Looks to me there is something wrong with the Cartesian Theater term.

Short presentation of the Cartesian Theater, according to wikipedia (see previous link):

The

Cartesian theateris a derisive term coined by philosopher Daniel Dennett to pointedly refer to a defining aspect of what he calls Cartesian materialism, which he considers to be the often unacknowledged remnants of Cartesian dualism in modern materialistic theories of the mind.Descartes originally claimed that consciousness requires an immaterial soul, which interacts with the body via the pineal gland of the brain. Dennett says that, when the dualism is removed, what remains of Descartes’ original model amounts to imagining a tiny theater in the brain where a homunculus (small person), now physical, performs the task of observing all the sensory data projected on a screen at a particular instant, making the decisions and sending out commands.

Needless to say, any theory of mind which can be reduced to the Cartesian Theater is wrong because it leads to the homunculus fallacy: the homunculus has a smaller homunculus inside which is observing the sensory data, which has a smaller homunculus inside which …

This homunculus problem is very important in vision. More about this in a later post.

According to Dennett, the problem with the Cartesian theater point of view is that it introduces an artificial boundary (from *Consciousness Explained* (1991), p. 107)

“…there is a crucial finish line or boundary somewhere in the brain, marking a place where the order of arrival equals the order of “presentation” in experience because

what happens thereis what you are conscious of.”

As far as I understand, this boundary creates a duality: on one side is the homunculus, on the other side is the stage where the sensory data are presented. In particular this boundary acts as a distinction, like in the calculus of indications of Spencer-Brown’ Laws of Form.

This distinction creates the homunculus, hence the homunculus fallacy. Neat!

Why I think there is something wrong with this line of thought? Because of the “theater” term. Let me explain.

The following is based on the article of Kenneth R Olwig

but keep in mind that what is written further represents my interpretation of some parts of the article, according to my understanding, and not the author point of view.

There has been a revolution in theater, started by

“…the early-17th-century court masques (a predecessor of opera) produced by the author Ben Jonson (the leading author of the day after Shakespeare) together with the pioneering scenographer and architect Inigo Jones.

The first of these masques, the 1605 Masque of Blackness (henceforth Blackness ), has a preface by Jonson containing an early use of landscape to mean scenery and a very early identification of landscape with nature (Olwig, 2002, page 80), and Jones’s scenography is thought to represent the first theatrical use of linear perspective in Britain (Kernodle, 1944, page 212; Orgel, 1975).” (p. 521)Ben Johnson,

So? Look!

“

From the time of the ancient Greeks, theater had largely taken place outside in plazas and market places, where people could circle around, or, as with the ancient Greco-Roman theater or Shakespeare’s Globe, in an open roofed arena.Jones’s masques, by contrast, were largely performed inside a fully enclosed rectangular space, giving him controlover both the linear-focused geometrical perspectival organization of the performance space and the aerial perspective engendered by the lighting (Gurr, 1992; Orrell, 1985).” (p. 522, my emphasis)“Jonson’s landscape image is both enframed by, and expressive of, the force of the lines of perspective that shoot forth from “the eye” – notably

the eye of the head of state who was positioned centrally for the best perspectival gaze.” (p. 523, my emphasis)“Whereas theater from the time of the ancient Greeks to Shakespeare’s Globe was performed in settings where the actor’s shadow could be cast by the light of the sun, Jones’s theater created an interiorized landscape in which the use of light and the structuring of space created an illusion of three dimensional space that shot from the black hole of the individual’s pupil penetrating through to a point ending ultimately in ethereal cosmic infinity. It was this space that, as has been seen, and to use Eddington’s words, has the effect of “something like a turning inside out of our familiar picture of the world” (Eddington, 1935, page 40).

It was this form of theaterthat went on to become the traditional `theater in a box’ viewed as a separate imagined world through a proscenium arch.” (p. 526, my emphasis)

I am coming to the last part of my argument: Dennett’ Cartesian Theater is a “theater in a box”. In this type of theater there is a boundary,

“… scenic space separated by a limen (or threshold) from the space of the spectators – today’s `traditional’ performance space [on liminality see Turner (1974)]” (p. 522)

a distinction, as in Dennett argument. We may also identify the homunculus side of the distinction with the head of state.

But this is not all.

Compared with the ancient Greeks theater, the “theater in a box” takes into account the role of the spectator as the one which perceives what is played on stage.

Secondly, the scenic space is not “what happens there”, as Dennett writes, but a construction already, a controlled space, a map of the territory and not the territory itself.

Conclusion: in my view (contradict me please!) the existence of the distinction (limen) in the “Cartesian theater”, which creates the homunculus problem, is superficial. More important is the fact that “Cartesian theater”, as “theater in a box”, is already a representation of perception, having on one side of the limen a homunculus and on the other side a scenic space which is not the “real space” (as for example the collection of electric sparks sent by the sensory organs to the brain) but instead is as artificial as the homunculus, being a space created and controlled by the scenographer.

**Litmus test:*** repeat the reasoning of Dennett after replacing the “theater in a box” preconception of the “theater” by the older theater from the time of ancient Greeks. Can you do it?*

On the beautiful idea of “aerography”, later.

Dear Prof. Buliga

I am studying a possible implication of the Stone representation

theorem relating a duality between certain logical algebras to certain

topological spaces and found your papers on spaces to be of great

interest. Might have you some time to entertain a few questions?

Kindest regards,

Stephen P. King

With pleasure, here or by e-mail, you can find the address by looking at my home page (link in the “About” post).

My questions center around whether or not it is possible to identify the notion of particles – as used in physics – with a Stone space (as in the topological space, S(B), that is dual to a Boolean algebra B).

I ask this because the Stone space of a Boolean algebra ‘looks’ exactly like a dust! A Totally disconnected Hausdorff space looks like a collection of blobs in an otherwise empty universe. See http://en.wikipedia.org/wiki/Totally_disconnected_space for example.

To answer this question I am trying to see if it is possible to construct or, at least, sketch what it would mean to say that for a given set of particles to exist there must be an algebra that is its dual.

If this idea ‘works’ then the duality extends to the case where the blobs as moving around with respect to each other, but in that case the algebra would have to ‘evolve’. The problem I have is that logics are usually considered in terms of static relations, I am looking at the possibility that there exists a dynamics or evolving logic structure.

Forgive me here, I am trying not to have to use mathematics to explain an idea. Does this make any sense at all so far? I may just be thinking of an abstract idea as if it was a concrete “thing”… but if this idea has some merit, then it might provide an alternative to think about the ‘stuff’ that physics considers.

I have some other question that are topical to your papers but not the time to write them up here now.

Dear Stephen, interesting, I have to think about this, but you may hit me with the math, I think I shall survive.

Three quick questions:

1. what becomes the Stone space if you replace a boolean algebra by an orthocomplemented algebra?

2. is there a simple description of the boolean algebra which has as Stone space the dyadic integers with the topology given by the (ultrametric) dyadic norm?

3. your space of particles is a “dust”, I think, only when you see it embedded into an ambient space, so by a sort of duality, this larger space corresponds to an algebraic structure inside the boolean algebra; what is it, then?

1. It looks like a plenum of spaces. The dust-like aspect would disappear.

Those there questions are *exactly* the kinds of questions that I am asking!

1) I am interested in the behavior of the Stone space that one obtains, if possible, from that replacement.

I found several clues so far. In the article ‘Quantum Logic’ by Maria Luisa Dalla Chiara and Roberto Guintini, found in the book ‘Handbook of Philosophical Logic’, 2nd ed. Vol. 6 (edited by D. M. Gabbayand F. Guenther) pg.177, there is a discussion of this in terms of ortho-valued models, taken to replace the usual Boolean-valued models:

“the set of truth-values is supposed to have the algebraic structure of a complete orthomodular lattice, instead of a complete Boolean algebra. Let B be a complete othomodular lattice, and let v, /lambda, … represent ordinal numbers. An ortho-valued (set theoretical) universe V is constructed as follows: …”

I will not try to reproduce the equations here because time, but does relate to the orthocomplemented algebra in your question? How do we shift from a fixed and static set of ordinals to successions of maps onto those ordinals? Cecilia Flori has done some work, elaborating on work by Isham et al, that considered this in terms of spectral presheaves, but it seems a bit too ‘clunky’ to me. http://topos-physics.org/

2) I found some discussions that refer to the Pontryagin duality between compact and discrete spaces that might generate answers to questions about the kind of ordinals and cardinals, such as the dyadic interger. See: http://ncatlab.org/nlab/show/Pontrjagin+dual

3) Yes, the dust-like appearance is visualized in that manner but is explicit in the definition of a Stone space S(B). The larger space is the set-theoretical complement of the S(B), not its dual per say. The dual of the complement space would be an algebraic structure but would not be ‘inside’ the Boolean algebra B except by implication. I think of it as all of the versions of that algebra that are ‘not true but could be true’ in some other version of that particular B that is the dual of S(B). In spatial terms one could say that the empty space is ‘all the places where something could be but is not’.

More soon.

You can find the book reference in Google books here:

Another comment in reply to your question 2). It is interesting that you mentioned ultrametric types of numbers because those are the easiest to identify as Stone spaces, since they have the completely disconnected property. In the before mentioned passage in the article by Dalla Chiara and Guintini, there is mention of “quantum-logical natural numbers”. These are defined in terms of some objects within the segments V(/omega) of V^B which is found in the discussion of the value ‘true’: “A formula /alpha is called ‘true’ in the universe V^B (|= v^B /alpha) iff {{/alpha}}^/delta = 1 (the identity projection as opposed to 0, the null projection).

I am unable to find more information of these quantum-logical natural numbers at the moment but will continue my search.

A comment about the homunculus fallacy in your article above. As Dennett explains in his book, the problem is that there will occur an infinite regress of homunculi inside of homunculi and your point about maps and territories does apply: Each successive homunculi will be a “territory” for the smaller homunculi within it which is acting as a map.

I have studied this problem in terms of simulations of simulations and have developed an algebraic model of this using the equivalence relation that holds between computational systems known as “bisimulation” and ‘bisimilarity”. What I discovered is that if we take into account the physical resources necessary to render a simulation, or in the case of the Cartesian theater a simulation of the play that might occur on the theater in a box, then there is an upper bound on the quantity of information that can be contained in the simulations.

Therefore, if there where to exists an actual infinite regress of homunculi then each one would have to have access to the equivalent of an infinite quantity of resources at each step in the regress. If there is a finite upper bound for the homunculi to generate a simulation of all of the homunculi that are inside it then the regress can only extend a finite number of times. The infinite regress vanishes simply because there is not enough “stuff” to each “turtle” so that it can hold up all of the turtles.

This situation, I think, is exactly what is found in the so-called Holographic Principe and in the AdS/CFT correspondence notion in physics. 😉

Does this make sense?

Interesting to this subject is the actual physicality of the bicameral brain which process images / sites on both sides and evaluates them differently. Yes … I took a human brain made models of it about 30 years ago and constructed a yes Cartesian model of human “echophysiology” based on trangular pyramid were the two sides of the brain were two globes with a limen based on the connective surface area of the corpse collossum. The third globe was input from the natural world into the material/ immaterial worlds of the two globes making a base trinity from which emerged the 4th globe self consciousness having no physical space but just an interactive state of existence emerging from the trinity… :-)… Yes it takes two image processing sites to have a 3rd dimension. Yes “echological” parallel computational processing of space. As it were… love to invent ideal words… for ideas :-)) Thanks for this blog.. great fun.- carl

Thank you for the comment Carl. I don’t know why I had to approve it, probably because there’s a long time since your last comment.