Physics Envy May Be Hazardous To Your Health– And Economy

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A previously empty bucket.  A man has filled that bucket only 50 red balls and 50 black balls (but you can’t see inside as you are picking.)  Choose a color, red or black; now reach in to pull out a ball.  If the ball you pick matches the color you chose, you win $10000.

1. Which color should you choose?
2. How much would you pay to play this game exactly once?

New game: another bucket, he again fills it with 100 balls that are only red or black, but you do not know the proportion of the balls, only that the total of the red balls and black balls is 100.  Choose a color, red or black; and reach in and pull out a ball.  If the ball you pick matches the color you chose, you win $10000.

1. Which color should you choose?
2. How much would you pay to play this game exactly once?

Notwithstanding a small, human preference for the color red, I don’t know anyone that would pay the same price to play game 2 as game 1; yet, in game 2, you know that the only choices are red or black balls.  So knowing the distribution is 50/50 and blindly pulling one should be the same game as not knowing the distribution and blindly pulling one.

This modified Ellsberg’s Paradox is supposed to show the difference between risk, which can be calculated, and uncertainty, which cannot.  And what it shows is that human beings have an aversion to ambiguity.

But the other thing it may show is that people are susceptible to information bias.


The video comes from a talk, “WARNING: Physics Envy May Be Hazardous To Your Health”  given at the MIT Sloan School of Management.

The paper runs 60 pages but is well worth reading.

In the video, he describes having meetings with Mark Mueller, a physicist who became a portfolio manager, which turned into a paper about a cause of financial crises: physics envy.

(6:47) Physics envy, is this desire to be able to explain 99% of all economic phenomenon with 3 laws. That’s what physicists can do. In fact we (economists) have 99 laws that explain maybe 3% of all phenomenon.

But he asks whether it isn’t the “laws” that were faulty (e.g. the models) but the way they are used.

Lo describes the history of economic analysis (8:12) starting with Paul Samuelson, who patterned his dissertation on physics. This set economics on the course of the efficient market hypothesis, in which prices fully reflect all available information.”  Now that hypothesis is doubted; human beings have been discovered to be irrational.

He offers the above red/black ball example, and finds that the audience would pay $5000 to play Game 1, but much, much less to play Game 2. Game 2 just feels harder.

Tellingly, even after you explain this to people, they still don’t want to play the second game, which suggests that there’s money to be made in the arbitrage.


Everyone on ycombinator is going to weigh in that my example is badly worded, not logically rigorous and etc.   And they will find reasons why Game 1 actually is the better game to play.  This only reinforces my point (and Lo’s): to the extent that life can be rigidly defined, people will find reasons to choose the way they want to choose– good reasons, real reasons– that still don’t have any effect on the game.  For example, someone might complain that you don’t know if the man made the black balls slightly sticky; or they become redder over time, such that he can delay or accelerate your picking based on what he hears you choose.

All of these possibilities may be correct; or none of them may be correct; and all of those possibilities eventually yield a probability of 50/50.  That’s how it goes.

For example, in game 2, don’t you still know that red is slightly preferred by humans?  And the game host is human, which means there’s a slight chance that he’ll stack the balls in favor of red… should you therefore choose red?  But the game host knows this as well; and he knows you know it; and he knows you know he knows it… ad infinitum, back to  50/50.

There’s another factor: if you choose game 1, and lose, that’s the way it goes.  But if you choose game 2, and lose, people will think you’re an idiot for having decided to play game 2.  That pushes you towards choosing game 1.  Which is how many hedge funds choose stocks– no one blames you if you lose money on Apple or Google.


An interesting piece from the paper concerning Level 5 uncertainty: Black Swan events and the limits of probability theory.

The language of probability and statistics is so well-developed and ingrained in the scientific method that we often forget the fact that many probabilistic mechanisms are, in fact, proxies for deterministic phenomena that are too complex to be modeled in any other fashion.

Coin tosses are random, but as they exist in the physical world and are governed by physics, they should be deterministic if we were able/motivated to control/know all the conditions, e.g. a coin flipping machine.

A black swan event in the market offers opportunity for the application of other models.  For example, an unexpected crisis may precipitate a selloff, but primarily a selloff in underperforming stocks (which are typically sold off first), so a mean reversion strategy would be to buy those underperfoming stocks.


An even larger source of trouble is simply the people in it.

Among the multitude of advantages that physicists have over financial economists is one that is rarely noted: the practice of physics is largely left to physicists. When physics experiences a crisis, physicists are generally allowed to sort through the issues by themselves, without the distraction of outside interference. When a financial crisis occurs, it seems that everyone becomes a financial expert overnight, with surprisingly strong opinions on what caused the crisis and how to fix it.

He offers three examples.

Is the science the problem?

Mortgages were packed into CDOs under a model that took mortgages of similar credit quality but from different parts of the country, and put them together in a collection to offset the risk.  For example, if $300k mortgages in Maine and California have nearly independent default rates, then packing them together protects the overall CDO, similar to diversification in a stock fund.

Was that premise of independent default risks sound?  Actually, yes: since 1933, there had never been a nationwide housing market downturn.

So it wasn’t that the model wasn’t useful; it was that the managers didn’t understand them and their limitations.  If they had understood their limitations, even if they could not fix them they could prepare for them (e.g  limit their exposure in specific ways.)  But they didn’t– they followed the models blindly.  Since the models had worked so far (and had been backtested) there was no reason to think they wouldn’t work in the future.  (No housing collapse for 80 years, so…)

Lo’s final paragraph is as applicable to medicine as it is to finance; simply substitute the professions:

Quantitative illiteracy is not acceptable in science. Although financial economics medicine may never answer to the same standards as physics, nevertheless, managers doctors in positions of responsibility should no longer be allowed to take perverse anti-intellectual pride in being quantitatively illiterate in the models and methods on which their businesses depend.

Are too many quants the problem?

If the models were too complex, then the problem was too few quants, not too many quants, running Wall Street.

In 1980 post-grads in engineering and finance made about the same money; since then, finance grads have made more and more.

On a logic of supply and demand, this suggests that the demand for finance grads is high.  Fine.

But if its true, e.g. #2, that the models are very complex and require considerable expertise, this graph should be troubling:


Lo observes that engineering PhDs are financed by the government (DARPA, NIH, etc) while finance grads are financed by the university.

I probably don’t have to point out that a similar argument can be made about medicine.

Did the SEC allow too much leverage by its 2004 rule change permitting leverage requirements to go from 12:1 to 30:1, precipitating the crash?

In a January 2009 Vanity Fair article, Nobel-prize-winning economist Joseph Stiglitz (2009) listed five key “mistakes” that led to the financial crisis and “One was the decision in April 2004 by the Securities and Exchange Commission, at a meeting attended by virtually no one and largely overlooked at the time, to allow big investment banks to increase their debt-to-capital ratio (from 12:1 to 30:1, or higher) so that they could buy more mortgage-backed securities, inflating the housing bubble”

New York Times:

Over the following months and years, each of the firms would take advantage of the looser rules. At Bear Stearns, the leverage ratio–a measurement of how much the firm was borrowing compared to its total assets–rose sharply, [from 12:1] to 33 to 1. In other words, for every dollar in equity, it had $33 of debt. The ratios at the other firms also rose significantly.

This paralleled the average citizen who was similarly overleveraged.

But, in fact that rule change didn’t have any effect on these levels at all– they had already been higher for years:


The point isn’t that they weren’t perhaps overleveraged; the point is that that rule change didn’t permit it, and hence re-changing it isn’t the logical solution.


when new information is encountered, our cognitive faculties are hardwired to question first those pieces that are at odds with our mental model. When information confirms our preconceptions, we usually do not ask why.

The authors also note that the NYT has “yet to print a correction of its original stories about the rule, nor did the Times provide any coverage” of the speech by the SEC director who said, “First and most importantly, the Commission did not undo any leverage restrictions in 2004.”

If the media’s mistake is not checking the popular hypothesis against available data, our mistake is taking what we see in the media as data.

News is not data. 

No related posts.

20 Responses to Physics Envy May Be Hazardous To Your Health– And Economy

  1. Sfon says:

    “I don’t know anyone that would pay the same price to play game 2 as game 1″
    Is that simply an assumption? Yes, humans are not good at logic, but that doesn’t mean we can never be right. The games as you described them both sounded to me just like the same “which hand is the money in?” game. Same for if there is only one ball and you had to guess its color. I’ve hung around smart people enough to know I am not one of them. If I saw it that way, many others will.

  2. localhost says:

    But the game host knows this as well; and he knows you know it; and he knows you know he knows it…

    So the game host is Sicilian?

  3. 2goldfish says:

    The problem is not everyone taking themselves for experts on economics, its economists taking themselves for scientists.

    • foxfire says:

      A little from Column A and a little from column B. Yes, economics isn’t an exact science, but physicists don’t have to deal with their theories altering the behavior of what they are trying to measure.

      Imagine if we developed a machine that allowed people to alter their local gravity by +/- 25%. The underlying theory of gravity wouldn’t change, but it would become very hard to do accurate experiments on gravity because there would be millions of noise sources that couldn’t be accounted for.

      Another way to look at it. Lets say that I come up with a beautiful set of economic theories that accurately explain the last thousand years to human economic activity. They are tested and peer approved, and they are flawless. They would become invalid the moment they are published, because once everyone reads the rules, many will modify their behavior to use these rules to their benefit.

      • pyrotix says:

        This is nonsense. If they were valid fundamental rules they would also properly predict everyone’s reactions to them.

        • johnbr says:

          but if the valid fundamental rules predict the behavior of the people, then people will know to review the fundamental rules and predict the predicted behavior….

          ad infinitum

          In theory, you could predict the exact economic result of an action, but you’d have to be outside the universe, observing the system, and find a way around the Heisenberg Uncertainty Principle.

  4. I would go as far as saying that the problem even more fundamental (Even though I haven’t seen the video nor read the paper yet). It’s not just that they try to model economies like it was physics, but they think about it like it was a thing in itself. Whatever an economy is, it seems obvious that it is a consequence of the inner workings of a society and the values shaping it. Once one starts to see this things as divorced from the goals that are shared by the people in the economy, you are not only devaluing democracy, you are making any discussion about economy seemingly about nothing. As if an economy would be a closed system not influences by anything else.

    Sure, I’m exaggerating. It’s not like they are that deluded. Ant it’s not like there are no questions about the workings of economies that are worth exploring by themselves. But a lot of things will continue to not make a lot of sense for as long we see economics more akin to physics than to sociology.

  5. GhostSpider says:

    That and the fact that when you interpret the result of an experiment in the natural sciences, you count on two things: the underlying laws being the same at any point/time (disregarding theories about the changes in fundamental constants), and the experiment being repeatable. Economics has neither advantage; knowledge of economics changes the way people behave, and there are billions of factors that can have an impact on how a nation’s economy plays out.

    There’s still cranks in physics whose publications lie on the spectrum from “wishful thinking” to “malice aforethought”, and that’s in a field where if you get blackballed, you won’t be able to get a job as a high school science teacher. It seems like it would be absurdly easy to make arguments from ideology or for personal benefit as an economist, since there are so many more “outs”, and even if you do end up completely disgraced, you’ll still have made enough money to make it worth your while.

    Also germane: when I read physics texts, clarity is the primary goal– things are explained in the level of detail required to make a concept understood. When I read an economics textbook, I can usually expect pages of lemmas and definitions before anything interesting is discussed. Maybe since economics isn’t my area of expertise, it really is harder than physics. But I believe that it’s just plain old obscurantism: if you make something so difficult to read that it serves as its own hazing and initiation, then the people who are likely to make it through aren’t going to be the sort of people who’ll criticize it.

  6. SNAFU says:

    One interesting thing is that people were willing to bet $5,000 on a 50-50 bet. I said $100 bucks for both, because I don’t have more than $100 to gamble with. Why take even odds on game 1?

  7. abf0400 says:

    From a probabilistic point of view Game 1 and Game 2 are identical — as long as you only play once. For Game 2, if the dealer is using some strange logic to dictate the proportion of the balls, you can protect yourself against that by randomizing your choice by flipping a coin, which will give you a 50% success rate in the long run.

    From a financial point of view, I’m pretty astonished that anyone would pay $5000 to play. I certainly wouldn’t put my last $5000 on the line. If you pay $5000, no matter how many times you play, you only have a 50% chance of coming out ahead. And if you happen to run out of money, you’re done.

    The “Kelly Criterion” is a pretty solid theory that suggests how much of your bankroll you should bet based on how good your odds are, in order to maximize the growth rate. If offered either of these games, at a price of $5000, the suggested allocation is 0%.

  8. sellyourkingdom says:

    Expected value:

    1/2(10,000)+1/2(0)=5,000, therefore any entry price up to 5,000 would be rational for a risk neutral person. The distinction is that individuals are risk averse whereas firms are risk neutral, you might not take the bet but a firm would. If we know an individuals wealth and can guess how much they value their money we can better predict if they will take a certain bet or not.

    The main problem with economics is that every major axiom is built upon an irrational assumption. The isomorphic nature of mathematics allows for the same flawed models to be applied to everything, e.g. supply and demand, the H-O international trade model, and CAPM are essentially all the same, not to mention the lynchpin of neoclassical economics, general equilibrium.

    I like that the lecture ended with a quote from Richard Feynman, one of the biggest skeptics of social science.

  9. Vigil says:

    “And what it shows is that human beings have an aversion to ambiguity.”
    Humans are also extremely risk-averse. No one is going to bet anything close to $5000.

    I didn’t watch the talk, but I skimmed the paper, which was worth it just to get to section 3.6. While it had its good moments, I was turned off in the end. He seems to be trying to make the case that people should understand and use economic theories responsibly, which I wholeheartedly agree with, and yet there he is comparing the Fourier transform of his modified harmonic oscillator to the Fourier transform of the US GDP as if it meant something (Look, two Fourier transforms that both don’t have significant peaks! Astounding!), and showing a graph of the number of engineering vs finance students in a single school, which is well known for its engineering program and not for its finance program. Oh shit, Juilliard graduated infinity times as many bassoonists as nutritional scientists last year! Does this mean that our country is trending towards a woodwind-based diet? I know he’s trying to make a real point, and I wish he wouldn’t ruin what would have been an excellent paper with misleading figures. Then again, I skimmed, so this is more of a gut reaction than anything.

    Mostly unrelatedly, I ran across some paper recently by psychologists in a huff that psychology is not considered a hard science and they can’t get the STEM money they feel they deserve, even though psychology is a science, and S is for Science. Lo+Mueller’s paper makes some comparisons between economics and psychology. How does physics envy affect psychology? Psychiatry? Other fields?

  10. johnbr says:

    for what it’s worth, there’s a great blog: that had pre-educated me on the test you just gave us. Not specifically that test, but recognizing the human emotional attachment to risk aversion and the “unknown == even odds” aspect of the second game.

    I don’t think Economics will ever be as rigorous as Physics because the “laws of economics” have to support infinite recursion.

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  13. boxo says:

    I’d pay the same for both without a second thought.

    From the Bayesian perspective I just have some prior probability distribution over the gamemaster’s selection of colors. If the priors were skewed towards a certain color I’d actually pay more for game II since I could take advantage of my knowledge, but since I don’t really know anything about what the gamemaster is going to choose I have a uniform prior over all color selections, from which it follows that my subjective probability of pulling out a red ball is 0.5, exactly the same as if I knew there were 50 red balls.

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  16. Jay says:

    Can you draw from #2 multiple times? If I’d just drawn five black balls in a row from #2, I’d be willing to pay more than $5000 for another draw.