Quantum minds: Why we think like quarks

Quantum minds: Why we think like quarks

Quantum minds: Why we think like quarks
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Read more: "Quantum logic could make better robot bartenders"

The fuzziness and weird logic of the way particles behave applies surprisingly well to how humans think

THE quantum world defies the rules of ordinary logic. Particles routinely occupy two or more places at the same time and don't even have well-defined properties until they are measured. It's all strange, yet true - quantum theory is the most accurate scientific theory ever tested and its mathematics is perfectly suited to the weirdness of the atomic world.

Yet that mathematics actually stands on its own, quite independent of the theory. Indeed, much of it was invented well before quantum theory even existed, notably by German mathematician David Hilbert. Now, it's beginning to look as if it might apply to a lot more than just quantum physics, and quite possibly even to the way people think.

Human thinking, as many of us know, often fails to respect the principles of classical logic. We make systematic errors when reasoning with probabilities, for example. Physicist Diederik Aerts of the Free University of Brussels, Belgium, has shown that these errors actually make sense within a wider logic based on quantum mathematics. The same logic also seems to fit naturally with how people link concepts together, often on the basis of loose associations and blurred boundaries. That means search algorithms based on quantum logic could uncover meanings in masses of text more efficiently than classical algorithms.

It may sound preposterous to imagine that the mathematics of quantum theory has something to say about the nature of human thinking. This is not to say there is anything quantum going on in the brain, only that "quantum" mathematics really isn't owned by physics at all, and turns out to be better than classical mathematics in capturing the fuzzy and flexible ways that humans use ideas. "People often follow a different way of thinking than the one dictated by classical logic," says Aerts. "The mathematics of quantum theory turns out to describe this quite well."

It's a finding that has kicked off a burgeoning field known as "quantum interaction", which explores how quantum theory can be useful in areas having nothing to do with physics, ranging from human language and cognition to biology and economics. And it's already drawing researchers to major conferences.

One thing that distinguishes quantum from classical physics is how probabilities work. Suppose, for example, that you spray some particles towards a screen with two slits in it, and study the results on the wall behind (see diagram). Close slit B, and particles going through A will make a pattern behind it. Close A instead, and a similar pattern will form behind slit B. Keep both A and B open and the pattern you should get - ordinary physics and logic would suggest - should be the sum of these two component patterns.

But the quantum world doesn't obey. When electrons or photons in a beam pass through the two slits, they act as waves and produce an interference pattern on the wall. The pattern with A and B open just isn't the sum of the two patterns with either A or B open alone, but something entirely different - one that varies as light and dark stripes.

Such interference effects lie at the heart of many quantum phenomena, and find a natural description in Hilbert's mathematics. But the phenomenon may go well beyond physics, and one example of this is the violation of what logicians call the "sure thing" principle. This is the idea that if you prefer one action over another in one situation - coffee over tea in situation A, say, when it's before noon - and you prefer the same thing in the opposite situation - coffee over tea in situation B, when it's after noon - then you should have the same preference when you don't know the situation: that is, coffee over tea when you don't know what time it is.

Remarkably, people don't respect this rule. In the early 1990s, for example, psychologists Amos Tversky and Eldar Shafir of Princeton University tested the idea in a simple gambling experiment. Players were told they had an even chance of winning $200 or losing $100, and were then asked to choose whether or not to play the same gamble a second time. When told they had won the first gamble (situation A), 69 per cent of the participants chose to play again. If told they had lost (situation B), only 59 per cent wanted to play again. That's not surprising. But when they were not told the outcome of the first gamble (situation A or B), only 36 per cent wanted to play again.

Classical logic would demand that the third probability equal the average of the first two, yet it doesn't. As in the double slit experiment, the simultaneous presence of two parts, A and B, seems to lead to some kind of weird interference that spoils classical probabilities.

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Comments 1 | 2

Gambling Odds

Fri Sep 02 17:54:11 BST 2011 by Felicity Harper

I'm not a logic expert, but the logic in the gambling experiment seems to stack up completely: 69% wanted to play again when told they had won; 59% wanted to play again when told they had lost; i.e. on average 64% wanted to play again WHEN TOLD THEIR RESULT; logically, and arithmetically, surely, 36% won't want to play again when NOT told their result. Which is what the experiment showed. Maybe some of the fuzziness is in the experimenters' thinking...

Gambling Odds

Sat Sep 03 06:42:59 BST 2011 by Eric Kvaalen

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

Gambling Odds

Mon Sep 05 16:39:05 BST 2011 by mb

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!

Gambling Odds

Tue Sep 06 15:33:38 BST 2011 by Felicity Harper

:-). You're quite right! My thinking went fuzzy!

Skewed Question

Sat Sep 03 11:43:42 BST 2011 by Keith Graham

"Suppose you ask people to put various objects", - "into ONE of two categories".

It seems I am only allowed one category from the question, it should have had asked one OR BOTH categories.

Blame the researchers for that skewed result.

Skewed Question

Sun Sep 04 06:46:26 BST 2011 by Eric Kvaalen

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.

Why Blame Logic?

Sun Sep 04 20:34:19 BST 2011 by Dave Marsay

The first two examples (2-slit experiment and gambling) are both based on conventional probability theory, so one could regard that as flawed rather than classical logic. I discuss a few more candidates on my blog. So why criticise the logic?

Why Blame Logic?

Mon Sep 05 12:30:28 BST 2011 by Joe Blogs

It seems that the article is about attempts to analyse human thinking, and ways of emulating its illogicality, using quantum maths, in machines.

But in humans there is a distinction to be made between intuition and thought, and if that distinction is not made, then thought appears to be more dimensional than its process actually allows. A consequence is that we try to find ways of programming computers for a quality that cannot be a part of computation. Quantum maths may harness some of the possibility that is lost by logic`s probability, but thought works efficiently and the pursuit of efficiency is growth, in which probability rules.


Why Blame Logic?

Mon Sep 05 17:55:55 BST 2011 by Dominic Widdows

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.

Why Blame Logic?

Wed Sep 07 14:16:05 BST 2011 by Mark

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.

Why Blame Logic?

Thu Sep 08 07:24:19 BST 2011 by Eric Kvaalen

It's not the same. In the experiment, they are told that the first game has already been played. They have no choice about that. They can only choose whether to go on to the second game.

This definitely should affect their decision, at least in real life. If someone won the first, then he no longer has to worry about being $200 down -- the options are $100 up or $400 up (if he plays) versus $200 up if he doesn't play.

Why Blame Logic?

Thu Sep 08 09:03:48 BST 2011 by Dave Marsay

Mark, "classical probability" is tied to utility maximisation. A flaw of the article is that it seems to assume that utility=$. As you say, it often is not.

Why Blame Logic?

Mon Sep 05 14:44:07 BST 2011 by Fritz

Just because the response is non-linear doesn't mean it's quantum.

Why Blame Logic?

Tue Sep 06 00:43:31 BST 2011 by Dominic Widdows

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.


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!

Why Blame Logic?

Tue Sep 06 12:35:36 BST 2011 by Illy Whacker

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

Why Blame Logic?

Tue Sep 06 15:10:42 BST 2011 by Dominic Widdows

There is no opposition between mathematics and the other disciplines you mention. You would be similarly mistaken to criticise a search engine for being based on a mathematical model "instead of" electrical engineering. All successful search engines use both.

Mathematics has been the core language of science for some centuries. Exploring this language does not make a scientist "unprincipled".

Why Blame Logic?

Wed Sep 07 06:10:43 BST 2011 by Eric Kvaalen

I somewhat agree with "My Whacker". It's not that we can't use simplified mathematical models to model human thinking, but why should our thinking be based on the mathematics of quantum mechanics of all things? The article doesn't really convince one that that works, it just says that people are not very logical! Even if there is evidence that our thinking really is approximately describable by the mathematics of quantum mechanics, one needs to show why this (very surprising) fact is true.

Why Blame Logic?

Mon Sep 05 14:44:46 BST 2011 by Fritz

Just because the response is non-linear doesn't mean it's quantum.

Why Blame Logic?

Wed Sep 07 20:29:52 BST 2011 by Diederik Aerts

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.

Why Blame Logic?

Thu Sep 08 08:29:56 BST 2011 by Eric Kvaalen

Thank you!

Why Blame Logic?

Mon Sep 05 18:03:57 BST 2011 by Dominic Widdows

One common thread in this field is that classical logic and classical probability are deeply related, as are quantum logic and quantum probability. So you can't really criticise one without the other.

This is using the terms "logic" and "probability" in the modern axiomatised senses, I'm not suggesting that Aristotle and Pascal invented the same disciplines at different times!

Why Blame Logic?

Mon Sep 05 20:31:23 BST 2011 by Ben Goertzel

One thing that's not clear to me is how strongly the results suggest quantum logic/probability in particular, versus just suggesting SOME non-Kolmogorovian uncertainty management and/or SOME non-Boolean logic

If it is quantum logic then, conceptually, it seems the explanation has somehow got to lie in the notion that "quantum logic is what you use when you in principle cannot measure some quantity".... The subtle point is: maybe the impossibility of measurement in some cases could be due to lack of computational resources. I.e., a certain cognitive process C can't get the resources to measure X, so then from C's perspective, X is un-measurable and should be reasoned about using quantum logic. Or something like that ;-) ....

I wrote a blog post touching on these themes a while back... (long URL - click here) .. inspired by Aerts and also papers by Atmanspacher and others...

Why Blame Logic?

Tue Sep 06 00:28:15 BST 2011 by Dominic Widdows

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.

Why Blame Logic?

Thu Sep 08 08:58:27 BST 2011 by Dave Marsay


According to Keynes and Whitehead, "classical" logic is just plain wrong, as shown by the so-called Ellsberg paradox. You may disagree with my criticism of classical probability, but have I managed to criticise probability without criticising logic? (I have also responded to Diederik.)

Why Blame Logic?

Fri Sep 09 10:33:30 BST 2011 by Eric Kvaalen

The Ellsberg paradox doesn't show that classical logic is wrong -- it simply shows that people often don't use logic at all! The "paradox" is simply that people tend to make paradoxical choices when presented with Ellsberg's question.

6 more replies

What's Quantum About Rocks?

Sun Sep 04 21:06:19 BST 2011 by Dave Marsay

The article notes that a conventional 'rock-song' search is not very effective at finding pages about rocks but not rock songs. What one wants is pages that contain the word "rock" but which are not about the topic "songs". The search method described seems a fair approximation to this. What is quantum about it?

What's Quantum About Rocks?

Mon Sep 05 17:45:32 BST 2011 by Dominic Widdows

It's "quantum" because the orthogonal projection on vectors used to model negation in the Infomap and SemanticVectors search engines is the same as the negation / complement operator used in quantum logic. Again, quantum mathematical, I make no claim yet that this is quantum mechanical. See http://www.puttypeg.net/book/chapters/chapter7.html (shameless plug of book but very relevant).

What's Quantum About Rocks?

Thu Sep 08 09:22:39 BST 2011 by Dave Marsay

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.

What's Quantum About Rocks?

Mon Sep 12 14:57:42 BST 2011 by Dominic Widdows

That's interesting. Probability comes from angles in geometric logics, and once orthogonality is defined the other angles follow. (Here I'm quoting Keith Van Risjbergen quoting a passage Von Neumann wrote in 1954). So probability and complimentarity are key for Von Neumann, and I confess I have thought about probability much less deeply.

I don't mean to disparage logic from the classical or the Victorian eras at all, simply to say that they're not always the right tools. As far as I know, Boole himself never made any claim that his algebra should be used to model learning as well as deduction. Personally I tend to avoid describing quantum logic as weird or classical logic as flawed: a screwdriver is not a weird hammer and a hammer is not a flawed screwdriver! But given the intended audience, I think Mark has done an excellent job that requires some tradeoffs, and I think this is part of where we seem to be arguing.

Furniture Categories

Mon Sep 05 13:03:03 BST 2011 by Michael Jenkins

I don't think that Furniture is a larger category than Home Furnishings. All Furniture is a Home Furnishing, but not all Home Furnishings are Furniture.

For example: Curtains. Curtains are Furnishings, but clearly not Furniture. The categories have not been given their correct relationship in this article, to my way of thinking.

Furniture Categories

Mon Sep 05 16:50:47 BST 2011 by Mr. T

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.

Furniture Categories

Tue Sep 06 07:07:40 BST 2011 by Eric Kvaalen

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


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.


Biological Perspective

Tue Sep 06 09:55:12 BST 2011 by Al

The "uncertainty of measurement" point is very relevant from biological perspective, considering that the senses and nervous systems have developed for billions of years to become as good as they are.

Is there a mathematical "threshold" for a quantum logical system to develop classical logic?

Biological Perspective

Tue Sep 06 15:40:23 BST 2011 by Dominic Widdows

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).

Biological Perspective

Tue Sep 06 18:42:52 BST 2011 by Joe Blogs

The sort of intelligence we can model, in principle, depends upon the intelligence of modelling, and not upon what we think about. Thought is a representational system of meaning which works efficiently, not intelligently, by the delegation of authority to methodology. Its main agenda is the growth of the status of representation in understanding, because that is where the efficiency is gained, and that agenda is not included as part of its content.

That is why, although neuroscientists conclude that the self/thinker is illusory, there isn`t a bunch of selfless neuroscientists. That seems to require meditation, which ignores the content of thought but reduces its status in understanding by cultivating stillness. Stillness is conceptually valueless, of course, because conceptuality is process.

Biological Perspective

Thu Sep 08 09:53:47 BST 2011 by Dave Marsay

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

Biological Perspective

Fri Sep 09 09:38:12 BST 2011 by Eric Kvaalen

The sort of "logic" shown in the two examples in the article is not better than classical logic. It's definitely worse!

Biological Perspective

Fri Sep 09 20:03:06 BST 2011 by Dave Marsay

The first example is the one at the top of page 36, involving decisions to take an evens gamble on $200 versus -$100. Elsewhere I have argued that by applying the principle of indifference you get the claimed "logic" of the article. But if we do not then we get an interval that is consistent with the actual experimental results. Why should the principle of indifference apply in this case? How would you convince a cynic?

Biological Perspective

Fri Sep 09 20:13:04 BST 2011 by Dave Marsay

Is the second example about classification? Following Diedriks links I see that people were asked about "typicality" and likelihood not probability. It seems to be common in this sort of experiment to confuse them. This usage certainly confuses me. Maybe people give a logical (my sense) answer to the questions that they honestly think they are being asked. It would be good to see the results of a very clear, unambiguous experiment, clearly reported on. On the other hand, I would not be surprised if people were often poor at answering artificial questions. More interesting (to me) is what they tend to do in realistic situations. Do they do better after being tought "classical" probability theory?

To Be Human Is To Interpret Particel Physics As Quantum

Wed Sep 07 04:54:35 BST 2011 by Michael Brand

I accept the article's premise that the mathematical language of quantum theory is descriptive of human decision-making, and I accept the extension in the final sentence of the article that "to be human is to be quantum" in the sense apparently intended by the author. After reading the article it occurred to me that the reason theoretical physicists have devised quantum mechanics is because it allows us to interpret experimental results in a way that is meaningful to humans. I personally doubt that humans are any more capable of understanding the fundamental forces of nature than a chimpanzee is capable of understanding calculus. The chimpanzee doesn't possess the physiologic mechanisms to process ideas as complex as calculus. I think it is naively anthropocentric to believe that humans possess enough additional cognitive processing power over chimps to understand nature's fundamental forces. I suspect that The Standard Model is not an accurate description of the fundamental forces of nature, but is instead merely our best attempt to give meaning to processes which are actually beyond our comprehension. That is, because we think in a quantum manner, the particle physics experimental results are interpreted to be quantum.

Gambling Odds Revisited

Wed Sep 07 09:01:25 BST 2011 by Felicity

At the risk of looking foolish again, I am still deeply disturbed by the gambling example. Can someone tell me whether classical logic would really say that the probability of people playing again if not told their result would equal the average of the first two results? If, of 100 people, you know that 69 want to play again when they know they have won and 59 want to play again when they know they have lost, you don't know to what extent these two sets overlap - how many of the 69 also wanted to play again when they lost and how many of the 59 also wanted to play again when they won. All you know is that at least 30 people wanted to play again in both circumstances. At the extreme, all the others might fall into 'only wanted to play again if they knew they had won' or 'only wanted to play again if they knew they had lost'. I don't know anything about mathematical logic, but this would surely fall into the erroneous logic of 'all dogs have four legs; my pet has four legs; therefore my pet is a dog' category. I may be looking at this the wrong way, but wouldn't averaging 69 and 59 only work if there were only 69 people, not 100?

Gambling Odds Revisited

Wed Sep 07 13:08:19 BST 2011 by Eric Kvaalen

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.

Gambling Odds Revisited

Thu Sep 08 10:34:02 BST 2011 by Dave Marsay

So the probability of such a player playing again is an imprecise [0.28,1.0]? But a precise answer is required. How about using the principle of indifference to get 0.64? This is the official answer, but somehow unconvincing. I wonder what the "correct" answer is?

Quantum World Is Not Really Weird

Sun Sep 11 15:02:44 BST 2011 by Srinivasa Rao Gonuguntla

An electron is apparently surrounded by a cloud of virtual particles that pop in and out of existence. Virtual particles are particle/ antiparticle pairs (electrons/ positrons) that get created from the vacuum and disappear by annihilating each other.

If this picture is true, the created particle/ antiparticle pairs may not adhere to and behave with sanctity and it is possible that the original electron may get annihilated by one of the virtual positrons created next to it. So the position of the real electron keeps changing in the cloud and we may feel that its exact position is unpredictable. This unpredictability is more to do with our ignorance and not to be considered as a fundamental character of the particle and I will clarify more on this later.

So this electron cloud when shot, is likely to travel through both the slits simultaneously and how much of the cloud goes through each slit depends on the size of the cloud (likely to be infinite), the distance between the slits and the direction it is shot.

When many electrons are shot at once, all will travel in the same way as above but the particle clouds/ virtual particles of different electrons can interact with their neighbors and hence can influence the position of the neighboring real electrons. This influence of particle clouds on one another can result in the interference pattern observed in the two slit experiment.

Quantum World Is Not Really Weird

Sun Sep 11 15:14:50 BST 2011 by Srinivasa Rao Gonuguntla

Imagine that some giant aliens, of the size of our universe and who live longer than this universe, are trying to study humans (much smaller than their Planck length!) whose presence they can barely feel.

For them we may be like virtual particles who just pop in and out of existence from nothing. But they may be able to appreciate the existence of a governor surrounded by a cloud of virtual humans. But they surely get confused and say that this governor is unpredictable like we have been talking about the electron. They probably can not guess that, this man actually keeps changing very often and comes (gets elected) out of the virtual humans, and that the term of/life of each governor is much smaller than the life of the virtual humans.

We know that the election of a governor or president is not a random or an unpredictable event and if any uncertainty exists, that is only because of our inability to read the human minds.

Uncertainty or unpredictability, whether it is in our everyday life or quantum world or cosmology, exists not because Nature is fundamentally endowed with this property, but because of the limitations we as humans have got in understanding the Nature and creation. Luckily we have a way to look beyond our ignorance ie by statistics/probabilities.

Now back to our electron clouds again. If we enlarge the electron cloud and slow down the time sufficiently, we will probably see a similar picture like the human clouds described above.

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