How transcendent complexes arise naturally in physical and chemical systems.

Here we will argue that transcendent complexes (TCs), and more specifically, self-assembly of higher-level  patterns from elemental patterns, are a natural consequence of the basic ingredients of physical reality: the fundamental forces of gravity, nuclear and electrical interaction and the quantum rules governing matter and energy, all obeying the second law of thermodynamics.

TCs as patterns making patterns.


Entropy cannot be reduced without introducing pattern (the two are mutually exclusive). Pattern necessarily implies coherence (spatial and/or temporal autocorrelation) and it brings with it the possibility of physical work because work is coherently organised action. By this, we mean microscopic forces acting together in a specific direction because of the constraints placed upon them by a physical pattern - for example the boundaries of a cylinder and piston*. TCs are the consequence of larger scale patterns being created from organising smaller scale patterns (for example, organising molecules into a structure). A reasonable analogy is the mosaic picture made from a large number of smaller pictures, each of those in turn being composed of a pattern of dots, wonderfully illustrated in the work of the photographer and artist Anna Halm Schudel.  (see examples here).

* (this idea is explained in more detail on our 'entropy' page)

The question is: why, in nature, do small patterns self-organise so as to form a larger pattern? What natural forces direct them to do this? If these forces directly created the pattern, then they must already embody the information needed to form it.

Physical forces act as the draftsman


At the largest macro-scale of all, the pattern forming force par-excellence is of course gravity. By its inverse square law shape, it orders matter with mass in space and time, to form galaxies, give birth to stars and more locally, it forms the surface of our planet, and even influences the anatomy of larger organisms, such as trees and humans. Gravity is strong at large scales, but very weak at the tiniest; it is at the scale of sub-atomic particles that the nuclear forces dominate in creating stable patterns: holding together groups of bosons to make atomic nuclei, without which the chemical elements would not be possible.

In between we see the rule of electric forces and it is these that are most responsible for the stable patterns that lead to (and are used by) life. Electrical forces also follow an inverse square law, binding electrons to nuclei, following the Pauli exclusion principle (which applies only to fermions), creating the set of chemical elements. The electrical force combines these elements together in a great variety of stable patterns which we call molecules and some of these are large enough to be macro-scale patterns (for example crystals and organic polymers). The iconically significant example of these must be the nucleic acid polymers which encode the information for life. In all of this, particles of matter that are influenced by the fundamental forces, locate relative to one-another into stable patterns to fulfil the command of the second law of thermodynamics. 

Why then is the electrical force, dominant over intermediate spacial scales between nuclear and gravity, responsible for such complex variety, when the other two are not? One great disadvantage for gravity is that it is one sided: with attraction the only option, it provides no option for subtle balance giving stable configurations that could in principle embody information. True, the balance between gravitational force and kinetic energy holds a star, a planetary system and a galaxy in dynamic form, but this is a small repertoire compared to the virtuosity of the electrical force which can balance attractive and repulsive forces to create a near infinite variety of stable configurations. Close-in nuclear forces are hampered by the quantum rules governing bosons, so that complexes of nuclei are highly unstable (!); the outcome being that nuclear-based chemistry is exceedingly simple. We are left, then, with the electrical force, its balance between attraction and repulsion and its action on fermions, especially electrons which themselves are a good balance between the flighty and imprecise (photons) and the solid pin-prick dullness of nucleons. This is where the possibilities for complexity reside.

Obeying the second law

In the physical world, these fundamental forces are the only source of work: ordering matter into patterns must be the unregulated effect of their joint action. Atoms ‘self-assemble’ into  ordered patterns because only in that way do they minimise their collective free energy, thereby maximising energy dissipation: maximising global entropy. That is certainly the case for simple small patterns such as those making highly ordered configuration of atoms, most obviously crystals, which simultaneously show low entropy and maximum dissipation of energy (when super-cooled water crystallises to ice, it warms its surroundings with the heat energy that it dissipates in the process). The geometry of the crystal is one of repetition. If a certain configuration of one atom relative to another is thermodynamically optimal (in the lowest energy state and therefore maximally dissipating), then that configuration will be found by the jostling atoms and it will be the same for all of them. The configuration is merely a ‘relaxed’ balance between the electrical force fields surrounding the atoms (a balance between attractive forces which dominate at a larger distance and repulsive forces operating nearby). This balance, identically applying to all the atoms present, will inevitably lead to a monotonous repetition of the configuration and hence the regular lattice of the crystal. From this static array, it seems no further complexity, no higher levels of organisation, are accessible. We can easily generalise crystals to the many polymers (both organic and inorganic), where the same principle of repetition applies. One may obtain from the process, indefinitely large structures, but still they are simple and static.

All covalent bonded molecules come into the same category: stable patterns are made by the energy-dissipating configuration of atoms via their mutual electrical field interactions. The variety of molecules (stable configurations of atoms) is down to the variety of ways in which the elements can be brought together and each embodies specific functional information - that which defines its architecture. This information too, can be found in the electrical force fields around atoms: molecules are nothing more than good energy dissipating arrangements of the atoms and the thermodynamics of chemical reactions show the relative entropies and energy concentrations of transfers among these configurations.

Supramolecular constructions


More complex and interesting for us are the supra-molecular structures formed from configurations of molecules, held together by weaker electrical forces such as hydrogen bonds and van der Waals forces. This supra-molecular construction requires a more precise matching of one molecular configuration with another: of all the possible configurations only one, or very few, result in a stable union. This means that the structure, once formed, embodies more information than even it would if the two molecules were identical and forming a polymer (especially because the selected configuration is one of a larger number of possible configurations of the two molecules). One of the prime movers in this field of science, Jean-Marie Lehn (Nobel Prize for Chemistry), describes such a process of matching molecular configurations as ‘molecular recognition’: specific receptor sites on the molecular surface ‘recognise’ their target (or one-another) and non-covalently bond at that site. In other words, we have the first sign of function in the shape of the electrical forcefield around, and created by, the molecules. Since its shape directly arises from the information instantiating and embodied by its configuration of atoms, we should refer to this as functional information. Lehn further describes the molecules with this function as being ‘pre-organised’, understanding that the recognition and binding is in fact the running of an elementary algorithm: software written in the electrical forces of the molecules. As Lehn says in “Towards Self-Organised and Complex Matter” {Science 2002, 295:2400-2403}, “the components [molecules] must contain the information required for their assembly into a well-defined supramolecular entity, through the operation of specific recognition algorithms”.  In 2007, he put it more explicitly: “Self-organisation processes may be directed via the molecular information stored in the covalent framework of the components and read out at the supramolecular level through specific interaction/recognition patterns, that define processing algorithms. They thus represent the operation of programmed chemical systems” {Lehn, Chem. Soc. Rev., 2007, 36, 151–160}. We note at this stage that molecules with recognition functions are thermodynamically ‘relaxed’ embodiments of information with latent potential to construct higher level patterns and recall the analogy with the elemental patterns found in Conway's Game of Life*. We already know that those elemental patterns may spontaneously (i.e. without additional intervention from a designer) combine to form complex dynamic systems, including the instantiation of a Universal Turing Machine (an information processor capable of computing anything that is theoretically computable).


* see our page on emergence.


Read more about molecular self assembly here