Human minds are the mother of all interesting things since anything that we might consider interesting is so because our minds make us believe so. Seems then reasonable that all kind of philosophical issues and scientific problems cannot be properly addressed unless we correctly understand how our minds work, but what we know about how they work?
Cognitive Science offers many theories on how any mind might work, but when it comes to our minds there seem to be evidences put forward by psychologists that, whatever the way they work, human minds do not abide to the laws of probabilities.
Several attempts have been made to explain these results, and one of the latest comes from the hand of Quantum Mechanics… No kidding.
So when I saw this valiant attempt from theoretical physicists to explain how the human mind works by using their all mighty and powerful Quantum Hammer, I thought it was a good moment to explain an alternative solution that I myself worked out long, long ago, after being exposed to this problem by philosopher Paul Thagard in his excellent book MIND.
Also, Sister Hot is my assistant and I need her to prove my point which is that our minds might abide to probability laws more than we think after all. If you want to know how she is going to assist me you need to keep reading; probability can be sexy 😉
Long ago I took a course in Cognitive Science and we were asked to buy the excellent book MIND from philosopher Paul Thagard. The book explores several approaches that attempt to explain how the human mind works, and in the Chapter 2 (pag. 38) dedicated to Logic we can read:
Just as Johnson-Laird has challenged the relevance of formal logic to human deductive reasoning, psychologists have done experiments that suggests that human inductive reasoning may not have much to do with probability theory.
As an example of evidences on why this might be so Paul Thagard continues:
Tversky and Kahneman (1983), for example, have shown that people sometimes violate the rule that the probability of a conjunction will also be less or equal to the probability of one of its conjuncts, P(p & q) ≤ P(p).
There are many examples to illustrate this, but I will give here a conspicuous one for clarity purposes. Imagine we ask people to compare probabilities, and we ask them about the probability of becoming a nun vs. the probability of becoming a nun AND a prostitute. Most people, even not religious ones, will say
P(becoming a Nun AND a Prostitute) < P(becoming a Nun)
And this is correct. Now imagine again we ask people about the probability of becoming a porn star vs. the probability of becoming a porn star AND a prostitute. Now, experiments seems to show that most people will say
P(becoming a Porn Star AND a Prostitute) > P(becoming a Porn Star)
And probability theory say this is wrong. So what is going on here? Do we need Quantum Mechanics, or even more complex formulations, to explain this phenomenon? I don’t really think so. This seems to me a clear case showing that for those that only have a hammer everything looks like a nail, but I don’t really blame the theoretical physicists for using their fancy hammer since we all are guilty of having our personal toolbox to deal with problems, and just like theoretical physicists have their toolbox, so do I have mine.
My Occam’s Hammer
I once read there was this French politician whose name I don’t remember (or maybe I never knew) who said something like “I am against referendums because French people never answer to the questions they are asked to”, and I believe this is exactly what is going on here.
When we are asked about P(becoming a Porn Star) our minds actually respond to the question P(becoming JUST a Porn Star), so what we are actually saying is:
P(Porn Star AND Prostitute) > P( Porn Star AND NOT a Prostitute)
And guess what… This is statistically absolutely TRUE! So there, that’s it, no Quantum Probability needed. If this is the reason for human bias when given these statistically unsound answers, the experiments published by physiologists would prove humans guilty of misunderstanding questions, but they say nothing against our abilities to asses probabilities.
I can understand why physicists would overlook this cognitive bias but I am surprised that psychologists did too. Maybe once you have an interesting result you are too excited to fool prove it? Maybe I am doing that myself right now? But I truly believe my explanation is way more reasonable than going Quantum and, among equally plausible explanations, I just go Occam.
Now, this alternative explanation is not proof that our minds are mathematically sound statistical machines since, unfortunately, we are subject to a whole fauna of cognitive biases and a number of these might lead us into wrongly estimating the probabilities of an event, but it shows that before going Nuclear (Physics) on a problem maybe we want to try some homey common sense.
Mr. Corey kindly pointed me to this post in lesswrong where it seems that Tversky and Kahneman knock down the interpretation I gave above about their results with another experiment which tries to make sure students interpreting the experimental instructions in an unexpected way is not the reason for the bias. Let’s see if that is truly so, this is the experiment:
Consider a regular six-sided die with four green faces and two red faces. The die will be rolled 20 times and the sequences of greens (G) and reds (R) will be recorded. You are asked to select one sequence, from a set of three, and you will win $25 if the sequence you chose appears on successive rolls of the die. Please check the sequence of greens and reds on which you prefer to bet.
The question never mentions the word “probable” so that students construct whatever solution they want without having to think what the researchers mean by “probable”. Okay, fair enough.
It turns out that 65% of the students gave the wrong answer (option two). So, do I need to eat my words and go Quantum? Or maybe is it possible that a tiny change in how the question is interpreted alters the results? Well, let’s do a tiny change and see what happens:
Consider a regular six-sided die with four green faces and two red faces. The die will be rolled
20 times and the set of greens (G) and reds (R) will be recorded. You are asked to select one set, from a set of three, and you will win $25 if the set you chose appears on successive rolls of the die. Please check the set of greens and reds on which you prefer to bet.
So now we have one set of five tosses and two sets of six tosses, let’s calculate which set among these is more likely to appear:
Oh well, look at that, now the option chosen by 65% of people is twice as likely as the “right” one! So what now? Do we go Quantum? I don’t think so, we still go Occam.
All these experiments trying to prove we humans suck big time at assessing probabilities introduce “poisoned candies” to lure the subjects of the experiment into the wrong answer, but what are they exactly proving? That we can be fooled? A skilled magician can turn the smartest person in the world into a sucker using all kind of deception tricks.
What psychologists are doing reminds me to those fortune tellers that they do not only fool their customers but themselves; their tricks bites them back. If we use “poisoned candies” in these experiments we are incurring in confirmation bias.
If psychologists truly want to prove we humans hugely miscalculate probabilities then they need to figure out experiments with no poisoned candies, that is, with options where no alternative probabilistic explanation makes right the “wrong” answer, but my feeling is that if they do so this huge effect they claim will disappear.
- Brain Wars Review (whatsinabrain.wordpress.com)
- Abhorrent conduct and the human mind (contrerasfabian.wordpress.com)
- Is Mind a Fluke of Nature? (santitafarella.wordpress.com)
- Can science and philosophy mix constructively? (thehindu.com)
- Quantum parallelism and scientific realism (oup.com)
- Does quantum uncertainty have a place in everyday applied statistics? (andrewgelman.com)
- NASA Google Quantum Computer: The World’s Most Expensive Computer Thinks Like a Human (policymic.com)
- The New Synthesis in Cognitive Science (psychologytoday.com)
- the operation of the human mind (tleducation.wordpress.com)