Monthly Archives: February 2019

Biology, eightfolds, fourfolds, Science

Four New Synthetic Base Pairs Added to DNA

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All life on earth uses DNA with four types of base molecules arranged in a “double helix” to encode information as sequences of Adenine-Thymine (A-T) and Cytosine-Guanine (C-G) pairs. Because A pairs only with T and C only pairs with G, DNA can be split into two halves and then each half may be completed so that two double helices with the same information can be obtained. Nature also uses the “genetic code” to translate the information in DNA into specific amino acids via its molecular machinery that assembles proteins in the correct sequence.

Now scientists have doubled the number of base pairs of DNA by adding four synthetic ones to the original four natural ones. Four new base molecules S (a Pseudo-T), B (a Pseudo-B), Z (a Pseudo-C), and P (a Pseudo-G) have been created so that S only pairs with B and Z pairs only with P. Now you have twice as many options as you had before and so this “hachimoji” (eight letter) DNA can have much greater information density. Plus if you re-engineer the molecular machinery to use these new bases you can have a brand new extended genetic code to build all sorts of synthetic proteins.

Further Reading:

https://www.scientificamerican.com/article/four-new-dna-letters-double-lifes-alphabet/

http://science.sciencemag.org/content/363/6429/884

https://gizmodo.com/freaky-eight-letter-dna-could-be-the-stuff-aliens-are-m-1832823430

[*11.46]

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fourfolds, religion

The Four Horse-persons of the Apocalypse

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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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eightfolds, fourfolds, Mathematics

Octonions

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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

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

[*11.33]

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fourfolds, Mathematics

Quaternions

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The Quaternions are a number system that enlarges the Complex numbers, just as the Complex numbers enlarge the Real numbers. In fact, Quaternions can be thought as special pairs of Complex numbers, just as Complex numbers can be thought as special pairs of Real numbers.

Quaternions can be used for all sorts of wonderful things, such as rotations in 3D space, instead of using matrices. Above is a pitiful diagram (although better than my last one) of the Quaternion units 1, i, j, and k used in the typical representation a + b i + c j + d k. Please read about them in the links below and be amazed!

Further Reading:

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

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

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

http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/

https://www.quantamagazine.org/the-strange-numbers-that-birthed-modern-algebra-20180906/

[*10.160]

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eightfolds, fourfolds, Psychology, sociology

Spiral Dynamics

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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

Fixing our world: Understanding Spiral Dynamics will help us get back on track

How to Use Grave’s Values Model for Psychological Development

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

Ken Wilber Summary of Spiral Dynamics model

[*11.41, *11.45]

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eightfolds, fourfolds, Psychology

Howard Gardner’s Theory of Multiple Intelligences

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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

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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eightfolds, fourfolds, Psychology, sociology

Erik Erikson’s Eight Stages of Psychosocial Development

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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

Erikson’s 8 Stages of Psychosocial Development

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

[*11.44]

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Consciousness, eightfolds, fourfolds, Psychology

The Eight Circuit Model of Consciousness

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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

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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eightfolds, fourfolds, Psychology

John Beebe’s Eight Function Model

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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/

Eight-Function Model

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

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

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

Also see my posts:

Carl Jung’s Psychological Types

The Myers-Briggs Type Indicator

[*11.41, *11.43]

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eightfolds, fourfolds, Metaphysics, Space and Time

An Eightfold Metaphysics

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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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