Essay on Man

February 6, 2013 Martin K. Jones Leave a comment

All nature is but art, unknown to thee;
All chance, direction, which thou canst not see,
All discord, harmony not understood,
All partial evil, universal good…

— From An Essay on Man by Alexander Pope

I was struck by the four divisions that the poet makes in the world, and how it echoes many other of the fourfolds shown here. Ignoring whether you think the former or the latter extreme of each division is correct, consider the aspect of the world that each division ranges over. Between nature and art lies the material and the parts of the world, either naturally occurring or fashioned by some intention. Between chance and direction lies the individual actions and occurrences of the world, either merely haphazard or towards something. Between discord and harmony lies structures of those materials and parts, and between evil and good lies functional arrangements of those acts and occurrences.

References:

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

[*7.98]

fourfolds, Physics, Science

Schrödinger’s Cat

January 11, 2013 Martin K. Jones 1 Comment

Now let’s look at another thought experiment, that of Schrödinger’s Cat. This thought experiment is supposed to confound the micro and macro worlds of quantum physics and ordinary, human-size physics. A cruel device is built consisting of a closed box which contains a sample of radioactive material, a mechanism to release poison into the box if an atom of the radioactive material decays, a living cat, and a door that must be opened to reveal the condition of the cat to an external observer.

The story of the experiment goes that if the observer waits to open the box until there is a 50% probability that an atom decays, the state of the cat (hidden in the unopened box) to the observer will be both alive and dead. The cat’s so-called wave-function will be a superposition of the wave-function of a live cat and that of a dead cat, which will collapse into one or the other only by the opening of the door and the observation of the actual condition of the cat. This is called the Copenhagen Interpretation.

Some say that the detector of the poison release mechanism will be the true observer in this experiment, and before the external observer opens the door the cat will be definitely alive or dead because of the action of the mechanism. This might be considered the objective collapse theory. Others say that the world splits in two between a world where the cat is alive and one where the cat is dead. This is called a many-worlds interpretation.

There seems to me a similarity between Maxwell’s Demon and Schrödinger’s Cat. The fourfold elements of the experiment are shown above, but now consider these elements in a system in terms of Aristotles’s Four Causes. The material causes are the discreet constituents of the experiment, everything from box to atoms to cat to observer. The efficient cause is the decay or non-decay of a radioactive atom. The final cause is action of the observer in opening the box. The formal cause is the poor cat in its ambiguous state, simultaneously both dead or alive.

It doesn’t make too much common sense to say that the opening of the box and the observing of the cat “causes” the atom to have really decayed or not, and so concretize the past and the cat into a certain way of being, but that is mostly what the Copenhagen Interpretation is saying. Indeed, Linear Logic, which has been described many times on this blog, has been used to describe aspects of quantum physics for decades.

References:

http://en.wikipedia.org/wiki/Schr%C3%B6dinger%27s_Cat

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

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fourfolds, Physics, Science

Maxwell’s Demon

December 17, 2012 Martin K. Jones 2 Comments

I am currently reading Tor Norretranders “The User Illusion”, and he opens the book with chapters on information theory and thermodynamics. His description of the thought experiment “Maxwell’s Demon” made me realize that this system has all the ingredients of a fourfold: the two chambers, the demon, the door between the two chambers that the demon operates, and the molecules that the demon allows to or prevents from passing through the door from one chamber to another. The only way between the two chambers is through the door. The molecules are in a gaseous state, with a distribution of velocities, so some are moving faster than others.

The major physical action that the demon can perform is to open or close the door. If the demon did this randomly, it would accomplish nothing, and the system would ultimately evolve the same as one without door or demon. Instead the demon is able to open and close the door so as to allow faster molecules to collect in one chamber and slower molecules to collect in the other. The demon doesn’t touch the molecules, but he is somehow able to tell whether a molecule is fast or slow so he can decide whether to open or close the door.

The purpose of the thought experiment is to suggest that this system could violate the second law of thermodynamics by increasing order. By letting faster molecules move to one chamber, the system would then be able to do work by, for example, powering an engine. Perhaps the temperature differential is also able to power the demon itself. We would then have a perpetual motion machine, one that could give us unlimited energy, as long as there was a surplus of energy after the needs of the demon.

However, the modern analysis of the thought experiment shows that entropy does indeed increase within this system because the demon would eventually have to forget information about the molecules, and his forgetting would increase entropy. The demon would have to be an irreversible process.

References:

http://en.wikipedia.org/wiki/Maxwell%27s_demon

Tor Norretranders / The User Illusion: Cutting Consciousness Down to Size

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alchemy, fourfolds

Fourfolds and Double Duals, Part 2

November 12, 2012 Martin K. Jones 1 Comment

In addition to the symbolic fourfold presented in the previous entry Fourfolds and Double Duals, which includes the alchemical symbols for the four elements, here is another generic representation. This fourfold reminds me of the fourfolds Bright-Light-Dim-Dark shown in the early entry with the Four Elements, as well as the newer fourfold of The One and the Many.

If one considers the outer ring and the inner circle to be “outer-as-inner”, then this fourfold is related to the One and the Many by letting One be white and Many be black.

Additionally, the symbols can be seen to map to the fourfold Bright-Light-Dim-Dark by noting that White-as-White is Bright, White-as-Black is Light, Black-as-White is Dim, and Black-as-Black is Dark.

For fun, this figure can be tweaked to reveal a deconstructed yin yang. It reminds me of John Dee’s Hieroglyphic Monad. Or someone holding a Vulcan Lirpa from Star Trek’s Amok Time.

References:

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

Notes:

Amusingly, I’m starting to think of the lower figure as a crossed fork and spoon: a fork to separate and a spoon to combine. Note the handles of the utensils (the circles) appear to be switched, but that is just the way it is.

Also: a c & t’s mouth and c ⅋ t’s eye; a d ⊕ g’s nose and d ⊗ g’s eye. These are the binary operators of Linear Logic!

alchemy, fourfolds, linear logic

Fourfolds and Double Duals

November 5, 2012 Martin K. Jones 2 Comments

For every aspect of the world that someone has thought to analyze into its components, it probably has been suggested to divide it into four parts. I suggest that many of the things that have a fourfold form, are a fourfold in the same way. Not in the trivial cardinal sense, but in a deeper structural sense. They are a combination of two dualities, a double dual if you will, such that one dual operates as interior and exterior, or true and false, a duality of opposites, and another (dual) dual operates as one and many, or unity and multiplicity, or discreteness and continuity, a duality of numeracy.

I have been gathering fourfolds for a time, and have written about some more than others. Some have been around a long time, and others I’ve been inspired to fashion. I have tried to orient them all in the same way to accentuate their common deep structure. For example, everything in the left position in the diagrams have a commonality across fourfolds, as does everything in the lower, upper, and right positions. The four ancient symbols shown in the diagram above represent the four elements of alchemy: fire, earth, air, and water.

Because of these relations between the fourths and the halves of these fourfolds, I have choosen the name “Equivalent Exchange”. In addition, the fourfolds themselves might be “equivalently exchangable” with each other because of their common deep structure. For many reasons, I believe that the best exemplar for these fourfolds is the recent logical system known as Linear Logic, which has two combining binary operators and two dividing binary operators.

Others before me have reached similar hypotheses about fourfolds in general, and I am grateful for their scholarship. I hope others will follow, and I’m sure they will present their findings more eloquently and convincingly than I have.

References:

http://en.wikipedia.org/wiki/4_%28number%29

http://www.samuel-beckett.net/Penelope/four_symbolism.html

http://www.unterzuber.com/4our.html

fourfolds

McLuhan’s Tetrad of Media Effects

October 23, 2012 Martin K. Jones Leave a comment

References:

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

http://earth-wizard.livejournal.com/56638.html

[*6.4, *7.122]

fourfolds

Antisynthesis

September 21, 2012 Martin K. Jones 1 Comment

In a mechanism, analysis coincides with antisynthesis.

— From Life Itself, by Robert Rosen

The triad thesis-antithesis-synthesis has been erroneously credited to Hegel, but it still widely mentioned. What if the triad becomes a fourfold? Then the first term that comes to mind to turn three into four is antisynthesis. The writer most familiar to me who used this term was Robert Rosen, a theoretical biologist.

Rosen thought that antisynthesis was analysis for what he calls mechanisms. Mechanisms are natural systems such that every one of its models is simulable, that is, computable as in a computer. One of Rosen’s main claims in his research was that living systems were natural systems but not reducible to mechanisms. His argument depended on an analysis of the causation or entailments in such systems.

Because so many of the fourfolds presented here are linked to Aristotles’s Four Causes, I feel that I may need to revisit Rosen’s Theory in a separate entry to do it justice. This entry was merely about the term antisynthesis and its relation to the original triad.

Notes:

In this fourfold there are two negations and two affirmations.

Hegel instead used concrete, abstract, absolute. To complete the four: bounded, partial, uncertain, finite?

References:

http://en.wikipedia.org/wiki/Thesis,_antithesis,_synthesis

Robert Rosen / Life Itself: A Comprehensive Inquiry into the Nature, Origin, and Fabrication of Life

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evolution, fourfolds, Science, technology

The Four Bases of DNA

September 12, 2012 Martin K. Jones 2 Comments

DNA neither cares nor knows. DNA just is. And we dance to its music.

— Richard Dawkins

DNA, the genetic code and biological machinery all life on earth shares, has been in the news lately. It was once thought that much of our DNA was useless junk, but recent research reveals that this portion of our DNA is very important to the operation of epigenesis. This portion of DNA could be called dark bio-matter, or better dark bio-information or even dark bio-code, since it contains switches and instructions that guide each individual organism’s developmental growth through time.

Previously, the parts of DNA thought to be important were those regions that define the proteins that assemble to form our tissues. Mutations in the DNA that specify proteins can lead to disease because the mutated proteins cannot perform the functions that they need to. Of course, mutated proteins can also be improved and increase health. Comparing protein sequences across species shows that we have many commonalities as well as important differences with our animal cousins. What was once considered a “great chain of being” is now thought to be a great tree of life, all shown by DNA.

DNA is also a fourfold, and a double dual as well, since for the four bases Adenine (A), Thymine (T), Guanine (G), and Cytosine (C): A pairs with T, and G with C. I am not saying that DNA is analogous to the other fourfolds presented here, but it makes a nice diagram.

Questions:

Why does DNA have four bases and not two, like binary computer code?

Even more of DNA determines our health and variation, the things that make us who we are. Does that constrain us even more, or will this knowledge make us more free?

Epistemic Virtues of Objectivity

August 22, 2012 Martin K. Jones Leave a comment

I recently finished reading Lorraine Daston and Peter Galison’s “Objectivity”. In this very interesting book, the authors argue that the notion of scientific objectivity has evolved over time. They have divided the course of this evolution into three main phases: truth-to-nature, mechanical objectivity, and trained judgement. During each phase, the main view of objectivity is dominant, but previous phases are still important to the overall idea of what objectivity means in the scientific community.

The epistemological virtues of objectivity can be divided into four major aspects: persona, ontology, image, and practice. For each phase of objectivity, each aspect has different qualities. For instance, the scientific persona becomes a sage during the truth-to-nature phase, a worker during the mechanical objectivity phase, and an expert during the trained judgement phase. Similarly, the ontology aspect passed through the qualities of universals-particulars-families, the image aspect passed through reasoned-mechanical-interpreted, and practice passed through the stages selection and synthesis-automated transfer-pattern recognition.

The evolutionary phases of objectivity, as well as the qualities of the epistemological virtues seen as the four aspects, is beautifully shown by many examples from a collection of scientific atlases. Anyone interested in the history of science as well as the notion of scientific objectivity should enjoy this book.

I thought it was also remarkable that these four aspects of objectivity were very similar to the four aspects of the Archic Matrix of Watson and Dilworth.

The Curry-Howard Correspondence

August 21, 2012 Martin K. Jones Leave a comment

The Curry-Howard Correspondence reveals a close correspondence between the constituents of Logic and of Programming. Also known as the Formulas as Types and the Proofs as Programs interpretations.

Existential Quantification (∃) of Logic corresponds to the Generalized Disjoint Sum Type (∑) of Programming. Universal Quantification (∀) of Logic corresponds to the Generalized Cartesian Product Type (∏) of Programming. Conjunction (⋀) of Logic corresponds to the Product type (×) of Programming. Disjunction (⋁) of Logic corresponds to the Sum type (+) of Programming.

There are associations between the Curry-Howard Correspondence and the fourfolds of the Square of Opposition, Attraction and Repulsion, and of course Linear Logic.