Have you ever tried to mock up the outcome from a series of coin flips? It turns out that we are horrible at simulating randomness.
But as a great article in Nautilus vividly illustrates, we’re also horrible at accepting randomness.
…when video games truly play by the rules, the player can feel cheated. Sid Meier, the designer of the computer game Civilization, in which players steer a nation through history, politics, and warfare, quickly learned to modify the game’s odds in order to redress this psychological wrinkle. Extensive play-testing revealed that a player who was told that he had a 33 percent chance of success in a battle but then failed to defeat his opponent three times in a row would become irate and incredulous…
…So Meier altered the game to more closely match human cognitive biases; if your odds of winning a battle were 1 in 3, the game guaranteed that you’d win on the third attempt—a misrepresentation of true probability that nevertheless gave the illusion of fairness.
This notion of actual probability somehow being “unfair” is something to ponder. As is how the perversion of genuine probability can feel fair.
Are we more concerned with outcomes than opportunities?
It really is an excellent article and I recommend reading it all. It ranges from loaded dice found in ancient Egyptian tombs, to “pity timers” and faux improvement embedded in modern games, to gambling:
The results of any modern slot machine are based on arcane random-number generators in a computerized network, not on the fortunate conjunction of three wooden wheels. But losing to that sort of luck can be dispiriting. So gambling machines often employ the fiction of physical luck—by, say, making it look as if you just missed out on a king’s ransom as the final matching bar of gold or lemon reels to a stop just shy of a jackpot payout. This entices you to once more bet on odds that remain astronomical.
As always my emphasis.
There’s a fascinating line in the opening pages of Here’s Looking at Euclid:
By age 16, school kids have learned almost no math beyond what was already known in the mid-seventeenth century, and likewise by the time they are 18 they have not gone beyond the mid-eighteenth century.
If the point of schooling is to teach the current best understanding of the world, we appear to be failing.
Granted, maths is unlike science in that the old ways are built upon rather than overturned. We still learn Pythagoras theorem but not geocentrism.
This necessitates teaching newer mathematical discoveries in addition to what came before it. But is there really no recent mathematical discovery that would be useful to learn in school? Or at least help us shape more rounded adults, equipped for the modern world? Boolean algebra mayhaps?
I was thinking about this as I came across the following passage in The Lady Tasting Tea:
As measurements became more and more precise, more and more error cropped up. The clockwork universe lay in shambles. Attempts to discover the laws of biology and sociology had failed. In the older sciences like physics and chemistry, the laws that Newton and Laplace had used were proving to be only rough approximations. Gradually, science began to work with a new paradigm, the statistical model of reality. By the end of the twentieth century, almost all of science had shifted to using statistical models… Popular culture has failed to keep up with this scientific revolution. Some vague ideas and expressions (like “correlation,” “odds,” and “risk”) have drifted into the popular vocabulary, and most people are aware of the uncertainties associated with some areas of science like medicine and economics, but few nonscientists have any understanding of the profound shift in philosophical view that has occurred
It’s definitely my experience that people are more comfortable with a deterministic model of the universe than a probabilistic one. But why are so many of us stuck in old paradigms even as our world has become immensely sophisticated and complicated?
If nothing else, a more widespread probabilistic model would lead to more nuanced discussions around new research and challenges like climate change. A more modern understanding of mathematics would help us all get the most of technological advances.
Many of the books I’ve read criticising modern education see it as a relic of the industrial revolution and empire, geared towards producing identical widgets to keep things running smoothly. Can’t help thinking that’s right. And we haven’t changed it much.
As always my emphasis.
I’ve just started reading The Lady Tasting Tea, the story of statistics in/and modern science. But one of the early examples has gotten me thinking – how would a scientist go about testing the general intelligence/retained knowledge of a group of students?
Whatever we measure is really part of a random scatter, whose probabilities are described by a mathematical function, the distribution function.
It seems unlikely a contemporary scientist dropped onto planet B would propose the kind of one-and-done tests that students generally encounter at the end of subjects, semesters, years and school itself.
From the book:
Consider a simple example from the experience of a teacher with a particular student. The teacher is interested in finding some measure of how much the child has learned. To this end, the teacher “experiments” by giving the child a group of tests. Each test is marked on a scale from 0 to 100. Any one test provides a poor estimate of how much the child knows. It may be that the child did not study the few things that were on that test but knows a great deal about things that were not on the test. The child may have had a headache the day she took a particular test. The child may have had an argument with parents the morning of a particular test. For many reasons, one test does not provide a good estimate of knowledge. So, the teacher gives a set of tests. The average score from all those tests is taken as a better estimate of how much the child knows. How much the child knows is the outcome. The scores on individual tests are the data.
I’m quite biased here as I’m absolutely horrid at standardised testing – for a variety of reasons including medical. But it does seem to be yet another aspect of schooling that should be updated given our increasingly sophisticated understanding of the world. Randomness is not to be messed with.
(As usual my emphasis)
Human progress isn’t a straight line. This is as true of knowledge as anything else. Only in a computer game does knowledge accumulate through discrete ideas, with defined benefits and pathways.
In real life knowledge is messy, unpredictable and often the result of jamming together ideas and experiences in unpredictable ways. While experts can identify pertinent questions and fields for investment, history is littered with examples of unexpected intellectual explosions.
All of this came to mind as I read that the Australian government wants recipients of research grants to prove that it “advance[s] the national interest”.
Let’s overlook that the “national interest” and common sense are subjective, ever changing, and at least partially driven by intellectual progress.
One such intellectual explosion is chronicled in The unfinished game. Keith Devlin tells the story of a series of letters between Blaise Pascal and Pierre de Fermat as they try to solve what is essentially a problem for gamblers.
Called the problem of points it posits a game where two players have equal chances of winning each round. For some reason the game is disrupted before anyone has won, and so the question is how to divide the pot fairly.
Pascal and Fermat exchanged a series of letters on this problem. Although this process doesn’t pass muster as research by modern standards, would this question have passed the politicians’ test? I doubt it. But the impact has been profound.
“Within a few years of Pascal’s sending his letter, people no longer saw the future as completely unpredictable and beyond their control. They could compute the likelihoods of various things’ happening and plan their activities—and their lives—accordingly. In short, Pascal showed us how to manage risk. His letter created our modern view of the future.”
From what else I’ve read, the author oversells the letters a little bit. But it was undoubtedly a precursor of modern probability theory. It was part of a movement that profoundly changed the world.
“Even those who are not schooled in the mathematics of calculating odds know that the future is not a matter of blind fate. We can often judge what is likely to happen and plan accordingly. Yet before Pascal wrote his letter to Fermat, many learned people (including some leading mathematicians) believed that predicting the likelihood of future events was simply not possible.”
“Without the ability to quantify risk, there would be no liquid capital markets, and global companies like Google, Yahoo!, Microsoft, DuPont, Alcoa, Merck, Boeing, and McDonald’s might never have come into being.”
“Within a hundred years of Pascal’s letter, life-expectancy tables formed the basis for the sale of life annuities in England, and London was the [centre] of a flourishing marine insurance business, without which sea transportation would have remained a domain only for those who could afford to assume the enormous risks it entailed.”
All of this isn’t to say that government’s can’t and shouldn’t roughly guide their research dollars. Some questions are more pressing or have more potential than others, which is why the current Australian system contains peer review.
But that knowledge is a simple widget or knob to be turned up or down for national benefit is an ahistorical view of progress.
…the human mind is built to identify for each event a definite cause and can therefore have a hard time accepting the influence of unrelated or random factors. And so the first step is to realize that success or failure sometimes arises neither from great skill nor from great incompetence but from, as the economist Armen Alchian wrote, “fortuitous circumstances.”
This from The Drunkards Walk by Leonard Mlodinow. You can see this phenomena everywhere from politics to sports. We are quick to assign cause and effect, blame and praise, without considering the probability of it having taken place.
It reminds me of the brilliant Thinking In Bets, which I might break out again for another read.
…When we look at extraordinary accomplishments in sport – or elsewhere – we should keep in mind that extraordinary events can happen without extraordinary causes. Random events often look like nonrandom events, and in interpreting human affairs we must take care not to confuse the two.