Category Archives: fourfolds

Computation, fourfolds, Mathematics

The Duality of Time and Information, V3

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The states of a computing system bear information and change time, while its events bear time and change information.

— from The Duality of Time and Information by Vaughan Pratt

The most promising transformational logic seems to us to be Girard’s linear logic.

— from Rational Mechanics and Natural Mathematics by Vaughan Pratt

Here we have three duals:

  • Information – Time
  • States – Events
  • Bear – Change

Further Reading:

Vaughan Pratt / The Duality of Time and Information http://boole.stanford.edu/pub/dti.pdf

Vaughan Pratt / Time and Information in Sequential and Concurrent Computation http://boole.stanford.edu/pub/tppp.pdf

Vaughan Pratt / Rational Mechanics and Natural Mathematics http://chu.stanford.edu/guide.html#ratmech

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Astronomy, fourfolds, Science

Cassini

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“Thanks, and farewell, faithful explorer.”

— Cassini program manager Earl Maize

Today, Cassini’s impetus succumbed to Saturn’s gravity.

Further Reading:

https://www.google.com/amp/amp.usatoday.com/story/667937001/

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fourfolds, mythology, religion

Behold, the Tetramorph

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I’ve felt a fondness for the Tetramorph for a long time. Four beings considered simultaneously: a man, an ox, a lion, an eagle.

They are the Babylonian symbols of the four fixed signs of the zodiac: ox or bull for Taurus (and earth), lion for Leo (and fire), eagle for Scorpio (and water), man for Aquarius (and air).

They can be thought of as representing the ancient four elements: earth, fire, water, and air.

They are mentioned in the Judeo-Christian Bible in the books of Ezekiel and Revelation. They have also been paired with the four evangelists and their books: Matthew, Mark, Luke, and John (although the pairing is not fixed).

They are shown on the Tarot card for the “Wheel of Fortune” in the Rider-Waite deck, and the card for the “World” in the Tarot of Marseilles.

Why these four creatures, and not others?

Further Reading:

https://en.wikipedia.org/wiki/Tetramorph

The Tetramorph; The Sumerian Origins of a Christian Symbol

Sacred Symbols: The Four Evangelists (Tetramorph)

Under The Sign Of Tetramorph

https://en.wikipedia.org/wiki/Astrology_and_the_classical_elements#Elements_of_the_zodiac

44. The Tetramorph and more

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fourfolds, religion

The Four Last Things

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Over the years, there has been much religious consideration of the four last things in Christian Eschatology. They are

  • Death
  • Judgment
  • Heaven
  • Hell

Many books have been written and many paintings have been painted. In my project to present every fourth thing, I imagine I’ll come to them eventually, but why wait until then? Or maybe I’m thinking of the “Last Four Things”.

Actually, I’d much rather play the video game on my Mac, because it looks like a lot more fun. Plus it uses classical music for a background soundtrack and images from Hieronymus Bosch’s paintings, such as the Garden of Earthly Delights. When will the Mac version be available? Anyone?

Further Reading:

https://en.wikipedia.org/wiki/Four_last_things

https://en.wikipedia.org/wiki/Christian_eschatology

https://en.wikipedia.org/wiki/Four_Last_Things_(video_game)

http://joemcrichardson.com/fourlastthings/presskit.html

Robert Southwell / A Four-fold Meditation of the Four Last Things

News:

FLT is finally out on Android and iOS! There is much rejoicing!

http://steamcommunity.com/games/503400/announcements/detail/1669015871902809029

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fourfolds, Psychology

I Dare You!

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In 1931, William H. Danforth published the book “I Dare You! Four fold development: stand tall, think tall, smile tall, and live tall.” Perhaps he is better remembered as the founder of the Ralston Purina Company, maker of many fine products and particularly of Chex Cereals. Indeed, Danforth saw life as a type of checkerboard, such that four key components (or “squares”) – the mental, the physical, the social, and the religious – needed to be in balance in order to achieve fulfillment and success in life.

His book was the expression of his personal philosophy of “Four-square” personal development, and was a early example of the “self-help” style of book that has become so popular. Success! Fulfillment! So much can become yours if you take chances and work hard. If only life was that simple! His four aspects of personal development are

  • Physical: Stand Tall!
  • Mental: Think Tall!
  • Social: Smile Tall!
  • Spiritual: Live Tall!

Further Reading:

https://en.wikipedia.org/wiki/William_H._Danforth

William H. Danforth / I Dare You! Only $1 in Kindle format from Amazon! Worth every penny! Don’t delay, buy today!

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fourfolds

Twin Peaks

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Through the darkness of future’s past,
The magician longs to see.
One chants out between two worlds…
“Fire… walk with me.”

— Mike from Twin Peaks

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Astronomy, fourfolds, Science

A Solar Eclipse

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Further Reading:

https://eclipse2017.nasa.gov/science

https://en.wikipedia.org/wiki/Solar_eclipse_of_August_21,_2017

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fourfolds, Philosophy

Four Philosophies, V2

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Thinking some more on Popper’s Three Worlds, here is a set of philosophical disciplines that seem to resonate with the themes of this blog.

  • Phenomenology: the philosophical study or theory of phenomena as distinct from that of the nature of being
  • Epistemology: the theory of knowledge, especially with regard to its methods, validity, and scope
  • Ontology: the branch of metaphysics dealing with the nature of being
  • Axiology: the philosophical study of the nature of value and valuation, and of the kinds of things that are valuable

I believe that one could also make a case for associations with phenomenology to the subjective, epistemology to the objective, ontology to the substantive, and axiology to the normative.

Further reading:

https://www.quora.com/What-does-ontology-epistemology-and-axiology-mean

http://cognitive-edge.com/blog/phenomenology-epistemology-ontology/

(Note that the author of the article above, David Snowden, is the creator of the Cynefin Framework.)

https://en.wikipedia.org/wiki/Phenomenology_(philosophy)

https://plato.stanford.edu/entries/phenomenology/

Phenomenology

https://en.wikipedia.org/wiki/Epistemology

https://plato.stanford.edu/entries/epistemology/

Epistemology

https://en.wikipedia.org/wiki/Ontology

https://plato.stanford.edu/entries/logic-ontology/

https://en.wikipedia.org/wiki/Axiology

https://plato.stanford.edu/entries/value-theory/

https://equivalentexchange.wordpress.com/2015/05/14/four-philosophies/

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Computation, fourfolds, Space and Time

A Digital Universe, V2

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A digital universe – whether 5 kilobytes or the entire Internet – consists of two species of bits: differences in space, and differences in time. Digital computers translate between these two forms of information – structure and sequence – according to definite rules. Bits that are embodied as structure (varying in space, invariant across time) we perceive as memory, and bits that are embodied as sequence (varying in time, invariant across space) we perceive as code. Gates are the intersections where bits span both worlds at the moments of transition from one instant to the next.

— George Dyson, from Turing’s Cathedral

Further Reading:

George Dyson / Turing’s Cathedral: the origins of the digital universe

Notes:

Embodied as Structure, Perceived as Memory

Invariant across Time: ¬ΔT
Varying in Space: ΔS

Embodied as Sequence, Perceived as Code

Varying in Time: ΔT
Invariant across Space: ¬ΔS

https://equivalentexchange.wordpress.com/2012/04/12/a-digital-universe/

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fourfolds

The Prisoner’s Dilemma

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A simple example from game theory shows how two rational individuals might not chose to cooperate if the result for not doing so might be in their favor.

Two prisoners are asked for more information about their common crime. They can each remain silent and thus collude with each other. Or they can confess their participation and thereby incriminate the other prisoner.

Unfortunately there is already enough evidence against them for a sentence, so if they both remain silent they will still serve some time (say 1 year each). However if they both confess they will both serve more time (say 2 years each). And if one confesses but the other remains silent the confessor will serve no time but the betrayed one will serve an even longer sentence (say 3 years)!

The thing to notice is that each prisoner will serve less time if they defect and betray the other prisoner than if they cooperate with them. You might even think the sentences are calculated to promote betrayal!

Further Reading:

https://en.wikipedia.org/wiki/Prisoner%27s_dilemma

https://plato.stanford.edu/entries/prisoner-dilemma/

William Poundstone / Prisoner’s Dilemma: John Von Neumann, game theory, and the Puzzle of the bomb

Note passage from SEP:

The new story suggests that the Prisoner’s Dilemma also occupies a place at the heart of our economic system. It would seem that any market designed to facilitate mutually beneficial exchanges will need to overcome the dilemma or avoid it.

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