Archive for the ‘Science’ Category

Four Forms Make a Universe

March 12, 2019

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 the Boolean True (A or ~A), A, B, and 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)


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)




Four New Synthetic Base Pairs Added to DNA

February 27, 2019

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:



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

[*11.41, *11.45]


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:



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:

Structures > Parts > Matter
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.

[*10.157, *11.26, *11.34]



The Free Energy Principle

November 27, 2018

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:






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:





The Standard Model of Particle Physics

September 5, 2018

Until a few years ago, the Standard Model of particle physics had sixteen particles verified. Recently, the Higgs Boson was added, so just imagine another triangle hanging off somewhere. Or, alternately, one may combine the Z and W Bosons when adding the Higgs, so a sixteen-fold scheme is maintained.

Also, the Standard Model is much more than a list of these seventeen particles and their attributes. Not shown are a plethora of equations that describe the properties of these entities and their interactions.

I admit that this diagram is not very useful for scientific knowledge, but the reader may contemplate it as they please.

Further Reading:




The Seasons and the Zodiac

August 22, 2018

This isn’t a bad little diagram of the four seasons along with the twelve zodiac names and symbols. However, it might be oriented wrong by convention or going clockwise instead of counter-clockwise.  Interestingly, old horoscope charts that show what was in the sky (the positions of the zodiac stars and the eight or nine planets in regards to the twelve “astrological houses”) at the time of a person’s birth were shown using the outside ring of twelve triangles instead of the more familiar circle that is used today. The inner square might be for notes or some nice drawing.

Further Reading:





Ohm’s Law

August 21, 2018

Unfortunately it has finally come to this: enter the sixteenfolds!

  • Voltage = V = P/I = sqrt(P·R) = I·R
  • Resistance = R = V^2/P = V/I = P/I^2
  • Current = I = V/R = sqrt(P/R) = P/V
  • Power = P = I^2·R = V·I = V^2/R

Further Reading:

[*8.4, *8.5, *8.8-8.10, *10.62, *10.112]




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