Consciousness: From Unity to Diversity to Unity

We read in the book A Universe of Consciousness by Edelman and Tononi as intro to Chapter 3: Everyman's Private Theatre: Ongoing Unity, Endless Variety:

• Our strategy for explaining the neural basis of consciousness is to focus on the properties of conscious experience that are the most general, that is, that are shared by every conscious state. 
• One of the most important of these properties is integration or unity. Integration refers to the fact that a conscious state cannot be subdivided at any one time into independent components by its experiencer. This property is related to our inability consciously to do more than two things at once, such as adding up a check while carrying on a heated argument. 
• Another key, and apparently contrastive, property of conscious experience is its extraordinary differentiation or informativeness: At any moment, one out of billions of possible conscious states can be selected in a fraction of a second. We thus have the apparent paradox that unity embeds complexity—the brain must deal with plethora without losing its unity or coherence. Our task is to show how it does so.

We learn that unity and differentiation are (apparently contrastive) important aspects of consciousness. 

We find precisely these aspects in the connection between gravitational potential $\phi (x,t)$ and mass density $\rho (x,t)$ as the basic relation of Neo-Newtonian Cosmology in mathematical terms expressed as follows, with $x$ a Euclidean space variable and $t$ a time variable:

• $\Delta\phi (x,t)=\rho (x,t)$     for all $x$ and $t$         (1)
• $\rho (x,t) := \Delta\phi (x,t)$  for all $x$ and $t$        (2)

where $\Delta$ is the Laplacian differential operator acting on the space variable $x$ and $:=$ is computer code for assignment. We thus express the connection between $\phi$ and $\rho$ in two different forms: 

In (1) $\phi (x,t)$ appears as a global solution for all $x$ and given $t$ of the Poisson-Laplace equation $\Delta\phi =\rho$ with $\rho$ given, which can be expressed as an integral over all of space:

• $\phi (x,t) =-\frac{1}{4\pi}\int\frac{\rho (y,t)}{\vert x-y\vert}dy$       (3)

In (2) $\rho (x)$ for a given $x$ is assigned the value $\Delta\phi (x)$ involving given local values of $\phi (y)$ for $y$ close to $x$. 

We understand that (1) represents a global summation process as integration, while (2) is a local process of extraordinary differentiation or informativeness. 

We thus find a mind-body relation in terms of $\phi$-$\rho$ expressed in (1) + (2) with $\phi$ representing global unity/mind/logos and $\rho$ local diversity/body/spirit. 

With the same $t$ on both sides in (3) formally requires instant action at distance, but since the kernel $\frac{1}{\vert x-y\vert}$ in (3) is quickly decaying with increasing $\vert y\vert$, instant action at distance is not required. In other words, (1) can be slow, while (2) as local process can be fast and must be to fit observation. 

Altogether, we see that the general features of consciousness presented by Edelman and Tononi, can be expressed in precise mathematical form in a cosmology context. 

Unity of consciousness restricts attention to only one thing at the same time, which can be seen as a limitation of performing (1) + (2) for only one mass density distribution/thing at a time, because of limited processing brain power.   

Incompressible Turbulent Fluid Mechanics vs Mind-Body

     Da Vinci contemplating incompressible fluid flow to solve the hard problem of consciousness.

Recall the previous post and the basic model of Neo-Newtonian Cosmology in terms of gravitational potential $\phi$ as primordial, mass density $\rho$, momentum $m$ and $u=\frac{m}{\rho}$ material velocity all depending on a Euclidean space coordinate $x$ and time coordinate $t$ with the dot on top representing differentiation with respect to time, as a model describing all of celestial mechanics:

• $\rho = \Delta\phi$                                    (inverse square law in differential form)
• $\dot\rho +\nabla\cdot m=0$                       (conservation of mass)
• $\dot m +\nabla\cdot (um)+\rho\nabla\phi=0$    (conservation of momentum: Newton's 2nd Law)  

We compare with the basic model of all of (inviscid) incompressible turbulent fluid flow as Euler's equations:

• $\nabla\cdot u=0$                                        (incompressibility)
• $\dot\rho +\nabla\cdot m=0$                       (conservation of mass)
• $\dot m +\nabla\cdot (um)+\nabla p=0$    (conservation of momentum: Newton's 2nd Law)  

where $p$ is pressure. Here incompressibility is imposed as a stipulation rather than law of physics, which can be realised through the physical law:

• $\Delta p = -C\nabla\cdot u$                        (pressure law)

where $C$ is a large positive constant forcing $\nabla\cdot u$ to be small. We see that pressure $p$ and gravitational potential $\phi$ serve similar roles in Newton's 2nd Law steering the dynamics, and that both appear as solutions to a Poisson equation with infinite speed of propagation of effects from source to solution. We see that the pressure has the double role to drive the flow while securing incompressibility.  

We thus see that both $p$ and $\phi$ act as omnipresent immaterial controls of dynamics with instant connection to a whole material universe, as solutions to Poisson's equation with source of material form, thus as connection immaterial-material or mind-body in the setting of consciousness in recent posts.

Gravitational Potential - Matter vs Mind - Body

This is a continuation of previous posts on the mind-body problem of consciousness.

In Neo-Newtonian Cosmology the gravitational potential $\phi (x,t)$ is immaterial, omnipresent and primordial assigning mass density $\rho (x,t)$ to matter by the action of the Laplacian differential operator $\Delta$ acting without delay on the Euclidean space coordinate $x$ for all time $t$:

• $\rho (x,t) = \Delta\phi (x,t)$              (1)

Immaterial potential thus meets material mass density in (1) as instant top-down local assignment. Material matter moves by gravitational force field $\nabla\phi$ according to Newtons laws of motion

• $\dot u = -\nabla\phi$            (2a)
• $\dot x =u$,                                        (2b)

where $u$ is material velocity, $x$ is position and the dot signifies differentiation with respect to time. There is also a feed back from mass density distribution $\rho$ to gravitational potential as solution of the equation $\Delta\phi =\rho$ as a slow bottom-up global process. 

We can find a parallel as connection between an immaterial omnipresent mind/soul and material body of a human being. The mind top-down assigns meaning/life to all the cells making up the body. There is also a bottom-up process giving sensory feed back from the body to the mind. The mind is then different from the material brain and embraces the whole body like the gravitational field embraces the Universe. 

The material brain would serve a crucial role of processing sensory input in an analog of (2) into planning and action, but the mind would stretch outside the brain.

It thus seems possible to relate ideas about morphic fields presented by Rupert Sheldrake to physics as a synthesis of immaterial and material or mind and body.  

It is natural to compare with Leibniz idea of pre-established harmony as a form of parallelism between gravitational potential and mass density in the form $\Delta\phi =\rho$, where neither $\phi$ nor $\rho$ has clear primordial priority. They just go together in a perfect way without discussion. The above argument can accommodate also Leibniz view.    

Picasso and His Model: Feelings

Let us see if the relation between Picasso/Painter and his Model can tell us something about the nature of consciousness, connecting to the previous post with a brain model of the exterior world as central concept (cf Nobel Prize in Medicine 2014).

We see Picasso looking at the Model to make a Painting or model of the Model on the canvas, which we can assume agrees more or less with some form of mental model in Picasso's brain. We see Picasso watching both the Model and the Painting to see if they agree and if not update the Painting. 

We see that Picasso is very aware about the whole situation with his mind switching between  (i) looking at the Model, (ii) looking at the Painting, (iii) making a comparison by projecting the Painting on the Model and (iv) deciding next brush.  

Here (i) and (ii) connect to direct perception, while (iii) seem to depend on some higher level evaluation and (iv) represents action after evaluation. 

More generally, we may think of watching a Landscape as making a model landscape in the brain which is projected on the Landscape and updated until fit, to make us experience the Landscape as something real outside us and not its brain model.

The brain model of your body is projected back onto the body, so that you experience the pain from a wound at its physical location and not in brain. This makes it possible to experience pain in a limb, even if the limb has been amputated, thus as a phantom limb.

Where does consciousness come in? Well, of course in the form of awareness as readiness to input from (i) and (ii) but also in the evaluation (iii) and action (iv). 

What is missing, as the so called hard problem of consciousness, is here Picasso's feelings for both Model and Painting. Picasso may be in love with Model (pleasure) but may not be happy yet with the Painting (pain) and this in not captured in (i)-(iv). 

Does it matter? Probably so, because this is gives Picasso motivation to decide to paint the Model and then actually do it under pain to eventually reach a state of pleasure with a finished Painting. 

Of course, motivation is central to get anything done and so may be an important aspect of consciousness as a goal and road to reach the goal. This seems to connect to self-consciousness offering a mental model where the capacities of the Self can be tested to set goals.

A robot painter with AI can be envisioned to carry out (i)-(iv) in a mechanical way and then without the burden of feelings, which often appear as bodily sensations even if not coming from the body, like love or fear felt in your breast. 

Ultimately, we may connect feelings to (early) sensory input of pleasure and pain, which would serve as basis for motivation to reach pleasure. This is something a robot would miss and so the goal for a robot would have to be set by some consciousness equipped with feelings setting the goals for the robot. 

Is it possible to equip a robot with feelings?

 

What is Consciousness?

The present hype of AI brings up questions about consciousness:

• Does ChatGPT express some form of consciousness?
• What are basic features of consciousness?
• What is the connecting to intelligence?  

A simple intuitive idea of consciousness of an organism might include, all for best survival: 

1. model of the external world formed in the brain and projected onto the world
2. updated by sensory organs and kept in a memory
3. guiding actions 
4. to reach certain goals
5. in a variable environment
6. self-consciousness allowing self-evaluation.

If the goals are reached one could say that the organism has some form of intelligence. The organism could be biological from flatworm to human being or some mechanical robot with AI. 

The model would be used to predict changes in the environment requiring actions by the organism. The prediction would involve testing different actions in the model as simulations and choosing the best to meet the goal.

A self-driving car continuously updates a 3d model of a variable environment and takes actions to reach a certain destination and so may be viewed to fulfil 1-5, while a human being would also meet 6.  ChatGPT would come near only to 1. 

A goal of seeking pleasure rather than pain would require sensory organs allowing the organism to feel pleasure and pain. This is not so far possible for mechanical robots (as far as we know), but maybe flatworms can. Pain is experienced in the brain and projected to the perceived origin of sensory input. 

One may ask if self-consciousness is a cultural phenomenon, which is not fundamental in primitive cultures where group-consciousness may be more useful? Maybe Greek gods served as some form of exterior self-consciousness.

Can Protein Folding be Computed?

Protein folding is a spontaneous process where a given unique string of amino acids folds itself in a solvent (water) into a macromolecule of unique 3d geometry, guided by 

• formation of hydrogen bonds
• hydrophobic interactions
• van der Waals forces. 

Modern physics in the form of quantum mechanics comes with the message that protein folding as a form of molecular dynamics can be described by a Schrödinger Equation SE modeling a collection of atomic kernels held together by a collection of electrons. 

Computing solutions over time of SE starting with a given string would then produce a simulation of the folding process allowing the folded protein to be predicted from given string, and so also reversely a string to be predicted from given folded geometry. This would be immensely helpful for understanding of biological processes and drug design. 

But there is big problem with such a grand scheme: Computational solution of SE is impossible because the work grows exponentially with the number of electrons and so is beyond the capacity of thinkable computers already for 10 electrons, while the true number may be 100.000.  The reason is that SE involves $3N$ spatial dimensions for $N$ electrons. 

Modern physics/chemistry thus has nothing to deliver as concerns computational protein folding, which is illustrated by the fact that the 2014 Nobel Prize in Chemistry was awarded to Artificial Intelligence AI for protein folding trained on large experimental data sets without use of SE theory. 

Instead of letting AI take over completely, let us give human intelligence another chance and ask if maybe there is some other mathematical model than SE that can describe the folding?

And yes, there is a candidate in the form of a different atomic model named Real Quantum Mechanics RealQM in the spirit of Schrödinger as system of non-overlapping electronic charge densities in 3d space geared Coulombic interaction, for which the computational work grows linearly with the number of electrons. 

So there we are: It may be that protein folding is computable by RealQM. The computational process proceeds in time where for a given configuration of atom kernels and electronic charge distributions in 3d, a new configuration is computed from Coulombic interactions through electric potentials, with work scaling with  number of electrons. 

RealQM connects to ad hoc simplified versions SE based on Electron Orbitals or Density Functional Theory, but RealQM is fundamentally different since it is based on a new single principle of non-overlapping charge densities in a parameter-free model. 

You find laptop computations with RealQM for atoms and molecules on RealQM and on this blog under tags RealQM and Real Quantum Chemistry including computer codes essentially consisting of three lines for update of kernel positions, charge densities and potentials.  

Who will do the first RealQM simulation of protein folding?

Recall that the crisis of modern physics is the result of not delivering anything new, in particular nothing for protein folding. We have identified the non-computability of SE as the big trouble. But this is just one aspect of the basic troubling aspect of SE namely that it is a non-physical model for which no convincing physical interpretation has been found despite intense efforts by thousands of highly intelligent physicists ever since the formulation of SE was made 100 years ago. 

The attractive aspect of SE is that it is quick to formulate, allowing physicists to speak with loud voice about wave functions denoted by $\Psi$ as solutions to SE, while covering up that they are uncomputable and lack physical meaning. 

The result is that today the foundation of quantum mechanics is no longer a topic of study at physics departments, and is only pursued by some isolated enthusiast philosophers at philosophy departments. This is clearly not an optimal situation. 

There is no reason for atomic physics models to lack physical meaning nor computability.

Can You Feel that Somebody is Looking at You?

This is a continuation of the previous post connecting to the possibility that our minds are field-like and extend beyond our brains and can have effects beyond our brains put forward by Rupert Sheldrake, a very heretical thought from the point of view of conventional science. 

Sheldrake recalls that children up to age 10-11 years spontaneously believe in visual extramission included in two-way transfer between object and eye. That's why Roald's Dahls Mathilda has eye beams that come out her that can move things (cf Superman and X-men). Children love that because that's the way they think vision works. 

But in school children learn that this is not possible because there is a one-way stream of photons from the object entering into the eye and creating an image in the brain without feed-back to the object. And so this is what educated people in the West believe, and what Sheldrake questions and so get critiqued. 

Two-way transfer object-eye directly connects to a new view of heat transfer between objects by radiation presented as Computational Blackbody Radiation CBB.

To see this let us replace object-eye connected by light as electromagnetic wave, with two bodies B1 and B2 of temperature T1 and T2 radiatively connected by electromagnetic waves. CBB describes how heat energy is transferred from B1 to B2 if T1 > T2 by a phenomenon of resonance between B1 and B2 carried by standing electromagnetic waves as a two-way connection between B1 and B2 like a vibrating rope between the bodies. 

The fact that heat transfer is one-way from B1 to B2 comes from the presence of high-frequency cut-off increasing with temperature, which makes frequencies carried by B1 above the cut-off frequency of B2 cause heating of B2, while shared frequencies does not involve heat transfer. Here B1 serves as the object and B2 as the eye. 

There is then main transfer of heat energy from object to eye, as in the conventional view as a stream of photons as light particles, but object and eye are connected by standing electromagnetic waves. With a two-way connection it is not unthinkable that the object can somehow feel (very weakly) the presence of the observing eye, while this is impossible with one-way stream of light particles.  

Two-way connection by standing electromagnetic waves is captured in Maxwell's equations, while the physics of a stream of light particles is missing. 

The conventional view is that knowledge is transferred one-way from scientists to unschooled, but a true scientist can learn from anything. 

Two-way connection by standing electromagnetic waves relates to a holistic view of things as being interconnected, as opposed to a classical reductionistic view separating things. Today we are all connected through a two-way web.  

Morphogenesis by Resonance

                                                       Patterns formed by resonance?

The book Morphic Resonance by Rupert Sheldrake addresses the fundamental problem of how organised structures are formed in physics, chemistry, biology from elementary building blocks seemingly without information about the overall structure. How does a flower, bird or human being develop from a genetic code, which contains recipes for protein building blocks but no information about the whole structure? Sheldrake seeks an answer in the form of morphogenetic fields carrying this information as collective resonance phenomena. 

We are familiar with resonance in physics as the wave harmonics of a vibrating string. We understand that wave patterns develop from instabilities with tendency to increase crests and troughs of certain wave lengths. Watch dropping a stone in a pond.

Thus we expect to see form develop from resonance serving as morphogenesis and find this in particular in the case of fluid flow with turbulent vortices developing from convective instabilities as shown in Computational Turbulent Incompressible Flow. 

The non-radiating stable ground state of an atom is represented by the lowest harmonic of a Schrödinger wave equation, while higher harmonics are triggered for a radiating atom. Real Quantum Mechanics gives a new explanation of the lack of radiation from the ground state, as the mystery Bohr struggled with. 

Computational Black Body Radiation presents a new analysis of the transfer of energy from a source of light to a receiver as an atomic resonance phenomenon carried by standing electromagnetic waves without need to introduce photons as particles of light. A similar transfer is seen between two tuning forks carried by standing acoustic waves. 

Sheldrake's concept of morphic resonance thus comes to expression in physics and may serve also in chemistry and biology in more general forms. Maybe memory is carried by resonance... Maybe the fertilised egg carries the blueprint as a resonance bringing the genetic code to life.

Musical harmony is based on tonal resonance, while musical rhythm represent patterns over time. Singing in a choir unites single souls into one. 

Resonance can have the material form of vibrating strings, or immaterial as a common gravitational potential (recall Neo-Newtonian Cosmology) or more generally beliefs forming a society. An immense subject…

Resonance appears as an expression of instability of a system in the sense that a small periodic forcing causes large oscillations in the system. This happens if the periodicity of the forcing agrees with an eigenvalue of the system and the corresponding eigenfunction represents the shape of the system response.  This allows patterns to develop from small forcing in creation of form as morphogenesis "by itself".

Gravitational Potential: Primordial Omnipresent Immaterial

This is a further reflection on Neo-Newtonian Cosmology expanding on the PS in the previous post on the work by Rupert Sheldrake on morphogenesis geared by immaterial presence.

The basic idea is that primordial omnipresent immaterial gravitational potential $\phi$ has been created from an infinitesimal fluctuation of a zero potential from which mass density $\rho$ emerges by the action of the Laplace differential operator $\Delta$:

• $\rho =\Delta\phi$    (*)   

inflating fluctuations into substantial mass density of variable sign. The gravitational potential assigns mass to material matter consisting of positive and negative electric charge densities emerging from an electric potential as in (*). 

The action of gravitational force separates matter into larger regions of substantial positive and negative mass, which repel each other as if subject to dark energy, with some part of $\Delta\phi$ appearing as immaterial dark mass. Further, gravitational collapse of regions of positive mass generates massive kinetic energy as vacuum energy. 

Altogether, structures as planetary systems and galaxies emerge from an omnipresent gravitational potential acting as immaterial organiser by assigning mass to matter in a form of cosmological morphogenesis. Here informations is directed from potential to mass density, which is the opposite of the current paradigm: 

• Each atom attracts all other atoms in the Universe with short time delay.   (**)     

With (*) as primary process, (**) appears as a secondary slow process. 

The main trouble with (**) is that the physics of the connection/attraction between atoms has no answer. The current idea of some form of particles carrying attractive force between all atoms in the Universe has not been fruitful. It remains to see if (*) is more fruitful. In particular (*) is local and as such can be instant without assistance of force carrying particles.

Connecting to the 2024 Nobel Prize in Chemistry on protein folding, it may be that the total electric potential of a protein, like the total gravitational potential, acts as an organiser of the morphogenesis of the folding. See this post with connection to Real Quantum Mechanics.

 

Vacuum Energy from Fabric of 3d Euclidean Space

The Head of Theoretical Physics at Cern Gian Guidice presents an idea of Big Bang powered by energy stored in the "fabric of space and time" as "vacuum energy", in an interview about the question "What happened before the Big Bang"?

This connects to the Neo-Newtonian Cosmology presented in previous posts starting from a small oscillating perturbation $\phi$ of a zero gravitational potential $\Phi = 0$, which creates mass density $\rho$ of variable sign through the action of the Laplace differential operator $\Delta$ on $\phi$ as

• $\rho =\Delta\phi$    (*)   

The action of differentiation inflates small oscillations of $\phi$ around zero into large oscillations of mass density of variable sign. By the action of gravitation mass separates into larger regions of positive and negative mass, which repel each other as if subject to dark energy, with small positive $\Delta\phi$ appearing as dark matter. Further, gravitational collapse of regions of positive mass generates massive kinetic energy seemingly out of nothing as vacuum energy.

The action of the Laplacian $\Delta$ in the equation $\rho =\Delta\phi$ thus offers explanations of (i) vacuum energy, (ii) dark energy and (iii) dark matter,  as an expression of the "fabric of 3d Euclidean space". If true, simplicity shows to be more powerful than the complexity of the current state of the art.

PS Matter made up electrons and protons appears as an analog to (*) with $\phi$ electric potential and $\rho$ charge density of variable sign, which form atoms and molecules into structures of matter as the material world endowed with mass from the gravitational potential. This leaves open the possibility that part of the gravitational potential remains to create dark mass according to (*) without material form. This connects to speculations by in particular Rupert Sheldrake.