Unreal Nature

October 25, 2010

The Jerk

Filed under: Uncategorized — unrealnature @ 8:25 am

… The first sentence of the first chapter of the first book I opened read as follows: “The first law of cam design is to minimize the jerk.” It was in the second book too.

Second of today’s posts from Re-Engineering Philosophy for Limited Beings by William C. Wimsatt (2007), this gives a little bit of biographical background on Wimsatt::

… I’ve been messy from the start — more of an engineer than a theoretician, and seldom able to get interested in an important classical philosophical problem until I found it blocking the way on some path I wished to travel. I grew up liking big flashy equipment with lots of dials and controls — the kind in 1930s “mad scientist” movies. I entered Cornell in 1959 as a freshman intent on doing a degree in engineering physics on the way to becoming an aeronautical engineer and running in the space race. My biologist father was a classical histologist and embryologist who worked also on the physiology of reproduction and hibernation. He was, by avocation, a naturalist, a falconer, and a woodsman. I grew up playing around his lab in Cornell, going with him on field trips, and building various mechanical (and sometimes explosive) things in our well-equipped basement shop.

… By the time I entered Cornell, I was — apparently spontaneously and naturally — a hard-core reductionist who worshipped the adamantine clarity, precision, and deductive power of classical mechanics and similar disciplines, which all sciences should try to imitate or deserved to wither. I expected my college education to show me how all of the important phenomena reduced to Newtonian mechanics, or its descendants — I already knew that it was possible. I was a walking breathing straw-man.

Fast-forward to a course that Wimsatt audited, given by Edwin L. Resler Jr.:

… Resler spent the first lecture on methodology. He covered three boards listing the equations relevant to solving problems in magnetoaerodynamics — 22 simultaneous equations starting with Newton’s laws of motion, but rapidly progressing to non-linear partial differential equations for hydrodynamic flow, compressible aerodynamics, the electromagnetic field equations, diffusion equations, equations for ionization kinetics, and the like.

… “These are the state equations for our system,” he said, “How many unknowns?” (Count them! — which he did just before the bell rang, as the suspense built.) “Note that there are also 22 unknowns.” he said with an air of discovery as if he’d never counted them before, “Therefore they are solvable in principle!”

There was a pause. I waited expectantly for him to produce the analytical solution in closed form — or to say he’d do it in the next class. I started to draw the kind of box you do in your notes for closed form solutions — but none were forthcoming. I didn’t know it yet, but this was the first time I had encountered a set of equations that we weren’t going to be expected to learn how to solve. He continued: “But you can’t really solve them, of course. What you do is lump a few variables to make dimensionless parameters, let 18 of the variable go to zero or infinity, make a few more approximations, pick interesting values for the other 4, and put it on the computer for the weekend. [Remember, it was 1962.]

Skipping ahead. Wamsitt is now taking a year off from Cornell and working in the engineering department at NCR [National Cash Register]. He’s been assigned to design a cam. He thought he was finished with his design, but he wanted to double-check:

… I headed off to the engineering library at Cornell over the weekend to read up on cam design. I’m glad I did. The first sentence of the first chapter of the first book I opened read as follows: “The first law of cam design is to minimize the jerk.” It was in the second book too.

Was this a joke? I’d never even heard of “the jerk.” (How many of you have before now?) Reading on, I discovered that this was the derivative of acceleration — the third derivative of displacement! The book nowhere said why you had to pay any attention to the third derivative, and neither did any of the others.

… Why had I never heard of the jerk derivative? I had taken some potent applied math, physics, and applied physics courses (drafting, metal-casting, machine shop, circuit design, . . . ), and lots of things in between. Nowhere had anyone thought it important to mention the jerk, which could have been taught in a high-school physics course. It was an intuitively motivating example for elementary differential calculus, with potential application everywhere.

My puzzlement got deeper, and my curiosity led me farther afield. I learned that this phenomenological law was exceedingly general and applies to the failure of all kinds of materials. It is important for crash safety in automobiles twice over — because it described the tendency for structures (including bones) to break, and also because in moving or stabilizing ourselves, we counterbalance or adjust to impressed forces (read: accelerations) and detect sudden changes in force (read: jerks). The lag time for our nervous systems to detect and respond to these changes produces potential stress and chaos-inducing deviations from our optimal set points. By the time we respond to a strong jerk, usually the damage has already occurred, even if we could have handled a more slowly applied stress. If theoretical physicists didn’t have to learn about the jerk, why at least weren’t future engineers taught about it?

… My experience with asking about the “jerk” derivative, and the blank stares I got, suggests that avoiding such questions may be self-amplifying. If the teachers of too many physicists were embarrassed about being unable to explain it, too may of them would never encounter it — and go on to teach others without ever knowing their error.

Moving to the conclusion of this chapter (which is actually the Epilogue):

… In our world, objectivity, reproducibility, control, and systematic investigation are all secured via regularized procedures that are finely tuned and contextually adapted on the fly to our abilities and the task at hand — modulated, not mechanized. They are embedded within a hierarchically nested set of social interactions that regulate the flow of information and our attitudes toward it while managing people and resources. We need to recognize these structures, and learn how to use them in theorizing about science.

-Julie

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