The bigger picture and the smaller picture
Even when we are sure we are being guided by the facts, we are well advised to zoom out as well as to zoom in
When I was a little boy, I used to wonder whether our own solar system, with the Sun as a nucleus and the planets like electrons orbiting around it, might actually be a single atom in some unimaginable huge object. Even though I know better now, occasionally I experience the same kind of awe now as I felt then, when I am reminded of the vastness of our universe, and of the amount of stuff we don’t know: there is always a bigger picture that we imagine.
Somehow I failed to become an astrophysicist, and instead ended up a student of human behaviour and cognition. Intriguingly, however, I find that a very similar notion of a bigger picture applies in this domain as well.
A strange pattern
You may have heard the remarkable story of the Polish village of Miejsce Odrzanskie (literally, just ‘place near the Oder’), in which for nearly 10 years not a single boy has been born. It’s hard to suppress an initial reaction of “Hey, that’s strange!”, isn’t it? We all know that, statistically, a new baby is pretty much equally likely to be a girl as a boy. So the image of an unbroken sequence of baby girls for 10 years certainly seems highly unusual.
But what do we know about this amazing place and its birth pattern? How large is that sequence of babies in our mind’s eye? If this was a sizable provincial town of 25,000 souls and 100 new-born citizens every year, it would indeed be a spectacular coincidence. But Miejsce Odrzanskie turns out to be a minuscule village: it has a population of just 328, which produced just 12 children since 2010. As the picture gets bigger, the surprise gets smaller.
Still, 12 girls in a row is by all accounts not very likely — the odds are 4096 to 1. So perhaps there is something strange taking place here — some bizarre mutation of the sperm of the male villagers, or some mysterious radiation perhaps? Well, those things are possible, but to understand how unlikely this story really is, we’d need to make the picture bigger still. In the UK there are just over 7700 cities and towns. Extrapolating this to all of Europe, there are probably at least 60–70,000 of them. If we’d take a snapshot at this precise moment, we would expect around 15 places (60,000 divided by 4096) in which the most recent 12 babies are girls, and similarly for boys. Unusual, yes, but not odds-defying unusual.
So why might we still think there is something really strange at play here? First, we see an event ( only girls being born) that appears to deviate wildly from what we believe to be the normal case ( roughly as many boys as girls are born), without realizing that in specific cases this general rule does not necessarily hold. For example, women whose children are all of the same sex are no more unusual than women who have an equal number of male and female offspring — if these women have two children. Next, we see a spurious quantification: “nearly 10 years in a row”. It doesn’t really matter whether the period in question is 10 days or 10 years. What counts is how many babies were born. An unbroken sequence of 12 girls is not the same as one of 200. And finally, we consider it peculiar that this particular village exhibits this unusual pattern of births, without considering how likely it is that any village in a collection does so.
What we see is all there is
Failing to see the bigger picture can also make us think that something is more likely, or more prevalent than it really is. We sometimes have a tendency to extrapolate from a sample of n=1, and project that observation much wider and farther than we should. Seeing one BMW-driver failing to use their indicators can be enough to confirm the assumption that this is typical. Reading one news report about a mugging in a seedy quarter one Friday night can solidify the belief that the whole town is a no go area after 8pm. What we don’t see is how many BMW-drivers conscientiously indicate when they turn, or how many people arrive at their destination safe and sound in the evening.
This is what Daniel Kahneman calls “ What you see is all there” is in his book Thinking, Fast and Slow. We tend to give more weight to what is prominent, and implicitly neglect what we don’t see.
I was reflecting on this big picture thing last weekend while visiting Bourton-on-the-Water, a little Cotswold village. One of its attractions is a 1/9 scale model of itself which, amusingly, contains a model of itself (which in turn contains an even smaller model!) There is not only an obvious bigger picture — the real-life version of the miniature village — but also a smaller picture. It’s like the obverse of my childhood fantasy: individual atoms, with their nucleus and a bunch of little electrons in orbits, might well be small solar systems, perhaps populated by tiny creatures well beyond our own ability to observe them.
Detail in the small picture
And just like we sometimes fail to see the bigger picture, we sometimes miss the smaller one too. We look at the wealth of nations (to coin a phrase) and see that the US has a GDP per capita just shy of $60,000. That puts the country 13th in the global stakes, well ahead of, say, a poorer country like Colombia with $14,500. It’s easy to assume an average American earning a decent income not a million miles from that GDP per capita number. (And indeed, the median annual US household income was $56,000 in 2015.) But that aggregate figure doesn’t show the smaller picture, in which we see that nearly 16 million American households must survive on less than $15,000 per year.
Smaller pictures may reveal qualitative rather than quantitative stories too. The British government maintains that there are alternative administrative and technology solutions which, in the imminent Brexit, would avoid a hard border between the republic of Ireland and the British province of Northern Ireland, without the need for the vexed backstop. Trusted trader schemes would eliminate the need for checks at the border itself, and replace it with checks at the final destination for participating businesses. That is at least the big picture, which reflects the bulk of the goods traffic between the two countries. But in the small picture, there are not only the small businesses for which this arrangement would be a lot harder, but also numerous individual situations for which a hard border would be all too real, as suggested in this twitter thread. Nurses who treat patients in both countries carrying medication and medical equipment to and fro, cross-border arrangements for medical emergencies with ambulances or helicopters, home deliveries of bread either side of the border, cross-border shopping — none of this would be addressed by the big picture interventions.
“People and their daily lives” are often invisible in the big picture, but that doesn’t make their personal story any less real and indeed dramatic in the small picture.
If we really want to understand the world, we need to be aware of our tendency to draw conclusions just from the current picture, and of the mistakes we may be making if that is what we do. If we consider the bigger picture, we can evaluate a specific situation against a wider reference and avoid mistaking it as representative, or as unlikely. By considering the smaller picture we avoid assuming that everything is like the average, or like the majority.
Perhaps it is a good idea to imagine ourselves in a model village, and remember to both look up to the real thing, and down to the model of the model.
Originally published at http://koenfucius.wordpress.com on August 30, 2019.
Thank you for reading this article — I hope you enjoyed it. Please do share it far and wide — there are handy Twitter and Facebook buttons nearby, and you can click here to share it via LinkedIn, or simply copy and paste this link. See all my other articles featuring observations of human behaviour (I publish one every week) here. Thanks!