Inquiry Into Inquiry

Re: Systems Science • Joseph Simpson

Let me step back and talk about the research intention driving this work.

In a very real sense everything I’ve been doing along this line of inquiry for the last fifty years falls within the larger traditions of AI, A-Life, cybernetics, and systems theory that first got my attention in the late 1960s.  Arbib, Ashby, McCulloch, Minsky and Papert, Wiener stand out among the early influences that whetted my appetite for computational and systems-theoretic approaches to inquiry.  It’s fair to say the questions they asked, the hints and tools they provided are always on my mind even today.

A few references, among many others …

• Arbib, M.A., Brains, Machines, and Mathematics.  1st edition 1964.  2nd edition, Springer-Verlag, New York, NY, 1987.
• Ashby, W.R., An Introduction to Cybernetics, Chapman and Hall, London, UK, 1956.  Methuen and Company, London, UK, 1964.
• McCulloch, W.S., Embodiments of Mind, MIT Press, Cambridge, MA, 1965.  3rd printing 1975.
• Minsky, M., and Papert, S., Perceptrons : An Introduction to Computational Geometry, 1st edition 1969, 2nd printing 1972.  Expanded edition, MIT Press, Cambridge, MA, 1988.
• Wiener, N., Cybernetics : or, Control and Communication in the Animal and the Machine, 1st edition 1948.  2nd edition, MIT Press, Cambridge, MA, 1961.

Time scarce and scattered, will get to the rest later …

cc: Ontolog Forum • Structural Modeling • Systems Science

What I’m doing this summer …

Eighteen years living in the same place and we blissfully forgot what it takes to pack up a house and find a new one.  Thankfully most of the renovation work is done but it’s looking like it will be August before I get my head above water.  Just bits and snatches of time till then …

The main functional test for me is getting a fully running version that works on the sorts of examples I stored at Google Drive.

• Theme One Guide

There’s a sample of commenting I started — just barely started — at this place.

• Theme One Program • Commentary 2005

There’s a lot that could be done with the interface, especially making it more visual, displaying the graphical data structures, etc.

There’s hand-generated examples of “animated proofs” in the cactus graph variant of the CSP–GSB calculus at this place.

• Proof Animations

There’s discussion of those examples here.

• Logical Graphs

And it would be wonderful to automate those eventually.

That’s all for now …

cc: Ontolog Forum • Structural Modeling • Systems Science

Re: Systems Science • Joseph Simpson

Warfield gets it right about the relationship between object languages and metalanguages.  Something about the prefix meta- has contributed to a not uncommon misconception that metalanguages are formalized to a higher degree than the languages they objectify whereas in fact the opposite is true.

As it happens, the relation of informal contexts to formal contexts and what I’ve elsewhere called the formalization arrows between them are themes of major importance in my study of Inquiry Driven Systems.  Being short on time at the moment, I’ll give just a pointer to one of many relevant discussions and hope to elaborate further at the next opportunity.

• Inquiry Driven Systems • Introduction
• Option of the Project • A Way Up To Inquiry
• Discussion of Formalization • General Topics
• A Formal Approach

cc: Ontolog Forum • Systems Science

Coding Logical Graphs

My earliest experiments coding logical graphs as dynamic “pointer” data structures taught me that conceptual and computational efficiencies of a critical sort could be achieved by generalizing their abstract graphs from trees to the variety graph theorists know as cacti.  The genesis of that generalization is a tale worth telling another time, but for now it’s best to jump right in and proceed by way of generic examples.

Figure 1 shows a typical example of a painted and rooted cactus.

Figure 2 shows a way to visualize the correspondence between cactus graphs and cactus strings, demonstrated on the cactus from Figure 1.  By way of convenient terminology, the polygons of a cactus graph are called its lobes.  An edge not part of a larger polygon is called a 2‑gon or a bi‑gon.  A terminal bi‑gon is called a spike.

The correspondence between a cactus graph and a cactus string is obtained by an operation called traversing the graph in question.

• One traverses a cactus graph by beginning at the left hand side of the root node, reading off the list of paints one encounters at that point.  Since the order of elements at any node is not significant, one may start the cactus string with that list of paints or save them for the end.  We have done the latter in this case.
• One continues by climbing up the left hand side of the leftmost lobe, marking the ascent by means of a left parenthesis, traversing whatever cactus one happens to reach at the first node above the root, that done, proceeding from left to right along the top side of the lobe, marking each interlobal span by means of a comma, traversing each cactus in turn one meets along the way, on completing the last of them climbing down the right hand side of the lobe, marking the descent by means of a right parenthesis, and then traversing each cactus in turn, in left to right order, that is incident with the root node.

The string of letters, parentheses, and commas one obtains by this procedure is called the traversal string of the graph, in this case, a cactus string.

Resources

• Theme One Program • Overview
• Theme One Program • Exposition
• Theme One Program • User Guide

cc: Conceptual Graphs • Cybernetics • Laws of Form • Ontolog Forum
cc: FB | Theme One Program • Structural Modeling • Systems Science