charles consult blog

After being invited to tweet about the cybernetition W. Ross Ashby, I tweeted a few ideas from cybernetics, and got no response – it occurred to me that no one knew what I was talking about. So, I thought I’d write an explanation of my first tweets on the subject to provide a background for the reader. I am going to be a brief as possible, without getting into philosophical matters such as epistemology, causation, and existence.

Ashby was a pioneer in the field of cybernetics. He made operational, important concepts such as: the determinate machine, markov machines, feedback, regulation, and requisite variety. His concepts such as the “black box” and stability are likely still part of most modern electrical engineering curricula.

These concepts are useful in situations where information is incomplete and or hidden, information is confusing, or when in complex and or competitive situations (think – “fog of war“). The subjects of stability and regulation are still relevant in light of current financial, economic, and political discussions. The subject matter is deep, long, and wide - I can only provide here, a brief glimpse into it.

This article was motivated by someone tweeting the well known quote:

“#Logic will get you from A to B. #Imagination will take you everywhere.” ~ Albert Einstein #systemsthinking #intuition

While I believe this to be true, I also believe that there needs to be something tethering imagination to reality, so I tweeted this:

Without logic, what’s the difference between imagination and hallucination? #systemsthinking #logic

I remembered that Ashby, in his book, An Introduction to Cybernetics¹, started the subject matter using logic, developing the concept of change, and the procedure for making a truth table. I will introduce the subject by defining systems and describing their general behavior, then move to the logic of tabular methods/truth tables. We will then look at matrix, and graphical representations of change or transformation. Later articles will cover future states, various system categories and theories, information, stability, requisite variety, and control.

Part I: Introduction

Systems are easy. They have an “inertia”. They stay in one state, until energy is added, then they go to another. #Ashby #systemthinking

What are systems and how do they behave?

We shall define a system simply as anything (material or immaterial) that is predictable and describable.

How do systems behave? Large scale abstraction of the behavior a simple system – first, they exist in one state, then after a change in energy, they change to another state. The simplest example of state change is ice transforming to water via addition of heat (as opposed to the simplest system – that of existence or non-existence). A more active example is, a pendulum, swinging from one side (state) to the other. The pendulum example is also similar (depending on the precise behavior and mechanism) to other system metaphors such as: duality, flip flop, yin-yang, “hunting” in feedback systems, simple harmonic motion, etc. The pendulum is the one simplest intuitive system metaphors and can reflect a number of different underlying mechanisms.²

System behaviors can be described directly in terms of the observed changes in that system, but they are commonly given names such as: result, behavior, outcome, move, etc. This is because systems can take an endless list of metaphorical names such as: life, sport, game, relationship, interaction, dilemma, conversation, communication, institution, economy, society, machine, idea, spirit, thought, etc. These metaphors are consistent by our definition – anything that is predictable or describable.
 

Part II: The Observation and Representation of Change

Toffler tells us in Future Shock, that “change” is the thing to deal with. In I.T.C. Ashby shows us how. #systemsthinking #transdisciplinary

The first step is learning to observe and record meaningful information. The idea is to observe change because it is change that can indicate how things behave, and can point the way to reality.

Ashby begins with a simple example. If you have pale skin, and you stand in the sun, your skin will transform into dark skin. Written thusly:

pale skin —–> dark skin

The important concept is that of transformation. In this example, pale skin is transformed to dark skin by use of sunlight. Other transformation involving sunlight cold be:

cold soil —–> warm soil

closed flower —–> opened flower

brown leaves ——> green leaves

etc.

The set of transitions on a set of operands (the thing being transformed) is called a transformation, and can be written as:

A —–> B

B —–> C

. . .

Y —–> Z

Z —–> A

Note that the transformation is sufficiently defined merely by giving a set of operands and stating what happens to them, and not necessarily why. We can shelve the idea of causality for right now because we are dealing with the first step – observation.³

Truth table – tabular methods
Any set of transformations can describe the behavior of a system (in this context, being anything with a predictable and describable behavior). Physical systems tend to be deterministic systems, unless you are observing large numbers of objects or are getting quantum mechanical – then it becomes statistical. Systems can be written by various tabular forms (vertical, horizontal), and can be represented as we shall see, as a matrix.
 
In the same way you assigned arrows between letters, you can put the same information in a tabular array. A, B, and C go on the top and side – where the transform goes to is denoted by an “+”.

Here, A transforms to A, and B and C transform to C. Visible in both vertical and horizontal tables. For both columns and rows, they are labeled A, B, C, vertically and horizontally.

Note that if you replace the “+” by “1″, you have the idea of a digital (0, 1) representation. Although it’s more complicated than I’ve suggested, the digital form is important because, Claude Shannon proved in his masters thesis⁴, that any analog assemblage of switching and routing equipment had an equivalent digital representation, thus, digital representations are “complete” representations for “real” systems.

Thus, a table of transformations can be equivalent to a described system, and has an equivalent transformation matrix. Matrices, like the systems they represent, can be classified by looking at the relationship within the elements. In the following examples, first is a 3 x 3 matrix to show it is the same as a table. Then we have a 4 x 4 matrix with {A, B, C, D,} as a set of states that the system goes to (state A to state B, etc).

 
Matrix representations
 

The matrix T is the equivalent matrix for the table given above, with the states {A, B, C}. The first row is the transformation of A to itself, the second row is no transformation, the third row is both B and C transforming to C. The columns also correspond to {A, B, C}. The matrices are square, that is the number of rows, columns, and states, are equal.
 

The identity matrix here, represents a transformation of the states {A, B, C, D} in which no change occurs (that is, A -> A, B -> B, etc.) and is represented by a matrix with “1″s down the main diagonal and “0″s elsewhere. This is also called an “identity transformation”. There are other kinds of matrices representing other kinds of relationships.

This is a matrix that is not single valued (notice that the first and last columns have repeating elements). This is equivalent to A -> A and A -> D, and or D -> B and D -> D, thus two elements each going to more than one state.

This is a matrix that is single valued. Ashby writes, “Of the single-valued transformations, a type of some importance in special cases is that which is one-one. In this case the transforms are all different from one another. Thus not only does each operand give a unique transform (from the single-valued-ness) but each transform indicates (inversely) a unique operand”.⁵

This is the matrix form of a function. Note: The algebraic expression y = f(x) is a function if it passes the vertical line test (a relation is a function if there are no vertical lines that intersect the graph at more than one point). It is a one to one function if it passes both the vertical line test and the horizontal line test (If a horizontal line  intersects a function’s graph more than once, then the function is not one-to-one.).  For the sake of clarity, these are also called injunctive functions.

This is a matrix that is single valued but not one to one. Called many to one. Not by definition a mathematical function. The efficacy of the matrix or tabular method is that it works even if there is no clear functional or mathematical relationship (because you are concerned here with behavioral consistency and not necessarily logical consistency).

Ashby goes into enough math concerning concepts like closure, and identity elements, to convince the reader that the cybernetics is mathematically correct, while logically and physically consistent.⁶ Closure comes up when you are dealing with repeated transformations, and identity transformations occur when there is a transformation with no change. These are important, but not important to develop the main idea, that all systems that can be observed can be written as a matrix (or truth table) representation (these days a spreadsheet would be used – or a programming language).

Graphical representations – Kinematic graphs:

There is another useful representation, that of a kinematic graph.

These are two representations of the same 5 state system {A, B, C, D, E} in tabular and linear graphic form. This graphical form can be re-arranged to provide a more convenient and revealing shape, where you can more easily see that state D is an endpoint, coming from two different states {A, E}, as seen below.

Kinematic graphs are just a way of representing a system with the connections shown, and are equivalent to both matrices and linked lists (a computer data structure). This is important because there are important behaviors that can be deduced from these maps. Important properties include: endpoints, cycles, and basins.⁷

The endpoint a state that has been reached where the transformations stop at one particular place or behavior, such as, when a piece of paper is burnt – it’s starting state is unburnt paper, its final transformation is into “ash.” A cycle is a behavior that goes from one state to another in a cycle – such as a stop light – it goes from green, to yellow, to red, then back to green. Finally, there is the basin, that is like an endpoint, where it goes to a state, and unless there is an addition of energy, the system will stay at that state – like a car that has run out of gas.
 

Part III Representation of possible states

The important thing about a system is that is should be predictable – that is, if it is in one state, there should be a predictable change of state (e.g. if it is summer, you know that autumn is next). There are ways of representing possible future states, Ashby calls this representation a “phase space” of possible behaviors, moves or outcomes.⁸

Phase space

All the possible behaviors of a system are called its “phase space”. Often – momentum vs position #systemthinking #transdisciplinary #Ashby

To be continued. . . .

Footnotes

I used to make educational software.
Ten years ago, I had put together a pretty workable situation where we made the software in Holland and sold it in Madison, Wisconsin, where I was also teaching web design at the local technical college. I had a couple of producers in Groningen making the music, creating the animations, and doing the programming, while I was in the US working with a educational curriculum consultant. I functioned as a photographer (for making images of the subject matter, and was the project initiator and organizer). I was also working with a nationally renowned artist, Dr. Jerry Butler (a wonderful man – always wearing the “white hat” and doing what’s right). Dr. Butler connected me to a professional video company that handled the pressing and distribution of the CD (including booklet and teaching guide) to thousands of school children.  He was also very connected and was instrumental in getting us a legitimate audience and market.

International production at its best
An American/Dutch production, we made these CD/ROMs that were designed for 9 to 10 year old children and the subject matter covered the entire curriculum for their education at that level, including: math, history, English, art, and other subject matters. The CD/ROM had tutorial information, quizzes, virtual reality walkthrough tours, photos, links to supporting subject matter on the internet. It was up-datable, and ran on both Windows and Apple computers. What’s not to like?

We had produced the CD/ROM, shown it to teachers, who then showed it to their classes. They loved it, both the teachers and the students alike. Students liked it because they were entertained, they learned, and they could go at their own pace. The teachers liked it too because they could teach more subject matters to more students, and it gave them time for one on one work with the student while the other students were absorbed in learning the other material (a good way to adjust to the possibility of large as class sizes). As a matter of fact, they liked it so much that they decided to include this project for government funding of this and other such programs to improve the educational opportunities of students in Wisconsin.

Forward to the Capitol
In what seems like a once in a lifetime connection, Dr. Butler had been able to arrange a large demonstration, that was to be given to the legislature, about the possibilities of educational software. That means that he had made arrangements to present to both sides of the legislature (the House of Representatives, as well as the state Senate), as well as the Governor. We had been selected to give demonstrations in the state capitol building, and we were to receive full press coverage. This was a big deal, and I planned to make the best of it.

The day before the event, we had meetings with teachers and students, and we rehearsed what we were going to say and do. We had a large screen TV projection unit brought in so that the screens would be visible from the gallery in the capital building. Extra seating was made available to students, teachers, the press, and the public. Everything was planned, and as far as I could tell, everything was going to go perfectly.

The day of the show was perfect. The weather was warm and sunny, and I had my stack of papers, laptop, remote control for the projector, and everything else ready for the big day. It was about 8:30 am, and I was putting on my suit and tie. Just before I left home, I flicked on the TV at home to make a check of the weather and headlines. The news program said the weather was going to be perfect that day, but there was some disaster in New York – it seems a plane hit a skyscraper. No time for bad news, I have a presentation to give, and out the door I went.

Chaos
When I got to the capitol building, I was in for a big surprise – they were moving out the projector, the big screen TVs, computers and the chairs. I was in total shock, this was my big day, and now everything is getting dismantled. I asked “What’s going on?” The Capitol Police replied “It’s because of what happened in New York.” I was confused, how could a plane accident cause this kind of response in Wisconsin?

It took me all day to go through the capitol, dismantle all of the equipment, get it back to a secure place, and see to all of the people you have to check in with to shut down such an event. Therefore, I never got in front of a TV news program to find out what was going on – until 5 PM that evening. That said, I knew there was a problem, because people were captivated by their televisions, some even crying.

I finally got home, pulled off my jacket, and turned on the TV. That’s when I saw the World  Trade Center buildings go down. My first thought was, how horrible for those people in the airplane and in the building. And almost at once, I realized – there goes my education career. I knew then and there that our economy would forgo education in exchange for military security.

By that time, I had begun to receive emails from my NY friends, as well as calls from family members in NY that called to say they were okay.  I also began getting emails from international friends to communicate to me how shocked they were over the events of the day.

Tallying the damage
This was a day of horrors, as was the aftermath. I am not tone deaf to what happened, and why. My life was not snuffed out in an instant. I did not fall flaming from the heavens, nor was I crushed into dust while rendering aid to others. I did not fight or die in the subsequent wars, nor did I have any direct relationship to any of the people who perished that day – I lived half a continent away from New York so my connections were minimal.

That said, I don’t know anybody who had the presentation of their career halted in its tracks that day. I don’t know anybody else that was going to meet with the highest levels of government to chart a new path for education within the state. I didn’t die – but, I had to deal with a catastrophic change in my career and in my life, and find a way to adapt to the present reality. We all did.

No safe haven from catastrophe
Because we are all interconnected, we are all affected by the events of that day. These events, not only destroyed lives, they destroyed possibilities. The kids that were then 9 to 10 years old, are now adults 19 to 20 years old – some making it to college, most not. I’m sure that their educational possibilities have been crimped due to long term effects of these events: the loss of educational funding, loss of choice, loss of competitiveness, and the weakening of the economy and society as a result.

When you look at the changes in the societies, economies, and politics, you can see that the events of that day have had a rather long-tail effect on the entire world and everyone in it – that is, no one is immune to catastrophic change.