Symbols And Borromean Links

31Jan07

The German Wikipedia arctile about Symbol mentions the works of Jacques Lacan and states:

Dass ein Symbol nicht im Sinne einer Bedeutungs-Verdichtung zu verstehen ist, wird deutlich bei Jacques Lacans Darstellung der Symbolisierungsfunktionen. Die symbolische Ordnung wird nach Lacan über drei Register organisiert, die zueinander in einem wechselseitigen und unauflösbaren Verhältnis stehen. Es sind dies die »drei Register der symbolischen Ordnung« | Reales | Symbolisches | Imaginäres |. Lacan hat ihr Verhältnis zueinander in Form eines Knotens dargestellt. Der »Borromäische Knoten« ist ein zentrales Element in der Lehre Lacans und dient dem Verständnis dreier möglicher Organistation der Psyche im Rahmen dreier psychischer Verfasstheiten: | Neurose | Psychose | Perversion |.

The mentioned symbolic order (or system) is established over three registers, which are on friendly terms which one another, represented in the form of a special knot: the Borromean rings (see the following image).

Filed under: Haymow, Pile, Space, Symbol, Visualization   |  1 Comment

Two Concepts Of The Symbolic

29Jan07

The last post to this blog dates back two month now. It dealt with my apparently favorite particle: the Pile object, and closed with the question, where does its z, which we will associate with the x- and y-coordinate at hand, come from?

One possible answer results in two different concepts of the symbolic. A symbol could be understood as a ’symbol for something’ or as a ’symbol composed of something‘. Inside of a Pile system, x- and y-coordinates are composed of something (the z’s of two other such particles). At the boundary between inside and outside we construe the terminal values, whereas the values are connected to symbols for something outside the system.

Terminal values are the result of a morphism, i.e. a process joining ‘objects’. This process joins a symbol for something and a mere number. Such a terminal value acts like a monad: the name of the beginning number of a series, from which all following numbers derived.

For example, in a binary world consisting of 0’s and 1’s, the 0 ‘is’ a symbol for something (e.g. FALSE). Our morphism now joins this 0 with our first number, i.e. 1 (which has btw nothing to do with the 1 in the binary world outside). The 1 outside is a symbol for something (e.g. TRUE), and the 1 at the boundary of our system is a mere number, the name of the outside 0 taken inside of the system as a z (number).

Filed under: Haymow, Pile, Space, Symbol, Terminal value (TV), Visualization   |  1 Comment

0000000010…

29Nov06

How to achieve persistence of a 2D coordinate system representing connexions? This post explains it in a bottom-up approach.

Let the binary string 0000000010… be an object description, a description of a coordinate system with two dimensions. Obviously there is some information ‘in’ the binary string. At position 9 we perceive a difference between this position and the positions before (and after): the binary digit 1 instead of all the other 0’s.

If we hand over this (marked by the binary digit 1 at position #9) to an inverse pairing function called split, we get two coordinates: split 9 = (0, 3).

Filed under: Haskell, Haymow, Pile, container, monad   |  1 Comment

Querks

27Nov06

“Querks are the wrinkles in nothingness [...]” (http://wikiworld.com/wiki/index.php/QuerkCalculus)

Thanks to Jim Whitescarver, whose posting to the LoF mailing list made me aware of Querk Calculus.

“For simplicity we can consider the ‘mark’ of Spensor-Brown’s ‘Laws of Form’ as the universal logical element represented by the dynamical bit or primitive querk where, it turns out, the laws of calling and crossing correspond, dynamically, to doubling or reflection and cancellation in quantum state. See http://en.wikipedia.org/wiki/Laws_of_Form for a good introduction, or use nand-delays or any other universal construct you are comfortable with to represent the idea of a dynamical bit or querk. Not X and Y it equivalent to saying X and Y are distinct which is exactly one bit of information.

The meaning of the bit, or information here does not have to do with cognition, or human knowledge of the bit, it has to do simply with the actual existence of a distinction anywhere in the logical system. We might posses an understanding not manifest within the system and the system may posses distinctions which we cannot determine exactly by interaction with it.”

BTW No Querk or animal was hurt or traumatised in the making of this webpage.

“What the Querks discover is that the animals do not want to be their friends until the Querks are true to themselves. The Querks discover that they are special, talented and terrific just being themselves.” (Found here)

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Farewell Pile Systems Inc.

27Nov06

I relocate to Basel (Switzerland). Hence, I’m currently reconsidering all of my activities. In view of the unresolved conflict between the founders of Pile Systems, I decided to leave the company and take on other duties.

I thank Peter and Erez/Miriam for some exciting and facinating years.

Take care.

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pwiki

07Nov06

Finally managed to deploy the MoinMoin Wiki Engine to http://pileworks.sourceforge.net/pwiki.

Feel free to

“Check the development environment, and improve where appropriate (automate, wiki,issue tracking)”

(One of Orcas’ Rules of Engagement)

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Interactive computation

28Oct06

Goldin, Smolka et al. (Eds.) 2006 – Interactive computation. Quote from the blurb:

The book challenges traditional Turing machine-based answers to fundamental questions relating to problem solving and the scope of computation.

Okay?! As there are relevant entries in the Web Links section of Pile Systems’ web site to the works of Dina Goldin

Dina Goldin (together with Peter Wegner) studies interactive approaches to computing as concepts beyond the current Turing machine.

and Peter Wegner

Another approach that points in a similar direction as Pile is the “Interactive Computing Paradigm” proposed by Peter Wegner.

it might be of some interest to take a closer look at this new book. Maybe I write a book review. In the meantime, the publishing house let us take a look at Sample pages here.

Cf. http://en.wikipedia.org/wiki/Interactive_computation

Interactive computation involves communication with the external world during the computation. This is in contrast to the traditional understanding of computation which assumes a simple interface between a computing agent and its environment, consisting in asking a question (input) and generating an answer (output).

Note: DINA GOLDIN’S HOMEPAGE HAS BEEN MOVED TO:

http://www.cs.brown.edu/people/dqg

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Pairing function

21Oct06

Basically, Pile is a system that uses coordinates (values) to establish position, one unique frame of reference for sequences of computation. A fusion and split function are vital to construe the Pile space. This Haskell script implements the Cantor pairing function and its inverse.

Haskell script: Cantor

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“Lady X”, ToPs, and Monads

09Oct06

“Beginning from the entity ‘Lady X’, just collect all its relations. That’s it.”

The other day, I read Miriam’s pile stories and her example of ‘Lady X’ as a ToP in the Pile plane. Miriam evoked the nightmare of total inclusion. But, how could ‘Lady X’ be digitized into the digital world inside the computer unless in fiction?

(Cf. the plot of the film Tron)

“The digital world comes alive after the MCP’s defeat. I/O towers light up all over the landscape, and the Programs rejoice in the fact that their world has become a free system.”

Is it this what the “FT-Movement” is all about?

Anyway, I’m currently investigating monadic I/O, a high-level model for functional I/O based on Wadler’s suggestion that monads can express interaction with state in a functional language.

[Wadler97] How to Declare an Imperative. ACM Comp. Surveys, Vol. 29, No. 3, September 1997, pp. 240-263.

http://www.haskell.org/haskellwiki/Books#Using_monads

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How to Assimilate a TGraph Representation in a PILE system: just another Exercise

30Jun06

Yesterday it was the PILE PETER Universe, let’s try a PILE ‘representation’ of a TGraph today. TGraphs, i.e. typed, attributed, and ordered directed graphs, were introduced by (Ebert/Franzke 1995), see the reference at the end of this post.

Our PILE (learning environment) user/agent likes to deal with a TGraph now. The following figure shows A TGraph Representation of a State Chart:

Filed under: Graphs, Pile, Space, Terminal value (TV)   |  Leave a Comment