At a meeting in Denver yesterday, a friend who's background is in electrical engineering advised me that if I was to speak of Gabor's "Theory of Communications" [1] I should address the question of "noise". He based this advice on the observation that there were three major works on communications theory in the 1940's era; the above referenced Gabor paper, and works by Shannon and Wiener, and that one of the reasons that the latter two theoretical treatises had had more impact than Gabor's paper on "communications theory" was because they addressed the question of signal/noise discrimination while Gabor's did not (or did Gabor simply have a broader view of what constituted signal?).

This note is then to address the issue of noise in the context of Gabor's ideas which are discussed elsewhere on this web page. I would forewarn the reader that I have no background in electrical engineering (other than indirectly through general geophysics) and am "bootstrapping" my way into inferences on the "techno-philosophic" aspects of signal/noise (S/N) issues.

The first point I'd like to make in this S/N discussion is that the thinking on what constitutes "signal" and what constitutes "noise" has changed significantly since the era of Shannon and Wiener. What once fell into the domain of "noise" is now termed "hidden order" by "Plectics" researchers ("Plectics" is the name proposed by Murray Gell-Mann for the transdisciplinary study of simplicity, complexity and complex adaptive systems.[2]).

Prigogine and others have shown how there is "antagonism" between the measures of spatial coherence (in system transition phases) and local statistical correlations, and that the "central limit theorem" breaks down in these zones. Thus the view of noise in the Shannon-Wiener era, as being "signal" which was statistically random when viewed in a local time-series "window", is not relevant to systems as we now understand them, since what is statistically uncorrelated in a local sense, may be spatially correlated. For example, the assumption of "stationarity" of a time series upon which Wiener noise discrimination filters are based, does not hold for nonlinear dynamical systems which are in a sustained learning or metamorphosing state. In these cases the fluctuations which appear on a local time series as random background noise, may in fact be highly spatially correlated. Thus, yesterday's noise is today's most meaningful signal.

This point was underscored by Torrance V. Johnson, Galileo Project Scientist in his keynote address at yesterday's (SEG) meeting. He explained why, in studying the nature of the moons of Jupiter, it was necessary to simultaneously (or contemporaneously) study the chemistry, electromagnetic fields and the physical dynamics of Jupiter and its orbiting moons (making the instrumention payload both complex and heavy). The contemporaneous observations were needed to shed light on dynamic nonlinear interrelationships which could be key to an understanding of Jupiter and its moons. The enormous magnetic field around Jupiter underscored this need for concurrency.

Johnson made the point that if separate missions were made for each of these specialized scientific study areas, the researchers would be faced with the proverbial blind-men-and-elephant situation, in which the "whole" would be impossible to reconstitute by separately "sensing" each of the parts out of the context of observations on overall dynamic interrelationships.

Independently studying the dynamics of the "parts" clearly leads to the discarding as "noise" of some portion of the "part-to-part" spatial correlations. For example, if there is nonlinear feedback between the motions of the elephant's "parts", emergent "events" arising from such spatially correlated fluctuations will not be detected without analyzing the movement of all parts in a relative (time and space) context. Similarly, if one were separately studying the development of the adult features of a human as zygote metamorphosed through embryo to infant, one would never detect the "replay of human philogeny" in a specific ontogeny. Complex spatial correlations carry more information than is in the sum of the information on the parts, particularly with respect to "spatial phasing". Furthermore, that portion of the spatial correlation which is viewed only in the context of a part, is exposed to being discarded as noise.

Definitions of complexity relate to the length of a description of the system or regularity. As noted above, fluctuations can appear locally random even though they are spatially correlated. In order to bring out the spatially correlated aspects of finely detailed local fluctuations, the description is going to have to become very long. If we truncate the description of highly "complex" systems, then valid regularity or "signal" may be seen as statistically random noise and discarded. In fact, this has already been a common problem in the macro world of productivity and reward systems as discussed in "Complexity and the 'Learning Organization'". If one approaches the appraising of a team by separately appraising the contribution of each member and adding the results, information on spatial correlation and synergy will be discarded as noise. Those team members who expend a significant portion of their energies on "spatial harmonizing" will not be credited for such effort, although it may make the difference between team success and failure.

This gets us to the nub of the question on "signal" versus "noise". How extensive and continuous must the time-space region be to ensure that what we are calling "noise" is not really regularities which appear as noise because our observations or descriptions are too limited and/or too fragmented?

For example, as is discussed elsewhere on this web page, David Bohm has pointed out that "rational law is not restricted to an expression of causality" ... "But, more generally, a rational explanation takes the form; "As things are related in a certain idea or concept, so they are related in fact.". This opens the door to higher dimensional forms of order or "regularity". Bohm suggests (based on the ideas of C. Biederman) that it is necessary; .... "to give attention to similar differences and different similarities." [3]

Ludwig Wittgenstein makes a similar point in "Tractatus ..." [4] on the limitedness of "causality" in his 6.2 - 6.3 series of propositions (i.e. on the "pseudo-ness of mathematics and the limits of logic). Wittgenstein points out that we cannot compare a process with "the passage of time" as there is no such thing, but we can compare it with another process (such as the workings of a chronometer). He further points out that the exact same analogy applies with respect to space. This leads once again to the focus on relative symmetries and asymmetries.

In discussing Kant's problem of the right hand and the left hand, Wittgenstein points out that "A right hand glove could be put on the left hand if it could be turned round in four-dimensional space". Now here is a regularity which only shows up if you can think in four dimensions which is no problem for the human mind, but would intuitively appear impossible to articulate in words or to code into a program (in a generalized form) via a real binary string of code.

Thus it seems that what may be randomness or "noise" in lower dimensional space, may be "regularity" or "signal" in higher dimensional spaces which our consciousness is fully capable of dealing with.

This seems sufficient justification to return to the idea, discussed elsewhere on this web page, of information being "complex". Instead of thinking in terms of characterizing information as a "real" binary string of "unipolar ons and offs", we could perhaps think of information in terms of a complex string of "dipolar ideas"; let's call them "claps" and represent them symbolically with the letter "I" and "0" (null) instead of the number "1" and "0". "Claps" can be thought of as "ex-nihilo" dipoles born out of a latent nothingness, much as thunderclaps are born out of the filling of a void. Once we have the concept of a "clap", or elemental dipolar idea ("I"), we might ask, as we do of the elemental number 1, what two congruent but assymmetrical things when multiplied together, yield a clap. In the case of a "clap", it would be "the sound of the left hand clapping", which we can symbolize by "-z" (i.e. "z" for Zen), and the sound of the right hand clapping, "z". When these two latent asymmetrical possibilities are conjugated, we get the "clap"; i.e. I = -z*z.

Apparently, there are things which do not appear as regularities in real 3D space and which will most certainly be classified as "noise" in any material causal analysis, which our higher dimensional consciousness can nevertheless quickly and easily identify as a regularity. Thus a real binary information stream may be incapable of carrying many categories of useful information which is complex in nature, i.e. whose regularities, symmetries and asymmetries can only be seen in a higher dimensional space. As was pointed out in "Complexity and the 'Learning Organization'", high dimensional regularities such as the ten dimensional phase space trajectories which convey a successful bicycle ride, are not expressible in words, nor are they voluntarily rememberable. Thus there may be practical as well as theoretical constraints involved in exploring complexity and information in terms of real binary strings.

The above thoughts bring to mind, once again, Argyris' "double loop learning". Should we be questioning the adequacy of representing information as a real binary numeric string? Perhaps we should extend our view of information to the complex domain by using a complex "claptic" or elemental dipolar idea string as defined above. "Plecto-claptics" could then allow us to extend the study of information and complexity beyond unconscious material-causal signal, into the domain of conscious latent-emergent signal. While the terminology sounds bizarre, this is clearly what creativity and "organizational learning" are all about, however, we have been approaching these topics as an art rather than as a science.

While no science can compete with the free and wild beauty of art, even ballet Prima Donnas use a refinable framework (archetypal positions and transitions) as a stairway to the narrow stage along the boundary of order and chaos. Perhaps its time for the "learning organization" to question, in a fundamental way, its approach to discriminating between what is signal and what is noise. Our consciousness equips us to discriminate aesthetic order and regularities which go well beyond the discriminating power of linear mechanical causal tools. When we use our consciousness, people are happier and their latent potentials more fully actualized. Does the emergence of "Plectics" flag science's readiness to fully embrace human consciousness?

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[1] Gabor, Denis, "Theory of Communications", JIEE, 1945

[2] Gell-Mann, Murray, "Let's Call it Plectics", Complexity, Journal of the Santa Fe Institute, Vol 1., No. 5 1995/1996

[3] Bohm, David, "Wholeness and the Implicate Order", 1980, pp 116-117, citing

Biederman, C., "Art as the Evolution of Visual Knowledge", 1948

[4] Wittgenstein, Ludwig, "Tractatus Logico-Philosophicus", 1921