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Physics Skills in Business: 3 Case-Interview Concepts I Learned From PhysicsPhysics has been defined as the study of the laws of nature, in all their broad glory! In contemporary physics curricula, students are supposed to study mechanics (descriptions of motion, generally), electricity and magnetism (which are two sides of the same coin), and even quantum particles (the unimaginably small constituents of matter as we know it). Yet a deeper understanding of “physics” typically emphasizes that analogous patterns exist across different natural phenomena — for example, the equations that describe a gravitational force and an electrostatic force are written identically, just with different letters. Due in part to this idea that regularities can be found in seemingly disparate fields, physicists find themselves in careers that range from basic research science to patent law, and even jobs like banking.
Analyzing the world from the perspective of physics has prepared me, in some ways expected and others unforeseen, for a career in consulting. More than this, some of the most essential, core business concepts to which I was exposed while studying for case interviews first made their way into my mind during my physics education. Today, I’ll discuss just three.
In popular culture, physicists seem to get famous for their ability to “completely solve” challenging, even esoteric, problems, from beginning to end. In practice, they frequently play another crucial role. When collaborating, say, with an engineer to design a product — or even in preparing academic articles for publication in a scientific journal — the role of the physicist is often to provide a proof of concept, or first-pass solution to the problem at hand. While it is indeed tempting (and intellectually rewarding) for so many scientific-minded students to flesh out every detail relevant to their projects, spending an inordinate amount of time learning the optimal parameters for any given problem leads inevitably to failure… even within academia.
The antidote is, of course, the 80/20 rule — although it goes by different names in the physics community. There, the 80/20 philosophy is encoded in the practice of concentrating the majority of one’s upfront time and energy investments in what is known as a “first-order” model. Sometimes, you’ll hear the term “zeroth-order model”; I shall avoid the spelling out the technical differences between the two names, for the sake of adhering to the 80/20 rule!
An illuminating, entertaining, and embarrassingly accurate example can be found in the joke about the physicist who wished to quantify the bodily radiation given off by a cow in the pastures. Since most of the animal’s mass and surface area is to be found in the rotund body, with the legs and tail contributing only minimally, the scientist declares: “Let’s assume for simplicity a spherical cow…” With perhaps 20% of the effort that would be needed to do the full calculation, the physicist can likely achieve accuracy within 80% of the original goal.
It is no mere accident that this philosophy shows up in physics as well as business. Italian economist and sociologist Vilfredo Pareto, whose surname name the 80/20 rule bears (i.e., “ the Pareto Principle”), trained first in mathematics and physics, becoming an engineer. While the actual history behind Pareto’s insights about disparities in the distribution of wealth and the reasoning behind this name is more subtle than a straightforward application of the physicist’s mathematical tools to a social problem, physics students should not be surprised if they take pleasure in perusing their business school buddies’ Microeconomics homework: many of the fundamental concepts therein, such as the price elasticity of demand, are more palatable and rewarding after a student becomes fluent in calculus and “optimization” ideas.
In case interviews — and on-the-job in management consulting — a critical skill is the ability to rapidly assess whether or not a given avenue of inquiry or analysis will be worth pursuing. In case interview training at FirmsConsulting, this is taught initially via estimation techniques.
In science, too, it is necessary to determine whether competing effects (say, a political voting influence posed by peers and another stemming from the media) are of the same or different magnitude, or at least strong enough to change a key model prediction or observable outcome. Somewhat ironically, the basic numeracy capacity of fluently navigating verbal and mental arithmetic (in which Ph.D. holding interviewees are notoriously held to be deficient) is something both strongly encouraged in the initial stages of a traditional physics education, and then proudly forgotten upon graduation to more abstract math manipulations.
This second aspect of business-relevant physics training provides, in part, an answer to one issue that is tacitly raised by introducing the 80/20 rule as some guiding principle for a physicist: it helps one assess the next-most profitable direction in which to move an analysis after the point the initial, “first-order” model starts giving diminishing returns.
The core elements for a well-executed estimation do not differ dramatically between physics and consulting.
All these, and the confident wherewithal to modify an approach if things don’t make sense by the time of the concluding “sanity check” will make for a more seamless estimation. Just as for decision trees, the main goals should be to establish a clear, tight problem scope from even ambiguously wide questions, and then to break this more “concrete” problem into progressively narrower subcomponents that can be efficiently tackled in one-by-one fashion.
Here, too, a famous (also Italian) physicist Enrico Fermi is credited, not incorrectly, as being a lead-by-example popularizer of the infamous “back-of-the-envelope calculation” style of estimation. An unignorable lesson that can be gleaned from Fermi’s approach is the need to keep careful track of the units in which each successive quantity is measured. Another tip is to become comfortable (more than many interviewees might expect should be necessary) manipulating powers of ten, including verbal conversions — say, “three quarters of a billion” = “750 million” — at a roughly conversational pace. Again, physics majors may start out with this level of fluency, but in my experience, it is taken for granted in academia, and yet, an ability that is surprisingly common in the business world, from second-year consultants to CEOs. It may be that the very language gap itself is a barrier to success for academics, who use terms like “one GigaWatt,” or even “ten to the ninth Watts” as shorthand, rather than the more socially acceptable (and no less dignified) “one million Watts.”
Today’s final physics-derived skill for the business world is just that — the wherewithal to derive an appropriate model, or tailored approach, for solving a particular case or problem from first principles. Admonishing interviewees to “avoid memorizing frameworks” is only half of the problem; they also need to be taught how to craft bespoke structures, ad hoc, by using a combination of their knowledge of case training fundamentals and business judgment (in a word, experience). FirmsConsulting trainees learn to ask not simply “what is the equation for profit?” but to think carefully about what components or factors drive a clear and quantitative objective one way or another.
A cautionary note is in order: theoretical physicists tend to gravitate (no pun intended) toward something more akin to philosophy than “decision tree” when prompted to derive an equation or model from first principles; this is partly because the “first principles” in physics are fundamental, almost axiomatic propositions about the natural universe. Yet, on the job, constrained within a single sphere of problem types, physicists do more tangible (and also useful!) things that can be instructive to consulting case-interviewees — and yes, the skills I am talking about are highly learnable tactics that are taught in all graduate-level classes.
What I am referring to is something called a symmetry argument; it’s just one way a physicist does exactly what is necessary in solving a case interview problem in a limited time frame. The idea is to eliminate all the things that cannot matter in determining the outcomes for a situation, so that you’re left with the (MECE) drivers. A fun “Physics 101” example is the deduction that the so-called kinetic energy of a rocket in space depends only on its speed. In principle, it could also depend on the rocket’s 3D coordinates, or its orientation! For example, far up in the Earth’s atmosphere, you feel less gravitational pull than on the surface; there, a difference in location from your on-the-ground coordinates matters a lot, if you are grading a lab assignment. Likewise, orientation is important in yet other circumstances: an 18-wheeler moving toward you is far more dangerous than one pointed in the opposite direction.
Yet in outer space, as long as a rocket remains distant from any particular planet or other large object, like a star, there is nothing else around to influence it. Its specific position no longer matters. Furthermore, positions are relative: if there are no large objects around by which to measure your position, orientation loses its meaning! If all directions are equivalent, and even an upside-down rocket can’t tell it’s upside down, the direction of motion can’t have anything to do with determining its energy, either. In other words, all that’s left (of the original three possibilities — speed, location, direction) to distinguish the kinetic energy of one rocket in space from that of any other is how fast it’s being propelled through the dark nothingness.
A famous theorem in physics bears the name of Emmy Noether for her contributions to this kind of reasoning. If you’ve ever heard of the laws of “Conservation of Energy,” or the “Conservation of Momentum,” you might enjoy knowing that it’s by invoking symmetries (as we did for the rocket) that professors teach graduate-level students to anticipate such laws. While an MBA graduate might be less ambitious about discovering new conservation laws, the most important takeaway for consulting is that one must get accustomed to reasoning through potentially relevant factors.
Combining this with the above techniques, and working in a little business judgment (something far from merely being domain knowledge, and, rather, another skill that must be rehearsed) will help an interviewee prioritize branches in their structures — and avoid trying to solve every interesting piece of the puzzle (i.e., not the “key question”) in any given case. While physicists-in-training are not necessarily in more privileged positions for success in a case interview than students of other backgrounds, I hope I’ve helped show that just about anyone can succeed with the right mindset, a little training, and a whole lot of practice.
The famous Richard Feynman said repeatedly that (and I paraphrase:) if you cannot explain what you’ve done in a project … in two sentences … to your grandmother, you don’t understand it well enough — you need to go back to the drawing board! It’s true in executive debriefs, and the very same also goes for your interviewer, whether she is an associate-level consultant or a partner. Your absolute “first priority” in a case interview should be to define — or refine — the key question. Ph.D. in Theoretical Physics or first-year undergraduate drawn to consulting: practice this for every case you do, and for every project on your resume!
This article was contributed by FC member with a physics background interested in transitioning into consulting. It covers physics skills/concepts that are useful as part of preparing for consulting case interviews, and overall for a career in business.
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Cheers, Kris
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