Abstract: The complex dimension has two axes: horizontal complexion —our classic systems of interacting elements and their models— and vertical complexion —overlapping systems, an elementary constituting a superior. A ‘platist’ trend sees this vertical axis as an illusion. I show that it is in fact a dualistic dead end excluding our mind. The metaphor of the two-sided piece structures the vertical complexion: one side is a multiple constitution, the other is a fusional property. The reality of this vertical complexion, in mathematical models, is hidden in the sign ‘=’, which often means ‘correlated to’ rather than ‘identical to’. The vertical complexion will lead us to understand how neural networks form consciousness.
We have seen the summary of How to solve the mind-body problem, its criticisms, specified the level of explanation required by the solution, affirmed the need to preserve the opposition of physicalist and phenomenological views because both are realistic. Nevertheless, we demanded the obligation of a unified reality and showed the interest of applying to it a new dimensional variety, the complex dimension, endowed with two axes:
Classic horizontal models
The horizontal axis is the one we know best. These are the systems of elements that recognize each other and create a set of relationships within a context. This context is not a universal backdrop. By defining their system together, the elements also define what is not the system. They participate in determining the context. They surimpose their framework on the pre-existing context that constituted them. System of elements and context are accessible to a model, that is to say a mimetic information structure of the system, codified by our neural networks.
Each system in its context thus becomes a small independent world in our minds. Relative independence of course, since strongly entangled with other models. Is this independence purely a property of our mental representation or is it also the property of reality? In other words, in the absence of the human and their minds, does independence disappear from reality or does it appear to other entities, including those without neurons? That is one of the issues we need to resolve.
The vertical axis of the complex dimension assumes that we have answered the question frankly. Independence must be a property of reality per se. The vertical axis can then “take off” the complexity by formalizing the tiered sequence created by the relative independence of the systems. A pyramid of reality levels appears.
What it means to renounce complex verticality
Without this axis, the models are all illusory. Their independence is only that of a reflection of reality, a reflection belonging to our mind, while reality per se is monolithic, a vast monobloc system, purely horizontal in terms of complexity, content to take on pseudo-staged aspects . Aspects only apparent to our mind. Illusion of verticality.
Unfortunately, this denial of a vertical axis locks us, as we have already seen, into an insoluble dualism. If illusion is not part of reality, neither is our mind. Our representations stand in another continuum totally independent of that of reality, Plato’s “world of ideals”, and we have no idea how to relate it to reality. One of our mandatory assumptions, keeping a unified reality, is not satisfied.
I will therefore maintain the two axes of our complex dimension, which I call ‘horizontal complexion’ and ‘vertical complexion’, with the reservation that at this point in my investigation I have no model for vertical complexion. Knowledge does not lack horizontal models, stored in the drawers of its disciplines; but it does not yet have a vertical model, a metaknowledge of itself. Neither the idealist look nor the materialist possess any, since they are content to reduce reality under the eye of a hypothetical divine spirit or that of a hypothetical physical foundation. To find a metaknowledge is first to consider reality as suspended between these two looks, waiting for them to coincide.
In the interface
The coin is an excellent metaphor for our level of reality, with its multiple constitution on one side, its fusional properties on the other. The pieces can be spread on the table by the horizontal look. The systems appear separate, easier to model. The pieces are distributed to their respective scientific disciplines. To reconstruct reality, however, is not to keep these pieces next to each other but to stack them and see if the scaffolding stands. For this the parts must adjust. The underside/constitution of one must match perfectly with the upperside/properties of the other. In this interface takes place the horizontal dimension of the system. The process explores and stops on stabilities. Stabilities are the building blocks of the upper piece.
The coin did not solve all our problems. What happens within the coin is not explained. Why does it show two foreign sides? It is here that the problem of consciousness declared “hard” by Chalmers arises: why does this physical constitution produce such a property, such a experienced phenomenon? How do the elements generate a flavor they are unable to perceive? In what independent is this perception located? The soul is the ancient answer by default, followed more recently by the homunculus of philosophers. But if we deny them reality, what do we put in their place to play the role?
A problem that is also that of matter
We have made a significant step forward, however. The problem is within the coin and the coin… there are a multitude of them. It is no longer an isolated affair at the neuron-thought interface. The problem can be generalized to the whole complex dimension, the totality of reality itself.
Let’s not be too quick to say that the problem has disappeared from matter because physicists have established a continuous causality between micro and macro. This continuity is mathematical, and many things are hidden in a sign ‘=’. It sometimes means ‘identical to’, sometimes ‘replaces’, sometimes ‘adds’, sometimes ‘correlated to’. Very different meanings that hide qualitative leaps in reality. Let us quote the famous Boltzmann formula: S = k ln W. The entropy S of the macroscopic is proportional to the logarithm of the number of configurations W of the microscopic. This sign ‘=’ contains a true qualitative emergence, while the simple quantitative identity 1 + 1 = 2 contains none.
Frames change around the ‘=’ sign
Declaring identical elements on either side of the ‘=’ sign is only possible if they belong to identical frames. But as soon as we involve complexity the framework subtly changes and ‘identity’ becomes ‘correlation’.
Since microscopic levels are made of very similar elements, they respond precisely to mathematical models. It is then possible to establish close correlations between material levels of reality. Their borders seem to be fading. A good model at the base is credited with an unlimited bottom-up “reach”. Let us restrain this enthusiasm. Some levels create their own information, be it quantum entanglement, topological classes, phase transitions and other symmetry breaks.
Of course, we must also talk about neurons, which integrate their information to build an impressive height of complexity. Their virtual vertical complexion is much more impressive than that of their material constitution. This gives us a glimpse of the spectacular nature of the resulting phenomenon: consciousness.
Huge vertical outlet
The extraordinary opening of complex verticality in the brain has immediate consequences on the neural-mental problem. The sign ‘=’ in neural=mental would then hide a considerable number of levels of complexity crossed discreetly, explaining the abysmal difference between the phenomena associated with the activation of the first neural groups and their whole.
For example, the excitation of 1st rank neurons by photons hitting the retina does not produce any consciousness of the ‘multiple points of light’ type in my mind. While the same signals reaching the top, in the global workspace, become ‘my beloved companion in a white dress crossing the living room’. In between, a network of physically identical neurons, which distorts our perspective. Because the height of vertical complexion traveled is enormous.
The mind is too amazed at its complexity to make good representations of it
Why hasn’t this assumption already won everyone’s mind, given its power of explanation? As we have said, it is still necessary that the mind has adopted all the dimensions necessary to represent itself in this way. Nicholas Humphrey, who is not an eliminativist, writes in ‘How to solve the mind-body problem’ this passage on neural=mental identity:
“If it is suggested for example that Mark Twain and Samuel Clemens are identical, Mark Twain = Samuel Clemens, we can believe it because both sides of the equation are in fact people. Or, if it is suggested that Midsummer Day and 21st June are identical, Midsummer Day = 21st June, we can believe it because both sides are days of the year. But were someone to suggest that Mark Twain and Midsummer Day are identical, Mark Twain = Midsummer Day, we should know immediately this equation is a false one.
Now, to return to the mind-brain identity: when the proposal is that a certain mental state is identical to a certain brain state, mental state, m = brain state, b, the question is: do the dimensions of the two sides match?
The answer surely is, Yes, sometimes they do, or at any rate they can be made to. Provided cognitive science delivers on its promise, it should soon be possible to characterize many mental states in computational or functional terms, i.e. in terms of rules connecting inputs to outputs. But brain states too can relatively easily be described in these same terms. So it should then be quite straightforward, in principle, to get the two sides of the equation to line up.”
The two examples chosen by Humphrey, ‘Mark Twain = Samuel Clemens’ and ‘Midsummer Day = June 21’, are not equalities but contextual approximations. The contexts in which they are verified are respectively ‘Is the marital status of these people identical?’ and ‘Is the day of the year the same?’. In most other contexts, these ties are false. Twain appeared long after Clemens, the mental configuration of Twain writing is not the same as that of Clemens going about other business, etc. Similarly, ‘Midsummer Day’ contains a great wealth of information about traditions, postmarked in ’21 June’.
The mind needs to approximate
These examples are valuable for two reasons: on the one hand, they explain why Humphrey takes his solution of the mind-body problem into a dead end; on the other hand, they point to the importance of approximation as a useful reduction to the mind, and its invisibility to consciousness. Major clue for the real solution of the problem.
Humphrey expresses himself as if vertical complexion did not exist, or at least as if it could be reduced, “flattened”, and reproduced by computation, which makes it disappear from reality to leave only the neural states. It adopts the common but pernicious dualism that is that of the real vs. virtual. Neurons would be a level of concrete reality, but not their representations, purely virtual productions. Another expression of the dualism between neural phenomenon and mental epiphenomenon. The metabolic activity of neurons is a physical reality, not the concepts they build, not independently at least. But then, is metabolism itself a reality independent of molecular processes?
An untenable dualism
This dualism is pernicious because it would lead to say that the neural is an epiphenomenon of cellular organelles, the organelles of their biomolecules, etc., to the point of making the whole of reality an illusion built on a foundation… hypothetical.
Renouncing the real-virtual dualism implies granting mental representations the same status of reality as neural metabolism, that is, that of entangled levels of information producing both a substantial appearance and a function for the context that observes them. This approach must curb the desire to reduce the mind to neurons as must be restrained the desire to reduce neurons to their quantons. By surrendering ourselves to one or the other of these desires, we no longer understand anything about the function of the complex entity or the experience it provides.
How do you physically go from a basic concept to a complex one?
To what to add these obligatory levels of information that must be concretized to obtain the mind? They settle not on individual neurons but on their networks. The neuron is an electrochemical powerhouse that, in isolation, builds no more meaning than a Morse manipulator without a translator. A concept is physically the synchronous activity of a neural group, an integrated electrochemical activity. But how do you go from a basic concept to a complex? Some neural groups symbolize luminous features on the retina, others make it the face of an intimate person, with all the procession of emotions and memories that accompany it. Physiologically these neural groups are almost identical. Writing ‘neural=mental’ indifferently for all groups is a dramatic shortcut. Obviously a very different reality separates them. What is it?
The next article takes us to a simulation of neural complexity: artificial intelligence.