Q.E.D.
O.R. and Physics
By ManMohan S. Sodhi
Like most lay people, I admire physicists and am fascinated by their studies of the large — solar systems, galaxies and even the universe — and of the small — quarks, neutrinos and hypothesized particles like gravitons. I particularly admire their perseverance in attempting to unify both large and small with a single theory. Physics is probably the most eye-catching of the physical sciences and, like O.R., it has strong mathematical roots. What can we learn from physicists?
Models and Modeling
Physicists build models, whether of the universe or of the atom or even the electron, to explain whatever they have observed thus far, leaving room for predictions to validate or invalidate these models. Models that can explain all (or most) of what has been observed thus far are better than those that can explain fewer observations ("completeness"). However, models can be attractive for other reasons: parsimony, ease of use, transparency and purpose of using the model. Newton's laws work extremely well for most of us, and we use those models for their transparency and ease of use, not because they are the "truth." Depending on the objective, a better model may always be around. Even completeness is at stake because an observation inconsistent with the model can always show up.
A physics model, e.g., gravity, "explained" by Newton or by Einstein, is still a model. Sometimes physicists confuse between models and the reality they are supposed to try to explain, at least in their claims. Particularly worrisome for a non-physicist like me from this perspective is "dark matter" and "dark energy." Based on accepted models, physicists can account for less than 5 percent of the mass or energy they estimate the universe as having (using the same models), so they explain away the remainder as being "dark." They may be right, but perhaps kicking the tires of their models would be a better start than blaming the universe for being dark and mysterious. What would you think if a student brought you a statistical model with less than 5 percent R-square and then said that "dark" forces explained the remaining 95 percent of the error but couldn't be tested? No wonder creationists are getting bolder!
We too build models — optimization, statistical, systems dynamics or others. We observe a subset of objectives and constraints from "reality" and come up with answers that are the best for the model in the hope these answers can be applied to the reality that we have partially captured in our model. As in physics, we need to keep our objectives straight: completeness, ease-of-use, transparency, parsimony and the intended use of the model. This is how we understand modeling as opposed to the result, the model itself. Over time, we seem to have lost the distinction, or at least our journals have focused on models and not on modeling that would help produce results that actually help organizations.
Mathematics for its Own Sake
The problem of focusing on models rather than on modeling applies to physicists as well. Doing mathematics can be quite seductive — pick up any major O.R. journal and you'll know what I mean. Even physicists who have the whole universe to draw on for motivation seem to hear the same siren song. Lee Smolin ("The Trouble with Physics") accuses physicists of losing track of physics and getting into mathematics instead, without producing testable hypotheses.
In science, any proposed theory is theory only if we can test hypotheses and reject or not reject these hypotheses in light of evidence. However, in mathematics, starting with any axioms, you can derive many correct theorems and, of these, publish those that appear interesting. If you are a physicist using mathematics, you can claim to have a "theory" using hypotheses that cannot be tested (and therefore cannot be rejected) provided you get some interesting theorems. You get published because you and your reviewers are doing the same. Somehow "reality" gets forgotten.
Context-free mathematics becoming a goal in itself is O.R.'s problem as well. This means over time "results" lose their significance because results are interesting only in context. As a result, useful results obtained using straightforward mathematics are less likely to get published in flagship O.R. journals than mundane results obtained using interesting mathematics.
Relevance
Much is debated in O.R. circles about relevance, but relevance is in the eye of the beholder. Physics has popular writers like Stephen Hawking ("A Brief History of Time"), Roger Penrose ("The Road to Reality"), the delightful Richard Feynman ("Surely You're Joking, Mr. Feynman!") and Brian Greene ("The Elegant Universe"). My favorite is Stephen Wolfram ("A New Kind of Science"). These writers make even obscure aspects of physics relevant for society that in turn funds large physics projects like particle accelerators and neutrino hunts. Perhaps we need some O.R. writers like these to get society to know O.R. better.
Shutting Out Ideas
This is a problem in academia in general. When something becomes important, researchers, writing for reviewers, work on topics more likely to get published, so eventually other topics or different approaches to the same problems get shut out. Doctoral students pick up topics more likely to get them a job, so many good ideas can go unexplored. At some point things get so much out of hand — they already have in physics — that senior physicists like Lee Smolin start asking for a reality check. Perhaps senior O.R. people need to weigh in, assuming of course there is a problem with O.R.!
ManMohan Sodhi (M.Sodhi@city.ac.uk) heads the Operations group at Cass Business School in London. He welcomes your comments.
OR/MS Today copyright © 2007 by the Institute for Operations Research and the Management Sciences. All rights reserved.
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