the whole is greater than the sum of its parts.

5, Networks

“Power is changing hands, from dying hierarchies to living networks.”

— Marilyn Ferguson.

A sotto voce piques from Ferguson’s quote alluding to an anima that whistles across a potential nucleating in all networks. A potential gradient sweeping from dissolution to thriving configurations.

Her words trigger that overactive word association trait of mine. Flooding my thoughts with a cascade of conservation laws. In particular, the conservation of energy that encapsulates the 1st law of thermodynamics: only transforms of energy persist in an isolated system, the sum of energy remains constant.

This leads on to further triggering flashbacks of my botched doctoral research. A barrage of bereavements exacerbated that nagging imposter syndrome along with my own intrinsic incompetencies with conforming to standardised structures. Womp, womp and healing cycles — we still stride toward the prize, while now prioritising holistic well-being.

My research at that time hinged on the Carnot cycle that builds its basis on thermodynamic laws. In short, and to spare me anymore PTSD, the carnot cycle dictates a maximum efficiency on the amount of work that can be siphoned from the migration of energy across a potential. Or in other words, there exists a theoretical limit on the amount of work gained from a perfect engine (no energy loss from auxiliary processes like friction). A helpful analogy: a limit on how fast, in theoretically perfect conditions, a waterwheel can spin under the migration of water over a potential (from top (source) to the bottom (sink) of the waterfall).


Abstracting the carnot engine concept over to a material’s intrinsic property essentially surmises my research in thermoelectric materials. Thermoelectric refers to the conversion of a heat gradient to electricity.

Envision a lattice not too dissimilar from the Menger sponge constructed earlier. Consider this to be a configuration of bonded atoms resulting in a distinct crystalline structure intrinsic to a material. The symmetry of the configuration articulates the thermodynamic phase (‘energy’) local to the system. A unit cell is the smallest scale in a lattice that conserves the symmetry sweeping across a crystal lattice.

Now imagine a heat source (hot) at one end of that crystal lattice and heat sink (cold) at another end. Due to the directionality entropy imposes on thermodynamic processes, heat strides from source to sink. Generally for solids, heat transfers via conduction; the thermal energy propagates via oscillations through the lattice structure.

Animation depicting phonons across a lattice.

Imagine a sort of Indiana Jones walk through the menger sponge, the walls (atomic bonds) erratically charging towards and racing away from you. The amplitudes, creeping over each unit cell towards the heat sink, can be discretised as phonons: a ‘packet’ of acoustic/vibrational energy.

This mechanism details the material’s lattice contribution to the heat transfer through the material. Thermal conductivity, an intrinsic property of all materials, dictates the rate and efficiency of that heat transfer through the material. Its basis components are the lattice contribution (detailed earlier) and an electronic contribution: where charge carriers (e.g. electrons) also share the burden of jostling the thermal energy across the temperature gradient.

In thermoelectric materials, the electronic contribution to a material’s thermal conductivity dominates. The limits on the electronic contribution’s efficacy is dependant on the material, its phase and its reservoir of available charge carriers. Nonetheless, the presence of a temperature gradient, elicits an electrostatic potential difference that drives a current across the crystal lattice. Voila, the Seebeck effect; and its reverse is the Peltier effect: inducing a potential difference to create a temperature gradient across the material. Hence, power arises from migration of one energy state to another.

Magnetic flux, over a cubic lattice of neodymium beads, engulfs its ‘prey’.

Magnetism arises in a similar fashion. The congruent orientation of magnetic dipole moments across each unit cell averages over the whole lattice into a flux we experience as magnetism. There are a number of examples, in materials science, depicting phenomena precipitating from this fractal abstraction that conserves intrinsic states and symmetry scaling over a lattice… a network.

IAC’s Isaac Newton group of telescopes on La Palma island with Cygnus overhead — Adrien Mauduit.

Phenomena that lunges beyond the remit of its own architecture. Akin to constellations, distant stars weaving patterns divined across the celestial sphere that lunge and captivate our myth and ambitions.

Ergo; following this logic, sentience lives on a manifold assemblage of branching neurons. That physiological fractal infrastructure, grafted from an orchestra of gene expressions, provides a medium for emotions and cognitive drives to thrive. The stream of consciousness you perceive as self lives on a summation of fractal abstractions.

I wonder how this translates for artificial neural networks & intelligence?




Threading a few concepts as a defence for Gaia and sustainable mental models

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