Technological Innovation as
an Evolutionary Process
The Orb construction and n-aries
4/27/2004
4:45 PM
Short “Systems AS-IS”
Paper
Short “Finding the Balance” Paper
The Orb construction and n-aries
previous discussion on
“structural holonomy” -> .
Brief Comment
First, I wish to make a brief comment to those reading the bead threads. We are working on providing a back-of-the-book index that is dynamic and visual to the bead threads. Once this is in place, the navigation within the beads will be more interesting and one can develop a profile, or allow a computer cookie, to develop a profile about what you have read and what is new and yet perhaps relevant. This will be by subject matter and thus will appear to anticipate your interests.
But right now, the beads threads are just being placed in chronological order of their posting, and within the fourteen threads identified on the home page (www.ontologystream.com) . The theoretical discussion about the bead games is at the BCNGroup site and some extended discussion about mapping memetic expression in real time is scattered here and there.
The Anticipatory Web principles are discussed in several beads, and yet current access is via an only partial completed interface using Readware. (Click here and type in Anticipatory Web in the search window.)
Using the ReadWare conceptual indexer
to find locations about the subject “Anticipatory Web”
The Orb construction and n-aries
This discussion is about the nature of the fundamental construction of Orbs (Ontology referential bases). An extended discussion is given in the notational paper. The application to modeling biological and other complex natural processes is discussed in various threads. Orb based control of biomass conversion technology provides on potential for wealth generation.
A technology applied to aggregating the conceptual representation in systems of weblogs is another Orb based activity having an economic impact.
But here we address the issue of the generality of the ordered triple in the form < a, r, b > where a and b are locations and r is a relational variable. The discussion follows extensive beads between Drs Richard Ballard, myself and Dr. John Sowa.
< a, r, b > is a two-tuple and can be written in the form < r, a, b >.
The n-tuple is written in the form < r, a(1), a(2), a(3), . . . , a(n) > where we use the indexing 1, . . . , n to allow the notation not to depend on exactly a single fixed number of “locations”. An arbitrary location is called an a(i) with the notion that i is arbitrarily chosen from the index set; { 1, . . . , n }. We can think of the locations as being elements of some set of symbols.
Figure 2: <boldface, readable, TYPE, easily> is a three-tuple
In Figure 2 the small blue circles are relationships, and the larger blue circles are words that are co-occurring in common with the relationship “boldface”. This is a bit odd until one understands what Subject Matter indictors are supposed to be indicating. They are supposed to be indicating concepts. For example the two concepts in the next figure are clear, but one will have a hard time specifying precise what they are in sentences.
Figure 3: Two Orb Subject Matter Indicators (from the FCC study)
How the Orb Subject-Matter Indictors are created is fully disclosed. { 1 }. { 2 }
The use of n-aries in the way illustrated in Figures 2 and 3 is simple and straightforward. However all of the work we are proposing, categoricalAbstraction, eventChemistry and generalFramework theory; have many uses. Many of these are not yet discovered. Like the uses of a number, two for example; the uses are limited only by one’s needs. The use we have employed so far is quite figuratively the very simplest use of the underlying construction having the form < a, r, b >, and the encoding that takes this form and manages it within the key-less hash tables.
The work we are describing may have the property of being very close to optimally addressing a number of first principles, such as data regularity in context and the nature of ordered sets and the use of ordered sets in laying out in-memory data structures.
A problem recently came up in looking at the development of a measurement of invariance in the data about a complex manufacturing process; silicon production. A similar problem comes up in the detection of cyber instruction events and events that occur in complex ecological event structures.
We have not developed the type of computer interface to the Orb data encoding so that the problem can be addressed in the way that the notation suggests.
The n-tuple in the form < r, a(1), a(2), a(3), . . . , a(n) > has a use that we have not exploited in the SLIP browsers. Part of our problem is that we need some resources to redevelop the visualization from first principles. The first principles are developed in notes, and the redevelopment of the original software has been planned.
Our problem is a practical one, the programmer who developed the SLIP browsers is no longer part of our project; due simply to our running out of operating funds.
In the current SLIP browsers the a(i)s are all of the same category. The linguistic Orb discussed in the notational paper and in tutorials sets up two columns where the first column is of one “type” and the second column is of a second “type”. In the linguistic Orbs, moving a window over the significant words develops the Subject-Matter Indicators. We nominate the center of the window to be the first column and the other elements in the window to be the second column.
( a, b, center, c, d ) à (center, a), (center, b), (center, c), (center, d)
It seems simple, and it is. The power comes due to the minimal representation of patterns of co-occurrence, as see by Figures 2 and 3, and the role that human tacit knowledge has in interpretation.
In the work we did with computer intrusion data, we had just 14 columns of data. Selecting two columns established a conjecture about an invariance of co-occurrences that are defined by the two columns and association of two values as being within the same record. So two records might be: (a, b) and (c, b). The link analysis then produces the triple < a, b, c > , or “there is a relationship between a and c and that relationship is both co-occur with b.
Our work on cyber event detection stopped at this point, and this is exactly the point where we are stopped today from going out beyond the simplest co-occurrence relationship.
But consider the three columns of data:
a, b, c
d, b, e
f, b, g
this gives the relationships < a, b, d > and < e, b, g > involves three columns
The transfer of relationship between three columns
This type of transfer of relationship can be instrumented quite easily using slight modification of the software design.