fanfare for a common Tao

Cremated, Ashes scattered scattered in a bower at the Tanglewood Music Center in Berkshire County, Massachusetts

Undecidable Tao

Proposition VI: To every ω-consistent recursive class c of formulae there correspond
recursive class-signs r, such that neither v Gen r nor Neg(v Gen r) belongs to Flg (c) (where v is the free variable of r).

or:

All coherent axiomatizations of arithmetic contains undecidable propositions.

In one of the most important works of logic of all time Kurt Gödel in 1931 proved two theorems limiting based on Principia Mathematica, but in fact valid (...and related systems) for every formal system powerful enough.

The first incompleteness theorem states that:

In every mathematical theory T expressive enough to contain arithmetic, there is a formula φ such that if T is consistent, then neither φ nor its negation Neg(φ) are provable in T.

with some simplification:

In any consistent formalization of mathematics that is sufficiently powerful to axiomatize the elementary theory of natural numbers - that is, powerful enough to define the structure of natural numbers with the operations of sum and product - it is possible to construct a proposition that is syntactically correct which can be neither proved nor disproved within the system itself.

The second incompleteness theorem of Gödel, already quoted, obtained, essentially, by formalizing the proof of the first incompleteness theorem within the theory itself, states:

For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, T includes a statement of its own consistency if and only if T is inconsistent.

with some simplification:

No consistent system can be used to prove its own consistency.

the Decalogue of Tao

The foreword to Kieslowski & Piesiewicz, Decalogue: The Ten Commandments, London: Faber & Faber, 1991

---

I am always reluctant to single out some particular feature of the work of a major filmmaker because it tends inevitably to simplify and reduce the work. But in this book of screenplays by Krzysztof Kieslowski and his co-author, Krzysztof Piesiewicz, it should not be out of place to observe that they have the very rare ability to dramatize their ideas rather than just talking about them. By making their points through the dramatic action of the story they gain the added power of allowing the audience to discover what's really going on rather than being told. They do this with such dazzling skill, you never see the ideas coming and don't realize until much later how profoundly they have reached your heart.

---

Stanley Kubrick, January 1991

K.K. was in France and was doing an audition to an actress who told him this story: years before he was ill, was destroyed on the verge of suicide ... one morning she was coming out of the house, in Paris, and she realizes that as he walks across the street is Marcel Marceau, the greatest mime ever, which is going about his business ... all of a sudden Marceau's glance, only a very brief look, just a moment ... she said at Kieslowski that look who saved her life, she no longer killed herself just for that look ... a look of Marceau clearly that's not really any one look, but this is not the point ...

the point is what Kieslowski says, with whom she is well along, that maybe the meaning of all  the life of Marceau, his birth, because he came to the world, was just to make that look, that one moment to save her life ..

Powazki Cemetery, Warsaw

Tao limits

In any type of system (artificial, conceptual, mental, living, natural) given a state variable or process, or the input-output relationship, its variation will always be limited in terms of another variable on which it depends. In other words, no system variable or process may tend to infinity indefinitely.A typical example is the output/input relation of the type:

 

In Part I it was assumed that the system is linear, if not you can always return to a linear graph by transforming the output axis, for example if the variable is exponential returns to the logarithm of the variable. At the beginning of Part II the output variable goes into a situation of saturation, where it loses linearity and becomes sub-linear. In Part III, for high values of input, the output undergoes oscillations until the destruction of the system.
In the words of Bateson:

THERE ARE NO MONOTONE "VALUES" IN BIOLOGY

A monotone value is one that either only increases or only decreases. Its curves has no kinks; that is, its curve never changes from increase to decrease or vice versa. Desired substances, things, patterns, or sequences of experience that are in some sense "good" for the organism - items of diet, conditions of life, temperature, entertainment, sex, and so forth - are never such that more of the something is always better than less of the something. Rather, for all objects and experiences, there is a quantity that has optimum value. Above that quantity, the variable becomes toxic. To fall below that value is to be deprived.
This characteristic of biological value does not hold for money. Money is always transitively valued. More money is supposedly always better than less money. Fore example, $1001 is to be preferred to $1000. But this is not so for biological values. More calcium is not always better than less calcium. There is an optimum quantity of calcium that a given organism may need in its diet. Beyond this, calcium becomes toxic. Similarly, for oxygen that we breathe or food or components of diet and probably all components of relationship, enough is better than a feast. We can even have too much
psychotherapy. A relationship with no combat in it is dull, and a relationship with too much combat in it is toxic. What is desirable is a relationship with a certain optimum of conflict. It is even possible that when we consider money, not by itself, but as acting on human beings who own it, we may find that money, too, becomes toxic beyond a certain point. In any case, the philosophy of money, the set of presuppositions by which money is supposedly better and better the more you have of it, is totally antibiological. It seems, nevertheless, that this philosophy can be taught to living things.

Places of Tao

Machapuchare or Machhaphuchhare (माछापुछ्रे) "Fish Tail" in English, is a mountain in the Annapurna Himal of north central Nepal, 6993 m. high. It is revered by the local population as particularly sacred to the god Shiva, and hence is off limits to climbing.

Machapuchare has never been climbed to its summit. The only attempt was in 1957 by a British team led by Jimmy Roberts. Climbers Wilfrid Noyce and A. D. M. Cox climbed to within 50 m of the summit via the north ridge, but did not complete the ascent; they had promised not to set foot on the actual summit. Since then, the mountain has been declared sacred, and it is now forbidden to climbers.

duality and complementarity of Tao

A painting by Jim Thompson  

In the process description is useful, having made a distinction of description, to move from a dualistic logic of opposites or the type or/or (good/bad, beautiful/ugly, black/white ...) to a logic of the type and/and, taking into account the recursion between form and process.

In 1976 Francisco Varela proposed to describe the recursive complementarity between process and form as:

the thing / the process that leads to the thing

as examples:

form/process
territory/map
describing/described
observer/observed
subject/object
environment/system
family/individual
context/ordinary action
whole/part
circle/line
recursive/lineal
mind/body
cybernetics II/cybernetics I
autonomy/control
organization/structure
aesthetic/pragmatic
art/technical
being/becoming
learning II/learning I

F. Varela, "Not one, not two", CoEvolution Quaterly, 1976

the Teh of Tao

- 9 -

Fill your bowl to the brim
and it will spill.
Keep sharpening your knife
and it will blunt.
Chase after money and security
and your heart will never unclench.
Care about people's approval
and you will be their prisoner.

Do your work, then step back.
The only path to serenity.  

(Antennae galaxies - Hubble image- ESA)