Yuri Tarnopolsky
23. On the Architecture of  Change

Christopher Alexander. transition state. pattern theory. Ulf Grenander. Sisyphus. Konstantin Stanislavsky. chemistry. social change. revolution.

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Essay 23. On the Architecture of Change

This Essay is central to my view of the world. No centrality comes easy, there is no simple way to explain how the complexity of the world can be simplified, and my task is difficult. It will be getting easier after this. In a way, I am rolling my stone to the top of the hill, like Sisyphus.

Zeus punished Sisyphus  for giving a truthful testimony about  Zeus' sexual misconduct. In the underworld, Sisyphus had to roll a heavy stone to the top of the hill, but the stone always rolled down to initial point, and he had to start it all over again for eternity.
                                                                    Here is a fragment from an engraving. -->

Interestingly, the animated pictures of Sisyphus do not show either the top of the hill or its other side.

        Here is my picture:

Sisyphus knows that even in the underworld there is the other, greener side of the hill and he hopes to dump his stone there and end the cycle.

It is not the first time I am trying to put my vision of the Everything on the electronic canvass. This time, as always, I hope my stone will roll down the other side of the hill. The probabilistic nature of our world does not guarantee it, however.          

Limited in my progress as painter by the lack of frames ( Essay 19), I  am dabbling here in architecture and design. Houses and kettles, unlike pictures, do not need frames.house

I want to build the House of Change where physical, chemical, technological, biological, and social types of change could meet as a family of  the general pattern.

Looking for a most general guidance, I found it in the book by Christopher Alexander: Notes on the synthesis of form, Cambridge, Mass: Harvard University Press, 1964.

The central concept of the author can be stated in a few points:

1. The object of design has to satisfy a set of requirements.

Example of a very general set of requirements:

        jointing (easy assembly and compatibility of materials)

  2. The requirements can enhance or contradict each other. Every such contradiction is a misfit of the design and each couple of contradicting requirements adds stress to the whole.

        Example: simplicity may reduce performance but increase jointing.

3. The relationships between the requirements can be portrayed as a configuration where the contradicting (antagonistic) and  enhancing (synergetic) requirements are given minus and plus signs respectively.  These relationships can be presented as a diagram of dots connected with lines. A table is an alternative presentation.  Some quantitative measure of  the interaction can be attributed to the lines.

The numbers and signs in the example on the left are intuitive and not factual. I did not take them from Christopher Alexander's book and followed my own intuition. At this level of generality the numbers do not matter. I present the original diagram from Alexander's book in the NOTES.

The antagonism is marked by red and the synergism by black lines.

The table version: 


Performance Simplicity Jointing Economy
 Performance 0 -0.2 -0.2 -1
 Simplicity -0.2 0 1.5 -0.5
 Jointing -0.2 1.5 0 -0.2
 Economy -1 -0.5 -0.2 0

NOTE: We could fill up a similar table for a social system with such requirements as democracy, justice, equality, etc.    

4. A good design is the one with the minimal stress.

As soon as we have a set of requirements, we start tweaking the design in various directions trying to reduce the stress-causing misfits and find compromise between opposing requirements.

Finally, one design among many possible ones is chosen and launched into production.

As an example, Christopher Alexander takes a kettle that in addition to the above general requirements has to satisfy some particular utilitarian requirements:

            a comfortable handle,
            sufficient capacity,
            access to the inside,
            good heat transfer to the water,    
            slow cooling down,  etc.

Thus, the handle and the heat transfer requirements can only be reconciled if the handle and the kettle are made of different materials, which increases complexity and jointing.

It is difficult and not always possible to find the relations between requirements, quantify them, and reconcile and the book shows how to do that on a few examples.

Reading Christopher Alexander, I felt a resistance of an individualist to his method.

There are at least three categories of kettles: cheap , upscale, and designer ones with different sets of requirements. The designer kettle is a piece of art and art is irrational. Its main requirement is to impress and entice the customer into buying. For that matter, any creation of a designer has the commercial success as the ultimate overriding requirement.

Alexander's approach reminded me of the Stanislavsky method ("system")  in scenic art.
Konstantin Stanislavsky believed that the actor should rely not on inspiration and mood but on a tool kit of standardized and honed techniques to display credible human emotions and behavior. One of his goals was to spare the actor of premature exhaustion.

I don't want to be cynical, but both methods, together with the host of modern combinatorial writing and other "how to" techniques, seem to cater to the general spirit of mass production in the twentieth century.  That one can create only by violating systems and methods is theory while money is reality. The democracy of Things dictates the ideology that is incomparably harder to fight than the political dictatorship. To cross the swords with the invisible hand is a pretty hard task even for a fairy-tale knight.

All that does not invalidate Alexander's concept. It contains a deep idea of stress as criterion for selection of viable versions among all possible ones. Moreover, it fits smoothly into the much more general framework of  Ulf Grenander's Pattern Theory.  The entries in Alexander's forms are Grenander's generators and the lines are bond couples of Pattern Theory ( Essay 18 ).  Instead of stress, Grenander attributes probability to bond couples and configurations.

is also Alexander's signature term and logo. The enthusiasts of his theory speak about PATTERNS movement, there is Patterns Web Page and such epithets as "a deeply spiritual work" make me feel my individualism as a cast over a broken arm.

Pattern theories of Christopher Alexander and Ulf Grenander were applied to pattern software .

We can now climb a step up and look again at the Everything as dots connected with lines. This time, however, I will be interested in the aspect of change more than in anything else.

Writers, like Graham Greene ( Essay 22 ), follow the laws of nature but are not constrained by them. They select the plot out of thousands other possible versions. The misfits in the final text are minimized in the eyes of an author of Greene's caliber. The author sets his or her own requirements. The editing of the text is not constrained by physical laws of nature either.

On the contrary, the world outside human mind and virtual reality is mostly impossible. What exists has been selected from countless other configurations of the world, among which the spilled water gathers in the glass and a person hits three lottery jackpots in a row (or even one). The laws of physics, biology, and probability leave only a limited number of safe passages from the present to the future moment. What can have a large number of outcomes is mostly as irrelevant as the biographies of the strangers in the street crowd. When we say "a matter of life and death," there are only two outcomes.

Christopher Alexander's concept investigates the process of the conception of a new Thing. Whatever the set of requirements is, with or without the theory, subconsciously or with clear intent, the artist selects the final creation among others and gives it a nudge from the tender world of fantasies into the harsh world of matter and  cut-throat competition.  A  piece of  a New or a Different is born and it can be seen by jubilant or recoiling spectators.

The less stress in the design, the more probable its materialization is. Stress is high internal energy. The lower the energy, the higher the probability of turning the design into the Thing.

At the foot of the Pattern, I, a skeptical chemist, stand in the crowd of Everything, whispering my Pattern Noster.

Chemistry is my next pattern subject because the problems of design seem to be related to chemistry in a rather dramatic manner. One should not be surprised by odd couples in the Everything: they could be real pattern soul mates.

Chemistry is the science of changing molecular patterns. Molecules are configuration of atoms. Unlike abstract combinations of dots and lines, and unlike patterns of plots in novels, chemistry is constrained by the laws of physics. It deals with matter, not dreams, not keyboards, and it scrutinizes the very fleeting and intimate moment of change, almost never directly observable.

Having drawn a line between knowledge and understanding (Essay 19, On Reading Across the Lines  and Essay 21, On Ethics
), I do not want to go into particulars of chemistry. The core of chemistry can be understood without any attention to the properties of individual atoms and molecules. I am taking transformation of graphs as a simplified model, which is also a kind of mathematical metaphor.

Graphs..(great page! ) in mathematics are combinations of points (dots) and lines that connect some or all of them, regardless of  position and shape. Christopher Alexander's diagrams are graphs, too.

Graph is neither drawing nor table. It is a topology: a set of points and a set of their connections. The points are called vertices and the connections edges. In simple graphs all vertices and all edges are of the same kind, but in other, more complex graphs, one can attribute various properties to them. Thus, Alexander attributes "strength"  to an edge. Ulf Grenander attributes probability.  A graph can be represented by both table and diagram, as well as a list. WWW is a graph, too, with sites as vertices and links as edges.

Molecular formulas represent real molecules by graphs. They portray the topology of the molecule, but in addition they  reflect some aspects of shape. They are not pictures of molecules.


   Water                              Hydrogen peroxide

(Compare with figures in  Essays 17, On Complexity and 18, On Everything

Now, I am starting to carry my stone uphill.

Let us take a configuration
A below as an example of a configuration consisting of two different molecules. What can happen with it?  In our imagination, the configuration can change in a large number of ways. Chemical reality, however, is rather complex and specific. Instead of real chemistry, I am suggesting a game that imitates it.

Instead of chemical formulas I am using colored dots and lines. The dots symbolize atoms and they cannot disappear or pop up out of nothing.  The lines, however, can be rearranged, added, or erased.

For the purpose of illustrating  what chemistry is about,  we need to follow only one rule of the game:

 Each atom has a constant number of bonds.

Stable molecules can sit in a jar on the shelf for many years.

There are, however, unstable molecular configurations that can be compared to Alexander's misfit and stressed kettles and houses. For example, at a very high temperature all molecules are practically atomized, as in configuration
K , but this is a highly unstable and even impossible configuration under normal conditions.

E, F, and G are stable because the rule is not violated. 


A big question is: why would A, after it has been sitting on the shelf for decades, suddenly decides to turn into G or F?  If that were as predetermined as the ball rolling downhill, it would happen immediately. In fact, a spontaneous change is very rare in chemistry.

The mystery of chemistry, which chemistry can generously share with any other study of change, is that the change needs a push, like the ball that should be rolled up before it can go downhill.

At the top of the chemical hill, the changing molecules take an irregular,  "hot," "stressed," "misfit,"  rich of energy, and short-living configuration: transition state. Energy is needed to bring them there. Sisyphus used his muscles. A chemist sometimes starts at the top by simply mixing the reacting components. Because of the distribution of molecules by energy (see Essay 14 ), there are always elite molecules hot enough to engage in reaction. If not, the chemist activates them by heating or radiation.

: Compare this with the sociological theories of Vilfredo Pareto about the role of elites in society (end note in Essay 16 ).

Usually, there is a wide selection of possible transition states, more or less stressed. The lower the stress (in Alexander's terminology), the higher the probability that the structure will reach the top of the hill.

The height of the hill is the energy of the transition state.  The imaginary thermal micro-Sisyphuses will carry the molecules to the top if they have enough thermal energy.

Whether the transition state rolls back or down the other side, will depend in chemistry on the ground level on both sides. Chemical systems are in principle reversible. The final result of a chemical reaction is determined also by of equilibrium. In complex biological and social systems  nothing is reversible. The irreversibility is the fundamental property of life. Evolutions of life, society, and technology do not know equilibrium.

Here is one transformation through a hot transition state (in chemistry it can run in both directions). The "illegal" stressful transient and temporary bonds are shown by broken lines. They are "misfits"  that increase the energy of the hot transition state B that can cool down  to either E or back to A.  To tell the truth, all bond couples in their neighborhood are not themselves anymore and they should be drawn by broken lines. I show the irregularity of the transition state by the red spot.

                                              Transition state: B

Here are two more (and more are possible):


                                                    Transition state: C

                                                    Transition state: D
The general principle of change through a transition state (it comes from physics)  applies to Everything.

Design is a transition state that can roll over the hill and generate a Thing or roll back to the initial stage. 

    The less stressed the design, the more probable its selection for production.

    The less misfits in a performance on the skating ring the closer the figure skater to the top rank.

    The fewer misfits in a beauty contestant's dress and body the closer she is to the crown.

    The less controversial a legislative proposal the higher its probability to pass the Senate.

    The lower the energy of the transition state the more probably the chemical reaction will go through it .

Any change of a complex system can be examined from this angle.
There is another aspect of the whole process. In order to change, the system has to be heated up or given a jolt of energy in some other form.

The designer, artist, scientist, politician, and general in the process of creation and making a decision is in an excited state, under the pressure of uncertainty, urgency, and responsibility. The figure skater and the beauty contestant are heated up by the nervous and uncertain atmosphere of the competition. Same applies to political debates over a hot issue.

In order to start a chemical reaction, if it does not start spontaneously at mixing, the chemist heats up the components or increases their energy by irradiation.

Revolutionary social change starts when the political atmosphere heats up as result of crisis, war, hunger, or discontent. 
Political and social reforms usually follow a transition state of turmoil, dissatisfaction, and anger.

Contest, crisis, war, and all such extraordinary situations are relatively short-living against the course of individual life and history. They are transition states loaded with chaos. Life and history is a series of ground level periods of regularity punctuated by flares of irregularity, the "points of no return"  of Graham Greene (Essay 22, On Errors). In history of  society, culture, and technology, the lucky Sisyphus has a name and is remembered for a very long time. Sometimes it is a horse.
Revolutions and reforms can never be completely reversed but they can vacillate back and forth as it was after the French Revolution and is apparently happening in the post-Communist Russia. sisyphus

In general,  my optimistic version of the myth of Sisyphus is a metaphor of change in a wide variety of systems.  The energy (stress, misfit, chaos, temperature) of the system increases, the invisible Sisyphus rolls it up the energy hill, and at the top there is always a chance that the system will roll down to the other side of the hill instead of going back to the starting point. And, by the way, a hill has many other sides.

To expand this concept would mean to go from understanding to knowledge, which is beyond my intent (see END NOTE 4 for a great source). I feel completely exhausted by rolling the stone of understanding in this Essay. I hope the stone fell onto the greener side of the hill. Let it sit there as a corner stone of the
House of Change. I need a break. There is more about Sisyphus to come.



        1. Here is the original diagram from Alexander's book on synthesis of forms:


        2.  The word pattern came to English from the Latin pater through the French patron that had gained a secondary meaning "a model" in the fourteenth century.

        Along  Eric Partridge, Origins: A Short Etymological Dictionary of Modern English, New York : Greenwich House, 1966.

        3. Some ideas of this Essay are further developed in our History as Points and Lines, together with Ulf Grenander. On Pattern Theory: Ulf Grenander, Elements of Pattern Theory, Baltimore and London: Johns Hopkins University Press, 1996.

        4.  The final result of a chemical reaction is determined also by factors other than transition state. The position of equilibrium, in particular, is important. Life and history, however,  do not know equilibrium.  There is a really wonderful and deep  site of Frank L. Lambert about some principles of thermodynamics and chemistry of general significance for the Everything.  Main topics:  Time's Arrow,  Murphy's Law, Activation Energy, Chemical Kinetics, Chemical Bonds.

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