Transcendent Complexes, Information and Emergence

This article was rewritten by Keith Farnsworth in January 2019

(Note: in conjunction with this, it is worth reading our page on Downward Causation).

What is a transcendent complex?

The national economy goes through cycles of fluctuating income, debt, employment rates and so on, but this is all really the consequence of millions of individual trading transactions aggregated: it is an emergent phenonomenon that arises from an interaction network, not from the agents doing the interacting. But, we all know that this phenomenon has some influence on the behaviour of the agents that by their collective behavior bring it into being. So, perhaps weirdly, the immaterial thing that emerges is in some way responsible for its own nature. Because it does not depend on the agents themselves, but only their behaviours, the national economy transcends them, but is still a emergent phenomenon with no material substance: it is purely informational. For these reasons, it is a trascendent complex of the trading transactions which collectively constitute it. Similarly, the former UK Prime Minister, Margaret Thatcher is famous for having said (though she did not quite) that "there is no such thing as society, there are just individual people". She may have been expressing a view on 'emergence' in complex systems, had she not been attacking socialism. In material terms, she was right - there really are only individual people and what we call 'society' is an emergent phenomenon, rather than a material thing. It emerges from the aggregated effect of interactions among the people taking part. And it exists as an informational structure because the interactions are not random, but in some way organised, which is to say of lower entropy than if they were random and thefore instantiating information. This information, which we recognise as 'society' influences the behaviour of its members, and does not depend on exactly who and who are in it: to this extent society trasnscends its component parts. As an information (cybernetic) structure, it has properties that we can describe, measure and predict with models. These properties are termed 'emergent' because they only exist at a level of organisation above that of the components (e.g. people) that create it through their interactions (by the way - emergence is more fully explained here).

Whenever an emergent phenomenon is independent of the component parts that compose it - strictly only depending on their relevant behaviours - and is responsible for influencing the behaviour of those  component parts, then it can be called a transcendent phenomenon. The component parts are effectively substitutable, what matters is only that they behave (and especially that they interact) the right way: that is, they must have the correct functions. In principle there is a whole class of potential components sharing in common the correct functions and this class is the Functional Equivalence Class (FEC).

Some examples
Because we can make a conceptual (e.g. computer based) model of, for example, an ecosystem which displays the same emergent phenomena as the real thing, we suspect that there is something about the ecosysem that does not strictly depend on the material (organisms) underlying it. In other words, there seems to be an informational structure embodied in the interactions, but it is hard to see. More obviously, a computer program such as a word-processor, is an observable phenomenon at a scale of organisation greater than the binary bits of data from which it is composed and it could in principle be implemented, not only in any digital electronic computer, but also in hardware composed of mechanical valves and tubes of water, i.e. digital plumbing (and this really has been done - the UK treasury model of the economy was for a long time just such a 'water computer' and, when one day I sat beside a senior economist in Oxford University, he told me with glee that it still exists and is still useful!).
The Turing machine is a fundamental concept in computer science: it is a conceptual machine that can in principle compute anything that is computable. So when a Turing machine was created using the plastic building toy ‘Lego’, it became possible, in principle, to make the word-processor from Lego. Clearly a word-processor is a phenomenon that is not determined by what it is made from.

The difference between a TC and a mere 'emergent phenomenon' is that the TC is functional in the sense that it executes a process which arises from the organised functional actions of its components. This idea is closely related to the IFB definition of biological function (A biological function is a process enacted by a biological system A at emergent level n which influences one or more processes of a system B at level n+1, of which A is a component part - Farnsworth et al 2017).

We shall use the term ‘transcendent complex’ (TC for short) for such entities because they transcend the particular method of implementation used. Their properties are that (a) they arises from the interaction among elements and (b) they may be realised (i.e. instantiated) in multiple ways, because they depend only on certain functions of the elements, not their whole nature. TCs are therefore multiply realisable, which is the concept used to define classes of functional equivalence in the hierarchical structure of cellular chemistry (Auletta et al (2008); Jaeger & Calkins (2012)).

Elements within an ensemble do not really interact with the TC of that ensemble, they only interact with each other. What makes the interactions act as something larger controlling the behaviour of the elements, is the additional functionality provided by the particular configuration that gives rise to the TC. The configuration of the ensemble is one that instantiates functional information so that a TC emerges. The TC is the aggregate of this functional information and it appears at the scale of organisation of the ensemble. It is the difference between a pile of jigsaw pieces and the completed puzzle. The relationship between one piece and the others in the pile is random and without function; that between one piece and the rest of the completed puzzle is special because the piece has a specific place in the configuration. The other pieces give it context: the information which it embodies ‘makes sense’ when placed in this context. ‘Makes sense’ here means that the embodied information of the piece forms part of a functional information pattern at the larger scale, once the other pieces are in the functional configuration. It is this functional pattern that is the TC. For a swarm (a flock of birds or shoal of fish) the functional configuration is the ordering of animals at specific distances and orientations (see e.g. Aoki, 1982). In this pattern, the (translational) movement of any one of them is highly correlated with the others. It forms part of a pattern built at a higher level of organisation and that pattern is functional and its function is one of causal power - the power to direct the movements of the animals. This causal power is implemented through the effective cause of neighbouring animals, but the causal power clearly arises at the higher level of organisation because it equally applies to all of the animals in the swarm.

Functional equivalence classes and emergence

The behaviour of assemblies of components, such as molecules in a gas, are conveniently decribed by averages taken over the assembly: what physicists refer to as 'course graining'. However, these avaerages are often not seen as simply that, but as new and apparently separate phenomena in their own right - for example pressure and temperature, which are based on the average of kinetic energies of molecules. We would interpret this by saying that phenomena at a given level of organisation (e.g. molecules) can produce effective higher level variables, so creating a higher level of organisation, reminding us that the new phenomena are really just a way to think of what is happening at a grander scale. If we start with a coarse-grained (effective) view at some level, we are denied information about the details at the fine-grained level below. For this reason, many possible states at the lower level may be responsible for what we see at the higher (which is exactly the micro-state / macro-state relationship used in statistical thermodynamics). There are, therefore, multiple realisations of any higher-level phenomenon, based on multiple micro-state configurations (many ways to get the same average from a set of numbers). The multiple ways of realising a single higher level phenomenon can be collected together as a class of functional equivalence: a set of states, configurations, or realisations at the lower level, which all produce an identical phenomenon at the higher. A functional equivalence class is by definition the ensemble of entities sharing in common that they perform some defined function. But a phenomenon can only be functional in a particular context, since function is always context dependent (Cummins, 1975). This context is provided by the TC, which organises one or more of the members of one or more functional equivalence classes into an integrated whole having ‘emergent properties’. The TC is an information structure composed of the interactions among its components. In practice, these make up the material body, which embodies the information that collectively constitutes the TC. It must be described in terms of functional equivalence classes because it is multiply realisable. Crucially, the TC does not integrate the lower level components per se, it integrates their effects, so the TC emerges from functional equivalence classes, not from the particular structures or states that constitute their members. Specifically, a TC is the multiply realisable information structure that gives lower level structures the context for their actions to become functional. It is an aggregate phenomenon of functions. For it to exist a set of components must be interacting to perform these functions; the components must collectively be members of the necessary functional equivalence classes.

Information as a transcendent complex

Now we will introduce the idea that information itself is a transcendent complex and go on to explore some of the implications of that.

Physical information (the most fundamental kind of information) is most fundamentally the physical location in space and time of physical things relative to one another. Again, it is useful to think of the pattern of different magnetisation on a computer hard disk, the string of bases in a DNA molecule or the pixels in an image. Clearly we can conceptualise physical information in ways that do not depend on any particular kind of (substrate for) its instantiation. Physical information is conceptually separate from the physical world, but its existence still depends on something physical to embody and instantiate it. When an image is printed, a surface is covered small dots of ink, but when we look at this from a suitable distance, we perceive a pattern formed among the dots: the pattern which is the image, is in our mind, not on the paper: it is a TC in information, a perspective on a pattern of dots.

The Universal Turing Machine  was first conceived as a mental tool to help understand the basic principles of computation. The UTM’s properties were thought about in abstract terms: the UTM as a concept depended on brains, pencil and paper, it was not a physical thing. Only later was a UTM actually instantiated with a physical embodiment, but as we saw here, the UTM was not a thing in itself, but rather an interpretation of a particular arrangement (pattern in space and time) of physical things. The UTM is a perspective on those patterns, one that reveals to us  many interpretable properties of information. In this example and all others, the properties of information can be described without reference to the elements from which they were constructed. Indeed, physical information itself is independent of the kind of things that are arranged in space and time to embody it: this information arises as a phenomenon of the arrangement alone; it is a ‘perspective’ on this arrangement and is therefore a transcendent complex.

Even meaning is a transcendent complex

This does not stop with physical information. We establish elsewhere that ‘meaning’ is a functional relation between particular structures of physical information. That is to say: meaning is the phenomenon of function arising from one information structure providing the context for another. Information - as meaning - is therefore a property of physical information, one that emerges from interaction among items of physical information. As a consequence, it also is a TC, this time of arrangements of physical information. Since an emergent pattern of a TC is also a TC, we can say that meaning is a TC of the physical location in space and time of physical things relative to one another.

A consequence for what constitutes life

One consequence of this is that meaning therefore cannot have a non-physical existence, though it may be thought of in abstract, just as any TC can, but then the thoughts themselves depend on physical objects such as neurons. The grand result seems to be, then, that all information is a TC of energy-matter in space-time. Assuming our main thesis that “living is information processing” to be correct, then this statement is equivalent to a denial of vitalism: the belief that something non-physical exists to give ‘life’ to living things. The consequence of this statement is that the properties of an organism are all a TC of the properties and relations of its parts, each of which in turn (perhaps through several levels of nested hierarchy) are properties of elemental physics. In other words, the emergence of life from the inanimate is an example of soft or weak emergence: it is a TC.

Further thoughts on information as a transcendent phenomenon

What follows here is an elaboration on the idea, to help draw out its meaning (so if you are already happy with that, you can skip this bit).
To illustrate some consequences of information as a transcendent complex, imagine a painting: clearly it is an embodiment of information. If it is (hypothetically) copied exactly in every detail, this copy will be a new creation, but it will embody the same information. In one sense it will be the same painting: different atoms in the same configuration (macrostate), with the same properties as the original painting (noting that atoms of the same kind are identical). In a deeper sense it can never be the same because this copy will not occupy the same space-time as the original. For this reason it will never interact with the rest of the Universe in precisely an identical way. It must always be distinct, even if only because it must have been created in a different part of space-time (either a different place, or later or both). In practice that means that it always interacts with different photons, or if the same, at a different time, with potentially different consequences for the whole Universe. Thus as a conceptual abstraction the original painting and its perfect copy are the same painting, but as physical embodiments, they can never be.

Now suppose no copy were made and the painting is destroyed completely. None of its embodied information remains you might think. However, the physical information is not destroyed when the painting is. The painting is a pattern in physical information: one particular macrostate from among many. Destroying the painting amounts to the dispersion of this macrostate, it does not destroy physical information, for that may be found in the new macrostate created from the destruction of the painting, which we see is only the total re-arrangement of the pattern. (Note: this is inherently confusing because the language of information is currently rather inadequate: reading this page will help).

At a higher level of abstraction, we may consider only the particular pattern: a specific configuration (e.g. the arrangement of colours etc. in a painting), and this may be represented in another medium or format, for example a photograph of the painting (ignoring texture etc. for the sake of argument). Given this interpretation, a copy is the result of an isomorphic map that transforms the information from one substrate to another, preserving or replicating it. Indeed a process may instantiate information that forms a set of instructions describing how to re-create the painting (the PDF file format is something like this). Given this higher abstraction of interpretation, the painting is destroyed only when there are no remaining copies of information (including instructions that could reproduce the painting). It should be clear now that the painting is an transcendent complex of physical information, which in turn is an transcendent complex of energy-matter in space-time. If we now replace ‘painting’ with ‘organism’, we can regard its DNA as an information pattern which is a set of instructions, that when followed, re-create the organism*. Thus the organism would be an transcendent complex of a pattern in atoms.

(* Note, this is a simplification. As we explain elsewhere, DNA does not carry sufficient information to recreate an organism).

Finally, we should notice that transcendent complexes are identified by human minds: they are convenient abstractions of the physical world and may not be 'real' in and of themselves. Of coure that depends on your defintion of 'real'. It seems that TCs are genuinely separate from their elemental substrates, but in fact they are not. The Turing machine may be conveniently thought of as independent of the components from which it is made (digital software or lego for example), but the fact that a TC, by definition, has properties that are independent of its elemental components only means that more than one elemental substrate can give rise to these properties. It turns out that the existence of a TC results from two phenomena. The first is that some properties of systems are generated by more than one kind of elemental substrate (e.g. the software and lego in the case of a Turing machine). The second is that these properties can be thought of by people in a way that is abstract from the generating substrate. In other words, TCs are really a consequence of the way we think. When we identify a TC, we are classifying a kind of pattern: a kind of information complex. The genetic code embodied by a DNA molecule is an informational pattern  and the organism created by following its instructions is quite another. Both, though, are patterns in the physical configuration of atoms and both can be considered in the abstract as transcendent complexes.

Aoki I. (1982). A simulation study on the schooling mechanism in fish. Bull. Jpn. Soc. Sci. Fish. 48:1081–1088.

Auletta, G.; Ellis, G.; Jaeger, L. (2008). Top-down causation by information control: From a philosophical problem to a scientific research programme. J. R. Soc. Interface, 5, 1159–1172.

Cummins, R. (1975). Functional analysis. J. Philos., 72(20):741–765.

Farnsworth, K.D.; Albantakis, L.; Caruso, T. (2017). Unifying concepts of biological function from molecules to ecosystems. Oikos, doi: 10.1111/oik.04171.

Jaeger, L., Calkins, E. (2012). Downward causation by information control in micro-organisms. Interface Focus, 2, 26-41.