When facing a problem with uncertain outcomes, of course, we do not think in probabilistic terms. At least, the vast majority of us don't. However, ideally, we could hope that, whatever our mind does, it would respect basic principles of rationality. On the other hand, at this point, given our failure in simple logic reasoning, it should be no surprise to learn that, when our abilities for uncertain reasoning were tested, it soon became clear that we failed to follow those principles.
Early tests of EUT showed clearly that we do not reason in a way that is compatible with it, if EUT is used as a description. Those results were initially called paradoxes of decision making, namely Allais' and Ellsberg's paradoxes, despite the fact there is nothing paradoxical in them. Both experiments just showed that people sometimes do not obey the principle that choice between two bets should depend only on the aspects where bets are different and not on those where they are equal. This principle is known as Cancellation Principle.
Things might not have been so serious if that were all. But the literature is filled with different examples of mistakes we make and attempts to understand what we actually do. In 1979, Kahneman and Tversky showed that if one assumes we change the probabilities we know to a different value, by using what they called weighting functions, we can still describe our reasoning, at least in the Allais' and Ellsberg's paradoxes, using EUT with those altered probabilities.
Basically, what they observed is that, when we get close to certainties, that is, when the probability of something happening gets close to zero or one, we make decisions as if there were more uncertainty than there really is. This is actually a well observed phenomenon. Per example, people usually make bets on lotteries that shows they consider their chance of winning to be much larger than it really is. For example, if there is just one chance in 50 millions that yu will win $ 10 millions, that means that, in average, you would win 0.20 per bet. But people happily pay more than that to enter such a lottery (actually, if you do think abut utilities, the problem is far more serious since the utility of each dollar decreases as you have more). What Kahneman and Tversk proposed in their Prospect Theory is that people would actually work with a modified probability value. In the lottery example, if you think you chance is actually one in 100,000, instead of one in 50,000,000, it might make sense to pay up to $ 100.00 (if you don't correct for decreasing utility, if you do, the value would be smaller, but it still can be much higher than $ 0.20). The same effect is observed at the other extreme, where there is just a very small chance that something will NOT happen.
It was later shown in newer experiments that Prospect Theory and other options that came later can not fully explain our mistakes. Birnbaum performed a series of experiments where he shows we even disobey a principle called stochastic dominance. Stochastic dominance is basically the simple fact that we should not choose alternatives that are obviously worse in at least one aspect, while equal in all other aspects. One example he tested was a choice between the bets G and G+, given by
G
90% chance to win $96.00
10% chance to win $12.00
G +
90% chance to win $96.00
5% chance to win $14.00
5% chance to win $12.00
Clearly the option G+ is better since it is exactly the same 95% of the time and, in the remaining 5%, it pays $ 2.00 more. That is what it is meant by saying that G+ stochastically dominates G. However, what Birnbaum observed consistently in a number of choices like this is that often people would pick the worse bet!
Monday, December 30, 2013
Saturday, December 21, 2013
Human Stupidity: Historical: Probabilistic thinking I
Probabilistic thinking still refers to reasoning made by just one individual. But, unlike the cases presented above, the reasoning happens about a subject that one can not be certain about. That means there are no absolute true answers, in contrast to the case of the cards, where one can finally convince oneself that some answers are exactly correct and others exactly wrong. This does not mean that there must be no evidence favouring one possibility over another. If you are evaluating if it will rain today, the fast formation of dark clouds in the sky does tell you it is very likely it will rain. But there is still a possibility rain won't come or that it does rain, but somewhere other than where you are. In principle, of course, you might have no probabilities associated with these outcomes. However, as we will discuss when talking about induction and probability, there is no theoretical reason why you couldn't associate subjective probabilities to each outcome. It is an open problem how to do that, but the possibility exists. Therefore, inductive and probabilistic reasoning will be used here as synonyms, except when noted otherwise.
In 1947, von Neumann and Morgenstern published Theory of Games and Economic Behavior
, a book about Expected Utility Theory, EUT. It is worth noting that a lot of confusion can happen here, caused by the not technically correct name of their idea. The problem is that, as a norm, EUT is not actually a theory, in the sense of a well tested set of ideas that describe the world well. Instead, it can be understood as a prescription for correct reasoning, in the same way Aristotelian Logic is. In this sense, its correctness should not be evaluated in comparison with how people think. EUT can, in principle, fail as a theory, as a description of the real world, and yet, be rationally correct. In the book, they laid out the basis for how a rational being should behave in situations of uncertainty. This was done by assuming that, when deciding on a course of action, these rational individuals would be able to assign a probability to each possible future outcome as well as measure how much they value that outcome. Different action choices would influence the world and therefore, the probabilities could be conditional on the choice made.
The classical example gives you the opportunity to choose between two bets. Per example, in bet A, you would receive $100.00 with a chance of 50%, getting nothing the other 50% of the times; bet B, on the other hand gives you $40.00 with certainty. In this case, according to expected utility theory, each individual should assign an utility value to the possible gains. This utility does not need to be a linear function of the monetary value, that is, doubling the money does not necessarily mean double the utility. And it should also depend on your total wealth, since it is obvious that $100.00 would be much more useful to you if you are broke and unemployed than they would be worth if you were a billionaire.
An interesting problem to play with is the St. Petersburg Paradox. Assume you can enter a bet, by paying a fee. In this bet, a coin will be tossed as many times as it takes until it lands as head. If you get head on the first toss, you will get $1.00; if it happens in the second toss, $2.00; each new toss needed to get head doubling the amount of money you get. If you get very lucky and head only happens in the 10th toss, you would actually receive $512.00. How much would you be willing to pay as fee to enter this game? Check your math.
Not many years after von Neumann and Morgenstern, Savage extended EUT to include subjective probabilities in his book The Foundations of Statistics
. Unlike what is usually taught nowadays in most introductory probability courses, probability is not necessarily defined as the proportion of times an event will happen if we made infinite measurements. This definition exists and it is actually called frequentist. But probability can also be defined as an individual degree of belief in the truth of a proposition. This leads us to a probability assessment that is subjective, in the sense that it depends on the data available to each individual and also on the initial probabilities (known as priors) each person choose.
This definition is the one used in Bayesian Statistics (see, for example, the books from Bernardo, Bayesian Theory
or from O'Hagan, Bayesian Inference
) and, despite problems with defining those priors, the Bayesian methods can be shown to respect principles of reasoning in a way that the frequentist definition fails to (a very good introduction to Bayesian methods as a logically sound method can be found in Jaynes' Probability Theory: The Logic of Science
). However, from an operational point of view, Bayesian methods depend on the specification of initial knowledge by means of the prior probability distribution, something we humans do not do well. In order to deal with this type of problem, extensions exist that consider imprecise probabilities, as proposed by Keynes in his
A Treatise on Probability.
In 1947, von Neumann and Morgenstern published Theory of Games and Economic Behavior
, a book about Expected Utility Theory, EUT. It is worth noting that a lot of confusion can happen here, caused by the not technically correct name of their idea. The problem is that, as a norm, EUT is not actually a theory, in the sense of a well tested set of ideas that describe the world well. Instead, it can be understood as a prescription for correct reasoning, in the same way Aristotelian Logic is. In this sense, its correctness should not be evaluated in comparison with how people think. EUT can, in principle, fail as a theory, as a description of the real world, and yet, be rationally correct. In the book, they laid out the basis for how a rational being should behave in situations of uncertainty. This was done by assuming that, when deciding on a course of action, these rational individuals would be able to assign a probability to each possible future outcome as well as measure how much they value that outcome. Different action choices would influence the world and therefore, the probabilities could be conditional on the choice made.The classical example gives you the opportunity to choose between two bets. Per example, in bet A, you would receive $100.00 with a chance of 50%, getting nothing the other 50% of the times; bet B, on the other hand gives you $40.00 with certainty. In this case, according to expected utility theory, each individual should assign an utility value to the possible gains. This utility does not need to be a linear function of the monetary value, that is, doubling the money does not necessarily mean double the utility. And it should also depend on your total wealth, since it is obvious that $100.00 would be much more useful to you if you are broke and unemployed than they would be worth if you were a billionaire.
An interesting problem to play with is the St. Petersburg Paradox. Assume you can enter a bet, by paying a fee. In this bet, a coin will be tossed as many times as it takes until it lands as head. If you get head on the first toss, you will get $1.00; if it happens in the second toss, $2.00; each new toss needed to get head doubling the amount of money you get. If you get very lucky and head only happens in the 10th toss, you would actually receive $512.00. How much would you be willing to pay as fee to enter this game? Check your math.
Not many years after von Neumann and Morgenstern, Savage extended EUT to include subjective probabilities in his book The Foundations of Statistics
. Unlike what is usually taught nowadays in most introductory probability courses, probability is not necessarily defined as the proportion of times an event will happen if we made infinite measurements. This definition exists and it is actually called frequentist. But probability can also be defined as an individual degree of belief in the truth of a proposition. This leads us to a probability assessment that is subjective, in the sense that it depends on the data available to each individual and also on the initial probabilities (known as priors) each person choose.This definition is the one used in Bayesian Statistics (see, for example, the books from Bernardo, Bayesian Theory
or from O'Hagan, Bayesian Inference) and, despite problems with defining those priors, the Bayesian methods can be shown to respect principles of reasoning in a way that the frequentist definition fails to (a very good introduction to Bayesian methods as a logically sound method can be found in Jaynes' Probability Theory: The Logic of Science). However, from an operational point of view, Bayesian methods depend on the specification of initial knowledge by means of the prior probability distribution, something we humans do not do well. In order to deal with this type of problem, extensions exist that consider imprecise probabilities, as proposed by Keynes in his
A Treatise on Probability. Wednesday, December 18, 2013
Season Carols- Alber Einstein is coming to town - Happy Newtonmas (Feliz Newtal)
Albert Einstein is coming to town
(My very obviously slightly altered version from "Santa Claus is coming to town")
You better watch out
You better not cry
Better think right
I'm telling you why
Albert Einstein is coming to town
He's making a list
And checking it twice
Gonna find out who's dumb or bright
Albert Einstein is coming to town
He sees you when you're thinking
He knows when you're a fake
He knows if you've been silly or smart
So be smart for smartness sake!
Oh! You better watch out!
You better not cry
Better think right
I'm telling you why
Albert Einstein is coming to town
Albert Einstein is coming to town
Saturday, December 14, 2013
On Human Stupidity, part III - A Short Historical Perspective b
The literature on how our reasoning is far from optimal is already huge and it keeps growing everyday. I have no intention to even try to be comprehensive here. While the subject is very interesting, ultimately, this whole text of mine is about how we can try to get as close to good answers as possible. Answers about anything and that, of course, means something some people would call scientific method, despite the problems with that name. There are already good introductory texts to the psychological aspects of human reasoning, such as the two I mentioned in the first post of some history on human stupidity (Plous and Baron) and I strongly encourage anyone interested in the matter to read them and others as well as the many papers in dedicated journals and sites. Currently, there is a very nice list of online resources and academic journals at http://www.sjdm.org/links.html.
What I find crucial to understand is how limited we actually are. The examples here are for didatic purposes at educating people on this specific question and do not, by any means, replace the existing literature. As we will discuss later throughout the book and especially in the Chapter "The Real Strength of Science'', it is fundamental to know what the really serious scientific community is discussing. Not because it is correct, scientists who do understand Epistemology well should never actually make truth claims about the real world. But because Science is always the best answer we have at the moment. On a sidenote, I just love this phrase: ``It is therefore a truism, almost a tautology, to say that all magic is necessarily false and barren; for were it ever to become true and fruitful, it would no longer be magic but science'' from James Frazer in the The Golden Bough
.
And, of course, in order to illustrate our known failings, likely to be a characteristic of the Homo Sapiens species, I take to class not just the card problem, but a number of now classical examples of our human stupidity. The second traditional example of the psychological literature I like to present to my students is already based on probability evaluations. This example is now known as the Linda problem. The text I present them is this:
"Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations. Which of the following two alternatives is more probable?
It is obvious after careful inspection that if the second alternative is true, the first must also be. Therefore we can easily prove that the first alternative must be more probable than the second. Equality would be theoretically possible, but it would demand that we are absolutely sure that, if Linda is a bank teller, there is no chance at all she wouldn't be active in the feminist movement. So, despite mentioning probabilities, the answer is known for certain here.
Amazingly, many people get somehow drawn by the word feminist in the second phrase, that seems to fit Linda description better and pick the second alternative. But the question is not if she is more likely to be a feminist or a teller. While the exact reason we do it is not completely clear, for me, there is some amount of evil fun in watching the faces of students realizing they are failing miserably in trivial problems. That their intuition can not be trusted at all. This is a lesson I can only wish they will carry through their lives, allowing them to be much more careful in their reasoning. And, hopefully, better at the decision making and judgement problems they will face in their lives.
Examples of our failure are numerous. And, while this previous example had a certain answer, it does raises the question that, in real life, it is quite common that the best we can hope to achieve in a specific situation is a solid probabilistic assessment of the problem. Which brings us to the question of how we deal with problems where there is uncertainty of some kind. Remember, we already fail where there is certainty to be had. Try to guess how we, as a species, will fare next, when we check what is know about probabilistic reasoning.
#reasoning #biases
What I find crucial to understand is how limited we actually are. The examples here are for didatic purposes at educating people on this specific question and do not, by any means, replace the existing literature. As we will discuss later throughout the book and especially in the Chapter "The Real Strength of Science'', it is fundamental to know what the really serious scientific community is discussing. Not because it is correct, scientists who do understand Epistemology well should never actually make truth claims about the real world. But because Science is always the best answer we have at the moment. On a sidenote, I just love this phrase: ``It is therefore a truism, almost a tautology, to say that all magic is necessarily false and barren; for were it ever to become true and fruitful, it would no longer be magic but science'' from James Frazer in the The Golden Bough
.And, of course, in order to illustrate our known failings, likely to be a characteristic of the Homo Sapiens species, I take to class not just the card problem, but a number of now classical examples of our human stupidity. The second traditional example of the psychological literature I like to present to my students is already based on probability evaluations. This example is now known as the Linda problem. The text I present them is this:
"Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations. Which of the following two alternatives is more probable?
- Linda is a bank teller.
- Linda is a bank teller and active in the feminist movement.'' Tversky and Kahneman, 1983.
It is obvious after careful inspection that if the second alternative is true, the first must also be. Therefore we can easily prove that the first alternative must be more probable than the second. Equality would be theoretically possible, but it would demand that we are absolutely sure that, if Linda is a bank teller, there is no chance at all she wouldn't be active in the feminist movement. So, despite mentioning probabilities, the answer is known for certain here.
Amazingly, many people get somehow drawn by the word feminist in the second phrase, that seems to fit Linda description better and pick the second alternative. But the question is not if she is more likely to be a feminist or a teller. While the exact reason we do it is not completely clear, for me, there is some amount of evil fun in watching the faces of students realizing they are failing miserably in trivial problems. That their intuition can not be trusted at all. This is a lesson I can only wish they will carry through their lives, allowing them to be much more careful in their reasoning. And, hopefully, better at the decision making and judgement problems they will face in their lives.
Examples of our failure are numerous. And, while this previous example had a certain answer, it does raises the question that, in real life, it is quite common that the best we can hope to achieve in a specific situation is a solid probabilistic assessment of the problem. Which brings us to the question of how we deal with problems where there is uncertainty of some kind. Remember, we already fail where there is certainty to be had. Try to guess how we, as a species, will fare next, when we check what is know about probabilistic reasoning.
#reasoning #biases
Card Problem answer (from the Historical Perspective entry)
The correct answer for the card problem is the set of cards "A'' and "5''. Almost everyone gets "A'' correctly. It is indeed quite obviously that if we turn it and find an odd number, the rule was proven wrong. "B'' can not do that, despite some people picking it, simply because nothing was said about what happens when the letter is a consonant. "2'' is a very interesting case. It can provide confirmation, but not proof, to the rule, if we find a vowel at the other side. But if it is a consonant, that means nothing. It is a wonderfully safe check for the rule, since it will not be proven wrong! Hence, a terrible check of the rule, a wrong answer. On the other hand, while "5'' is often neglected, if we find a vowel in the other side, the rule was indeed broken
Thursday, December 12, 2013
Just a simple post while other related things get done
This is almost just a filler.
I am still working on the blog and the texts, but I made a little detour. I just had to learn how the very nice Tufte LaTeX style really works, since the plan is to make a book out of what I write here. I now have the first posts nicely displayed in that style for books. It is more beautiful to look at (sorry, no previews right now, maybe soon) and this should help me write more. Both because I can see it as a book and I am old enough to love books much more than blogs, and for the aesthetic value as well.
More to come on the Historic Perspective soon.
I am still working on the blog and the texts, but I made a little detour. I just had to learn how the very nice Tufte LaTeX style really works, since the plan is to make a book out of what I write here. I now have the first posts nicely displayed in that style for books. It is more beautiful to look at (sorry, no previews right now, maybe soon) and this should help me write more. Both because I can see it as a book and I am old enough to love books much more than blogs, and for the aesthetic value as well.
More to come on the Historic Perspective soon.
Wednesday, November 27, 2013
About USP - Leste (links are in Portuguese)
The links take to two articles in Portuguese. It is about some of the several problems we are facing in our new campus, due, in my opinion, to serious incompetence of a few.
Dois artigos sobre diferentes problemas da EACH (vulgo, USP-Leste). Só li cada um na diagonal, por enquanto. Mas acho que valem a pena. Pode ajudar a explicar os problemas que, na minha opinião, são todos gerados por grave incompetência na criação da escola:
Tensões e contradições do conceito de organização aplicado à universidade: o caso da criação da USP-Leste
Como um campus da USP foi transformado em aterro sanitário
Dois artigos sobre diferentes problemas da EACH (vulgo, USP-Leste). Só li cada um na diagonal, por enquanto. Mas acho que valem a pena. Pode ajudar a explicar os problemas que, na minha opinião, são todos gerados por grave incompetência na criação da escola:
Tensões e contradições do conceito de organização aplicado à universidade: o caso da criação da USP-Leste
Como um campus da USP foi transformado em aterro sanitário
Human Stupidity, part III - A Short Historical Perspective
Individual Thinking
How smart we really are is an old question. In the Western tradition, it is easy to remember the phrase attributed to Socrates “I know that I know nothing”. And yet, despite a few people who recognized how untrustworthy knowledge can be, most people actually think they have correct answers about special issues. When some people say they believe in something, be that a religion, a political ideology or a scientific result, they often mean that they know that to be true and are only using the word believe to acknowledge that not everyone has seen the truth. Of course, that is not the only use of the term and we also often use it in a probabilistic way, like in “I believe it will rain tonight”. This tells us that the speaker considers more likely that rain will happen than not. But there is no certainty. As such, if it doesn't rain, the speaker is not at fault, as long as the reasoning and evidence used to make the prediction were solid enough. This different meanings of believing will be discussed later.
The problem is clearly linked to the question of what it means to know something. After all, if any opinion or statement were equally valid, an assassin vision sadly shared by many people, we wouldn't be able to speak of smart. Anything anyone said would be acceptable, any premise could lead to any conclusion, and we would have no way to measure smartness. What actually happens is that there are conclusions that anyone sane agree are correct. The trivial examples of Aristotelian Classic Logic come to mind. If I accept as true that all texts about Logic are boring and that this one you are reading now is a text about Logic, it is unavoidable to conclude that this text is boring. If you don't think it is boring, you must obviously disagree with at least one of the premises (as I hope you do). On the other hand, if you accept as true that all plants are green, the fact that you have a green car is not reason enough to conclude your car is a plant. These cases are so obvious that you need to training in Logic to agree with basically everyone else on Earth.
Unfortunately, we are not allowed the luxury of dealing only with trivial cases or those our brains are already well adapted for. By adapted, I mean either from an evolutionary point of view, that is, problems our ancestors had to deal with so often some wiring might have happened, or from a learning point of view, that is, problems we have encountered very often in our daily lives we learned to solve them. For everything else, we need good standards to compare with. And the sad part is that if you take just one step further in still trivial Aristotelian Logic problems, all hell breaks loose.
P.C. Watson and P. Johnson-Laird describe in chapter 9 of their book Psychology of Reasoning: Structure and Content
the results of experiments performed to test how well people
reason on such simple problems. What they observed is quite
troubling. The now classical example has four cards on a table, so
that you can see just one side of each one. This deck is known to
always have one letter at one side of the card and one number at the
other. The problem is to test if a simple rule can be proven false:
“Whenever there is a vowel in one side, the other side will always
have an even number”. The four cards, obviously, show one of each
possible cases. Per example, they might show “A”, “M”, “2”,
and “5”. The question each subject has to answer is: “If you
turn the cards to inspect what is in the side that is not visible,
which of these four cards can prove the rule to be false?” Answers
are open, so any set, from the empty set (none of them could prove
that) to all of them can prove it is false, is an acceptable answer.Think a little and give your own answer. Don't look ahead, where I will eventually provide the right one. Whenever I am teaching TADI (Treatment and Analysis of Data and Information), I present the card problem (among others) to my students in the second meeting. While of very little value as experimental evidence, I observe an astonishing tendency to errors, typically 1 in 60 get the correct answer fast. That is, if you got it wrong, it just means you are human. The original experiment observed better proportions, making the species look less dumb. Of course, there are important differences, among them, the lack of control and a proper setting in my classes. The original experiments also didn't include things like peer pressure and the fact I don't give the students a lot of time to think. I actually ask them to commit soon to the answer they feel to be correct. My goal in the classroom is to make a clear point about how what we feel to be the right answer is often VERY wrong.
It is curious to see that this result is actually dependent on the problem that is presented to the subjects of the experiment. If, instead of unusual cards, the same logical question is about violations of a non-drinking while underage rule, people tend to perform very well and very easily. This suggests that while competent learners, we need to be trained if we are to have any chance at getting the right answer in some very easy problems. And sometimes even training might not be enough. Extra details on this problem and several others that I will speak about later can be found in two very interesting books. The one from, Scott Plous, The Psychology of Judgment and Decision Making
, is already 20 years old (1993) but it still has a wide range of
experiments on the way people think. Jonathan Baron also discusses
the same problem in his newer (2007) book Thinking and Deciding. Both are very interesting readings.One of the reasons for this phenomenon seems to be a characteristic of our reasoning called confirmation bias. Basically, when analyzing an idea, we tend to look for cases that confirm it. But this is not a true tests. Cases where the idea seems to work well are interesting examples. But, if you really want to test any idea, you must look for cases where the idea can fail.
And while being prey to confirmation bias
(as many people seem to do in the card problem) is a bad strategy, we do even
worse than that. We actually choose not to look at arguments and data
that contradicts our beliefs, or we actually interpret them
erroneously. Recently, Dan
Kahan and collaborators have reported results that
show that mathematically educated people make serious errors
when analyzing data that conflicted with their personal opinions. In a control scenario, if
the same data was about a neutral problem, people with better
numeracy skills performed better at interpreting the data. However, when the problem was gun
control, a very controversial issue in USA, people with better
numeracy interpreted the data in ways that agreed with their initial
points of view, regardless of the real data. People with improved
numeracy would become even more polarized on the subject than people
less well trained in Mathematics. This strongly suggests that smarter
can mean more ability to, perhaps unconsciously, distort reality
description to conform to one's own point of view! A more pedestrian
discussion of these results can be found here
by Mark Kaplan.
1) This text will probably be expanded later. If and when I do, I will make a new post warning about the fact.
2) The correct answer for the cards problem will only appear here later. Try leaving yours in the Comments section. No cheating.
3) I will strongly welcome suggestions of literature and results to add here. Note that probabilistic biases as well as group and societal effects will come later, in new entries. Therefore, they are not discussed here, just logical problems are.
Monday, November 18, 2013
On Human Stupidity, part II
And, the more research is done on animals, the clearer it seems that some species are also capable of some decent reasoning and solving problems. Humans have created ways to preserve knowledge and opinions that are far more efficient than copying the behavior of others. This has opened the possibility that what individuals know about the world is actually a sum of what they observe and whatever knowledge was transmitted from their predecessors. Writing made our species smarter than a single individual; the advances in scientific methodology allowed us to circumvent many of the limitations of our brains. But it is crucial to understand those limitations and recognize fully that they apply to ourselves.
It is very easy to point out how other people are dumb. This is so easy because they are dumb, but so are we. We actually must learn how we are very dumb ourselves. I am human, this makes me quite limited. There is no shame in that, although, I have to admit, it really bothers me to notice how we are bad at reasoning.
And there is more. My knowledge is limited to what I have observed myself and what I have learned from others. Since it depends on unreliable thinkers, it must be subject to far more uncertainty than anyone seems to acknowledge. Our civilization has created tools to deal with our limitations, but we don't always use them when making decisions. We can fly, we can visit space and the depths of the oceans, we can endure any climate conditions on our planet. And we don't do any of those because it is a special power of mankind. We do that because we have created tools and methods for that. It is the same with thinking. However, while there are very clear standards that must be obeyed for aircraft to be allowed to fly, the same is not true on the quality of our supposedly rational analysis. And yet, left alone, each of us is just a little smarter than the other animals. We have a horrible tendency to arrive at wrong conclusions about any subject that is not a problem we experience in our daily lives. Of course, we are completely incompetent, far from that.
This exception, that we are actually reasonably competent with understanding people and other issues we have to deal with at a daily basis, has also bad consequences. While it is better to be good at something, it also helps people to feel confident about how they reason.Our intuition is well adjusted to the things we encounter often. But this does not mean it will work when facing new or difficult problems. And yet, people have a certainty about their choices that is completely unjustified, often with disastrous consequences. People express certainty in political, economical, religious, and, sometimes, even about scientific questions they don't understand but that we actually know the answers. Evolution, Medicine and Quantum Mechanics are the first examples that come to mind and I don't need to argue how damaging it might be to have wrong convictions in a health area. This does not mean that errors in areas not directly linked to health might not be equally damaging as well.
It is crucial, in order to answer any questions as competently as possible, that we recognize our own shortcomings. As we will debate later, we must even learn to always doubt our own opinions. Our current society not only accepts but encourages people to make choices between options. And it is expected that people should act as if that choice meant some kind of truth. This kind of belief is actually very wrong. A rational being should not lie to itself by ignoring other possibilities. And yet we do that all the time.
In order to understand why this is so, we will need to answer a number of questions. We need to understand what knowing something means, if it is actually possible to know something. We also need to be able to reason, reaching conclusions from premises and understand when this kind of analysis is a proof and when it is actually just an inference, where, at best, we can hope to assign probabilities to our conclusions. Comparing how normal, untrained humans perform under different circumstances will show us where we are actually weak at it. And that it is very likely that our brains use many different heuristics in decision-making. This allows the brains to get close to the correct answers in a number of situations. But it has serious consequences on how much we can trust things like intuition when we are out of our comfort zone. Finally, one issue that must be addressed very carefully is when we can trust what other people tell us, whomever they are.
I realize that this text and the ideas I will present here might have a difficult time reaching everyone who should be made aware of them. Many people won't like the idea of admitting they are actually stupid, in an absolute sense. It is certainly easy to find the errors I will talk about here on others. But we must learn to notice them on ourselves and correct them. My Master adviser, Henrique Fleming, used to tell his students a phrase from Niels Bohr: “An expert is a person who has found out by his own painful experience all the mistakes that one can make in a very narrow field.” While there is some truth to it, Bohr forgot to include a crucial part of it. That is that the expert should have learned from those mistakes and not make them anymore. People quite often don't learn when their objective is to prove that they are right, as opposed to find out what is actually the right answer.
Monday, November 11, 2013
On Human Stupidity, part I
The first real post here should come in a few days, I hope. It will be on human stupidity. Since 2005, I teach a course called "Treatment and Analysis of Data and Information" (or TADI, as the students call it, the first letters are the same in Portuguese). My own hypothesis for the name is that the people who planned the school believed in Jane Austen interdisciplinarity. Something is interdisciplinary as long as you add an "AND" to the name. Luckily, this specific course makes sense and it is actually about basic thinking, some epistemology, scientific method and the VERY basics of data analysis.
My second class in this course (the first is traditionally about the problem of the huge amount of information we have to deal with) is about human stupidity. The aim is to convince the students about the absolute need to learn reasoning techniques, including things like logic, probability, statistics, and the scientific method. They are absolutely necessary simply because we are humans. And humans, despite being the smartest species ever known to mankind, are amazingly dumb. So, I tell all students as the first thing in the class that they should not feel ashamed about making mistakes in that class. They will, for sure, not because they are dumber than others, but because they are humans. And I proceed with a number of traditional experiments, taken from Psychology literature, asking them what they think is the correct answer. The problems are actually trivially easy and simple. And, in classes of 60 students, typically, one person gets it right. Quite often, zero, sometimes two. And different people for each question.
While the classroom observation is not a true controlled well conducted experiment, it serves to make a very clear point. When faced with situations that are not common in our daily lives, our intuitions are basically disastrous. All of us need instruments to deal with this absurd failure. And, of course, it is also interesting to understand possible reasons for this human stupidity (and no, animals are not better in any sense, most of them really have no chance at understanding Quantum Mechanics, you know). This kind of stupidity also has serious consequences in everyday life, in all kind of decisions, including the most important decisions about our health. It is no exaggeration to say that millions die (my personal wild guess would be millions every year) simply because we do not acknowledge the simple fact we must have tools for reasoning. Or we make awful mistakes.
I always wanted to write a book about methods and general epistemological problems and mistakes that are done even today in Science. Some of them are either not recognized as such or recognized by very few. Some of the posts that will follow (but, of course, not all of them) are my first draft of that book. And some basic material for TADI, as, starting February of 2014, I will be teaching it once more. And this time, I plan to make a number of changes and make the students work hard, despite what the initial planners of the subject in my school may or may not think.
Or, on a personal note (and, unlike Sheldon, I know I belong to the "others" set as well, even if my belonging, in a fuzzy theory sense, is smaller than that of the majority):
My second class in this course (the first is traditionally about the problem of the huge amount of information we have to deal with) is about human stupidity. The aim is to convince the students about the absolute need to learn reasoning techniques, including things like logic, probability, statistics, and the scientific method. They are absolutely necessary simply because we are humans. And humans, despite being the smartest species ever known to mankind, are amazingly dumb. So, I tell all students as the first thing in the class that they should not feel ashamed about making mistakes in that class. They will, for sure, not because they are dumber than others, but because they are humans. And I proceed with a number of traditional experiments, taken from Psychology literature, asking them what they think is the correct answer. The problems are actually trivially easy and simple. And, in classes of 60 students, typically, one person gets it right. Quite often, zero, sometimes two. And different people for each question.
While the classroom observation is not a true controlled well conducted experiment, it serves to make a very clear point. When faced with situations that are not common in our daily lives, our intuitions are basically disastrous. All of us need instruments to deal with this absurd failure. And, of course, it is also interesting to understand possible reasons for this human stupidity (and no, animals are not better in any sense, most of them really have no chance at understanding Quantum Mechanics, you know). This kind of stupidity also has serious consequences in everyday life, in all kind of decisions, including the most important decisions about our health. It is no exaggeration to say that millions die (my personal wild guess would be millions every year) simply because we do not acknowledge the simple fact we must have tools for reasoning. Or we make awful mistakes.
I always wanted to write a book about methods and general epistemological problems and mistakes that are done even today in Science. Some of them are either not recognized as such or recognized by very few. Some of the posts that will follow (but, of course, not all of them) are my first draft of that book. And some basic material for TADI, as, starting February of 2014, I will be teaching it once more. And this time, I plan to make a number of changes and make the students work hard, despite what the initial planners of the subject in my school may or may not think.
Or, on a personal note (and, unlike Sheldon, I know I belong to the "others" set as well, even if my belonging, in a fuzzy theory sense, is smaller than that of the majority):
Tuesday, November 5, 2013
A new kind of prejudice?
Don't forget to check the manifesto at the right side!
Não se esqueça de checar meu manifesto, aí do lado direito!
Não se esqueça de checar meu manifesto, aí do lado direito!
Monday, November 4, 2013
About this blog (sobre esse blog)
This blog is my plan to make public I absolutely feel I must say. It will be mostly written in English, with the possible exception of a few local things, of local interest to Brazilian people around me. The reason for this is simple. While I'd rather use my own language, I prefer to be accessible to more people.
There is one main exception to that. The Manifesto put in the side of this page was originally written in Portuguese, as a part of a book of short tales I am currently working on (link to be inserted when it becomes public). I used Google Translate as base for the English version and made lots of corrections to get the meaning right. While I can write a regular English (for a foreigner, at least), I am not good with translating. But I think that Manifesto was important enough to be there in both versions.
As for post frequency, it will be random. I suffer from clinical depression and I am quite aware that, while I can be reasonably sure I will keep posting in the long run, I can't be sure how able to work I will be in a given week. If anyone is interested in what I have to say, I will also make announcements whenever I post anything by using my Twitter account @Andre_CRMartins.
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Este blog é meu plano de tornar público uma série de coisas eu realmente quero dizer. Ele vai ser escrito predominantemente em inglês, com a possível exceção de algumas entradas, de interesse local para os brasileiros ao meu redor. A razão é simples. Eu preferiria usar minha língua, mas, mais do que isso, prefiro ser acessível a mais gente.
Há uma exceção a essa regra. O Manifesto que coloquei no lado da página foi originalmente escrito em português, como parte de um livro de contos que estou escrevendo (o link vai aqui quando o livro for público). Para a tradução para o inglês, usei o Google Translate como base e corrigi muita coisa que não estava certa. Eu até que escrevo um inglês regular (para estrangeiros), mas não sou bom em traduções. Mas acho o Manifesto importante o suficiente para ter ambas as versões.
Quanto a frequência dos post, essa vai ser aleatória. Eu sofro de depressão e sei que, enquanto tenho certeza suficiente de que manterei postando no longo prazo, não posso garantir como vou estar em uma dada semana. Se alguém estiver interessado no que tenho a dizer, planejo avisar cada vez que postar algo através da minha conta no Twitter, @Andre_CRMartins
There is one main exception to that. The Manifesto put in the side of this page was originally written in Portuguese, as a part of a book of short tales I am currently working on (link to be inserted when it becomes public). I used Google Translate as base for the English version and made lots of corrections to get the meaning right. While I can write a regular English (for a foreigner, at least), I am not good with translating. But I think that Manifesto was important enough to be there in both versions.
As for post frequency, it will be random. I suffer from clinical depression and I am quite aware that, while I can be reasonably sure I will keep posting in the long run, I can't be sure how able to work I will be in a given week. If anyone is interested in what I have to say, I will also make announcements whenever I post anything by using my Twitter account @Andre_CRMartins.
-----------
Este blog é meu plano de tornar público uma série de coisas eu realmente quero dizer. Ele vai ser escrito predominantemente em inglês, com a possível exceção de algumas entradas, de interesse local para os brasileiros ao meu redor. A razão é simples. Eu preferiria usar minha língua, mas, mais do que isso, prefiro ser acessível a mais gente.
Há uma exceção a essa regra. O Manifesto que coloquei no lado da página foi originalmente escrito em português, como parte de um livro de contos que estou escrevendo (o link vai aqui quando o livro for público). Para a tradução para o inglês, usei o Google Translate como base e corrigi muita coisa que não estava certa. Eu até que escrevo um inglês regular (para estrangeiros), mas não sou bom em traduções. Mas acho o Manifesto importante o suficiente para ter ambas as versões.
Quanto a frequência dos post, essa vai ser aleatória. Eu sofro de depressão e sei que, enquanto tenho certeza suficiente de que manterei postando no longo prazo, não posso garantir como vou estar em uma dada semana. Se alguém estiver interessado no que tenho a dizer, planejo avisar cada vez que postar algo através da minha conta no Twitter, @Andre_CRMartins
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