Brains make models of their worlds and of their own activities, some of which we experience in our streams of consciousness. Indeed each of us individual selves is the model we have made of our own body and history, constantly updated as time rolls on and memories accumulate. Which raises a huge question; how can we best model these models? Artists and novelists depict them in all their beauty and ugliness but their pictures, however insightful, are never more than descriptive. Musicians and poets achieve profounder depictions, so our intuitions often tell us, but ones that are essentially ineffable. Which leaves science in the firing line – especially neuroscience and its offshoot ‘consciousness studies’. The latter does tend to veer off into discussion of semantic and philosophical issues which can confuse attempts to build models. Unfortunately metaphysical issues can’t be avoided altogether, mainly because of problems arising from the incompleteness of both quantum field theory and general relativity, but I’ll try to deal with them as clearly as possible in what follows.

The major difficulty for neuroscience, when it comes to formulating models of brain models, is that it’s faced with impenetrable thickets of complexity. To name some of these: at least 50 different chemicals are produced to trigger or modulate mind-relevant nerve cell activity, many of which affect more than one type of cell receptor; then there are complex hierarchies of (mostly ‘small world’) anatomical networks which reciprocally affect one another; to confuse matters further the tiny dendritic spines that mediate most nerve cell connectivity are as motile as waterweed in a turbulent river, while so-called ‘gap junctions’ can open up between components of formerly separate brain cells and then close again at the behest of a range of influences; to add to the problems, it has recently been found that brain cells are far more various than previously supposed in that thousands of varieties can be distinguished by their differing epigenetic make-ups. In brief, recent hopes that elucidating ‘connectomes’, for example, might allow the development of anything more than very partial models of brain modelling were never more than pipe dreams, if only because brain systems are in constant flux over time scales ranging from milliseconds to years.

A good first step towards developing a comprehensive picture of how brains do what they do involves asking two very general questions;  (a) what exactly is it that brains model? (b) what do they do with their models? Computer metaphors for mind suggest a popular answer to the first question: namely that brains register information, about the structure of that face over there, or the sequence of sound frequencies in a song, or the sensations associated with task performance and then perform some sort of functional operation on the information that results in an appreciation of its meaning. But that offers a very distorted view of the actual dynamics involved.

What actually happens, in the case of seeing a face for example, is that aspects of the dynamics of light reflectance from the face are integrated, via a long series of intermediate steps, into the dynamics of neural activity in the brain. Any idea of ‘information’ is relevant only in the broadest (Batesonian) sense of its referring to ‘differences that make differences’. Similar ‘integration’ occurs, not only in relation to the dynamics of the world out there but also, because of its ‘small world’ connectivity, to dynamics within the brain. Brain ‘models’ whether of their environment, the bodies that harbour them or their own internal activities are always dynamic happenings ‘resonating’, to use Stephen Grossman’s picture (see his . Conscious Mind, Resonant Brain; how each brain makes a mind. Oxford University Press. 2021), with other dynamic happenings. A somewhat misleading computer analogy for these models is with the ever-changing content of RAMs, not with rigid ROM architecture.

Models do get remembered, however, in forms that allow their resurrection when contexts are appropriate. To answer the second question posed earlier, that’s what brains do with them; they facilitate model perpetuation and/or recreation, using memories of outcomes to predict what’s likely to happen over timescales of milliseconds in the context of playing a sport to years in the case of studying for a PhD. Learning is a process of refining accuracy of model re-construction in order to optimise predictions. Can these answers to our two questions tell us anything about how best to put detail into a model of neural models?

The behaviour of extremely complex dynamic systems can be represented as the content of features in ‘dynamic state spaces’ where each of the billions of causative factors contributing to the space is regarded as having its own ‘dimension’. Quantum field theory involves much the same notion, using an infinite dimensional ‘Hilbert’ space. Weather systems provide good examples of the ‘content’ of a dynamic state space; they embody features like clouds or snow storms along with the ‘attractors’ that predispose to the manifestation of particular events. Neural models are like ‘clouds’ in the dynamic state spaces of mind, while memories provide the attractors. The main difference from the weather out there is that reciprocal feedback from ‘cloud’ to ‘attractor’ and back is direct in the state space of mind, but is very much looser and more indirect in the state space of weather.

An important implication of this picture is that neural models must be fractal, like the Mandelbrot sets that adorned so many T-shirts in the 1990s. To see why it’s worth taking a look at the rotating sketches of tesseracts that are pictured on Wikipaedia and elsewhere. Tesseracts are simple shapes, just four dimensional cubes, but their two dimensional representations on a laptop screen undergo quite complex nested changes as they rotate – now imagine what a billion dimensional ‘cloud’ would look like when represented in a three dimensional brain! Perhaps the only features of neurology that could achieve useful representations are the ever changing patterns of ion shifts with their associated electromagnetic fields.

Ions principally involved include sodium, potassium, chlorine, calcium and magnesium. Of these, calcium ions are likely to be the most directly involved in model building for two reasons. First, they’re known to undergo structured, often wavelike, concentration changes on scales ranging from that of dendritic spines, through entire nerve cells to macroscopic volumes of neuropil (i.e. dendritic plexi which include contributions from both neurons and astrocytes). Larger scale patterning still is achieved by nerve firing and its ‘projection’ of smaller scales onto a broader, electromagnetic field, ‘canvas’.  Second, locally increasing calcium ion concentration activates a group of related enzymes (CaMKll enzymes which comprise around 1.5% of all protein in the brain) that have important functions in relation to memory formation. It follows that patterns of increased calcium ion concentration can be regarded as principal actors in the translation of ‘cloud’ models into the ‘attractors’ which enable their resurrection.

There’s an interesting question to do with where models involving the world out there should be thought to exist. Clearly memories of them are all in the brain, but the ‘clouds’ themselves are features of dynamic state spaces that include contributions from a brain’s total environment, which means that there’s a valid sense in which that’s where they are along with their brains. Psychologist Max Velmans has written at length about this calling it ‘reflexive monism’ and the idea is adumbrated in philosophical discussions of the concept of ‘extended mind’. It offers a route to understanding why a pain in your toe feels as if it’s in your toe, not in your brain or in some abstract ‘model space’, why familiar tools feel like natural extensions of our own bodies, or how the ‘group mind’ phenomena that manifest in mob violence, football crowds, theatre performances and elsewhere can occur. Aspects of the phenomenology of love and extravertive mysticism also fit the idea that our models are somehow ‘out there’.

One can put a rough figure on the relative contributions of environment to brain in the case of visual state spaces, since around 10% of synaptic inputs to primary visual cortex neurons come directly from our eyes – all the rest are from recurrent intra-brain sources. Presumably the missing 10% of dimensionality contributes to making memories of what we see so much less vivid than the original experience. But of course that doesn’t tell us why we should experience sights, or indeed why we should consciously experience anything. This is where any attempt to model modelling becomes far more speculative and controversial.

People often opt out at this stage, claiming that conscious experience is just an axiomatic feature of the natural world or of some ‘spiritual’ realm. However we know that neurology and conscious experience inter-relate so it should be possible to do better. That’s what Sir Roger Penrose and many others have tried to do over the last 50 years or more, mainly via proposing quantum theoretical models of a ‘ground’ of consciousness. I think it’s fair to say that, despite remarkable ingenuity and sophistication, none of them have worked out satisfactorily. And there are lots of reasons for supposing that this is because contemporary quantum theory, for all its magnificent successes, is itself an incomplete model in a wide range of respects, as many physicists themselves have readily acknowledged.

Everyday features of the world that can’t be modelled, not even ‘in principle’, by quantum theory include consciousness and time along with gravity (since string theory and loop quantum gravity models are far from usable at present). It’s natural to wonder whether these unexplained but ubiquitous features could be connected in some way. ‘Time’, of course, is generally taken to be a contributor to the dimensional ‘spacetime’ of relativity theory but the term in fact refers to measurement of the durational separation of causal events mediated by photons. Since photons have no intrinsic duration (so special relativity tells us) it follows that time is always an observer-dependent phenomenon. Moreover position in time, unlike position in space, is not a ‘quantum observable’. Acquisition of a position in time is therefore an observation dependent happening, which means that it is associated with ‘quantum measurement’.

Many models have been proposed for the quantum measurement process (e.g. Copenhagen, von Neumann, Bohmian, decoherence, transactional), all equivalent for practical purposes despite their differing metaphysical implications. Creation of durational temporality is one of the secondary consequences, along with all the ‘eigenstates’ whose probabilities are already modelled in quantum wave functions. ‘Measurement’, in other words, is always associated with what might be termed a process of ‘horation’ (creation of hours) along with manifestation of definite positions, momentums, energies, spins, etc.

Even though quantum modelling doesn’t include temporal positionality it does include notional (de Broglie) frequencies which are measures of energy, along with a (Heisenberg) time/energy uncertainty relationship analogous to the more familiar spatial position/momentum uncertainty. Since frequency, energy and mass are equivalent measures, gravity and time are clearly linked on some basis that is independent of their arbitrary elision in the ‘spacetime’ of relativity theory. Similarly ‘observation’ and ‘horation’ are equivalent processes. Might the process of ‘horation’ be pictured as relating to consciousness in what amounts to a mirror image of the von Neumann model of quantum measurement?

The answer to this question depends on whether one can envisage structured patterns of ‘horation’ as having something in common with the patterning of ionic shifts that model mind. It’s generally assumed that minimal durationality is the Planck time, defined by the time it would take for a photon to traverse the Planck distance. However this provides a model that must be entirely unrealistic since any photon confined to the Planck distance would be so energetic as to instantly become a singularity; moreover photons lack intrinsic durationality and therefore can’t act like stop-watches for durations, which are indeed the observer dependent measures that relativity theory describes. Minimal temporal durations are realistically modelled, however, in the durations associated with time/energy ‘measurement’ uncertainties; these are always context dependent and therefore do have the potential to model  their worlds of origin. They will generally be so brief as merely to provide a background ‘hum’ of temporality that provides a negative image for the so-called ‘vacuum energy’, conceived as a sea of virtual particles, that pervades the universe.

Brains, however, harbour vast numbers of energetic events owning very small energy uncertainties and therefore durational uncertainties of up to as much as a tenth of a second, well into the range of neural activity frequencies. The organisation of these durational events is bound to be intimately, albeit reciprocally, related to neural modelling. Could they be the models that we actually experience while we are conscious? Is ‘consciousness’, in other words, a concomitant of acquisition of temporal extension occurring in association with ‘quantum measurement’? Affirmative answers to these questions are likely to involve abstruse issues modelled by number, knot and graph theories but I’d like to finish up by describing one implication of the idea which is testable – indeed many would claim that it has been tested.

The implication is that any ‘horational’ patterning will be of intrinsic durationality and thus independent of time’s arrow. The passage of time may add further patternings to some pre-existing total but, as Einstein himself remarked, the disappearance of the past “is only a stubbornly persistent illusion” – perhaps he should have added ‘at least as far as any conscious models are concerned’. The co-ordinate system describing them would not be Minkowskian but more like that applying to quantum entanglement relationships. There is a wide range of evidence already that the model is realistic, ranging from some of the phenomenology of abreactive and eidetic memories, through frequent reports of  ‘terminal lucidity’ to the careful documentation of ‘past life’ memories that have been provided by children. More specific tests involving a search for consciousness-associated energy anomalies could be devised.

Of course it’s tempting to suppose that conscious models must be imaginary in some sense, which is true enough in a way. But then one has to remember that they are pictured as woven from threads of durationality that endow the world with manifest existence; so maybe it’s the world that’s more truly ‘imaginary’! Whatever the truth of all this, one thing remains certain – that there’s a huge amount of interest and enjoyment to be gained from investigating it.