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Wednesday 13 April 2011

Investing at the Edge of Reality

Relief from the Bizarre

Mostly we expect scientists to make the world a more understandable place – or at least a more comfortable one. After all, science has helped us move from a state in which we prayed to invisible deities for deliverance from natural disasters to one in which we rely on functionally illiterate politicians to direct relief operations. So, perhaps prayer isn’t entirely irrational...

Unfortunately, as we’ve dug deeper into the mysteries of the multiverse, increasingly we’ve been forced to face the fact that reality is more bizarre than we can possibly imagine and that our senses offer us only a limited window on the world. Oddly, though, it also hints as to why we make investing mistakes.

Interfering with Reality

We’ve already looked at the genesis of quantum theory in Quantum Consciousness is Market Uncertainty; the astonishing insight of Albert Einstein that light really behaves as a wave in some situations and as a stream of particles in others. This, however, was simply the opening salvo in science’s savage attack on reality, a mere peek through the curtained window. The next step was to throw a brick through it.

Because light acts like a wave most of the time it produces effects that are consistent with this. Most notably if you beam a light wave at a screen with two slits in it the waves recombine after going through the slits to create an interferences pattern which looks like an evenly spaced bar code rather than the simple pair of bright lines which you might expect.

However, because light is also made up of particles – photons – it’s also possible to perform the double slit experiment with individual particles. If you send a beam of single photons, one at a time, at the double slit target you should expect to see a pair of bright lines rather than an interference pattern because as each photon arrives individually it has nothing to interfere with. Instead the interference pattern reappears.

Which suggests that somehow each individual photon is going through both slits at the same time.

Two Doors, No Models

We can represent this mathematically – it’s a statistical phenomenon – but this doesn’t help us understand what’s really going on because we have nothing in our experience which prepares us for something this bizarre. We’re left with the peculiar circumstance of knowing that quantum reality, out of which our macroscopic reality is built, seems to behave very differently from what we’re used to in everyday life.

What this brings home is that just because we can model something successfully it doesn’t mean we understand it, nor can we build useful models of macroscopic behaviour based on statistics because macroscopic behaviour isn’t generally statistical: if I approach two doors I measurably go through only one of them, unless I’m a magician (hint: in which case I actually go through neither).

Quantum Darwinism

However, one idea of the way that the microscopic builds up to the macroscopic is through the application of Darwinian evolutionary theory to quantum mechanics. Wojciech Zurek’s Quantum Darwinism suggests that some quantum states survive and prosper and become stable while others die off. As Campbell puts it:
“Quantum Darwinism portrays quantum interactions in terms of a Darwinian process where information is copied from the quantum system to its environment. Only a limited subset of available information can survive the transfer and forms the ‘classical’ reality we witness and are composed of”.
If you didn’t get that don’t worry. No one does.

Bayesian Updating

What’s interesting, for the financial analyst, is that this process is essentially Bayesian. The problem that Bayes’ Theorem solves is known as “inverse probability” and is a way of updating probabilities when new data is received. This is vital in areas like life assurance where figuring out that an epidemic of current obesity will reduce future life expectancy and increase future health costs will be very useful in calculating future premiums for gym rats.

In Quantum Darwinism the idea is that quantum states are continually probing and performing Bayesian updating based upon new data. What we see, at the macroscopic level, is the result: a stable environment as defined by the laws of entropy which, as we saw in Maxwell’s Demon Investor, define the default state of everything.

If this is true we live in a universe that’s governed by statistics and managed by Bayes’ Law, which also happens to be the statistical process that underpins most assumptions about efficient markets. Markets are supposed to be efficient because we update our expectations about future prices by incorporating new information based on a process that approximates to Bayes’ Theorem.

A Mammoth Problem

Behavioural economics doesn’t really dispute this idea, but imposes limits on our ability to process this new information. So we try to apply Bayesian reasoning but fail, because we have limited processing power. However, another strand of the research suggests that this is complete rubbish and that we don’t think this way at all.

The so-called heuristics and biases approach, which we looked at in Satisficing Stockpicking, argues that we don’t operate on the basis of probabilities at all, because until the Swedes started counting heads in 1749, we never actually had access to information about probabilities. We simply didn’t know how many people, on average, died by being run down by runaway woolly mammoths. What we did know was that our uncle, two cousins, a great niece, thirteen hunters from the next village and our prize hen had been stomped by stray pachyderms in the past year or so.

Observed Frequencies

This means that we had access to so-called observed frequencies – i.e. the repeated patterns we can see about us – about mammoth related deaths but had no way of knowing that these were simply down to a spate of bad luck rather than a more general danger. Most likely we would have inferred that mammoths were excessively dangerous and would start to take extreme precautions like wearing anti-elephant charms, worshipping chickens and developing a liking for very high tree houses which modern anthropologists eventually interpreted as a Sky God cult.

The underlying point here is that if reality is essentially Bayesian in nature then it would be peculiar in the extreme if our brains weren't also. Martins in Probability Biases as Bayesian Inference argues that any evolutionary tendency towards Bayesian processes would have given our ancestors an adaptive advantage over their mammoth-fearing competitors:
“It is clear that, whatever our mind is doing when making decisions, the best evolutionary (or learning) solution is to have heuristics that do not cost too much brain activity, but that provide answers as close as possible to a Bayesian inference".
Adaptive Bias

In fact this idea, known as adaptive bias, argues that we actually do reason as Bayes’ theorem would predict, but our results are biased by uncertainty and limited sample sizes. In fact, Martins argues that the ideas of bounded rationality proposed by Simons and enhanced by Gigerenzer, that we looked at in Behavioural Finance's Smoking Gun, ignore the problem of uncertainty faced by our ancestors.

In an extremely odd twist the idea here is that our brains are evolved to deal with uncertainty and if we’re faced with certainty – so an exact probability of a particular outcome – we convert this back into uncertainty. Our behavioural biases – our errors – are then explicable because we don’t know how to cope in conditions of certainty. Which, if you think about it, is pretty much what we're forcing on the universe in the double-slot experiment.

Investing Under Conditions of Certainty

Ultimately the argument is that, like the universe, we are fundamentally Bayesian in nature but, unlike the universe, we can’t probe every possible state all the time so we have to make do with a limited sample and assume a level of uncertainty. This manifests itself in behavioural biases which get exposed in the financial equivalents of the double slit experiment when we remove the uncertainty.

Occasionally, of course, we can make the universe do the same. The double slit experiment is the perfect example: we force it to make a choice between two equally likely outcomes and it responds by vacillating. It’s nice to know, at root, that reality’s human as well.

Related Articles: Maxwell’s Demon Investor, Quantum Consciousness is Market Uncertainty, Darwin’s Stockmarkets

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