Archive for the ‘religion’ Category

The Arcane Arts of Ramon Llull : the Dignities

July 7, 2019

Oh, Ramon Llull, where have you been all my life? I’m sure he’s been there all along, death now over seven hundred years in the past, just like always. His legacy seems at first glance to be quite the essence of medieval religion and scholastic philosophy, but still significantly and obscurely different to be enticing to this one. And on further examination, much more.

My schema above has little to do with his grand elaborate figures, except for listing the sixteen attributes he called “dignities”. Llull’s diagrams are full of clock-like wheels within wheels, complicated tableau, and combinatorial patterns. He wished to create a universal model to understand reality, and who wouldn’t want to discover the same? It is said that his methods are akin to an early computer science, and I’m just now starting to understand why.

The magister based the substance of his methods on his Christian faith, although he converted in midlife from Islam. Living in Barcelona, it was probably a good place to make such a change, but felt his calling was to convert others as well, so traveling he went. The methods he developed to convince others of their errors in belief were quite remarkable, as were the volume of his writing.

Like Gottfried Wilhelm Leibniz, who lived four hundred years later and was influenced by him, Llull wished to automate reasoning. But instead of building mechanical devices, Llull built computers from paper and ink, rulers and drawing compasses, scissors and glue. And instead of numbers as the smallest tokens of his computer, he used abstractions (i.e. words) that he felt would be understood by everyone in exactly the same way.

For example, he enumerated these sixteen dignities or aspects of his Christian diety, although sometimes he used the first nine. His constructions allowed one to pose questions and then obtain answers mechanistically that would be convincing to all observers of the correctness of the result. Too bad he was ultimately stoned to death while on his missionary work, although he lived to be eighty two.

Llull’s devices remind me of some of my pitiful charts and diagrams, and make me wonder if I may either adapt some of his techniques to my own use, or be inspired to develop others. I suspect I have locked myself into limitations by my approach, or are these constraints to my advantage? It might be hard to have spinning elements, but I can envision sliding elements like Napier’s Bones, origami-style folding and pleating, and even physical constructions like linkages and abacuses.

Now a martyr within the Franciscan Order, Llull’s feast day is June 30, which I’ve now missed. I hope to remember him to repost or improve on this by next year.

Further Reading:

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

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

http://trepanatus.blogspot.com/2007/06/ramon-llull.html

https://history-computer.com/Dreamers/Llull.html

http://www.ramonllull.net/sw_studies/studies_original/compsale.html

“Let us Calculate!”: Leibniz, Llull, and the Computational Imagination

http://www.ncregister.com/blog/astagnaro/bl.-raymond-lull-and-the-worlds-first-computer

https://dangerousminds.net/comments/the_13th_century_thinking_machine_of_ramon_llull

The memory wheel

https://www.google.com/search?q=ars+magna+llull&tbm=isch

[*11.118]

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The Four Horse-persons of the Apocalypse

February 26, 2019

In preparation for the “Good Omens” TV (specifically, Amazon Prime and BBC Two) series, I started reading the 1990 novel by Terry Pratchett and Neil Gaiman. Concurrently, and after watching too much TV news, I started to think (again) about the Four Horse-persons of the Apocalypse. In the book, personifications of these entities appear as characters working conscientiously to bring about the end of the world (but so far without their trusty steeds). They are (by one interpretation):

  • War (or Conflict) (said to ride a Red Horse)
  • Famine (said to ride a Black Horse)
  • Disease (said to ride a White Horse)
  • Death (said to ride a Pale Horse)

These four riders famously make their appearance in the biblical book of Revelation, after the Four Living Creatures (essentially, the Tetramorph) say “Come” or “Allons-Y!”, depending on your translation. And indeed the Four Horse-persons are a powerful “meme” and are referenced in many popular entertainments and real-life derivative nomenclatures. I’m looking forward to the video series as I enjoy the main actors playing the “odd couple” of angel and demon, and after viewing the various trailers and photos.

Who says Armageddon (or the struggle against it) can’t be fun? Ok, I admit it’s scary but sometimes you just have to laugh!

Further Reading:

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

https://en.wikipedia.org/wiki/Good_Omens_(TV_series)

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

https://en.wikipedia.org/wiki/Living_creatures_(Bible)

https://publicdomainreview.org/collections/the-four-horsemen-of-the-apocalypse/

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

Here Death is the end, but it’s only the beginning of the end (or is it the end of the beginning?) in the four-fold “The Four Last Things”:

https://equivalentexchange.blog/2017/09/06/the-four-last-things/

[*8.118, *11.20]

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Behold, the Tetramorph

September 15, 2017

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

http://occultum.net/the-sacred-tetramorph/

http://eden-saga.com/en/under-the-sign-of-tetramorph.html

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

https://quadriformisratio.wordpress.com/2013/07/01/the-tetramorph-and-more/

[*8.38, *8.96]

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The Four Last Things

September 6, 2017

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

[*10.32]

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Religion and Science

September 20, 2015

sq_religion_vs_scienceWhat is the relationship between religion and science? Instead of one answer, Templeton Prize winner Ian Barbour presents us with four possibilities: independence (or autonomy), conflict, dialogue, and integration.

These four relationships described by Barbour can be useful to consider, as they describe what may exist between the two entities in the mind of an individual or the social discourse of a culture. For religion and science, what is their stance towards one another? Would you say they are independent of one another like Stephen Jay Gould’s non-overlapping magisteria, or in constant conflict as they appear to be in the media? Or are they in helpful dialogue with one another or even harmoniously integrated with one another? Or are they one thing some times, and then another thing at other times?

It seems that these four relationships are not restricted to just religion and science, as any two distinct institutions could have one or more of these interactions between them. For example there is religion and government, science and business, or public education and certain political organizations, to name just a few. Also, any two different religious institutions or any two different scientific fields could be in any of these relationships. For example there is the Catholic Church and all Protestant Churches, Sunni Islam and Shia Islam, and even Christianity and Buddhism. For science, consider physics and biology, chemistry and sociology, etc.

So why pick on religion and science? Is it because there seems to be so much conflict between them in our own minds? Are they frequently at odds with one another in the public and private spheres? And is that a good thing or a bad thing?

What is religion, anyway? Is it the sum total of all religious institutions and cultural behaviors? Is it the sum total of all religious beliefs held by individuals? Or is it the total of both of those things, plus more? And what is science? Is it the sum total of all scientific facts and literature, or the actual institutional structures and methodologies for all scientific practitioners? Is it the sum total of all scientific knowledge along with all the evidence for all that knowledge that are in the current minds of scientists and even non-scientists?

Without people, all you would have left of religion are the buildings, the texts, and the relics. Without people, all you would have left of science are the buildings, the writings, the instruments, and the facts. Both obviously have very large individual and social components that are sustained through teaching and learning. If post-humans or alien visitors found only the material residue of human religion, they could possibly understand it to some extent with enough anthropological work. If visitors found only the material residue of human science, I think they would be able to follow the chain of reasoning and the body of evidence to support the factual conclusions. Some facts and theories might be incorrect, certainly, but not most. Thus science contains an objective component not found in religion.

The first sentence about each from Wikipedia:

“A religion is an organized collection of beliefs, cultural systems, and world views that relate humanity to an order of existence.”

“Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe”.

The definition of science is pretty clear, but the one for religion is a little vague. I’m not sure what an “order of existence” is supposed to be, and it’s not defined there on Wikipedia. Is it an ordering of things that exist, so humanity is assigned to fit in a certain place in a hierarchy, say between gods and animals, i.e. a “great chain of being”? Is that the same as a “world view”? It seems that a world view could contain an order of existence, but not necessarily the other way around. So one could have a world view without an order of existence.

Only you can decide for yourself which relationship exists between religion and science, and unless you have public writings on the matter, no one can investigate and draw their own conclusions of what you think. And anyone can produce a claim for the ultimate stance between religion and science, but of course such claims must be substantiated by reason and evidence. Scholars can produce informed discussions on the matter, to greater or lesser acceptance.

References:

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

https://en.wikipedia.org/wiki/Relationship_between_religion_and_science#Perspectives

http://www.religion-online.org/showchapter.asp?title=2237&C=2064

https://scienceandtheology.wordpress.com/2010/11/11/science-and-religion-barbours-4-models/

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

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

Also please see the previous post:

https://equivalentexchange.wordpress.com/2011/07/27/the-four-conic-sections/

[*9.42]

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The Book of Nature

July 26, 2015

sq_four_senses2The purpose of a system is what it does.

— Stafford Beer

The natural world we find ourselves in is of sufficient wonder, beauty, pain, and terror that many insist that some demiurge had to have made it, and fashioned us as well. For centuries before the dawn of science, the notion of the “Book of Nature” was an influential concept of how knowledge about the world was to be found and understood, borrowed from ideas on how to read and interpret religious writings: exegesis or hermeneutics. Nature was a text, writ by its creator.

Back in Medieval times, there were four ‘senses’ of reading and understanding scripture:

  • Anagogia: the higher meaning (I.I.)
  • Allegoria: the deeper meaning (I.V.)
  • Historia: the literal meaning (V.V.)
  • Tropologia: the moral meaning (V.I.)

Perhaps the meaning of these senses were more or less literal. Therefore on my diagram I have placed the higher above, the deeper below, the historical in the past, and the moral in the future. Morals inform us what we should do or what our purpose is. A heuretic of systems thinking coined by Stafford Beer is “the purpose of a system is what it does.” And remember the immortal words of Yoda: “Try not. Do or do not. There is no try.”

Fortunately or unfortunately, nature is nothing like a text. All texts are written by people, and are structured by human thought and language. Nature requires other methods for understanding its basis and processes. The so-called scientific method evolved by fits and starts to explore the workings of nature, its components, causes, structures and functions. And it continues to evolve because it is not in itself entirely mechanistic: no precise algorithm that we know of can be specified to turn the crank and do ‘science’. Does that mean it’s unscientific? Not at all.

References and Links:

https://quadriformisratio.wordpress.com/2013/07/01/the-four-senses/

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

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

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

[*8.48, *8.52]

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The Religion of the Future

April 6, 2015

sq_four_flawsIf religion remade itself for the present and for the future, what should it be like? Robert Mangabeira Unger thinks religion is an important aspect of human existence but doesn’t serve our own needs and those to each other or to the world that we find ourselves in and are so dependent on. In “The Religion of the Future”, he continues the program that he introduced in his previous book “The Self Awakened”.

There are four major existential flaws of human existence: mortality, insatiability, groundlessness, and belittlement. Our mortality is the inevitable end of our struggle within life, although some scientists think it may be overcome someday. Our insatiability does seem to be part of human nature, a yearning for more of life and even life itself, but perhaps it could be quelled with training and resolve. Our groundlessness is due to the incompleteness of our knowledge as to the reasons of our existence and the future that we should pursue.

Unger considers belittlement to be a repairable flaw, unlike the other three. Belittlement may be different because we could learn to not reduce each others dreams and goals, but it may also be part of human nature to raise ourselves up by belittling others. We are social beings, but we are also confrontational and competitive. Even if we can learn, what is to stop the world itself from belittling us by placing physical limits on our actions and resources, or constraints on our abilities and plans?

These four flaws make us craven, clueless, needy, and terrified. sq_four_failingsCould a revolution of religion make us face up to our flaws in a mature and dignified way? Unger seems to think so and lays out his ideas. Four important principles that this religion must serve are apostasy, higher cooperation, plurality, and deep freedom. Four needful virtues that this religion must promote are self-transformation, connection, purification, and divinization.

The major religions of the past have the themes of overcoming the world, struggling with the world, and humanizing the world. What would the theme of the religion of the future be? Accepting the world? Embracing the world? Loving the world? Many religions avoid or even despise the world because it is only a means to an end, instead of an end in itself. We are indeed part of the world and must learn to accept, embrace, and love it as well as ourselves.

From the book description:

How can we live in such a way that we die only once? How can we organize a society that gives us a better chance to be fully alive? How can we reinvent religion so that it liberates us instead of consoling us?

These questions stand at the center of Roberto Mangabeira Unger’s The Religion of the Future. Both a book about religion and a religious work in its own right, it proposes the content of a religion that can survive faith in a transcendent God and in life after death. According to this religion–the religion of the future–human beings can be more human by becoming more godlike, not just later, in another life or another time, but right now, on Earth and in their own lives.

Unger begins by facing the irreparable flaws in the human condition: our mortality, groundlessness, and insatiability. He goes on to discuss the conflicting approaches to existence that have dominated the last 2,500 years of the history of religion. Turning next to the religious revolution that we now require, he explores the political ideal of this revolution, an idea of deep freedom. And he develops its moral vision, focused on a refusal to squander life.

The Religion of the Future advances Unger’s philosophical program: a philosophy for which history is open, the new can happen, and belittlement need not be our fate.

References:

Roberto Unger / The Religion of the Future

http://robertounger.com/english/docs/religion.pdf

Other links of interest:

http://bigthink.com/think-tank/the-shortcomings-of-religion-and-the-coming-revolution-with-roberto-unger-2

https://ndpr.nd.edu/news/49986-the-religion-of-the-future/

[*8.75, *8.102]

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The Four Conic Sections

July 27, 2011

To teach superstitions as truth is a most terrible thing.

– Hypatia of Alexandria

In mathematics, the four conic sections are the different shapes that can be formed by the intersection of a three dimensional right double cone and a plane: the circle, the ellipse, the parabola, and the hyperbola. The conics have been studied since the dawn of Greek mathematics. These shapes have interest as pure mathematical constructions, as well as many practical uses in applied mathematics.

Special points (focus or foci, plural) and lines (directrix or directrices, plural) can also be used to generate the conic sections in analytic geometry. A circle or parabola has one focus; the ellipse or hyperbola has two. The circle is a special case of the ellipse, one whose two foci coincide at a unique center, and in a different sense, the parabola can also be considered as a special case of the ellipse, having one of its foci at infinity. All circles can be transformed into each other by uniform scaling, a property shared by all parabolas. Thus the circle can be considered to be a singular shape, as well as the parabola. In contrast, ellipses and hyperbolas have a multitude of shapes and cannot be transformed into others of the same kind by uniform scaling. However, a nonuniform scaling or affine transformation can be used to achieve this goal. In even more abstract projective geometry, one could consider that all the conics are the same.

If the double cone is considered as the so-called light cone in Minkowski Space-time, many interesting concepts in special relativity can be considered. In this simplified model, space has two dimensions and time has one. The light cone divides all of space-time into four parts: the past, the present, the future, and the rest. The observer is located in time and space at the common apex of the two cones. Light travels on the surface of the cones, in straight lines towards and away from the observer. Anything traveling strictly within the space-time of a cone must necessarily be traveling slower than the speed of light. One cone can be thought of as the past: the interior of which contains all space-time that could have been observed by the observer, bounded by the circles of light traveling towards her. The second cone can be thought of as the future: the interior of which contains all space-time that could possibly be observed by the observer, bounded by the circles of other observers observing her light. Everything outside of the light cone cannot be observed or influenced by the observer at that instant, since light from it would have to travel faster than the speed of light in order to be seen or acted on by the observer.

Letting my analogical thinking run rampant, I can think of several associations with other fourfolds presented here. The circle is the shape of perfection, of identity and wholeness. It has one center or focus. In Minkowski Space-time, it is formed by the plane cutting the light cone at a constant time, so that all light arrives at the observer simultaneously from the past. Thus it is the shape of the knower or perspective. The parabola has the shape of gravity, the arc of an object thrown from and falling towards the earth. The shape reminds me of a reality that flies up from the opaque depths of the knowable only to fall away again. Numbers that are perfect squares may have started ancient mathematicians thinking about arithmetic. The ellipse has the shape of cosmology. Once astronomers could consider orbits of planets not to be circles or epicycles, only then science changed from idealism to empiricism. The hyperbola’s asymptotes form the crossed lines of my ever-present double duals, dividing yet unifying, as well as the profile of Minkowski Space-time. In fact, space and time occur over and over in many of the fourfolds I have considered.

Circles and ellipses could be considered the shapes of time, subjectivity, conjunction, and content: closed, finite, and bounded, yet cyclic. Parabolas and hyperbolas could be considered the shapes of space, objectivity, disjunction, and expression: open, infinite, and unbounded, acyclic.

In the recent movie Agora, the main character is Hypatia, the daughter of the last librarian of the great Library of Alexandria. A mathematician, astronomer, and philosopher, only fragments of Hypatia’s writings are available to us today. After the sack of the library, Hypatia is shown in her new study with a beautiful wooden model of the conics that she saved from destruction. For any that love wisdom over superstition, the movie is heartbreaking. As an echo to the loss of the contents of the library, it is offered (without any proof) that she considered the truth of the Heliocentric model of the solar system with the planets moving in elliptical orbits. Her senseless murder meant her insights were destroyed without legacy, falling away into the gravity of the dark unknown. Fortunately, even if she had, Copernicus and Kepler rediscovered these insights well over a thousand years later and brought them to light. The library’s loss will never be recovered.

References:

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

http://www.mathacademy.com/pr/prime/articles/conics/index.asp

http://www.npr.org/blogs/13.7/2011/07/11/137743796/agora-most-intelligent-movie-on-science-and-religion-ever?ft=1&f=114424647

http://babelniche.wordpress.com/2010/09/28/more-on-agora-and-hypatia/

http://www.skepticforum.com/viewtopic.php?f=85&t=14979

[*6.170, *6.172]

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