The Known Knowns of Donald Rumsfeld

July 9, 2019

The stars madden, and satellites hum silently
Where no sound can awaken a sleeper. She dreams
A language which cannot trouble her, a vocabulary

Without voice. She has forgotten the ugly grammar,
The deformed sentences. She has forgotten
The irregularities of memory, the unknown knowns,

The can-no-longer-remembers, the slow impeachment
Of experience. She rises, stunned and serene,
Toward the promise of nothing.

— From Sad-faced Men, by William Logan

  • Known Knowns: what we know we know
  • Known Unknowns: what we know we don’t know
  • Unknown Unknowns: what we don’t know we don’t know
  • Unknown Knowns: what we don’t know that we know

Further Reading:

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

https://academic.oup.com/jxb/article/60/3/712/453685

https://english.stackexchange.com/questions/35284/known-unknown-vs-unknown-known

The Known Unknowns Matrix

https://ianmchugh.wordpress.com/2014/04/15/the-rumsfeldian-knowledge-matrix/

https://www.google.com/search?sa=X&q=known+unknown+matrix&tbm=isch

Also see:

The Johari Window

The Quadralectics of Marten Kuilman

[*11.121]

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The Arcane Arts of Ramon Llull : the Dignities

July 7, 2019

Oh, Ramon Llull, where have you been all my life? I’m sure he’s been there all along, death now over seven hundred years in the past, just like always. His legacy seems at first glance to be quite the essence of medieval religion and scholastic philosophy, but still significantly and obscurely different to be enticing to this one. And on further examination, much more.

My schema above has little to do with his grand elaborate figures, except for listing the sixteen attributes he called “dignities”. Llull’s diagrams are full of clock-like wheels within wheels, complicated tableau, and combinatorial patterns. He wished to create a universal model to understand reality, and who wouldn’t want to discover the same? It is said that his methods are akin to an early computer science, and I’m just now starting to understand why.

The magister based the substance of his methods on his Christian faith, although he converted in midlife from Islam. Living in Barcelona, it was probably a good place to make such a change, but felt his calling was to convert others as well, so traveling he went. The methods he developed to convince others of their errors in belief were quite remarkable, as were the volume of his writing.

Like Gottfried Wilhelm Leibniz, who lived four hundred years later and was influenced by him, Llull wished to automate reasoning. But instead of building mechanical devices, Llull built computers from paper and ink, rulers and drawing compasses, scissors and glue. And instead of numbers as the smallest tokens of his computer, he used abstractions (i.e. words) that he felt would be understood by everyone in exactly the same way.

For example, he enumerated these sixteen dignities or aspects of his Christian diety, although sometimes he used the first nine. His constructions allowed one to pose questions and then obtain answers mechanistically that would be convincing to all observers of the correctness of the result. Too bad he was ultimately stoned to death while on his missionary work, although he lived to be eighty two.

Llull’s devices remind me of some of my pitiful charts and diagrams, and make me wonder if I may either adapt some of his techniques to my own use, or be inspired to develop others. I suspect I have locked myself into limitations by my approach, or are these constraints to my advantage? It might be hard to have spinning elements, but I can envision sliding elements like Napier’s Bones, origami-style folding and pleating, and even physical constructions like linkages and abacuses.

Now a martyr within the Franciscan Order, Llull’s feast day is June 30, which I’ve now missed. I hope to remember him to repost or improve on this by next year.

Further Reading:

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

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

http://trepanatus.blogspot.com/2007/06/ramon-llull.html

https://history-computer.com/Dreamers/Llull.html

http://www.ramonllull.net/sw_studies/studies_original/compsale.html

“Let us Calculate!”: Leibniz, Llull, and the Computational Imagination

http://www.ncregister.com/blog/astagnaro/bl.-raymond-lull-and-the-worlds-first-computer

https://dangerousminds.net/comments/the_13th_century_thinking_machine_of_ramon_llull

The memory wheel

https://www.google.com/search?q=ars+magna+llull&tbm=isch

[*11.118]

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Tanabata, V2

July 3, 2019

Soon it will be Tanabata (七夕) in Japan on July 7th.

Make a wish!

  • Orihime : Vega
  • Hikoboshi : Altair
  • Bridge of Birds : Deneb
  • Silver River : Milky Way

Further Reading:

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

http://www.iromegane.com/japan/make-a-wish-for-tanabata/

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

[*10.48, *11.114]

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Richard McKeon’s Aspects of Knowing, Part 3

July 1, 2019

Previously on this blog:

Each method can be associated with a discursive process: operational with debate, dialectical with dialogue, logistic with proof, and problematic with inquiry. Each method is also associated with a mode of thought which in turn has two moments and one dependency or assumption: the operational method is debate by discrimination and postulation dependent on chosen theses, the dialectical method is dialogue by assimilation and exemplification dependent on changeless models, the logistic method is proof by construction and decomposition dependent on indivisible constituents, and the problematic method is inquiry by resolution and question dependent on discoverable causes.

For this diagram, the four dependencies or assumptions are in the center, and the associated methods are adjacent to them. Filling out the outer edge are the four pairs of moments. Listed, these facets are:

  • Methods (associated discursive process): Operational (Debate), Dialectical (Dialogue), Logistic (Proof), Problematic (Inquiry)
  • Assumptions: Chosen Theses, Changeless Models, Indivisible Constituents, Discoverable Causes
  • Modes of Thought: discrimination and postulation, assimilation and exemplification, construction and decomposition, resolution and question

The second diagram comes from a chart in McKeon’s “Philosophic Semantics and Philosophic Inquiry”. Here, the four methods are in the upper left corner (Universal) and lower right corner (Particular), and four principles are in the lower left corner (Meroscopic) and upper right corner (Holoscopic). Four interpretations are in the center (the vertical pair is Ontic, and the horizontal pair is Phenomenal), and four selections are adjacent to them. Listed, these facets are:

  • Methods: Operational, Dialectical, Logistic, Problematic
  • Principles: Simple, Actional, Comprehensive, Reflexive
  • Interpretations: Existentialist, Entitative, Ontological, Essentialist
  • Selections: Knower (Types), Knowable (Matters), Knowledge (Hierarchies), Known (Kinds)

Note that the Archic Matrix of Watson and Dilworth is essentially derived from this, and even has many of the same terms. However and obviously, the sixteen-fold arrangements of the two diagrams are different.

Further Reading:

http://www.richardmckeon.org

https://equivalentexchange.blog/2011/01/16/richard-mckeons-aspects-of-knowing/

https://equivalentexchange.blog/2017/10/10/richard-mckeons-aspects-of-knowing-part-2-v3/

https://equivalentexchange.blog/2018/09/13/the-archic-matrix/

[*5.184, *5.185, *6.20, *11.102, *11.106]

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Combogenesis and Evolution

June 23, 2019

There is grandeur in this view of life, with its several powers, having been originally breathed into a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved.

— Charles Darwin, from The Origin of Species

Another important part of Tyler Volk’s theory of combogenesis that I didn’t mention previously is the role that evolution plays in the dynamical realms of biology and culture. He even illustrates evolution as a three-part braid where the strands are the processes of propagation, variation, and (natural) selection. He argues that these processes are fundamental to an abstract notion of meta-evolution that can be seen working to cause change in both of these different domains.

I don’t think that there is anything controversial in listing these three processes as being essential for biological evolution. Other diagrams and schemas available on-line also mention overproduction or fecundity, or having more off-spring than is strictly needed to continue the population, and heredity or heritability, or the ability to pass on special traits from parents to children.

Overproduction not only allows for greater survival chances for the organism but also gives genetic variation a better chance at producing something beneficial or interesting. This depends on what your chance of variation is, of course, but it seems that it is just a facet of propagation. Likewise, heredity seems like it is also included in propagation, as the continuance of the same or similar attributes to one’s descendants.

I previously proposed that four processes were essential to the workings of evolution: generation, variation, selection, and speciation. Generation is basically another word for propagation, although propagation might more clearly suggest having same or similar dependents, whereas generation just means having descendants. Overproduction can also be combined into either of these aspects if so desired. But I’ll say that (at least in my mind) generation and propagation are roughly the same.

But what about the process of speciation? Is it as fundamental to biological evolution as we see it working on our planet today as the other three processes? Speciation only means the formation of new and distinct species by evolutionary process. So generation, variation, and selection don’t really allow for the “endless forms most beautiful” in the famous quote of Darwin, or do they? Speciation also implies the heritability attribute of evolution, so maybe both generation and speciation subsume the aspect of propagation in most biologists or at least Volk’s mind.

But an important question is, is specification implied by the other three, like three mathematical axioms implying a theorem, or is it independent of them? If you don’t have speciation, don’t you essentially just have one type of organism? Or would you just have a continuum of variation within the population, without any barriers for reproduction between them? I’ll admit that these questions are too complicated for me to answer at this time.

Getting back to Volk and combogenesis, he and others have argued that cultural change is an evolutionary process as well. Another important question then is, if speciation is fundamental to evolution, then is the differentiation of cultures fundamental to the evolutionary process of culture? If so, culture may never be ‘one thing’, and we will always have different cultures competing for dominance.

The competition of different cultures isn’t necessarily a bad thing, as perhaps they can also be pluralistically cooperative. And perhaps having multiple cultures are best in case the society heads down an evolutionary dead-end, longevity-wise. But still, this might be the reason that we will always have multiple cultures that just can’t agree, can’t get along, and can’t really live together.

You might hope that by language and reason, different societies and ideologies can bridge gaps in understanding. You might hope that good-will and morality might win out, and destructive vitriol will be held in check. You might indeed hope. But research has shown that people are very resistant to changing their minds once they think they are right. I think it has been shown that new types of media (I’m looking at you, internet) has exacerbated this problem to the n-th degree.

There is the fourfold Means and Ends (of course there is) that includes cooperation and competition, as well as conflict and coalition. It is based on looking at the compatibility and incompatibility of different means and ends. Even if you can’t have full cooperation, perhaps you can have (mere) competition or coalition within cultures, instead of out-and-out conflict. Perhaps the key is to find those common goals, and even those common values that might allow our factious society to move forward. But many others have said these types of things.

Interestingly, there are also four types of geographic biological speciation, so looking at these might give us clues as to what might be occurring for our speciation in cultural evolution (there’s a nice diagram at the Wikipedia entry). Do the same processes that produce species in the biological world also produce societal divergences in the cultural world? Are these processes the origins of tribes, nations, and even wars? Are there analogues of allopatric, peripatetic, parapatric, and sympatric speciation when considering different cultures and their conflict and cooperation?

Further Reading:

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

https://sciencing.com/four-factors-natural-selection-8140305.html

https://metapatterns.wikidot.com/nyusjm1-1:flott-evolution

https://evolution.berkeley.edu/evolibrary/article/evo_43

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4816541/

https://www.nature.com/scitable/definition/speciation-183

https://equivalentexchange.blog/2012/06/08/the-theory-of-evolution/

https://equivalentexchange.blog/2015/12/30/means-and-ends/

https://www.newyorker.com/magazine/2017/02/27/why-facts-dont-change-our-minds

Read the rest of this entry »

Four Sociological Traditions

June 18, 2019

A blurb found on the web for this 1994 book:

The updated version of Collins’s critically-acclaimed Three Sociological Traditions, this text presents a concise intellectual history of sociology organized around the development of four classic schools of thought: the conflict tradition of Marx and Weber, the ritual solidarity of Durkheim,the microinteractionist tradition of Mead, Blumer, and Garfinkel, and–new to this edition–the utilitarian/rational choice tradition. Collins, one of the liveliest and most exciting writers in sociology today, traces the intellectual highlights of these four main schools from classical theories to current developments, introducing the roots of sociology and indicating the areas where progress has been made in our understanding, the areas where controversy still exists, and the direction in which sociology is headed.

Further Reading:

Randall Collins / Four Sociological Traditions

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

https://equivalentexchange.blog/2015/11/16/the-four-requisites-of-randall-collins/

[*4.6, *11.110]

Read the rest of this entry »

Category Theory

June 10, 2019

I’ve been interested in Category Theory for a substantial number of years, but have never dedicated the time necessary to learn it properly. But it seems to me that these are great days (salad days?) for learning at least the rudiments of the subject. There are now wealths of copious materials available on-line for free for one’s self-study and enrichment, as well as new and classic treatises on Categories and their theory.

Category Theory has been called “abstract nonsense”, but while it is very abstract, it is hardly nonsense. Like set theory, it can be used to study the foundations of mathematics. Like algebra, it can be used to study generalized structure and relationships in math. Like the assortment of tools that is computer science, it can be used to study the essence of logic and computation. And like calculus, it can be used for all sorts of applied and scientific purposes.

Like all good math, Category Theory (CT) generalizes concepts that lie at the heart of many branches of mathematics. These concepts allow the mathematician to see similarities between these different branches, and carry them over into others as well. You might think “maths” is all one thing, and it is, roughly, but like science, it has evolved into a myriad of subjects and specialities. Ontologically (or perhaps even categorically), CT is listed as a topic under algebra, and it in turn has its own distinct branches.

And like all good math, CT benefits from a judicious choice of definitions and properties, that balance generality with precision to great expressive advantage. This balance between abstraction and concreteness gives it the power and utility that it has enjoyed for the better part of seventy-five years. This makes CT rather a new-comer to mathematics, but please don’t mistake youth for lack of expertise.

If I wanted to represent CT emblematically, I might suggest the diagram above. At root, a category merely consists of a collection of objects and the pairwise morphisms (or arrows) between them. But additionally, the arrows must also obey a small set of conditions, so the objects usually have a similar nature. This nature can be quite abstract though, and one of the most familiar “concrete” categories is that of sets and the functions between them.

If arrows are the mappings between objects, then “functors” are mappings between categories, that once again have to obey some rules to maintain structure. So you can think analogically that arrows are to objects as functors are to categories and you wouldn’t be too wrong. Next, you can imagine generalizing to a higher level that there are mappings between functors, and “natural transformations” are indeed defined to be so.

There are many types of entities and characters that inhabit the theory that serve to propel the plot threads along. Some turn out more important than others, but most are essential to the overarching tale. Mathematics as storytelling? What an interesting and novel concept!

Further Reading:

https://www.math3ma.com/blog/what-is-category-theory-anyway

Why Category Theory Matters

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

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

https://en.wikipedia.org/wiki/Category_(mathematics)

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

https://plato.stanford.edu/entries/category-theory/

https://ncatlab.org/nlab/show/category+theory

https://bartoszmilewski.com/

https://www.youtube.com/user/DrBartosz/videos

Rina Zazkis, Peter Liljedahl / Teaching Mathematics as Storytelling

[*6.180, *11.104]

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The Four Loves

June 7, 2019

The Four Loves of C. S. Lewis:

  • Storge: affection or empathy
  • Philia: friendship
  • Eros: romantic love
  • Agape: charity or unconditional love

Further Reading:

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

[*11.78]

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The Mouse’s Tale

June 7, 2019

No apologies to Lewis Carroll.

Further Reading:

https://en.wikipedia.org/wiki/The_Mouse%27s_Tale

[* 11.100]

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The Tangram

June 1, 2019

Further Reading:

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

https://equivalentexchange.blog/2018/02/24/a-game-of-fourfolds-part-5/

[*11.100]

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