Tag Archives: greek theater

A year review at chorasimilarity, second half

In parallel with the stuff about chemlambda, described in the first half, there was something else happening. I prepared some noted for a talk at the 4th Offtopicarium, in the form of a post here:

Notes for the “Internet of things not internet of objects”

The starting point is that what almost everybody describes as the Internet of Things is actually an Internet of Objects. We don’t want an Internet of Objects, because that would be only the usual accumulation of gadgetry and fads, i.e. only a very limited and uninspired construction. It is as imaginative as a big budget movie or as tasty as a fastfood menu.

Because reality is not objective. Reality is made of things, i, e. discussions between us humans about everything. When a certain agreement (or boredom, or faith, etc) is attained in the discussion, the said thing dies and dries into an object.

Discussions between humans thrive when individualities are respected and where there is a place which allows free mixing of ideas. A space. A theater.

Not the theater-in-a-box of perception, where the space is a scene, the dual of the homunculus, the king of fallacies. Because a scene is not a thing, but an object. On the scene the discussion is replaced by an ideology (see this or, from the scenographer point of view this).

Instead, a Greek theater under the sun could be a good starting point. As a machine which implements a theatrical distributed computing.

In order to do so, a necessary step is to separate computation from meaning. That would be only a small step forward after the separation of form from content principle. That’s a very short post, I reproduce most of it here:

One of the principles which make the net possible, as stated by Tim Berners-Lee,

separation of form from content: The principle that one should represent separately the essence of a document and the style with which it is presented.

Applied to decentralized computing, this means no semantics.

[One more confirmation of my impression that logic is something from the 21st century disguised in 19th century clothes.]

At this point the thread described here meets the one from the first half review: one of the discoveries of chemlambda, seen as artificial chemistry, is that it is possible to make this separation.


I stop here with the second half, there will be surely more halves to come ūüôā


Theatrical distributed computing

…looks like an apt name for several threads from this blog, which are now converging to a common point.

To make it more clear, here is a modification of the figure which appears in the post Theatron as an eye.


The red decorations changed. Let’s see.

  • DESIGNERS are the new programmers. They are no longer write programs, but instead they design good behaving distributed GLC computations. They deserve the front seats for observing the actors.
  • ACTORS¬† occupy their right place in the greek theater: the orchestra.¬† They are, of course, GLC actors, which are released into the wild after the preparation stage, effected by the designers. Each actor is an autonomous, reactive entity, which lives by exchanging very short, highly schematized messages with other actors (like the script one actor has, given by the director-designer; there is not very important what the actor says, only that it is communicating a repertoire of basic — emotional, in real theater — universal messages). There are many actors in the greek theater (assimilated here with the members of the chorus, to be clear), they are almost indiscernable one from another, they dress the same, they look the same, they have a very limited way of expression, but together they form the powerful chorus. Like neurons in a brain, they are in a limited variety, but they “compute” in a distributed and asynchronous way, without exchanging messages which need external competences to make sense.
  • the USERS of this distributed computation, aka theatrical performance, are the beneficiary of the show.
  • ACTORS CREATION: new actors are entering through the PARODOS, that’s related to the fact that the creation of new actors is a process which looks like the cells binary fission. This is implemented in chemlambda, look for example how the B,C,K, W combinators are multiplying in this post.
  • CORES: behind the skene is what should not be visible to the public or actors. This is a interface with other computing devices. like for example the coloured rectangles representing various stacks in the post A machine for computing the Ackermann function in graphic lambda calculus.¬† Recall that each core has to be embedded in a mask (which IS the actor which is communicating with that core), or, masks are decorating the¬† skene.
  • Finally, all this happens in the NET. Worldwide, circled by the sun [annalema].

The gnomon in the greek theater of vision, I

In the post Theatron as an eye I proposed the Greek Theater, or Theatron (as opposed to the ‚Äútheater in a box‚ÄĚ, or Cartesian Theater, see further) as a good model for¬†¬† vision.

Any model of vision should avoid the homunculus fallacy. What looks less understood is that any good model of vision should avoid the scenic space fallacy. The Cartesian Theater argument against the existence of the homunculus is not, by construction, an argument against the scenic space. Or, in the Cartesian Theater, homunculus and scenic space come to existence in a pair. As a conclusion, it seems that there could not be a model of vision which avoids the homunculus but is not avoiding the scenic space. This observation is confirmed by facts: there is no good, rigorous  model of vision up to date, because all proposed models rely on the a priori existence of a scenic space. There is, on the contrary, a great quantity of experimental data and theoretical partial models which show just how complex the problem of vision is. But, essentially, from a mathematician viewpoint, it is not known how to even formulate the problem of vision.

In the influent paper “The brain a geometry engine”¬† J. Koenderink proposes that (at least a part of) the visual mechanism is doing a kind of massively parallel computation, by using an embodiment of the geometry of jet spaces (the euclidean infinitesimal geometry of a smooth manifold)¬† of the scenic space. Jean Petitot continues along this idea, by proposing a neurogeometry of vision based essentially on the sub-riemannian geometry of those jet spaces. This an active mathematical area of research, see for example “Antropomorphic image reconstruction via hypoelliptic diffusion“, by Ugo Boscain et al.

Sub-riemannian geometry is one of my favorite mathematical subjects, because it¬† is just a¬† particular model of a metric space with dilations.¬† Such spaces are somehow fundamental for the problem of vision, I think. Why? because there is behind them a purely relational formalism, called “emergent algebra“, which allow to understand “understanding space” in a purely relational way. Thus I hope emergent algebras could be used in order to formulate the problem of vision as the problem of computing with space, which in turn could be used for getting a good model of vision.

To my surprise, some time ago I have found that this  very complex subject has a respectable age, starting with Pythagora  and Plato!  This is how I arrived to write this blog, as an effort to disseminate what I progressively understand.

This brings me back to the theater and, finally, to gnomon. I cite from previous wiki link:

Hero defined a gnomon as that which, added to an entity (number or shape), makes a new entity similar to the starting entity.

In the greek theater, a gnomon sits in the center of the orchestra (which is the circular place where things happen in the greek thater, later replaced by the scene in the theater in a box). Why?

The Cartesian Theater: philosophy of mind versus aerography

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 theater is 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 there is 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

“All that is landscape is melted into air: the `aerography’ of ethereal space”, Environment and Planning D: Society and Space 2011, volume 29, pages 519 – 532.

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 control over 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 theater that 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.