Saturday, July 04, 2009

** Drunkards Walk by Leonard Mlodinow

Life is random. Now you have proof. I always like to ponder that my existence has to do with the fact that the sperm on the left or right of the egg didn’t conceive first, otherwise someone else would’ve taken my place. So you are conceived in randomness, and it will rule your life from that moment on. You’d think that owing our existence to randomness would clue us into how to handle it and how to take advantage of it. But it turns out we’re pretty bad at dealing with random things. We always seek patterns, so we weave superstitions and ignore facts to buttress our delusions.

Maybe if I yell louder that will help?

Why do we think that yelling and getting mad at people improves performance, when all studies show that encouragement is the key to change behavior and train others, including animals? The answer lies in regression towards the mean… Here’s how it works in the example of fighter pilots… Any especially good or poor performance was mostly a matter of luck. So a landing far above his normal level of skill would mean that the odds are good that he would perform closer to his norm – that is worse – the next day. And if the instructor praised him, it would appear that the praise did no good. But if a pilot made an exceptionally bad landing, then the odds would be good that the next day he would perform closer to his norm – that is better. And if the instructor screaming ‘you clumsy ape’ when a student performed poorly, it would appear that this harsh criticism did some good. In this way an apparent pattern would emerge: student performs well, praise does no good; student performs poorly, instructor berates student, student improves. P8

When you put it that way it seems to obvious!

Which is greater? – The number of 6 letter English words having an N as their 5th letter OR 6 letter words ending in ING? Most people choose the ING option. Why? Because such words are easier to think of. But you don’t have to survey the dictionary to prove that guess wrong. The group of words ending in ING are contained in the group of words with N as the 5th letter. P28

The Greeks had math problems.

The order in which ones, tens, and hundreds didn’t really matter: sometimes all order was ignored. Finally, the Greeks had no zero. The concept of zero (really just the absence of a number) came to Greece when Alexander invaded the Babylonian empire in 331BC, but the idea of zero as we know it (anything multiplied by it equals 0 and anything added to it equals the number you started with), wasn’t introduced until 9th century by the Indian mathematician Mahavira. P30

And the Romans had Greek problems

The Romans generally scorned math, especially the math of the Greeks… A Greek textbook focused on the proof of congruences among abstract triangles, a typical Roman text focused on such issues as how to determine the width of a river when an enemy is occupying the other bank… The Romans didn’t produce even one mathematician. In Roman culture it was comfort and war, not truth and beauty, that occupied center stage. So while finding little value in abstract geometry, Cicero wrote that “probability is the very guide of life”. P31

Let’s examine DNA trial evidence:

The probability of a lab error is 1 in 100. The probability of someone else matching your DNA is 1 in 1 billion. That is given by our sum rule: the probability of an error is 1% + .000001%. That the latter is 10 million times smaller, we can just round this to 1%. Given both possible causes we should ignore the fancy expert testimony about the odds of accidental matches and focus on the lab error rate – the very data courts often don’t allow attorneys to present! P37

Does the best team always win the World Series?

If one team is good enough to warrant beating another in 55% of it matches, the weaker team will nevertheless win a 7 game series 4 times out of 10. And if the superior team could be expected to beat its opponent on average 2/3 of the time, the inferior team will still win a 7 game series about 20% of the time. In the lopsided 2/3 probability case, you’d have to play a series of 23 games to determine the winner with statistical significance, meaning that the weaker team has less than a 5% chance of winning the series. In the 55% probability, a tedious 269 games would be warranted. P71

Isn’t this a reality TV game show?

Everyone who plays pays a dollar. One will win a fortune, and one will be put to death in a violent manner. Would anyone play this game? Is this from ancient Rome? No, it’s called the California Lottery… Applying highway statistics, many millions of contestants drive to and from their local ticket vendors to purchase tickets, and a reasonable estimate is that 1 of them will die in an accident per game. P78

Would you believe it?

A faithful husband, with a great job, and charming daughter, one day discovers that he is missing something in his life. One night as he returns home he spots a beautiful woman gazing with a pensive expression out the window of a dance studio. Each night as his train passes her studio, he falls further under her spell. Finally, one evening, he impulsively rushes off the train, and signs up for dance lessons, hoping to meet the woman. He finds that his haunting attraction withers once his gaze from afar gives way to face to face encounters. He does fall in love, however, not with her but with dancing. He keeps this new obsession from his wife and colleagues. Eventually his wife discovers he’s not working late. She figures the chances of his lying about after work activities is far greater if he’s having an affair than if he isn’t, so she concludes he is. But the wife is mistaken not just in her conclusion, but in her reasoning: she confused the probability that her husband would sneak around IF he were having an affair with the probability that he is having an affair IF he was sneaking around. P107

This makes no sense whatsoever until you read it

What is the probability of a family having 2 daughters if you are told that one of the children is a girl? It’s 1/3 because this additional fact eliminates the possibility of the family having 2 boys, so the only remaining combinations are (girl, boy), (boy, girl), and (girl, girl). So (g,g) is 1 out of 3. Simple really. Now, what is the probability if I tell you instead that the family has a daughter named Florida? Would you believe it improves to 1 in 2? Take a seat, this is complicated. First, there’s only a 1 in a million chance that a family has girl named Florida. And thus you can assume that the family will not name 2 daughters Florida. So now the combinations become (boy, girl named Florida – girl F), (boy, girl-NotF), (girl-NotF, girl-F), (girl-F, girl-NF). Of these 4 possible combinations, 2 have 2 girls, or 50%. P113

Don’t freak out – yet.

If you take an HIV test with 1 in 1000 false positive rate, and you come out positive, is it time to panic because the chances are 999 out of 1000 that you’ll be dead from this disease? Not quite yet… Assume that only 1 in 10,000 heterosexual, non IV drug using males is infected in the general population, and a false negative rate of 0 (that means if you do have HIV the test doesn’t miss it). This means that 1 in 10,000 will test positive. And in addition, since the false positive rate is 10x higher, there are 10 others who are not infected who will test positive as well. So now you’ll have 11 positives of which 10 are false. So the chances are really only about 9% not 99.9%. Make sure to demand a 2nd test to confirm. P116

Urine testing for performance enhancing drugs for Olympic athletes has a 1% false positive rate. This probably makes many people comfortable that an athletes chance of guilt is 99%, but as we have seen that is not true. Suppose you test 1000 athletes. 1 in 10 is guily (doing the drug), and the guilty had a 50/50 chance of the drug being revealed in the test. Then for every 1000 athletes, 100 are cheating, the test would find 50 of them. Meanwhile, the other 900 who are not cheating, 9 of them will be found positive falsely. So the chance of guilt is not 99% but only 50/59=84.7%. p118

The nose knows not

Hold a chunk of horseradish under your nose, and you’d probably not mistake it for a clove of garlic or the inside of your sneaker. But if you sniff clear liquids, all bets are off. In the absence of context, there’s good chance you’d mix up the scents. At least that’s what happened when researchers presented experts a series of 16 random odors: the experts misidentified about 1 out of 4 scents. P133

Another reason to stick with beer
Given all these reasons for skepticism regarding wine experts discrimination, one method to test an expert is the wine triangle; each expert is given 3 wines, 2 of which are identical. The mission is for them to choose the odd one out. In a 1990 study, the experts could do this only 2/3 of the time. P133

A 1000 fallen 9/11 victims whom we’ve not recognized

After 9/11/01, when travelers were afraid to take airplanes, their fear translated into about 1000 more highway fatalities. The hidden casualties from the 9/11 attack. P159

Researchers concluded: “That people have a very poor conception of randomness; they don’t recognize it when they see it and they can’t produce when they try.” And we routinely misjudge the role of chance in our lives and make decisions that are demonstrably misaligned with our own best interests. P174

Since there’s no difference, why have one?

A Columbia/Harvard study of large corporations whose bylaws made them vulnerable to shareholders’ demands that they respond to rough periods by changing management. They found on avg that in 3 years after firing there was no improvement in operating performance. No matter what the difference in CEOs ability, they were swamped by the effect of the uncontrollable elements of the system. P188

How to avoid confirmation bias

The human brain evolved to be very efficient at pattern recognition, but the as the confirmation bias show, we are focused on finding and confirming patterns rather than minimizing our false conclusions… We should spend as much time looking for evidence that we are wrong as we spend on searching for reasons that we are correct. P191

Get out there, and get lucky

In the real world, if several similar sized firms entered a market, small fortuitous events – unexpected orders, chance meetings with buyers, managerial whims – would help determine which one received early sales and over time, which came to dominate. Economic activity by individual transactions that are too small to forsee, and these small random events could accumulate and become magnified by positive feedback over time. P204

There are many high quality but unknown books, singers, actors, and what makes one or another come to stand out is largely a conspiracy of random and minor factors – that is luck. In this view, traditional media executives and talent hunters are just spinning their wheels. And thanks to the internet this has been tested… Participants were divided into 8 separate ‘worlds’ and could only see the data on music downloads of the people in their own world. All artists in all 8 worlds began with 0 downloads… If the deterministic view is true, the same songs ought to have dominated in each of the 8 worlds, and popularity rankings in those worlds ought to have agreed with the intrinsic quality as determined by the isolated individuals. But researchers found exactly the opposite: the popularity of individual songs varied widely among the different worlds, and different songs of similar intrinsic quality also varied widely in their popularity. P206

Maybe the editors knew something that the prize committee didn’t?

The Times of London conducted an experiment. Its editors submitted typewritten manuscripts of the opening chapters of 2 novels that had won the booker prize to 20 major publishers. The submissions were made as if they were the work of aspiring authors, and none of the publishers appeared to recognize them. How did they fare? All but one of the replies were rejections. P215


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