Thinking in Shades
Issue #40
How do you interpret “70% chance of rain”?
Is the forecast wrong because it didn’t rain that day? The forecast means that, under these weather conditions, it would rain on (about) seventy out of hundred days – leaving the possibility of several dry days. This is more nuanced than rain or no rain. ?????
But was the forecast correct?
Probabilistic predictions are hard to evaluate because we need many observations to evaluate them. Daily weather forecasting is an area where lots of information is available, but even here a tendency to cater to the audience reduces accuracy.
Nate Silver founder of fivethirtyeight.com (a website he’s no longer associated with) elaborates in his book The Signal and the Noise. For instance, The Weather Channel generally overpredicts rain because people prefer unexpected sunny days over rainy ones.
Applying probabilistic thinking to less frequent events like elections is harder, and that’s an area where Nate Silver made his name – and has taken flack, as when he predicted Trump had about a 30% chance to win in 2016. ???
But elections, as with many other things in life, have discrete outcomes so people want a black or white prediction – and are then disappointed when the predicted event does/not happen.
The human tendency is to simplify the world to understand it. This urge to see the world in orderly (often mathematical) terms goes back at least a couple of thousand years to Euclid and the early conception of shapes. Even a few hundred years ago, Cartesian coordinates (for example x,y axes in a chart) and Newton’s laws generally described an orderly universe.
Chance was a topic that wasn’t studied in a formal manner for a long time and was usually relegated to unsavory domains like gambling. Gerolamo Cardano was among the first to formalize chance, and eventually it became inseparable from other areas of study.
But as with the chance-of-rain example it is not as though everyone today easily engages in probabilistic thinking.?
So, here’s the question. . . ???????
Is thinking probabilistically an ability that we had to slowly evolve over time? Were we simply incapable of thinking like that before?
One way to answer such questions is to look for comparison groups – in this case the animal world, where we find some fascinating studies.
The first place one would look in the animal world would be our closest animal cousins (the Great Apes like Chimps, Gorillas and Orangutans), right? Turns out our cousins do quite well when it comes to statistical reasoning.
Okay, let’s go further down in the evolutionary tree. How about Corvids (crows and ravens)? When a team of researchers led by Dr. Melissa Johnston trained crows to peck on a screen for rewards, they learned to consistently pick the option associated with a higher probability of reward. ????
In human terms, as Dr. Johnston explains, imagine choosing a place for brunch. When you choose a place that’s less likely to be busy at this time given other factors, you are thinking probabilistically based on prior experience – which is what the crows were doing. And more stunning was that the crows continued to exhibit this behavior for a full month after their training. ????????
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What if we go further down the tree? It’s hard to find probabilistic thinking, but there is more evidence of thinking than we realized. For instance, a new study offers evidence that spiders can extend their minds (as we saw recently with humans) by using their webs to think. ?
Going even simpler, how about jellyfish? Another recent study shows that, even with no brains – think about that – jellyfish can learn from their mistakes and change their behavior.
Doesn’t all of this indicate that evolutionarily we should be more than capable of higher cognitive actions like probabilistic thinking? We seem to be endowed with it – but just don’t do it very well.
Why? ?
One reason could be that we live in a highly stimulating environment, are blessed with great information processing ability, and paradoxically, have to simplify everything in order to not get overwhelmed.
In the process of simplifying, we do things like seeing the world in straight lines when it is fractal, in black and white when it is gray, in ones and zeroes when it is everything in between (i.e., probabilistic).
What to do about that?
One solution is to think in terms of placing bets as Annie Duke (the former poker champ) has suggested. Wagering even small amounts of money is likely to make our thinking more considered and probabilistic.
Another solution is from Luca Dellana, whose work on ergodicity we examined before. When faced with a decision, imagine a range of outcomes (or parallel universes) from one extreme to the other. How likely is it that the outcome you desire will occur in a majority of those scenarios? This is more likely to help us arrive at the right decision. ?
(Some) birds do it. (Don’t know if) bees do it. But we certainly can and should do it. ?????
End Notes
A quick and easy read on crows' ability to think probabilistically:
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#probabilisticthinking, #insight, #learning, #animals, #natesilver