A Nagelian Neurology of Consciousness?

The aim of this paper is to explore the possibility that Nagel’s well-known account has implications for understanding the neural basis of consciousness. In a world assumed to be non-dualistic, it is argued that Nagel’s view (i.e. that consciousness is what an organism possesses when there is something that it is like to be itself) implies that consciousness is an attribute of some system in the brain that maps patterns of spike train activity. Various considerations suggest that any such system is likely to operate on analog principles.

An example is briefly described of a system that could realistically be supposed to meet these requirements. It maps spike activity into varying patterns of calcium concentration. These patterns have wave-like properties, and will therefore show interference effects of the sort that are at the basis of holography. It is proposed that the interference effects are ‘recorded’ by a protein, CaMKll, which is widely distributed in the brain and which can undergo permanent change in response to increased calcium concentration in a manner closely analogous to the response of a photographic film to increased light intensity. Since CaMKll changes also affect synaptic sensitivities, any hologram which they Consciousness refers only to a small proportion of the brain activity that is going on at any given moment record will be capable of ‘re-creation’ by appropriate neural inputs; there is no requirement for an analog of the reference laser that is necessary for viewing ordinary optical holograms.

It is further pointed out that the hologram will have a fractal-like structure (i.e. will be self-similar over a wide range of scales). On small scales this structure will be found mainly in dendrites, but on large scales may chiefly be supported by astroglia. Coupling to the diffuse electromagnetic (EEG) fields of the brain may play an essential part in upscaling. On large scales the structure could, in principle, be viewed via suitably tuned MRI. The most important prediction of the paper is that patterns in a fractal structure of varying calcium concentrations will be found to correlate with reported consciousness more closely than the correlations with consciousness shown by other MRI measures (such as the BOLD signature of current fMRI).

Introduction

Nagel’s well-known (1974) description of consciousness is arguably still the best, as well as one of the most succinct. He in effect defined consciousness as that which exists when, for a particular organism, there is something that it is like to be that thing. The ‘thing’ in question is whatever it takes for the organism to be in the appropriate state to have a particular conscious experience (since organisms are not always conscious, while we know from introspection that different internal and external circumstances engender different sorts of conscious content). It is a formulation that has been widely patterns in a fractal structure of varying calcium concentrations will be found to correlate with reported consciousness more closely than the correlations with consciousness referred to because of perceived usefulness and has stood the test of time. Unlike most brief definitions which tend to involve such phrases as ‘possession of awareness or subjective experience’, although self-referential, it is not obviously circular. Nagel’s relative success is surely an indication that he managed to encapsulate an essential aspect of the truth about our conscious There has been much discussion as to what it is like to be bat experience. There has been much discussion of the implications of *What is it like to be a bat?* for the ontology of consciousness, but might it still carry any useful message for us if we make the prior assumption that the world is non-dualistic (i.e. standard materialism is correct)? In what follows, I argue that it may.

A Nagelian neurology – general principles

In Nagel’s brief description of consciousness there are both a ‘something that exists’ and a condition of ‘likeness’. If we assume that the brain is the sole generator of consciousness, then the ‘something that exists’ must refer to an aspect of its structure or function. The condition of ‘likeness’ is a more slippery concept, however. In the real world, it is a condition constrained by the nature our conscious experience, which can include all sorts of things; percepts, feelings, cognitions, dreams, hallucinations. There is clearly an implication that the condition must be taken to refer not only Consciousness refers only to a small proportion of the brain activity that is going on at any given moment self-referentially, to the ‘something that exists’, but also to the actual content of that something; for example an awareness of seeing a rose, an experience of an emotion, or an hallucination of pink elephants. All such contents, we generally suppose, are encoded in varying patterns of neural activity. Nagel’s definition, when viewed in the context of standard materialism, can therefore be taken to imply the existence of an (unknown) aspect of brain function which embodies the ‘something that exists’ of consciousness, plus neural activity embodying the ‘likeness’ condition.

One might be tempted to suppose that the two neural conditions are simply two differing aspects of the same neural activity or property, but this is unlikely because we know that consciousness refers to only a small proportion of the brain activity that is going on at any given moment. Moreover, the proven occurrence of unconscious perception (e.g. Kihlstrom, 1996) shows that the type of material on which the ‘likeness’ condition may be based does not necessarily get into the ‘something that exists’. It therefore seems far more probable that (at least) two distinguishable aspects of brain function are involved. There is neural activity encoding percepts and so forth, and there is other, distinguishable neural activity embodying consciousness. But Nagel’s definition requires that the two should somewhere embody ‘likeness’. The simplest way of envisaging such embodiment is to propose that it lies in their relationship; i.e. that the relationship between them is one of mapping or modeling. Because the flow of neural activity in perception is from eyes, ears and so forth, via nerve tracts, ultimately to the cortex ‘Being like something’ is surely not equivilant to ‘being something that it is like’ of the brain and only later into consciousness, it would be reasonable to suppose that the neural activity encompassing conscious perception of the external world models that embodying ‘raw’ percepts, rather than vice versa. The requirements of parsimony imply an analogous directional flow of mapping in relation to other types of conscious content. Literal interpretation of Nagel apparently leads to the view that consciousness is a process in which neural activity of some sort models a selection of other, on-going neural activity.

It might be thought at first sight that introducing transitivity into Nagelian ‘likeness’ changes his consciousness definition into something else. ‘Being like something’ is surely not equivalent to ‘being something that it is like’, one might reasonably suppose. Indeed, for this reason, there was a good deal of debate at one time over the questions of whether the definition implied dualism and, if so, what sort of dualism. When set within the context of neurological materialism, however, introducing transitivity probably does not pose a problem for the following reason:- Nagel’s definition treats consciousness as a ‘black box’, to use a concept that pervaded psychological thinking at the time, constrained only by the requirement that there be something that it is like to be ‘x’, where ‘x’ is an organism in some particular neural state. In a non-dualistic world, since consciousness is a property of the organism, this must surely be taken to mean that ‘x’ is like itself. While it is true that everything is trivially like itself, the success of Nagel’s formulation suggests that trivial likeness is not what is involved. The alternative, non-trivial likeness emerges from the fact that that, if the whole system envisaged here (i.e. pattern of spike activity, plus process that maps it and resultant model) is put back inside the black box, it can once more be envisaged as embodying a self-referential condition of likeness.

The question of what constitutes a ‘model’ in this connection is, however, far from clear. As Edelman and Tononi (2000) in particular have emphasized, much brain activity is re-entrant, or at least recurrent, and might therefore be said to be mutually self-modeling. These authors suppose that complex re-entrant activity *is* consciousness. Their view is, however, hard to reconcile with the spirit of Nagel’s definition. There is the obvious point that re-entrant activity also occurs in relation to unconscious perception. Even though the re-entrant activity may be less extensive than that associated with conscious perception, why is unconscious perception not at least a little bit conscious on their view? That it is not, or at least is not Does ‘something that exists’ may possess a different physical structure from the embodiment of the ‘something that it is like’? reportably conscious, suggests that self -modeling of the re-entrant type is not sufficient for ordinary consciousness, which is reportable. We are in fact conscious of wholes, things like seeing a friend’s face, not of the separate visual edges, colours, and so forth which compose it (unless we pay special attention to them), although these are the objects that are mutually self-modeled in the course of re-entrant nerve activity. The sort of model of interest from a Nagelian point of view is more holistic. It can be regarded as analogous to those found in the everyday world in computer-generated images, for example. When translated into neural terms, this concept of a model refers to the total of nervous activity that is both (a) relevant to, or about, any particular conscious content, and (b) shares a common format or means of encoding information, such as a pattern of increased spiking or synchronicity. On this definition the entire spike activity involved in Edelman’s re-entrance is a ‘model’, but its sub-components are not.

This concept of a model immediately suggests that the Nagelian ‘something that exists’ may possess a different physical structure from the embodiment of the ‘something that it is like’. The something that is mapped certainly depends on patterns (temporal, spatial or both) of spike activity since that is how the brain encodes both afferent and efferent information. Perhaps the ‘something that exists’, the model whose process of construction *is* consciousness from a Nagelian point of view, is encoded differently. This possibility is particularly attractive because it provides a possible solution to the problem of why so much brain activity is unconscious. One has merely to propose that all information that is encoded only in spikes is always unconscious. An interesting argument due to Mulhauser (1998) is pertinent here. He has argued in exhaustive detail that analog computation should be considered to underpin consciousness. Spike activity, he thinks, is unconscious for the same reason that computers are unconscious, namely that it is inherently digital. The best computer simulations are limited by the digital logic that they use. As a consequence of this, they can represent things only in terms of the countably infinite, rational numbers. They therefore miss out on most of the fine detail of reality. If the fine detail is to be precisely described, it has to be done in terms of the uncountably infinite, irrational numbers that manifest so ubiquitously in nature, especially in the phenomena of fractality, chaos and turbulence. Consciousness may require computation by systems able to cope with irrational numbers without having to resort to approximation, namely analog systems (quantum computational systems can also, in principle, cope with irrational numbers, but Mulhauser thinks that analog ones are the more realistic option. Indeed MacLennan, 1999, has subsequently shown that a formalism which can be used to describe analog, field computation overlaps with the formalism of quantum computation). From a Nagelian point of view, it might be proposed that the inherently coarse-grained nature of representations encoded in spike activity prevents them from embodying the condition of ‘likeness’ to a sufficient extent to fulfil the consciousness definition.

It would in fact be inherently all but impossible for a system dependent on spikes accurately to map another such system, or even its own activity at a different time. This is because much of the spike activity in the brain is stochastic in origin (Koch, 1999, points out that arrival of an action potential at many cortical synapses has a chance of only around 30% of releasing any neurotransmitter, while there is only ever a probability that neurotransmitter release will trigger an ongoing spike). A fully accurate spike train model would itself be based on stochastic activity, and would therefore have to include sufficient trains to ensure that at least one set of trains was ‘right’ (i.e. represented what had actually occurred in the activity being modeled). It would thus have to be exponentially larger than what it modeled, which is clearly impossible given the limitations on space in the brain. It seems reasonable to conclude, therefore, that the condition of ‘likeness’ that is required by the interpretation of Nagel’s definition developed here is unachievable in any rigorous sense by spike activity.

The main motivation for pursuing the materialistic interpretation of Nagel described above is that regarding this formulation as valid entails conversion of the so-called ‘hard problem’ of consciousness into an ‘easy’ one. It has been argued that Nagel’s ‘something that it is like’ must, from a neurological point of view, refer not only to the neural structure or function that underpins consciousness but also to the informational content of consciousness. The latter is known to be derived from patterns of spike activity that are themselves certainly mainly unconscious, and may be entirely unconscious. A process of ‘being like’ (i.e. of accurate mapping or modeling) results in Nagelian consciousness. Because the ‘something that exists’ of consciousness should probably be envisaged as embodied in analog form, the argument suggests a starting point when it comes to looking for what are often called the Neural Correlates of Consciousness. As Revonsuo (2001) has pointed out, however, just about any neural activity can *correlate* with consciousness in one way or another. A different term is needed for neural activity that might be supposed to *generate* consciousness, which is the present focus of enquiry; the term ‘neural mechanism of consciousness’ (NMC) may suffice.

An obvious question to ask at this point is whether the picture that has been developed of an analog system modeling meaningful patterns of spike activity has plausibility in the light of current knowledge about the brain. The main problem is not that it is difficult to find suitable mechanisms, but that there is am embrassingly wide range of choice The short answer is that it does; indeed the main problem is not that it is difficult to find suitable candidate mechanisms, but that there is an embarrassingly wide range of choice. Rather than try to describe the whole range, I shall sketch an outline of one particularly plausible candidate, in order to provide an example of the sort of Nagelian NMC that may one day be found to exist.

A neural mechanism of consciousness?

Koch (1999, p. 475) has tabulated the various computational mechanisms that appear to exist in, and are possibly used by, single neurons. There are fourteen of these, ranging from routing information via neuromodulators, through differing calcium concentrations in intra-cellular pockets, to molecular flip-flop in dendritic spines. Around half of the mechanisms appear to be analog rather than mainly digital. When looking for a Nagelian NMC, the analog mechanisms must be regarded as the front runners. Among these, varying calcium concentrations hold particularly attractive possibilities. They are dependent on synaptic activity (among other factors) and are therefore able to model preceding spike activity. However, other analog mechanisms are similar in this respect. The principle attraction of varying calcium concentration, when it comes to looking for a Nagelian NMC, can be seen in relation to the question of how the information content of consciousness might be encoded.

As Edelman and Tononi (2000) have emphasized, consciousness has two especially striking features that must enter into any adequate account of it. First, it handles information slowly and in small quantities relative to the huge amount that is processed by unconscious brain systems. The visual system for instance can and does transmit millions of bits of information per second, yet we can consciously handle at most only a few hundred of these. An up-to-date estimate by Nolte (2001), for instance, shows that the optic nerves transmit around 7 megabits per sec., while consciously reading, watching sign language, or patterns of illuminated light bulbs in an experimental set-up, typically handles around 25 bits per sec. (ie. 0.00035% of the information potentially available). When reading, of course, consciousness also contains a certain amount of non-verbal information, but not necessarily very much. Consciousness handles information slowly and in small quanities relative to the huge amount that is processed by unconscious brain systems Second, there exist huge numbers of uniquely distinguishable conscious mental states, many of which can be accessed almost instantaneously through memory. What can be inferred about a Nagelian NMC from these two facts? The limited information handling capacity suggests that the computational or modeling system involved is both slow and extensive so that there is not ‘room’ in the brain for many sub-components. The alternative, that it might be confined to a tiny area incapable of dealing with large amounts of information, is surely ruled out by the second feature. If the NMC were confined to a microscopic zone, it seems unlikely that it could possess such enormously varied content as it does.

Koch (1999, op cit.) listed the time scales on which his various computational systems might work. The range is from under a millisecond to over a second. Clearly mechanisms working on intermediate time scales are the more promising candidates for the underpinnings of consciousness because its characteristic time scale is of the order of 100 msecs. Changing calcium concentrations fill the bill here.

The need for a capability uniquely to specify a vast range of mental content within a single type of overall structure also constrains how NMCs can be pictured. Structures with the necessary capability include fractals, widely thought to be of possible importance in brain function (e.g. MacCormac and Stamenov, 1996), holograms, and a few less popular options such as knots (Nunn, 1996). Actually, in relation to the nuts and bolts of neurology, there is probably less difference between these structures than might be supposed. Because they are likely to be self-similar over a range of temporal and spatial scales, both holograms and knots (in the guise of braids, which are topologically equivalent to knots) will possess a fractal, or at least pseudo-fractal, structure. Since all three concepts can be expected to be roughly equivalent from a practical point of view, one is free to use whichever best fits the neurological context under consideration . In the case of patterns of changing calcium concentrations, which will show informationally significant interference effects, the most appropriate concept to use is that of holography. Pribram (2000) has of course been advocating for thirty-five years the idea that holography is a useful notion when it comes to understanding the brain and especially memory. It has to be admitted that his view is not particularly fashionable at present in neuroscientific circles, despite the close analogies that exist between the functioning of neural networks and dynamic optical holography (see Nolte, 2001 chapter 8, for a clear, non-technical account of these analogies). One reason for the lack of popularity of what would seem, on the face of it, to be an attractive notion may have lain in the difficulty of envisaging how holograms could be ‘recorded’ in the brain. Thanks to very recent research on a protein called CaMKII (calcium/calmodulin-dependent protein kinase II), there is no longer any such difficulty as the properties of the protein are such that it must inevitably record a particular type of hologram.

The essence of holography is recording information about phase relationships between waves. The essence of holography is recording information about phase relationships between waves. There is some ambiguity in the term ‘hologram’ as it can be used in three different senses. It may refer to the ‘image’ generated from a holographic record, or to the interference fringes that allow formation of holographic records, or to the records themselves. In what follows, holographic records will be referred to as such and the term ‘hologram’ will be used to refer to the actual waves and their interference effects. In the familiar optical holography, what happens is that a photographic film is more affected where light waves from different sources (typically those reflected from a scene and others from a ‘reference’ source) have constructively interfered and is less affected where they have destructively interfered. The film responds to more light by precipitating a greater density of granules. The image of the scene can later be recovered by illuminating the pattern of deposited granules with light having similar characteristics to that from the original ‘reference’ source. Holographic records also work the other way round in that, if re-illuminated with light reflected from the scene recorded, they will generate a replica of the ‘reference’ beam.

CaMKII, the properties of which have recently been reviewed by Lisman et al. (2002), provides an ideal recording medium for the phase relationships of calcium waves. ‘It’ is actually a family of related proteins with similar functional capacities, which constitute 1-2% of the total amount of protein in the brain. It is particularly associated with excitatory synapses and is thought to play a vital part in initiating and/or maintaining long term potentiation of the NMDA type of glutamine neurotransmission. There is good evidence that potentiation of this type underlies some forms of memory and learning. The protein may also activate the AMPA type of receptor, thus increasing sensitivity to relatively low frequency synaptic stimulation. The functional properties of the protein are remarkable. Basically, it responds to increasing calcium concentration by switching to an active form. As concentration increases, the time for which CaMKII remains in active form initially increases in a graded manner; eventually, however, a threshold is reached and it remains in active form indefinitely, regardless of the ambient calcium concentration. Of course proteins in the brain tend to have a short half-life and that of CaMKII is around one month. However there is evidence that, when replaced, the replacement adopts the same activation state as its predecessor. Memories of calcium concentration that are recorded in the protein may last indefinitely, though relatively short-lived records also form in relation to lower amplitude calcium waves.

Recall of declarative (i.e. conscious) memory would, according to this picture, involve re-creation of some appropriate subset of the spike activity associated with the original event, enabled by CaMKII-dependent alteration in synaptic weightings. The resurrected spike activity would be mapped into renewed calcium wave patterns, resulting in Nagelian consciousness and reinforcement of the CaMKII record. It is worth noting, however, that resurrecting spike activity can never be a wholly accurate process (because of the stochasticity of spikes), so the holographic record may undergo some alteration as a consequence of each recall.

Doubt and prediction

The picture of a possible Nagelian NMC that has been sketched out shows that varying patterns of calcium concentration analogically map spike activity, thus generating Nagelian consciousness. The patterns are recorded in alterations of activation of CaMKII, which in turn feed back to modulate future spike activity via changes in synaptic sensitivity. Because the altered enzyme activity must retain information about Astroglia are known to show whole-cell changes in calcicum concentration and to support the existence of calcium waves phase relationships between waves of varying calcium concentration, it can be regarded as a holographic record. Nagelian consciousness is thus seen to be intimately involved with memory (on all time scales, ranging from the very short term to the permanent), and to be efficacious in the sense that its structure can profoundly influence future brain activity. It is, in these respects, clearly consciousness as we know it. There is a problem with scale, however, which affects both this specific picture and would probably affect any alternative Nagelian NMC that might be proposed (because the Nagelian ‘models’ are extensive, holistic entities). The changes in calcium concentration considered hitherto are largely confined to the dendritic spines, on which nearly all excitatory synapses are situated. Consciousness, although it can occasionally appear to be determined by activity in single neurons, generally seems to involve extensive areas of the brain. Because holograms have a fractal-like structure up-scaling might be expected, but its occurrence requires the presence of some suitable physical substrate to support the relevant waves.

Changing calcium concentration is not entirely confined within dendritic spines (Hering and Sheng, 2001). These are highly dynamic structures; the actual calcium concentration and degree of confinement following synaptic activation depend on their shape. There is certainly scope for the occurrence of calcium waves on the scale of the entire dendritic tree of a single neuron. The situation with respect to even larger scales is more problematic. One could perhaps make up some story about waves spreading through dendritic plexi, either extracellularly or through gap junctions, but such a story is not convincing. In particular extensive diffusion would take too long to provide a plausible basis for consciousness. A more satisfactory account of spread is that it could be mediated via coupling between the diffuse electro-magnetic fields of the brain (to which calcium ion fluxes themselves make a small, direct contribution; their indirect contribution to these fields is greater) and voltage activated channels, some of which are responsive to voltage changes smaller than those associated with spike activity. The most obvious drawback to this proposal is that it adds an extra layer of analog computation, which might be regarded as an unwelcome complication. However, inordinate complexity does seem to be inherent in the nature of the brain, so the proposal may not be unrealistic. It is consistent with the evidence (e.g. McFadden, 2002) that some brain e-m fields appear to embody or ‘carry’ consciousness.

It also seems possible that astroglia could play an essential part in supporting up-scaling. They are known to show whole-cell changes in calcium concentration and to support the existence of calcium waves (Haydon, 2001). They are also known to be capable of reciprocally influencing synaptic function, while the spatio-temporal size distribution of inter-glial calcium waves follows a power law, i.e is fractal (Jung et al., 1998). Furthermore, these waves appear often to be initiated by activity of neuronal NMDA synapses (Harris-White et al., 1998). Astroglia are thus well suited to providing a medium to support the larger scales in the hierarchical structure of patterns of calcium activity, which would seem to be required if the picture of Nagelian consciousness is to be realistic. In their case, calcium wave spread between glia may partly depend on gap junctions, but also appears to be a consequence of sodium entry upsetting normal sodium/calcium exchange (Jung et al., 1998). The sodium entry itself may be mediated by some unknown chemical transmitter but it is possibly relevant, too, that tetrodotoxin, which blocks voltage gated sodium channels, abolishes single glia calcium oscillations and attenuates larger scale waves (Harris-White, 1998). This finding suggests that coupling between calcium waves in glia and diffuse e-m fields may occur. In summary, it seems that astroglia may well play an essential role in the generation of the type of Nagelian consciousness that is envisaged here. To quote Haydon (op. cit., p. 192) ‘Perhaps it is no coincidence that the ratio of glia to neurons increases through phylogeny. For example, the nematode . . . has about one glial cell for every five neurons, whereas the ratio in the human brain is thought to be at least ten glia per neuron’.

Patterns on the largest scales (temporal, spatial, or both) might in principle be viewed via magnetic resonance imaging (MRI) suitably tuned to pick up some close correlate of calcium concentration . The obvious prediction to be made here is that any such patterns should show closer correlations with particular conscious events than the correlations found between those events and MRIs of other brain components. Another prediction, much harder to test, is that any MRI ‘calcium’ patterns should be found to be fractally related to similar calcium patterns on smaller scales detected by other means, for example multi-photon calcium imaging (e.g. Euler et al., 2002). Evidently the theory would be refuted by failure to find such relationships.

If a Nagelian candidate for the NMC were to prove capable of passing basic neurological tests, such as MRI based ones, the next step required would be provision of an account of how the NMC might be orchestrated by arousal and attention. If things ever get as far as this, it is likely that global workspace theory (e.g. Baars and McGovern, 1996) will be found to play an essential part in the account. In view of the reciprocality noted earlier between holograms and fractals, Bieberich’s (2002) description of how a fractal neural anatomy might provide the basis for a suitably flexible workspace could prove especially relevant. Should it pass this next hurdle, the Nagelian theory would then face the still greater challenge of explaining why conscious contents take the form that they do. Why is red usually experienced as red, for example, and not as the sound of a bell? After all, the phenomenon of synaesthesia shows that colour can occasionally be experienced as sound. The seed of an answer to this question may lie buried within an understanding of what it is to be a hologram, but trying to cultivate the seed at this stage would clearly be premature.

Footnotes

1. There seem to be two implied definitions of what constitutes analog computation in current usage. The stronger, to which Mulhauser (1998) adheres, refers to computational systems which can deal with irrational numbers without having to resort to approximation. Systems capable of such computation include slide rules (though only in principle, not in practice), and ones involving smooth electrical or chemical gradients. Another, weaker, definition might roughly be stated as ‘computation which is linear and smooth for all practical purposes’. Hahnloser et al. (2000) may implicitly have used this definition in a paper entitled ‘Digital selection and analogue amplification co-exist in a cortex-inspired silicon circuit’. It is not clear from their paper whether the outputs of the individual ‘neurons’ in their circuit modeled the action potentials of real neurons by coming in discrete packages, though their ‘neurons’ were recruited to contribute to the output of the system as indivisible units. If the individual ‘neuron’ outputs did model spikes, their system could not have been analog in the stronger sense. It appears, therefore, either that their ‘analog amplification’ corresponded with the stronger definition but their circuit was not like a neural circuit involving all-or-nothing action potentials, or their definition of ‘analog’ fitted the weaker version only, i.e. not the definition regarded as relevant to the argument in this paper. In other words, they either used the weaker definition of ‘analog’ or else their paper was relevant, not to neurons in their aspect as spike producers, but to dendritic plexi, say, in which smooth electrical and chemical gradients do occur.
2. There may also be formal equivalences between these various notions. For example knots are best described mathematically by means of polynomials, while MacLennan (1999) remarks that there are ‘field polynomials’ expressing a series of products between input fields and fixed, co-efficient fields, which are thus holographic. See Psaltis et al., 1990, or Reiter, 1994, on the other hand, for discussion of overlap between fractals and holograms. They remarked that fractals can be transformed into holographic records that are themselves fractal.
3. Ionized calcium is likely to have a different MR ‘signature’ from the mainly mineralized calcium in the skull, which would otherwise swamp any ionized calcium signal from the brain. Even so, calcium itself would probably be technically difficult to image. Given that the current fMRI BOLD signature depends on detecting relatively small increases in the concentration of oxygenated versus unoxygenated haemoglobin, it seems not impossible that it might prove technically feasible to detect relative concentrations of calcium/calmodulin complexes versus calmodulin alone, or even changes in the activation state of CaMKII itself.

© 2003, C.M.H. Nunn

C.M.H. Nunn M.D. F.R.C.Psych.,

chrisnunn@compuserve.com

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Acknowledgements

I am most grateful to many people, especially to Erhard Bieberich, Stan Klein and Sue Pockett, for much patient discussion of topics touched on in this paper.