Taleb on Writing History

In his 2007 effort The Black Swan, Nassim Nicholas Taleb described history writing in a way that has stayed with me since I read it.

Our problem is not that we donot know the future, we do not know much of the past either. [...]

Consider the following thought experiment borrowed from my friends Aaron Brown and Paul Wilmott:

Operation 1 (the melting ice cube): Imagine an ice cube and consider how it may melt over the next two hours [...]. Try to envision the shape of the resulting puddle.

Operation 2 (where did the water come from?): Consider a puddle of water on the floor. Now try to reconstruct in your mind’s eye the shape of the ice cube it may once have been. Note that the puddle may not have necessarily originated from an ice cube.

The second operation is harder. [...]

The difference between these two processes resides in the following. If you have the right models [...] you can predict with great precision how the ice cube willl melt – this is a specific engineering problem deviod of complexity [...]. However, from the pool of water you can build infinite possible ice cubes, if there was in fact an ice cube there at all. The first direction, from the ice cube to the puddle, is called the forward process. The second dircetion, the backward process, is much, much more complicated. The forward process is generally used in physics and engineering; the backward process in nonrepeatable, nonexperimental historical approaches [p. 196*].

I wonder if there’s something to it. I think it’s a bad metaphor. For one thing, historians usually do not only see the final outcome (the puddle) of a history (the melting), but they can observe historical accounts and observations made underway; if one were to describe the shape of the ice cube, it would for example help if someone had written down a description of the shape of the ice cube at some given time in the melting process. In general, I don’t see a clear analogy between Taleb’s clear cut example and the work of historians.

Taleb’s main message about history is that we cannot rely on it when it comes to predicting the future. It is unreliable when it comes to describing the past, he argues, and simply unsuited to foretell the future. I think I’m more in line with Taleb on his main view than his strange example of the melting ice cube.

* Page numbers refer to the British edition.

The Mandelbrot Fractal

Nassim Nicholas Taleb mentions Benoît Mandelbrot in his latest book, ‘The Black Swan’. I was surprised to learn that Mandelbrot has worked in a number of different fields in addition to mathematics. He is, however, best known as a mathematician and the ‘father of fractal geometry.’ Maybe the best known fractal of all is the Mandelbrot fractal. (A fractal, by the way, is, loosely speaking, a mathematical structure that is self-similar on all scales; they are often products of iterative procedures.) The Mandelbrot Fractal is generated from the very simple iterative equation

I won’t go into the details, but the equation above illustrates the simplicity, and it is almost magical how such a simple equation can generate such complexity one finds in the Mandelbrot Fractal. (If you are interested in the details, go to the Mathworld page from the link above.) The pictures of the Mandelbrot Fractal in this post are all stolen from Wikipedia (sorry!), and they say more than a thousand words; the Mandelbrot is magical!

I once wrote a small program that drew the Mandelbrot set (okay, I got some help with the programming, and due to limited computing power it had to be an approximation; it looked good though). It was written in Delphi‘s implementation of the Object Pascal programming language. The program is currently trapped in an old, unconnected hard-drive, but I’ll upload it whenever I get around to it. In the meantime, you should google for Mandelbrot images and post links to the most beautful ones in the comment section!

UPDATE: I had to add another image and link to the Wikipedia page dedicated to the Mandelbrot itself. Check out the zoom animations; truly amazing!

Taleb on the crisis

In this essay, Nassim Nicholas Taleb writes on the recent turmoil on Wall Street. He writes in an entertaining way and makes sure to mock a few financial ’celebrities’. His basic message is that most people does not understand statistics. What he has in mind may seem like minor subtleties, but I trust him they are important. Here are a few quotes to tease your curiosity:

Are we using models of uncertainty to produce certainties?

I have nothing against economists: you should let them entertain each others with their theories and elegant mathematics, and help keep college students inside buildings. But beware: they can be plain wrong, yet frame things in a way to make you feel stupid arguing with them. So make sure you do not give any of them risk-management responsibilities.

I find it interesting that he puts things like climate- and environmental problems in a category of problems that are predictable enough to have a ‘linear payoff’. The same category contains terrorism, casinos, political economy, and finance. In the category of problems with ‘nonlinear payoffs’ are calibration of nonlinear problems, dynamically hedged portfolios, volatility trading, and societal consequences of pandemics. Regarding certain environmental problems, I beg to differ.

In the latter half of the essay, Taleb discusses the inverse problem (the greatest epistemological difficulty he knows) and his way of getting to grips with it. This involves fractal power laws and is very superficially described. He repeats that the details are spelled out in the appendix, and I am sure they are. Unfortunately, however, parts of the essay presents itself as half-scientific nonsense to me.

Taleb ends his essay with nine ‘phronetic’ rules, a dos and don’ts in ‘the Fourth Quadrant’ (the part of real life that involves nonlinear payoffs). (Phronetic is from greek and can be translated into ‘practical wisdom’ or ‘prudence’.) The first: ’Avoid Optimization, Learn to Love Redundancy.’ Another: ‘Do not confuse absence of volatility with absence of risks.’ And from the rule on metrics:

Conventional metrics based on type 1 randomness [random walk, I presume] don’t work. Words like “standard deviation” are not stable and does not measure anything in the Fourth Quadrant. So does “linear regression” (the errors are in the fourth quadrant), “Sharpe ratio”, Markowitz optimal portfolio, ANOVA shmnamova, Least square, etc.

Great stuff, I love this guy! Here is his homepage, check it out.