The observation of pi numbers in eventChemistry

An example of a Pi number is the number 3.14... which is called pi in geometry. Stu Kaufman discovered a number of pi numbers - one related to the ignition of autocatalytic sets... In physics, these are the constants such as Plank's constant or the c in E = mc^2.

In generating the input.txt, ngrams.txt, and output.txt one can count the number of n-grams, branches or trees and put that number at the end of the file.

We can use this count in the study of CCM-Powered conceptual roll-up of 3, 30 and 300 fables. The localization and globalization transforms establishes a bi-level measurement of linguistic variation that when comes into focus reveals many Pi numbers.

One sees this also with the SLIP results on "fractal compression"

http://www.ontologystream.com/cA/tutorials/citationIndex.htm

http://www.ontologystream.com/bSLIP/S&FT.htm

there are many ratios to look at... It is just that the NdCore mechanism might be tuned to see these pi numbers. This tuning can be first studied in the experimental system and then some of the functionality discovered disclosed as patents.....

as discussed (in general terms) at:

http://www.ontologystream.com/area2/KSF/Sections/researchNote21-2.htm

Then we are talking about science, not simply a specific patented innovation.

Let us look at just one of these.

size(output)/size(input)

becomes constant as the size of the collection increases - then we have a pi-number for the process. The pi-number is the limiting distribution, a single point, of the sequence of ratios as we increase the sample size.

but we need to see how this ratio evolves...

One can predict that

size(3)(output)/size(3)(input) < size(30)(output)/size(30)(input) < size(300)(output)/size(300)(input)

and that we do not come close to the pi number in this simple experiment ... a constant ratio that does not change beyond a certain point.

Why is this prediction reasonable? It is because the compounds begin to have the properties of atoms.... and the atoms begin to have properties of compounds. But we do not as yet have the specific atoms and the specific eventChemistry in focus.

When this focus happens, one passes through an organizational constraint. And the result is that one has all of the atoms needed to talk about the open eventChemistry related to that specific domain of discourse.

http://www.ontologystream.com/CCM/CCMnotation.htm#_Section_7:__1

So I am looking for these three ratios and we need for the Experimental System to generate this type of information.

If we can redo the experiments with 3, 30 and 300 fables; using the NdCore 2.0 then we can look at the ratio

size(CCM-defined meta-concepts)/size(input bag of branches).

These ratios will tell us about the degree of structural consistency within the fable collection. This ratio will be a lower limit on the same measurement of other collections when those collections are randomly selected like the test corpus of TREC or MUC.

This is part of the new knowledge science that we are trying to found.

http://www.ontologystream.com/distanceLearning/VKC.htm