Friday, October 26, 2007

The meaning of the title

This writing is all about everything and about nothing; it is about certainty and uncertainty; it is about determinacy and about indeterminacy; it is about stability and about change.

I call it Foundation Theory, because we tend to create these distinctions that transform little by little, bit by bit, so that what we once revered as everything changes to nothing;what we once swore upon as a certainty now seems more uncertain; what we once relied upon as stable no longer offers that same security. The opposite pattern also occurs, where from nothing something grows, uncertainty tends to find a surer more certain footing, the insecure gain confidence.

The goal of writing this is to free up our functioning world-wide, that is expressing itself differentially in better environments, but not as potently as it ought to universally, to bring hope and prosperity to all societies, and all of humanity within those societies beyond the cloistered environs of religion and science.

This is exactly the same expressed aim of Jesus, as written, when he declared, "I have come so that you might have a more abundant life." There are millions living the abundant life, but there are billions who are not. Nothing here changes the earlier prophetic messages. The intent of this writing is to express the generality that underlies all of our religion, our scientific effort, and our productivity.

We need a principle that states the commonality, and provides a method for all of us to sort out the contradictions in our speech, to lend strength to our good intentions.

The God particle; where we come in

Mankind has always attempted to define conclusively and exclusively, what is super-natural, beyond understanding, and all powerful. It is a never ending quest that has centered upon strong leaderships, upon stupendous natural events, upon the heavens and upon particular heavenly bodies.

We know intuitively that we haven't the full tool set to realize what we do not know, but that our living with any kind of prosperity and success depends upon our search.

Formalistic based searches, as proved by Kurt Godel,are incomplete. He identified the source of our tool-making developments as discoverable by Intuition alone.

Intuition is a dimensionless concept, like the concept of a point, a line, and a circle. It is therefore a birth-right tool, as meaningful, and as meaningless, as the first life-indicating response of a new borne child.

If we in error, continue to fix a concept of God, we will always end up shackled in service to a god, a particle of understanding, less expressive than our first awakening cry.

The Exodus is my inspiration for the Generality principle.
It is written that Moses, unable to express what he was confronted with, asked how to identify the indicator of the law. "Say that, I Am that I Am." Form begets Form, the source of all indication, the beginning and the end of all indication.
In order to restore indeterminacy, gained during the trials of the Exodus, but lost to the rigidity of the Form of the religions of his day, Jesus exhorted his followers to act in Faith. God is helpful, and is expressed intuitively, in continuous indication. Without faithful action, freely and intuitively expressed, God is not revealed.

So, A stifled people, no matter how religious in observance, will fail to grow in understanding and prosperity, when the natural birth-right of a oneness with God is denied or qualified by intercession.

The form of Buddha is not God. The form of Roman Catholicism is not God. The form of Allah is not God.
We are at war now because we are all idolaters to the forms of our incomplete understandings. God is still, and always will be, beyond the explication of our keenest endeavors.

A better understanding depends upon our acknowledging all humanity at the borders of our societies. We won't find a peaceful solution in any particular religion or religious study. We do need to heed with great caution, and with great humility, the relativity of Form and Function, and do all we can to create a better fit for all within our societies and without, and determine the truth of this Foundation Theory through daily observance in general activity.

The Uncertainty Principle: Heisenberg

The more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa.
--Heisenberg, uncertainty paper, 1927

The above quote is taken from the following source:
http://www.aip.org/history/heisenberg/p08.htm

That there is a search for the forces defining the shape of the electron, in the Higgs boson, the so-called "God particle", will not alter the concept and the reality of the uncertainty principle first described by Werner Heisenberg as a generality in Foundation Theory.

Foundation Theory must ever relate to the sensibility of living matter. Just a Kurt Godel distinguished Intuitive Truth from Formal verification, and even as for example, the fluidity of water is an emergent quality of water, not found in a single molecule of water, There can be no such intelligible thing as a "God particle".

There is no end to formal discovery. Ultimate congruency is no more meaningful than a new borne baby's first cry, which means the whole totality, if we had but ears to hear it's message entirely.

The Incompleteness Theorems: Godel

In my earlier discussion, I attempted to illustrate that the function of any form is a relative concept, essentially indeterminate, and that no indication of a form is sufficient to satisfy congruency, that the broader currency of the indication relies upon an interpretation within a language structure.

Kurt Godel, 1906-1978, put it another way in his Incompleteness Theorems:
http://www.exploratorium.edu/complexity/CompLexicon/godel.html
The following is copied from the above reference site.

"In 1931 the mathematician and logician Kurt Godel proved that within a formal system questions exist that are neither provable nor disprovable on the basis of the axioms that define the system. This is known as Godel's Undecidability Theorem. He also showed that in a sufficiently rich formal system in which decidability of all questions is required, there will be contradictory statements. This is known as his Incompleteness Theorem.
In establishing these theorems Godel showed that there are problems that cannot be solved by any set of rules or procedures; instead for these problems one must always extend the set of axioms. This disproved a common belief at the time that the different branches of mathematics could be integrated and placed on a single logical foundation."

The Generality Statement

David Hilbert, the outstanding formalist of Europe, 1862-1943, made this observation: The art of doing mathematics consists in finding that special case which contains all the germs of generality.

I looked for what it was that defined mathematics, whether it was in geometry, symmetry, algebraics, or whether it was in logic, in intuition, or whether it was in an appreciation of beauty. I couldn't find any discipline that exactly and exclusively defined what mathematics was.

My concern was this: is mathematics a natural tool of all form, or not? Clearly if a tool of all form, then it has to be accessible to all form, both consciously and unconsciously.

Whatever mathematics may be, therefore, must be found in this generality:

Form determines function;function alters Form.

The indeterminacy of Form and Function

Because any form begins as an indicated encirclement within an undefined form, and because the event of indication is either arbitrary or without any perceived cause, it must be understood to be indeterminate.

There is no doubt that our forms and our functions are invested with undoubted reality. But that is not the point. When we are caught up in our pursuits, and fully engaged functionally, we have no real concept of our form. When we are fully and properly defined according to any perceived status, we have no real concept of our potential functionality.

Indeed, definitions of form may limit function; definitions of function may limit form Some may say, "Ah,ha! Clearly this means determinacy." Perhaps practically, this may seem so. Yet, virtually all of the current problems in our world society may begin to find resolution when humility establishes as a "universal" truth, the intuitive truth that as we grow, our forms, our functions, our tools, our comprehensive capacities and capabilities change.

This leads me to offering a formal expression of Foundation Theory.

Function: a form of a tool within a Form

The idea of a function is simply this: a function is that which indicates a Form.

The study of genetics and epi-genetics is revealing more clearly how mechanically we form in interaction with our environment. The formation is one-to-one in reaction to sensibility.

The indicative function compounds with experience to increase the formal congruency internally and externally, or to increase an understanding of a potential congruency. In general, as a concept, the boundary activity never ceases.

This may be understood as an indeterminacy.

Is a tool a form?

We interact with our environment with a set of tools. When we need anything, we reach out for it with the tools we were born with. We all have a natural set of tools. Every living thing is born with a natural set of tools. We are tools both in form and in function. We are tools in form when we populate a form larger than us.

The idea of utility is a specificity independent of the form of the tool.

A form may encircle a function within a form, and that encirclement may be a tool.

Termites have cellulose digesting bacteria within their guts. Do the bacteria serve the termites with their digesting set of tools, or do the termites serve the bacteria with their cellulose gathering activities?

The utility of the Form

The concept of the circle as a boundary device is an emergent effect of sensibility. It may be congruent with any physical manifestation, but whether it is or not, is or no consequence in itself. The utility of the concept of the form of anything, manifest or imaginary, is external to the form itself.

In other words, a form may by conceived to identify a function, but the form itself is not defined by what it expresses. The utility of the form is relative to form that encloses it.

A word means nothing except how it is interpreted within a language. The utility of the language depends upon the education of the group using the language. The utility of the education depends upon whether it helps development of productivity and trade within a family of groups. This is true for the entire family of forms to the limits of the known universe.

The form is explicative of nothing;of everything

The very act of understanding anything is an act of resolution, and it is a formative indication. We indicate something by sensing it. Sometimes we verbalize; sometimes we touch; in general, we indicate because our form is impinged upon by the Form or environment external to us.

This impingement is a limited interaction. Whether we are in concept, a function of the form interacting with an environment that includes us, or whether we are the arbitrary prime mover in control of an inferior form is a matter resolved arbitrarily.

I once observed a cat run out of a field with a mouse in its jaws, only to get run over by a car running in traffic along the curb lane.

Because of the continuity of forms, the cat may be seen as an expression for any living creature from whether a bacterium, a nematode, or any group of living creatures;a colony, a herd, a nation, or a tribe, or a cultured view;an art, a science, a political creed, or a religion.

Only to the uninformed is the form explicative of everything. The informed ought to know the limitations of the essentially, limiting device. As a concept, the form has no content. It is explicative of nothing.

Is a word a form?

Since a form is a timeless event without dimension, and can appear as a point or a line or a simple notion, depending upon how it is indicated,or perceived by a prime moving intent, either by a god, or by a new borne child, or indeed any life form struggling to problem solve it's environment, any uninformed indication, response, grunt, may be conceived as an encircling concept.

Therefore, a word is a form. By definition, a word indicator is particularly formative, and limited, in the sense that it depends upon a system of Forms external to what it indicates, in order to define its utility, or, function.

To the uninformed speaker however, it is always the case, that the word indicates completely the content responsible for the notion. This is an autism experienced by all living matter. Informing the speaker is always a relative exercise, and language is a group expression informing both the group and each individual in the group.

The group is of course language bound, and uninformed, relative to any larger encompassing group.

This reality of language as an ultimate problem solving agency suffers not from its special utility, but suffers from a lack of understanding by the speakers, and by the groups of speakers, of the formal basis of the function of speech.

What is a form?

When I studied physics during the short time I spent at a university forty years ago, I learned a potent problem solving technique requiring the solver draw a circle around the problem. The circle drawing is an indicating endeavor, and as may be seen comparing the results of the exercise given to a group of students, the circle though shaped differently by every one in the class is still a circle. In other words, the circle is a concept independent of content.

Another key point is that, the drawing of a circle is independent of the talent of the solver. A solver of any level of intuitive capacity and capability may draw a circle.

The purpose of the circle is to provide a boundary at which to measure any variance in the problem. The task of the solver is to identify the function of the form, that is, to measure boundary transactions in an attempt to formalize the problem circled, in terms of function, it's interaction to the environment of the Form. It is to be understood, that the environment of the Form, is an undefined encompassing larger Form.

This is scientific endeavor.

What tends to escape monitoring is, what is happening to the solver? Will the problem-solving influence the development of the solver?

The answer is YES, the action of resolving a form always has an effect on a larger Form , in this case, the form incorporating the solver.

Another facet to this study is: The positioning of any concept such as an encompassing circle is purely arbitrary. The circle is related to line which curves uniformly in such a way that one end bends around to touch the other end. As a concept, it has no dimension, and content is undefined, This circle therefore can be conceived as a point and also as a line. As a boundary it has no real limit, and as a separating device, it essentially bisects an infinity where both sides form an identity.

Another point worth making in this introductory discussion is, without dimension, the form of a circle is a timeless concept.

Why am I doing this?

I'm constantly in awe of the exponential developments that are occurring in all scientific endeavor. There is cross-linkage, or connectivity between a great many disciplines. The internet with inquiry software such as the extraordinary Google, is a vast, powerful resource enabling cross-linkages of any conceivable kind. Facebook created just a few years ago, enabling any group of interest, inter-connectivity, is just the latest resource.

At the same time, there are nations and religions in the world that find inter-connectivity challenging and destabilizing. In a world where scientific endeavor depends upon open resource sharing for development, a major portion of the world population remains unconnected, aware, and in some cases, huge populations are prevented by sanctions, from attempting to inter-connect, or if successful in crossing a proscribed boundary, are penalized for any development attempted which incorporate elements received through unsanctioned inter-connectivity.

The root of the problem is in how we are formally established, and in the boundary defenses we have developed unconsciously and consciously, to maintain the integrity of our form saving boundary.