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,
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
he tries to compose a passage which modulates 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
