that the situation is probably worth avoiding. The geometric "near enough" approach taken in (say) statistical machine learning may be closer in spirit to what creatures actually do in practice, and this geometric approach has become more embedded in quantum than in classical logic.

Perhaps the best thread of research to examine this contrast between mathematical deduction and the reasoning of living creatures is the "New Logic" work of Gabbay and Woods (http://jigpal.oxfordjournals.org/content/9/2/141.short).

I am not sure what you mean by develop. Regress? Keynes argued that classical (numeric) probability is okay under those situations where it makes sense: e.g., a state-based world with fixed transition probabilities. One may also be able to use such classical logic as an approximation if the transition probabilities change slowly or infrequently: one learns and adapts to them. But according to Prigogine (see my blog - from being to becoming) systems such as quantum systems (and perhaps humans) can innovate. If they do this too much then there is selective pressure on other entities to adopt a more appropriate logic (which we are calling quantum). If the situation is too stable there may also be selective pressure to save some brain cells (or whatever) by allowing the ability to reason under uncertainty to atrophy. But I would not call it development

The number who would play again should, by fairly good logic, be between 28 and 100. If the 59 who would play if they lost consists of all 31 who would not play if they won plus 28 of the 69 who would play if they won, then we have 28 who would play in either case and 100 who would play in some case. So if they don't know whether they won or lost, all the 28 should play, and possibly as many as 100.

This is related to the Bonferroni inequalities.