Lecture 7

For the texts I wanted you to get a different sense of the background of the algorithm -- light reading from Berlinksy, but it will help us loosen our heads about this.

As for the Deleuze reading on Foucault, I thought it would be useful to have a formal description of the "diagram."

Hopefully we can see what is so strange about the algorithm from Berlinksy'spoint of view.

Btw as a summary of Tues, what I wanted to get at was as many possibly different ways of looking at the "analogy" between computation and architecture. Many offered up points about computation and CA (the output) and architecture. Others looked at a methodological relation.

I think this is interesting because I think I specified a Turing machine, but I didn't specify what I meant by Architecture. To the extent that many questioned the diagrammatic aspects of CA, it was important to linger on a bit about that. What I liked most was the question of whether we could read the diagram in the rule set. This is really important. The fact that Durand had already in a way done much of this ought to show us how we might be able to avoid metaphors from other fields by which we return computation to a diagram. Matt's point that the child's game I mentioned is not in architecture is perfectly right. So the point was after reading the discussions posted on the blogs, maybe we could just practice an analogy with something more basic, more innocent and avoid momentarily too much pressure with architecture. I think that was asking a lot. But I think it was the right question. The Berlinksy reading might provoke us to think a bit differently about this.

CA = TM = RS

System = Hardware (processor and monitor) + Software

• the processor is a generic machine.
• the monitor is a means of display (tape, grid, could be other).

Hardware is only the means.

Software = RS (rule set)

Syllogism:
1) TM is RS
2) CA is RS
3) CA is TM

Perception

What is perception ? How do we consistently perceive a reality and commune, celebrate, document and discuss its existence. Conventions must exist. An economy of descriptors must exist.
What for us is a picture, may for another -- say a blind person -- be meaningless. The CA approach to documenting and calculating variables within a reality allows for vibrancy in the way this information transposes from what is happening to an understanding of what is happening.

The flexibility -- and deceptively basic simplicity -- of this transposition naturally disposes it(CA) to be adapted to projective exercises such as art, design, and architecture.

Relegating to the Pictorial

Perhaps the Turing machine can be likened (albeit possibly a stretch) to some of the architectural ideals set forth in the 1960s.  Most specifically, the best known work of Superstudio and the conceptualized Continuous Monument, wherein nomadic people could plug in at any point on an immense grid which hyper-consumed major cities, theoretically freeing these people from the fragmentary space of the modernist tower-block, and spontaneously materializing a minimal domestic fantasy life.  This method of providing the means for the complex needs of living by way of a seemingly simple predisposed urban megaplan is interesting in the fact that it breaks down living to its most simple set of needs (the ruleset) and reconfigures it in a spatially succinct realm (the infinitely long tape, or here, the plane which stretches around the Earth).  Similar to the Turing Machine, the Continuous Monument was also very much conceived as a "paper" architecture, and should be viewed as a way of understanding the possibilities of technology instead of so much as a prescriptive model.

Cellular automata act as a diagrammatic model for the output of a predetermined ruleset.  This diagram can be used as a measure for the level of complexity able to be achieved by these rules and needs a further set of criteria applied in order to see the physical effects.

02.26.08 email questions

What is the equivalent of a Turing machine in architecture?

I think it would be difficult to find an equivalent of a Turing machine in architecture. While both processes have a physical output the way they get to that point seems to be different. In a Turing machine there is an established set of limited states and values by which the entire system operates to produce physical output on the tape, when this tape is analyzed it can be seen as the pure result of the procedure of the machine. It is not always evident in architecture how the “result” and “procedure”, and in many cases the procedure acted out is not one of a limited amount of states or values but one of flux where new unanticipated obstacles are implemented. Where as the turning machine runs a procedure without being effect by anything outside the machine architecture, at times has to absorb these outside influences during the course of a procedure.

The best equivalent to a Turing machine I can see in architecture is the high rise building as the construction and space is produced repetitively up the entire building, each one the same. When occupied these similar cells or spaces will adapt to various functional needs, in a scenario where these functional needs can be seen as analogous to the states of the turning machine the variation could be the result of such a producer playing out.



And in what sense do cellular automata "picture" a state of affairs?

The “picture” created by cellular automata is a result of the rule set it follows. This demonstrates a state of affairs in that the rule set acts upon the line previous to it. Like a precedent study or a virgin site the new line is an advancement forward, some type of improvement upon the next, based on the rule set. In this way cellular automata can illustrate a model of simplification which can help us visualize this process.

False choice.

I’ve spent the week mulling over this. Bluntly, it is neither pictorial nor diagrammatic. The elements of Turing Machines et. al. are information.

We can abstract the output of a CA by agreeing on a convention and call this a diagram. A similar scheme on a universal CA, Turing Machine, or GOL simulation would net a visual appearance nearly as verbose as the original, and therefore would not be terribly diagrammatic. There’s no “meta” message to be pulled out of these systems other than the rule sets.

Nor can I gain much traction in describing even Lindenmayer systems as pictorial. They speak about topological relationships of the plant’s branching, but rarely fool me for a second as to their origin. Additionally, there is some fancy, and I mean _FANCY_, math on the back end to get {{a->a},{b->a,b}} to look like my houseplant. As for CA, come on… It’s just not a picture. It’s not representing anything beyond the information itself.

I feel like the pictorial trap is precisely where so many have gone wrong. These systems provide a rich test bed for theories of morphogenesis, social systems and a dizzying array of other phenomena, but it is often forgotten that these are models of phenomena and not the phenomena itself. The substitution of a model for its phenomena is endemic, and is demonstrated with whip cream on top the philosophy of Nick Bostrom, who believes we are living in a simulation. WTF?! A group of mathematicians has placed the probability at 1 in 20. No joke.

Perhaps this can feed into the other question on the table:

Computation between Geometry and Topology

On the one hand, these systems excite me to a degree that I’m uncomfortable relegating them to a prepositional phrase, yet they’ve enjoyed a grammatical identity in the hands of Noam Chomsky in his research into linguistics. In the interest of completely dorking out this evening I re-checked his Wikipedia entry, and, lo, he’s got this automata theory of formal languages. I read about this a while back and quite honestly couldn’t make any sense of it, but I would guess that Peter’s four food groups would have a place on Chomsky’s table. Turing machines are mentioned by name.

In his “Computational Theory of Morphogenesis”, Przemyslaw Prusinkiewicz, draws the axes of his consideration along three lines.

1. One or many
2. Computing capability (a finite automaton or an automaton with counters)
3. Information exchange with the environment

The last of these certainly involves communication, or this kind of go-between again. In modern agent based programing, the geometry takes the role of the discrete unit, but it seems like a computational grammar serves the role of the information exchange. (Or was that topology). I'm not positive these mix and I need to think about this. More later.

State of Affairs of the cellular automata

Frozen in time; a momentary consequence of the inputs that brought it to its current configuration.