Two stories, superficially unrelated, neatly tied together by a deep lesson at the end.
The first is the case of Lucia de Berk, a Dutch nurse sentenced to life imprisonment in 2003 for multiple murders of patients under her care. However, there was very little direct evidence tying her specifically to the deaths of the individual cases. Much of the prosecution’s case against her was statistical: it was simply extremely unlikely, they argued, that so many patients would die under the care of a single nurse. Numbers like “one in 342 million chance” were bandied about.
But statistics can be tricky. Dutch mathematician Richard Gill has gone over the reasoning presented in the case, and found it utterly wrong-headed; he has organized a petition asking Dutch courts to re-open the case. Gill estimates that 1 in 9 nurses would experience a similar concentration of incidents during their shifts. And he notes that there were a total of six deaths in the ward where de Berk worked during the three years she was there, and seven deaths in the same ward during the three years before she arrived. Usually, the arrival of serial killers does not cause the mortality rate to decrease.
But patients had died, some of them young children, and someone had to be responsible. Incidents that had originally been classified as completely natural were re-examined and judged to be suspicious, after the investigation into de Berk’s activities started. The worst kinds of confirmation bias were in evidence. Here is a picture of what de Berk actually looks like, along with a courtroom caricature published in the newspapers.
Also, she read Tarot cards. Clearly, this is a woman who is witch-like and evil, and deserved to be punished.
The other story involves a brilliant piece of psychological insight from Peter Sagal’s The Book of Vice, previously lauded in these pages. It involves the reason why people play slot machines, or gamble more generally. There are many complicated factors that go into such a phenomenon, of course, but it nevertheless remains a deep puzzle why people would find it so compelling to roll the dice when everyone knows the odds are against you.
Peter asks us to consider the following joke:
An old man goes to the synagogue and prays, every day, thusly: “God, let me win the lottery. Please, just one big win. I’ll give money to the poor, and live a righteous life. . . . Please, let me win the lottery!”
For years, he comes to the synagogue, and the same prayer goes up: “Let me win the lottery! Please, Lord, won’t you show your grace, and let me win the lottery!”
Finally, one day, after fifteen years of this, as the man mutters, “The lottery, Lord, let me win the lottery. . . ,” a golden light suffuses the sanctuary, and a chorus of angels singing a major C chord is heard. The man looks up, tears in his blinded eyes, and says, “Lord . . . ?”
And a deep resonant voice rings out, “Please . . . would you please BUY A TICKET already?”
And that’s why we gamble: so God can answer our prayers. Fortune’s wheel, in other words, might occasionally want to favor us, but how can it if we don’t give it a chance? By playing the slots, we make it so much easier for Providence to bestow its bounty upon our deserving heads.
The common thread, of course, is the deep-seated aversion that human beings have to accepting randomness in the universe. We are great pattern-recognizers, even when patterns aren’t really there. Conversely, we are really bad at accepting that unlikely things will occasionally happen, if we wait long enough. When people are asked to write down a “random” sequence of coin flips, the mistake they inevitably make is not to include enough long sequences of the same result.
Human beings don’t want to accept radical contingency. They want things to have explanations, even the laws of physics. They want life to have a purpose, chance events to have meaning, and children’s deaths to have a person to blame. They want life to make sense, and they want to hit the triple jackpot because they’ve been through a lot of suffering and they damn well deserve it.
Of course, sometimes things do happen for a reason. And sometimes they don’t. That’s life here at the edge of chaos, and I for one enjoy the ride.
As an aside:
So is it necessarily irrational to gamble because statistically you lose money on it?
How about insurance, almost everybody is going to pay in more then they get out. In a way insurance is like gambling on the event that something bad happens to you.
The point is that the many small payments into the insurance don’t decrease our quality of life significantly, whereas the big loss in the unlikely event that something bad happens would have a significant negative impact outweighing the cumulative small negative impacts of the cost of the insurance.
The same logic in reverse can be applied to gambling, gambling would not make sense if you paid in 6€ and had a 50-50 chance to win 10€ back. but paying in 6€ and having a 1 in a million chance to get 5 million € back makes sense, since the cumulative negative impact of 5€ a week is insignificant (just give up smoking) compared to the positive impact of winning the lottery once (even accounting for how unlikely this is).
“We are great pattern-recognizers, even when patterns aren’t really there. ”
This also explains the tendency of many to invest deeply in various conspiracy theories.
I agree with your basic sentiment, but for sake of argument, let me push a little. The only indeterminism in the laws of nature is in quantum measurement (assuming, for the moment, the standard interpretation). So are you saying that the vagaries of life are quantum in nature? How, then, do we observe any regularity in the world at all? Does it go back to cosmological ICs? If so, then everything *does* happen for a reason!
George
Unless we know the precise state of the universe, the exact laws of physics, and have access to a computer comparable in size to the universe itself, there’s a whole lot of randomness other than that arising from quantum mechanics.
Lovely post 😀
aph
“When people are asked to write down a “random” sequence of coin flips, the mistake they inevitably make is not to include enough long sequences of the same result.”
Well, 95% rate of difference is not “inevitable” – I’d like to know about the people who *can* do a good enough fake, just like I’m interested in those who did not follow through on Milgram’s obedient torturer experiments, etc. These are the ones we can learn from, psychology etc. is too fixated on the norms (except for intelligence per se and illness.)
There is regularity in the universe because quantum theory makes very accurate predictions of the probability of events occurring.
This is true whether you accept the Copenhagen Interpretation or are sane and accept the unitary evolution of the wave function and favour the Everett interpretation. The calculations come out the same.
“Cosmology is the Killer App for Everett Quantum Mechanics” – James Hartle
I think people buy lottery tickets because of the feeling of exitement that you can get by knowing that you will probably lose but you might win. You can actually get a kick out of that even though you are perfectly rational and know that if you keep buying tickets you will lose in the long run. It’s not about thinking wrong, it’s about playing with the emotions you can induce in your body. Nothing strange about that.
But that kind of game should have nothing to do with what’s going on in a court room.
Each of us beat considerable odds just to be here worrying about randomness. We probably realize that fact at some deep level and gambling is just another method we use to validate that fact. What’s with that?
Sean, you have changed the question from “do things happen for a reason?” to “will we ever know the reason?”
George
Sean, you have changed the question from “do things happen for a reason?” to “will we ever know the reason?”
But in the sense you seem to be taking it, “this happened for a reason” is a pretty vacuous statement. Consider a toy model universe: a bottle of classical ideal gas in which the initial position and velocity of every particle is known. Suppose you take a snapshot of the gas, draw a line down the middle of the bottle, and count the particles on each side. You find that there are 1.03 billion particles on the left side of the bottle, and 0.97 billion particles on the right. Then you ask me, “did this happen for a reason?” I could answer you by writing down the equations of motion, plugging in the initial conditions of the particles, and showing that at the time you took the snapshot, there would be 1.03 billion particles on one side of the bottle and 0.97 billion on the other; the equations of motion and the initial conditions would be the “reason.” But if you accept my answer, you are forced to conclude that everything happens for a reason, so answering the question “did this happen for a reason?” doesn’t give you any information at all.
If you argue (as I think you’re doing) that most of everyday life is essentially classical, and that everything therefore happens, trivially, “for a reason,” go ahead—but I don’t think your definition of “for a reason” is a good one, because it doesn’t give me any useful information about the world!
And once they think they’ve found those patterns, they usually need to be hit with a cinderblock to convince them that those holes in their theories are more than incidentals.
“That’s life here at the edge of chaos, and I for one enjoy the ride.”
Reminds me of the two pieces of music I’d like played at my funeral: Richard and Linda Thompson’s “Wall of Death,” and The Band’s “Life is a Carnival.”
Enjoy the ride.
Aaron, I don’t need to know any of the details of elementary particles to live my life, but that doesn’t stop me from wondering what happens down there. There’s a big conceptual (and, in some cases, empirical — cf. Bell) difference between uncertainty in principle and uncertainty in practice.
George
B. F. (Burrhus Frederic) Skinner [20 March 1904 – 18 August 1990), Ph.D., leader of Behaviorism, was offered a lucrative consulting contract from a slot-machine manufacturer to make a more addictive gambling device. They’d heard him comment that gambling is addictive precisely because of the random mixture of reward and punishment. He declined, on ethical grounds.
I had a period of about a year in which I was working at a customer’s site in Virginia. People seemed to buy a candy bar or some other treat or go out for drinks on payday. Instead I spent two dollars for two lottery tickets. Yes, my chances of winning the millions were poor. However I received as much satisfaction as those who bought a candy bar and far more than those who were nursing a hangover the next day.
Spending a trivial amount in a contest where a win provides an amount similar to a lifetime’s wages is not necessarily an irrational act.
Changing focus slightly, you say “Here’s a picture of what de Berk actually looks like…” – its interesting that you place so much credence on the accuracy of the photograph. It would probably be just as easy to look through her family snapshots and find a picture of her where she looked like any stereotype you care to name and say “this is what she actually looks like”. Photographs can be just as misleading as statistics.
Having grown up in the horse racing industry, I’ve never bought more then a few lottery tickets, because I know what five to one means and if I gave serious consideration of the odds lotteries entail, I wouldn’t be able to get out of bed in the morning, given the fact that the odds of dying are far, far greater then of winning the lottery.
Hi George. You may not remember me, but I used to pester you on occasion with evidence against BBT and you were kind enough to respond.
fh: Your comparison of gambling and insurance is interesting. According to Kahneman and Tversky people are loss averse–a loss has about 2 1/2 times the impact of a gain of the same magnitude. Thus, we would expect people to pay about 2 1/2 times more for insurance to avoid a loss than for lottery tickets that offered a potential gain with similar expected returns. For a $200K home, given a 1/500 change of total loss by fire, the expected return of fire insurance would be about $400. Given that the average state lottery returns about 50% of the ticket proceeds to ticket buyers, buyers would need to buy about $800 in tickets for an expected return of $400. Even without loss aversion we should not expect rational people to buy lottery tickets.
following on the insurance theme, I think this is exactly why insurance coverage should be state sponsored program paid for by income taxes on people/employers. Insurance has the economic effect of a VAT tax and a parasitic one at that because only the insurers profit.
If you calculated all the insurance that you pay and is embedded in the cost of goods and services you buy it would be staggering. It would not surprise me if 25-40% of take home income is spent directly indirectly on insurance.
e.
“Human beings don’t want to accept radical contingency. They want things to have explanations, even the laws of physics.”
This reminds me of Dirac’s large numbers hypothesis. This idea was based on the observation of (numerological?) coincidences in certain dimensionless length and force scales set by the size of the observable universe, planck’s constant, G etc.
Was Dirac unwilling to accept this “radical contingency?”
I’ve always been troubled with Dirac’s sudden interest in physics numerology.
The key observation is that we must acknowledge that radical contingency is a possibility without asserting that we can ever know for sure that it is the case.
At some point, talking about reasons for things may not even make philosophical sense. At some point, we may just never be able to answer some questions, nor, even more oddly, even know if those questions make philosophical sense.
I’ve always wondered why the fundamental equations of physics involve integer or “simple” rational powers (e.g. 1/2, 2/3) of physical quantities. Of course, when it comes to fluid dynamics and Chaos theory, for example, we begin to see messy equations. But until one achieves that level of mastery, the formulae encountered are mathematically elegant and simple. Anyone here care to elaborate?
“I’ve always wondered why the fundamental equations of physics involve integer or “simple” rational powers (e.g. 1/2, 2/3) of physical quantities.”
The simpler the pattern, the sooner it’s discovered.
Modern physics is only 350 years old. We’ve discovered many of the simpler patterns, but might not for many millennia discover any pattern whose most concise statement is, say, a gigabyte long.
It seems not too harsh that we require the laws of physics to be mathematically necessitated, and that we inquire into the origins of that relationship at the most fundamental levels. Causality is logical, and science works, b!tches 🙂