An Other Space

09Jan08

A visual proof of the existence on an anti-symmetric complementary space S* of gaps (an other space) within the traditional mathematical continuum X=[0,1].

Found in (Anishchenko, Zenkin et al. 2003 – Semantic symmetry of a spiritual)

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Jessicatz Fairymeadow’s Pile Implementation

06Oct07

Jessicatz Fairymeadow tries to do another Pile Implementation with a view to implement the used data types as C++ Templates. The code is meant for Linux32- and 64-Bit (not yet tested for Win).

Please find it in the SVN Repository with the URL: http://data.fieldsofnoise.org/repository/jessicatz/pile.

The main program is pile_test.cpp, the other six files having some resemblance to a “framework”.

Cf. also the thread “Logical Domains in Pile” in the pile development mailing list.

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An open public letter to the “Pile Systems” team (Revisited)

08Aug07

Just revisited George’s open public letter and read the comments from May 17th ff., which I had not noticed but now. I feel, George understood me correctly. I maintain a mostly academic inspiration about the subject.

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TVs, Tops, and the primary (primordial) self-reference

04Aug07

In Dominique Paß’s book “Bewußtsein und Ästhetik” ¹ you find a short excerpt of L. H. Kauffman’s paper “Self-reference and recursive forms” ².

Figure: “primary (primordial) self-reference”

 

The same visualization could be found in (Westphal 2006 – Freeing Data From the Silos)³, but without the mathematical background provided by Kauffman’s paper.

Kauffman’s visualization of the “primary (primordial) self-reference”, where the aspect of the original self-reference is stressed, has the same qualities as Spencer-Brown’s “mark of distinction”. Besides “mark”, Kauffman denotes the marking, that is given in the form of the arrow here also pointing the way ahead, as “barb” or “pointer” as well. (cf. combinative pointer)

Paß writes on p. 162 quoting Kauffman:

“Therefore, self-reference and the idea of distinction are inseparable (hence conceptually identical).” (…) Die Markierung (“pointer”) wird konstruktiv, insofern mit der Markierung der Raum entsteht, auf den die Markierung verweist. Mehr noch: “the mark points [...] to its own location, and in this process becomes a locus of reference. The mark referes to itself. The whole refers to itself through the mark.” (…)

 

 

 

1Paß, Dominik (2006): Bewusstsein und Ästhetik. Die Faszination der Kunst. Bielefeld: Aisthesis. (http://www.aisthesis.de/titel/3895285889.htm)

2Kauffman, Louis H. (1987): Self-reference and recursive forms. In: Journal of social and biological structures, 10, pp. 53–72.

3Westphal, Ralf (2006): Freeing Data From the Silos. A Relationistic Approach to Information Processing. Available online at http://www.pilesys.com/new/Documents/Freeingdatafromthesilos-Pileexplained.pdf, esp. pp. 13–14.

Filed under: Combinative Pointer, LoF, Pile, Visualization   |  1 Comment

Junctions, Perl 6, Haskell, …

22Jul07

Perl 6 introduces the concept of junctions: values that are composites of other values. [24] In the earliest days of Perl 6’s design, these were called “superpositions”, by analogy to the concept in quantum physics of quantum superpositions — waveforms that can simultaneously occupy several states until observation “collapses” them. A Perl 5 module released in 2000 by Damian Conway called Quantum::Superpositions [25] provided an initial proof of concept. While at first, such superpositional values seemed like merely a programmatic curiosity, over time their utility and intuitiveness became widely recognized, and junctions now occupy a central place in Perl 6’s design.

(Source: http://en.wikipedia.org/wiki/Perl_6)

Keywords: junctions, composite value, superposition, Perl 6, design

Since the action of joining or being joined is evidently one of the central issues of this blog, a definition of junction might be useful (definition understood as communicative act to describe a phenomenon).

WordNet 2.1 Synonyms Only says:

/noun./ spot, topographic point, place, unification, union, connexion, link, connection, connective, connector, connecter, joining,

. …

The Quantum::Superpositions module provides a new scalar data structure: the superposition. In a metaphor drawn from quantum mechanics, superpositions store a collection of values by overlaying them in parallel superimposed states within a single scalar variable.
. …

A junction is a superposition of data values pretending to be a single data value.
. …

junction – the shape or manner [sic!] in which things come together and a connection is made
. …

Filed under: Boundary Mathematics, Combinative Pointer, Haskell, Haymow, Junctions, Perl6, Pile, Space, Superposition   |  Leave a Comment

The Prolog Theorem Prover “mflogic.exe”

03Jun07

–> http://multiforms.netfirms.com/multiforms_1.html#download

[...] A Prolog Theorem Prover simplifying Logic, by using Multiple Forms The strategy of this Prolog program (“mflogic.exe”, which you can download) is essentially the same as the strategy of a (human) theorem-prover, who knows the Axioms of Multiple Forms: As much as possible, all logic formulae are progressively reduced, by cancelling out “Outer Parts” if these are also found in “Inner Parts” of expressions (using Axiom 3). They are also reduced by “ the All” (=One) “absorbing anything” that “exists outside itself” (using Axom 1), or (finally) reduced by pairs of identical forms “ collapsing” when they apply to each other, “distinguishing each other” (XOR-wise, by Axiom 2).

The Prolog program “includes some extensive automatic comments, sprinkled over the derivation steps, so it can become an educational tool for learning Multiple Form Logic™.”

Find a screenshot here:

George, a.k.a. Omadeon,

“wrote it recently, coming back to Multiple Form Logic™ after a long period of absence from this field, and it is still Version 1. Future versions planned may include graphic representations of Multiple Form simplifications, which are quite spectacular, even on paper, like watching an avalanche of ‘bubbles’ breaking and re-organising themselves.”

By the way, what are traditional Propositional Logic formulae? The Prolog program translates them into Multiple Form Logic™, and then uses repeatedly the Three Fundamental Axioms of Multiple Form Logic as re-write rules, until the resulting expression is irreducible. (You can either pick a formula from a library, or write your own). Then, the result is converted back into Propositional Calculus. Multiple Form Logic™ is supposed to do better than just ‘prove theorems’ to be ‘true’ or ‘false’; but actually “optimizes logic expressions, regardless of whether or not they are reducible to true or false.”

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Entailments_Context.mov @ 00:03:30

03Jun07

Had a closer look at the video Entailments_Context.mov of Dr Paul Pangaro teaching Cybernetics and Pask’s Entailment Meshes at Stanford:

• Coherence
• Unit of memory

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Pask’s Entailment Meshes

02Jun07

Going through omadeon’s LoF bookmarks on del.icio.us, I found Nick Green’s paper: (Green 2004 – Axioms from Interactions of Actors). It deals with Gordon Pask’s Interactions of Actors Theory and his earlier Conversation Theory.

The introduction of Nick’s paper talks about a special form as a computing element comparable to the “Pile object”:

The central object is the stable concept triple which takes the form of the Borromean link. The potential of this form as a concurrent computing element and a model of continuity is discussed.

Cf. the earlier item Symbols And Borromean Links inserted in this blog, and the videos of Dr Paul Pangaro teaching Cybernetics and Pask’s Entailment Meshes at Stanford:

[Regarding Semantic Nets]

In a sense, there is too much freedom. And if you have too much freedom, there is no way to go.

A decision restricts the degree of freedom of another decision thus constructing a beginning-midpoint-end configuration, i.e. one way. (German: Eine Entscheidung begrenzt den Freiheitsgrad der anderen Entscheidung, konstruiert aber eine Anfang Mitte Ende – Konfigurtation, d.h. einen Weg.)

And then one day, these entailment meshes came along.

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Multiple Form Logic revisited (after one year)

19May07

One year after the “Multiple Form Logic” post (see [1] ), George A. Stathis alias omadeon is part of the “Pile” community for some inspiring days now. You are welcome!

We can correct a small mistake in that one year old post (see George’s recent comment [2] ). The mistake is all about boundary (and a self-reference operator).

Filed under: Boundary Mathematics, Combinative Pointer, Haymow, LoF, Logic, Pile, Space, Symbol, Terminal value (TV), Visualization, container   |  5 Comments

Ralf Westphal’s “Intuitive Data Model”

21Feb07

Starting from what he calls the “Container-Reference Dichotomy” since an earlier paper (Westphal 2006 – Freeing Data From the Silos, pp. 1-3), Ralf now tries to get along with ‘containers’ only. [1] [2]

He questions the necessity of making a decision between container and reference. Further on, he conceives of ‘data’ and ‘containers’ as a (only one?) hierarchy of values in a “universe of unique values“ (a distant salute to the Pile space).

Filed under: Pile, Terminal value (TV), container   |  1 Comment