Constraints and Indications

[Jon Awbrey]

All & Sundry ...

Here's some thoughts on the concept of “constraint” I wrote up
a few years back. I had planned to follow up with a discussion
of the related concept of “indication” but all I've found so far
is the figure I drew to show their relationship, so maybe I'll
actualize that intention in the present time frame if I can
remember how it went.

• Constraints and Indications : 1
https://inquiryintoinquiry.com/2012/12/23/constraints-and-indications-1/

The system-theoretic concept of “constraint” is one that unifies a manifold of
other notions — definition, determination, habit, information, law, predicate,
regularity, and so on. Indeed, it is often the best way to understand these
other concepts.

Entwined with the concept of constraint is the concept of “information”,
the power signs bear to reduce uncertainty and advance inquiry. Asking
what consequences those ideas have for Peirce's theory of triadic sign
relations led me some years ago to the following thoughts.

• Semiotic Information
http://intersci.ss.uci.edu/wiki/index.php/Semiotic_Information

Here I'm thinking of the concept of constraint that constitutes one of the
fundamental ideas of classical cybernetics and mathematical systems theory.

For example, here is how Ashby introduces the concept of constraint
in his Introduction to Cybernetics (1956).

<QUOTE>

A most important concept, with which we shall be much concerned later,
is that of “constraint”. It is a relation between two sets, and occurs
when the variety that exists under one condition is less than the variety
that exists under another. Thus, the variety of the human sexes is 1 bit;
if a certain school takes only boys, the variety in the sexes within the
school is zero; so as 0 is less than 1, constraint exists.
(1964 edition, p. 127).

</QUOTE>

At its simplest, then, constraint is just an aspect of the subset relation.

The objective of an agent, organism, or similar regulator is to keep within
its viable region, a particular subset of its possible state space. That is
the constraint of primary interest to the agent.

Incidentally, Ashby's book, in my estimation still the best introduction
to classical cybernetics going, is available online in PDF form:

• Ashby, W.R. (1956), Introduction to Cybernetics, Methuen, London, UK.
http://pespmc1.vub.ac.be/books/IntroCyb.pdf

Regards,

Jon

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[joseph simpson]

Jon:

Very interesting points.

A primary theme associated with large scale system design, production and operation is the integration of many different points of view and perspectives.

There is a range of well defined engineering and management groups that each have a different point of view and role in the system production process.

Many of these well defined groups have their individual formal design and analytical techniques which are expressed in terms of mathematical equations.

The total system control process must integrate these different points of view and formal techniques.

The integration process may well encounter logical,  process and evaluation constraints.

Constraint Theory is designed to identify well formed relation collections that may be computationally evaluated.

As we will discuss in Technical Report 23, natural language may be used to identify operational and computational constraints.

These natural language techniques do not provide numeric values, but they do identify compatible combinations of a given collection of mathematical relations.  

In many cases, the identification of compatible relation groups will reduce the resources needed to achieve the program goals.

Take care, be good to yourself and have fun,

Joe

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Joe Simpson

“Reasonable people adapt themselves to the world. 

Unreasonable people attempt to adapt the world to themselves. 

All progress, therefore, depends on unreasonable people.”

George Bernard Shaw

[Jon Awbrey]

Joe and All,

The requirements of critically and reflectively dealing with collaboration,
communication, context, integration, interoperability, perspective, purpose,
and the reality of the information dimension are precisely the reasons for
upgrading our conceptual architectures from those based on dyadic relations
to those constructed from triadic relations, with special reference to the
triadic sign relations of pragmatic semiotics. I think one or two folks
here have been saying this in one form or another for a number of years.

I'll get back to the logical and mathematical requirements for dealing
with constraints in another post but speaking of the constraints arising
from cross-cultural and cross-disciplinary integration I could recommend
a paper Susan Awbrey and I wrote a few years ago for a conference devoted
to those very issues.

Here is the conference version:

• Awbrey, S.M., and Awbrey, J.L. (September 1999),
“Organizations of Learning or Learning Organizations : The Challenge of Creating
Integrative Universities for the Next Century”, Second International Conference
of the Journal ‘Organization’, Re-Organizing Knowledge, Trans-Forming Institutions :
Knowing, Knowledge, and the University in the 21st Century, University of Massachusetts,
Amherst, MA. [ http://cspeirce.com/menu/library/aboutcsp/awbrey/integrat.htm ].

Here is the journal version:

• Awbrey, S.M., and Awbrey, J.L. (May 2001),
“Conceptual Barriers to Creating Integrative Universities”,
Organization : The Interdisciplinary Journal of Organization,
Theory, and Society 8(2), Sage Publications, London, UK, 269―284.
[ http://org.sagepub.com/content/8/2/269.abstract ].

Regards,

Jon

>> it is often the best way to understand these concepts.

[joseph simpson]

Jon:

Thanks for the additional information and commentary.

It is interesting to note that models may be constructed using informal (natural) languages as well as formal languages.

The careful application of a series of different language types, as well as model analysis types, appears to hold the key to many problematic areas.

The simple example from constraint theory is one kind of approach.

There are others, that should be explored as time allows.

Take care, be good to yourself and have a fun 4th of July,

Joe