Archive for the ‘eightfolds’ Category

Octonions

February 25, 2019

Octonions are the fourth, the last, and the greatest of the so-called normed division algebras based on the Real numbers. When I first learned about the Octonions way back when, I didn’t like them because they weren’t associative like the Quaternions, the Complex numbers, and the Reals. But now I’m fine with that, and they may be important for new theories of physics!

Octonions have the general form:

a0e0 + a1e1 + a2e2 + a3e3 + a4e4 + a5e5 + a6e6 + a7e7

Where the coefficients ai are Real and the bases ei have (something like) the following relations:

e0 = 1 (and -1 = e12 = e22 = …)

e1 = I = e2e3 = e7e6 = e4e5

e2 = J = e5e7 = e3e1 = e4e6

e3 = IJ = e1e2 = e6e5 = e4e7

e4 = K = e5e1 = e6e2 = e7e3

e5 = IK = e7e2 = e1e4 = e3e6

e6 = JK =e5e3 = e1e7 = e2e4

e7 = IJK = e6e1 = e3e4 = e2e5

In addition, if any of the products like e2e3 = e1 are reversed you get the negative, so e3e2 = -e1.

Non-associativity is demonstrated by going through the list of triples:

(e1e2)e3 = e32 = -1

e1(e2e3) = e12 = -1

(e1e2)e4 = e3e4 = e7

e1(e2e4) = e1e6 = -e7

(e1e2)e5 = e3e5 = -e6

e1(e2e5) = e1e7 = e6

so it is hit or miss I guess. Also note that e7 = (IJ)K = -I(JK). And for all (eiej)ek and ei(ejek), if they are not equal, is one equal to the negative of the other? And do I have to multiply them all out to find out?

Further Reading:

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

http://math.ucr.edu/home/baez/octonions/

https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720/

http://mathworld.wolfram.com/Octonion.html

http://homepages.wmich.edu/~drichter/octonions.htm

https://ncatlab.org/nlab/show/normed+division+algebra

[*11.33]

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Spiral Dynamics

February 21, 2019

Spiral Dynamics is an intriguing model for the different levels of development and interaction that individuals (and even cultures) may exhibit towards each other and the world. It has interesting parallels to Erikson’s Eight Stages of Psychosocial Development and even Leary’s Eight Brain Circuit Model of Consciousness.

Below is a list of these levels by (Catchy) Name, Social Structure, Motives, and Means of Coping:

  • SurvivalSense, Loose Bands, Survival, Instinctive
  • KinSpirits, Tribes, Magic/Safety, Animistic
  • PowerGods, Empires, Power/Dominance, Egocentric
  • TruthForce, Pyramidal, Order/Morality, Absolutistic
  • StriveDrive, Delegative, Autonomy/Achievement, Multiplistic
  • HumanBond, Egalitarian, Approval/Equality/Community, Relativistic
  • FlexFlow, Interactive, Adaptability/Integration, Systemic
  • GlobalView, Global, Compassion/Harmony, Holistic

And maybe another, further step if we don’t destroy ourselves and the Earth by just being stupid.

Further Reading:

Don Edward Beck, Christopher C. Cowan / Spiral Dynamics: mastering values, leadership and change

Don Edward Beck, et. al. / Spiral Dynamics in Action: humanity’s master code

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

http://www.cruxcatalyst.com/2013/09/26/spiral-dynamics-a-way-of-understanding-human-nature/

https://www.biznews.com/good-hope-project/2017/09/04/understanding-spiral-dynamics

https://scottjeffrey.com/spiral-dynamics/

https://en.wikipedia.org/wiki/Integral_theory_(Ken_Wilber)

http://www.awaken.com/2014/04/ken-wilber-summary-of-spiral-dynamics-model/

[*11.41, *11.45]

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Howard Gardner’s Theory of Multiple Intelligences

February 16, 2019

Next we examine (oh so superficially!) Howard Gardner’s Theory of Eight(-ish) Multiple Intelligences. To wit (ha-ha):

  • Intra-personal
  • Interpersonal
  • Bodily-kinesthetic
  • Nature-existential
  • Visual-spatial
  • Verbal-linguistic
  • Musical-rhythmic
  • Logical-mathematical

Further Reading:

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

https://www.tecweb.org/styles/gardner.html

http://www.institute4learning.com/resources/articles/multiple-intelligences/

Howard Gardner / Frames of Mind: The Theory of Multiple Intelligences (1983)

Howard Gardner / Multiple Intelligences: The Theory in Practice (1993)

Howard Gardner / Multiple Intelligences: New Horizons in Theory and Practice (2006)

[*11.41]

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Erik Erikson’s Eight Stages of Psychosocial Development

February 12, 2019

Erik Erikson developed an eight stage developmental model of the psyche for the full life of the human individual. Each stage has a key conflict (with both positive and negative sides), its resolution into a “virtue,” and the typical age range for that conflict.

  • Trust vs. Mistrust, “Hope”, Infancy (0-1 years)
  • Autonomy vs. Shame, “Will”, Early Childhood (1-3 years)
  • Initiative vs. Guilt, “Purpose”, Play Age (3-5 years)
  • Industry vs. Inferiority, “Competency” (or “Ability” or “Skill”), Schooling (5-12 years)
  • Ego identity vs. Role confusion, “Fidelity”, Adolescence (12-18 years)
  • Intimacy vs. Isolation, “Love”, Young Adult (18-40 years)
  • Generativity vs. Stagnation, “Care”, Adulthood (40-65 years)
  • Ego integrity vs. Despair, “Wisdom”, Old Age (65-? years)

I would think that these ages would depend significantly on cultural norms.

Further Reading:

https://en.wikipedia.org/wiki/Erikson%27s_stages_of_psychosocial_development

https://courses.lumenlearning.com/teachereducationx92x1/chapter/eriksons-stages-of-psychosocial-development/

https://www.simplypsychology.org/Erik-Erikson.html

http://www.crowe-associates.co.uk/psychotherapy/erikson-life-stages/

[*11.44]

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The Eight Circuit Model of Consciousness

February 7, 2019
Timothy Leary’s dead…
No, no-no, he’s outside, looking in…

— The Moody Blues

Timothy Leary came up with this scheme of eight circuits of consciousness and Robert Anton Wilson expanded and renamed most of them. It’s basically a “great-chain” of evolutionary brain circuitry, leading from lower to higher states of consciousness.

I’ve labeled my diagram with RAW’s names, but below I also list Leary’s names in parentheses.

  • Oral Bio-survival (Vegetative-invertebrate)
  • Anal Territorial (Emotional-locomotion)
  • Semantic Time-binding (Laryngeal-manual Symbolic)
  • Socio-sexual (Socio-sexual Domestication)
  • Neurosomatic (Neurosomatic)
  • Metaprogramming (Neuro-electric)
  • Morphogenetic (Neurogenetic)
  • Non-local Quantum (Neuro-atomic Metaphysiological)

Pretty wild stuff!

Further Reading:

https://en.wikipedia.org/wiki/Eight-circuit_model_of_consciousness

https://web.archive.org/web/20110723133512/http://www.futurehi.net/docs/8circuit.html

http://www.phinnweb.org/neuro/8-circuit/

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

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

[*11.42]

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John Beebe’s Eight Function Model

February 5, 2019

After my last post about an ad-hoc eightfold metaphysics, I spent a few minutes trying to create an eightfold psychology. Feeling insufficient to the task, I quickly put this aside and instead wondered if there was any prior work for this, and lo and behold, I found a wealth of such things. Eight seems to be a popular number for the enumeration of the psyche and related subjects.

I’ve already mentioned Robert Plutchik’s Emotions and Mihaly Csikszentmihalyi’s Flow, which are both sort of psychological dissections. If you’re into Jung and related psychologies, Jungian analyst John Beebe developed his eight-function model of personality types that blends Jungian concepts together into an interesting system. The eight types are split into two sets of four: for every type in the first “positive” set (ego-syntonic) there is a corresponding type in a “shadow” set (ego-dystonic). Each set of four has a superior, an auxiliary, a tertiary, and an inferior function.

  • Hero/Heroine (superior function)
  • Father/Mother (auxiliary function) (or good parent)
  • Puer/Puella (tertiary function) (or eternal child)
  • Anima/Animus (inferior function)
  • Opposing persona (shadow of superior) (villain?)
  • Senex/Witch (shadow of auxiliary) (or critical parent)
  • Trickster (shadow of tertiary) (added deceiver for balance)
  • Demon/Daimon (shadow of inferior) (daemon?)

In my diagram, I’ve shown each function paired with its shadow function. And of course being Jungian, the terminology is full of gender distinctions, which could fairly easily be eliminated. There are also lots of arcane associations to MBTI and such, so this will take more than a quick look. Please just wait here, and I’ll be back with an update soon (or not)!

Further Reading:

https://presentobsessions.wordpress.com/2013/12/03/the-john-beebe-8-function-model/

http://www.apt-nc.org/type-theories/eight-function-model/

http://www.erictb.info/archetypes.html

http://thedepthcoach.com/eight-function-model/

https://www.careerplanner.com/8CognitiveFunctions/Cognitive-Functions-Simply-Explained.cfm

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

Also see my posts:

https://equivalentexchange.blog/2011/08/26/carl-jungs-psychological-types/

https://equivalentexchange.blog/2018/09/07/the-myer-briggs-type-indicator/

[*11.41, *11.43]

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An Eightfold Metaphysics

February 1, 2019

If one juxtaposes the fourfold Space-Time-Matter-Energy with the fourfold Structure-Function-Part-Action, one sees that there are several relations between them. These are simple common-sense relations, not modern-physics types of relations. Below they are listed by Space-type relations and Time-type relations.

Space is required for the extension of Structures.
Matter constitutes Structures.
Parts in an arrangement make up Structures.

Structures extend and are organized in Space.
Matter is located in Space.
Parts occupy Space.

Time allows the expression of Functions.
Energy is required for the operation of Functions.
Actions in a sequence constitute Functions.

Functions have duration and reoccur in Time.
Energy requires and is dependent on Time.
Actions take place within Time.

Several analogies are also evident in this diagram.

  1. Space : Structures :: Time : Functions
  2. Space : Parts :: Time : Actions
  3. Space : Matter :: Time : Energy
  4. Structures : Parts :: Functions : Actions
  5. Structures : Matter :: Functions : Energy
  6. Parts : Matter :: Actions : Energy

Notice that analogies 1.-3. are “contains” relations, and 4.-6. are “part of” relations. One obtains the nesting of entities:

Space > Structures > Parts > Matter
Time > Functions > Actions > Energy

I suppose that any analogy could be shown in a figure like the one on the right (or even written as A / B // C / D) or with the two squares side by side, and that sets of four or six analogies that overlap could be nicely shown as above. If so, I wonder what can be gained by such representations? Probably individually not so much but with overlaps I think it would be interesting.

Further Reading:

The study of parts and wholes relations is called Mereology.

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

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

[*10.157, *11.26, *11.34]

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Flow

December 17, 2018

Speaking of flow, I see that the psychological concept of flow is based around a distinction of low-to-high challenge vs. low-to-high skill. When both challenge and skill are high, an efficient mental state can be engaged. From Wikipedia:

“In positive psychology, flow, also known colloquially as being in the zone, is the mental state of operation in which a person performing an activity is fully immersed in a feeling of energized focus, full involvement, and enjoyment in the process of the activity. In essence, flow is characterized by complete absorption in what one does, and a resulting loss in one’s sense of space and time.”

  • Flow: high challenge and high skill
  • Control: medium challenge and high skill
  • Relaxation: low challenge and high skill
  • Boredom: low challenge and medium skill
  • Apathy: low challenge and low skill
  • Worry: medium challenge and low skill
  • Anxiety: high challenge and low skill
  • Arousal: high challenge and medium skill

Missing is medium challenge and medium skill. I wonder what that is?

Further Reading:

https://en.wikipedia.org/wiki/Flow_(psychology)

Mihaly Csikszentmihalyi / Flow: The Psychology of Optimal Experience

[*11.22]

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The Eight Planets

September 16, 2018

Now that Pluto has been kicked out of the League of Planets (poor Pluto!), with the eight remainders I can present the above diagram.

The Sun and the Moon, not planets either, are usually thought of as a pair. I’ll add them in by themselves for good measure.

Further Reading:

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

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

[*10.149]

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Fearless Living

June 30, 2018

We can live with no fear if we remove these four pairs of opposites and have Right View.

— Thích Nhất Hạnh

  • No Birth
  • No Death
  • No Sameness
  • No Otherness
  • No Coming
  • No Going
  • No Being
  • No Non-being

Further Reading:

https://en.wikipedia.org/wiki/Th%C3%ADch_Nh%E1%BA%A5t_H%E1%BA%A1nh

https://tnhaudio.org/tag/pairs-of-opposites/

[*9.226]

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