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Bennett's theory of the enneagram suggests a process subject to modifying corrections in 3 parts as: process-correction-synthesis. The 3 steps or parts of the triadic operator are also found in symbolism such as the enneagram. This has not yet been done because of the problems of providing quantitative and objectively observable measures to the 3 parts. However, conversations might be typified and predicted. In actual conversation, where the rules of trialogue do not prevail, it is proposed that there is some mechanism such as permutation to give rise to fluctuations rather than to a progressive trend. We have set price rise as equivalent to 'moving towards the unknown' and vice versa. Price rise - comment - reflecting further We can diagram the cyclic operator of trialogue in much the same way as a Mandlebrot fractal. Here, there is not so much 'success' or 'failure' but a concern with 'making meaning' (or an addition of, or extension of, meaning). There is a succession of acts of speech - as question, answer and comment - the comment feeding into the next cycle. Such a procedure is similar to that applied in our 'trialogue'. With only the most rudimentary conception of 'best' and enough time/energy for very many attempts, evolution becomes inevitable. Otherwise, the process can continue, given the resources to continue. If the result is 'failure' the process can also stop, such as in the case of the death of an organism or the extinction of a species. However, if the result is 'success' the process can stop there - e.g. The sequence is therefore a triad of: best step-results-next best step and implies, as before, a progression. Before one chooses the next best step, one has seen the results of the previous 'best' step. The context is important, such as a game board or an environment. Kurtzweil's evolution device involves what first seems to be an extremely vague concept: 'choose the next best step'. It excludes any notion of 'guiding intelligence'. This random element introduces more complexity. The six permutations ate akin to faces of a die cast at each step.
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Here we have a parallel with the 'six laws' discussed in detail by John Bennett. The 3 parts of the operator are considered as in loose association and hence capable of 6 combinations in sequence. This is done in successive stages to produce whatever degree of detail is required - in this case right down to the frequency of individual transactions. (a) is accomplished by self-similarity, the shape of the fractal (the 3 parts) applied to each part, scaling down and, in the case of the falling or second part, in reverse. The application of the model includes (a) making it more detailed and (b) using it predictively.
A multifractal walk down wall street series#
The operator can be altered - making a series of fractals - by changing the first part of the line, making it a 'faster' or 'slower' rise. Like Mandlebrot's operator there is, implicitly or otherwise, an assumption of overall progress (or price rise). The Hegelian model is usually rendered as: thesis-antithesis-synthesis (this last being then a new thesis, so that the operation continues). A little reflection reveals the Hegelian model lying behind this operator (Mandlebrot calls it a 'generator'). The basic unit of such fluctuations is taken to be of the form:Ī picture of this unity as a graph of price against time would show a zigzag line, first rising then falling then rising again. Mandlebrot's multifractals apply to fluctuations of the price of stocks on the exchange market. Two examples may suffice: Mandlebrot's multifractals and Kurzweil's evolution machine Such operators operate on themselves, generating complex patterns.
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Complexity results from such simple 'triads' applied as repeating operators. In this guise, it is an operator of 3 steps or parts. As a re-iterative form, it is common in complexity theory. The 'law of three' turns up in may fields. The essay is also offered as a commentary on William Pensinger's concept of 'identity transparency'. The main inspirations for this essay, besides those quoted in the text, are Steve Mitchell's novel 'Albion' and Spencer Brown's 'Laws of Form'. THE LAW OF THREE IN COMPLEX PROCESS - A FRACTAL ESSAY