Modulating cognitive transformations: electrical metaphors and semiconduction

In Quest of a Dynamic Pattern of Transformations (Part #6)

---

[Parts: First | Prev | Next | Last | All] [Links: To-K | From-K | From-Kx | Refs ]

---

Very extensive use is made of metaphor in discussion of systems of every kind. A valuable summary of the relevance of metaphor, including electrical metaphor (in passing), is provided by Samuel McNerney (A Brief Guide to Embodied Cognition: why you are not your brain, Scientific American, 4 November 2011) in the light of the work of George Lakoff and colleagues on cognitive linguistics. This has notably given focus to the conduit metaphor valued in the experience of flows in systems.

In the midst of a global financial crisis that has been compared to a hurricane -- and a major concern with liquidity -- it is appropriate to note early efforts to articulate understanding of complex systems through meteorology by John W. Thompson (Meteorological Models in Social Dynamics, Human Relations, 1961; Mental Science, Meteorology and General Systems Theory, General Systems, 1960; Modes of Though in Meteorology, General Systems, 1967). Exposure to weather transformative processes readily leads to comparison with cognitive experience, exemplified by "pressure" and "depression".

Electrical metaphors: Even more extensive use is variously made of electrical metaphors. As noted by Marlene Johansson Falck (Electrifying Performances and Brains that Fuse: metaphor and the cognitive function of electricity, 2005):

As is evident from my material, which consists of a large number of metaphorical expressions from the OED, CIDE and 20th CW1, there is remarkable consistency among the instances with respect to the kinds of experiences that may be structured by means of our experiences of electricity. Almost all the mappings exemplify the use of electricity to conceptualise people's actions or emotions. (pp. 52-53)

In an extensive review, Dedre Gentner and P. Wolff (Metaphor and Knowledge Change, 2000) discuss the subsequent implications of the widely-cited earlier work on comprehension of electricity (D. Gentner and D. R. Gentner, Flowing Waters or Teeming Crowds: mental models of electricity, 1983). Much of this literature offers insightful comment on the cognitive implications, notably for learning and comprehension (cf. John M. Carroll and John C. Thomas,(Metaphor and the Cognitive Representation of Computing Systems, 1EEE Transations on Systems, Man, and Cybernetics, 1982, 2; Aristotle Tympas and Dina Dalouka, Metaphorical Uses of an Electric Power Network, metaphorik.de, 2007, 12)

In the light of Freud's own use of such a metaphor, Don M. Tucker and Phan Luu discuss An Electriclal Metaphor for the Neurophysiological Mechanisms (In: Cathexis Revisited: corticolimbic resonance and the adaptive control of memory, Annals of New York Academy of Sciences, 1998). They note:

In drawing from the models of neuronal function of his day, Freud considered their properties as electrical, and theorized about their operations as involving the storage and management of quantity of energy. (p. 137)

In the daily organization of experience, the limbic networks seem to resonate to the motivational (i.e., personal) significance of each event. In doing so, they engage the consolidation of that event in proportion to its significance. Because the adaptive control is integral to the representational process, the phenomenon of "memory" could be redefined as "motive-memory." The significance of each event is integral to the representation itself. In Freud's terms, an event becomes organized in memory to the extent that it is affectively "cathected." (p. 139)

Curiously it would appear that there is surprisingly little effort to explore systematically the correspondences between electrical phenomena and psychosocial phenomena, whether to enable comprehension or as characteristic of cognitive processes and their transformation. As indicated by the reference above to "flowing waters", widespread use is made of the so-called hydraulic analogy, treating electrical circuits as water flows:

• Electric potential, corresponding to hydraulic head
• Electric charge, corresponding to the quantity of water.
• Current, corresponding to quantity of flowing water over time.
• Voltage, or potential difference, corresponding to a difference in pressure between two points: the higher the water, the higher the voltage. Negative voltage could then correspond to having water levels lower than some arbitrary zero level.
• Resistance, corresponding to the degree of constriction in the water conduit
• Inductance, corresponding to a second loop of water that must be sped up or slowed down by the circuit and that resists the change in current.
• Capacitance, corresponding to a dam preventing water from crossing and allows a buildup of different water heights on either side.

Yet to be articulated is a systematic adaptation to psychosocial transformation processes -- most notably in relation to the movement of individual or collective attention (as discussed below). There are however many indications of this possibility, as with respect to dialogue (Electrical Systems as a Guiding Metaphor for Stages of Group Dialogue, 2001) or optimizing the organization of an initiative (On Mind, On Play and Productivity, 2010). How many characteristics are theoretically significant to description of electrical phenomena? How many of these might offer insights into the transformation of attention, and the flow of communications in social networks? Perhaps most intriguing is the possibility that the variety of well-defined electronic symbols used in circuit diagrams could be decoded with respect to attention and communications flows.

Modulating communication: The comparison may be taken further in terms of understanding of the full range of ways in which a signal can be manipulated -- as a guide to understanding of the variety of ways in which communication (more generally) can be transformed or deformed. In the case of signal modulation in telecommunications and electronics, this is the process of varying one or more properties of a high-frequency periodic waveform. The properties subject to modification are recognized as corresponding to those of modulation in music -- more readily understood by many. They are amplitude ("volume"), phase ("timing") and frequency ("pitch"). Eight types are recognized in the case of music:

Common chord modulation Enharmonic modulation Common-tone modulation Chromatic modulation

Phrase modulation Sequential modulation Chain modulation Parallel key modulation

These distinctions are readily perceptible to the ear (hence the case for sonification), whereas the waveform modulation of a telecommunications signal would be comprehensible to a lesser degree when visualized on an oscilloscope.

Clearly music enables a degree of identification with the transformation process which is less evident in the case of signal transformation. Arguably however, "resistance" and "capacitance", whether so named or not, are characteristic of common experience in cognitive processes and interpersonal communication, notably in social networks.

The metaphor offers the fascinating possibility that in a computer-enabled knowledge-based society, any articulated text -- such as this one -- could be understood as a form of "printed circuit board". This possibility could be further developed in the light of current research on contested discourse (Anna De Liddo, AgnesSandorandSimon Buckingham Shum, Contested Collective Intelligence: rationale, technologies, and a human-machine annotation study,Computer Supported Cooperative Work (CSCW), 2012). There is the considerable irony that global agreements merit exploration in such terms -- as cognitive "printed circuit boards", whereby "hard-wired applications" can be run.

Matching patterns in communication: Anticipating the argument to follow, it is appropriate to note a degree of recognition from an electrical perspective between switching and the Chinese denotation of yin-yang (Ian Wright and Rob Newman, Electrical or photonic ying and yang of switching, Lightwave, 18, 2001, 6; Ting Cao, Stephen Blackburn, et al. The Yin and Yang of Power and Performance for Asymmetric Hardware and Managed Software, National Science Foundation of China, 2012).

This "yin-yang" switching perspective is especially striking in relation to the widely used Smith Chart, invented by the electrical engineer Phillip H. Smith (and independently by Kaneyuki Kurokawa, a Japanese engineer). This is a graphical aid for electrical and electronics engineers specializing in radio frequency engineering to assist in solving problems with transmission lines and matching circuits. A generalized 3D Smith Chart based on the extended complex plane (Riemann sphere) and inversive geometry has recently been proposed (as discussed below). Using the 2D chart, Randy Rhea notes:

Any impedance with a positive real part may be displayed on the standard, unity radius Smith chart. The horizontal line is pure resistance. Circles with a center on this line are constant resistance. Arcs converging at center right are constant reactance. The top half of the chart is inductive and the bottom half is capacitive. (The Yin-Yang of Matching, High Frequency Electronics, Part 1: Basic Matching Concepts, March 2006, Part 2: Practical Matching Techniques, April 2006):

Rhea explores the matching of both real and complex impedances in networks. Of potential relevance to social networks? At a single frequency, any positive-real complex impedance can be matched to any other positive-real complex impedance using no more than two reactive elements. He presents Smith Chart diagrams of matchable impedance space for 8 types of conditions -- whose resemblance to distinct features of the Tao symbol he describes in the following terms:

Notice these curves are the familiar shape of the Chinese Yin-Yang for the four topologies that include both an inductor and a capacitor.... Smith's unique ability to graphically express important concepts encompasses yin-yang!

8 elements of Tao symbol represented on a Smith Chart (redrawn versions, using dashed lines, of the 8 figures by Randy Rhea in The Yin-Yang of Matching, High Frequency Electronics, 2006)
Type 1 (blue) and Type 3 (red)	Type 2 (blue) and Type 4 (red)

Type 5 (red) and Type 7 (blue)	Type 6 (blue) and Type 8 (red)

Indication of a dynamic pattern of transformations (through experimental animation of the 8 types above on a Smith Chart)

In the light of potential implications regarding recognition of elements of the symbol of the Tao in relation to the Smith Chart, what further insights might be suggested by the superposition of the ("right-facing") Lauburu on the Smith Chart in the left-hand image below? The animation above may then be understood in relation to the horizontal branches of the Lauburu. The animation in the right-hand image below then corresponds to the geometry of the vertical branches of the Lauburu -- potentially indicative of a further "8 types". Note that the animation encompasses both right- and left-facing variants of the Lauburu.

Experimental superposition of Lauburu on Smith Chart (including geometry by which the Lauburu is constructed)	Animation indicative of a "complementary" pattern of transformations (modifying the orientation of the 8 types on the Smith Chart above)

Of particular interest is that the geometry of the construction of the Lauburu in the left-hand image above contains the larger scale geometry of the Tao symbol, presented twice (namely vertically as well as in the horizontal form recognized by Randy Rhea). In addition this is indicative of the possibility of articulation on a smaller scale of that geometry (as shown below), through which the Tao symbol is presented:

• 4 times, namely on each of the 4 branches of the Lauburu (as shown in the left-hand image above).
• 16 times, on an even smaller scale (namely 4 Tao symbols within each of the branches of the Lauburu)

Of particular interest is how the "eyes", traditionally associated with the Tao symbol, emerge from the geometry as a consequence of the last articulation. Further animations could be produced to clarify and explore the associated dynamics on the different scales.

Superposition of a reduced version of the geometrical construction of the Lauburu as a whole within each branch of the Lauburu (as with a fractal)	Shading of the geometry of the Lauburu (left-hand image) to highlight one orientation of the Tao symbol and emergence of the "eyes" from the geometry

Experimental animation of the right-hand image above between 8 orientations indicative of the possibility of more complex animations with rotation of the nested structures of smaller scale

The value of the Smith Chart has been frequently noted in relation to transmission problems -- readily understood more generally as communication problems (cf. Smith Chart Resources; Smith Chart and Matching Transformers, 30 June 2011; Jay M. Jacobsmeyer, What you see is what you get, Urgent Communications, 1 June 2012).

As indicated, the 3D Smith Chart (and associated free Java demo) is a new telecommunications design tool. It was presented at a European Microwave Week (Manchester, 2011). The question with respect to the above argument is how its primary applications in high frequency engineering could offer indications of relevance to comprehension of psychosocial transformations. A new application of the chart is to be presented at the Asia-Pacific Microwave Conference (Taiwan, December 2012).

Comparison of 2D and 3D Smith Charts

Relevant articles: The 3D Smith Chart and Its Practical Applications (July 2012); A 3-D Smith Chart Based on the Riemann Sphere for Active and Passive Microwave Circuits (June 2011);

The remarkably unusual images, by which the 2D Smith Chart is represented as circles on the unit sphere, are powerful triggers for the imagination. The 3D representation is based on a mathematical "trick" notably used by Escher in his paradoxical images and by Mandelbrot in fractal rendering. With respect to the insights of recent research by Stephen Hawking and colleagues, have shown that the universe may have the same surreal geometry as some of art's most mind-boggling images (Lisa Grossman, Hawking's 'Escher-verse' could be theory of everything, New Scientist, 9 June 2012). This offers a way of reconciling the geometric demands of string theory, a still-hypothetical "theory of everything", with the universe as observed -- through a negatively-curved Escher-like hyperbolic geometry (essentially a hyperbolic space). Their results rely on a mathematical twist previously considered impossible.

Similar insights might apply to a pattern of cognitive transformations, especially since the implications of hyperbolic geometry offer a cognitive reconciliation with what is otherwise understood as a form of "netherworld" and its challenges (cf. Designing Global Self-governance for the Future: patterns of dynamic integration of the netherworld, 2010).

The commentary in relation to the demo notes:

• The north hemisphere is only for passive circuits.
• The south hemisphere is for active circuits
• The West of Greenwich meridian is made of capacitive circuits.
• The East of Greenwich is made of inductive circuits
• The perfect matching point is the north pole of the sphere
• The infinite mismatch is in the south pole of the sphere
• Moving along a transmission line is represented by the movement on a latitude circle
• Stability circles are very easy to be seen in a compact manner on the 3D Smith chart.

What do these indications suggest for conscious engagement in transformation processes? The "geographic" language suggests the possibility of exploring these in terms of cerebral hemispheres and the long-standing interest in lateralization of brain function, if only for mnemonic purposes. That language also recalls the continuing Chinese interest in the correspondence between the aspects of life represented by the trigrams of the Ba Gua (discussed below) and the cardinal directions.

Technomimetic challenge of electronics: Given its fundamental role in a computer-enabled knowledge-based society, electronics merits careful consideration as a carrier of insights into processes of transformation and their representation. The argument can be developed in the light of that made for technomimicry as a source of insight -- for the same reasons as are more commonly recognized in the case of biomimicry (as mentioned above). The question is what is the pattern of thinking which enables emergence of such a technical application -- and what other insights might potentially emerge from its application as a "carrier" or "vehicle"?

Whilst selected attributes of electrical circuits are discussed as metaphors (resistance, etc), of relevance to the argument here is the degree to which any experiential identifications with these attributes and processes are implicit (if considered) in contrast with the manner in which they serve as explicit explanatory devices (as favoured by the objectivity of conventional science). It is unclear whether there is any effort to identify systemically any correspondences between subjective experience and the range of processes of electrical circuits. How might such processes be internalized or matched to subjective experience?

Is the use of such metaphors itself indicative of how thinking is able to comprehend within an internal "language" what is conventionally articulated in an external, formal, technical "language?

The concern here, however, is not whether the metaphor is useful for objective explanation but rather whether it enables more fruitful subjective engagement in the transformational processes experienced cognitively. To the extent that "objectivity" itself implies a cognitive process, there is also the question as to how the complementarity of these processes might be more fruitfully understood (cf. ¡¿ Defining the objective ∞ Refining the subjective ?!: Explaining reality ∞ Embodying realization, 2011).

Semiconductors: There is little reference to the semiconductor as a metaphor, although in a paper to a colloquium at the Max Planck Institute for History of Science, Andrew S. Reynolds (Metaphors and Models in Cell Communication Science, September 2011) notes that the most dominant metaphor construes cell communication on the model of electronics and computer engineering. The signalling mechanisms by which cells communicate with one another are conceived on the model of an electronic circuit, hence the centrality of the concept of signal "transduction". Attempts to understand the intra-cellular signalling pathways by which messages are received at the cell membrane (amplified and transduced) involve computer model simulations and actual attempts to re-engineer cells as logic gates and transistor-like circuits.

A semiconductor (as the term indicates) is intermediate between a conductor and an insulator. It is significant as the foundation of modern telecommunications, including radio, computers, and telephones. In the form of a transistor, used to amplify and switch electronic signals and electrical power, it is typically embedded in integrated circuits on printed circuit boards. Light signals may also be modulated in optical modulators with the aid of semiconductors.

Of particular interest, in relation to indications above regarding (Chinese) encoding of transformations, is the role of the semiconductor. The Chinese encodings use either a binary system (as in the yin-yang, characteristic of the I Ching) or a ternary system (as in the Tao Te Ching or the T'ai Hsüan Ching). The distinctions are typically represented by an unbroken line, or a line broken once (binary) or twice (ternary).

Pattern comprehension: "connecting the dots": The question then is whether the very extensively studied operation of a "semiconductor" offers otherwise unrecognized insights into the distinctions between:

• comprehension / agreement / bonding , understood as "connectivity" (through conduction), potentially to be represented by an unbroken line. The connectivity implies (collective) knowledge and intelligence through adequate explanation, and consequently a degree of closure against alternative interpretations. This is what is so desperately sought as the only basis for viable global initiatives, however questionable the assumption may be (cf. The Consensus Delusion, 2011).
• incomprehension / disagreement / alienation -- namely the lack of "connectivity" (through insulation), potentially to be represented by a broken line. The lack of connectivity implies ignorance. It may well be characterized by logical non sequitur. Desperate efforts may be made to ignore or overcome this (cf. Social organization determined by incommunicability of insights, 1995). As disconnectedness, the lack of connectivity may however imply a degree of openness and variety, perhaps in the form of "unknowing".

Whilst the contrasting conditions invite binary representation (the broken or unbroken line of the I Ching), the dynamic between them could be represented by a twice broken line (as in the T'ai Hsüan Ching). The latter is then indicative of partial comprehension or partial agreement, namely a degree of connectivity exemplifed existentially by the experience of liminality (cf. Living with Incomprehension and Uncertainty: re-cognizing the varieties of non-comprehension and misunderstanding, 2012; Towards the Systematic Reframing of Incomprehension through Metaphor, 2012; Living as an Imaginal Bridge between Worlds: global implications of "betwixt and between" and liminality, 2011).

This is consistent with the role of incompleteness central to the argument above of Terrence Deacon (Incomplete Nature, 2012). Apparent non sequitur may however obscure the non-linearity of Knight's move thinking, whether in its creative or pathological sense (Knight's move thinking: appreciated or deprecated, 2012; Reframing "monkeying" in terms of Knight's move patterns, 2011). The cognitive implications of this line coding -- in making or breaking a psychosocial connection -- are usefully to be contrasted with the seemingly similar Morse Code, offering no such connotations.

The Chinese encoding is reminiscent of some qualities attributed to a sacred language. It can be seen as a representation of the flow of attention or attentive connectivity characteristic of the organization of knowledge in memory. As an experience, "attention" embodies interest, curiosity, communication, receptivity and sensitivity to difference.

This suggests the possibility of "re-cognizing" self-reflexively the cognitive processes of:

• pattern recognition as a form of closure through an assumption of connectivity -- having "got it" -- namely recognizing a "fit" with an explanation and assuming it to be adequate. This is evident in making use of a metaphor -- thereby enabling assumption of knowledge and associated clarity
• pattern rejection through dissatisfaction with the adequacy of any proposed pattern, namely an absence or loss of connectivity -- effectively acknowledging ignorance and confusion

Any condition of partial comprehension then involves alternation between several possible patterns, or none at all, namely a condition of questioning doubt and uncertainty -- potentially creative, as with the classic argument for so-called "negative capability", as the ability to transcend and revise contexts. The transformational dynamic between these conditions is evident in considering the implications of any complex argument (as with this text).

Geometrical interrelationship of quantitative and qualitative information: Rhea's matching argument, and its representation on the Smith Chart, would appear to be potentially related to the argument from a quite distinct perspective offered by Peter Collins (Number and Transformation, Integral Science, 22 September 2012). He is fascinated by the fact that the two binary digits (1 and 0) when used in a quantitative manner can potentially encode all information processes. He therefore considers that the same two digits when used in an appropriate qualitative manner can likewise potentially encode all transformation processes:

So transformation itself (in all its manifestations) is basically encoded in number when appreciated in a qualitative manner. Now as geometrical symbols, 1 can be identified with the straight line and 0 with a circular circumference. So the relationship of 1 and 0 in qualitative terms implies the relationship between (rational) linear and (intuitive) circular understanding. (In this context circular refers to the indirect rational attempt through paradox to portray the nature of intuitive understanding).

From a physical perspective this would imply that all transformation processes entail the interaction of a visible phenomenal aspect together with an equally important invisible holistic dimension. At a deeper level this circular aspect relates to the manner in which the fundamental polarities - which necessarily underlie all phenomenal relationships - are configured.

With the 0 as circle, there is an alternative representation as suggested by the I Ching, where the broken line implies a space which could be a circle more elusively understood. The break is occasionally represented by a small circle on a continuous line.

---

[Parts: First | Prev | Next | Last | All] [Links: To-K | From-K | From-Kx | Refs ]