Cargo Cult Math comes home to roost, (mis)modelling the markets and the virus
Gerd Gigerenzer is a fascinating guy, not nearly well known as he should be. He is famous for promoting the concept of ecological rationality: the idea that ‘rationality’ is not universal and axiomatic but depends on the circumstances in which decisions are to be made, or on their ‘ecology’. This might seem like a dull truism, but it is primarily useful as a direct challenge to rational choice theory, and, by extension, much of behavioural economics.
I first became interested in Gigerenzer’s work last summer following an off-hand Twitter comment by Ole Peters. Regular readers will already be racing to deduce connections between ecological rationality and ergodicity economics. The fact they both think behavioural economics is a bit silly is a good starting point, but I would personally aim much higher. I believe they will become two of the three most important new areas of study in economics in the coming years that maybe — just maybe — will save the discipline from its cargo cult mathematical suicide in the twentieth century. The third is the B-word:
and, indeed, the very next day, Bloomberg was on the case!
The paper mentioned in this article, The Bias Bias in Behavioural Economics, is fantastic, and I would further recommend The Heuristics Revolution: Rethinking The Role Of Uncertainty In Finance.
The popular expression of Gigerenzer’s work usually comes down to two precepts: i) it is very important to distinguish situations of risk and uncertainty, and, ii) in situations of risk, modelling is appropriate, whereas in situations of uncertainty, heuristics are appropriate. “Heuristics”, of course, being the bane of behavioural economists and setting up this long running academic spat.
The idea behind a model is straightforward enough to grasp (even if individual models are incomprehensible, as we shall soon see): we crunch the historical numbers and churn out as many parameters as are necessary to fit to the level of accuracy we desire. The danger is fragility. The better we fit a model to the past, the worse it will blow up when the future is different. Gigerenzer would claim that the ideal heuristic is something along the lines of a behaviour that has no free parameters, but is simply an instruction that has been observed to work in a wide range of circumstances. This is thought to give it a natural robustness as it has emerged via a kind of evolutionary trial. It probably reflects some correct underlying explanation, even if we don’t know what this is. Indeed, we don’t need to know what it is. We can always execute it without expending time or energy parameterising our decision. But then, of course, the converse is true also: the more the future is like the past, the more money we leave on the table, so to speak, by ignoring this.
The task of ecological rationality, broadly defined, is to assess just how much uncertainty exists in a given situation, how much really can be known, and hence whether or not the best approach is one of models or heuristics. There is no universally correct answer as there is really no such thing in real life of something with either “zero” or “total” uncertainty. There is a fascinating rabbit hole we could go down here in terms of the meta game of being uncertain about the extent of uncertainty, but I shall not, because I don’t have time for another onslaught of clueless Talebites. Fragile Nassim actually has pretty good stuff on this, if you can stomach the made-up words.
Given the lack of a “scientifically correct” approach, it is dangerous to call any particular behaviour “irrational” — even ones with no articulated explanation — without understanding the circumstances in which the decisions are to be made. My initial attraction to Gigerenzer’s work actually had little to do with ergodicity, although that was the citation I followed, so to speak, but rather to my true specialty of confusing abstractions of finance, which I like to take with a dash of Hayek and a sprinkling of complexity science.
Taking a long-term view to financial markets is the epitome of an uncertain endeavour. It is also highly likely to be misinterpreted as solely constituting risk, simply on account of how much data markets throw off. The typically naïve response to uncertainty is to grasp for information that allows the modeller to try to reduce the space to one of probability instead. If copious such data exist, the temptation is greater still. Worst of all, in this exact environment, the shorter the periods we consider, the more data we get and the less uncertainty seems to matter. Yet, obviously, the more we lose any explanatory power whatsoever. The more we think markets simply are random variables, the more inexplicable it will be when something causes our model to blow up.
This is all very timely, and readers may be scrambling to remember the name of Taleb’s one-time protégé … zen master, practitioner philosopher, rightful King of Austria and all its (intellectual) domains: Mark Spitznagel. Oh also, returner of 4,000% year-to-date. I put a comma in the number so you are sure you read it properly. Four thousand percent means he is up 41x.
Now I don’t have the slightest clue how Spitznagel does what he does. But what is fascinating is that I believe our approaches come from a practically identical intellectual starting point (in fact, I know this because I’ve read his book). Real investing as opposed to speculating requires embracing the fundamental uncertainty of entrepreneurial endeavours. And there is nothing wrong with speculating, by the way; I don’t use the word as a slur, I just think it is important to distinguish the two. Besides, speculators are investors’ best friend because they ensure there is always somebody willing to buy or sell. The problem is conflating the two, but that’s another essay for another time.
Real investing sets itself up to intuit shifts in technology, society, and business models, and to capture whatever value creation or destruction is not being priced in, what with the efficient markets hypothesis being farcical, and all. In other words, it is ecologically rational. Given finance is more or less an abstraction of everything, it is possible to behave in entirely different ways, even from the same intellectual starting point, simply by inhabiting different niches within the ecology.
So, while I would prefer to look for inappropriate conflations of risk and uncertainty that allow me to long fat tails on the upside, Spitznagel looks for such conflations that allow him to short fat tails on the downside. I say, others think this is a risk that can’t be managed, but are really under-exposed to potentially wonderful uncertainty. He says, others think this is a risk that can be managed, but are really over-exposed to potentially disastrous uncertainty. And we are both right, because we both read Menger, even if Spitznagel mysteriously doesn’t get Bitcoin (yet).
While finance may be an abstraction of everything, to most people it remains exactly that: an abstraction. Numbers in the newspapers that occasionally grind the world to a halt because bankers are evil, or something to that effect. But there is a far better, and even more timely, example of all of this that we can discuss in depth: modelling the impact of the virus and the public health benefits of a lockdown.
The Imperial Model, as it has come to be known, decidedly influenced UK government policy, and was held up as some kind of top-of-the-line “science”. I put “science” in scare quotes because, upon the release of the code, we know it was no such thing. It was farcically, tragically, hilariously stupid. If you think using cargo cult math to engender financialization and monetary collapse is bad, wait until you get a load of the mathematical epidemiology racket.
It’s hard to know where to start, so I direct the reader primarily to what I consider to be the most reliable resource I have come across, with the unfortunately edgy name, lockdown sceptics. This is sobering reading:
Code Review of Ferguson's Model - Lockdown Sceptics
by Sue Denim (not the author's real name) [Please note: a follow-up analysis is now available here.] Imperial finally…
I should be clear, once again, as I belabour whenever I go near this topic, that I am not an epidemiologist, nor a virologist, nor do I even really know much about biology or chemistry. But I know a shit ton about math and computers and stuff, and I know that this mathy computer stuff is cargo cult garbage. That’s my point here. It has nothing to do with the virus.
And I ought to be crystal clear that nothing I am about to say means the Imperial Model is actually wrong. It is possible that, by some freak coincidence, everything that is stupid about it turns out not to be relevant, or cancels out some other stupid thing, and it models the virus perfectly. Whenever I say something like “the model is wrong”, I mean that, the methodology that went into building and running the model is unforgivably flawed as it cannot possibly be understood, but I don’t want to bend over backwards with my grammar every other sentence, given analysing this single claim makes up 2/3 of this post. Potential accidental model rightness aside, my point is more an epistemological one: there is no way to know this. And since proper science kinda requires being relatively sure you know things, this is therefore not proper science.
I’ll give a brief summary of what is wrong with the Imperial Model, but caveat all of this by saying that I trust the link given above, and, by extension, Ole Peters and Luboš Motl, who independently pointed me to this material. I’m going to do my best to bullet point the highlights — or “lowlights” if you prefer; these are the most laughably stupid parts:
· It’s a 15k line file that has been built over a decade.
· If you change the file format of identical inputs, you get an inexplicably different output. i.e. if you loaded the same inputs as an excel rather than a csv, you would get a different output. It’s not that simple but that’s the gist of it.
· If you change the processing mechanism given identical inputs, you get an inexplicably different output. i.e. if I ran it on my shiny but dysfunctional Mac and you ran it on your dull but useful PC, we’d get different outputs. It’s not that simple, but that’s the gist of it.
· There are bugs in the code they themselves cannot explain.
· Microsoft couldn’t fix it. They tried and gave up.
· It’s impossible to test it. Like, you literally can’t run a meaningful test. You have to just throw it straight into production and cross your fingers.
· There are undocumented equations in the code and literally nobody can figure out what they are supposed to mean. The best hunch is that they were machine translated from a different model written in a different programming language.
· It has nondeterministic outputs that do not follow from seeded pseudorandomness but are rather an inexplicable part of the process. I am not using “inexplicable” rhetorically here: nobody can explain this. This is one of the great issues in Complexity Science. Clearly there is a stark mathematical difference between deterministic and non-deterministic. But there is also a fuzzy, and arguably more important, difference between non-deterministic and really, really, really NON-DETERMINISTIC.
The code may give non-deterministic outputs, but these could conceivably still be made sense of if subtle changes in inputs produced subtle changes in outputs, or, if they did not, we could explain why not, either by looking at the code or by understanding the meaning of the parameters. As we will see, neither option is remotely plausible here. This is probably the single best flaw (amongst a million God-damned flaws) for demonstrating that while the model could conceivably be “correct”, there is no way any human can possibly confirm that.
· They haven’t released the actual code. The pseudonymous author of the blog post above surmises they won’t because it’s such a godawful embarrassment that is, nonetheless, owned by the public, that they only released “a derivative”. This could very easily go to court.
So, yeah, it’s a bit shit, really. And there are even greater cultural problems at play here. As my final bullet point demonstrates, this was all done more or less in secret. It’s like none of these people have ever read The Cathedral And The Bazaar, or ever heard the expression, “with enough eyeballs, all bugs are shallow,” better known as Linus’s Law, after the guy who catalysed the obliteration of Microsoft’s aspirations for dominance of the market for data centre operating systems. Microsoft was full of super duper smarty pants, by the way. Not smart enough to solve the Imperial model — or perhaps exactly smart enough to give up? — but still pretty smart. But there weren’t enough of them, and they had the wrong incentives. Linux worked because it had everybody, and they contributed openly and freely because it was the right thing to do. The Imperial contributors are now desperately scrambling to keep their paid-for contributions secret.
Ole Peters’ tweet below covers many of the same points, but his first is intriguing and is not mentioned in the lockdown skeptics post:
Indeed, this is not how to do Complexity Science. Gigerenzer is shaking his head somewhere. If he thought Markowitz was stupid advocating Modern Portfolio Theory over equal weighting everything and checking back in 50 years, wait until he gets a load of the 15k line incomprehensible mess on account of which every Brit has been trapped in their homes for a month. It’s just astonishingly stupid. It’s actually amusingly similar to Modern Portfolio Theory in that it is so complex in its stupidity that you have to be quite smart to even believe it in the first place.
A nice enough seeming Twitter user named Katya had a thread that similarly caught my eye. I have no idea if this is true, to be clear, but given the above I am inclined to believe it:
Now we have to be careful here because maybe 445 of these parameters contribute nothing at all, or reduce to dependencies on one another. It’s possible. But, again, do we know that? No, because we don’t and can’t know anything about this. So we have to assume the worst, which is that there are, in fact, 450 independent parameters. I will continue as if that is the case …
Are you kidding me? It might not be obvious at first glance what this means. Viral pandemics are complicated, no?
No. They are not that complicated. And if they are that complicated, then we should model them more simply because nobody can possibly comprehend this.
We live in 3 dimensions of space and one of time. What “dimension” actually means in this claim is that to pinpoint an event in spacetime, you need 4 pieces of information which are in no way related to one another (“linearly independent” in mathspeak). If I pick 3 of these randomly, you still know nothing about the fourth, so I need to give you all 4.
That is straightforward enough, by design, because we are all perfectly used to comprehending this. In fact, arguably, real life only has two dimensions of space in polar coordinates because in most circumstances when you specify a “place”, it is pretty obvious what “height” you mean. But for the sake of argument, let’s keep it at 4. You might be in a metropolis and need to know the floor as well as the address. And in fact, it’s even worse than this because “places” are meaningful to humans but not to computers. So, in terms of interpreting and sense checking the output, you really have to imagine that the three dimensions of space are just a string of numbers for longitude and latitude, plus something in metres (not “floors”) that mean absolutely nothing to you until you go there and see what you are looking at. And that’s in 3 dimensions.
Okay, now imagine that space actually had 449 dimensions. Got it?
Of course you haven’t got it because nobody can imagine that. It’s insane. When string theorists get laughed out the room for proposing 23 dimensions, only 4 of which we can experience, they are still lowballing the Imperial Model by a factor of 19. The Imperial model is effectively suggesting that the coronavirus outbreak could in theory be, but we can’t tell because nobody understands it, 19 times as complicated as the universe, which is itself 6 times as complicated as the model of the universe that works perfectly well most of the time anyway.
Now I should be clear that, maybe, the virus is that complicated. But it doesn’t matter. Because we can’t possibly understand this. And actually I lowballed it by a factor of 450 (Oh, God …). Because if this system is linear, which it surely is not, what this really means is that a single set of parameters can be represented as a 450-dimensional column vector acting on a 450x450 matrix with 450² = 202k independent numbers. Because, remember, the parameters can be anything. Katya suspects they are totally made up.
So it’s not just the dimensions we need to account for. The surface of the earth has 2 dimensions but more than 2 locations. Assuming every entry in this matrix has only two possible states, which it surely does not, this model maps a system with at least 2²⁰² k bits of information we need to be clear on to understand it. And probably some recursive exponent of this given how absurd the code itself is and the fact the system is almost certainly not linear. I asked my computer how big this lower bound is, and it told me it isn’t a number. I’m pretty sure it is a number, but I don’t blame my poor old computer. This is CPU-ese for, “are you kidding me?”
Hopefully it is clear now that, even if by some physics-bending anomaly, this model is a good one, we still shouldn’t use it, because no human, or collection of humans, is capable of understanding it.
But I’m just saying that to be nice, as a kind of best-case scenario. Of course this model is not a good one. It’s a steaming pile of blatantly politicised shit.
Boy, that escalated quickly! I mean, that really got out of hand!
Readers uninterested in conspiracy theorising are advised to stop now and get on with their day. Of course, I have no interest in actual conspiracy theories, but I’m sure I will be slandered as such by people who also admit to not bothering to read the whole thing.
Here’s the rub: Ferguson has a history of this kind of crap. In 2001, he advised action on foot and mouth that is since estimated to have been completely unnecessary and to have cost the UK farming industry £8bn net. In 2002, he predicted up to 150k human deaths from mad cow disease. There were 177. In 2005, he predicted 200m global deaths from bird flu. There were 375. In 2009, he predicted 65k UK deaths from swine flu. There were 457.
And more importantly, the Imperial Model was extremely influential. There was no lockdown in 2001, 2002, 2005, or 2009, whereas you are probably only reading this because you are trapped in your home and have nothing else to do. There are supercuts on YouTube of the mainstream media in the US saying “2.2m Americans could die,” over and over and over. That came from this model. There was no other source. It’s all been bullshit from day one.
How does somebody like Ferguson get to the position of being a chief advisor to the UK Government when he is so often and so consistently wrong about the only thing on which he is expected to advise? Who else ran for this post? Can I run? I know nothing but at least that’s more than less than nothing, right? Does it work like that?
The answer may honestly be that if a scientifically illiterate policymaker asks, “does the model account for the emergence of COVID zombies?” — a model with 450 parameters can always say, “yes”, because there are at least 100²⁰² possible outcomes and that could easily be one of them, I guess …
The great challenge for real Complexity Science is that the scientifically illiterate intuitively equate complexity with intelligence, sophistication, and explanatory power. The point of studying complexity is to explain it, not to pick up tools that allow you to make things so complex as to be “I’m sorry but that isn’t a number”-esque inexplicable.
As Antoine de Saint-Exupéry wrote in Airman’s Odyssey,
“Perfection is achieved, not when there is nothing more to add, but when there is nothing left to take away.”
In this light, the ability to add “explaining zombies” takes us decidedly further away from perfection, not closer.
Remember when Michael Gove was mocked for saying that the British people have had enough of experts? And then remember when Nassim Taleb (rightfully) defended him on the basis that we don’t need experts for everything? We need them for some things but not for other things? Well, it turns out that they are horrific at the things we — apparently — need them for. Great.
It gets even better. If you somehow didn’t know this already — if you stopped watching the news a long time ago to spend the lockdown on something productive, and good for you — but Ferguson doesn’t even believe his own bullshit. How do I know this? Because he repeatedly violated the lockdown he spent every waking minute defending to have an affair, while he was infected. You can’t make this shit up. Do what he says, not what he does … but also his revealed preference is to bang a married woman while secretly carrying an infectious disease. It’s almost impressive the number of ethical norms he has violated all at the same time.
More people need to say this publicly, by the way. I appreciate Sue Denim’s reasons for remaining anonymous, given at the end of the code review linked to above. Credentialism is indeed an annoying distraction that contributed to this mess in the first place. But I am not citing my own credentials here. I am encouraging the reader to understand this for themselves and to realise how much it all reeks of bullshit that they do not need to take seriously. My credentials are merely that I do math real good, and I write snarky blogs and swear a lot, and hence all of the above is just another Sunday for me.
But unfortunately, the actual decisions made by the government following such bullshit as the Imperial Model are made on the basis of credentialism, as they probably should be to a small extent. So can people with better credentials than me please find the guts to say that this is all bullshit, has been bullshit from day one, and needs to stop? Also, Ferguson needs to be fired. Also, the Imperial code needs to be released. Also, mathematical epidemiology with 5 million parameters, a slide on zombies, and a history of consistent, damaging wrongness, needs to be defunded because it is cargo cult science. It also gives real epidemiologists a bad name and a harder time.
Also whatever else has come to mind while reading this. Stop being intimidated by these people. Just say what you think.
Sue Denim posted a followup in which it all gets even worse:
Second Analysis of Ferguson’s Model — Lockdown Sceptics
by Sue Denim (not the author’s real name) I’d like to provide a followup to my first analysis. Firstly because new…
I have (or would like to think I have) decimated all of this so thoroughly that this link is really just a courtesy to the reader. I won’t dwell on it, but I will pick out a few gems: the Imperial researchers have been making false statements about the code; there seems to be a culture amongst these people of repeatedly averaging as a way of ironing out mistakes. As “Ms Denim” puts it: “the average of wrong is wrong”; quite a few politicians are now on the case (hurray!); and, shock horror, insurance companies, who do this kind of thing with actual skin in the game, have both produced better models and had the good sense not to use them.
The simple truth here is that many governments (certainly the UK) under-reacted to the virus at first and then overreacted out of shame, embarrassment, and opportunism. Complex nonsense is what drove both insane decisions. Some Gigerenzerian heuristics that would have helped might be, viruses are bad, and, shutting down society is worse. It may seem rather confusing to any readers still desperate to find a political narrative in all of this that I do not believe there is one at all. Balaji put it best:
It has absolutely nothing to do with politics. It has everything to do with competence. I haven’t given this much thought but it may have something to do with the culture around academia too. I couldn’t really tell you why the Imperial Model was taken so seriously in the UK and the US but, apparently, not at all in Australia. I can’t even explain why Scotland seems to be both laxer than England and better off. I’m just thankful. Not to The SNP, but to the actual human beings who comprise my government. I don’t see colour, innit. I value what they do, not what they say. Plus, Nicola Sturgeon seems to have picked up the delightful habit of trolling Boris Johnson in an entirely official capacity. I do love a good troll, but a troll that saves lives is the jackpot.
And then of course there are the questions of what to do about the WHO? What to do about the tech platforms that censored anybody straying from the known-to-be-complete-bullshit party line? What to do about the rampant political opportunism from just about every political stripe? These are other essays for other times. But that other time is fast approaching. People are getting pissed and word is getting out. Expect a torrent of such thought pieces soon.
Luboš Motl, whom I referenced earlier, summarised this well just yesterday,
“A posteriori, we see that the models producing cataclysmic predictions were wrong. But it wasn’t just a matter of bad luck. It is not a matter of bad luck that everything that Neil Ferguson has ever predicted was wrong. Even a priori, there was absolutely no reason to think that computer models such as Ferguson’s would be accurate or helpful in predicting complex phenomena in the world — and by complex, at least in this text, I mean “having very many interacting ingredients”.
What is such a “computer model” from a scientific viewpoint? It has some aspects that are totally unrelated to science — as a method to look for the truth about Nature. It could have a nice graphics, good PR, whatever. Clearly, a person with the IQ above 80 understands that these aspects shouldn’t influence our trust in the predictions at all. They have nothing to do with the science.”
Gigerenzer could have told you this. It’s all very ecologically irrational. Ole Peters did tell you this. Christ, even Taleb was right about this. Imagine that! (academic fraud notwithstanding). If you take one message away from all of this, it should be the following:
Computer modelling is not science. If the system being modelled is sufficiently complex, it isn’t even useful. It’s cargo cult bullshit.
The rest of this Reference Frame post is well worth reading, but this was the pertinent extract for our purposes. It is on the long side, and gets very deep into theoretical physics, so ought to be bookmarked only by the very curious and competent. Even in the above, Motl was (uncharacteristically) polite when what he meant was: this is all bullshit. He also cites some fantastic reporting from Dr Deborah Cohen at the BBC which serves as a wonderful conclusion to my own post:
Almost every line in here is great but I will pick out just one: “we stopped widespread contact tracing and testing in the middle of March, a move that many now see as a mistake.” Cohen is, similarly, being too polite. What she means is that we stopped doing real science and went all in on the cargo cult variety. It was, indeed, a mistake.
And finally, just because I am a man of my word …
… I will tie everything together with one of my favourite Solzhenitsyn quotes,
“Watch Burn Notice. It’s lit.”
follow me on Twitter @allenf32
thanks to Max Falkenberg for edits and contributions.