Tuesday, 29 April 2014

When being wrong is right

I attended the Mathematical Cultures workshop/conference a the London Mathematical Society at the start of the month where I presented Is fairness a mathematical concept in the context of how the culture of mathematics contributed to the Financial Crisis.  Specifically, I began my talk with this quote from the UK's Parliamentary Commission on Banking Standards Report (Volume 2)
89. The Basel II international capital requirements regime allowed banks granted “advanced status” by the regulator to use internal mathematical models to calculate the risk weightings of assets on their balance sheets. Andy Haldane described this as being equivalent to allowing banks to mark their own examination papers.  A fog of complexity enabled banks to con regulators about their risk exposures:
[...] unnecessary complexity is a recipe for […] ripping off […], in the pulling of the wool over the eyes of the  regulators about how much risk is actually on the balance sheet, through complex models
 (my emphasis) 
and I ended it with this clip from a 1999 BBC science program on Black-Scholes-Merton and the collapse of LTCM (the speaker is Paul Samuelson) (the clip starts at 12:20 in the original programme)


My observation is that there is a culture of mathematics being a magical language that unlocks the secrets of the universe.  This is captured in many popular representations of mathematics: in  Darren Aronofsky's film Pi, that links maths, kabbalah and finance

the Da Vinci Code

Marcus Du Sautoy's The Code

even Simon Singh's book on the Simpsons

(for those who don't want to buy the Simpson's book, there is a long standing web-site)

On Saturday, I listened to Bridget Kendall's show 'The Forum'.  Kendall is well known in the UK for having been the BBC's Moscow correspondent during the 1991 coup and rise of Boris Yeltsin, and then the BBC's Washington correspondent.  Less well known, she is the daughter of Britain's most important probabilist of the twentieth century, David Kendall, and her brother is a probabilist at Warwick - I suspect she has a good grasp of mathematics.

Kendall begins the programme by asking Max Tegmark, an MIT cosmologist, about the idea of "maths as a kind of key" in this excerpt starting at 2:35 of the programme.  Tegmark is committed to mathematical realism and believes that ultimately, mathematics enables us to "ultimately predict the future" (at 0:55 in the except, 3:30 in the original).

I see a strong connection between Haldane's criticism of the use of maths in finance and Samuelson's and Tegmark's mathematical realism.  To paraphrase William Tait's description of mathematical realism:
A mathematical proposition  is about a certain structure, financial markets. It refers to prices and relations among them. If it is true, it is so in virtue of a certain fact about this structure. And this fact may obtain even if we do not or cannot know that it does.
The maths makes the financial theory true.

Following the meeting Heather Mendick shared a post where she contrasts Will Smith being constrained by the mathematical fact that 2+2=4,

with Orwell's presentation that "Freedom is the freedom to say that two plus two equals four".

Heather sees Smith's approach as being an example of "extreme neoliberalism", (I think she means extreme liberalism), but I argued that there is a connection between Orwell's "freedom" to claim 2+2=4 in the context of empiricism and Will Smith's (I assume, metaphorical) rejection of 2+2=4 as a rejection of imposed authority.

What struck me when listening to The Forum was how the discussion developed immediately after the except above.  In this excerpt, starting at 3:41, Kendall asks Tegmark to explain how  accepting the rules of mathematics leads to a belief in parallel universes.  I have recently shared my views on multi-verses, and my belief is that they are a fiction resulting from an incomplete understanding of the mathematical physics.  Tegmark supports my view that multi-verses are a mathematical consequence but his Platonism forces him to believe in multi-verses.  In this context, comparing Will Smith to Max Tegmark, who is wrong in rejecting mathematical truths.  We all recognise Smith is wrong, even probably Smith, but at the same time it is difficult to reject what Tegmark argues, despite the fact that Kendall comments that to the "unititiated" it all looks like make-believe (at 2:30 in the except, 6:11 in the original).

We label Smith as "ignorant" for presenting the claim that 2+2=5 in the context of advocating people reject the status quo, but we are expected to believe in multiverses.  Haldan'e criticism (probably) referred to the London Whale, where by presenting mathematics traders at J.P. Morgan reduced the liability of a portfolio from $22 billion to $13 billion (I may be inaccurate here, but the order of magnitude is correct).  To the "uninitiated" it all looked like make believe, but, like multi-verses, it carries the authority of mathematics.

Something that always appealed tome about science is its iconoclasm: science is right because it is happy to destroy its icons and move on.  We criticise Smith but venerate Galileo for rejecting the Ptolomaic system, despite the fact he the Dialogue is spectacularly wrong on the tides (e.g. Aiton, Brown).  Galileo is wrong, as the Inquisition realised, but he was right.

If economics is real in the Platonic sense, and can be described by exact mathematical equations, it will eventually grind to a halt.  This was the concern of many economists in the first half of the twentieth century, Knight, Keynes and the Austrians all agreed on the significance of uncertainty and unpredictability in determining economic affairs.  The organiser of the Mathematical Cultures conference, the philosopher Brendan Larvour, remarked
a repsonse was
My response is that Piketty, a French economist, is mathematically sophisticated, but in a different way to that of the realists/Platonists like Samuelson and Tegmark.  My disquieting suggestion is that in order to prevent Financial Crises we really need to examine how tenable mathematical realism, and the science built on this basis, is.

PS A Tweet from a French mathematician quoting another section of the Guardian


  1. You left me wanting more, which I suppose is a fine feature for a blog - or any other writing.

    The juxtaposition of Tegmark and Smith is brilliant.

    But you need a whole post on expectations,

    And more to the point, a more direct explanation of what Math IS, rather than what it is not. Though its a relief to see that it isn't God, seemingly a tool for describing him?

  2. Perhaps this is just the clueless raving of a minor academic. That said, I have always felt very strongly that math is a bunch of rules with no more reality than the rules of bridge or basketball. When our mental gymnastics turn out to be useful in dealing with life, we can jump on this as a great tool. A tool that works, like a shovel or a saw, partly because of its fit with the user, the human mind. When the fit is rough but provides help, there is no reason to worry about ultimate reality.

    The example I give is a simple one (and perhaps wrongheaded). A cubic equation such as (4/3)pi r^3 = 1 will have three solutions. Only one will work as the radius of the sphere being investigated. The other two complex solutions are generally ignored until they find use in such things as periodic solutions to differential equations. The fit is rough but it works OK. Why the need to worry over some sort of ultimate reality? Multiverses? Why not ignore them until they are useful in some concrete sense?

  3. Mathematics is about manipulating symbols, but those symbols can apply to any number of real world entities. Much as a title insurer guarantees the words of a title description, not the land it describes, mathematics guarantees truth about statements. The canonical example is Euclid's geometry without the 5th postulate which can describe plane, spherical or hyperbolic geometry. When the bank produces a risk model, it often finds it profitable to describe risks in a manner than allows the mathematics to produce a minimal result, and there is nothing short of strict government regulation and enforcement to prevent this. It's easy to prove that the sum of the interior angles of triangle is anything you want if you are allowed to embed your triangle in a space of your own choosing.

  4. You have to think seriously if the universe actually exists http://www.digitalcosmology.com/Blog/2012/09/14/is-our-world-a-simulation-or-even-an-interactive-computer-game/

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