Strange attractors.............
Back from lunch (you need to have read the last Blog first which confusingly is below this one). We had left off having jumped from the deterministic to the chaotic. Now we will go back to the transitional phase between the two. A place that is both stable and unstable at the same time. A phase space – that little place were ice decides its water now but is for a time both.
Looking for a metaphor let’s consider a person carrying too many things. These things are arranged and held in a stable way (or they would no longer be being carried) and yet at any point can tip into instability and chaos. This edge of chaos is actually the highest point of complexity - the boxes resting on the floor being perhaps the lowest. There are many parameters working on the boxes being carried and at same time the structure of the pile may be quite complex (but complex and complexity are not the same in this context). What exactly makes the pile stable is quite difficult to fathom – but to the causal observe it can actually appear stable. Let’s face it if the carrier believed it to be too unstable they would stop and re-arrange – wouldn’t they?
Useful for carrying strategies but does this have meaning beyond the removals industry? If we consider the arrangement of box files, folders and latte to be a system, working with various forces of balance and pressure, then we can extend our theories to other systems. This will require another addition to our Gedankenexperiment. Systems also have rules. The rules associated with boxes are fixed and known; they refer to Newtonian physics. The difficulties come in measurements of states not in understanding of interactions. The boxes fall because we are sensitive to initial conditions and cannot predict the tipping point simply through measurement error (so not true chaos). If we start to look instead at social and economic structures we can start to suggest that there are (made) rules and these rules can emerge over time or operation of the system. Now we have a model both hard to measure accurately and where the rules and goals are shifting – a good challenge!
Adding just one more twist we can start to think about the way these rules emerge and groups self organise. About the way that stability seems to exist and can be based on the simplest of rules even in what appears the most complex patterns of behaviour – cue fractals. Langton’s Ant is one of the easiest fractal type images to understand and can be seen moving here, here or here. The poor little ant has only two rules:
· Rule One : if on a white square turn left and move one square forward. The square it was on turns black.
· Rule Two : if on a black square, turn right and move one square forward. The square it was on turns white.
So white square left and black square right. Simple enough and, not surprisingly, quite a complex pattern emerges. So far so straightforward. However after 104 moves the ant always, and I mean always, forms a straight path and marches off into infinity. Those simple rules have emerged to produce self organising behaviour (see Waldrop’s text Complexity). So from quite simple rules quite complex patterns of behaviour can emerge that seem unpredictable. We could ‘predict’ that the ant would make a funny pattern but that it would lock into a road was less obvious. (Un)fortunately no 104 exists in patterns of human behaviour or in economic markets but perhaps we can explore some of the rules and self-organising behaviour that emerges.
Let’s start with the most difficult and look at human relationships. What rules apply and emerge here? We are fortunate to have at our disposal a test bet is social media. Before our eyes new rules are emerging with regards to communication. Let’s ignore the rather pathetic ‘rules’ of American romcoms (how many days do you leave it to call her/him after a date, etc.) and consider some more basic and perhaps emerging ones. Now I regularly perplex my friend by telling her I have asked someone (of the opposite sex) to lunch or dinner. “You can’t do that” she declares, clearly quite correctly. “How else am I to talk with someone and eat” I ask, but it seems there are rules, signifiers and meanings here I am missing. Place this against the backdrop of social media and its emerging rules and you can see my dilemma. In social networks and SMS texts it seems absolutely fine to declare love and to use ‘x’ as punctuation (if you are not on FaceBook or have few ‘friends’ find a real one with an account and have a look :-) xxxx love u). Rules in social networks seemed to have emerged that convert passing familiarity to love and any type of relationship to require a kiss if not many (and it is interesting to note the expansion in number of x’s we now see). How has this emerged and has it stabilised yet are two interesting questions. Will it, like the use of LOL, begin to retreat or has point stability (called self-organising criticality) been reached? Will it tip into a new ordering of behaviours?
Did the same happen to News International we can ask? Clearly a set of rules emerged that allowed a tolerance of sensationalist journalism. Clearly that hegemony broke recently with the collapse of the News of the World. What now becomes a question is whether media culture has managed escape velocity. If we think of attitudes to media being an orbit around a point in culture what we need to analyse is whether this strange attractor (the body being orbited) exerts enough hold on attitudes to hold them in orbit. If it doesn’t or if the change in attitude is great enough we will cross one of those complexity tipping points and spin off into Chaos until another attractor is reached and stability returns. The phrase strange attractor slipped in there; Lorenz’s is perhaps the original example and can be seen here (much more is available in Gliek’s Chaos). What makes an attractor ‘strange’ is that we cannot predict where it occurs.
So that has taken us through social interactions and culture, albeit too quickly, what of economics? Ormerod has really explored this area and I can’t recommend his texts highly enough (starting with the ironically titled Death of Economics – Ormeod predates Telabs’s Black Swan etc and writes the texts Telab would like to write if could and if he wasn’t trying to maximise sales – but read both if you can). The opportunities for strange attractors are multiple in economics; consumer behaviour and taste perhaps being a starting point for considerations of this in the real economy. We can easily see that fashions come and go but that they also stabilise for a time. What combination of culture, pressures and economics conspire to make one genre of music popular for a year or two and when will it tip? Considering skateboarding as an example we see rapid growth and saturation in the 1970s (caused by the introduction of new wheel manufacturing technology); some cultural shift saw a resurgence during the 1980s with street skating, only to be killed off partly by regulation; and the late 1990s saw the re-emergence of skating this time driven by... well the interesting thing it is hard to measure why the sport has resurfaced around the strange attractor of street skating. Let’s assume some of those skaters became market traders, unlikely in many respects as there exists a cultural hegemony around the City but nevertheless possible. What attractors are there in stock markets?
In theory the stock market exists to make investments in companies more liquid thus attracting more capital at a lower price and allowing economies to grow – in theory. In practice the market is beset with speculation and gambling. Much of the trading activity that occurs is not of the slow and calculated kind exemplified by the likes of Buffet and Graham but rather more akin to that found in Las Vegas. Why will this create attractors? Well in truth even the considered style of investment practiced by value investors can lead to attractors; it is that speculation seems to increase their occurrence and reduce their longevity. We see narratives develop in markets and spread via the media. These narratives usually take the form of post-hoc rationalisation about the cause of events. Based on these narratives ‘truths’ develop and money flows. This flow is not, however, based on economic principles but on narratives (ok I know economics is a meta-narrative). A reality is created around a position and it holds. For example we can see how stubborn the property market is against full correction or how insane gold prices have become with commentators even suggesting they are overvalued. The crashes we see are simply shifts out of self organising criticality and into Chaos. The market usually self stabilises around some other lower point after a short time – it finds another planet to orbit. Broker’s even try, somewhat naively, to describe the parameters of these orbits with the use of support and resistance points (these points assume that share prices are moving within a normal distribution and disregards outliers – see here to show nothing is new and here ).
Have we finished? No I think in truth this series may have only just begun however I am pretty sure some rules have emerged governing the acceptable length of blogs and in truth my neck now hurts from bending over the lap-top. I shall return and will look at Chaos and Complexity again, in the meantime if there is a certain point you would like me to dwell on then drop me a line...........
PS – if ask you to lunch i am hungry, if I end a text with a x I know you and it’s your birthday and if I actually kiss you it’s probably because I’m happy for you to be the last person I ever kiss – I’m not completely without a sense of romance....
Back from lunch (you need to have read the last Blog first which confusingly is below this one). We had left off having jumped from the deterministic to the chaotic. Now we will go back to the transitional phase between the two. A place that is both stable and unstable at the same time. A phase space – that little place were ice decides its water now but is for a time both.
Looking for a metaphor let’s consider a person carrying too many things. These things are arranged and held in a stable way (or they would no longer be being carried) and yet at any point can tip into instability and chaos. This edge of chaos is actually the highest point of complexity - the boxes resting on the floor being perhaps the lowest. There are many parameters working on the boxes being carried and at same time the structure of the pile may be quite complex (but complex and complexity are not the same in this context). What exactly makes the pile stable is quite difficult to fathom – but to the causal observe it can actually appear stable. Let’s face it if the carrier believed it to be too unstable they would stop and re-arrange – wouldn’t they?
Useful for carrying strategies but does this have meaning beyond the removals industry? If we consider the arrangement of box files, folders and latte to be a system, working with various forces of balance and pressure, then we can extend our theories to other systems. This will require another addition to our Gedankenexperiment. Systems also have rules. The rules associated with boxes are fixed and known; they refer to Newtonian physics. The difficulties come in measurements of states not in understanding of interactions. The boxes fall because we are sensitive to initial conditions and cannot predict the tipping point simply through measurement error (so not true chaos). If we start to look instead at social and economic structures we can start to suggest that there are (made) rules and these rules can emerge over time or operation of the system. Now we have a model both hard to measure accurately and where the rules and goals are shifting – a good challenge!
Adding just one more twist we can start to think about the way these rules emerge and groups self organise. About the way that stability seems to exist and can be based on the simplest of rules even in what appears the most complex patterns of behaviour – cue fractals. Langton’s Ant is one of the easiest fractal type images to understand and can be seen moving here, here or here. The poor little ant has only two rules:
· Rule One : if on a white square turn left and move one square forward. The square it was on turns black.
· Rule Two : if on a black square, turn right and move one square forward. The square it was on turns white.
So white square left and black square right. Simple enough and, not surprisingly, quite a complex pattern emerges. So far so straightforward. However after 104 moves the ant always, and I mean always, forms a straight path and marches off into infinity. Those simple rules have emerged to produce self organising behaviour (see Waldrop’s text Complexity). So from quite simple rules quite complex patterns of behaviour can emerge that seem unpredictable. We could ‘predict’ that the ant would make a funny pattern but that it would lock into a road was less obvious. (Un)fortunately no 104 exists in patterns of human behaviour or in economic markets but perhaps we can explore some of the rules and self-organising behaviour that emerges.
Let’s start with the most difficult and look at human relationships. What rules apply and emerge here? We are fortunate to have at our disposal a test bet is social media. Before our eyes new rules are emerging with regards to communication. Let’s ignore the rather pathetic ‘rules’ of American romcoms (how many days do you leave it to call her/him after a date, etc.) and consider some more basic and perhaps emerging ones. Now I regularly perplex my friend by telling her I have asked someone (of the opposite sex) to lunch or dinner. “You can’t do that” she declares, clearly quite correctly. “How else am I to talk with someone and eat” I ask, but it seems there are rules, signifiers and meanings here I am missing. Place this against the backdrop of social media and its emerging rules and you can see my dilemma. In social networks and SMS texts it seems absolutely fine to declare love and to use ‘x’ as punctuation (if you are not on FaceBook or have few ‘friends’ find a real one with an account and have a look :-) xxxx love u). Rules in social networks seemed to have emerged that convert passing familiarity to love and any type of relationship to require a kiss if not many (and it is interesting to note the expansion in number of x’s we now see). How has this emerged and has it stabilised yet are two interesting questions. Will it, like the use of LOL, begin to retreat or has point stability (called self-organising criticality) been reached? Will it tip into a new ordering of behaviours?
Did the same happen to News International we can ask? Clearly a set of rules emerged that allowed a tolerance of sensationalist journalism. Clearly that hegemony broke recently with the collapse of the News of the World. What now becomes a question is whether media culture has managed escape velocity. If we think of attitudes to media being an orbit around a point in culture what we need to analyse is whether this strange attractor (the body being orbited) exerts enough hold on attitudes to hold them in orbit. If it doesn’t or if the change in attitude is great enough we will cross one of those complexity tipping points and spin off into Chaos until another attractor is reached and stability returns. The phrase strange attractor slipped in there; Lorenz’s is perhaps the original example and can be seen here (much more is available in Gliek’s Chaos). What makes an attractor ‘strange’ is that we cannot predict where it occurs.
So that has taken us through social interactions and culture, albeit too quickly, what of economics? Ormerod has really explored this area and I can’t recommend his texts highly enough (starting with the ironically titled Death of Economics – Ormeod predates Telabs’s Black Swan etc and writes the texts Telab would like to write if could and if he wasn’t trying to maximise sales – but read both if you can). The opportunities for strange attractors are multiple in economics; consumer behaviour and taste perhaps being a starting point for considerations of this in the real economy. We can easily see that fashions come and go but that they also stabilise for a time. What combination of culture, pressures and economics conspire to make one genre of music popular for a year or two and when will it tip? Considering skateboarding as an example we see rapid growth and saturation in the 1970s (caused by the introduction of new wheel manufacturing technology); some cultural shift saw a resurgence during the 1980s with street skating, only to be killed off partly by regulation; and the late 1990s saw the re-emergence of skating this time driven by... well the interesting thing it is hard to measure why the sport has resurfaced around the strange attractor of street skating. Let’s assume some of those skaters became market traders, unlikely in many respects as there exists a cultural hegemony around the City but nevertheless possible. What attractors are there in stock markets?
In theory the stock market exists to make investments in companies more liquid thus attracting more capital at a lower price and allowing economies to grow – in theory. In practice the market is beset with speculation and gambling. Much of the trading activity that occurs is not of the slow and calculated kind exemplified by the likes of Buffet and Graham but rather more akin to that found in Las Vegas. Why will this create attractors? Well in truth even the considered style of investment practiced by value investors can lead to attractors; it is that speculation seems to increase their occurrence and reduce their longevity. We see narratives develop in markets and spread via the media. These narratives usually take the form of post-hoc rationalisation about the cause of events. Based on these narratives ‘truths’ develop and money flows. This flow is not, however, based on economic principles but on narratives (ok I know economics is a meta-narrative). A reality is created around a position and it holds. For example we can see how stubborn the property market is against full correction or how insane gold prices have become with commentators even suggesting they are overvalued. The crashes we see are simply shifts out of self organising criticality and into Chaos. The market usually self stabilises around some other lower point after a short time – it finds another planet to orbit. Broker’s even try, somewhat naively, to describe the parameters of these orbits with the use of support and resistance points (these points assume that share prices are moving within a normal distribution and disregards outliers – see here to show nothing is new and here ).
Have we finished? No I think in truth this series may have only just begun however I am pretty sure some rules have emerged governing the acceptable length of blogs and in truth my neck now hurts from bending over the lap-top. I shall return and will look at Chaos and Complexity again, in the meantime if there is a certain point you would like me to dwell on then drop me a line...........
PS – if ask you to lunch i am hungry, if I end a text with a x I know you and it’s your birthday and if I actually kiss you it’s probably because I’m happy for you to be the last person I ever kiss – I’m not completely without a sense of romance....
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