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Units—SI-Only, or Multicultural Diversity?
1.“Information for Contributors,” Am. J. Phys. 67 (1), 5 (1999).
1.For some interesting takes on units issues, see The Metric Debate, edited by David F. Bartlett (Colorado Associated University Press, Boulder, 1980);
1.see also David F. Bartlett, “The g vs. the m/sec2: No Contest,” AAPT Announcer 28 (1), 56 (1998).
1.And for a truly eloquent statement of the SI-Only position, see Ernest L. Asten, “Confusion worse confounded,” Nature (London) 346, 506 (1990);
1.Ernest L. Asten, reprinted in Am. J. Phys., “A plea for the metric system,” Am. J. Phys. 59 (2), 103 (1991). I realize, by the way, that this editorial is overly long (but, unlike the previous editor, I don’t write an editorial every month), and perhaps overly provocative (but I have been subjected to intermittent SI scrutiny for a number of years and have finally been moved to respond).
2.See, for instance, John S. Rigden, “Editorial: Are SI units tending toward the ideological?” Am. J. Phys. 52 (3), 205 (1984).
3.That year I had run Boston as a “bandit,” too slow to be a qualified entrant. A few years later, I immodestly observe, my marathon increased (eventually to a personal best of 3.25 m/s, a speed which, maintained for 26.2 miles, sounds impressive, at least to me), and I have since run Boston several times as a legitimate entrant. Lucky for me, by the way, that I said “speed” and not “velocity,” for if you say “velocity” without specifying the direction, some physics professor is apt to write you a letter. I suppose “from Hopkinton to Boston” would do.
4.A term also used by geologists, for their own special purposes.
5.Occasionally described in antiquity by the term “tenthmeter”; my thanks for this information to AJP’s Formidable Assistant Editor, my Distinguished Colleague and occasional Department Chair, Kannan Jagannathan;
5.see, for instance, McGraw–Hill Dictionary of Scientific and Technical Terms, edited by Sybil P. Parker (McGraw–Hill, New York, 1984). I would not accept “tenthmeter” in AJP, nor the spelling “Armstrong” that appeared in one manuscript that we received. From a fundamental point of view, the Bohr radius, would of course be preferable to the ångström. Weisskopf refers to as “the only dignified unit of length in the atomic world:”
5.Victor F. Weisskopf, “Of Atoms, Mountains, and Stars: A Study in Qualitative Physics,” Science 187 (4177), 605–612 (1975). One of the many fascinating observations in this paper is that the wavelength of minimum velocity wavelets on a lake is roughly the geometric mean of the Bohr radius and the maximum height of a mountain!
6.Which is how his magnificent experiments were characterized by E. A. Guggenheim, Thermodynamics, An Advanced Treatise for Chemists and Physicists (North-Holland, Amsterdam, 1957), p. 103.
7.And perhaps, as Heisenberg remarked to Bloch, that space is blue and birds fly through it. See Felix Bloch, “Heisenberg and the Early Days of Quantum Mechanics,” Phys. Today 29 (12), 23–27 (1976);
7.Felix Bloch, printed as a “page filler” in Am. J. Phys. 60 (4), 317 (1992).
8.The Gilbert, in case you had forgotten, is “the unit of magnetomotive force in the electromagnetic system, equal to the magnetomotive force of a closed loop of one turn in which there is a current of 1/4π abamps,” and the Maxwell is “a centimeter-gram-second unit of magnetic flux, equal to the magnetic flux which produces an electromotive force of 1 abvolt in a circuit of one turn linking the flux, as the flux is reduced to zero in 1 second at a uniform rate. Abbreviated Mx. Also known as the abweber (abWb); line of magnetic induction.” (See Parker, Ref. 5.) I believe this implies that and that 1 Gilbert/cm is a magnetic field of 1 gauss (oersted?), though the latter may very well be off by a factor of 4π/10 (or perhaps even more).
9.I do recall that as an undergraduate I had a good, though confusing and inconclusive, learning experience as a result of the existence of various units for charge. Somehow I came across the fact that electrostatic and electromagnetic units of charge had different dimensions! The coulomb seemed to be something unto itself, but the dimensions of esu were clearly and of emu The electronic charge had (at least) three different numerical values: and Very puzzling to an undergraduate. Different dimensions for the same thing. And fractional powers into the bargain. Could something like that also be true of other quantities? Could miles and meters, say, have different dimensions? Or could the length of my arm and the radius of the earth perhaps have different dimensions? As nearly as I can remember, neither my textbook nor my professor could do much to alleviate my distress on this matter. I think I was astute enough to notice that if I took the ratio of the dimensions of esu and emu, the funny fractional powers disappeared and I was left with dimensions of But, for some reason, I do not think that I then took the obvious next step of finding the numerical value of that velocity. (Perhaps it was because we had no pocket calculators in those days, only slide rules?) In the long run, it may have been just as well that no one dispelled those mysteries for me then, for I was left with some nagging confusion about E&M that stayed with me on into graduate school. (Not that I would pretend that I am not now sometimes confused or that there are not still wonderful discoveries to be made in the field of classical electromagnetism! See, for instance, Neil M. Zimmerman, “A primer on electrical units in the Système International,” Am. J. Phys. 66 (4), 324–331 (1998), especially pp. 327–328, and
9.J. D. Jackson, “A curious and useful theorem in two-dimensional electrostatics,” Am. J. Phys., accepted for publication.)
9.After all, research has shown that confusion has important instructional benefits, and if a little confusion is good, then, following the universally accepted principle that “more is more,” perhaps we should go back to teaching undergraduate E&M with esu and emu for pedagogical reasons? (Somehow, examination of does not provide quite the same air of mystery as do “the electromagnetic experiments of Kohlrausch and Weber” or “the ratio of electrostatic and electromagnetic units of charge.”) No, I think not. There is just too much potential for confusion here; what might be great for a handful of students would probably only provide lasting frustration for the majority. We can find plenty of valuable confusion elsewhere in electromagnetism without torturing students (and professors) with abamps and Gilberts.
9.Start them out with what Griffiths [David J. Griffiths, Introduction to Electrodynamics (Prentice–Hall, Englewood Cliffs, NJ, 1989), 2nd ed., p. 517] refers to as “SI, or ‘rationalized’ (sic) mks” and then gradually introduce them to Gaussian (cgs) as an alternative. Perhaps graduate school is the time to begin serious use of Gaussian units, though I am disappointed—as is the author himself, so he confesses—to see that the new (third) edition of Jackson (Wiley, New York, 1999), the “blue Jackson” as opposed to its green and red predecessors, has dropped Gaussian units in favor of SI in the early chapters.
9.[For Maxwell’s wonderful statement about the significance of the numerical value of “the number of electrostatic units in one electromagnetic unit of electricity,” see the “page filler,” “Maxwell’s Great Discovery,” Am. J. Phys. 58 (12), 1130 (1990).]
10.H. G. Jerrard and D. B. McNeill, A Dictionary of Scientific Units (Chapman and Hall, London, 1980), 4th ed., p. 123.
11.See, for instance, Robert H. Romer, Energy—An Introduction to Physics (Freeman, San Francisco, 1976);
11.“A Shopper’s Guide to Room Air-Conditioners,” New York Times, April 8, 1989, p. 52;
11.Robert H. Romer, Consumer Reports 62 (6), 24–27 (1997).
12.Barry N. Taylor, Guide for the Use of the International System of Units (SI), NIST Special Publication 811, 1995 Edition (U.S. Department of Commerce, 1995);
12.see also The International System of Units (SI), NIST Special Publication 330, 1991 Edition, edited by Barry N. Taylor (U.S. Department of Commerce, 1991).
13.When I first read the manuscript of K. R. Brownstein’s paper [“Angles—Let’s treat them squarely,” Am. J. Phys. 65 (7), 605–614 (1997)], on a really controversial topic, the units and dimensions of angles, I thought that I could use his arguments to prove that Fortunately, Brownstein was able to convince me that I had misunderstood his arguments. (Otherwise I could not now give an AJP page reference for his paper.)
14.The New York Times of 6 October 1998 reports the acceleration of Deep Space 1 as about (30 ft/sec)/day, and (miles/hr)/sec seems a very reasonable unit for describing the acceleration of an automobile.
15.I wish I knew who deserves credit for inventing the Jelly Donut (which should be adopted as an official SI “supplementary unit”). I have found it extraordinarily useful in teaching, and were I ever to publish a second edition of my Physics & Energy text, I would replace the frontispiece photo of cow, windmill, and power line with a photo of the official Jelly Donut, under glass, like the photos of the standard kilogram that graced the pages of some of the dreary physics texts of my youth. One of my favorite informal units, invented by one of my nonscience students, is the Pizza (defined as half the energy released in the annihilation of a pizza and an antipizza),
15.For some other informal units, including the pizza (lower case p) and the mosquito pushup, see “SI Units (Système Irrégulier d’Unités),” Am. J. Phys. “page filler,” 60 (6), 576 (1992).
15.Then there is the Smoot, [see “Le Système M.I.T. d’Unités,” Am. J. Phys. “page filler,” 60 (5), 450 (1992)], the units in which the Harvard Bridge between Boston and Cambridge is calibrated. (The Harvard Bridge, 364.4 Smoots and one ear in length, crosses the Charles River at M.I.T. and is about 1500 Smoots, or 2.5 kilometers, from Harvard. Go figure.)
15.Some other AJP “page fillers” on metric issues are “Down with the Metric System,” 63 (5), 470 (1995);
15.“The triumph of cold calculation,” 64 (12), 1534 (1996);
15.“Antimetric arguments,” 65 (6), 578 (1997).
16.I will not allow the ambiguous m/s/s as a unit for acceleration (just as ambiguous as the arithmetic expression 17/29/13; follow the programmer’s maxim: “When in doubt, use parentheses”), even though all of us know exactly what the author intended. Am I being inconsistent in insisting on editing that to m/s2? Yes.
17.But I must say that the fact that George Will apparently shares my tolerance for diversity gives me pause; see George F. Will, “A kilometer too far,” Boston Globe, 31 August 1992. Except for his opposition to the designated hitter rule (a position which he now appears to have abandoned), there are very few issues on which he and I have ever been in accord.
18.The Boston Globe published on 26 September 1998 an article about Quabbin Reservoir, a large reservoir a few miles from my home, operated by the state’s Metropolitan District Commission to supply drinking water for much of the metropolitan area of Boston. (I occasionally ski on the surrounding land area of the Quabbin Reservation; skiing there is not allowed, and so there is less congestion on the ski trails. Unlike the SI Police, the MDC Police have not yet noticed my transgressions; here’s hoping they do not examine this January issue.) In the Globe’s article, it was stated that Quabbin holds more than twice as much water as Lake Erie! A long subsequent piece on 19 October by the Globe’s ombudsperson blamed the error on the difficulty of converting between gallons and cubic miles: “Not a reporter alive has the skill to convert one to the other.” Of course the original author also made the mistake of not thinking a bit about the claim. It does not require a Ph.D. in physics to be able to glance at a map and guess that unless Quabbin is extremely deep and/or Lake Erie rather shallow, the claim must be false.
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