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Byron Jennings | TRIUMF | Canada

View Blog | Read Bio

Shut Up and Calculate

Andreas Osiander (1498 – 1552) was a Lutheran theologian who is best remembered today for his preface to Nicolaus Copernicus’s (1473 – 1543) book on heliocentric astronomy: De revolutionibus orbium coelestium. The preface, originally anonymous, suggested that the model described in the book was not necessarily true, or even probable, but was useful for computational purposes. Whatever motivated the Lutheran Osiander, it was certainly not keeping the Pope and the Catholic Church happy. It might have been theological, or it could have been the more general idea that one should not mix mathematics with reality.  Johannes Kepler (1571 – 1630), whose work provided a foundation for Isaac Newton’s theory of gravity, took Copernicus’s idea as physical and was criticized by no less than his mentor, Michael Maestlin (1550 – 1631) for mixing astronomy and physics. This was all part of a more general debate about whether or not the mathematical descriptions of the heavens should be considered merely mathematical tricks or if physics should be attached to them.

Osiander’s approach has been adopted by many others down through the history of science. Sir Isaac Newton—the great Sir Isaac Newton himself—did not like action at a distance and when asked about gravity said, “Hypotheses non fingo.” This can be roughly paraphrased into English as: shut up and calculate. He was following Osiander’s example. It was not until Einstein’s general theory of relativity that one could do better. Even then, one could take a shut up and calculate approach to the curved space-time of general relativity.

Although atoms were widely used in chemistry, they were not accepted by many in the physics community until after Einstein’s work on Brownian motion in 1905.  Ernst Mach (1838 – 1916) opposed them because they could not be seen. Even in the early years of the twentieth century Mach and his followers insisted that papers discussing atoms, published in some leading European physics journals, have an Osiander-like introduction. And so it continues: in his first paper on quarks, Murray Gell-Mann (1929) introduced quarks as a mathematical trick.  If Alfred Wegener (1880–1930) had used that approach to continental drift it might not have taken fifty years for it to be accepted.

We see a trend: ideas that are considered heretical or at least unorthodox—heliocentrism, action at a distance, atoms, and quarks—are introduced first as mathematical tricks. Later, once people become used to the idea, they take on a physical reality, at least in people’s minds.

In one case, the trend went the other way. Maxwell’s equations describe electromagnetic phenomena very well. They are also wave equations. Now, physicists had encountered wave equations before and every time, there was a medium for the waves. Not being content to shut up and calculate, they invented the ether as the medium for the waves. Lord Kelvin (1824 –1907) even proposed that particles of matter were vortices in the ether. High school text books defined physics in terms of vibrations in the either.  And then it all went poof when Einstein published the special theory of relativity.  Sometimes, it is best to just shut up and calculate.

Of course, the expression Shut up and calculate is applied most notably to quantum mechanics. In much the same vein as with the ether, physicists invented the Omphalos … oops, I mean the many-worlds interpretation, of quantum mechanics to try to give the mathematics a physical interpretation. At least Philip Gosse (1810 –1888), with the Omphalos hypothesis, only had one universe pop into existence without any direct evidence of the pop. The proponents of the many-worlds interpretation have many universes popping into existence every time a measurement is made.  Unless someone comes up with a subtle knife[1] so one can travel from one of these universes to another, they should be not taken any more seriously than the ether.

The shut up and calculate approach to science is known as instrumentalism—the idea that the models of science are only instruments that allow one to describe and predict observations. The other extreme is realism—the idea that the entities in the scientific models refer to something that is present in reality. Considering the history of science, the role of simplicity, and the implications of quantum mechanics[2] (a topic for another post), realism—at least in its naïve form—is not tenable. Every time there is a paradigm change or major advance in science, what changes is the nature of reality given in the models. For example, with the advent of special relativity, the fixed space-time that was a part of reality in classical mechanics vanished.  But with an instrumentalists view, all that changes with a paradigm change is the range of validity of the previous models. Classical mechanics is still valid as an instrument to predict, for example, planetary motion. Indeed, even the caloric model of heat is still a good instrument to describe many properties of thermodynamics and the efficiency of heat engines. Instrumentalism thus circumvents one of the frequent charges again science: namely that we claim to know how the universe works and then discover that we were wrong. This is only true if you take realism seriously and apply it the internals of models.

The model building approach to science advocated in these posts is perhaps an intermediate between the extremes of instrumentalism and realism. The models are judged by their usefulness as instruments to describe past observations and make predictions for new ones; hence the tie-in to instrumentalism. The models are not reality any more than a model boat is, but they capture some not completely determined aspect of reality. Thus, the models are more than mere instruments, but less than complete reality.  In any event, one never goes wrong by shutting up and calculating.

Additional posts in this series will appear most Friday afternoons at 3:30 pm Vancouver time. To receive a reminder follow me on Twitter: @musquod


[1] The Subtle Knife, the second novel in the His Dark Materials trilogy, was written by the English novelist Philip Pullman

[2] In particular Bell’s inequalities.

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