source file: mills2.txt Date: Wed, 27 Nov 1996 07:39:07 -0800 Subject: Post from Brian McLaren From: John Chalmers From: mclaren Subject: Muddy thinking, con artistry, and John Cage - part I of 2 -- Many thanks to Eric Lyon for falling into the Bengal tiger trap hidden in my post in Topic 3 of Tuning Digest 803. By helpfully committing so many flagrant logical errors, he has given me leave to dilate on important points which the brevity of Topic 3, digest 803 did not permit me to discuss. My post stated (in part): "Exactly what is an experimental composer? "Which hypothesis does the experimental composer conduct an experiment to test? "What is the experimental control? What kind of statistical methods does the experimental composer use to analyze hi/r results--linear regression, chi square, least squares, ANOVA? "Which laws of nature does the experimental composer seek to investigate?" Lyon describes this criticism as "inane" insofar as "Most of these questions are irrelevant because musical experimentation does not equal scientific experimentation." -- This is a classic example of the slovenly thinking best satirized in Charles Dodgson's "Through the Looking Glass" : "I don't know what you mean by `glory,'" Alice said. Humpty Dumpty smiled contemptuously. "Of course you don't-- till I tell you. I meant `there's a nice knock-down argument for you!'" "But 'glory' doesn't mean 'a nice knock-down argument,'" Alice objected. "When *I* use a word," Humpty Dumpty said, in rather a scornful tone, "it means just what I choose it to mean--neither more nor less." "The question is," said Alice, "whether you *can* make words mean so many different things." [Lewis Carroll (nee Charles Dodgson), "Through the Looking Glass"] -- In this case the word being grossly misued is "experimental." "Experimental" does not have an infinite variety of possible meanings. It does not mean just what Eric Lyon chooses it to mean. The American College Dictionary defines "Experimental" as: "1. pertaining to, derived from, or founded on experiment: an experimental science. 2. based on or derived from experience; empirical; experimental religion. 3. Of the nature of an experiment; tentative." John Cage's use of the word "experimental" violently contradicts all three of these meanings. -- Lyons' logical error is his assumption that he can misuse and abuse and warp and twist the word "experimental" at will. (Notably, this is one of John Cage's most flagrant errors as well.) And, like Cage, Lyon has not only misused the word "experimental," he has demonstrated his ignorance of the meaning of the word -- and of its profoundly important implications in our culture. The word "experimental" inevitably takes on overtones of the scientific method whenever it is used nowadays. "Of the nature of an experiment" (the dictionary definition which refers to this implication of the word) refers to the use of experimental technique and methodology in the course of applying the scientific method. What is the scientific method? Clearly Eric Lyon does know. He states that "the scientist makes the utmost effort to *disprove* his hypothesis to determine its veracity." This is not the scientific method. It is never enough merely to "make the utmost effort to disprose" an hypothesis, since one's utmost efforts are likely to be futile-- life is short, experiments are complex, and there are too many possible ways of doing the wrong experiment. For example, suppose I hypothesize that light is a form of electromagnetic radiation. Such radiation is--as we all know--produced by accelerating an electric charge or a magnet. To test this hypothesis, I shake a magnet with my hand. No matter how rapidly I shake the magnet, it never emits any light. To do my utmost to disprove my hypothesis, I hook up the magnet to a widget which agitates the magnet over a wide range of frequencies, up to thousands of times a second. Having "done my utmost" to disprove the hypothesis that light is electromagnetic radiation, I conclude that my hypothesis is false. What's wrong with this "experiment"? The problem is that I would have had to agaitate the magnet at a rate of about 10^15 cycles per second to get it emit visible light. Doing "my utmost to disprove" the hypothesis wasn't remotely adequate, because I didn't know the range of requencies required for visible light. Another variant of such bad science would be to fire up a radio broadcast tower, transmit over a wide range of frequencies, and show that in no case was light ever emitted. Again, this fails the test of a scientific experiment because experimental scientists do NOT try to "do their utmost to disprove the hypothesis." Rather, in the real world they calculate an expected result from a mathematical model and perform repeatable experiments to determine whether the calculated values match the observed experimental results. Moreover, Lyon's claim is obviously false for another reason. It is *never* possible to "make the utmost effort to *disprove*" an hypothesis, since one can never prove a negative. The effort required to disprove an hypothesis is infinite and thus the utmost effort is unending and without limit. For example, a scientist who hypothesizes that a psuedorandom number generator produces a good simulation of an ergodic stochastic source would--by Lyon's criterion-- have to perform an infinite number of tests on an infinite number of runs by the pseudo- random number generator. Otherwise, the scientist would not be "doing his utmost to disprove his hypothesis." Of course, no scientist does what Eric Lyon suggests because this is not science. Lyon clearly does not know what science is, what constitutes an experiment, or the nature of the scientific method. "Experiment is the sole source of truth. It alone can teach us something new; it alone can give us certainty. These are two points that cannot be questioned. (..) It is not sufficient merely to observe; we must use our observations, and for that purpose we must generalize. This is what has always been done, only as the recollection of past errors has made man more and more circumspect, he has observed more and more and generalized less and less. (..) What then is a good experiment? It is that which teaches us something more than an isolated fact. Without generalization, prediction is impossible. The circumstances under which one has operated will never again be reproduced simultaneously. The fact observed will never been repeated. All that can be affirmed is that under analagous circumstances an analagous fact will be produced. To predict it, we must therefore invoke the aid of analogy-- that it to say, even at this stage, we must generalize. (..) Experiment only gives us a certain number of isolated points. They must be connected by a continuous line, and this is a true generalization. But more is done. The curve thus traced will pass between and near the points themselves. Thus we are not restricted to generalizing our experiment, we must correct it. (..) Detached facts cannot therefore satisfy us, and that is why our science must be ordered, or, better still, generalized." [Poincare, Henri, "Hypotheses in Physics," pg. 142, from Science and Hypothesis, Dover Edition, 1952] One of the finest mathematicians of all time, Poincare had a good idea what the scientific method involved. "Every experiment must enable us to make a maximum number of repdictions having the highest possible degree of probability. The problem is, so to speak, to increase the output of the scientific machine. I may be permitted to compare science to a library which must go on increasing indefinitely; the librarian has limited funds for his purchases, and he must, therefore, strain every nerve not to waste them." [Poincare, op. cit, pg. 144] Lyons' claim about the scientific method grossly violates Poincare's principle of experimental parsimony. This is as we would expect, since Lyon understands nothing of the scientific method; but Poincare makes it pellucidly clear that quick rejection of an hypothesis is of the utmost importance. "Every generalization is a hypothesis. Hypothesis therefore plays a necessary role, which no one has ever contested. Only, it should always be as soon as possible submitted to verification. ...If it cannot stand this test, it must be abandoned without any hesitation. (..) If [the hypothesis] is not verified, it is because there is something unexpected and extraordinary about it, because we are on the point of finding something unknown and new. Has the hypothesis thus rejected been made sterile? Far from it. It may even be said that it has rendered more service than a true hypothesis. Not only has it been the occasion of a decisive experiment, but if this experiement had been made by chance, without the hypothesis, no conclusion could have been drawn; nothing extraordinary would have been seen; and only one fact the more would have been catalogued, without deducing from it the remotest consequence." [Poincare, Henri, op cit., pg. 151] Notice that this latter pointless activity is *precisely* what Cage advocates. From this "experiment...made by chance" without an hypothesis, no conclusion can be drawn; the outcome is "without the remotest consequence." This is not science. This is not an experiment. It is not "experimental." Neither Eric Lyon nor John Cage understood this--because neither of them understood the meaning of the word "experiment," the nature of the scientific method, or (apparently) any of the other technical vocabulary they have chosen to misuse. This discussion of the the experimental method is particularly appropriate to microtonality because, as we've seen, time and time again xenharmonic intonations have been dismissed as "useless" and "impractical" and "unmusical" on the basis of abstract calculations--yet these same intonations prove superbly useful for composers of microtonal music. Barbour, for instance, dismissed 19-tet: yet reams of excellent 19-tet music has been composed. Fox- Strangways dismissed just intonation as impractical--yet Partch and the members of the JIN have composed enormous amounts of beautiful music using ji. 15-tet has been pooh-poohed as "unmusical," yet Easley Blackwood has proven that it is not only musical but fertile ground for microtonal composition. And so on. Thus, it is especially vital when discussing microtonality to have a firm grasp on the scientific method, for new tunings must always be *tested* by *experiment* before they can be accepted or discarded. And Eric Lyon makes this difficult because he has given a series of utterly false definitions of "experiment" and by implication the scientific method. Instead, what scientists actually do is to try to prove their hypotheses by measuring physical events and comparing the results with calculations based on mathematical models derived from their hypotheses. To proceed in the opposite way, by trying (and failing) to disprove one's hypothesis, is futile and in fact a profound logical fallacy. For Lyon reasons that if a large enough number of instances in which an hypothesis is not true cannot be demonstrated, the hypothesis must be correct. This is obviously false, and it has been known to be false for more than two thousand years: Aristotle discussed this logical error, and it has been used as a textbook example of faulty reasoning in universities throughout Medieval Europe, the great institutions of learning of the Renaissance, and up to the modern day. This reasoning is faulty because no matter how many experiments you perform to disprove your hypothesis, it doesn't guarantee that *both* your hypothesis *and* the null hypothesis might be false, and the truth might be a third possibility you hadn't thought of. Notice that this is *exactly* and *precisely* the same logical fallacy into which critics of JI and microtonality have consistently fallen; a theorist here and there attempts to compose in a xenharmonic intonation, and knowing nothing about the intonation, produces unlistenable junk. From this they conclude that microtonal tunings are "useless" and "unmusical." Barbour is a prime example: his misuse of JI--in which hs tries to compose a passage which modules from C to F# without changing any of the pitches by a comma-- does not show that JI is "useless" or "unmusical," it merely shows that Barbour's use of JI is inept, unmusical and willfully ignorant. This should be so obvious as to require no explanation, but apparently this kind of 2500-year-old logical fallacy is news to many of you, including Eric Lyon. (Sigh) The scientific method does not stress disproof, but positive demonstrations, for precisely this reason. A million pieces of bad music composed by people ignorant of JI do not disprove the utility of JI: but one good piece of music composed by someone knowledgable of JI *DOES* prove the intonation's utility. Eric Lyon clearly does not understand the scientific method, nor the logic behind it. These concepts are apparently alien to him, just as they were to John Cage, just as no "experimental" composer appears to have known what the scientific method involves or why it is *vitally* important when dealing with new intonations. As John Backus pointed out, "terms borrowed from the field of science must be used with their precise scientific meanings." Otherwise, the result will be pseudo-science, "disregard for the accepted meanings of scientific terms, (..) unintelligibility, and (..) complete lack of any reference to the results of other workers as support for (..) statements." [Backus, J. "Die Reihe--A Scientific Evaluation," Perspectives of New Music, Vol. 1, No. 1, pp. 161, 171] The concluding half of this post deals with some concrete examples which show why an understanding of the scientific method (and use of the word "experimental" in accord with its specific dictionary definition) is so crucially important in dealing with microtonal scales. --mclaren Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Thu, 28 Nov 1996 01:32 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA10179; Thu, 28 Nov 1996 01:34:22 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA10275 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id QAA26911; Wed, 27 Nov 1996 16:34:19 -0800 Date: Wed, 27 Nov 1996 16:34:19 -0800 Message-Id: <14961128002841/0005695065PK2EM@MCIMAIL.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu