Monsters
Monads are a tight family, infinitesimal differences in their qualities – no discontinuities allowed – You wanna be a MONAD! - conform, hold hands, share a little of yourself with those you touch – no room for Monsters here, this is blood brothers.
The Studio Review Algorithm
Input:
Result presented by Wannabe Architect
Studio Review Algorithm operation:
1. Take Wannabe Architect’s Result
2. Demean It
3. Select randomly from all remaining Possible Answers; if none remain goto Step 8
4. Instruct Wannabe Architect to rework accordingly by next Review
5. Schedule next Review for 4 days or less
5. Remove Answer from Possible Answer Set
6. If no Answers remain, invite Jury to next Review; declare it the Final Review.
7. Goto Step 1 within 4 days
8. Speak into your cell phone and leave the room
Tuesday, April 15, 2008
Monday, April 14, 2008
what if/then what
Considering the connection between algorithm and topology, I am drawn to the idea raised in our last discussion regarding the fundamental nature of the if/then operation. In reading an essay about topology, I came across the Jordan Curve Theorem, which I think has an interesting correlation with the if/then algorithmic operation in both its function and simplicity.
A simple closed curve (one that does not intersect itself) is drawn in a plane. This curve "C" divides the domain into two domains, an inside "A" and an outside "B." Even if the plane and the curve are deformed, these two classes persist and force any curve traversing A to B to cross C, regardless of the deformations.
Within the topological theorem, there are discrete operations concerning discrete elements (in this case, geometrical forms). While a curve may be reducible to a set of points, this operation is contingent on this curve being irreducible. It is essential to this particular function, and therefore it is discrete. While I do not intend to deny the divisibility test for discreteness, I do think this speaks to the nature of discrete in terms of algorithm.
For instance, the if/then statement, as part of a rule set, functions in a similar fashion as the curve in the Jordan Curve Theorem. It acts as a dividing line that creates, or forces the emergence of, two distinct states that are both contingent on the single statement.
Furthermore, the sequence of rules (rule set) can be discrete when the the operation of another algorithm is contingent upon the entirety of this rule set. Von Neumann speaks to this in his discussion of self-reproduction in the General and Logical Theory of Automata.
If we look at the nature of the algorithm through the lens of "topology," does the algorithm change if the order of rules are re-organized to yield different results? Is the Turing machine "topologically" consistent even if the order of operations are varied based on inputs?
While I think the idea of an infinite rule set is logically sound, I think it should be appended to reflect the necessity for recursion in this infinite string. This would suggest genetic instructions akin to evolution, rather than a sprawling sequence that simply doesn't end.
A simple closed curve (one that does not intersect itself) is drawn in a plane. This curve "C" divides the domain into two domains, an inside "A" and an outside "B." Even if the plane and the curve are deformed, these two classes persist and force any curve traversing A to B to cross C, regardless of the deformations.
Within the topological theorem, there are discrete operations concerning discrete elements (in this case, geometrical forms). While a curve may be reducible to a set of points, this operation is contingent on this curve being irreducible. It is essential to this particular function, and therefore it is discrete. While I do not intend to deny the divisibility test for discreteness, I do think this speaks to the nature of discrete in terms of algorithm.
For instance, the if/then statement, as part of a rule set, functions in a similar fashion as the curve in the Jordan Curve Theorem. It acts as a dividing line that creates, or forces the emergence of, two distinct states that are both contingent on the single statement.
Furthermore, the sequence of rules (rule set) can be discrete when the the operation of another algorithm is contingent upon the entirety of this rule set. Von Neumann speaks to this in his discussion of self-reproduction in the General and Logical Theory of Automata.
If we look at the nature of the algorithm through the lens of "topology," does the algorithm change if the order of rules are re-organized to yield different results? Is the Turing machine "topologically" consistent even if the order of operations are varied based on inputs?
While I think the idea of an infinite rule set is logically sound, I think it should be appended to reflect the necessity for recursion in this infinite string. This would suggest genetic instructions akin to evolution, rather than a sprawling sequence that simply doesn't end.
Thursday, April 10, 2008
Lect 13
Continuing the discussion of the discrete. Keep in mind that the background is to rethink the concept of computation in algorithm vis a vis Turing's paper among other things. We've looked at analogies with architecture and other fields and now we're looking at his thought experiment discretely, that is in terms of one aspect of what his thought experiment requires which is the discrete terms of what is the output, 0 and 1. The blog entries were terrific because they approach that style of thinking.
We want that grammatical grasp of our concepts and the flexibility of thought to see it redefine our architectural ones. On algorithm and geometry our points suggested no internal connection save in a few instances. Algorithm expanded into any notion of operation means geometry is constructed from operations but not defined by them but by geometrical axioms. Geometry as an organization specific to matter is a language by which to characterize it but doesn't describe the process of formation. Topology, on the other hand might be more internally connected. There is always an order to the execution of the steps and they are related to each other in specific fundamental ways.
We want that grammatical grasp of our concepts and the flexibility of thought to see it redefine our architectural ones. On algorithm and geometry our points suggested no internal connection save in a few instances. Algorithm expanded into any notion of operation means geometry is constructed from operations but not defined by them but by geometrical axioms. Geometry as an organization specific to matter is a language by which to characterize it but doesn't describe the process of formation. Topology, on the other hand might be more internally connected. There is always an order to the execution of the steps and they are related to each other in specific fundamental ways.
We were asking what is discrete. Today the elements, objects, entities, etc which remain constant (a variable can be one of these I suppose) upon which the rule set acts. Q: is the space in which a sequence run an "element"? We possibly reduced this with the fruit shopping analogy to an if/then condition. And this might seem on the whole more to do with toplogy. It certainly brings us back to the problem of logic.
On a few definitions:
What is a rule space as opposed to a rule set?
Can there be an infinite rule set?
Can the terms of an algorithm magically change? (Can 0 just become 1)? In contrast to: Can the rules or rule ste change?
Are we looking at anything like Descartes' invention of analytic geometry? (I mean the axiomatization of geometry? The application of algebraic procedures to geometrical terms?)
What is discrete?
1) Are Rule Sets Discrete
2) Are Objects, elements, terms and entities discrete? (That is, those things upon which the rule set acts)
3) Is a step in the carrying out of the rule set discrete?
4) Is the if/then conditional discrete?
One thing to keep in mind is that computation has changed the relation between geometry and toplogy - but this is perhaps a feature of analytical computing.
Another thing to consider is whether algorithm and toplogy are possible more connected than algorithm and geometry.
In other words, algorithm might act on geometrical elements but in order for it to act geometry isn't essential to its function. The if/then and the question of loops and so forth seem to suggest an internal connection with topology.
In terms of continuous, we mean possibly divisible. Do we mean infinitely divisible?
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Friday, April 4, 2008
Wednesday, April 2, 2008
On algorithms and boats
We have to do something to celebrate the seminar. I suggest renting a sailboat. Any ideas. Please be discrete.
Design Office for Research and Architecture
155 Remsen Street
No. 1
Brooklyn, NY 11201
USA
646-575-2287
info@labdora.com
Design Office for Research and Architecture
155 Remsen Street
No. 1
Brooklyn, NY 11201
USA
646-575-2287
info@labdora.com
Tuesday, April 1, 2008
Lect 12
Today we were going to look at a few problems about the discrete and the continuous regarding the chu and delanda text. Chu is obviously a proponent of the discrete as the basis for everything. Delanda is really a proponent of the continuous. Both are talking about genetic, that is, algorithnic systems. I'll get to that later. You're blog entries for this week were to discuss 1) the relationship between the algorithm and geometry and 2) to identify in any narrative form something about the discrete and the continuous. William offered a theory somewhat close to Newton's that where there is matter there is geometry but that algorithm as such isn't really connected. That is, it isn't an essence. One might want to ask what we mean about geometry as inhering in matter. It is after all a formal language. Bill offered an insight into the notion that algorithms are only always operations on geometry. But it raised an interesting point that although there may be axioms for geometry we can't say that, yet, for algorithm since it is not a formalized structure as such and so althought there may be infinite ways inwhich to construct a triangle there are limits to the definition of what is a triangle. Well, let's say this is a provocative idea. Frank suggested that in a way every schema of the algorithm has imbedded in it certain principles but that, surprisingly, these were topological if anything. Not geometrical. At a certain point we also discussed the question again of experience. I would like to edit my comments about that since I felt a bit rushed at the end of class to say something but I'm not at all satisfied with what I said. In any event, I would return to my previous claim that the experience of a system, say of language, is not the same as an explantion or even a definition of language. To say that we operate with rules is not yet to say whether and how we experience them and whether we intend them when we express certain things. If I give you a basice set of instructions to add 2 to the next number and you get to the 50th operation but come up with an odd number, for whatever reason, it is hard to say that I intended for you to carry it out such that you always get an even number after 50. This is something from Wittgenstein.
There were also provocative notions on the snowflake: geometry can describe it but can't account for the process by which it formed. And the question also of the operations of the coin toss when the coin is a sphere - the contrast between the discrete and the continuous.
There were also provocative notions on the snowflake: geometry can describe it but can't account for the process by which it formed. And the question also of the operations of the coin toss when the coin is a sphere - the contrast between the discrete and the continuous.
I'll try to say more about this later. To return to chu and delanda, let me just emphasize two things: for chu. Material systems are themselves products of algorithm. Algorithm doesn't derive from dynamical systems. What does this mean? For Delanda, populational, intensive and topological thinking are essential to genetic algorithms. Why does he exclude the discrete? Finally, why in Leibniz are there no such thing as monsters?
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Fw: Summary lect 10
Design Office for Research and Architecture
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-----Original Message-----
From: "Peter Macapia" <peter.dora@tmo.blackberry.net>
Date: Sun, 30 Mar 2008 08:27:26
To:"Peter Macapia" <petermacapia@labdora.com>
Subject: Summary lect 10
Conflict, Problem, Question
We looked at two problems, one relating to Turing's invention as a thought experiment - how it led to computation and the other about algorithm and geometry. Instead of looking at Turing's problem as a problem we could relate in its entirety to architecture I was asking if we could just understand something of the implications of his use of a binary system, or of the discreteness of something being 1 or 0. And so I was asking in what sense can we think of cases of the discrete. And we looked at mathematical and other types of discrete, integers vs irrational. And then I asked us to consider continuity. Discrete, it seems is the basis of computation, of the algorithm. It is a whole unto itself. Frank suggested at first that there is a problem of representation here, of symbolization. But we soon came to the issue of the fact that the discrete in its essence doesn't really require that. It is a structural and formal property, not one of symbolization.
Design Office for Research and Architecture
155 Remsen Street
No. 1
Brooklyn, NY 11201
USA
646-575-2287
info@labdora.com
155 Remsen Street
No. 1
Brooklyn, NY 11201
USA
646-575-2287
info@labdora.com
-----Original Message-----
From: "Peter Macapia" <peter.dora@tmo.blackberry.net>
Date: Sun, 30 Mar 2008 08:27:26
To:"Peter Macapia" <petermacapia@labdora.com>
Subject: Summary lect 10
Conflict, Problem, Question
We looked at two problems, one relating to Turing's invention as a thought experiment - how it led to computation and the other about algorithm and geometry. Instead of looking at Turing's problem as a problem we could relate in its entirety to architecture I was asking if we could just understand something of the implications of his use of a binary system, or of the discreteness of something being 1 or 0. And so I was asking in what sense can we think of cases of the discrete. And we looked at mathematical and other types of discrete, integers vs irrational. And then I asked us to consider continuity. Discrete, it seems is the basis of computation, of the algorithm. It is a whole unto itself. Frank suggested at first that there is a problem of representation here, of symbolization. But we soon came to the issue of the fact that the discrete in its essence doesn't really require that. It is a structural and formal property, not one of symbolization.
Design Office for Research and Architecture
155 Remsen Street
No. 1
Brooklyn, NY 11201
USA
646-575-2287
info@labdora.com
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