Category Archives: Science

eightfolds, sociology

Patrick Geddes and the Notation of Life

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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:

[1] https://en.wikipedia.org/wiki/Patrick_Geddes

[2] http://hodgers.com/mike/patrickgeddes/feature.html

[3] https://equivalentexchange.blog/2017/07/13/a-study-in-synthesis/

[4] https://equivalentexchange.blog/2010/06/10/ken-wilbers-aqal/

[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

Further Reading:

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

4.1.4.1. The Ideal City

Patrick Geddes / Cities in Evolution

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

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eightfolds, Metaphysics, Physics, Space and Time, spacetime

Noether-Pauli-Jung, V2

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What happens when the fourfold of Noether’s Theorem is spliced together with the fourfold of Pauli-Jung? Both have Space-Time and Matter-Energy. The former has Conservation and Symmetry, and the latter has Causality and Synchronicity. And if Space-Time and Matter-Energy are both divided into Space and Time and Matter and Energy, one obtains this eight-fold.

Causality means that some action or cause in time (say a process) of things in space can have an effect (another process, say) on different things in space, and Synchronicity means that different events (say processes) separated in space can have non-causal relationships between them.  Conservation means the consistency of a quantity of matter or energy or matter-energy through time, and Symmetry means the consistency of a measure of a structure or form through space.

I am reminded of my fourfold Four Bindings, consisting of Chains, Grids, Blocks, and Cycles. Causality and Synchronicity are Chains (or non-chains for the latter) Space and Time are Grids (or flexible meshes), Matter and Energy are Blocks (or chunks of stuff), and Symmetry or Conservation are Cycles (of the group-theoretic kind or the equivalence class kind or just loops).

Further Reading:

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

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

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

https://equivalentexchange.wordpress.com/2012/05/04/noethers-theorem/

https://equivalentexchange.wordpress.com/2018/01/23/atom-and-archetype/

Four Bindings

This is a reworking of a previous six-fold diagram that I believe is served better as an eight-fold.

Noether-Pauli-Jung

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eightfolds, Physics, Science

Colors of Light and Matter

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Colors of light and colors of matter operate somewhat differently from each other. Colors of lights are additive, but colors of material pigments are subtractive. Of course, they both are conditioned by the biology of the human eye and cultural preferences. Above I have tried to create a synthesis of sorts for both types, and whereas it is pleasing in some ways, it is lacking in others.

White light is combined red, green, and blue light, and combinations of green and red light yield yellow light, combinations of red and blue light yield magenta light, and combinations of green and blue light yield cyan light. Similarly, black is mixed yellow, magenta, and cyan pigments, mixing cyan and magenta pigments produce blue pigment, mixing cyan and yellow pigments produce green pigment, and mixing yellow and magenta pigments produce red pigment.

Further Reading:

Primary Colors of Light and Pigment

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fourfolds, logic, Mathematics, sixteenfolds, Space and Time

Four Forms Make a Universe

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How could I not love a paper with this title? I’ve struggled with it for a bit, and I’ve only managed a couple of diagrams relating the author’s LICO (Linear Iconic) alphabet made up of 16 letters. However, I see that there are a few other papers by Schmeikal available on ResearchGate that look easier to understand. But also however, the first one says to read the “Four Forms” paper first!

At any rate, I present a sixteen-fold of the LICO alphabet, and another of the binary Boolean operators that are in a one-to-one mapping with LICO. There is much to understand from these papers, including much syncretism between various mathematical sixteen-folds, so please forgive me if I don’t explain it all with immediate ease. However, I believe it is well worth the effort to understand.

(Please note that the characters of the LICO alphabet are oriented so that the bottoms of the letters are downward, but the Boolean operators are oriented so that the bottoms of the equations are towards the right angles of the triangles.)

The title comes from the result that four elements of LICO can reproduce the other twelve via linear combinations. These four forms are 1) Boolean True (A or ~A), 2) A, 3) B, and 4) A=B. These are within the interior right-hand triangles in the LICO diagram. Of course, it is well known from Computer Science that the NAND operator (~A or ~B) can also generate all other fifteen operators, but this is by multiple nested operations instead of simple Boolean arithmetic. There are several other “universal” binary gates that can do this as well.

Two other representations that have four elements that can generate the other twelve via linear combinations come from CL(3,1), the Minkowski algebra. These representations are called “Idempotents” and  “Colorspace vectors”. Because of this algebra’s association with space and time in relativity, Schmeikal claims that LICO has ramifications in many far-ranging conceptualizations.

Further Reading:

Bernd Schmeikal / Four Forms Make a Universe, in Advances in Applied Clifford Algebras (2015), Springer Basel (DOI 10.1007/s00006-015-0551-z)

https://link.springer.com/article/10.1007/s00006-015-0551-z

At http://www.researchgate.net:

Bernd Schmeikal / Free Linear Iconic Calculus – AlgLog Part 1: Adjunction, Disconfirmation and Multiplication Tables

Bernd Schmeikal / LICO a Reflexive Domain in Space-time (AlgLog Part 3)

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

https://www.allaboutcircuits.com/technical-articles/universal-logic-gates/

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fourfolds, sociology

Education is Not a Product

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A recent meme popular in education:

  • Education is not a product.
  • Students are not customers.
  • Professors are not tools.
  • The University is not a factory.

I’m not sure who originally came up with this interesting saying.

Examining the anti-analogy, you have “customers buy products made in a factory with tools”. Perhaps a better fourfold would be to change this to “workers use tools to make products in a factory”, so you could say “Students are not workers.” But then you lose the capitalistic “consumer culture” geist.

Or you could say the Professors are (not) factory workers and the Students are (not) the raw material. As a homework assignment, write an essay or develop a mathematical theory comparing this anti-analogy fourfold (or a close derivative thereof) to Aristotle’s Four Causes. Please show your work.

Further Reading:

Note the similarity with some of the elements of the following (which also reminds me for the Four Causes):

J.-Y. Girard’s Transcendental Syntax, V2

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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

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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

Spiral Dynamics Integral: How to Use Grave’s Values Model for Psychological Development

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

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

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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

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

Erik Erikson’s Stages of Psychosocial Development

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eightfolds, fourfolds, Metaphysics, Space and Time

An Eightfold Metaphysics

5 Comments

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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fourfolds, Mathematics, Science

The Free Energy Principle

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Below is a link to a fascinating article about Karl Friston, whose research on the “free energy principle” (also known as active inference) tries to explain how biological (or even artificial) systems maintain or even increase their organization. Without much explanation, here are some details. The model is a system with four main variables:

  • Sense (s)
  • Action (a)
  • Internal States (r or μ)
  • Hidden States (ψ)

Sense and action divide the internal states of the system from the hidden states external to it. This division is called a “Markov Blanket”. I’ve tried to show the equations between the variables correctly but I’m not too sure if I have them right. They seem to change from paper to paper. F is an expression of the free energy, but I’m not sure what f is at the moment, except for being some sort of “flow”.

Further Reading:

https://www.wired.com/story/karl-friston-free-energy-principle-artificial-intelligence/

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

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

http://rsif.royalsocietypublishing.org/content/15/138/20170792

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