'The Gravity of Error', ... or 'The Error of Gravity'

June 1, 1998


"Anziehen" und "Abstossen" in rein mechanischem Sinne is eine vollstaendige Fiktion." ... "Wir koennen uns ohne eine Absicht ein Anziehen nicht denken, ..." ... "Der Glaube an causae faellt mit dem Glauben an [Telos]

Friedrich Nietzsche, 'Der Wille zur Macht' (comment 627)


According to Nietzsche, thinking about attraction and repulsion in a purely mechanical sense is bullshit. We can't think about 'attraction' without thinking about 'purpose'. And we can only bring ourselves to believe in 'causality' if we psychologically coerce ourselves to swallow the unimaginable; i.e. that events occur without purpose.

Nietzsche points out that the belief in 'cause' collapses with the belief in 'purpose' or perhaps more aptly, the belief in 'purpose' collapses with the belief in 'cause'.

Causal explanations, as suggested in prior essays, are 'analytical backfill'. For example, one can say Madonna got pregnant 'be-cause' of a (long and detailed) series of physico-chemical transactions while omitting the 'purposive detail' that Juan broke out of prison and Madonna traded in her jewelry for a ticket to be together. Traditional science applauds those disciplined explanations which elevate rationality above sensory perception. More than that, western culture applauds the primacy of structured knowledge (e.g. 4.0 GPAs) over ontogenetic understanding (getting in touch with who we are meant to be). Apparently, the spirit of Parmenides lives on!

In any case, what Nietzsche was alluding to was that 'attraction' cannot be fully explained in terms of 'things' and their mechanical transactions. After all, gravity is more of a top-down property of space-time than something describable in terms of mechanics; i.e. gravity is the coherency-producing integrative characteristic of space-time wherein all things attract all other things, and this attractive 'purpose' transcends our variously permutated spreadsheets of mechanico-causal transactions which we habitually serve up as 'explanations' of natural phenomena.

The deficiency in the causal view ties directly to the assumption of a flat, inert, bivalent ('thing' or 'not.thing') space with its assumed temporal independence. The realization that euclidian flat space was an abstract special case in a family of curved space possibilities (Bolyai, Lobachevsky, Riemann, in the 1829 - 1868 time frame) opened the door to fundamentally new rational perspectives wherein, as Einstein asserted, space could be viewed as a participant in natural phenomena. The curved space possibility took on further meaning with the work of Poincare (deterministic chaos, 1889), Minkowski (space-time interdependence, 1908), Einstein (general relativity, 1915) and Bohr, Heisenberg and many others (Quantum Theory etc.) in the first half of the twentieth century.

So the 'word' on the arbitrariness and limitedness of flat-space, has been out in the culture at large for some time, in fact it was already out in 500 BC., embedded in the philosophical propositions of Heraclitus. His assertion that 'The learning of many 'things' does not teach understanding' highlighted the fact that knowledge must be brought into resonance with sensory experience to deliver understanding.

Nevertheless, the western culture seems to have been more caught up in the perceived arrogance of those like Nietzsche and Heraclitus who dared to launch polemics against rationalist tradition, on the basis of mere sensory experience. Today, the equation with respect to mainstream migration to curved space-time perception and inquiry remains clear; i.e. there is a tightly integrated web of publicly esteemed, causality-oriented rationalists voting 'nay' and a sparse and scattered motley crew of purpose-oriented sensory empiricists voting 'yea'.

What is the problem here?

In spite of the message on 'purpose' which we garner from 'lived sensory experience', the rationalist tradition of the west builds its perspective and inquiry only on the basis of 'bottom-up' 'mechanical' argument and eschews 'top-down' arguments. The rationalist- reductionist ('bottom-up') approach rests 'squarely' on the assumption of a rectangular, non-participative (euclidian) space, and it is subtly reinforced by language.

This dependency can be generally illustrated by the example of the game of pool. A causal explanation of how a game of pool is played and won will focus on the series of transactions (shots and collisions) which 'caused' the final system state (e.g. all of the opponents balls being sunk). In this view, the 'space' between the balls (i.e. the evolving space-time dynamic) is not considered a 'participant' in the game and we focus exclusively on the transactional skills of the players.

However, as almost anyone who has played pool knows, space-time is indeed a participant and the good pool player must simultaneously consider the transaction (e.g. sinking a ball) and the space-time transformation ('table shape' transformation) associated with that transaction. In essence, this says that assumptions that are associated with causality, as described by Henri Poincare in 'Science and Hypothesis' (1903) are not fully valid; i.e. homogeneity, relative independence of remote parts, and simplicity of the elementary fact.

Certainly all transactions which entail sinking the 5 ball are not 'more or less the same'. In one case, the 5 ball may be ready to drop into pocket if given the slightest nudge. In another, the cue ball may have to miss another ball by an impossibly small margin to strike the 5 so as to sink it. On one's 'work record', however, which is largely a compendium of causal transactions, all it is likely to say is 'he sank the 5 ball'.

With respect to 'the relative independence of remote parts', if I can get the cue ball, after it has sunk the 5, to go up the table and take the 6 ball off the rail, 'setting it up' for the next shot, this may be very important to the outcome. By now, it is becoming clear that the pool player is playing not just with 'things' (balls and mechanical transactions) but also with space-time geometry, and he is trying to shape it with respect to a particular goal. That is, his space-time geometry shaping efforts will be very different if his goal is (a) to separate (i.e. sink) the solids (1-7) and the stripes (9-15), or (b) to separate the evens from the odds. This need to manipulate overall space-time geometry invalidates the assumption of 'relative independence of remote parts'.

The third assumption of 'simplicity of the elementary fact' asserts that a 'bottom-up' or transaction-oriented solution is always possible. This assumption also falls down, and in a Goedel's theorem type manner, in that in spite of our best logical generalization, it is possible to 'snooker ourselves' during the play. For example, if we were to program a robot to play pool (a much more realistic challenge for machines, incidentally, than playing chess since pool, like life, involves deterministic chaos), we would have difficulty going beyond describing the situations and responses in terms of 'things' and their spatial coordinates.

It is not possible to describe, in written explanation, the space-time geometry which the human player is purposefully manipulating since it is subject to 'sensitive dependence on initial conditions' (deterministic chaos). On any given shot, perhaps a written explanation could be prepared to convey what must be done. However, the ontogeny of a pool game, like all ontogenies, is unique and non-generalizable. We can only deal with it on the basis of 'attractors' (purpose) and 'integration' over the life of the space-time dynamic (yin-pull). Thus, while the human player is continually reconciling his purpose of separating solids and stripes with the evolving space-time geometry, this is a non-causal exercise which cannot be pre-specified by a series of generalized 'thing'-based transactions. That is, each game (like a life experience) is ontogenetically unique, and statistically averaging transactions over many games is not going to cancel out the effects of deterministic chaos. Thus, the robot would have to be programmed for each and every shot. Hmmm, seem like our human cognitive process is already is doing this to an internal robot-self which we refer to as the rational mind, and in many cases we have delegated overall game responsibility to him/it.

Looked at from another stance, purpose-oriented perspective and systems inquiry is about 'strange attractors' inducing co-resonant integrated responses over the life of a space-time dynamic while causality-oriented perspective and systems inquiry is about generalized transactional behaviors.

If we take the general principles outlined in the above pool example, we can say that the space-time geometry associated with phenomena must be accounted for as well as, and at the same time as, causal transactions (i.e. space is not inert but is a participant). Applying this principle, self-similarly, to a scale-up where we have multiple players and multiple games which must come together (e.g. as in a tournament or a commercial business operation), we can see that the space-time geometry between people and processes must be managed along with the causal-transactional aspects of people and processes. The obvious question to ask, as in the pool game, is; 'how effectively, relative to organizational purpose, does a person (or a process)' contribute to the manipulation of space-time geometry?'

As professional pool players in 'Scotch Doubles' competitions will tell you, not only is the transactional record of players NOT a good indicator of tournament winning potency, the best transactional records are necessarily at the expense of purposive space-time manipulation which is the mother of causal-transactions. This is not to say that you do not want the superb shot-maker, but it is to say that one can maximize one's personal transaction RECORD by playing in assertive mode and executing each and every transaction to the best of one's ability. This mode is 'win-lose' with respect to one's team since superior opportunities to purposefully manipulate space-time geometries are being subordinated to the optimization of transaction quality. In the presence of deterministic chaos (participating space-time) however, the curved-space purpose-induced integrative mode, wherein transactional skills are subordinated to geometrical transformation skills, is the shortest path to a desired system state.

The migration from flat-space to curved-space perception and inquiry goes well beyond transforming our view of problem-solving methodologies; as Lev Vygotsky (1896 - 1934) implicitly argued, it changes our whole outlook on 'thought and language', 'development and instruction', 'understanding and knowledge'.

While early oral traditions and ideographic languages (hieroglyphics etc.) had more 'carrying capacity' that our current language, our language evolved and prospered because of its orientation to simple commercial transactions and inventorying needs (Phoenician and Greek trade and commerce). It is impossible to directly convey, via our current language, high dimensional space-time geometric concepts involved in such phenomena as riding a bicycle or playing a game of pool, and an understanding of them remains in the domain of unarticulable 'experience'. Since language is our prime means of sharing experience, it is natural for us to 'reduce' our explanations of what we have experienced to causal, transactional terms. Thus our reliance on language almost 'reverse engineers' the euclidian flat-space assumption. And if we insist on linguistic explanations and causal rule formulations rather than trusting in each other's experience, we are once again back in non-purposive transaction-optimization or 'win-lose' mode.

Returning to Vygotsky's views, the basic geometric notion which emerged from Vygotsky's research into concept development was that there are two processes involved which together form a unity; spontaneous concept development which is of a space-time geometric nature associated with our ontogenetic sensory experience, and non-spontaneous concept development which is of a systemic or 'scientific' nature. While the former 'comes naturally', "the difficulty with scientific concepts lies in their *verbalism*, i.e., in their excessive abstractness and detachment from reality" (Vygotsky, 'Thought and Language').

It is clear from Vygotsky's overall argument that the term 'spontaneous concept' refers to ontogenetic (reality-based space-time unfolding) relationships of the type discussed in the pool example. With respect to unity in ontogenetic and scientific conceptual development, he says; "We believe that the two processes --- the development of spontaneous and nonspontaneous concepts --- are related and constantly influence each other. They are parts of a single process: the development of concept formation, which is affected by varying external and internal conditions but is essentially a unitary process, not a conflict of antagonistic, mutually exclusive forms of thinking."

Vygotsky goes on to suggest that these two yin-yang enfolded components of conceptual development must not be separated (as is the belief of mainstream western educators since Piaget), but must be kept in close proximity or 'within the zone of proximal development'. In terms of educating children, this means that instruction must be oriented to the child's strength rather than to his weakness. Vygotsky says; "For each subject of instruction, there is a period when its influence is most fruitful because the child is most receptive to it. [Vygotsky's results clearly apply to adults as well as children though he here refers to his research with children]. It has been called the 'sensitive period' by Montessori and other educators. The term is used also in biology, for the periods in ontogenetic development when the organism is particularly responsive to influences of certain kinds. During that period an influence that has little effect earlier or later may radically affect the course of development."

Vygotsky's ideas appear to be undergoing a significant revival these days, and the power of 'situational instruction' which has become evident in business organizations, is underpinned by these more basic ideas on concept formation.

The 'gravity of our error' then, lies in the error of assuming a purely mechanical nature to gravity and natural forces of attraction and repulsion. Whether we are speaking of complex social systems or the formation of crystals, we are able to perceive and inquire into them on two bases; non-verbalizable ontogenetic space-time evolution relative induced by desired states or 'attractor basins' (Vygotsky's 'spontaneous concept development') and verbalizable series of causal transactions (Vygotsky's 'non-spontaneous concept development'). Clearly, an exclusive dependence on the euclidian flat-space assumption precludes us from seeing (or valuing) the former 'spontaneous' concept development. Though if we adopt the non-euclidian curved-space or 'participative space' assumption we are able to 'see' and value both types of concept development in a mutually enfolding top-down and bottom-up geometry; i.e. we can 'play' space-time geometry and transactions at the same time.

The 'bottom line' here is clear. If our purpose is true spontaneous understanding and ontogenetic development rather than the stock-piling and non-purposive exploitation of by-rote or non-spontaneous knowledge (see 'Understanding Knowledge: A Symphonic Liberation'), then we must not separate spontaneous conceptualization and transactional execution as we have been doing and as has become mainstream practice in business, education and society. Keeping the two in proximal resonance, however, requires 'trust' and western society seems to prefer 'rules' to 'trust'. That is, businessmen and educators have preferred to generalize and systemize concepts well 'upstream' of their incorporation in business and educational transactions.

In this regard, Francis Fukuyama ('Trust: The Social Virtues and the Creation of Prosperity'), notes a progressive shift in modern society as a whole away from 'purposive' agreements based on trust towards 'contractual' agreements based on policed or litigated rules, which stifle human and social ontogenetic development. Fukuyama notes some exceptions to this general trend, i.e; "German society is 'high trust' because it discourages the separation of conception and execution."

As long as the rewards systems in our commercial and educational institutions are geared to the quality of transactions, the prospects of a graceful migration out of the flat-space paradigm are dim. While it is imperative that purposive conceptualizing and causal transactioning stay together within the zone of 'proximal development', it is an even greater imperative that the non-purposive causal be subordinated to the purposive ontogenetic. This 'purpose-over-cause' geometry can be as 'symphonically liberating' for Madonna and Juan as for society as a whole.

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