Walter Shewhart and Complex Systems

["Jonathan Siegel" <JMSiegel.Info.Research@worldnet.att.net>]

In this post, I am going to try, as best I can, to explain my view that =
Walter Shewhart was doing very fundamental scientific work when he wrote =
"Statistical Method from the Viewpoint of Quality Control," (1939, =
Reprinted, Dover Publications, 1986). I will do this by providing a few =
hints and examples. I'm not sure I'm competent, at this time, to do =
more.=20
=20
Shewhart was trying -- and in some ways succeeding -- to devise both a =
theory and a general set of methods for studying complex systems in a =
scientific way.
=20
Shewhart is remembered for being the founder of scientific industrial =
quality control, and in particular his invention of the control chart. I =
believe it would be better to regard the control chart as being only one =
application of a much more general and fundamental endeavor. And that =
endeavor was no more limited to being "about" control charts than the =
field of statistics -- if you will forgive the analogy -- is "about" =
improving ones play at cards. Shewhart's work was about how to learn, =
and operate successfully, in a world in which certain fundamental =
assumptions, on which previous methods for learning and operating were =
based, can no longer be made.=20
=20
I offer the following example to justify my claim that Shewhart was =
doing this at a surprisingly deep level.=20

The following quote is from an article by Dr. Roderick V. Jensen of Yale =
University (now of the Wesleyan University Nonlinear Research Group), =
entitled "Classical Chaos" (American Scientist, Volume 75, pp. 168-81, =
at p. 180). All citations in [brackets] are Jensen's.
=20
"The difficulty with the continuum of real numbers lies in the fact =
that, although most real numbers can be proved to have random digit =
strings, it is impossible to prove that a given digit-string is random. =
You simply can never exhaust all the possible tests for underlying =
order. This is a specific example of a class of true statements which =
cannot be proved, statements first shown to exist by Godel in his =
celebrated incompleteness theorem. [D. Hofstadter, Godel, Escher, Bach: =
An Eternal Golden Braid, 1979]. (For a clear discussion of the =
connection between random digit-strings and Godel's incompleteness =
theorem, see [G.J. Chaitin, 1975, Randomness and Mathematical Proof, =
Scientific American, Volume 232, May, p. 47; G.J. Chaitin, Godel's =
theorem and information, International Journal of Theoretical Physics, =
Volume 21, 1982, p. 941].) Moreover, by definition these numbers cannot =
be computed by any algorithm shorter than the digit-string itself. As a =
consequence, most real numbers are uncomputable. Therefore, now that our =
understanding of chaotic dynamical systems has revealed that the root of =
the disease lies in these mathematical pathologies of the real numbers, =
Joe Ford has suggested that these uncomputable and undefinable objects =
should be excised from any meaningful physical theory [J. Ford, "How =
Random is a Coin Toss?" Physics Today, Volume 36, April, p. 40; J. Ford, =
"Chaos: Solving the Unsolvable, Predicting the Unpredictable!" In =
Chaotic Dynamics and Fractals, Academic Press]. In addition to providing =
some logical consistency in the description of natural phenomena, this =
restriction might also provide the missing argument for the validity of =
the second law of thermodynamics. For example, if we assume that nature =
is a finite-state computer (or Turing machine), then the inevitable =
truncation of real numbers could provide the coarse-graining necessary =
to ensure the irreversibility of chaotic systems.=20
=20
A superficial reading of Shewhart's 1939 work (above) parallels the =
above passage. Even a glance at the table of contents shows that =
Shewhart is immensely concerned with the definition of randomness; with =
the fact that we cannot prove a given sequence is random; with =
operational definitions and their consequences; with the fact that given =
operational definitions we cannot meaningfully make statements about =
infinite sequences; and with a belief that ths fact has mportant =
consequences for an applied theory of knowledge, which Shewhart wrote =
was an application of certain philosophical theories of C.I. Lewis. But =
there is more than this. The resemblance is more than superficial. As I =
explained in my discussion of C.I. Lewis's 1928 "Review of Principia =
Mathematica" article, (The American Mathematical Monthly, 25(4) 1928, =
pp, 200-205. Reprinted in  Collected Papers of Clarence Irving Lewis, =
Stanford University Press, 1970,at pp.  394-399), Lewis' critique of the =
Principia was based on the very reformulation of logic or mathematics -- =
and our understanding of our ability to physically realize our =
conceptions in this regard -- that would ultimately lead to Godel. (See =
the postscript to my "Re: Optimization is suboptimization of a bigger =
system?" post located at =
http://deming.eng.clemson.edu/pub/den/archive/98.01/msg00110.html ) =
Shewhart can be fruitfully reread as an attempt to ascertain how =
scientific (and industrial) learning can occur under conditions based on =
these principles. In particular, Shewhart realized the connection =
between these arguments and the definition of randommness -- and the =
implications of that connection for theory of knowledge and science, if =
not thermodynamics -- half a century before Chaitin's 1975 article was =
written.=20
=20
 The continuation of the same passage in Jensen's article should help =
explain just how far ahead of his time Shewhart not only was, but still =
is:
=20
"Such a conclusion would herald a revolution in natural =
science...However, it is possible that the scale at which the truncation =
of real numbers occurs may be so small that no practical consequences of =
the distinction between continuum and discrete theories can be deduced =
or verified. In that case the issue of the ultimate discretization of =
the real world will pass from the domain of physics to that of =
philosophy."=20
=20
W. Edwards Deming's thinking was based, in large part, on the =
proposition that the consequenses are not only practical, but immensely =
so. And yet, sixty years after Walter Shewhart was applying these ideas =
to industry, a scientist of Professor Jensen's caliber, in addition to =
believing the ideas to be new, still wonders whether they will ever =
leave philosophy and make it even to physics.=20
=20
Deming predicted that it would be another 50 years before people ever =
understood how fundamentally significant Shewhart's work was.
=20
Jonathan Siegel

P.S. The continuum hypothesis assumes that real (and complex) numbers =
are contiguous. Most classical existence theorems in analysis are based =
on it. For example, the definition of a limit from college calculus is =
based on this assumption, because it assumes that if a sequence of =
points is getting 'closer and closer together' (is Cauchy), it must =
converge to some point, even if we cannot define what that point is. =
When we reject the continuum hypothesis, we cannot accept this =
principle, and we therefore cannot accept that a mathematical quantity =
exists unless we construct a method for producing it. It thus constrains =
us to use operational definitions, and to limit the operations we posit =
to achievable ones. As Joe Ford wrote in "How Random Is a Coin Toss" =
(above), just because we can conceive of something infinite does not =
mean we can physically experience it. "Do not let your reach exceed your =
grasp." Operational definitions force us to base much of mathematics on =
an inductive rather than a deductive method. It requires a very =
fundamental change in thinking. The change is as radical for theoretical =
work as it is for applied work.=20
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