Sunday, August 12, 2012

Teach Your Children (Probability Theory) Well


So here we are, in the waning weeks of summer 2012, facing a remarkable paradox: on the one hand, we have a record-shattering drought, crop failures and a threat to global food security, and on the other not a whisper of climate change or its challenges in a political contest on track to suck as much as $2 billion into advertising.

There is a political economy dimension to this mess, of course: disruption of the carbon cycle remains an inconvenient problem, especially for those who profit mightily from it.  A part of our paralysis, however, can be chalked up to the fact that the twentieth century’s most important cognitive revolution, the shift from deterministic to probabilistic thinking, is still confined to a tiny sliver of the population.

Although the foundations stones of probability theory were set in earlier centuries, it was not until the first decades of the twentieth that the practical uses of probability, in forecasting and hypothesis testing, emerged.  At the same time, humans acquired vast new powers to manipulate nature and each other—powers that could be understood and regulated only through an understanding of probabilistic relationships.  Whether the topic is food additives, air pollution, or the effect of propaganda campaigns of various intensities and expense on voter behavior, intelligent discussion is impossible without a familiarity with the nature of stochastic processes.

Yet most people think in much simpler terms.  A either causes B or it doesn’t.  If you can point to an A without a corresponding B, there’s no cause—end of story.  Poverty doesn’t hold back promising students; just look at all the kids who succeed despite their background.  Don’t worry about the warning label on the package: smoking can’t cause cancer because I know someone who is almost 90, in great health and still smokes a pack a day.

I know that there are studies that tie beliefs about climate change to value systems, political affiliation and so on, but just listen to the debate between worriers and deniers on its own terms.  The worriers, like me, point to the increasing likelihood of catastrophic impacts; it means something to us to say that, while a specific climate event cannot be tied deterministically to carbon loading, droughts and other severe impacts are now more likely to occur.  The deniers point to individual exceptions like periods of cooler weather and say, see, you can’t prove causation—it’s all a hoax.

Thinking probabilistically isn’t something we’re born with.  It has to be taught; in fact it has to be taught over and over because it seems to go against our natural cognitive tendencies.  A lot of readers of this blog (insofar as a high percentage of a low number can be “a lot”) are teachers.  Whatever your subject, there is no more important goal you can strive for.

8 comments:

rjs said...

what's the probability of this?

http://www1.ncdc.noaa.gov/pub/data/cmb/images/us/2012/jul/YTD_allyears_Jul2012.png

Scott said...

The simple answer: Even though citizens of the USA think they are the world, 1934 was an average year in temperature for the world. 1934 is not even one of the 10 warmest years for the world. Inferring Global Temperatures probabilities from US data is silly.

Wade-Kelman said...

Hi, Scott.
That's a pretty clever way to prove Peter Dorman's point.
Mr. Dorman:
I thought that the twentieth century's greatest cognitive revolution was that most of the people in the world learned to read. (Still some exceptions, though.) Saying that they now need to shift to probabilistic thinking, when millions of years of evolution have superbly adapted us to jumping at the rabbit, might be a bridge too far.
My education was is Physics, so I am intimately familiar with the fact that we are well adapted to survive naked on the Serengeti, but struggle to understand that velocities don't combine with simple addition.
I sympathize with your goals, but I think that we will run out of time as a species before you get people to reflexively think in terms of probabilistic outcomes.
A more effective approach might be to set up systems that enforce certain good behaviors, like forced savings for retirement, or placing the controls for engine spark advance and air-fuel ratio where the driver can't screw with them.
Unfortunately, I don't have any ideas for how this can be done in relation to climate change. It may just be, as Joseph Tainter and Jorgen Randers believe, lights out for large mammals on this planet.

Matthew Martin said...

I disagree. I think that to a certain extent everyone has an intuitive ability for probabilistic thinking--just look at how people engage in precautionary savings and other behaviors.

I think that the point about global warming isn't about deterministic thinking. People understand that global warming doesn't mean that every single day will be warmer. Rather, there are two things going on: one is that they are continuing to use the counter-example argument even thought they know that it is logically invalid. The other aspect is that people have to form an opinion on the basis of extremely small datasets--while in statistics, if the data set is too small to establish an effect with 95% confidence we say that the study is inconclusive, in the real world people still have to form opinions. Hence, a single cold day weighs much more in people's minds where we only think about a handful of days from the most recent years, than in empirical datasets where we have every day for 200 years.

Anna Paradox said...

I like your point. More people who can think in terms of probabilities would help. So, here's a heterodox suggestion:

If you want your children to understand probabilities, the simplest approach might be the after-dinner poker game. Analyzing die rolls was the start of probability theory -- actually observing random events over many trials is the best way to get a feel for what probability means. Poker is compelling enough to gather interest over time, and also teaches about incomplete information, psychology, when to act under risk. When I took Econometrics, I found my poker background gave me a head start on a lot of my classmates, who struggled to think in a way they found counter-intuitive.

Poker also teaches why the other players might not be telling you everything. That's a useful correction to the assumption of complete information.

Wade-Kelman said...

Hi, Matthew.
I agree that people form opinions from small data sets. We have evolved that way. We jump at the rabbit, even though it may be being followed by a tiger, because most of the time, we get to be the eater rather than the eaten.
But modern systems are much more complex than chasing rabbits, and 99% of the population is not able to think in probabilistic terms. Here, test yourself. Which door should you open?:
http://marilynvossavant.com/game-show-problem/
This is a problem in probability. How did you do? Were you, an obviously intelligent modern human, the eater or the eaten?
Would it be too much to say that the probability of continued life (mammalian life - reptiles and insects will do just fine) on this planet depends on getting the answer to this question right? And if you were the eaten, how can we ensure that we get this answer right?

Dan Crawford (Rdan) said...

Hi Peter...may I repost?

Peter Dorman said...

Dan -- feel free.