# Hyper-analogies

I’ve written a few times about relating two different fourfolds and juxtaposing or comparing them in one eightfold diagram. A normal analogy is usually written as A:B::C:D, which means A is to B as C is to D. So if you have two such fourfolds, one way to write it as an eightfold is A:B::C:D:::E:F::G:H. I think a good name for this is a hyper-analogy. I couldn’t really find anything of merit about this concept, but perhaps it goes by another name.

I’m not sure what diagram arrangement shows this the best. Some ideas are 1) A-D are arranged vertically (as well as E-H) and both are arranged horizontally (side-by-side), or 2) A-D are the triangles pointing down, and E-H are the triangles pointing up. Or, 3) A-B can be the upper left and C-D the lower right squares, and E-H can be the upper right and lower left squares. Or, one can use the radial eightfold schema, and have 4) A-D are the triangles on the inside, E-H are the triangles on the outside (or vice-versa).

For example, here I show the Four Causes combined with my Structure-Function. Also, please examine my Eightfold Metaphysics, which combines Space-Time-Matter-Energy with Structure-Function. Additionally, another I like is the one for Tanabata, which relates the astronomical with the symbolized. I could go on and on, and probably will.

https://equivalentexchange.blog/2019/02/01/an-eightfold-metaphysics/

https://equivalentexchange.blog/2019/07/03/tanabata-v2/

https://equivalentexchange.blog/2019/04/10/noether-pauli-jung-v2/

[*12.54]

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# The Tao of Thoth

Ethan Indigo Smith’s recent book, “The Tao of Thoth,” is a companion to a previous book of his I reviewed, “The Matrix of Four“. But instead of dwelling on fourfolds from ancient and esoteric sources, this book’s appeal to me is mainly for eightfolds. The sources are again traditional and occult, and indeed the title’s constituents come from ancient Asian and Egyptian cultures. Smith encourages us to contemplate these venerable concepts to reclaim simplicity in our lives and move away from any unnecessary complexity of modern life.

Certainly Smith is legitimate in critiquing present-day institutions and mentalities that valorize profit and consumption over ecological and humanitarian well-being. Can we learn from ancient cultural precepts and use them to heal the earth as a whole as well as enhance the health of our own lives, our descendants lives, and that of our follows? We seem to be avoiding the simple fact that current lifestyles are unsustainable for the earth and even harmful to our own psyche.

The first chapter introduces us to the Taiji, or Yin Yang, as well as the Tao of Asian study. The “Tao of Thoth” is also introduced and seems to be the relationship between the Taiji and the Tenets of Thoth (also referred to as Thoth Energy). Several claims are then made as to their separate and related simplicity and applicability. The next two chapters deal with this so-called Thoth Energy and the Taiji in more detail.

In Chapter 1 the Egyptian god Thoth is described in some detail, and his connection to gods in other mythologies, both Eastern and Western. The term Thoth Energy seems to describe the principles conceptualized by his attributes. That these principles are found in separate traditions is indicative our common humanity, rather than cultural approbation (maybe except for continuity between the Egyptian (Thoth), Greek (Hermes), and Roman (Mercury) gods). Next the Eight Trigrams of the Bagua and the eight deities of the Ogdoad are discussed.

A list of the Seven Tenets of Thoth close the chapter: Mentalism, Correspondence, Vibration, Polarity, Rhythm, Cause and Effect, Gender, and their relationship to the Tao. Hermetic and occult principles are often associated with individual self-development and not social coherence common to institutions. These tenets are the Seven Hermetic Principles mentioned in Chapter II of the Kybalion. Hermeticism is also deeply connected with Alchemic principles.

Chapter 2 discusses the Tao, Taiji (Yin Yang), and Taiji practice (Tai Chi). The Eight Layered Body is mentioned (the physical body, the chi body, the emotional body, mental body, psychic body, causal body, body of individuality, and the body of Tao). The next seven chapters deal with the seven hermetic principles which are hinted to align with Taoist principles as well, but do they do so in clear ways? Perhaps I need to study both the Kybalion and the Taiji in depth before I understand their connection.

And so briefly:

• Chapter 3 (Mentalism) mentions The Eightfold Path.
• Chapter 4 (Correspondence) mentions the Seven Minor Physical Planes (Chapter VIII of the Kybalion).
• Chapter 5 (Vibration, Chapter IX of the Kybalion) mentions the Eight Limbs of Yoga.
• Chapter 6 (Polarity, Chapter X of the Kybalion) mentions the Eight Energies or Gates of Taiji and the fourfold Known Knowns.
• Chapter 7 (Rhythm, Chapter XI of the Kybalion) mentions the Bagua and Eight Taiji Principles.
• Chapter 8 (Cause and Effect, Chapter XII of the Kybalion) mentions the Eight Auspicious Symbols of Buddhism.
• Chapter 9 (Gender, Chapter XIII of the Kybalion, and Mental Gender, Chapter XIV) mentions the Eight Auspicious Offering Bowls and the Eight Secrets of the Tao Te Ching.
• In Chapter 10, I am certainly glad that Smith rounded out the Seven Tenets to Eight with Patience. Mentioned are Chakras and the Spectrum of Light and the fourfold Wu Wei. In contrast, the last Chapter XV of the Kybalion deals with “Hermetic Axioms,” discussing several of the principles together.

After each chapter discussing a tenet, Smith suggests a Taiji or Taiji-inspired meditative practice that embraces a core concept: standing meditation, champion posture, shaking, arm swinging (Renunciation/Reintegration, Evaporation/Condensation), spiraling balance, pressurization, integrating Yin and Yang, walking.

It would be nice to have a bibliography and index included in this book, as many sources are mentioned and it would be convenient to have it as a quick reference. I must say that I didn’t find this short book as rewarding as “The Matrix of Four,” nevertheless, I found it worth reading and it piqued my interest for trying Tai Chi.

Ethen Indigo Smith / The Tao of Thoth

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

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

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

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

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

The Three Initiates / The Kybalion

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

https://www.sacred-texts.com/eso/kyb/index.htm

http://www.gutenberg.org/ebooks/14209

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

[*12.50, *12.51]

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# Who Do You Love?

Who do you love?
Who do you love?
Who do you love?
Who do you love?

— From Who Do You Love by Bo Diddley

The constituents of this list had pretty much congealed in my mind when I ran across information on the eight kinds of love. I thought that in this difficult time it might be useful to consider what is most important by examining all the people and all the things one can love as well as their myriad ramifications. Indeed, love may be the most considered and talked about emotion. Might one even say it is at the root of all of human action?

I know that in order to substantiate my claims I should justify these particular selections by comparing and contrasting them with each other, or to show their association to the eight kinds of love, and to do both would be a worthwhile effort. If I just show my diagram and my little list no one will think much of it. I could say I would return later but we all know how I tend to be distracted by the next bright shiny thing.

At the very least I could do some research, or do some hard thinking about why I’ve chosen these particular eight. I’m not sure if such diligence will reap any benefits but all one can do is try their best. So therefore I invite you to continue reading and perhaps you will be enlightened or perhaps you will be disappointed by what I say in the following analysis, if it even manages to appear at all.

I see that there are some modern analyses of love like Robert Sternberg’s Triangular Theory of Love, based on concepts of passion, intimacy, and commitment. This theory seems to be devoted to interpersonal relationships but maybe so is the Greek Eight types. But I’m thinking of love in a broader sense than just interpersonal, although maybe that doesn’t agree with certain definitions of love.

Love doesn’t have to reciprocated, of course, or directed towards another loving entity. For example, Agape is love of humanity in general, but humanity in general cannot return one’s love. One can also love negative things, like hate, or strife, or friction, and some even make a career out of it. But I’m going to leave that out for now. Alas, my interest has waned on this post and so I will have to try again at a later time.

• Love of Self
• Love of Group
• Love of Other
• Love of Nature
• Love of Ideas
• Love of Gods
• Love of Things

https://en.wikipedia.org/wiki/Who_Do_You_Love%3F_(Bo_Diddley_song)

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

https://en.wikipedia.org/wiki/Category:Love

https://en.wikipedia.org/wiki/Category:Philosophy_of_love

[*11.76]

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# The Eight Kinds of Love

There are several mentions of eight types of love purportedly discussed by the ancient Greeks, but I’m short on the actual references.

In no particular order:

• Agape: unconditional love
• Eros: romantic love
• Philia: affectionate love
• Philautia: self love
• Storge: familiar love
• Pragma: enduring love
• Ludus: playful love
• Mania: obsessive love

I had an earlier post on The Four Loves by C. S. Lewis, but now I see that he just left out half of them for some reason. Missing are Philautia, Pragma, Ludus, and Mania, which seem important, but since I haven’t read the book, I don’t know his reasons.

https://lonerwolf.com/different-types-of-love/

https://www.lifehack.org/816195/types-of-love

https://www.ftd.com/blog/give/types-of-love

https://www.organicauthority.com/energetic-health/learn-the-8-types-of-love-according-to-the-ancient-greeks

8 Types of Love – Which One Are You?

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# The Devolution of Trust

The Prisoner’s Dilemma is a simple game designed to show how the success or failure of cooperation between individuals can be contingent on various factors, primarily some sort of reward. Shown above is a representative payoff matrix between two players; each square shows the two choices and the two winnings for each. Each player cooperates (A or B) or cheats (A’ or B’) with the other player, so for example if A and B’ obtains (A cooperates but B cheats) then A loses 1 and B wins 3.

Each player knows all the values of the payoff matrix so it is said they have perfect information, except they don’t know what their opponent will do. If they are rational and believe their opponent to be as well, the wisest thing to do is for both to cooperate to maximize their winnings, knowing that their opponent knows that they could also cheat. If the game is played only once, however, that is clearly not the case.

If the game is iterated, things change. If each player remembers what their opponent did previously, and it is considered to be informative for what they might do next, then the player could use it to condition their decision to cooperate or cheat. Different algorithms or personalities can be considered for the players, with more or less thinking about what to do and more or less willingness to cooperate, and it is interesting to try different strategies, all the while seeing what adjustments of the payoff matrix might do to the results.

This Evolution of Trust site is a very nice lesson in some of the complications that can result for such algorithms and adjustments. On the whole, this site indicates that rationality and consideration for others can thrive, if conditions are right. In the traditional Prisoner’s Dilemma, the reward values in the payoff matrix are usually considered to be jail sentence time (so less is better), or for the site mentioned above where I’ve taken the representative matrix, monetary value (so more is better).

One thing of note in these examples is that each player doesn’t distinguish their opponent by anything other than their posteriori plays, because these players are supposed to be all part of the same group or society. But what if there is an a priori distinction that conditions their decision? So, if your opponent is a known Y, and you are a X, then you might want to raise your social credit with your other Xs by punishing a Y, even if it punishes you or even other Xs in the long run.

For example if you are a member of gang X, you wouldn’t want to cheat against another X. But cheating against a member of gang Y might raise your in-group social capital and be as important as the value of the reward. Or you might want to punish your opponent in group Y by not granting them any benefits even at the cost of your own benefit. Such distinctions are not usually part and parcel of the Prisoner’s Dilemma game, but they would add an interesting and realistic dimension to the game.

And thus lend insight into the woes of our modern political scene and culturally diverse society.

https://ncase.me/trust/

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

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

https://equivalentexchange.blog/2017/08/03/the-prisoners-dilemma/

https://en.wikipedia.org/wiki/Devolution_(biology)

[*11.24, *11.172]

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# Tractatus Logico-Philosophicus

Just the facts, ma’am.

— Detective Joe Friday

1. The World (Die Welt): The world is everything that is the case.
2. The Case (Der Fall): What is the case, the fact, is the existence of atomic facts.
3. The Picture (Das Bild): The logical picture of the facts is the thought.
4. Thought (Gedanke): The thought is the significant proposition.
5. Propositions (Der Satz): Propositions are truth-functions of elementary propositions.
6. The Form (Die Form): The general form of truth-function is: [p-bar, xi-bar, N(xi-bar)].
7. Silence (Schweigen): Whereof one cannot speak, thereof one must be silent.
8. ( ):

The Tractatus has seven propositions, most with sub-propositions and sub-sub-propositions, etc. I have added the eighth, which is the actual silence of all one cannot speak of. Quite a large section, for all its emptiness.

I also thought it would be nice to have an internet version where you could click and expand down through the sub-sentences. There are already many such versions available for your enjoyment.

I can’t decide whether I like the English or the German version better, so here are both.

https://en.wikipedia.org/wiki/Tractatus_Logico-Philosophicus

http://www.tractatuslogico-philosophicus.com/

http://www.bazzocchi.com/wittgenstein/tractatus/eng/index.htm

http://www.kfs.org/jonathan/witt/ten.html

https://pbellon.github.io/tractatus-tree/#/

https://tractatus-online.appspot.com/Tractatus/jonathan/index.html

http://daxoliver.com/tractatus/

http://people.umass.edu/klement/tlp/

The Tricky Truth about Tractatus Trees (updated)

[*11.170]

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# Patrick Geddes and the Notation of Life

Over the last few decades, there has been renewed interest in the work of biologist, sociologist, and city planner Patrick Geddes [1]. This is due to his efforts for holistic considerations for the entirety of the modes of human life and the facilities appropriate for their function. That is, he asked what makes a city or a town ideal for life, and how can we plan to bring this ideality into being? To this day, cities fail in many important ways.

Geddes embraced the new (at the time) Victorian notion of evolution in his work and thought of how cities could and should evolve to meet their shortcomings as well as provide environments for future developments. For example, common institutions such as schools, churches, and governments (polity) need to cooperate with family dwellings to provide for synergy and functional enrichment.

Geddes often used grids of words to explore relations between concepts, such as place, work, and folk. Placing these words along the diagonal of a square allowed one to consider the paired concepts of place-work, work-place, place-folk, etc. For example, how does the place-work compare with the work-place? His “notation of life” was a complicated schematic for exploring relations between a city’s facilities and the activities that they should promote.

• Town / Acts : place, work, folk
• School / Facts : sense, experience, feeling (alt. lore, learn, love)
• City / Deeds : ethno-polity, synergy, achievement (alt. polity, culture art)
• Cloister / Dreams (Thoughts) : emotion, ideation, imagery (alt. ideals, ideas, imagery)

Two locales are objective, two are subjective, two are passive, and two are active:

• In-World (Subjective) : School and Cloister
• Out-World (Objective) : Town and City
• Passive : Town and School
• Active : City and Cloister

And so:

• Passive & Subjective : School
• Active & Subjective : Cloister
• Passive & Objective : Town
• Active & Objective : City

Any important thinker is inspired and influenced by those that were previous or are contemporary to them and in turn is inspiration to those that follow. James H. Cousins was an important syncronic influence on Geddes, and please see [2] and [3] for information about him. The integral theory of Ken Wilber [4] is also compared to Geddes in [5]. I understand architect Lewis Mumford was a disciple of Geddes and I hope to find out more at a future time, perhaps by reading my copy of [6].

References:

[5] Theodore S. Eisenman, Tom Murray / An Integral Lens on Patrick Geddes, Landscape and Urban Planning,
http://dx.doi.org/10.1016/j.landurbplan.2017.05.011

[6] Donald T. Miller / Lewis Mumford, a Life

http://architectureandurbanism.blogspot.com/2010/10/volker-m-welter-biopolis-patrick-geddes.html

https://www.dundee.ac.uk/geddesinstitute/projects/citythink/

http ://medium.com/@designforsustainability/design-and-planning-for-people-in-place-sir-patrick-geddes-1854-1932-and-the-emergence-of-2efa4886317e

View at Medium.com

Patrick Geddes / Cities in Evolution

https://archive.org/details/citiesinevolutio00gedduoft/page/n10

[*9.12, *9.14, *11.92]

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# The Lambda Cube

More or less from Wikipedia:

In mathematical logic and type theory, the λ-cube is a framework introduced by Henk Barendregt to investigate the different dimensions in which the calculus of constructions is a generalization of the simply typed λ-calculus. Each dimension of the cube corresponds to a new way of making objects depend on other objects, namely

1. terms allowed to depend on types, corresponding to polymorphism.
2. types depending on terms, corresponding to dependent types.
3. types depending on types, corresponding to type operators.

The different ways to combine these three dimensions yield the 8 vertices of the cube, each corresponding to a different kind of typed system.

So in the diagram above, we have emblazoned the names of these type systems ordered from lower left to upper right:

• λ→: the simply typed lambda calculus, our base system
• λ2: add 1. above to λ→, giving what is also known as System F or the Girard–Reynolds polymorphic lambda calculus
• λP: add 2. above to λ→
• λ_ω_: add 3. above to λ→
• λP2: combine 1. and 2., λ2 and λP
• λω: combine 1. and 3., λ2 and λ_ω_
• λP_ω_: combine 2. and 3., λP and λ_ω_
• λC: combine 1., 2., and 3., giving the calculus of constructions