25th March 2006 | Draft

Cognitive Feel for Cognitive Catastrophes: Question Conformality

- / -


Annex to Conformality of 7 WH-questions to 7 Elementary Catastrophes: an exploration of potential psychosocial implications



Introduction

As a human response to the perception of a cognitively chaotic situation, WH-questions (when, where, which, how, what, who, why) might be considered to lend themselves to analysis with the tools of catastrophe theory as developed by Rene Thom and others. Thom had developed differential topology into a general theory of form and change of form as a mathematical way of addressing the work on morphogenesis done by C.H. Waddington in the 1950's. Thom's Classification Theorem culminates a long line of work in singularity theory. The term "catastrophe theory" was suggested by C. Zeeman (1977) to unify singularity theory, bifurcation theory and their applications. The crucial theorems rigorously establishing Thom's conjecture were proven by Bernard Malgrange (1966) and John N. Mather (1968). Its essential concern is change and discontinuity in systems (cf Robert Magnus, Mathematical models and catastrophes). WH-questions may be considered as triggered and formulated in response to discontinuity -- when habitual adaptive responses to change are inadequate.

It is possible therefore that the set of WH-questions may in some way be mapped onto elementary catastrophes. This is partially suggested by mathematical techniques of conformal mapping where, for example, the "cognitive flow field" around one known shape (as with an elementary catastrophe) might be mapped onto the flow field around a particular WH-question -- preserving the "angles". Conformal mapping notably makes use of complex variables as combinations of real and imaginary numbers. [applet]

This exploration develops aspects of earlier work on WH-questions (Functional Complementarity of Higher Order Questions: psycho-social sustainability modelled by coordinated movement, 2004; Engaging with Questions of Higher Order: cognitive vigilance required for higher degrees of twistedness, 2004).

Cognitive feel and conformality

Given this context, the 7 types of WH-questions might therefore be explored as corresponding to a "cognitive feel" for features of the "problematic space" defined by seven particular kinds of cognitive catastrophe. Such an exploration could be understood as part of the wider investigation of the "conformality" of mental representation to reality, whether from a geometric perspective (Waldo R. Tobler. The Geometry of Mental Maps, 1976), from a classical philosophical concern dating back to Aristotle [more], from a process understanding of religious experience (Nancy Frankenberry, The Empirical Dimension of Religious Experience, 1978), or in the extensive literature on the comprehension of military situations (Human Factors in the Design of Tactical Display Systems, 1995; Lawrence J. Prinzel III et al, Head-Up Displays and Attention Capture, 2004).

With regard to "head-up displays" (HUDs), for example:

Broadly speaking, the definition of conformality used by HUD developers refers to the degree to which a symbol forms an object within the scenery. The idea is that a conformal symbol should serve as a virtual analog for far domain elements. In other words, symbology that is an accurate graphic representation of an actual object represented in the far domain, or that forms a one-to-one correspondence with the world is deemed to be conformal (cf Jerzy Jarmasz. Towards the Integration of Perceptual Organization and Visual Attention, 2001).

Conformality in philosophy

In clarifying the classical philosophical perspective on conformality, citing Aristotle, Peter King (Scholasticism and the Philosophy of Mind: the failure of Aristotelian psychology. In: Scientific Failure, 1994), notes:

Understanding, like sensing, is a process of taking on the form of the object.... Just as the sense-faculty takes on formal features of the external object, the intellect too takes on formal features of the same object. The faculty in the intellective soul which is passive and receptive (of the form of the object) is called the 'possible intellect' or the 'material intellect.' The reception of the form of the object determinately actualizes the intellect, previously only potentially the same as the object, such that the intellect is actually identical with the object (formally speaking). When the intellect takes on a form and so is determinately reduced to act, it becomes a thinking of the object.

This description suggests that conformality also provides an explanation of intentionality. If so, then is sensing, which is also explained through conformality, intentional? Some distinctions have to be drawn to avoid conflating the phenomenality of pains, the 'pseudo-intentionality' of sensing, and the genuine intentionality of thinking; drawing these distinctions was an important project in Scholastic philosophy of mind.

Sense of a question

In what ways can the "feel of a question" then be understood? To what extent are these limited by restrictive arguments regarding the "sense of a question" -- such as:

In general, the sense of a question -- its meaning as such a question-- is determined by the gamut of possible answers that the questioner would accept as appropriate when she puts this question to somebody in a specific situation. (Capitolina Díaz-Martínez and Pablo Navarro, Meta-analysis of Surveys from a Qualitative Perspective, 1997)

Irrespective of the problematic logic associated with "begging the question" as noted by William Safire (That old question: to beg or not to beg? 1998), also of relevance is the validity of a question, as understood by "science", as clarified by Gaspare Mura (Agnosticism: In: Interdisciplinary Encyclopaedia of Relgion and Science):

Although contemporary epistemology has strongly contested the Kantian and positivistic conception of knowledge, it did not know how to remove from scientific agnosticism its implications. In effect, the Kantian anti-metaphysical prejudice has remained present in almost all forms of contemporary epistemology, in the sense that although science itself evolves and the same evaluation of objective value of scientific theories transforms itself, science nonetheless continues to be considered the sole area of knowledge valuable for humanity. The questions that go beyond the domain of science - the problem of God in particular - can at most be accepted as questions that, as in Kant, have sense for the existence of man, but not for his knowledge. Scientific agnosticism consists precisely in dismissing the idea that science, however one understands it, represents an area where metaphysical and religious questions can be formulated or at least recognized as significant, i.e., have the sense of a question and the value of knowledge.

The nature of any "higher sense of a question", in relation to any synthesis resulting from a question, is the subject of a useful comment in The Opposition of Being and Nothing in Ordinary Thinking in Hegel's Science of Logic:

Becoming is this immanent synthesis of being and nothing; but because synthesis suggests more than anything else the sense of an external bringing together of mutually external things already there, the name synthesis, synthetic unity, has rightly been dropped. Jacobi asks how does the pure vowel of the ego get its consonant, what brings determinateness into indeterminateness? The what would be easy to answer and has been answered by Kant in his own manner; but the question how means: in what peculiar manner, in what relationship, and so forth, and thus demands the statement of a particular category; but there can be no question here of a peculiar manner, of categories of the understanding. The very question how itself belongs to the bad habits of reflection, which demands comprehensibility, but at the same time presupposes its own fixed categories and consequently knows beforehand that it is armed against the answering of its own question. Neither has it with Jacobi the higher sense of a question concerning the necessity of the synthesis; for he remains, as has been said, fixed in the abstractions in order to maintain the impossibility of the synthesis. [emphasis added]

The "sense of a question" may however depend upon assumptions about such a synthesis, as pointed out by Jeremy W. Hayward (Mindfulness and Awareness. In: Perceiving Ordinary Magic, 1984):

Writing of the traditional attitude to ikebana and its role in Japanese life, Gustie Herrigel [Zen in the Art of Flower Arrangement, 1999] says: "Now is such a flower-piece a product of nature or of art? Or does it stand midway between the two, so that it is more than nature and not yet pure art? An unequivocal answer is extraordinarily difficult to give. For the Japanese, life and art, nature and spirit form an indissoluble unity, an unbroken whole. He experiences nature as having a soul, and spirit as part of nature, without purpose. So he cannot make sense of a question which presupposes a division of nature from spirit, life from art, as though they were alien to each other. For him nature is neither dead nor unspiritual, nor yet a mere symbol and semblance".

Formalization of questions

It is however curious that neither mathematics nor logic appears to have any formalization (or associated notation) of WH-questions themselves (cf Kevin H. Knuth. What is a Question? 2002; David Sandborg, Mathematical Explanation and the Theory of Why-Questions, 1998; Marina Terkourafi and Aline Villavicencio, Toward a Formalization of Speech-Act Functions of Questions in Conversation, 2003), although the use of erotetic logic (he logic of questions and their answers) with respect to why-questions should be noted. Erotetic logic is a focus of research relating to content-driven question-asking technologies using heuristic-driven question-answering procedures [more].

Such a formalization might offer insight into why there are only a limited number of WH-question types and how they might be formally related to each other. One indication is provided by Arthur Young (Geometry of Meaning, 1976) who pointed out that a minimum of six observations is required to determine the behaviour of a free agent -- six questions to determine the behaviour, plus an additional one to determine why? [more] (cf Functional Complementarity of Higher Order Questions: psycho-social sustainability modelled by coordinated movement, 2004). "When" requiring 1, "where" (2), "which" (3), "how" (4), etc? Another possibility is the cognitive constraint highlighted by George A. Miller (The Magical Number Seven, Plus or Minus Two. Psychological Review, 1956), but now framed differently [more].

As an operational contrast to such cognitive discontinuity, it is useful to compare it with the Japanese understanding of "wa" as social-group harmony and a feeling of oneness with nature and people. "Wa" is considered the most fundamental of Japanese values and cultural concepts, affecting interpersonal and business relationships and cultural identity. It derived from the Chinese understanding of a sense of harmony, peace and balance and is associated with the Chinese term "ho" (universal harmony) and the cultivation of T'ai Chi or T'ai-Qi. Such understandings suggest an association to spiritual understandings of the dynamics of the cosmic plenum -- and to mathematical understandings of manifold as, for example, explored in Kant's principle of a "transcendental unity of apperception" as a synthesis of the "knowledge of the manifold" (cf G A Mashour, From Kant to Quantum Neurodynamics, NeuroQuantology 2004, 1).

The primal beginning was understood to flow from the essence of wholeness, the balance between Yang and the Yin (exemplified by the harmony and proportion in the I Ching). As the starting point of reflection, "Wa-Qi, meaning "that which precedes the primal" was represented by the symbol of the circle. This concept of the pre-primal was then incorporated into the concept of the "primal beginning", represented by the character for a ridge-pole "T'ai-Qi", because it divides the circle into two equal halves, that of darkness and of light -- the Yang and the Yin [more]. This might be understood as the primal "cognitive catastrophe".

8-fold Continuity of flow
When the timing is right
And where is well-found
Which way needs no choosing
For emergence of know-how
To enable what is called for
Through embodying an identity
In fulfilment of purpose --
Thus engendering a new cycle
Any questions?

The nature of this "cognitive feel" for the geometry has been variously explored (cf Dominic Widdows, Geometry and Meaning, 2005; Ron Atkin, Multi-Dimensional Man: can man live in 3 dimensional space? 1981; Fred L. Bookstein, Geometry as Cognition in the Natural Sciences, Psycoloquy, 1993: 4, #65; Mildred L G Shaw and Brian R Gaines. Kelly's "Geometry of Psychological Space" and its Significance for Cognitive Modeling, The New Psychologist, 1992). Of particular interest is the experiential quality of "cognitive catastrophes" in psychosocial evolution (cf Jochen Fromm, Types and Forms of Emergence, 2005). For Wolfgang Wildgen (Catastrophe theoretical models in semantics, 2004):

The analysis of sensory inputs (I shall primarily consider vision here, but similar methods can be applied to audition) consists of serioparallel mappings from a basically three-dimensional input which enables a very precise control of activity in space and time. The basic problem in the transition between perception - cognition - motor control is the proper mapping from one internal representation to the other. The mapping must conserve basic topological and dynamic characteristics and can forget metrical details, variations of a type of object or event. Therefore, the problem of a structurally stable mapping lies at the heart of every theory of representation and of semantics....

The basic "morphologies" furnished by elementary catastrophe theory... can be interpreted as a universal set of perceived or enacted situational schemata, which are exploited by human languages as minimal scenarios for utterances....What calls for explanation is the almost "unlikely" stability and constancy of patterns of interaction in a domain which has so many degrees of freedom. An initial clue as to the basis for such patterns can be found in animal behaviour, where specific paths exist for the contact behaviour. They can be lines of contact... or lines followed in the bodily orientation of one animal... These lines stabilize in very specific regions and select a very small sub-field of the body surface.

With the aid of Functional Magnetic Resonance Imaging (fMRI) techniques, cognitive neuroscience, in its search for the neural correlates of consciousness, is able to explore the distinction between the WH-questions with respect to their locus within the brain in terms of the pathways triggered -- although there is a curious lack of self-reflexivity in the use of WH-questions, whilst failing to apply the techniques to their use (cf Friedemann Pulvermüller, Words in the Brain's Language, Behavioral and Brain Sciences, 1999; Susanne Maria Reiterer, EEG-Coherence Analysis and Foreign Language Processing, 2002) (see also KurzweilAI.net online discussion of What kind of system of 'coding' of semantic information does the brain use?, Edge Foundation, 2002). The issue of interest is the relation between any objective representation and any subjective sense of the "shape-feel" of a when-question -- in contrast with that of a how-question, for example. Any such sense may be related to the phenomenon of synaesthesia (cf Richard E. Cytowic, Synesthesia: phenomenology and neuropsychology -- a review of current knowledge, 1995).

A quite different approach to formalization of WH-questions might be usefully based on Heisenberg's Uncertainty Principle (cf Dominic Woolf, To be or not to be? In: The Möbius Trip, 2004). An "answer" when given could then be understood as collapsing a probability function representing the range of possible answers to a "question" of a particular form (as with the classic example of Schrödinger's cat):

  • With respect to the standard quantum theory, Mae-Wan Ho (How Not to Collapse the Wave Function, 2004) comments that a quantum system is in a "superposition of states or in quantum entanglement" which is invariably destroyed by measurement or observation. This is the reduction or "collapse of the wave function" -- of the probability amplitudes defining the system, so the system ends up in one definite state and no other. "Superposition" refers here to a system existing simultaneously in multiple states -- "even states that, common sense tells us, are mutually exclusive". A number of collapse theories have been developed, as summarized by Giancarlo Ghirardi (Collapse Theories, Stanford Encyclopedia of Philosophy, 2002). Optical analogues may offer insight (cf K. D. Moll et al. Self-Similar Optical Wave Collapse Physical Review Letters, 2003)

  • With respect to the set of WH-questions, can the probability function be understood to collapse in a variety of (seven?) distinct ways -- "elementary catastrophes" -- when quenched by an answer that "fits" the form of "when", "where", "who", etc? ? This would seemingly constitute a development of the theory that consciousness causes collapse of this kind in the case of a conscious observer (as popularized by Gary Zukav, The Dancing Wu Li Masters, 1980). Here the observer is to be understood as the person whose WH-question is in process of being answered. This collapse is to be contrasted with the continuous, unitary (reversible) evolution of a system according to the Schrödinger equation -- multiple realities in potentia in anticipation of a question that forms them in a particular way to engender an answer. To the extent that the answer is not of the yes/no variety, the collapse of the probability function may be progressive as the answer takes form -- a cognitive topography that progressively becomes apparent and known, as with the various forms of the elementary catastrophes.

    As noted by Harald Atmanspacher (Quantum Approaches to Consciousness, Stanford Encyclopedia of Philosophy, 2004), the act or process of measurement/observation is a crucial aspect in the framework of quantum theory, that has been the subject of controversy for many decades. Atmanspacher notably summarizes the theory of quantum state reductions as conscious acts as formulated by H P Stapp (A quantum theory of the mind-brain interface. 1993; H P Stapp, Attention, intention, and will in quantum physics, 1999). Other variants have been proposed including: quantum field theory of mind/matter states (H. Umezawa, G. Vitiello); quantum mechanics at the synaptic cleft (F. Beck and J. Eccles); quantum gravity and microtubuli (R Penrose and S R Hameroff).

Although the implications of quantum theory for consciousness have attracted much debate, some hold that the distinction between such interpretations and those of classicial information theory are artificial and misleading. Thus Chris Lucas (personal communication) takes the view that:

... there is no difference here between the quantum and classical worlds and the so-called collapse is exactly what happens in the classical world when we obtain information about any system. In other words any system (take a boolean net for example) has many possible states. In our ignorance these states are all in a superposition, how could they not be ? Once we check the current state we obtain information and thus the uncertainty is dissolved..... Thus questions are very relevant here and we can say that the WH forms are alternative dimensions in state space -- which we ask about determines which orthogonal dimension we access for information.... The Schrodinger equation, like all such dogmas, is another incomplete confusion of map (fantasy) with territory (reality) [more]

Peter Collins (Quantum Mechanics and the Existential Decision, 1998) endeavoured to show that a mirror image cognitive psychological interpretation always necessarily existed for the supposed quantum state. So rather than just a conformity as between both aspects, rather a closer identity exists so that a quantum physical system strictly has no meaning in abstraction from its cognitive manner of interpretation. He now argues (personal communication):

It seems to me that the standard exposition of the collapse of the quantum probability wave function is much too simplistic and geared to explain the extreme transition from paradoxical to an unambiguous classically perceived state. However the nature of reality is in truth - literally - more complex with continual interaction taking place as between multiple events in both a real (actualised) and imaginary (potential) manner (with both aspects continually influencing each other).

So putting it in cognitive terms, all concepts are strictly probability wave functions which are actualised through collapse to to the actual perceptions (that are associated with the corresponding conceptual classes)... So the physical collapse of the quantum probability state is inseparable from the corresponding psychological collapse of the associated cognitive understanding. However... the answers we get from the questions we pose with respect to reality are of a partial limited nature. So in each actualised answer through collapse of a quantum state (with its complementary physical and psychological aspects) there is another unanswered question which causes modification in the wave function. In other words the wave function - as well as undergoing collapse - also undergoes continual resuscitation, which given appropriate development, enables ever more refined and open-ended questions to be asked of reality (leading in turn to more refined answers which are still necessarily of a provisional nature).

The correspondence between reflections on quantum aspects of consciousness and some Buddhist insights has been frequently remarked. Of particular interest is the relationship of entailment to Buddhist understanding of "dependent origination" (cf P. A. Payutto, Dependent Origination: The Buddhist Law of Conditionality) or "dependent co-arising" (cf Thanissaro Bhikkhu Tr., Analysis of Dependent Co-arising) . The relationship of co-arising to singularities is explored by Kent D Palmer (Reflexive Autopoietic Systems Theory) but not explicitly to the forms of the "elementary catastrophes". Stefan Arteni (Painting as Polycontexturality: a collage of commented reading notes) points to further related insights.

Subjective and cultural factors

Complementing the feel for geometry are the constraints imposed by subjective response to time documented by Benjamin Libet (Mind Time: the temporal factor in consciousness, 2004). His experiments reveal a substantial delay (up to 0.5 seconds) -- the "mind time" -- before any awareness filters into consciousness. If all conscious awarenesses are preceded by unconscious processes, as Libet observes, it is necessary to conclude that unconscious processes initiate conscious experiences. Freely voluntary acts are found to be initiated unconsciously before an awareness of wanting to act -- a discovery with profound ramifications for understanding of free will.

Damir Ibrisimovic (personal communication) suggests that since most decisions (reactions or thoughts) are made with much shorter delay than Libet's 0.5 seconds -- as discussed (below) in relation to kinetic intelligence -- there must be some underlying principles that are not well reflected in the post facto math of seven elementary catastrophes. These do not then seem to take into account personal and cultural differences in the structure of WH-questions (cf Systems of Categories Distinguishing Cultural Biases, 1993). He argues for a math that integrates catastrophe theory with complexity theory (with Libet's findings taken into account) in order to get a clearer picture of both, personal and collective behaviour and decision making.

Within these constraints, a sense of the characteristics of such cognitive feel for discontinuity or disharmony may be obtained from personal recollection of (the joy or agony) occasioned by the following common WH-questions:

  • When: When will he/she telephone? When will we have a child? When will I have a relationship? -- When am I authentic / real / sincere? -- When is the discontinuity apparent?
  • Where: Where will I get a job? Where will I find shelter / food / help / security? Where can I get a drink / "fix"? -- Where am I at home? -- Where is the discontinuity apparent?
  • Which: Which object should I purchase? Which partner should I choose? Which job should I accept? Which restaurant / party / cafe should we go to? -- Which person am I ? -- Which approach mitigates the discontinuity?
  • How: How should I achieve my goal? How should I protect myself? How should I express myself? -- How am I? -- How can the discontinuity be handled and navigated?
  • What: What to do? What to say? What to believe? -- What am I? -- What is the discontinuity evoking the question?
  • Who: Who to contact? Who to trust? Who is coming? Who is going to leave? -- Who am I? -- Who engendered the discontinuity evoking the question?
  • Why: Why am I doing this? Why did I do that? Why do I want this? Why did this happen to me? -- Why am I (alive)? -- Why is a discontinuity apparent?

Representation of questions

A valuable line of exploration is how questions are represented in consciousness, especially when use is made of metaphor or tropes. Martin E Rosenberg (Dynamic and Thermodynamic Tropes of the Subject in Freud and in Deleuze and Guttari, Postmodern Culture, 4, 1, September, 1993) comments that:.

The problematic of the subject becomes the problem of representation when the particular forms of representation of the subject, such as tropes, come into question.... By the term trope, we may refer to what Hayden White calls the irreducible nature of metaphor in imaginative and realistic discourses. A trope is a turn of phrase that links an abstract concept to the physical world, and as such, establishes a correspondence between the physical world and human ideation.

In discussing the neurodynamics of representations through the transformation of serial computations into parallel neurodynamics, George McKee (The Engine of Awareness: Autonomous Synchronous Representations, 1997) notes:

It is possible to develop a series of conjectures about the results that may emerge in development of this line of research. As the spectrum of recurrence intervals in an asynchronous neural net broadens from the sharp line that corresponds to full synchronization, certain modes will appear in which one set of units operating at a long interval are linked to another set of units operating at a much shorter interval... This will indicate the appearance of a "rehearsal" capability. The appearance of multiple, linked recurrence modes will permit the introduction of three-dimensional phase portraits. These will make it possible to view certain system components from the perspective of a "potential" as is required for the use of catastrophe theory in analyses.

With the help of catastrophe theory, it will be possible to classify the modes of appearance of stable constellations of attractor basins out of an undifferentiated embryonic net. These stable constellations will have properties that correspond to important psychological phenomena. These phenomena include the "catastrophic" reclassification that occurs in the course of insight learning and categorical perception, the resistance to reorganization of conceptual structures that controls the historical evolution of phonology, syntax and semantics in human language, and most importantly for our purposes, the explicit representing transformations that are necessary for conscious awareness.

David Vernon and Dermot Furlong (Relativistic Ontologies, Self-Organization, Autopoiesis, and Artificial Life: a progression in the science of the autonomous, 1992) helpfully summarize assumptions associated with the preferred approach of science:

Modules of geometric and spatial reasoning facilitate recognition and manipulation of these models and, optimistically, the vision system can then formulate the appropriate actions required to intelligently react to the stimuli. This information processing paradigm is unashamedly positivistic in its outlook, being based entirely on the premise that there is, indeed, an absolute knowable world which has only to be apprehended by our senses (or the senses of our robotic system).

They take a different approach:

Not because we wish to challenge or supplant the useful role of conventional, representational, approaches for they have an important part to play in, e.g., engineering control systems but because we wish to challenge the ability of such approaches to deal with the issues of true autonomy, with all its attendent concerns of perception, cognition, intelligence, adaptivity, and understanding. Following the work of others, perception in particular, and cognition in general, are explained not as processes of information acquisition, abstraction, or representation, but in terms of the systemic activities of closed self-referential self-specifying autonomous entities. Such cognitive systems are necessarily open systems, from the point of view of the components that comprise the system, but they are organisationally closed: they exhibit a well-defined complete self-organization which is independent of the particular make-up of the structure supporting that organization. From this perspective, the modelling of perception is an ill-posed problem; rather it is by studying and modelling autonomous systems that an understanding of perception emerges.

Such framings may be of greater relevance in considering how questions are held.

Postmodernism and cognitive discontinuity

In exploring the significance of catastrophe theory for any cognitive feel, and given Thom's generalization of morphogenesis to include semantic dimensions, there is a case for noting speculation on intersection between the controversial work on morphogenetic fields and quantum gravity. Writing as a physicist, Alan D. Sokal (For Transgressing the Boundaries: towards a transformative hermeneutics of quantum gravity, Social Text, 1996) provides a helpful introduction to the language used:

Finally, an exciting proposal has been taking shape over the past few years in the hands of an interdisciplinary collaboration of mathematicians, astrophysicists and biologists: this is the theory of the morphogenetic field. [Rupert Sheldrake, et al]. Since the mid-1980's evidence has been accumulating that this field, first conceptualized by developmental biologists, is in fact closely linked to the quantum gravitational field: (a) it pervades all space; (b) it interacts with all matter and energy, irrespective of whether or not that matter/energy is magnetically charged; and, most significantly, (c) it is what is known mathematically as a "symmetric second-rank tensor''. All three properties are characteristic of gravity; and it was proven some years ago that the only self-consistent nonlinear theory of a symmetric second-rank tensor field is, at least at low energies, precisely Einstein's general relativity. Thus, if the evidence for (a), (b) and (c) holds up, we can infer that the morphogenetic field is the quantum counterpart of Einstein's gravitational field. Until recently this theory has been ignored or even scorned by the high-energy-physics establishment, who have traditionally resented the encroachment of biologists (not to mention humanists) on their "turf''. However, some theoretical physicists have recently begun to give this theory a second look, and there are good prospects for progress in the near future.

The author later revealed the article to be a hoax (A Physicist Experiments With Cultural Studies, Lingua Franca, May/June 1996), to the embarassment of many exploring this intersection, and reinforcing the view of sceptics (cf Sokal Hoax, The Sceptics Dictionary). Of relevance to the discussion regarding any relation to catastrophe theory is the discontinuity in cognitive space that the disagreement highlights -- ironically implied by Sokal's original title "transgressing the boundaries". The implication is that for physics there are boundaries that should not be transgressed -- an implication seemingly contrary to the basic premiss of complexity theory regarding the dynamic interconnectedness of everything.

An entry in the FreeDictionary on the Sokal Affair points to limitations in any comments by a qualified physicist on philosophical issues on which he is not comparably qualified (and makes no claims to be):

Mathematician Gabriel Stoltzenberg has written a number of essays with the stated purpose of "debunking" the claims made by Sokal and his allies. He argues that Sokal and company do not possess a sufficient understanding of the philosophical positions that they criticize and that this lack of understanding renders their criticisms meaningless. Defenders of Sokal have responded that postmodernists have a vested interest in denying the validity of his criticisms, which could not be accepted without serious harm to many careers and incomes.

In passing, Flemming Funch (Quantum Physics and Elections, 2004) usefully notes with regard to the hoax that:

Actually, the crux of the matter seems to be that Sokal believes in one finite objective reality, so therefore he considers all other views unscientific, and he tried to prove that point by satirizing them.... Maybe the joke is that mutually exclusive views on the world can all be right, because you do essentially get back what you start off trying to prove.....For the first group to consider themselves right, they have to consider the second group wrong, as there can only be one objective reality. Whereas the opposite isn't particularly the case. Anyway, I choose to bet on the models that explain the most possible phenomena in the world, rather than the models that have to suppress and ridicule all the stuff that just doesn't fit into them.

This points again to the challenge of bridging such cognitive discontinuity. Funch cites Mara Beller (The Sokal Hoax: At Whom Are We Laughing?; Quantum Dialogue: the making of a revolution, 2001) who argues that much of what Sokal was saying (and which he himself considered utterly ridiculous) had been said before by much more respected scientists than himself, like Bohr, Born, Einstein, Heisenberg, Pauli and Wheeler, who had even gone a good deal further in relating theoretical physics concepts to sociology, psychology and politics. Sokal later developed his thesis (Fashionable Nonesense: Intellectual Impostures, 1997). Beller however concluded::

In an exchange several months after his New York Review of Books [3 October 1996] article, Weinberg admitted that the founders of quantum theory had been wrong in their "apparent subjectivism," and declared that "we know better now". What exactly do we know better now? Do we know better that one should not infer from the physical to the political realm -- and if yes, why? Or do we know better that the "orthodox" interpretation of quantum physics -- the one that confidently announced the final overthrow of causality and the ordinary conception of reality -- is not the only possible interpretation, and that, ultimately, it might not even be the surviving one? .... The opponents of the postmodernist cultural studies of science conclude confidently from the Sokal affair that "the emperors ... have no clothes". But who, exactly, are all those naked emperors? At whom should we be laughing?

As noted elsewhere (Avoiding Dialogue with Alternative Worldviews at any Cost, 2005), the existential timidity in the face of "extreme dialogue" is unworthy of a civilization "reaching for the stars" and potentially dependent on fusion energy. The latter is famously dependent on the craziest "Theories of Everything", as illustrated by the much-quoted statement by Niels Bohr in response to Wolfgang Pauli: "We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct. My own feeling is that is not crazy enough." To that Freeman Dyson added:

"When a great innovation appears, it will almost certainly be in a muddled, incomplete and confusing form. To the discoverer, himself, it will be only half understood; to everyone else, it will be a mystery. For any speculation which does not at first glance look crazy, there is no hope!" (Innovation in Physics, Scientific American, 199, No. 3, September 1958)

Sokal hoax highlights good criticism of transdisciplinary borrowings in terms of the criteria of the conventional scientific method. He effectively rejects as improper the possibility of explanations that rely to a high degree on isomorphism and metaphor -- however much the role of metaphor has been fundamental to scientific creativity. With respect to the value of such borrowings and their relevance to cognitive discontinuity, even among scientistis, it is worth noting the remark of Kenneth Boulding (Ecodynamics; a new theory of societal evolution, 1978):

Our consciousness of the unity of the self in the middle of a vast complexity of images or material structures is at least a suitable metaphor for the unity of a group, organization, department, discipline, or science. If personification is only a metaphor, let us not despise metaphors - we might be one ourselves. (p.345)

And, with respect to a catastrophe theory understanding of cognitive discontinuity, the nature of a "hoax" and "craziness" merit careful reflection in relation to appropriate WH-questions. Hoaxes play a significant role in human psychosocial interaction (including courtship behaviour) and in predator-prey relations. Perhaps a degree of self-reflexivity is called for.

A trap is a function of the nature of the trapped
(Geoffrey Vickers. Freedom in a Rocking Boat :
Changing values in an unstable society
, 1972)

creative commons license
this work is licenced under a creative commons licence.