Tuesday, 24 December 2019
Out of Chaos – A Mathematical Theory of Coherence
And new philosophy calls all in doubt,
The element of fire is quite put out,
The sun is lost, and th’earth, and no man’s wit
Can well direct him where to look for it.
And freely men confess that this world’s spent,
When in the planets and the firmament
They seek so many new; they see that this
Is crumbled out again to his atomies.
‘Tis all in pieces, all coherence gone,
All just supply, and all relation;
Prince, subject, father, son, are things forgot,
For every man alone thinks he hath got
To be a phoenix, and that then can be
None of that kind, of which he is, but he.
The keyword in all of this (and a word which got me into trouble this year because people didn’t understand it) is “Coherence”. Coherence, fundamentally, is a mathematical idea belonging to fractals and self-referential systems. It is through coherence that systems can anticipate future changes to their environment and adapt appropriately, and the fundamental driver for this capacity is the creation of fractal structures, which by definition, are self-similar at different scales.
In work I’ve done on music this year with Leydesdorff, this coherent anticipatory model combines both synchronic (structural) and diachronic (time-based) events into a single pattern. This is in line with the physics of David Bohm, but it also coincides with the physics of Peter Rowlands.
When people talk of a “mathematical theory” we tend to think of something deterministic, or calculative. But this is not at all why maths is important (indeed it is a misunderstanding). Maths is important because it is a richly generative product of human consciousness which provides consciousness with tangible natural phenomena upon which its presuppositions can be explored and developed. It is a search for abstract principles which are generative not only of biological or social phenomena, but of our narrative capacities for accounting for them and our empirical faculties for testing them. Consciousness is entangled with evolutionary biology, and logical abstraction is the purest product of consciousness we can conceive. In its most abstract form, an evolutionary biology or a theory of learning must be mathematical, generative and predictive. In other words, we can use maths to explore the fundamental circularity existing between mind and nature, and this circularity extends beyond biology, to phenomena of education, institutional organisation and human relations.
When human organisations, human relations, learning conversations, artworks, stories or architectural spaces “work”, they exhibit coherence between their structural and temporal relations with an observer. “Not working” is the label we give to something which manifests itself as incoherent. This coherence is at a deep level: it is fractal in the sense that the pattern expressed by these things are recapitulations of deeper patterns that exist in cells and in atoms.
These fractal patterns exist between the “dancing” variables involved in multiple perceptions – what Alfred Schutz called a “spectrum of vividness” of perception. The dancing of observed variables may have a similar structure to deeper patterns within biology or physics, and data processing can allow some glimpse into what these patterns might look like.
Fractal structures can immediately be seen to exhibit coherence or disorder. Different variables may be tried within the structure to see which displays the deepest coherence. When we look for the “sense” or “meaning” of things, it is a search for those variables, and those models which produce a sense of coherence. It is as true for spiritual practice as it is for practical things like learning (and indeed those things are related).
2019 has been a deeply incoherent year – both for me personally, and for the world. Incoherence is a spur to finding a deeper coherence. I doubt that we will find it by doing more of the same stuff. What is required is a new level of pattern-making, which recapitulates the deeper patterns of existence that will gradually bring things back into order.