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Normally this group plays in the senior amateur league, and we would not claim more. Today my theme is one on which you and I are experts: screwing things up. Simply by staying alive for 60 years or so gives us ample experience of our own mistakes, mistakes by those around us, mistakes by the leaders and electorates of our countries. Last year we saw the British vote for Brexit and the American one for Donald Trump. We are aware of Japan's attack on Pearl Harbour, Napoleon's and Hitler's invasions of Russia, and Chamberlain's trust in Hitler at Munich. The poppies we wire on Saturday remind us of the dreadful mistakes of August 1914, when sensible statesmen who did not hate each other drifted into a cataclysmic European war. In both small and large cases we ask: what were they or we thinking of? Wasn't it obvious at the time that these decisions were really dumb?

If we can improve our chances to avoid errors of judgement only a little through understanding, the effort is well worth it. This is a philosophy group, and we look for general rather than particular insights, and I won't relitigate the examples. Fortunately there has been some recent and convincing research on systematic and probably innate biases of human nature that lead us into error. This is worth knowing.

Our guide will be cognitive psychologist Daniel Kahneman, and his very readable book Thinking, Fast and Slow (“TFS” below) (Ref 6), published in 2011. In this he summed up his life’s work, most of it in a close collaboration with Amos Tversky. Their collaboration was immensely productive, and ranks with that of Crick and Watson in the cracking in the genetic code. Tversky was apparently the theory and ideas man, like Crick; Kahneman more the careful workhorse, like Watson (though both seem much nicer people). Tversky died in 1996. Six years later, Kahneman received the Nobel Prize in economics – there isn't one in psychology. If you don’t feel like buying the book, his Nobel Prize lecture is free (Ref 7).

Tversky and Kahneman are or were Israeli, and much of their early work was carried for the Israeli Defence Forces, who were very interested in the often very costly mistakes made by their pilots and soldiers. They were much less interested in blaming the young men who made them, who were often dead anyway. This intensely pragmatic approach marked the style of the two researchers, and their dismissal of the moralising lens is refreshing and constructive. Moral condemnation has its place, but it’s not an explanation.

Before we get to the recent findings, I would like to look briefly at three other explanations: machine error, Aristotle’s weakness of will – emotions overcoming reason - , and Bacon’s idols. Actually I won’t: you will find my thoughts on these in the printed version of this paper on my website (Ref 9). For now, let me just stipulate that Kahneman’s cognitive errors don’t cover everything and don’t claim to.

We rely heavily on automatic cognitive processes, for example when walking or cycling or driving a car or in sport. These sometimes go wrong: we think we can get round the bend at 80km/h when it should be 60, or we trip on our shoelaces. The same goes for our cats: Pussy may guess wrong which way the mouse will run, or wrongly think she has time to cross the road in front of a car. In both cases, the consequences may be anything from trivial to tragic. What they are not is a puzzle. We face exactly the same problems building a robot to do the same things. The algorithm may be buggy, the processor too slow, the sensors inaccurate, the bandwidth of the communication channels too restricted, or we may be defeated by countermeasures. The way to reduce such errors is learning and practice. Polar bear and lion cubs are born with an instinct to hunt, but they are at first very bad at it, and only acquire skill from their mothers.

The puzzles are about our conscious bad decisions. Why should we make them at all? We are descendants of 3 billion years of survivors. We are the most intelligent animal, with sophisticated sensory and motor skills and reasoning abilities. When we can't solve a problem by ourselves, we have speech and social networks so we can bring in the help of others and the experience and wisdom of a community.

There is bad luck of course, but it's an excuse rather than a theory. The oldest general theory I can find is “reason overcome by the passions”. It’s implicit in the myth of Cain and Abel. Aristotle used the term akrasia, usually translated as “incontinence” (Ref 2). It's also the foundation of his theory of tragedy (Ref 3) as the destruction of a hero by a tragic flaw, an uncontrolled desire overwhelming common sense: Oedipus' obsession with learning his origins, Paris' lust for Helen, Agamemnon’s desire for glory. We can add Othello's jealousy and Macbeth's ambition. The Stoics went so far as to call all passions intrinsically evil. Aquinas is okay with passions only as slaves to reason (Ref 1).

Aristotle does distinguish between akrasia where the emotions simply sweep aside reason (Othello) and the more common case where they seem to hijack reason, and we talk ourselves into error with specious arguments (Macbeth), without any loss of self-control. The point was made elegantly by the Oxford philosopher J.L. Austin, in this bloodcurdling description of academic depravity¹:

I am very partial to ice cream, and a bombe is served divided into segments corresponding one to one with the persons at High Table: I am tempted to help myself to two segments and do so, thus succumbing to temptation and even conceivably (but why necessarily?) going against my principles. But do I lose control of myself? Do I raven, do I snatch the morsels from the dish and wolf them down, impervious to the consternation of my colleagues? Not a bit of it. We often succumb to temptation with calm and even with finesse.

Clearly this mechanism is real. All too often we sit down to play poker with men called Doc, pursue women nicknamed Good-time Gertie or men known as Heartbreak Henry, seek wealth at the expense of happiness, and so on. There are two difficulties. One is that there are many cases where it doesn't seem to fit. The Japanese did not attack Pearl Harbour out of an unreasoning hatred for Americans.

A bigger one is that the passions – immoderate passions, not milk-and-water tame ones - drive success as well as failure. Henry VII was as ambitious as Richard III, and it worked out well for him and his country. Cortez, Darwin, Gates, Beethoven were ambitious men. In our own lives, we can very probably think of instances when our desires have overwhelmed our judgement and led us to small or great disasters. But when we look on the other scale at our best decisions and achievements, were these not also driven by the strong desires that enabled us to take a chance and strive for some difficult goal? We seek out sexual partners and life companions out of need, and very often find them. We could not in fact function as passionless automata. Our desires provide us with the frame of values that allow us to choose, and the energy to put our choices into effect. So it’s wrong to see the passions as automatic enemies of good decisions. There must be something else as well.

Fast-forward 2000 years to the Renaissance. You have heard of Francis Bacon, one of the founders of the scientific method. He was also a cold careerist: he abandoned his protector Essex just in time, signed off on torture warrants as James' Attorney General, and was eventually fired for taking unusually large bribes. Still, of all the world's great thinkers, he was the one with the longest career in high-level politics. Bacon left us in his Novum Organum (Ref 4) a very picturesque proto-theory of cognitive mistakes, which he labeled Idols, objects of false devotion, fixations in error. He proposed four:

“The Idols of the Tribe have their foundation in human nature itself, and in the tribe or race of men. ... The human understanding is like a false mirror, which, receiving rays irregularly, distorts and discolors the nature of things by mingling its own nature with it.” (§41)

Examples are the tendency of the human understanding “to suppose the existence of more order and regularity in the world than it finds” (§45) and confirmation bias (§46). Fair enough.

“The Idols of the Cave are the idols of the individual man. For everyone (besides the errors common to human nature in general) has a cave or den of his own, which refracts and discolors the light of nature, owing either to his own proper and peculiar nature; or to his education and conversation with others; or to the reading of books, and the authority of those whom he esteems and admires; or to the differences of impressions, accordingly as they take place in a mind preoccupied and predisposed or in a mind indifferent and settled; or the like.” (§42) This fits Trump all right.

“There are also Idols formed by the intercourse and association of men with each other, which I call Idols of the Market Place, on account of the commerce and consort of men there. For it is by discourse that men associate, and words are imposed according to the apprehension of the vulgar. … Words plainly force and overrule the understanding, and throw all into confusion, and lead men away into numberless empty controversies and idle fancies.” (§43) Twitter!

“Lastly, there are Idols which have immigrated into men's minds from the various dogmas of philosophies, and also from wrong laws of demonstration. These I call Idols of the Theatre, because in my judgment all the received systems are but so many stage plays, representing worlds of their own creation after an unreal and scenic fashion. Nor is it only of the systems now in vogue, or only of the ancient sects and philosophies, that I speak; for many more plays of the same kind may yet be composed and in like artificial manner set forth.”(§44) Marxism!

This is clearly very interesting stuff. There are two problems. One is fair enough: the focus of the Novum Organum is theoretical not practical belief. He does not draw on his experience of the world, his close observation of the end of Mary Queen of Scots,, the executions of Babington, the Jesuits, and Guy Fawkes, the defeat of the Spanish Armada, and the fall of Essex. This is not the hands-on Bacon who writes, in the Essays (Ref 5, Of Counsel), of the importance of seating plans in meetings. It is also exceedingly sketchy. The main conflicts of belief in his day were about religion, and being explicit would possibly have been dangerous and certainly lost him half his potential audience in Europe.

The bigger problem is that for all his advocacy of the scientific method, Bacon presents zero evidence for the Idols, not even learned anecdotes from classical authors. They just serve as bogeymen to contrast with the true method, the scientific one. The brilliant speculation sparked no research, and passed into obscurity.

Unlike Bacon’s or Aristotle’s, the work of Kahneman and Tversky is based on actual experiments, replicated and documented. There are two sides to it. One is a set of effects. The other is a general explanation for them. I won't try to cover all the effects, it's more important for you to get the style and method.

The first experiment is a quite famous one about a woman called Linda. The test subjects were shown a short description and a list of eight possible outcomes describing her present employment and activities. I'll leave out the dummy questions and ask you to write down your answers. Here's the description.

philosophy. As a student she was deeply concerned with issues of discrimination and social justice and also participated in antinuclear

How many put C second? A majority. That is absolutely standard. Whoever you ask, you get 85%-90% saying the same. That includes doctoral students at Stanford in a programme on decision science. But the majority is wrong. As a matter of logic, the joint probability of two outcomes must be lower than that of either. Suppose we rate the feminist probability at 95% and the bank teller one at 5%. The joint probability is 4.75%.

What happened here? The description shouts FEMINIST! at us. The light bulb is so bright it cuts out logic. This is the fallacy of similarity: we use a criterion of representativeness to stand in for a judgement of probability.

You may say: that was true but artificial, a trick question. So let's try another which is closer to the problems we face.

Here is a profile of Tom, a graduate student, written by a psychologist when Tom was in high school, on the basis of personality tests of dubious validity:

Tom W. is of high intelligence, although lacking in true creativity. He has a need for order and clarity, and for neat and tidy systems in which every detail finds its appropriate place. His writing is rather dull and mechanical, occasionally enlivened by somewhat corny puns and by flashes of imagination of the sci-fi type. He has a strong drive for competence. He seems to have little feel and little sympathy for other people and does not enjoy interacting with others. Self-centered, he nonetheless has a deep moral sense.

Participants were given this description along with a list of nine fields of graduate specialization, including computer and library science, as well as business administration. They were again asked to rank the fields in order of likelihood. Computer and library science came out on top, business administration low down.

There is no logical incompatibility here, but it is still unsound to blindly follow the stereotype. The problem is that there are six times as many graduate students in business subjects in the USA as in computer and library science combined². If we know nothing about Tom's character, the best way to assess the probability is to use the base rate. This means that we should put business as six times more likely than computer science. In the experiment, the subjects were in addition told that the profile was of dubious validity, so it should have been ignored. Even if it were accurate, the best way, as recommended by the Reverend Bayes, is to start with the base rate and adjust for additional information. So we should start at 6:1 for business and mark down. Doing it this way, we are not very likely to get to equal odds, let alone a lead for computer science.

Base rate errors of this type are very common and surely of practical importance. Failure to use them properly is compounded by massive ignorance of what they are. In a survey of students at Eugene (Oregon) asking them to compare risks of death, the average estimate of the relative risk of death from accidents and from diabetes was 300 to 1 for accidents. The true ratio is 1 to 4; diabetes is by far the higher risk (TFS, Ch. 13). One of the secrets of professional expertise may well be better knowledge of base rates.

Another way we fail at statistics is looking for narratives in the most picturesque and salient rather than the most relevant features of a problem. A survey looked at death rates from kidney cancer in the 3,141 counties in the United States in a recent year. The lowest rates were in sparsely populated, rural counties in the South, West and Midwest, typically with Republican politics. Your brains are setting to work. Is it the Republican politics? Probably not. The greasy food, alcohol and opiates? Nah. Something about rural. Maybe it's air pollution.

Now what if I told you about the counties where deaths from kidney cancer were highest: sparsely populated, rural counties in the South, West and Midwest, typically with Republican politics (TFS, Ch. 10). What is going on here? The key adjective was the one you ignored. It's all about small. Small counties will always show more extreme results than big ones, up and down. Throw two dice, and your chance of both sixes is 1 in 36. Throw four dice, and your chance of all sixes is 1 in 1,296. Bill Gates has spent a fortune promoting small schools, which have the best scholastic results. Sure they do: they also have the worst ones.

That's enough statistics for now. Let's look at framing, through another of Kahneman and Tversky's problems.

Imagine that the United States is preparing for the outbreak of an unusual Asian disease, which is expected to kill 600 people. Two alternative programmes to combat the disease have been proposed. The exact scientific estimates of their consequences are as follows:

If Program B is adopted, there is a one-third probability that 600 people will be saved and a two-thirds probability that no people will be saved.

In this version of the problem, a substantial majority of respondents favour programme A, indicating risk aversion. Other respondents, selected at random,

receive a question in which the same cover story is followed by a different description of the options:

If Program B is adopted, there is a one-third probability that nobody will die and a two-thirds probability that 600 people will die.

A clear majority of respondents now favour program B, the risk-seeking option. There is no substantive difference between the versions to justify the change in judgement. The phenomenon, which has passed into common discourse, is called framing: how a question is presented affects our judgement considerably. It affects experienced professionals like doctors as well as the hoi polloi. The effect is also why politicians don't answer the questions Jeremy Paxman puts to them – it's not dishonesty, they are trying to control the framing.

We have time for one more so I'll go for a marvellous experiment where the researchers took out panel ads for a period in two student newspapers on the same Michigan campus. The panels included, without explanation, vaguely Turkish-sounding nonsense words: kardirga, saricik, biwojni, nansoma, or iktitaf. The frequency of the words varied. When students were later asked about their feelings about the words, those that had been repeated often evoked more positive feelings (TFS, Ch. 5). Other experiments have shown that a word or image or number can supply a mental anchor and prime us to be more likely to respond soon afterwards in a particular way, which would not have been news to David Hume. Repetition makes certain. If it's familiar, it's better. This explains the fortunes spent on advertising; it is not direct persuasion, but priming by repetition to create a favourable attitude.

There are a lot more data in Kahneman's book – one of his articles with Tversky listed 20 different forms of cognitive bias. I have given you a big enough sample for you to judge the flavour and solidity of their work. The most important aspect to my mind is the theory they built to hold it together. This is of two mental systems of judgement:

an intuitive mode in which judgments and decisions are made automatically and rapidly, and a controlled mode, which is deliberate and slower.

Kahneman misses a trick by not tying these to the ancient metaphors of the Hare and the Tortoise, which I propose to do. The intuitive system 1 (the Hare) is fast, automatic, unconscious and effortless. It can't be turned off.

Just how fast and automatic can be illustrated by a simple mention of two unrelated words:

In the fraction of a second it took your minds to process these words, three things happened.

1. A negative reaction of disgust to the second word. Your heart rate increased and the hair on your arms rose a little. Your face may have twisted.

3. You started searching for a story to resolve the incongruity, perhaps rotten bananas. This happened in spite of my telling you the words were unrelated.

You had no conscious control over any of this. For a short while, you will look differently at bananas – don't worry, it will fade.

For our purposes, the problem with the Hare system is that it cuts corners. Most of the time its quick-and-dirty Brummagem methods serve us well. But not always; we have to learn to steer into the skid, or centering the rudder in an aircraft spin, these actions do not come naturally. Kahneman is your guide to its quirks. It is worth spending time to learn more about them, it will help your inner Tortoise to stay on top.

Some problems the Hare system can't handle at all. What is 17 times 24? No even approximate solution comes to mind. It has to be worked out, using a machine or a laborious algorithm we learned at school. The emphasis is on work. The Tortoise System 2 takes effort, and we don't like effort. The Tortoise also acts as a censor or pilot instructor for the Hare, and is capable of taking over.

The evolutionary story behind the double system is very plausible. Our minds evolved for the life of bands of hunter-gatherers on the African savannah. This is a complex and dangerous place. To stay alive, negotiate your place in the band, and hunt game and search for fruit and edible roots successfully you need to take a lot of snap decisions. Is that shadow a lion? Which way will the warthog run? Is the dominant male's snarl a real threat or for show? But these were not the only problems our ancestors faced and solved. Some of them hunted hippos: a very large and aggressive animal that spends most of its time in water. Palaeolithic men and women and their dogs sailed to Australia. Later, Polynesians learned how to get food from the seed pith of sago cycads, which is extremely poisonous without repeated washing. You can't do these things by intuition, only careful planning, and in the sago case, experiment.

The work I have described to you is important and solid. It does not cover everything. We may not yet have the full list of intuitive biases. More important to my mind is the fact that System 2, the Tortoise, also errs. The errors of systematic reason were baptised Idols of the Theatre by Bacon, and they are still waiting for their modern Kahneman. There are many examples in the history of science and medicine of learned men clinging to refuted theories; and more in the history of politics and religion of cruelties and follies carried out in the name of complex schemes of ideas owing everything to the Tortoise system 2. At times, they have overwhelmed ordinary moral intuition. We mustn't give food to the starving Irish peasants, it will only encourage their fecklessness and unsustainably large families, doctrinaire English liberals said in the 1840s.

Kahneman's book actually includes one experiment that sheds light on such aberrations. Researchers shot a video of a simplified basketball game, which you can watch on the Internet³. From the website:

You are asked to watch a short video in which six people - three in white shirts and three in black shirts - pass basketballs around. While you watch, you must keep a silent count of the number of passes made by the people in white shirts. At some point, a gorilla strolls into the middle of the action, faces the camera and thumps its chest, and then leaves, spending nine seconds on screen. … When we did this experiment at Harvard University, we found that half of the people who watched the video and counted the passes missed the gorilla. It was as though the gorilla was invisible.

Counting the passes calls for intense concentration on a difficult task, under conscious control. It looks as if this focused effort sucks up all our mental energy, or cashes all our attention budget, incapacitating our normal background awareness. I suspect a similar process is at work when the intense conscious effort of absorbing a complicated ideology asphyxiates our normal moral empathy and intuitive judgement. We become the superior intelligences that have passed beyond the unthinking prejudices of the common herd. In fact, we have sunk below them.

So stay suspicious. Let the Hare and the Tortoise keep a good eye on each other. Slow down in judgement when it’s possible. It’s much easier to do this than to change our reflexes or emotions.

A final and more cheering thought. Kahneman underlines the strain of thinking, conscious Tortoise system thinking, which well explains why so many people seem to give it up. But it does not explain the Nerja Philosophy Group. You come here regularly and entirely of your own free will for a couple of hours of demanding mental effort. Thinking can be fun. It is like physical exercise: once you get into the habit, you don't want to stop. The couch potatoes don't understand it at all.

1. Aquinas, Summa Theologica, 1274, Question 24, Article 2 http://www.newadvent.org/summa/2024.htm#article2

2. Aristotle, Nicomachean Ethics, ca 350 BC , Book VII, (akrasia translated as “incontinence”) http://classics.mit.edu/Aristotle/nicomachaen.7.vii.html

3. Aristotle, Poetics, ca 350 BC, section XIII http://www.gutenberg.org/files/1974/1974-h/1974-h.htm

4. Bacon, Francis. Novum Organum (The New Organon), 1620 (in Latin), sections 37-68 http://www.constitution.org/bacon/nov_org.htm

8. US National Center for Education Statistics, website, table 318.30. https://nces.ed.gov/programs/digest/d15/tables/dt15_318.30.asp?current=yes

1A Plea for Excuses, 1956. Cited at https://guylongworth.wordpress.com/tag/j-l-austin/

2 In 2013, the number of master's and doctoral degrees awarded was 192,367 in business, 5,891 in library science, and 26,514 in computer science. Ref 8.