Consider three concepts T1, T2 and T3|
T3 is derived form T2 which in turn is derived from T1. This is tautological by virtue of its serial dependence. A trivial case. If T1, T2 and T3 exist concurrently they are not distinct or different and represent normal dynamical behaviour differences i.e. they are changes or non-interactive, decaying evolutions in time of the same concept.
The first significant epistemolgical case: T1 and T2 are topics or concepts concurrently existing and derive a third topic or concept T3.
We may write: T1 + T2 => T3 here + means combined with and => means produces.
Similarly we may write T2 + T3 => T1
and T1 + T3 => T2.
We may say pairs of concepts are analagous where the third concept is a distinguishing difference. This is the stable concept triple. This "cylicity" of derivation may be shown graphically.
In setting up Interacting Actors and the forces of self-organisation and learning Pask made the loops of cyclicity dominant and resonating. They produce the orthogonal intersecting Borromean links which form a model of continuity around a non-void.
From an off-axis perspective a residual clockwise/anticlockwise parity or spin effect can be projected on an observer. Perturbation may not be necessary. This provides a novel basis for a new interpretation of quantum uncertainty. This mechanism might be experimentally verifiable. Comments welcome.
In discussing invariance I quoted Atomic Number as a good example of invariance in Nature. "Ah", said Pask "the atomic hypothesis". Four years later fractional electron charge (thought not to exist) was the subject of a Nobel Prize to Laughlin, Störmer and Tsui (1998).
It is likely that all systems are adaptive and, indeed evolutionary in the way their components excite, aggregate, disaggregate and organise to avoid thermodynamic death.
This behaviour may be limited to distortions in the Borromean link continuity model. As a model of the non-void and this is an analaogy (a mapping with a distinction and a restriction). How close will it prove to be to the behaviour around the scale of a Planck volume, ~10-105 m3 ? As the Gravitational Imperative force becomes equal in magnitude to the Electromagnetic Imperative force, the Planck condition, IA can still be applied. If the void proves to be yet smaller the applicability of the Pask calculus persists. An extraordinary achievement.
Does this have implications for Chemical Valency Theory?The orthogonal repulsion to Pask's tail-eating "+" force (see IA Axioms page 3 and figure 3; page 4 and figure 6; page 12 and figure 8) sets up a carapace of stability. These imperative forces become particularly strong as cooling, due to lack of interaction, asserts the change of state from gas to liquid and solid. Can the tail-eating force of closure account for all the oxides of chlorine, for example? These kinds of structure strains the credibility of current valency theory. Can the "+" force account for the stability of combination rules in organic chemistry? Can we forecast protein folding structure given this new approach?
Sceptics might care to note the most energetic form of the "+" force seeking closure, a tail to eat as it were, is seen in the sucking forces around tornadoes and whirlpools and generally orthogonal to the direction of rotation of the "whirl". Contemplate your bath emptying down the plug hole and consider the principal processes maintaining continuity. Whilst transport flow rates of the order of ~1m/s might be expected recall molecular speeds of an order around 1 km/s are encountered in a molecular level continuity process so "Borromean" processes will account for 99.9 % of dynamical activity. Note also that wherever a velocity gradient exists so does vorticity, the propensity to make vortices, thus generating a recursive vortex within a vortex structure so characteristic of Pask Concept packing.