That is why I was surprised to learn that Physics envy is actually a serious affair that is much debated about and has even been the subject of research as well as books. The term is a somewhat pejorative reference to the presumed attempt of the softer sciences and the social sciences to emulate Physics in their studies in different ways. These include an emphasis on quantitative reasoning, building and using Mathematical models for processes and a tendency towards empirical testing and deductive reasoning as embodied by the broad definition of the scientific method. The tendency has been both a success and a disaster depending on where and when people have tried to employ it. From my own exposure during undergraduate studies, I can mark off areas of Biology such as studies of population growth and epidemics that make remarkably good use of Mathematical modeling. On the other hand, 2008’s financial crisis is often pointed out as a massive failure of quants’ attempts to do Physics with the markets. That is why there is an abundance of both critics and proponents of Physics envy. My aim here is to explore why some methods of the physical sciences may not prove to be as good a tool when extended to other areas of human knowledge.
First let me delve into what could be the possible motivation for being envious of Physics in the first place. There is a vast number of unsolved puzzles and competing theories in Physics; there are also issues of experimental uncertainty when Physicists measure and report values, and then there are fundamental limits placed on certainty by quantum mechanics itself. In spite of these features, Physicists have been immensely successful in understanding and predicting how the universe ought to work, from the sub-atomic to extra-galactic scales. Take, for example, the anomalous magnetic moment of the electron which has been calculated up to fourteen significant figures and its experimental measurement agrees with the calculated value to more than ten significant digits.[i] That implies an accuracy of one part in a billion. Such an overwhelming vindication of theory can perhaps inspire people to seek similar predictive power in other fields through mathematical reasoning. In principle, everything we know – from bacteria to human beings or from diseases to democracies – is an aggregate of atoms and forces that we do understand in terms of mathematics; and therefore, we should be able to use similar mathematics to make predictions about those aggregates as well. So, why doesn’t that work?
It doesn’t work because the ‘jump to aggregates’ as suggested above is actually a departure from Physics and not an accurate mimicry of how it works. The whole sometimes works very differently from the parts. In fact, as elegantly described by Lisa Randall, Physics thrives on effective theories with different domains of validity separated by scales.[ii] These scales can be in terms of energies of particles, the distances between them or their speeds. For instance, Newtonian mechanics is an excellent theoretical framework when we’re talking about the scale of planetary orbits (or speeds << c). However, when operating on atomic or sub-atomic scales, it is no longer an effective theory and we’re compelled to look towards quantum mechanics in that domain. Similar is the case on very large scales, when we have to abandon Newton and use General Relativity to understand cosmological dynamics. Furthermore, in Physics, the demarcation between these scales is relatively well understood. We often know exactly when to ignore the contribution from gravity and when not, because we are able to compute the impact of taking it into account for all practical purposes. It is this convenience of distinguishing between scales, that is not available when Physics envy tries to make the transition from the physical to the social universe. We do not yet have an analogue of shifting from Newton to Einstein when we shift from the scale of particles to people, who add an infinite amount of complexity to real world problems. Sure, the behavioral patterns can be studied and regularities can be assumed, but there is a lot that we simply do not know to accurately mimic Physics to discover the fundamental laws of finance – if there are any to begin with. Richard Feynman put it this way while addressing Caltech graduates,
“Imagine how much harder Physics would be if electrons had feelings!”
Another useful idea to understand the problem is how our ability to solve problems changes with what sort of uncertainties are involved. Uncertainties span an entire spectrum or levels as discussed by two MIT professors here. First, there are the completely deterministic systems of classical Physics where you can predict with certainty what value a particular variable would take under given conditions; then there are systems with probability distributions where your ability to predict is reduced to confidence intervals; then there are levels where in the absence of any probability distributions you’re forced to rely on gathering data, using Bayesian methods and making statistical inferences. The uncertainties progressively build up to levels where no amount of data or stochastic modeling is sufficient to make any reliable predictions. [iii]Problems involving humans are mostly uncertain to that extent and therefore forcing upon them a mathematical model that is only appropriate for much lesser levels of uncertainty, is wrong. As Emanuel Derman - a theoretical Physicist turned financial engineer – says,
“Whenever we make a model of something involving human beings, we are trying to force the ugly stepsister’s foot into Cinderella’s pretty glass slipper. It doesn't fit without cutting off some essential parts. And in cutting off parts for the sake of beauty and precision, models inevitably mask the true risk rather than exposing it.”[iv]
This also exposes the flaw of forced quantitative analysis in some situations. The power of quantifying an idea is undoubtedly amazing as it makes your claims precise and testable. However, when pushed in the face of uncertainties, a number can be more misleading than helpful. This is because the number of assumptions that go into arriving at that single quantity can completely distort reality. For example, imagine trying to assign a single number – let’s call it People’s coefficient - to describe the potential of a political movement to bring about revolution. It will be very surprising if that made sense because there are so many dynamics of the individual and collective actions of people that are simply too complicated to fit an arbitrary mathematical description. In fact, Physics envy can prove to be embarrassingly dangerous in such circumstances, as exemplified by the famous prank of Alan Sokal.
In the end – in my humble opinion - there is one area where an emulation of the hard sciences is justified and that is empirical testing. Every theory – whether it is arrived at through Maths or dialectics – should be subjected to some kind of validating procedure that opens it to falsification. After all, it is empirical evidence that separates a valid theory from mere opinion or speculation. Of course, it is not possible to test every possible theory experimentally at a given time in history, and that should not be a reason for scientists to constrain their imaginations in any way. However, it is probably also not a good idea to prefer explanatory power or elegance over predictive power and empirical verification – especially when the theory or model in question is going to be used to make decisions that impact lives.
[i] Rym Bouchendira1, P. C.-K. (2011). New Determination of the Fine Structure Constant and Test of the Quantum Electrodynamics. Physical Review Letters , 080801
[ii] Randall, L. (2011). Knocking on Heaven's Door. HarperCollins.
[iii]Lo, A.W., Mueller, M.T. (2010). Warning: Physics Envy may be hazardous to your wealth
[iv] Emanuel Derman’s Blog