How to see into the future

Most people think that it would be a useful skill to see into the future. Probably they are right. It would certainly be valuable for investors to be able to know which shares were going to perform well. But perhaps, even if you could see into the future, you wouldn’t.

Literature is full of characters who can see into the future, and are ignored.   Tiresias.  Cassandra. The fool in King Lear. My favourite example is Laocoön, a Trojan priest who tries to convince his fellow Trojans not to be taken in by the wooden horse that the Greeks have left outside their gates. For this impiety, he dies in a horrible way.  The gods send snakes from across the sea to shut him up kill him and his sons. (see Barbara Tuchman, in the March of Folly for more detail)

This sort of thing goes on more often than we’d like to admit in real life. Aristarchus of Samos a mathematician who lived around 300BC used his knowledge of geometry to suggest that the earth revolved around the sun. He supported his heliocentric model of the universe with calculations but the model failed to catch on for a couple of thousand years. This is despite the fact that his model fitted the evidence better, men just preferred to think that they were at the centre of the universe – and made lots of complicated calculations to allow for their geocentrism.

So very often prophesying the future only requires us to focus on some unpleasant intuitions that we would prefer to ignore.

What surprises me is that this doesn’t just happen in politics, law, and other areas where people can hold opinions. It happens in science. It even happens in maths. You would think “proof” is logical, and once a mathematician has a convincing proof it would be immediately accepted. But that isn’t the case.

And for that reason, I think the sociology of mathematics is fascinating. I ended up finding out about this by accident, because I came across a 1982 essay by the philosopher of science David Bloor,Polyhedra and the Abominations of Leviticus.”

It’s a wonderful essay – that starts with the question “How are social and institutional circumstances linked to the knowledge that scientists produce?”

The essay compares the way that German mathematics professors responded to difficulties with one of Euler’s geometric proof to do with polyhedra. Bloor discovers the response was exactly the same way that primitive tribes respond to animal “taboos”.

The reason why is that both funny geometric shapes (polyhedra) and animals don’t fit into the taxonomy. The pig, for example, fails to satisfy the proper conditions of being a ruminant: it doesn’t chew the cud. Mary Douglas, the anthropologist argued in Purity and Danger that Leviticus declared pigs unclean because the place of pigs in the natural order is superficially ambiguous, since they shared the cloven hoof of the ungulates, but do not chew cud.

This principle explains why the list of abominations in Leviticus includes eels, rock badgers, and others whose status perplexed biblical commentators. Later these Jewish food taboos became about identifying who was collaborating with the occupying power, and who was an “unpolluted” Jew. It was impossible to eat with the Romans and not break the food taboos, and hence anyone who did so was likely to be a turncoat. But originally the food taboos were about animals that did not fit into the right boxes. Black swans.

The basic idea of the essay is that taboos (whether they are mathematical or animal) break the orderly boundaries of our thinking. Whether it be a counterexample to a proof (does a cube within a cube still count as a polyhedron?); or an animal which does not fit into the taxonomy; or a deviant who violates the current moral norms (Alan Turing?), the same range of reactions is generated. No matter how high the level of thinking, the stone-age responses to category-violation apply. It’s true even for pure geometry.

For the mathematically inclined the example that David Bloor gives is Euler’s proof that for a polyhedra the number of faces (F), edges (E) and vertices (V) are related in the formula V – E + F = 2. This holds true for “simple” polyhedra, but what about a cube with another cube sitting on top of it in the middle of one of it’s faces? What about a cube hollowed out from within another cube? The equation breaks down. The latter were first spotted by Lhuiler in 1812 then rediscovered by Hessel in 1832.

You could argue that is trivial. The word “polyhedron” has to be strictly defined. We could say that if you start arguing about the word “bachelor” to cover men who merely behave like bachelors then of course it won’t be true that all bachelors are unmarried men. But the point is more subtle than that, it emerges a polyhedron is not to be thought of as solid, it is a system of surfaces, through any arbitrary point it must be possible to draw a plane that will slide the polyhedron into only one polygonal cross section etc.  Because when you start thinking about these abstract structures in a precise way, you gain all sorts of insights about the “real world”.  Mathematics often develops the tools which physicists use to understand nature.  

This happens all the time in mathematics. And it takes a while for ideas to become accepted – whether it is non Euclidean geometry, or theory of infinite sets, Turing’s concept of a “computer” or whatever. There was nothing to stop anyone playing with these abstract ideas, people just didn’t because it was easier to think along the same lines, and in the same boxes, that people had always thought.

And I think this really helps understand the investment process. Because by and large people follow simple rules of thumb like “buy stocks which pay a high dividend” or “buy stocks where the growth in revenue is accelerating” or “shares in supermarkets are low risk, defensive investments” or even AAA rated securities are all low risk. These rules of thumb can be effective most of the time, but can also fail catastrophically.  For instance, banks were all paying high dividends ahead of the financial crisis, on this measure they did not look risky.  This was the primary reason most fund managers owned banks.  They then got analysts to build very complicated models, with divisional forecasts to justify the rationale – to show they had “done their homework.”

But one income fund manager, Neil Woodford, was one of the very few who identified that these dividends were not sustainable.  He followed a different, but equally simple rule of thumb –competition was driving down margins and the banks were responding by lending more money, and making increasingly risky decisions to pay their dividends.  To Woodford this looked like a recipe for disaster.

So you don’t really need to be able to see into the future. And some people, even if they could see into the future…they wouldn’t.  The trick of being a superior investor is to look for the anomalies in the present. The exceptions that don’t fit into the taxonomy and understand them. This also explains to me why Buffett is such a big fan of Bertrand Russell. And why Soros is a fan of both Russell and Popper. These men thought hard about thinking.  They also wrote about subjects that were taboo to most people. They focused on the present, but were decades ahead of their time. But eventually the majority catches up with the views of a Russell, a Popper, a Buffett or a Soros.

So the trick is to focus on what is widely available now but which other people find uncomfortable. Sadly most fund managers don’t pay analysts to do this – they pay for very clever, analytic people to work very hard building models to justify their existing beliefs. Some of these sophisticated models could no doubt show that the earth is at the centre of the universe.