The Quantum Pontiff

George Soros Meets Kochen-Specker

I’ll admit it: I like reading George Soros’ books. I mean, here’s a guy whose made a godzillion dollars in the financial markets, has been behind political destabilizations/stabilizations worldwide, taken on a U.S. president (can you guess which one?), and yet, in spite of this, can write a book in which he talks his own brand of….philosophy and how it relates to life, the universe, and the current financial crisis. Whah?

As you might have guessed I just finished reading one such book: the rushed to market The New Paradigm for Financial Markets: The Credit Crash of 2008 and What It Means by George Soros. The book is a bit odd: it is short, rehashes many of Soros’ prior points, but contains all sorts of food for thought. Soros is at his best when he’s talking about financial markets, at least from my point of view. But this may just be because I don’t spend my days encased in the workings of things like CDOs, SIVs, CLOs, and the Case-Shiler Home Price Index. But I like to give Soros the benefit of the doubt so I suspect that these portions will be of general appeal to those interested in the take of someone who has either been lucky in the financial markets, or might actually have some skills at understanding how the financial world works. I’d heartily recommend the book to those of the “markets will solve all problems,” not because I think it will change their minds, but because I think it might make them angry.

But what I find most interesting about the book is Soros’ ideas (which are, even he would probably admit, only half shaped) about a point of philosophy he calls “reflexivity.” Here is a 1994 speech by Soros gave on the subject:

I was invited to testify before Congress last week and this is how I started my testimony. I quote: “I must state at the outset that I am in fundamental disagreement with the prevailing wisdom. The generally accepted theory is that financial markets tend towards equilibrium, and on the whole, discount the future correctly. I operate using a different theory, according to which financial markets cannot possibly discount the future correctly because they do not merely discount the future; they help to shape it. In certain circumstances, financial markets can affect the so-called fundamentals which they are supposed to reflect. When that happens, markets enter into a state of dynamic disequilibrium and behave quite differently from what would be considered normal by the theory of efficient markets. Such boom/bust sequences do not arise very often, but when they do, they can be very disruptive, exactly because they affect the fundamentals of the economy.” I did not have time to expound my theory before Congress, so I am taking advantage of my captive audience to do so now. My apologies for inflicting a very theoretical discussion on you.

The theory holds, in the most general terms, that the way philosophy and natural science have taught us to look at the world is basically inappropriate when we are considering events which have thinking participants. Both philosophy and natural science have gone to great lengths to separate events from the observations which relate to them. Events are facts and observations are true or false, depending on whether or not they correspond to the facts.

This way of looking at things can be very productive. The achievements of natural science are truly awesome, and the separation between fact and statement provides a very reliable criterion of truth. So I am in no way critical of this approach. The separation between fact and statement was probably a greater advance in the field of thinking than the invention of the wheel in the field of transportation.

But exactly because the approach has been so successful, it has been carried too far. Applied to events which have thinking participants, it provides a distorted picture of reality. The key feature of these events is that the participants’ thinking affects the situation to which it refers. Facts and thoughts cannot be separated in the same way as they are in natural science or, more exactly, by separating them we introduce a distortion which is not present in natural science, because in natural science thoughts and statements are outside the subject matter, whereas in the social sciences they constitute part of the subject matter. If the study of events is confined to the study of facts, an important element, namely, the participants’ thinking, is left out of account. Strange as it may seem, that is exactly what has happened, particularly in economics, which is the most scientific of the social sciences.

What I find fascinating about this idea, is not really whether it is valid as a philosophical idea, or whether it has helped Soros in his financial deals (or whether, as one of his son claims, that his success has more to do with his backaches than anything else!) No, what I find fascinating is how close this idea is to the works of the Kochen-Specker theorem of quantum theory. While what Soros says is true of old-school natural sciences, I claim that quantum-schooled researchers wouldn’t necessarily be shocked by his idea of “reflexivity” (as to whether it is a valid description of how financial markets work, however, is a separate question!)

The Kochen-Specker theorem says, in its most obtuse form, that any hidden variable theory of quantum theory cannot be non-contextual. For my own Christmas inspired discussion of this theorem see here. Quantum theory gives us a procedure for calculating, from a description of our quantum system, the probability that a different observable will have a particular outcome. For example, a measurement might have three outcomes call them red, blue, and green and when we measure our system we see one of these outcomes (with some probabilities calculateable by quantum theory.) Now one might think that instead of using the quantum version of how to calculate these probabilities, that maybe it is just that a quantum system has a definite hidden state, one corresponding to each of the three colors, and that when we make a measurement we just reveal that color, albeit with some probability of color preexisting. This would be a hidden variable theory of quantum theory. What the Kochen-Specker theorem tells us is that such hidden variable theories have a twist. Suppose that in addition to measuring red, green, and blue, we can measure any three colors of our system (of course my “colors” are analogies here…this is not a real experiment, just an illustrating example!) Suppose instead of measuring red, blue and green, we instead measure red, brown, and purple. Well then we would hope that for identically prepared quantum systems, the hidden variable representing our red outcome shouldn’t be affected by our choice to make the other colors brown and purple. However, what the Kochen-Specker theorem says is that this is not possible: there isn’t a consistent way to construct a hidden variable theory where the correspondence between hidden variables and measurement outcomes is one to one, independent of what other observations are being made.

Back to Soros. Soros conjectures that one reason for boom-bust cycles is the fact that participant’s expectations of a market are influence by how the market acts. There is no way for a participant to get any sort of measurement of the market which is independent of what other measurements are being performed on the market. Okay I’m stretching things here for fun (what does it mean to “measure a market?”) But I do think this has some important consequences for “reflexivity.” In particular Soros insists that the fact that market participants expectations cannot be separated from the market itself leads naturally to the idea that this means that any theory of such markets cannot be scientific. But, while I also share his trepidation of “scientific” theories of financial markets, I’m not sure I share his confidence in the inseparability of the participants from the market they create as a valid reason for why scientific theories will not hold. My counterexample is the Kochen-Specker theorem: there is no hidden variable theory where measurements can be thought of as revealing information independent of the context of the masurement. But this doesn’t mean that we can’t develop a scientific theory of how quantum theory works! So, George Soros, meet Kochen-Specker. Maybe, you three can get together and come up with something new and exciting?!

Comments

  1. #1 Michael Nielsen
    June 6, 2008

    Soros was a student of Karl Popper’s at the London School of Economics. Among Popper’s other interests were the foundations of quantum mechanics. So I’m not sure this is so surprising.

  2. #2 Michael Nielsen
    June 6, 2008

    Ahem – let me add to my slightly fuddy-duddy comment that it’s certainly still very interesting! :-)

  3. #3 Dave Bacon
    June 6, 2008

    Fuddy-duddy! :)

  4. #4 Blake Stacey
    June 6, 2008

    Quantum physics has been conjoined with finance in far loopier ways. . . . :-)

    The theory holds, in the most general terms, that the way philosophy and natural science have taught us to look at the world is basically inappropriate when we are considering events which have thinking participants.

    Duh. This is why the second fundamental postulate of Hari Seldon’s psychohistory is that the Galactic population at large is ignorant of psychohistory’s predictions. (The first postulate is just that the population is large enough for psychohistory to apply, which seems to require N greater than a few billion, and the second is that all individuals at all times fit the same general behavioral profile, i.e., that human reactions to stimuli remain constant and no aliens show up.)

  5. #5 Blake Stacey
    June 6, 2008

    It’s also why Lewis Fry Richardson said of his attempts to model the breakouts of war, “The equations are merely a description of what people would do if they did not stop and think.”

  6. #6 Ian Durham
    June 6, 2008

    This is actually quite interesting. Oddly enough, for many years now physicists have been some of the most prominent players on Wall Street. In fact, according to a good friend who owns his own trading company, the most powerful person on Wall Street is a physicist.

    In any case, addressing your question of what it means to “measure a market.” I know nothing of this new field of econophysics, but would guess some of these folks have asked that very question. Like quantum mechanics, I would bet there are actually “measurements” of a financial market that can, in fact, affect that market. For instance, taking the micro-economic view, the very act of requesting your credit score can, in fact, change that score. On a more macro scale, one might even argue that the Dow Jones Industrial Average (or Nikei Average, etc.) is a market measurement that affects the market (most investors are lemmings).

  7. #7 John Sidles
    June 6, 2008

    The notion of “reflexity” closer to home hits mathematicians and scientists with every passing decade.

    First Harry Collins wrote vividly about the intersection of politics and science within the LIGO project in Gravity’s Shadow.

    Now SynBERC’s Kenneth Oye (author of Explaining Cooperation Under Anarchy) is studying how cooperative behavior emerges among scientists … not ex post facto, but as a matter of prospective planning.

    If the mathematical and scientific community were indeed rational, these problems would be “merely” NP-hard. :)

    Thus Soros is right … modern complexity theory guarantees that marketplaces cannot be rational, insofar as the participants have “only” P-time and P-space resources. :)

  8. #8 JM
    June 6, 2008

    “what does it mean to “measure a market?”

    Price. What he’s neglected to say (because it’s obvious to anyone familiar with the market) is that the market is measured by price.

    And a price is only obtainable from the last concluded deal – or in many circumstances the last posted bid or offer. So if I’m thinking of buying (or selling) something I look at the last deal, bid or offer and that tells me (pretty closely) what the current price is. I set my price accordingly, conclude a new deal, bid or offer and then that price becomes the new “measure of the market”. My observation becomes the latest fact.

    I think that’s he means when he says that fact is not separate from observation. In markets facts and observations are exactly the same thing.

  9. #9 Jonathan Vos Post
    June 7, 2008

    Blake Stacey:

    I regret every day that Isaac Asimov is not around anymore for me to ask directly, f2f or by phone, but I remember the parameters slightly differently.

    You wrote:

    “This is why the second fundamental postulate of Hari Seldon’s psychohistory is that the Galactic population at large is ignorant of psychohistory’s predictions. (The first postulate is just that the population is large enough for psychohistory to apply, which seems to require N greater than a few billion, and the second is that all individuals at all times fit the same general behavioral profile, i.e., that human reactions to stimuli remain constant and no aliens show up.)”

    I agree, except remember N as being roughly 10^18. The equivalent of statistical mechanics in psychohistory requires the right minimum number of nano-moles of people. He was analogizing to the perfect gas law and Boltzmann at first, and maybe had other phase-transition cooperative effects in his later years. And finally, of course, undercut his whole model with a chaos-based skepticism.

  10. #10 David Meyer
    June 7, 2008

    I guess if you are a self-made billionaire, you can say anything you like and it is plausible that there is some underlying meaning that a literal interpretation misses, but really, it is ludicrous to say “an important element, namely, the participants’ thinking, is left out of account. Strange as it may seem, that is exactly what has happened, particularly in economics”.

    While Soros may not have learned it at the LSE from Karl Popper (who must have been too busy talking philosophy to get down to basic economics), every introductory economics course includes an analysis of the effects of participants’ expectations about inflation. The mathematical analysis of these effects dates back to Cagan, Bailey and Phelps in the 1950s and 1960s, but the idea that the expected inflation rate is important dates back much further in the economics literature, to Fisher’s analysis of interest in 1896 and, 150 years earlier, to Douglass’ 1740 (!) discussion of American colonial currencies.

    So really, omitting participants’ thinking is exactly what has not happened in economics, over the last 268 years or so!

  11. #11 John Sidles
    June 7, 2008

    Ian Durhan says: “according to a good friend who owns his own trading company, the most powerful person on Wall Street is a physicist”

    Most likely, that would be David Shaw. Who is more of a quantum chemist than a physicist … but his work and ideas on large-scale molecular modeling are top-quality.

  12. #12 Jonathan Vos Post
    June 7, 2008

    So… what the “quants” a.k.a. “rocket scientists” do is nonabelian economics?

  13. #13 Dean Loomis
    June 8, 2008

    It seems to me that what Soros is saying is that financial markets are unsolvable in the sense of Godel’s second incompleteness theorem. The statement that a market has an equilibrium is equivalent to the statement that the logical system represented by the market is self-consistent. Godel proved that this kind of statement can be true only if the system is inconsistent, i.e. that the market equilibrium doesn’t exist.

    This kind of reasoning cannot be captured in quantum theory because of the principle of linear superposition. There’s no room in QM for the kind of recursive self-interaction that Soros and Godel are talking about. In QM all the “strange loops” are fully unwound.

    The only reason that there’s even the illusion of equilibrium in financial markets is the “bounded rationality” of traders that Herbert Simon studied so famously. As long as the complexity of derivative instruments grows more slowly than the time to convergence of the market, there will be some semblance of stability. But if people start trading futures in “types of derivatives”, look out! Yet another singularity on the horizon.

  14. #14 Eric
    June 8, 2008

    “Quantum physics has been conjoined with finance in far loopier ways. . . . :-)”

    I would like to think that your use of the word “loopie” here refers to my attempts to develop a term structure model via categorfying the Black-Schole framework via “loop space” methods. But I doubt that :)

  15. #15 Blake Stacey
    June 8, 2008

    Jonathan Vos Post:

    I agree, except remember N as being roughly 10^18. The equivalent of statistical mechanics in psychohistory requires the right minimum number of nano-moles of people.

    I don’t have the book at hand to check, but I believe it’s in “— And Now You Don’t” (1949, the Arkady Darrell story) in which the First Speaker says that psychohistory is strictly applicable only to “planetary populations” and larger. I figure this means the population size has to be at least a few billion. Any difference between this figure and another I will cheerfully handwave away with the supposition that the Second Foundationers made some progress in the three centuries after Hari Seldon.

  16. #16 Andrew Foland
    June 8, 2008

    Isn’t the phenomenon Soros describes more accurately described as strong coupling?

  17. #17 Ian Durham
    June 8, 2008

    John,

    Could be. Was Shaw once President of Stony Brook? If so that must be him. In any case, this friend of mine has a partner who is a physicist and they were looking to hire a few years back. They specifically wanted a physicist and not a mathematician. Too bad I have no interest in working a job with normal hours…

  18. #18 David Meyer
    June 9, 2008

    Ian,

    Your friend is probably thinking of Jim Simons, who runs one of the most successful hedge funds and is also a billionaire, with a net worth in the same neighborhood as Soros. He’s actually a mathematician (once chair of the math dept at Stony Brook), but since he is the “Simons” of Chern-Simons theory it is not surprising that he gets misclassified as a physicist.

    David Shaw is a computer scientist, and not on Wall Street any longer, although his eponymous company still exists. He went back to doing (bioinformatics) research and is affiliated with Columbia.

  19. #19 Ian Durham
    June 9, 2008

    David,

    That must be him then. Of course, as someone with a PhD in mathematics myself, I think applied mathematicians (and even a few pure mathematicians) are essentially physicists or vice-versa. There’s a fine line between the two (which is why I was a tad surprised my friend refused to look at mathematicians when he was hiring).

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