People like us are sometimes paralysed by our incredible sense of the possible, but possibilities are not infinite. All contexts have constraints or parameters that limit possibility. A good bricoleur can look at a situation and deduce that "there are only five (or however many) possible routes from here" and then make a choice. In order to do this you have to be aware of as many variables in your environment as possible. The only available possibilities may not be perfect, but they are all that is possible and one (or a combination if possible) has to be chosen in order for you to move forward ... or outward ... or wayward - as you prefer.

The greatest obstacle to doing this well is the fact that you never have enough information to know exactly what is going on. In order to predict anything perfectly you would have to know what is happening at that moment in the entire universe. Usually you don't need such a big data set in order to fry an egg, or catch a bus. Planning a business or writing a book or making music is more complex because your data sets are bigger and the space of the possible is more complex. Solving problems like AIDS and rape and poverty is even more complex because it requires even bigger data sets. When making choices you have to decide on the size of the "circle", or data set, or context you are working within. You sacrifice information outside of that circle, because you are satisfied that its influence on the circle will be negligible.

If your current space of the possible is not helping you flow in the direction you wish you may need to add something to it, or take something away from it. You may need more information, skills or resources. You may also need different beliefs, or other consciousnesses with their own complex phase spaces to interact with yours and add to your possibilities.

Anyway, here follows a summary of the idea of "phase space" as discussed by Ian Stewart and Jack Cohen. They are speaking in the metaphors of evolution, mathematics and game strategy, but I'm sure you can apply these to your own situation.

Ian Stewart and Jack Cohen's story of evolution not only contains the standard textbook version, which focuses on genes, but also a contextual version, which focuses upon emergent dynamics in phase space.

"In this view, organisms change because the geography of the surrounding space-of-the-possible makes change inevitable. Evolution runs “downhill” in its phase space. The hidden complication is that the dynamic is emergent, not prescribed once and for all, and the phase space changes complicitly with it" (Stewart & Cohen, 1997:78).

An increase in complexity may have something to do with the available phase space.

"There is no where else to go ... the next simplest layer is already occupied by creatures that are doing their thing in a pretty effective manner, so a new arrival will have enormous difficulty in gaining a foothold" (Stewart & Cohen, 1997:130).

The idea of “phase space” comes from dynamics - the mathematical theory of systems that change over time. The term was coined by Henri Poincare.

"In Poincare's day dynamics was reductionist: if you wanted to understand how a system behaved, then you began writing down its mathematical equations and solving them. Then you looked at the solutions and worked out what they actually did. Poincare changed all that. He did so because all too often the programme falls apart: you can write down the equations, but you can't find the solutions. His search for an alternative was motivated by the three-body problem in celestial mechanics: given three masses attracting each other by Newtonian gravity, what do they do? For two bodies the answer is simple: the equations can be solved, and the solutions tell us that the bodies follow elliptical orbits. But for three bodies the equations couldn't be solved. Mathematicians grappled with them for well over a century before they realised that there is no solution. How can you work out what the bodies are going to do, then, if you can't solve the equations? That was Poincare's great insight, and it led to today's geometric approach to dynamical systems. It goes like this. The state of such a system is described by various “state variables” which change over time. The changes obey a prescribed rule, or dynamic: “if the current state is this, then the next state will be that.” Now, you can introduce a visual point of view by thinking of the state variables as coordinates for a point that moves around in a fictitious mathematical “phase space”. As time passes, those coordinates change, so the representative point moves, tracing out a path. In fact the entire temporal development of the system boils down to a wiggling wormlike path through phase space. Phase space includes not just the actual values of the state variables, but all the potential values: it is a formalisation of the notion of context. By studying the geometry of phase space for the three body problem, Poincare recognised the existence of what is now called “chaos” - dynamical behaviour so complex that it appears to be random, but having entirely deterministic (non-random) causes" (p. 49).

Ian Stewart and Jack Cohen appropriated the metaphor of phase space for their theory of evolution. (Stewart & Cohen, 1997:49) It differs from Poincare's strict use of the term, in which all trajectories are completely determined by the initial state. In Stewart and Cohen's version there are more than one possible trajectory, and there is the possibility of choice, and therefore strategy.

They see two types of evolutionary change. The first, "explorations": investigate the immediate vicinity of an existing phase space, like improvements in the lens of the eye. The second, "explosions": which change phase space itself - opening up new possibilities like single cell eukaryotes exploiting oxygen. (Stewart, 1997, p. 129) These “explosions” are like emergent phenomena. They cannot be predicted, not even with all the information that precedes them.

The nature of phase space is determined by certain environmental, physical and chemical constraints. “Mutations make phenotypes (physical traits) fluid enough to change, selection implements particular changes preferentially, but the overall result is more like water flowing through a landscape.” Creating the illusion of a preferred “direction” of some grand narrative. (The previous sentence is crucial, so I am referring back to it for your attention!)

In the theory of evolutionary holism an evolutionary trajectory is punctuated with whole, robust systems (capable of survival and reproduction) as steps along the way. In other words change does not happen as radically all the time. Systems need time to practice being what they have changed into before they can change radically again. (This is an important insight for change junkies like us. If we just keep changing and do not spend enough time practicing new states before moving on, we burn out.) While practicing a new state exploratory structural alterations may occur, but before each new state a revolutionary evolutionary explosion takes place.

Stewart and Cohen use game strategy metaphors to explain how different organisms utilise (most unwittingly, others less so) the available phase space, or space of the possible. They translate “phase space” into a “game tree” - all possible states, or positions, in a game. The dynamic of this phase space, or game tree, "… is the rules that tell you how to get from one state to the next... So we can interpret a game as a kind of dynamical system... The idea of strategy is on a “higher” level than the rules of the game, and it brings the need for a phase space into sharp focus. Of necessity, the concept of strategy involves the overall structure not just of one game, but of all possible games... Tactics and strategy center around what moves you or your opponent make. So in playing a game you must be aware of more phase space than just the part that actually gets used; and the same goes if you are watching a game, otherwise the moves don't make any sense" (Stewart & Cohen, 1997:50-51).

"Strategies are emergent properties of games." (Stewart & Cohen, 1997:68).

"Biologists will tell you that evolution has no goal, and on one level of description they are right. It has no present purpose, it contains no coded representation of its own future. But neither does water, and it still flows downhill, not up: this shows that dynamics in phase space can impose an overall directionality on processes, goals and purposes notwithstanding. And on a different level of description evolution does have a goal, one that exists only in retrospect. The goal of evolution is to stay in the game. Players who (unwittingly) achieve this goal continue playing; all the rest become losers in the most brutally literal sense - they die without breeding. “Goal” is of course the wrong word. The usual sense of “goal” is a reductionist one: look inside the system and you will find a “search image” of the future, which acts as a cause of present behaviour. The word applies to a sparrow seeking an earthworm, or to a human seeking religious enlightenment, but not to evolution. “Unforeseen destination determined by contextual constraints” is what we mean, but the only common word with that meaning seems to be “destiny”, which has all sorts of misleading mystical overtones. “Attractor”, in the dynamical sense, probably comes closest...

Evolution, then, is a five billion year-old self-modifying planetary scale game, which carries around partial records of its own past. And just as it has a (contextual analogue of a) well-defined goal, this strategy becomes apparent only in retrospect: make winning moves. A winning move, of course, is one that lets you stay in the game. And the way you find out what moves win is ... you try as many moves as you can, and sometimes one of them works. Because evolution is a learning process, and because today's creatures are the descendants of players that have consistently made winning moves, the creatures that inhabit present-day Earth have become pretty good strategists. They don't know what strategy they are playing, but they pay one that wins often enough to be useful. Individuals may die, or even whole species, but the Game goes on forever and it gets wilder and more convoluted as it does so" (Stewart & Cohen, 1997:96).

{I would like to interrupt my discussion of Stewart and Cohen's book with a few words about goals. People object to the use of this term with regards to evolution or to species who are not conscious in a human sense - in other words, species that do not know that they know. In his delightful book Kinds of Minds (Phoenix; 1996) neuroscientist Daniel Dennett explores the notion of mind, and illustrates an evolutionary path through various kinds of minds, or principles of organisation. He sees a countless variety of "information-modulated, goal-seeking systems." This is the vision I described of the pageant of evolution. A system does not have to know that it has a goal in order for there to be a goal. An amoeba avoids salt and heat, because salt and heat will kill it, but it doesn't have any conscious knowledge of this. Dennet uses the analogy of a thermostat, like that in a kettle that switches itself off, or an air-conditioning system that changes its temperature. Dennet pictures a colony of information seeking micro-agents: "Evolution created armies of specialized internal agents to receive the information available at the peripheries of the body. There is just as much information encoded in the light that falls on a pine tree as there is in the light that falls on a squirrel, but the squirrel is equipped with millions of information-seeking microagents, specifically designed to take in, and even to seek out and interpret this information... Each of these tiny agents can be conceived of as an utterly minimal intentional system, whose life project is to ask a single question, over and over - "Is my message coming in NOW?" "Is my message coming in NOW?" - and springing into limited but appropriate action whenever the answer is YES. Without the epistemic hunger (the "desire" for information), there is no perception, no uptake. Philosophers have often attempted to analyse perception into the Given and what is then done with the Given by the mind. The Given is, of course, Taken, but the taking of the Given is not something done by one Master Taker located in some central headquarters of the animal's brain. The task of taking is distributed among all the individually organised takers. The takers are not just the peripheral transducers - the rods and cones on the retina of the eye, the specialised cells in the epithelium of the nose - but also all the internal functions fed by them, cells and groups of cells connected in networks throughout the brain" (Dennett, 1996:108). The goals that determine the gestalt of human experience are the goals of not one but many different recursively related self-organising systems. For example, our immune system, endocrine system and nervous system are in a very real sense three distinct 'information-modulated, goal-seeking systems" that communicate with each other through peptides - like hormones, enzymes and neurotransmitters (a phenomena discovered by Candace Pert of the National Institute of Mental Health in Maryland) to form an integrated system. Phase space is utilised by all organisms to help them achieve their "goal" - deliberately or not.}

Stewart and Cohen suggest that by analysing the game tree of games with a small phase space, one can determine what are winning positions, and what are losing positions. One can also verify the defining properties of these positions. One can draw game trees backwards from winning positions to determine winning strategies. The whole thing can be done using reductionist approach to uncover the winning algorithms. There are games, however, in which game trees are too complex to be resolved into simply defined winning strategies. The answer, they suggest, is contextual thinking. Like Poincare, a combination of classical reductionist low-level arithmetic equations with the high-level geometry of phase space... (p. 72) They suggest some general mechanisms that come together to generate emergent phenomena. “Reproductive sequences of events” is one mechanism. These are “not sequences that replicate precisely by following the same scenarios with a rigid periodicity, but sequences that re-create in a flexible manner the same qualitative type of conditions that gave rise to them” (p. 73). They use the analogy of maintaining a “break” in snooker or pool - “a repetitive but not strictly periodic sequence of shots designed to reproduce, stably, the conditions required to keep the sequence going... A key feature is that during the present “generation” of the reproductive cycle (potting the current ball) the player also sets up conditions that will permit the next generation to occur (gaining position on the next ball)” (p. 74). In evolutionary biology this is known as “privilege.” Stewart and Cohen suggest “what privilege does is to link successive generations together so that to some extent selection can act on both, simultaneously, as a kind of evolutionary unit. Selection acts on the entire cycle, not just on one stage - the parent, or the child - which results in cycles that are robust and successful” (p. 94). In fact, many evolutionists are now speaking of the evolution of whole ecosystems not just individual species.

Another mechanism is “complicity” - “when two (or more) rule-based systems interact: when two separate phase spaces join forces to “grow” a joint phase space that feeds back into both components and changes them recursively until after a while hardly any trace of their original, separate forms can be found.” (p. 74) This is, according to them how evolution works. “Self-modification,” with the purpose of maintaining the “break,” can only occur when two or more phase spaces are interacting and influencing each other complicitly.

As Stewart and Cohen said: “Evolution, then, is a five billion year-old self-modifying planetary scale game which carries around partial records of its own past” (p. 96). They suggest that you can consider evolution as having “trillions of players (all living creatures) or only one (the global ecosystem).” (95) It all depends what level of abstraction you are conceptualising. As the mystic cliché (you know all too well) says - the only thing that doesn't change is the process of change itself (complex recurrent dynamics). Recent excursions into complexity and chaos theory have attempted to identify the eternal unchanging algorithms of change. (Refer back to my idea of the "habits" or "trends" of the universe which are driven by the organising principle of connectivity.)

They offer a bizarre example of complicity, which is worth reproducing for you. "There is a parasitic flatworm that spends part of its life inside an ant, while its reproductive stage is inside a cow. The technique that it has evolved to affect the transfer from one animal to the other shows how subtle the effects of “blind” evolution can be. The parasite infects the ant, and presses on a particular part of its brain. This interferes with the normal behaviour of the brain, which causes the ant to climb a grass stem, grasp it with its jaws, and hang there, permanently attached. So when a cow comes along and eats the grass, the parasite enters the cow" (p. 63).

"It is (at least) a three-way complicity, whose component systems include the ant's brain and the cow's grazing habits, as well as the parasite. The ant's brain evolved the ability to grasp grass stems and let go again because this was a useful thing for an ant to be able to do. The cow evolved a liking for grass because that was good for the evolution of cows. Lurking in the combined phase space, with grass as the connecting feature, was a horrible trap, which the parasite discovered by accident. The resulting behaviour makes no sense either in ant-space or in cow-space alone, but it got built into their combined phase space because it set up a beautiful snooker break for the parasite" (p. 75).

The metaphor of phase space becomes interesting when applying it to your own thoughts and feelings. Perhaps some of your thoughts and feelings are the result of the surrounding space-of-the-possible. They arise as a result of your own system’s processes “flowing downhill.” While they may not be the inevitable result of structured determinism in a narrow sense, they may well be an “unforeseen destination determined by contextual constraints.” In order to break pattern and maintain your dynamism (something most people do not wish to do once they have a pattern that works - well, works "well enough") you may require an unexpected crisis, the addition of more experiential data to your phase space, or another phase space to interact with.

A last thought - something I find extremely profound. Evolution cannot project into the future, but humans can. We have an edge over evolution itself, we can adapt the process of adapting. We may be evolution's own way of seeing into the future. This has amazing implications for the ways in which we flow downhill. We can set up that flow deliberately. We can adapt our phase space to suit our future goals.

Play nicely.

Regards,