Hans-Joachim Rudolph: 

Dan, you say "... thinking involves the real world, it is not something which is contained in the head, so if there were an interaction which thinking is, it would be an interaction between people and the world" and elsewhere you write: "I am experiencing ... things, and not representations of these things in a mind located in my brain bounded by my skull. My mental activities are dispersed in the world that I am involved in" and you quote: "might the "mind", if we do allow it a place in our vocabulary, be less bounded than the brain inside the skull".

Basically, this approach has been brought forward in Andy Clark and David Chalmers' seminal work "The Extended Mind" (1998), where they present the idea of active externalism (similar to semantic or "content" externalism), in which objects within the environment function as a part of the mind, isn't it? They argue that it is arbitrary to say that the mind is contained only within the boundaries of the skull.

Moreover, they opine that the separation between the mind, the body, and the environment should be seen as an unprincipled distinction. Because external objects play a significant role in aiding cognitive processes, the mind and the environment act as a "coupled system". This coupled system can be seen as a complete cognitive system of its own. In this manner, the mind is extended into the external world. Their main criterion for classifying the use of external objects during cognitive tasks as a part of an extended cognitive system is, however, that the external objects must function with the same purpose as the internal processes! But this is something which you didn't mention: Internal processes and external objects must be ruled by the same causa finalis. So, suppose, two persons have different intentions about an object: Their realities obviously overlap in that object. Nevertheless, the object itself has, if at all, an own destination. Finally, you are ending in dualism.

Dan Hetherington: 

Hans-Joachim - Yes, that's right. It is very much like the Extended Mind Hypothesis. I'm just drawing from sources other than Clark and Chalmers who spoke of the issue in other terms, well before Clark and Chalmers wrote their paper. You can also see a similar view in Phenomenology. "The Extended Mind" comes across as a pretty radical idea, but it had humble origins. Putnam's "The Meaning of 'Meaning'" is a fairly early discussion of Semantic Externalism (1975), and contains the "Twin Earth Thought Experiment" I mentioned. There is also a similar notion in early forms of Enactivism. O'Regan, who is a perceptual psychologist specializing in vision, speaks of vision as not being located within the brain, but between the perceiving organism and the object of perception as an interaction. What these positions share is a rejection of the representational theory of perception and mental functioning. 

Hans-Joachim Rudolph: 

But, suppose, two persons compete in buying some parcel of land. 'A' wants to build a hotel, 'B' prefers to use it for himself and his family and friends. The plot itself might like to remain untouched. So, the land is part of the 'complete cognitive system' of 'A' as well as of 'B', and it also has an existence of its own, isn't it? So, I don't know how to avoid dualism in such cases, which is, additionally, preconfigured in our languages, as they are using objects and subjects in almost every sentence. 

Anyhow, we can maintain that our controversy is about dualism and monism and their application in representational and non-representational theories of perception and mental functioning, yes?

Dan Hetherington: 

Definitely our controversy is over representational and non-representational theories of mind. For the sake of convenience, I'd say that it is also over Dualism vs. Monism, but Monism implies a substance that underlies Mind and Matter, and I feel uncomfortable attributing the status of "substance" to lived experience. William James comes pretty close, but I don't wholeheartedly agree. 

It is, as you point out, nearly impossible to avoid speaking in "non-dualist" terms, but that doesn't mean we have to accept Dualism as a metaphysical position. I think of Aristotle as non-dualist, despite the discussion of Mind. Emergentism is also non-dualist, and I'm thinking of Michael Polanyi's work here, as well as a certain reading of Merleau-Ponty. De Chardin was also non-dualist. I think of the cosmologist Paul Davies as an Emergentist and non-dualist as well. Hegel is somewhere in the background. All emphasize process and interaction. 

Hans-Joachim Rudolph: 

I understand that the mind is not confined to the skull. It's reaching out to far distances in space and time (mostly in the past, sometimes also in future). But, in my model, this is realized in imaginary space-time!

We had discussed the same issue earlier, when you agreed with Kauffman's conclusion that "it is the imaginary that is real". And you added that it is similar to the Phenomenological take, where it is the psychic, the consciousness or the experience, which is real.

Nevertheless, I didn't follow Kauffman's conclusion, maintaining that there is also an objective world, which would be situated in "real space-time". You didn't share this stance, adding, however, that "our awareness is always an opening onto the world and others", whereupon I replied that this is where you place the interface with the other space - a space that I label (x, y, z, t).

So, in the example with the parcel of land, 'A' as well as 'B' have 'complete cognitive systems'. But, as you say, these must have "an opening onto the world and others". This is the interface I'm talking about. And here you also have to acknowledge that something like "the world and others" exists, isn't it?

Dan Hetherington: 

Hans-Joachim - The way I see it, we have two different conceptions of what is basic, or fundamental. I believe you place quantum theory and mathematics as fundamental, while I place everyday experience, the "life world" as fundamental. From my perspective, the construction of mathematical models is a secondary project, and relies on a description of what it is that is being modeled, which I assume to be human experience. The goal of Phenomenology, the philosophical stance that I identify with here, is to provide descriptions of human experience, rather than to model it, or explain it.

Models do, if they are productive, highlight aspects of human experience that one might not otherwise see without them, and I think that is true of the model you have been proposing using a space described by both imaginary and real numbers. I see a connection between imaginary numbers and the psychic, and real numbers as the physical, in that the space of real numbers is a space defined by the limit case of complex numbers, where the imaginary component is null. It suggests the founder of Phenomenology, Husserl's insight that physical properties are really idealizations, limit cases of our lived experiences. "Velocity" is a mathematical abstraction. In order to model velocity things such as friction have to be set aside. We can describe velocity with real numbers. Interestingly, imaginary numbers come into play when we try to model things like the effects of friction, because we are now in the realm of Chaos Theory.

My commitment to Phenomenology is loose. I believe that Chaos theory and complex systems theory do offer promise in modeling experience, or at least certain aspects of experience which Newtonian physics is unable to provide. That is why I find your use of imaginary numbers in modeling experience very interesting.

Hans-Joachim Rudolph:

Since long I felt that a "four chamber model" based on quaternion = hypercomplex space-time is a fairly good model - a mathematical structure, comparable to a skeleton - but without flesh. In the course of our discussion I learnt that the missing flesh is "everyday experience". As you say, Phenomenology and the features of hypercomplex space-time can be complementary to each other. They might even be like content and form. As an overall justification, I found in Peter Sloterdijk's Zeilen und Tage - Notizen 2008-2011 - the following sentence (p 225): 

Nicht-physikalische Zeit meint existentielle Zeit, sprich die vom Dasein und den Tendenzen seiner "Sorge" "gezeitigte" Zeit, die durch das Herz der Subjektivität geht.

Non-physical time means existential time, that is the time brought about by existence and the tendencies of its "concerns"; a time that goes through the heart of subjectivity.

He wrote this as an extension to Heidegger's "Sein und Zeit" (1927), and elaborates the idea on the following pages.

Dan Hetherington:

You may want to take a look at the philosophical position, "Enactivism". It is, in part, an integration of Merleau-Ponty's work on lived experience, particularly lived, embodied experience, and Dynamic Systems Theory. I suspect that your "four chamber model" may apply in some interesting ways.

In Enactivism, the idea of psycho/physical isomorphism has been given new life, in the form of comparing the complex dynamics of neural systems with the lived dynamics of experience. One example I can think of is using the model of "bifurcation" to describe, on the one side the dynamics of the neural systems involved, and on the other the lived experience of forming a perceptual "Gestalt". There has also been some thought given to using Husserl's analysis of "lived" or experiential time as a window into the neural underpinnings of the perception of time.

Nevertheless, how would we go about matching up the "four chamber model" with lived experience? The way I see it, and I am taking liberties with the model because I don't think I understand it, the complex number space is the space of lived experience, while the real number subset space is the space of determinate objects.

Hans-Joachim Rudolph:

As suggested by its name, the "four chamber model" doesn't consider just an imaginary and a real space-time, including all interactions between the two. Rather it takes, as you already concluded, that the space opened by real numbers is defined as a limit case of complex numbers, where the imaginary component is null.

On the other hand, the space-time opened by imaginary numbers is multiplied, using a special type of hypercomplex numbers, i.e. quaternions, to allow for three subspaces, plus the limit case as mentioned before (again including all interactions between the four). Therefore the "lived experience" will always be seen as an exchange between the four chambers, where consciousness is the interaction, and the agents allowing such interactions are the "atoms" of this precious quality of life. 

Mathematically, the dimensional gap between these spaces, i.e. 4 space-times with 4 dimensions each, can be bridged only by operators, eventually represented by square matrices. In non-mathematical terms such "atoms of consciousness" have been named "Microvita" (*). They are constitutive for all forms of life.

But why is it necessary to have three imaginary subspace? It is because our phantasies are fed and supported by archetypes on the one and an observer/several observers on the other side, both being purely subjective (of course, they also get input from the objective world, but this doesn't relate to the imaginary spheres). 

Dan Hetherington:

So, to what in experience do the four chambers correspond? You mentioned that the 3 chambers defined by complex numbers correspond to archetypes on the one side and observer/observers on the other. That is two spaces. What about the third? What I imagine is that the 4th chamber defined by real numbers is the objective world, as a crystallization of, or precipitate from the imaginary. In this way, the imaginary or subjective realm corresponds to lived experience, and the objective realm is derived from experience. I am probably oversimplifying things here.

Hans-Joachim Rudolph:

No, you're not simplifying, rather you use words which are more suitable than the ones I usually applied: precipitate - that's very nice, as it depicts the process of reduction, taking place in the transition, or, in alchemist terms, the transmutation from the third to the fourth chamber. 

And the third chamber? It's the battlefield of our existence, the place of the inner Kurukshetra, the Citta of Indian philosophy ...  

(*) Microvitum in a Nutshell by P.R. Sarkar, Ananda MargaPublications, Calcutta, 1988