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.