# Four-Dimensional Vistas

The Fourth Dimension has been an interest of mine since I was a child. I’m not sure when I first heard about it, but I still have my coverless copy of “Geometry of 4 Dimensions” by Henry Parker Manning that I bought in a used book store. (I wonder why it hasn’t ever been reissued by Dover?) Maybe I heard about the fourth dimension in some science fiction TV movie, or in some mathematical survey book like “Mathematical Snapshots” or “Mathematics and the Imagination”.

Once I tried to explain to my best friend about my newly discovered insight how a hypercube could be folded up in four-dimensional space from its so-called three-dimensional net consisting of eight cubes, just as a regular three-dimensional cube could be folded up from its two-dimensional net of six squares. This 3D net somewhat resembling a cross is famously seen in Dali’s “Crucifixion (Corpus Hypercubus),” although I probably didn’t refer to this painting in my explanation.

I’m not sure who came up with the take-away message from my exposition, but it remains clear in my memory that the “junk in the middle” of the hypercube was a piece of the fourth dimension, just as the faces of a cube enclose a piece of our normal third dimension.

I recently came across Claude Fayette Bragdon, architect, author, draughtsman, stage designer, and mystic. At first I was interested in his drawings found on-line. His book “Four-Dimensional Vistas” started off with a good if overly wordy introduction to the concept of the fourth dimension. But then he suggests that many esoteric concepts such as the meaning of dreams, reincarnation, past-life regression, prognostication, ESP, etc. could possibly be explained by higher dimensional space or even higher dimensional time.

Even though I initially found many of these hypotheses too far-fetched for my tastes, I still found some interesting ideas to mull over in this little book.

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

https://www.gutenberg.org/ebooks/author/4128

https://theosophy.wiki/en/Claude_Fayette_Bragdon

https://theosophyart.org/2018/03/30/claude-fayette-bragdon/

https://rbscp.lib.rochester.edu/bragdon-family-papers-claude-bragdon-architectural-drawings

The art of Claude Fayette Bragdon, 1866–1946

https://rbscp.lib.rochester.edu/3514

https://bauarchitecture.com/research.loshuworldofwonderous.shtml

Claude Fayette Bragdon / Four-Dimensional Vistas (1930)

Claude Fayette Bragdon / The Beautiful Necessity (1910)

Claude Fayette Bragdon / Architecture and Democracy (1918)

For my gratuitous anime tie-in, Bragdon’s world-view suddenly reminds me of the anime character  Haruhi Suzumiya, who wished for her aliens, time-travelers, and ESPers so much that she willed them into being. If only she had known about the fourth dimension!

https://reelrundown.com/animation/Anime-Philosophy-1-Melancholy-of-Haruhi-Suzumiya

[*3.139, *12.121, *13.50]

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# The Four Immeasurables

May all beings have happiness and the causes of happiness.
May they be free of suffering and the causes of suffering.
May they never be separated from supreme joy beyond all sorrow.
May they abide in equanimity free from attachment and aversion.

— Buddhist Prayer

I’m currently watching a beautiful anime called “The Heike Story”, based on the Japanese Tale of the Heike. The central character is a child plagued with the ability to see visions (usually of death and destruction) of the future and remote events. She is anguished to witness  these and is powerless to do anything about them,  but finally (spoilers!) determines that she might ease her mind by praying for those involved.

This character is not portrayed as any sort of  religious individual, so I wondered what kind of prayer might be appropriate for her. Searching for an “Atheist Prayer”, I quickly found the Buddhist Prayer above that might be something like she would say, that encodes the “Four Immeasurables” of Buddhist thought. This prayer is not offered to any god or gods, but just a wish and hope for those in mind and indeed for all sentient beings.

The Four Immeasurables of Buddhism are

• Maitri: Loving kindness
• Karuna: Compassion
• Mudita: Sympathetic Joy
• Upeksha: Equanimity

https://iai.tv/articles/prayer-for-atheists-auid-1181

The Four Immeasurables

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

[*13.16]

# Neon Genesis Evangelion Rebuilt, V2

The fourth movie was finally made and finally shown! Thank you Hideaki Anno, for finishing your rebuild, and Amazon Prime, for letting us easily see all four.

Full of battles between giant robots and kaiju called angels, full of teenage, human, and non-human emotional struggles, and full of signature Evangelion nonsense, about midway I was getting a bit unhappy with it. But as it coming to a close I thought that this was indeed a good ending.

So what does “Thrice Upon a Time” mean? That this is the third ending? First for the series, second for the movies after the series, and thirdly for the rebuilt movies? And what does the designation “3.0+1.0” mean? Three movies plus one more?

https://www.cnet.com/news/anime-epic-evangelion-gets-a-worthy-conclusion-heres-the-ending-explained/

‘Evangelion: 3.0+1.0 Thrice Upon a Time’ Review: Hideaki Anno’s Iconic Anime Finally Gets a Proper Ending

https://www.polygon.com/22627444/watch-evangelion-franchise-amazon-netflix

https://en.wikipedia.org/wiki/Evangelion:_3.0%2B1.0_Thrice_Upon_a_Time

Neon Genesis Evangelion Rebuilt

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# Neon Genesis Evangelion Reshown

Like an angel with cruel and merciless intent
Go forth, young boy, and you’ll become a legend!

— From A Cruel Angel’s Thesis, lyrics by Neko Oikawa

I’m sure all that are interested have already heard that Netflix is streaming some version of the original Neon Genesis Evangelion anime beginning 6/21/2019. This diagram shows the names of the first four pilot children from the series, ignoring possible later ones and new characters from those problematic Rebuilt movies.

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

https://www.crunchyroll.com/anime-news/2019/03/22-1/neon-genesis-evangelion-anime-makes-its-netflix-debut-on-june-21

‘A Cruel Angel’s Thesis’ took just two hours to write says Evangelion lyricist Neko Oikawa

Excellent reviews of the first few episodes (but spoilers of course!):

Neon Genesis Evangelion – Episode 1

Neon Genesis Evangelion – Episode 2

http://wrongeverytime.com/tag/neon-genesis-evangelion/

[*11.15]

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# The Four Mythological Beasts

Another item for my fourfold menagerie is the four symbolic mythological beasts of China. They are associated with the Four Cardinal Directions and the Four Seasons.

• The Vermilion Bird (South, Summer, named Zhūquè or Ling Guang)
• The Azure Dragon (East, Spring, named Qīnglóng or Meng Zhang)
• The Black Turtle (North, Winter, named Xuánwǔ or Zhi Ming)
• The White Tiger (West, Fall, named Báihǔ or Jian Bing)

They are also part of Japanese folklore and I show the Japanese names of these four god beasts to the right, mostly because I am more familiar with them: Suzaku, Seiryu, Genbu, and Byakko.

https://en.wikipedia.org/wiki/Four_Symbols_(China)

http://tvtropes.org/pmwiki/pmwiki.php/Main/TheFourGods

https://allthetropes.org/wiki/The_Four_Gods

http://koei.wikia.com/wiki/Four_Gods

https://en.wikipedia.org/wiki/Twenty-Eight_Mansions

Notes:

It was nice to see the Four Beasts in the opening ceremony at the 2018 Winter Olympics in South Korea.

[*8.104, *10.64]

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# Neon Genesis Evangelion Rebuilt

The final movie of this tetralogy has been named:

• Evangelion 1.0: You Are (Not) Alone
• Evangelion 2.0: You Can (Not) Advance
• Evangelion 3.0: You Can (Not) Redo
• Evangelion 4.0: You Will (Not) Happen

Alternative facts are (not) fun!

References:

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

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

Seen post-post:

Post-post-post:

https://www.crunchyroll.com/anime-news/2019/12/26-1/evangelion-3010-finally-set-to-be-released-in-japan-on-june-27-2020

Not so fast:

https://en.wikipedia.org/wiki/Evangelion:_3.0%2B1.0_Thrice_Upon_a_Time

And finally:

https://www.animenewsnetwork.com/review/evangelion/3.0-1.0/thrice-upon-a-time/.170407

[*9.198]

<+>

# The Medicine Wheel

The Native American Medicine Wheel is a symbol system that associates several fourfolds together, such as the Four Seasons, the Four Cardinal Directions, the Four Elements, etc. Another fourfold that does this is the Four Temperaments.

There should be a good word for this amalgamation of fourfolds into one hyper- or mega- or uber- fourfold. What about quadriphilia? No, that’s just love of fours, but it is in the Urban Dictionary. Quadrasyncretism? I like the neologism tetrasyncretism, from tetra meaning four, and syncretism, meaning combining different (or many) beliefs into one.

The aspect of the Medicine Wheel illustrated above is similar to the Four Temperaments.

The colors Red, White, Black, and Yellow are important for the Medicine Wheel. The colors often occur in a certain order within quadrants of the circle of the wheel. The colors also correspond to the Four Seasons: Black for Autumn, White for Winter, Yellow for Spring, and Red for Summer, although there can be other mappings.

These same four colors are also important in alchemy and represent stages of the Magnus Opus or Great Work, where Red is Rubedo or Iosis, White is Albedo or Leukosis, Black is Nigredo or Melanosis, and Yellow is Citrinitas or Xanthosis. The order is usually Black, White, Yellow, and then Red, through beginning to ending stages of the work.

In addition, the current anime RWBY has characters with these main costume colors. Apparently it is a story with some magic and much fighting with large weapons by four young women.

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

http://en.wikipedia.org/wiki/Magnum_opus_%28alchemy%29

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

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

Angeles Arrien / The Four-Fold Way: Walking the Paths of the Warrior, Teacher, Healer, and Visionary

Google search for images of the Medicine Wheel.

Google search for images of the Four Cardinal Directions.

[*7.194, *8.12]

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# Equivalent Exchange

There is an old riddle that asks, what is the value of a human body? It goes on to enumerate the quantities of the various chemicals that constitute an average body, and then price those chemicals to come up with a total material value. This might come as a shock to the one who tried to answer the riddle, because the value is so low.

Of course that analysis ignores the real value of the body because it ignores the spatial arrangement of those chemicals in the various tissues and organs of the body. It ignores the form of the body as an hierarchical arrangement of structured parts. These parts are very valuable for someone needing an organ donation, for example.

This static analysis is lacking as well because it neglects the dynamic actions that a body can perform. Taken as a set of discrete individual acts, this is like considering the individual chemicals that constitute a body. One can enumerate the acts too, as in counting the number of breaths or the number of heart beats over a lifetime.

But we are still not finished, because this enumeration of actions also overlooks the functions that a body can perform, as arrangements of actions in time. These functions are the most important value of a body because they include but are not limited to being alive, thinking, and feeling.

So it seems to me that there is a heirarchy here, that goes from parts to structure to actions to function, with parts being at the lowest level and function being at the highest. Each level of the hierarchy is dependent on the level below, but the nature of a level is fundamentally different from the level below it, as well as the level above it. Please see my previous post Structure-Function.

The term “equivalent exchange” comes from an alchemy-centric anime, where through a process called “human transmutation” it is attempted to recreate a body starting from a pile of the basic chemicals that constitute it. Even with some high-powered magic, the attempt fails due to the fact that much more is required to fashion a body or even a living, breathing person.

http://www.datagenetics.com/blog/april12011/index.html

https://briankoberlein.com/post/four-elements/

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# Bending the Elements

You and your forefathers have devastated the balance of this world. And now, you shall pay the ultimate price!

— From Avatar: the Last Airbender

I recently finished watching the animated series “Avatar: the Last Airbender”. I know I’m a bit late with my praise, but I thought this was an excellent series. It had fascinating world-building, well thought-out plotting, and believable characterization. It had humor, drama, fantasy, even teen romance. Something for all ages!

It could be because I’ve been thinking alot about the Four Elements and how I view them as analogies for the four relations I’ve been discussing for some time on this blog. In Avatar, they are literally the four elements of the world: fire, earth, water, and air. But in addition, these elements correspond to the four peoples of this world. The people of the Fire Nation are willful, the people of the Earth Kingdom are resolute, the people of the Water Tribe are empathic, and the people of the Air Nomads are reflective. Some individuals are able to “bend” the element that is associated with the people they are born into, so that for example a member of the Fire Nation might be able to produce and control fire with thought and gesture. Not everyone has this ability, however.

The Avatar is a continuously reincarnated individual that embodies the spirit of the world. He or she is born into each of the four peoples in a repeating cycle, but the Avatar is also the only individual that can learn to bend all four elements, and even all at the same time. Because of his or her unique powers, the Avatar is known to be able to bring and restore balance to the world, and to tie the real world to another, spiritual world. Avatar: the Last Airbender is the story of Aang, a descendent of the Air Nomads, but the last of his people due to genocide. He has been in a state of suspended animation for the last 100 years and awakes to a troubled world of war and turmoil. Can Aang save his world?

Hopefully I’m not spoiling anything in saying that he does. Indeed a sequel is currently being produced called “The Legend of Korra” that is planned to run 52 episodes. This sequel takes place a number of years after the end of Avatar, and the next Avatar after Aang is Korra from the Southern Water Tribe. The world is now somewhat more advanced technologically than it was during Aang’s time, and although not at war because it is still enjoying the peace that Aang initiated, there is still some strife and unrest for Korra to eventually bring the Avatar’s balance to. I am enjoying it also!

http://en.wikipedia.org/wiki/Avatar:_The_Last_Airbender

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

Note:

It is interesting to note that fire is the only element that can be generated by the will ex nihilo. With enough skill, water can be extracted from living matter and the air. Of course, air is ever present and earth is seldom far away.

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# Introduction

“Humankind cannot gain anything without first giving something in return. To obtain, something of equal value must be lost. That is alchemy’s first law of Equivalent Exchange. In those days, we really believed that to be the world’s one, and only truth.”

Alphonse Elric, in the first opening to Fullmetal Alchemist

The concept of Equivalent Exchange introduced in the anime quoted above inspired the title of this blog. “To obtain, something of equal value must be lost.” Though this term was recently coined, the concept is a familiar one and has been around for a long time. It is found as guides, rules, and laws in philosophy, religion, and science. For example:

• Do unto others as you would have them do unto you.
• Don’t take more than you give.
• Give and you shall receive.
• What goes around comes around.
• There’s no such thing as a free lunch.
• You get what you pay for.
• You get what you deserve.
• An eye for an eye, a tooth for a tooth.
• You scratch my back, and I’ll scratch yours.
• Energy is neither created nor destroyed.
• Every action has an equal and opposite reaction.
• Yin and yang.
• Karma.

I’m sure many more can be listed. I invite my readers to submit them.

These are all conservation laws: total value is maintained, even while it changes hands. And they certainly seem to be “conservative”:  all things being equal, they usually hold.

That being said, this blog isn’t specifically about “equivalent exchange”, except for hopefully obtaining the value of knowledge for the effort expended. Instead, I hope to explore a common thread that runs through philosophy, logic, and semiotics in the form of “double duals” (which themselves seem to have the property of equivalent exchange), with the goal of understanding and classifying different philosophical subjects and systems, exploring the nature of pluralism, and enhancing dialogue between opposing viewpoints. The image of the Tower of Babel in the title banner was chosen because public discourse has become fragmented and even broken.