Derek – I think your examples illustrate an important part of the answer to Jack’s question about a recipe for interventions in complex situations: Simple rules, models, and patterns (whether or not we conceptualize them as mathematical) can contribute significantly to understanding and dealing with complexness and complexity. Of course, it is not always simple to discover applicable simple rules. I am attaching an article related to this issue.
From: syss...@googlegroups.com [mailto:syss...@googlegroups.com]
On Behalf Of Ken Lloyd
Sent: Saturday, August 17, 2013 8:45 AM
To: 'profhitchins'; syss...@googlegroups.com
Cc: 'Hitchins Derek'; 'Richard Martin'; 'Kent Palmer'; 'Tony Pizzarello'; 'Oris Friesen'; 'Byron Davies'; 'Thomas Tenorio'; 'Elliot Axelband'; 'Don Greenlee'
Subject: [SysSciWG] RE: stAGES of Complexness
Re: “ … it may be possible to diagnose the nature of a complex problem without recourse to mathematics.”
I suppose it depends upon your conceptualization of what constitutes mathematics. If, by mathematics, one merely thinks in terms of the manipulation of numbers (arithmetic) or numeric substitution symbols (traditional algebra), that is a very limited conceptualization.
We probably all understand that complexity can occur from interaction through simply described relationships. Some of us ask, (in some sense) mathematically, how objects, and categories of structures of objects, may be ‘composed’ and morphed. There are subtle assumptions at play in our traditional conceptualization of mathematics that often confound our understandings. The primary assumption is that mathematics takes place (in its comparisons) at equilibrium. What if that were not the case? This gets to one of the founding issues in category theory – what do we mean by equal? Equivalent classes? http://www.cwru.edu/artsci/phil/BJPSMacLane.pdf
Ken Lloyd
From: profhitchins [mailto:profhi...@gmail.com]
Sent: Saturday, August 17, 2013 3:30 AM
To: syss...@googlegroups.com
Cc: Hitchins Derek; Ken Lloyd; Richard Martin; Kent Palmer; Tony Pizzarello; Oris Friesen; Byron Davies; Thomas Tenorio; Elliot Axelband; Don Greenlee
Subject: Re: stAGES of Complexness
Jack & Joe,
I wonder if we are, perhaps, approaching the subject of "unravelling complexity," if indeed it may be described that way, from an inappropriate end of the horse—the one of a different colour, that is. Consider for a moment how complexity is generated in the first place.
Mathematicians propose that the Mandelbrot set is the most complex mathematical entity, yet it is generated by the simplest of equations: z=z^2 + C. Examining the Set shows it to be full of variety, different forms of interconnectedness, and above all fractal convolutions, so that one may delve deeper and deeper into the set without ever reaching the 'floor.' Imagine if you did not know how the Set was generated—how would you go about trying to 'solve the problem,' unravel the knot, or whatever. And the key is probably in recognizing the repeating fractal patterns.
And then, of course, there is the problem of understanding, diagnosing and hopefully curing problems within the human body—a la House. Doctors are faced with probably the most complex system on the planet, yet they diagnose—occasionally correctly—without a sign of mathematics, or concerns over degrees of complexity. They do, however, have a major interest in symptoms, contexts, histories, emergent properties and behaviours, etc.
Similarly, detectives seem—sometimes almost miraculously—to be able to solve a complex crime when there are few clues, many suspects and no apparent motive. To some, it seems that detectives approach to solving of crime in a way not unlike the doctor diagnosing some (societal) bodily dysfunction...
All of which suggests that it may be possible to diagnose the nature of a complex problem without recourse to mathematics, or to levels of complexity, and it may be possible similarly to synthesize and manage complex solutions to complex problems.
Just a thought...
Derek H
On Saturday, August 17, 2013 4:47:00 AM UTC+1, Jring7 wrote:
Consider, for examples, these perspectives on complexness
· About age 8 we learned about simple, compound and complex sentences and the underlying rules of grammar. We laughed at “throw the horse over the fence some hay.” Why is a specific arrangement of words considered complex?
· About age 12 we learned about simultaneous equations so that we could deal with situations involving N mutually interacting variables. We learned that we needed N different equations. We learned the mechanics of isolating a variable in one of the equations then substituting the term equivalent to that variable for that variable in the other equations. And we learned something more important --- how to select the equation and variable that made the substitution most effective in reducing the complexity of the whole set of equations. Unfortunately, we did not learn how to characterize the degree of complexity of any given set of equations.
· About age 13 our encounter with algebra (complex sentences) taught us about transforms. Viewing a problem set from a different perspective often made the discovery of a solution much easier --- if you could do the inverse transform at the end. Beyond algebra we now are able to exchange knowledge using the “if I were you, I would have…” transform, c.f., Conceptual Blending,
· For those who were ready in the 1960’s we learned about System Dynamics which highlighted a) the notions of influences or causalities between variable and patterns of such relationships and b) the effect of time delays on the relationships.
· A few in college may have experienced implicit differential equations and second order implicitness that helps deal with the rate of change of stimuli, resources and system gradients and structure.
· In the 1970's a co-worker, Bob Wengert, figured out how to use Maximum Likelihood to apportion uncertainties throughout a system of non-stationary components. It was immediately classified.
· Along came Bayesian Belief Networks
· Then genetic algorithms as agents.
· Probably very few have studied or experienced category theory in the field of mathematics. Likewise the calculus of sets. The successful design of effective complex systems is greatly helped by knowledge in these areas.
What clues do these give for a recipe for design and engineering of interventions to complex problematic situations?
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"In physical science a first essential step in the direction of learning any subject is to find principles of numerical reckoning and methods for practicably measuring some quality connected with it. I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind: it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science, whatever the matter may be.”
I am surprised that Lord Kelvin has not been quoted yet. Here is his exact quote from one of his lectures:"In physical science a first essential step in the direction of learning any subject is to find principles of numerical reckoning and methods for practicably measuring some quality connected with it. I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind: it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science, whatever the matter may be.”
From: Hybertson, Duane W.Sent: Saturday, August 17, 2013 6:45 AMCc: 'Hitchins Derek' ; 'Richard Martin' ; 'Kent Palmer' ; 'Tony Pizzarello' ; 'Oris Friesen' ; 'Byron Davies' ; 'Thomas Tenorio' ; 'Elliot Axelband' ; 'Don Greenlee'Subject: RE: [SysSciWG] RE: Stages of Complexness
Derek – I think your examples illustrate an important part of the answer to Jack’s question about a recipe for interventions in complex situations: Simple rules, models, and patterns (whether or not we conceptualize them as mathematical) can contribute significantly to understanding and dealing with complexness and complexity. Of course, it is not always simple to discover applicable simple rules. I am attaching an article related to this issue.
From: syss...@googlegroups.com [mailto:syss...@googlegroups.com] On Behalf Of Ken Lloyd
Sent: Saturday, August 17, 2013 8:45 AM
To: 'profhitchins'; syss...@googlegroups.com
Cc: 'Hitchins Derek'; 'Richard Martin'; 'Kent Palmer'; 'Tony Pizzarello'; 'Oris Friesen'; 'Byron Davies'; 'Thomas Tenorio'; 'Elliot Axelband'; 'Don Greenlee'
Subject: [SysSciWG] RE: stAGES of Complexness
Re: “ … it may be possible to diagnose the nature of a complex problem without recourse to mathematics.”
I suppose it depends upon your conceptualization of what constitutes mathematics. If, by mathematics, one merely thinks in terms of the manipulation of numbers (arithmetic) or numeric substitution symbols (traditional algebra), that is a very limited conceptualization.
We probably all understand that complexity can occur from interaction through simply described relationships. Some of us ask, (in some sense) mathematically, how objects, and categories of structures of objects, may be ‘composed’ and morphed. There are subtle assumptions at play in our traditional conceptualization of mathematics that often confound our understandings. The primary assumption is that mathematics takes place (in its comparisons) at equilibrium. What if that were not the case? This gets to one of the founding issues in category theory – what do we mean by equal? Equivalent classes? http://www.cwru.edu/artsci/phil/BJPSMacLane.pdf
Ken Lloyd
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I would add to this the arbitrariness of English grammar - unsurprising given its origins - and the over 20 dialects spoken today which have not yet diverged so far to become separate languages and can with a little coaching be understood by the speaker of any one of them. I view this as a triumph of processing (some) complexity without symbolic intermediaries.
Could you please explain "utter rubbish"?
In a message dated 17/08/2013 17:32:56 GMT Daylight Time, axel...@rand.org writes:I would add to this the arbitrariness of English grammar - unsurprising given its origins - and the over 20 dialects spoken today which have not yet diverged so far to become separate languages and can with a little coaching be understood by the speaker of any one of them. I view this as a triumph of processing (some) complexity without symbolic intermediaries.Utter rubbish. The English language, applied and used correctly is accurate and definitive.Been there, done it for 40 years.George Caple.Englishman
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George
Clearly you have never worked in Government! "Yes Minister" is an interesting object lesson in the power and value of ambiguity in the English language.
Hillary
(A Scotsman!)
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Clearly you have never worked in Government! "Yes Minister" is an interesting object lesson in the power and value of ambiguity in the English language.
__________________________________________________________________________
proper English, common English, Cockney, Hackney, the Middlesex, Yorkshire, Scottish, Irish, and Welsh dialects, and Gaelick Scottish and Irish
Be an advocate or make something better
__________________________________________________________________________
George, I feel sorry that you've missed out on all the improvements we've made in the English language since independence.John(An American)
Gee, this just goes to show the complexity of language, let alone the list of problems we need to solve to untangle complexity for systems . . . I hope we are trying to provide something for the average System Engineer to understand – maybe we need to look at what the level of training our average SE has received – then can we match up descriptions of complexity that can be useful to the current practicing SE. Or do we need to update the list of skills the SE needs to master? Much of what has been suggested as methods to control and understand complexity will require advanced math concepts. This is very similar to the complexity of understanding the various dialects of English. I have enough trouble understanding different groups within the US . . . I have had fun trying to understanding Brits, Scots, and Aussies peaking their version of English on their home turf. I remember one memorable event in Yorkshire trying to understand the word “flyover” regarding directions to my hotel. Regards, Dave
From: syss...@googlegroups.com [mailto:syss...@googlegroups.com] On Behalf Of JohnK
Sent: Sunday, August 18, 2013 9:25 AM
To: syss...@googlegroups.com
Cc: axel...@rand.org; profhi...@gmail.com; profhi...@mac.com; kent.d...@gmail.com; bda...@starshineacademy.org; teno...@gmail.com; Don.Gr...@AmericanSystems.com; azad....@usc.edu; georgej...@yahoo.com
Subject: Re: [SysSciWG] RE: Stages of Complexness
George, I feel sorry that you've missed out on all the improvements we've made in the English language since independence.
--
Not sure what “peaking” means! Should have been “practicing.” The use of a keyboard adds to complexity also. Dave
Gee, this just goes to show the complexity of language, let alone the list of problems we need to solve to untangle complexity for systems . . . I hope we are trying to provide something for the average System Engineer to understand – maybe we need to look at what the level of training our average SE has received – then can we match up descriptions of complexity that can be useful to the current practicing SE. Or do we need to update the list of skills the SE needs to master? Much of what has been suggested as methods to control and understand complexity will require advanced math concepts. This is very similar to the complexity of understanding the various dialects of English. I have enough trouble understanding different groups within the US . . . I have had fun trying to understanding Brits, Scots, and Aussies peaking their version of English on their home turf. I remember one memorable event in Yorkshire trying to understand the word “flyover” regarding directions to my hotel. Regards, Dave
From:
syss...@googlegroups.com [mailto:syss...@googlegroups.com] On Behalf Of
JohnK
Sent: Sunday, August 18, 2013 9:25 AM
To:
syss...@googlegroups.com
Cc: axel...@rand.org;
profhi...@gmail.com; profhi...@mac.com; kent.d...@gmail.com;
bda...@starshineacademy.org; teno...@gmail.com;
Don.Gr...@AmericanSystems.com; azad....@usc.edu;
georgej...@yahoo.com
Subject: Re: [SysSciWG] RE: Stages of
Complexness
George, I feel sorry that you've missed out on all the improvements we've made in the English language since independence.
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Because all communications follow a standard format and nomenclature. Unless you are a pilot, you probably don’t speak “air tower” English.
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I am surprised that Lord Kelvin has not been quoted yet. Here is his exact quote from one of his lectures:"In physical science a first essential step in the direction of learning any subject is to find principles of numerical reckoning and methods for practicably measuring some quality connected with it. I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind: it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science, whatever the matter may be.”
From: Hybertson, Duane W.Sent: Saturday, August 17, 2013 6:45 AM
Subject: RE: [SysSciWG] RE: Stages of Complexness
Derek – I think your examples illustrate an important part of the answer to Jack’s question about a recipe for interventions in complex situations: Simple rules, models, and patterns (whether or not we conceptualize them as mathematical) can contribute significantly to understanding and dealing with complexness and complexity. Of course, it is not always simple to discover applicable simple rules. I am attaching an article related to this issue.
--
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Huber, G. & Lewis, K. (2011). Cross understanding and shared social theories. Academy of Management Review (Dialogue), 36(2), 422-424.
Huber, G. & Lewis, K. (2010). Cross understanding: Implications for group cognition and performance. Academy of Management Review, 35(1), 6-26. ** Lead Article, Finalist for Best Paper.
The message below (in purple text) is from Kyle who shared some metrics with those who attended the session:
Contact info for Kyle:
Kyle Lewis, PhD
Associate Professor
CBA Foundation Advisory Council Centennial Fellow
University of Texas - Austin
Department of Management
1 University Station B6300
Austin, TX 78712-0210
phone: (512) 232-5862
fax: (512) 471-3937
email: kyle.lewis@mccombs.utexas.edu
web: http://www.mccombs.utexas.edu/faculty/kyle.lewis
I hope you find this digression from your sparring to be at least intriguing. Carry on!
Mary
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