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Steve Hoy

Physics Envy

Economics and Business are poorly served by the overuse of confusing jargon and mathematics to seem more rigorous than is actually possible. Many try to reduce these fuzzy subjects to formulae and frameworks, and while this can help understanding, more often it is just a veneer of nonsense over something unknowable.

Part of my distrust of economics as a subject and profession is its overuse of mathematics. Economists like maths because it lends an aura of certainty which doesn’t exist. To establish the sort of certainty that this is so, economists look to the harder sciences, especially Physics which uses maths to describe actual deterministic things which can be reliably reproduced in experiments. The fact that this can’t be done in economics cannot be allowed to get in the way. This is Physics Envy.

Andrew Lo and Mark Mueller wrote a very entertaining paper, Physics Envy May Be Hazardous To Your Wealth! in which they say that predictive models of economic systems create a false sense of mathematical precision. They argue that the kind of uncertainty affecting economic interactions is critical in determining the successes and failures of the models created by economists. They propose a six-level taxonomy of uncertainty, which is very entertaining.

By the way: they use the correct meaning of uncertainty as being Knightian Uncertainty. Not that this distinction should make the slightest bit of difference.

  • Level 1: Complete Certainty
    All past and future states of the system are determined exactly if initial conditions are fixed and known—nothing is uncertain. However, any system with even a small amount of complexity cannot be completely certain because small perturbations in initial conditions can lead to large changes in the evolution of the system. Some Physics models sit here, such as Newton’s three laws of motion, but nothing in business and economics can be Level 1.

  • Level 2: Risk without Uncertainty
    This level of randomness is Knight’s definition of risk: randomness governed by a known probability distribution for a completely known set of outcomes. At this level, probability theory is a useful analytical framework for risk analysis. The modern axiomatic foundations of probability theory is given precisely in these terms, with a specified sample space and a specified probability measure.

  • Level 3: Fully Reducible Uncertainty
    This is risk with a degree of uncertainty, an uncertainty due to unknown probabilities for a fully enumerated set of outcomes which is completely known. By “fully reducible uncertainty”, they are referring to situations in which randomness can be made arbitrarily close to Level-2 uncertainty with sufficiently large amounts of data using the tools of statistical analysis.

  • Level 4: Partially Reducible Uncertainty
    By Level-4 or “partially reducible” uncertainty, we are referring to situations in which there is a limit to what we can deduce about the underlying phenomena generating the data. There is a non-trivial degree of uncertainty regarding the underlying structures generating the data that cannot be reduced to Level-2 uncertainty, even with an infinite amount of data. Here, we depart from the certainties of the hard sciences; markets are tools developed by humans, not immutable laws of Nature, and are subject to all the complexities of human behaviour.
    While Bayesian statistics, in which probabilities represent degrees of belief can be useful, we have no way of knowing the full range of factors contributing to the complexity of the situation. Mathematical models are useless (except to other mathematicians), and very likely deceptive for a non-mathematician.

  • Level 5: Irreducible Uncertainty
    Lo and Mueller say that irreducible uncertainty is “the polite term for a state of total ignorance; ignorance that cannot be remedied by collecting more data, using more sophisticated methods of statistical inference or more powerful computers, or thinking harder and smarter”. I think the language goes too far: the total ignorance they are referring to is the unknowability of certain factors (either their presence or their influence or how to measure them).

  • Level ∞: Zen Uncertainty
    “Attempts to understand uncertainty are mere illusions; there is only suffering”. Physicist humour, I guess. Illusion and suffering are poor translations from Sanskrit and describe philosophical concepts which I think we’d all be better off understanding more.

So, any given phenomenon may contain several levels of uncertainty at once, with some components being completely certain and others irreducibly uncertain, and each component’s categorisation can vary over time as the situation changes, technology advances or our understanding deepens.

The other key point in Physics Envy is that physics papers are written for other physicists, and mathematical papers are written for mathematicians. These people have training and experience in their fields, and are all too aware of the boundaries of their knowledge.

Nothing in Business, or Economics, or other social ‘sciences’ can be Level-3 or below, which means that we are always dealing with uncertainty. Business Strategy has a bad dose of physics envy, with five-year plans, metrics and measurement, and cost-cutting efforts.

Economics though, has by far the worst case. Much of it is written in mathematical terms but it uses stupid simplifications to get the models to work. Economics has a steely grip on thinking about social issues, including Business. Business leaders and politicians, educators and writers, pundits and LinkedIn influencers are nearly all enslaved to the theories of some long-dead economist, to paraphrase John Maynard Keynes.

Lots of things cannot be reduced to numbers, because they are uncertain. Formulas and frameworks can help with understanding a process, but they are poor tools when used as a substitute for understanding Uncertainty.

We need to consider uncertainty; the things we know we don’t know, and the things we don’t know we don’t know. Most people simply can't do this, through hubris or ignorance or incapacity; and often it's just too hard to explain upwards that these things are uncertain and possibly unknowable.