Performance Principles

unclosed infinities, transGödel collectives

two letters bound into meaning by reading them - together
educed from the external universe - vivid in your thoughts

---

[1]  ePost to Robert Cutler on the NECSI listserv 09 Mar 1999
"Complexity-informed views of the growth of knowledge"

"The only way to cope with the issues you are addressing is to reduce them to the relational-fundamentals. The main challenge: how to reconcile closed-systems with open-systems, since the two types operate with and define content and boundaries in quite distinctly different ways. Before assessing different mechanisms and functions (proving or disproving one thesis or another) it's required to designate a broad mathematical architecture that can cope with both.

One possibility is "Nested Cantorian Infinities" . It is essentially a dimensional-analysis architecture.

The main proposition is this: Whenever and wherever we designate a 'numerical-value' in some formula or another, we should treat the locus the same way we do the number/integer 'zero' now .... as a place-holder that in
one sense has a fixed value, but in another sense represents all possible values that can reside in that locus ... and that is an independent infinite continuum ... a Cantorian Infinity.

For example, we glibly use exponents to specify relationships that use a baseline number-line as 'frame of reference'. X raised to some exponent value 'n'. X is indicative of the frame-of-reference number line. But the
'n' is its own independent number line. "Simple" exponential configurations are really indicative of juxtaposed Cantorian Infinities ... open unbounded continuums.

And this situation is compounded by dimensional densities: Exponents in integer form have been used to specify "number of dimensions". 'Squared' indicating 2 dimensions, 'third' indicating 3 and so on. Now, instead of limiting the concept of exponential dimensions to the 'positive integers', the step is taken to permit all exponential values to 'be dimensional' (relative to X) in some considered way. Fractals are then viewed as competent dimensional members, even though it goes against the original notion of discrete integer 'dimensions'. Too, we can then consider 'negative dimensions' (akin to squareroot of -1) , and, most important, "zero", which can be considered a viable dimensional state, competent to store non-zero information (in coded form).

Since this goes off in wilder-than-traditional ways of considering what 'dimensionality' is, with unusual attributes and relationships ... combining closed-system concepts with open systems concepts ... I use the word 'fluence' to refer to each of these denotable Cantorian Infinities and continuums (rather than 'dimension'). This is done partly to distinguish the mathematical architectures, and partly to enable taking about the extended architecture and relationships in linguistically less cumbersome ways.

Conjoined intersections of these continuums can be called "confluences" and the dynamic effects of functions on one another can be called "influences", and so on. The phoneme "fluence" also carries with it the conceptual meme
of 'variable, maleable'. In this regard, it's apropos for topology. Domains can retain essential qualities, characteristics and relationships even while stretched or otherwise transformed ... they are 'fluid, plastic'.

Other nice features of this archtecture include new options for juxtaposing several stochastic potentials at the same time .. which was it's essential goal and reason for derivation in the first place. Extended option spaces (eigen- spaces) and pluralities of option spaces. Stochastic considerations include sub-partitioning in overlapping internal- sets ... the broad field of Zadeh/Fuzzy Logic. In fact, since open structure (continuum) precedes demarcation (quantization), Zadeh Logic is the larger framework which embraces/includes the traditional statistical methodologies.

All in all, "Nested Cantorian Infinities" is a novel way to coordinate much if not most of the current diversity found in mathematics, but especially, it's an attempt to confluence open and closed systems, which seems to me to be the crucial challenge. There may be other proposals on the table, but this is at least one of them. 

Ceptual Institute, ceptualinstitute.com

[2] ePost to NECSI listserv  Re the discussion prompted by Robert Cutler 19, March 1999
"Complexity and the scientific method"

 

One of my favorite quotes comes Harry Nillson's 1970 movie "The Point". You all probably remember it's popular song, "Me and My Arrow". In the Pointless Forest, the main character Oblio, meets a beatnik type, a pile of geology calling himself the "Rock Man".  Oblio is on a quest.  He's searching for the answer to the question, "Does everything have a point (even things that are 'round')?"

Nillsen has the Rock Man character share this bit of advice on how to go about evaluating the things and experiences you encounter on such a quest,

                     "You see what you wants to see, and you hear what you wants to hear, dig?"

Silly little words, you might say. Trivial. Childish.

But, gee, isn't that the fundamental notion that the world is agog about regarding Kuhn? Every generation deals with a body of information and experience, encountered in modeled mindsets, and so 'sees' the world with one agreeable paradigm or another. And sometimes enough anomalies or new information occur that the paradigms shift, or competing approaches out do one another, or come to a better compromise of approaches.

It's all the same thing really. Every personal - or 'shared' - knowledge set enables certain understanding of things.

In the millieu of "totality" ... which we project to exist as some singular coherent consistent conprehensive whole ... there can be godelian incompletenesses, even while the fullness of existence tantalizes us with the potential of 'perfect understanding". Or should I say, from the scientific standpoint, perfect 'understandable-ness'. Ultimately
comprehedable in all its machinations.

This means that every 'point of view' has the capacity to be locally valid (even if not 'perfectly' applicable to other information and points of view) .... and, to the point of Robert's comments, each viewpoint tends to use itself as the basis-locale. It's experiences are the "full data set", and anything less is ... a model. There are frames-of- reference and there is codified information used to evaluate the experiential information.

If we can be non-egoistic in the extreme (a difficult thing to do, but not impossible) then we can look at two homeomorphic information presentations and ask, "Which is the basis, and which is the model?". Regardless of
personal convenience, or what we are used to, we might even come to some unusual conclusions ... like "It really doesn't matter. Just pick a stance and if it works, use it."

Take a binary bitstream. Re-organize it with certain strings juxtaposed to other strings in two dimensions. The first is a temporal sequence of information. The second is a 'flash' presentation that eliminates the time (dimension) required to encounter the information.

Two presentations exist. Sequentially temporal, and, wholistic with one temporal component removed.

The first can be ballbearings dropped through pegs and slots. The second can be the gaussian curve generated.

The first event is the 'information'. The second is the 'model'.  The first can be a communication data stream. The second can be an image of the Mona Lisa.

The first is the 'model'. The second is the 'information'.

What's important is to recognize is that the Rock Man was right. There are plural accurate (not 'perfect') ways of encountering and understanding information. The more complicated and intricate that systems and assemblies become the more potential behavior and interactive patterns become possible. The viability of one doesn't automatically invalidate others out of hand. The plurality of dynamics and functions can grow hyperexponentially as well as emergently.

The key then becomes: coming to an understanding of how information can be codified ... zipped and unzipped .. through all sorts of dimensional and practical configurations. It is the relationships between extants that counts. It is transformations and transductions of information that counts. Some information stays resident even though coded into atypical, not imediately recognizable, forms. Some new relations bring added 'local' information. Some transformations or relationships expose new information.

What's important is that all these 'things' and intangibles are connected, can morph into one another. There is local utility if not always pandemic utility. "You see what you wants to see and you hear what you wants to hear, dig?"

Godel's incompleteness theorems are interesting. What is more important is a post-Godel perspective. Information which is 'potential' (on the far side of a godel boundary or limit) can be incorporated inside the maleable boundary. It is compatible with what is 'known'. Information is transmittable and can be plurally resident in many possible ways and configurations.

We know something about information which may now only exist on the other side of godel's seemingly once impregnable 'knowledge boundary'. We know something about it.

Whitehead said Godel's thesis first with his image of a wall ... inference isn't 'proof' ... there is no way of knowing if a wall is paper thin or 5 light years thick. Godel formalized it to mathematics: information "is" and non-information "isn't".

Well, I assert to you, that that isn't enough ...or accurate. We can paradigm shared dynamics ... the intangible yet objective qualities of existence ... the relationships of systems behaviors. We can recognize requisites for interaction.. that qualitative potentials are real and just as important as quantitative measurings. It is the extended behavior spaces of systems that matters most, and how entities function within those behavior spaces which are present ... and potential.

And, "relativity" is an important attribute in complexity. The universe has to be evaluated as if it were totally open and unbounded. Even if we use equations that are essentially local and limited ... that do not specify extended applications. Performance and experience have been our primary yardstick to guage 'reality'. It's really time to look deeper than that.

'Information' isn't just a tool or a sizable definable 'unit', it's a process. Communicating and counterpoised processes, actually.

Pick an energy unit that you are familiar with. What is it exactly? A convenient information name/unit that markers a phenomenon. Multiply it times pi. Give the new number a name. Throw away the old name/unit and use this one instead. Then take a step back and ask yourself, "which is the 'real' unit energy and which the 'information' components that 'model' the energy?'

You pick a point of view, a frame of reference, and you design a model to correspond with/to all the rest that you know about. If 'energy' and 'information' are somehow interchangable, then its real real important to look into the nature of our Information Universe. Energy supplies 'information'. Space provides 'information'. Time provides 'information'.   Sequence provides 'information'. Relationship provides 'information'. And so on.

If we confuse dynamic principles and laws of nature with models of performance per se, then we will always suffer repurcussions of error and inaccuracy. To say the only statistical models should mimic an economy, to say that only fractal infromationand models are sufficient to mimic economic behaviors, to say that only fuzzy logic will accurately mimic systems behaviors, and so on, is to set ourselves up for ignominious failures time after time.

There are 'performance principles' that underscore systemic behaviors ... and they go far beyond a few choice locally usable and 'sufficient' formulae. Because the rest of the universe is functionally open and interactive. Not restricted or closed in any way. "Boundaries" are only local and conditional limiters of interaction. Not permanent nor impervious firmaments, the way modern science tends to miss-think of them as.

/ CI Commentary /
webposted June, 2000 

---

§  §  §  §  §  §  §

CI Website Sections

What's new and Where to find it

---