Computation, fourfolds, Science, technology

The Four Basic Electronic Components

June 10, 2011 Martin K. Jones 2 Comments

A fourfold has recently been in the news. The physical realization of the memristor completes the four basic electronic components, along with the resistor, capacitor, and inductor. Theorized to exist since 1971, the memristor may revolutionize computational devices.

References:

http://en.wikipedia.org/wiki/Memristor

[*6.126-*6.128]

alchemy, evolution, fourfolds, Narrative, Science

A Story for Everyone

June 9, 2011 Martin K. Jones 2 Comments

Wouldn’t it be nice if everyone had a common story we could all learn and share? A story about who we are, what we are, and maybe even a little about the how and the why. Could it be told in such a way that each of us could accept it as our very own? A film and companion book coming out soon will attempt just that, titled Journey of the Universe.

Previous books by Loyal Rue and Brian Swimme have tried to achieve this ideal. Swimme is involved in this new movie, and is the narrator. Rue’s book is a personal favorite. Astrophysicist Eric J. Chaisson has written many books on this topic. Their common theme is evolution, expanded from the biological to encompass the cosmos. Cosmic evolution, if you will.

Evolution merely means change over time, i.e. transformation. Most people agree that things have changed over time, but many disagree on how much, how long, and how come. How can we decide what information to accept, and what to reject? The great unifier of human knowledge is science, yet science is often disparaged even while making the modern world possible. Partially, I’m sure, for that very reason.

Different cultures have had their own creation stories since the very beginning of humanity. Many have said that a large part of being human is the impulse to tell and the need to hear stories. All narratives are built from atomic parts that answer questions: who, what, how, and why. Or, to cast them into modal verbs: may, can, must, and should. Who may? Intention or agency: the characters. What can? Chance or contingency: the setting. How must? Structure or necessity: the plot. Why should? Obligation or responsibility: the theme.

Would a story simplistic enough for everyone to accept be so dilute as to be worthless? All life as we know it requires water, and pure water is ultimately ‘diluted’. But water is certainly not worthless. Daniel Dennett calls the concept of evolution the ‘universal acid’, an alchemical alkahest. Can we replace the corrosive acid in his metaphor with sustaining and nurturing water?

http://www.npr.org/blogs/13.7/2011/03/31/135008214/journey-of-the-universe-the-challenge-of-telling-everybodys-story

http://www.journeyoftheuniverse.org/

Loyal Rue / Everybody’s Story: Wising Up to the Epic of Evolution

Brian Swimme / The Universe Story: From the Primordial Flaring Forth to the Ecozoic Era–A Celebration of the Unfolding of the Cosmos

Daniel Dennett / Darwin’s Dangerous Idea: evolution and the meaning of life

Eric J. Chaisson / Epic of Evolution: seven ages of the cosmos

Marjolein Groefsema / Can, May, Must and Should: A Relevance Theoretic Account, in Journal of Linguistics, Vol. 31, No. 1 (Mar., 1995), pp. 53-79

fourfolds, linear logic, logic

J.-Y. Girard’s Linear Logic

March 9, 2011 Martin K. Jones 13 Comments

Linear logic is a substructural logic invented (or discovered, if you’re a Platonist) by logician Jean-Yves Girard. Many other logics can be embedded into it, including classical and intuitionistic logic, so in a sense it is a “logic behind logic”. Linear logic can be partially derived from the rejection of the structural rules of weakening and contraction, the first of which adds arbitrary propositions and the second reduces duplicated propositions to single occurrences. Due to these changes in the logical rules, logic is transformed from being transcendental (truth transcends its use) to pragmatic or materialistic (truth is restricted by use). Therefore linear logic can be given a “resource interpretation” that makes it a logic not of truth but of things: producing and consuming, giving and taking, pushing and pulling, like the desiring machines of Deleuze and Guattari (see Hjelmslev’s Net).

The fragment of linear logic I show here is called MALL, for Multiplicative-Additive Linear Logic. The two exponentials that interconvert additive and multiplicative operations are not shown, which also allow for the weakening and contraction rules to be reintroduced.

Note that the two additive operations allow for propositions to be created and destroyed and the two multiplicative operations contain exactly the same propositions. One could say the additive operations allow for change, and the multiplicative operations allow for bearing. In the resource interpretation, note that additive disjunction (⊕) is creative and additive conjunction (&) is destructive. Both additive conjunction (&) and multiplicative disjunction (⅋) are reversible, whereas additive disjunction (⊕) and multiplicative conjunction (⊗) are irreversible.

Linear logic was a major inspiration for naming this blog “Equivalent Exchange” (see Introduction), since it is a logic of production and consumption. Linear implication, written as A –o B (and equivalent to A^⊥ ⅋ B), can be thought of as exchanging A for B.

Linear logic has also been adopted as the logic for “radical anti-realism”. How can it have both a physicalistic interpretation, and yet describe an anti-realism more radical than ordinary anti-realism? I will need further study to understand these claims.

References:

http://en.wikipedia.org/wiki/Linear_logic

http://plato.stanford.edu/entries/logic-linear/

[*5.68-*5.70]

fourfolds, logic, semiotics

The Tetralemma and Semiotic Square

January 28, 2011 Martin K. Jones 2 Comments

The Tetralemma is a list that is supposed to exhaust all logical possibilities. Something is either X, or not X, or both X and not X, or neither X nor not X. Nagarjuna’s Fourfold Negation expresses a paradox by negating the Tetralemma, and asking what is not X, nor not X, nor both X and not X, nor neither X nor not X.

The Semiotic Square is an analytical tool to explore relationships between two semiotic signs, usually considered opposites of each other. The S1 and S2 in the figure are the signs in opposition, so that S2 is the dual of S1. S1+~S2 (S1 and not S2) would be X, ~S1+S2 would be not X, S1+S2 would be both X and not X, and ~S1+~S2 would be neither X nor not X.

References:

http://en.wikipedia.org/wiki/Tetralemma

http://en.wikipedia.org/wiki/Semiotic_square

[*4.84, *5.182]

architectonics, Discourse, epistemology, fourfolds, Philosophy

Richard McKeon’s Aspects of Knowing

January 16, 2011 Martin K. Jones 10 Comments

Richard McKeon’s system of Philosophical Semantics arises from the sixteen pairwise and ordered relations between his four aspects of knowing or cognates: knower, knowledge, the known, and the knowable. These sixteen relations can be sorted in four groups of four elements each: methods, interpretations, principles, and selections.

Between knower and knowledge, and between the knowable and the known, arise the four methods of two each: the universal and the particular.

From knower to knowledge, the operational method.
From knowledge to knower, the dialectical method.
From the knowable to the known, the logistic method.
From the known to the knowable, the problematic method.

Between knower and the known, and between the knowable and knowledge, arise the four interpretations of two each: the phenomenal and the ontic.

From knower to the known, the existential interpretation.
From the known to knower, the essential interpretation.
From the knowable to knowledge, the entitative interpretation.
From knowledge to the knowable, the ontological interpretation.

Between knower and the knowable, and between knowledge and the known, arise the four principles of two each: the meroscopic and the holoscopic.

From knower to the knowable, the actional principle.
From the knowable to knower, the simple principle.
From knowledge to the known, the comprehensive principle.
From the known to knowledge, the reflexive principle.

Between each of the aspects of knowing with itself, arise the four selections.

From knower to itself, the perspectival selection.
From knowledge to itself, the transcendental selection.
From the knowable to itself, the reductive selection.
From the known to itself, the functional selection.

Each method can be associated with a discursive process: operational with debate, dialectical with dialogue, logistic with proof, and problematic with inquiry. Each method is also associated with a mode of thought which in turn has two moments and one dependency or assumption: the operational method is debate by discrimination and postulation dependent on chosen theses, the dialectical method is dialogue by assimilation and exemplification dependent on changeless models, the logistic method is proof by construction and decomposition dependent on indivisible constituents, and the problematic method is inquiry by resolution and question dependent on discoverable causes.

References:

Richard McKeon / On Knowing–The Natural Sciences

Richard McKeon / Freedom and History and Other Essays: an introduction to the thought of Richard McKeon

Sadly, the following pages are no longer available:

http://net-prophet.net/mckeon/mckeon.htm

http://forums.abrahadabra.com/showthread.php?2331-Unifying-Astrology-and-I-Ching

[*4.47, *5.184-*5.187, *6.20, *6.106]

alchemy, Cartesianism, fourfolds, Metaphysics, Mind-Body Dualism, Philosophy

Arthur M. Young’s Fourfold Theory of Process

January 2, 2011 Martin K. Jones 4 Comments

I have recently come across the philosophical work of Arthur M. Young (AMY). This is an initial impression of that work since I have only read what is available from the web links below, and even then there is a great deal to digest. In addition, there is difficulty in presenting a summary of his theory because of similarities to my ideas as well as substantial differences. I am sure I will need to return to AMY’s theory after more consideration.

I have hinted at a correspondence between several double duals presented in this blog, but I have steered away from claiming that they are all linked to each other – that they are essentially equivalently exchangeable. AMY’s theory links the four elements, the four causes, Jung’s functions of the psyche, geometrical elements and transformations, as well as several other fourfolds into a cosmic theory of reality.

Some of these same fourfolds are present in my theory, and I am considering how others may be introduced. Some not mentioned by AMY are only mentioned in earlier entries on this blog, without presentation. However, from many of these same fourfolds I have reached substantially different conclusions from AMY. I believe this is because AMY’s theory of process is essentially dualistic, whereas my theory appears to be physicalistic, although one might also say it is a process and/or relational theory.

Below is a table of some of the correspondences for AMY’s theory of process:

	Aristotle’s Four Causes	Jung’s Functions of the Psyche	Four Elements of Empedocles	Geometric Transform- ations
Purpose	Final	Intuition	Fire	Rotation	Spirit
Value	Material	Emotion	Water	Scale	Soul
Form	Formal	Intellect	Air	Inversion	Mind
Object	Efficient	Sensation	Earth	Translation	Body

Below is a table of some of the correspondences for my theory:

Four Elements of Empedocles	The Here and the Now	Aristotle’s Four Causes	Duality of Time and Information	Hjelmslev’s Net
Fire	Before	Efficient	Change time	Substance of content
Water	After	Final	Bear time	Form of content
Air	Above	Formal	Bear information	Form of expression
Earth	Below	Material	Change information	Substance of expression

References:

Arthur M. Young / The Reflexive Universe

Arthur M. Young / The Geometry of Meaning

http://www.arthuryoung.com/barr.html

http://www.arthuryoung.com/4levels.html

http://www.arthuryoung.com/the2exc.html

[*6.84-*6.89, *7.78, *7.79, *8.2, *8.62, *8.63]

fourfolds, Philosophy, semiotics

Hjelmslev’s Net

November 29, 2010 Martin K. Jones 10 Comments

“God is a lobster, or a double pincer, a double bind.”

— From A Thousand Plateaus by Deleuze and Guattari

Linguist Louis Hjelmslev developed a semiotic model which elaborated Saussure’s two part signifier and signified into the double dual of the substance of content, the form of content, the substance of expression, and the form of expression. Contents are “formed matters”, and expressions are “functional structures”. Both are further separated into a substance and a form. The original signifier can be considered the form of expression, while the original signified can be considered the form of content. The two types of forms are like a net of warp and woof (why else a net?), dividing an undifferentiated unformed matter (Earth, purport) into two types of substances.

Deleuze and Guattari cast this net from Hjelmslev’s use in language into universal application by way of examples in geology and biology: sedimentation/folding and molecular genetics. The two planes of content and expression are the First Articulation and Second Articulation, respectively, the first of which “chooses or deducts”, and the second of which establishes “functional, compact, stable structures”. In their geology example, the First Articulation is the process of sedimentation, and the Second, folding. Generally, the two substances deal with territorialization, deterrritorialization, and reterritorialization, and the two forms are concerned with coding and decoding (and recoding?).

Additionally, there is talk of the molar versus the molecular (as continuous/discrete or unity/multiplicity?) but the molar is not form, nor is the molecular substance, nor vice versa. The First Articulation moves from molecular substances to molar forms; the Second Articulation moves from molecular forms to molar substances. How confusing! What does it all mean? One could spend a lifetime lost in these fun-house reflections!

I propose that the four basic logical operators of Linear Logic are in correspondence to the double articulation of Hjelmslev’s Net. Content is Conjunction, Expression is Disjunction, Substance is Additive, and Form is Multiplicative. Content and Expression is Substance or Form; Conjunction and Disjunction is Additive or Multiplicative.

References:

Gilles Deleuze and Felix Guattari / A Thousand Plateaus: capitalism and schizophrenia

Manuel De Landa / The Geology of Morals: a neo-materialist interpretation http://www.t0.or.at/delanda/geology.htm

Luke Feast / The Science of Multiplicities: post-structuralism and ecological complexities in design http://researcharchive.vuw.ac.nz/handle/10063/142

[*3.170, *4.46, *4.88, *4.112, *4.146, *5.70, *5.174, *6.10]

evolution, fourfolds, Science, technology

Kevin Kelly’s Philosophy of Technology

November 19, 2010 Martin K. Jones 1 Comment

Kevin Kelly’s new book “What Technology Wants” is an exploration of what technology is and what it does. Technology has many of the same attributes as biological evolution, and as such, its effects cannot be fully predicted. At best, we can try to evaluate a particular technology’s advantages and dangers before it is let loose into the world; at worst, we will have no control over it at all.

Kelly describes evolution as shaped by structural, historical, and functional factors; and goes on the describe technology as dependent on structural, historical, and intentional factors. However, he also maintains that technology is an evolutionary process, and evolution in turn is a technological process. Kelly seems to say both processes have all four of the factors shown in the double dual above.

Kelly says that human language is the first big human technology (or was it fire? or stone tools?). But I also agree with him that the mechanisms of biological evolution can be considered technology. What is technique except a method that can shared and perpetuated by others? Molecular genetics grants us the ability to pass (most of) our attributes on to our progeny, including the ability to pass (most of) their attributes on to theirs. Once techniques can be shown or told to others, biology becomes the basis for the showing or telling, but not the mechanism of it.

Kelly calls the entire system of evolution/technology the technium. Because we have been continually shaped by our human technologies, they are not foreign to us. On the whole, we are better with them, than without them. One could argue that without them we wouldn’t even be human!

References:

Kevin Kelly / What Technology Wants

[*5.92, *6.60]

fourfolds, linear logic, Metaphysics, Philosophy

Monism = Pluralism

November 5, 2010 Martin K. Jones Leave a comment

PLURALISM = MONISM

– From A Thousand Plateaus by Deleuze and Guattari

Jeffrey Bell’s blog entry about William James’ radical empiricism reveals relations between Hjelmslev’s Net and Linear Logic. To begin with, Hume was concerned with disjunctive relations (of expression) to the exclusion of conjunctive relations (of content). In addition, James sought the solution to the problem that consciousness (here content) has between the “one and the many”, one consciousness in relation to many consciousnesses. Unable to resolve this problem, James did not realize that conjunction can come in two modes, an additive one and a multiplicative one, a substance and a form.

The substance of content (here consciousness, agency, …) is constituted incrementally from choices between actions, either thoughts (thoughts-as-action) or actual actions (actions-as-action). This is additive AND. The form of content (essence, existence) is assembled by the ordering of those choices, a multiple choice of choices. This is multiplicative AND. These are the powers of AND.

However, Hume’s disjunction (expression) also comes in two flavors: additive and multiplicative (substance and form). It also has a problem with the “one and the many”. The substance of expression is either identity or generation (accident, substance). This is additive OR. The form of expression doesn’t seem like much in Linear Logic, but it is the very form of the logic, invertible with the connective tissue of the calculus (the comma). This is multiplicative OR. These are the powers of OR.

Content and expression are dual to each other, as conjunction is logically dual to disjunction. Is content the “subjective” and expression the “objective”? Is substance the “one” and form the “many”? Each is dual to the other, not distinguishable except by perspective. Perhaps these double duals are like a Mobius Strip, which only has one side, weaving in and out and forming a unity out of multiplicity.

Note that the elements of the double dual shown here are taken from the Protreptikos page “Monism and Pluralism”. The fourfold is made up of different “compositions in being”, each in two parts. There are many echoes to other double duals in these compositions, such as potency/actuality (existence) and substance/form.

References:

Gilles Deleuze and Felix Guattari / A Thousand Plateaus: capitalism and schizophrenia

http://schizosoph.wordpress.com/2010/08/11/monism-pluralism/