Of Matter and Mind:
One way of interpreting the “Fourier” diagram is that it indicates matter to be an “ex-formation”, an externalized (extruded, palpable, concentrated) form of flux. By contrast, thinking and its communication (minding) are the consequence of an “internalized” (neg-entropic) forming of flux, its in-formation.
Hiley (this volume) comes to a similar perspective in that he stresses the formative aspect of in-formation. As noted, in discussing Bohm's quantum potential, Hiley begins with the Wigner-Moyal approach to the Schroedinger wave function. The real part of the equation describes what, in my formulation, is ex-formation. The virtual part of the equation describes the quantum potential: “it has no external source in the sense that the electric field has its source in a distribution of charges. Thus it does not emerge from an interaction Hamiltonian as does classical force. - - - In this sense it cannot be thought to act as an efficient cause. It is more like a formative cause that shapes the development of the process. - - - Thus we can think of the information as active from within giving shape to the whole process and this shape depends on the environment [the material context] in key ways.“ In the Fourier diagram this formative cause is labeled action (after Feinman).
Flux, measured as spectral density, is here defined (see Pribram and Bradley 1998) as change or lack thereof, basic to both energy (the amount of actual or potential work involved in altering structural patterns) and inertia (measured as the rotational momentum of mass). David Bohm (1973) had a concept similar to flux in mind which he called a holomovement. He felt that my use of the term “flux” had connotations for him that he did not want to buy into. I, on the other hand, felt holomovement to be vague in the sense of asking “what is moving?” We are dealing with fluctuations, and in the nervous system with oscillating hyper- and depolarizations characterized by the field potentials we can map from the fine fibered parts of the system.
Quantum physics is a science of matter. In quantum physics the Fourier transformation is primarily applied in relating the position in space of a mass to its rotational momentum (spin). Much has been written regarding the indeterminacy of this relationship at the lower limit of measurement, that is, that at the limit it is impossible to accurately measure both position and moment. This is also known as Heisenberg's uncertainty principle.
In the physics of matter the terms moment and position refer to a stable status: “moment” to the inertia of a mass and “position” to its location. By contrast, “energy” and “entropy” in thermodynamics refer to change measured as a quantitative amount of work necessary to effect the change and the efficiency with which the change is carried out. Both moment (rotational momentum) and energy are measured in terms of frequency (or spectral density) (times Planck's constant). Position is measured with respect to location, entropy as it evolves over duration for instance as power, the amount of work per unit time).
The Fourier relation envisions the waveforms involved in measuring frequency not as a linear continuum but rather as a clock-face-like circle – thus one can triangulate and obtain the cosine and sine of the waveform to produce their interference and measure phase in the spectral domain. This was Fourier's definitive insight (or was it that of the mathematicians in Egypt with whom he discoursed during Napoleon's expedition?) that has made his theorem “probably the most far reaching principle of mathematical physics” as Feynman has declared it. Thus, the Fourier energy-time relation becomes, in a sense, “spatialized”.
In quantum physics very little has been made of the uncertainty involved in relating energy and time. Dirac and especially Wigner (1972) called attention to this indeterminacy in discussing the delta function, but for the most part quantum physicists (e.g. Bohr) have focused on the relationship between energy and mass as in Einstein's equation: E=mc*. By squaring c, the constant representing the speed of light, a linear measure of time becomes “spatialized” into an area-like concept, Minkowsky's space-time. I will return to a discussion of this version of time when considering brain processes. In short, much of the thinking that has permeated theories describing matter has been grounded in space-time, not the spectral aspects addressed by the Fourier transformation. For quantum physicists interested in the composition of matter, the Einstein/Minkowsky spatialization of time and energy comes naturally.
For brain function, Dirac's and Wigner's indeterminacy in the relation between energy and time is the more cogent. As noted, during the 1970s and 1980s the maps of dendritic receptive fields of neurons in the primary visual and other sensory cortexes were described by a space-time constrained Fourier relation, the Gabor elementary function, a windowed Fourier transform, essentially a sinc function, a kind of wavelet in phase (Hilbert) space. Gabor had used the same mathematics that Heisenberg had used; he therefore called his unit a “quantum of information” warning that by this he meant only to indicate the formal identity of the formulation, not a substantive one.
Gabor had undertaken his mathematical enterprise to determine the minimum uncertainty, the maximum compressibility, with which a telephone message could be transmitted across the Atlantic cable without any loss in intelligibility. He later (1954) related this minimum uncertainty to Shannon's BIT, the measure of a reduction of uncertainty. In turn, Shannon had related his measure of uncertainty to Gibbs' and Boltzman's measure of entropy. The stage was set for the issues of current concern in this part of the essay: a set of identical formalisms that refer to widely different substantive and theoretical bodies of knowledge.
Thermodynamics:
Contrast the referents of the formulations in classical, relativity and quantum physics to those in thermodynamics: First there are no references to the momentum and position of a mass. Second, the emphasis is on energy as measured not as a pseudo-spatial quantity but as dynamic, often “free” energy. The utility of energy for structured work (as in a steam engine) is of concern in thermodynamics; its efficiency in structured use or rather, its inefficiency as dissipation into unstructured heat is measured as entropy. In the diagram of the Fourier relation, thermodynamics focuses on the upper part of the relationship (the dynamics of energy and time) just as physics focuses on the lower part (the statics of momentum and location of a mass or particle).
The distinction devolves on the conception of time. As noted, time in relativistic and quantum physics has been spatialized as clock time, the Kronos of the ancient Greeks. Time in thermodynamics is a measure of process, how quickly energy is expended. This amount of time, its duration, may vary with circumstance. It is the “Duree” of Bergson, the Kairos of an “Algebraic Deformation in Inequivalent Vacuum States” (Correlations, ed. K.G. Bowden, Proc. ANPA 23, 104-134, 2001).
Brain processes partake of both aspects of time. In the posterior parts of the brain, the processes described by the Fourier transform domain, by virtue of movement, form symmetry groups that describe invariance, that is, objects in space and in Kronos, clock time. Alternatively, in the frontal and limbic portions of the brain the processes described result in the experience of Kairos, the duration of an episode. The evidence for these statements is reviewed in detail in Lecture 10, “Brain and Perception”.
Meaning:
Shannon (1948; Shannon and Weaver 1949) insisted that his measure of the amount of information as the amount of reduction of uncertainty did not provide a measure of meaning: “One has the vague feeling that information and meaning may prove to be something like a pair of conjugate variables in quantum theory, they being subject to some joint restriction that condemns a person to the sacrifice of the one as he insists on having much of the other”. Looking at the Fourier diagram, we can ask, which of the conjugate relationships are appropriate to serving Shannon's intuition with regard to meaning? My answer is that it is the relationship between Shannon's and Gabor's measures of information as negentropy and the location (the placement, the sampling) of a mass on the right side of the diagram.
Meaning is, in a nontrivial sense, the instantiation in matter of information. We might say, meaning matters. Bohm noted that his “active information “ did something, had an influence on the course of the quantum material relationship. Charles Pearce stated: “What I mean by meaning is what I mean to do.” Doing acts on the material world we live in.
This returns us to the statements made by Stapp: “Brain process is essentially a search process – the brain searches for a satisfactory response – and then dissipates [increases the entropy of] its energy in the initiation of the action that it represents”. Llinas also emphasizes the primacy of the motor systems in implementing thought and in the experiencing of the self. A “satisfactory” response is a meaningful one. “Implementation” involves acting on the world we live in.
With regard to language, meaning is the semantic relationship between linguistic “informative” patterns that ultimately lead to the deictic, “the pointing to the lived- in material world” to which that pattern refers (Pribram,1975).
But there is another meaning to meaning, the meaning in music and in the pragmatics (the rhetoric) of language (Pribram, 1982). This meaning of meaning does not involve doing. Rather it is evocative, it engages not the striped muscular system of the body but the smooth muscles and endocrines. What is needed to account for this form of meaning is an addition to Pearce's “what I mean to do”. This addition is: “ What I mean by meaning is what I mean to experience.” When I walk into a concert hall I am prepared to experience a familiar or not so familiar rendition of a repertoire. When Marc Antony addressed the crowd at Caesar's funeral he proclaimed: “I come to bury Caesar, not to praise him”. The prosodics of this declamation as well as the semantics play into the expected experience of the audience. Prosody is a right hemisphere, semantics a left hemisphere process.
The time is ripe for untangling patterns of information from patterns of meaning. The proposal presented here stems directly from the other analyses undertaken. I continue to be amazed and awed by the power of mathematical conceptualizations in understanding the roots of brain function. These roots grow in the soil of the pattern processing of the brain, patterns we call information and meaning.
To summarize: The formal, mathematical descriptions of our subjective experiences (our theories) of observations in the quantum, thermodynamic and communications domains are non-trivially coordinate with each other. They are also coordinate with brain processes that, by way of projection, unify the experiential with the physical. By this I mean that the experiences of observations (measurements) in quantum physics, in thermodynamics and in communication appear to us to be “real”, that is, extra-personal. Adaptation to living in the world makes it likely that this coordination of mathematical descriptions thus represents the useful reality within which we operate.
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As noted in the text, I am deeply indebted to David Bohm and to Basil Hiley for inspiration and corrective management of my course of theorizing. Additionally I have learned much in my association with Henry Stapp and Geoffrey Chew and more recently from Sisir Roy. I hope this manuscript will challenge them to continue to critique what often I feel they think of as my wayward ways.
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