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One more thing regarding the formalized similarity principle (http://www.forexfactory.com/attachment.php?attachmentid=1539695):
kprsa summarized / translated it here: http://www.forexfactory.com/showthread.php?p=7893960#post7893960. I can’t give a profound opinion on that but after some reading I think that this definition is elaborated emptiness. An impressive encoding, not wrong and that’s it. Formally describing a problem without containing any solution. If anybody is inspired by this formalization: fine, let us know!
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Yes, the ~93% probability is only true if the numbers are generated by a random process (not independent random numbers as the theorem says, then it would be ~83%, nitpick, anyway…) and, more important, only if you look at the complete 5-sequence after being formed, not during its formation. If you scan for sequences where only a subset of the equations are fulfilled (unavoidable if you don’t know the future), you also increase the probability of finding those patterns where the theorem doesn’t hold. The theoretical/posteriori probability is indeed 15/16 but the probability when applying the idea in an “online” way to an incomplete pattern as vaguely suggested by Eurusdd is 3/4.
Ok, so you probably know of the “Bonzion forex system” on ghanaweb.com and other self-profiling spam threads à la “I can coach Nigeria!!!”, an affiliation with a snowball system, etc. (https://web.archive.org/web/20050225060939/http://www.eternal.esmartdesign.com/guil.htm, https://web.archive.org/web/20050209020041/http://www.eternal.qn.com/). But actually I meant his passion for almost proving some famous unsolved problems in mathematics.
http://www.offthekuff.com/mt/archives/000702.html
http://www.artofproblemsolving.com/community/u9922
http://planetmath.org/node/7239
Sorry to sound a little cynical – I neither have the competence nor the courage to try proving such stuff – but it is always the same pattern again and again: announcements in capital letters, impatient reactions to criticism and disappearing after disproof.
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Just a personal note: I honestly appreciate your patience and thoroughness investigating Eurusdds fragments of a concept. However, don’t take them too seriously. If you gathered any valuable insights based on those threads (I think you did), it is likely that they are an outcome of your very own research inspired by some of his remarks and less of an enlightenment on the path of his teaching. There is a not inconsiderable chance that Eurusdd was the one who knew least what exactly he was talking about. Whenever someone claims to be “way out of your league”, he “almost surely” is not. I don’t know if you searched for his (presumed) identity and activities apart from trading. Personally, after doing so and reading his threads on the web, I come to my conclusion that basically Eurusdds ego is ahead of himself. This does not imply that one should not draw inspiration from his way of thinking. I decided to not invest additional time to dig for that potential burried treasure but I’m anytime keen to hear that I was wrong. I wish you success!
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Thanks for your extensive reply. I think I understand your encoding but I disagree with the implicit assumpion of a uniform distribution of binary combinations. Computing the relative frequency with (32 – 2) / (32) requires that each binary pattern occurs with the same probability of 1/32. As you pointed out, at least one inequation (i) – (iv) must hold for all binary patterns except for 01010 and 10101 (resp. x1010 and x0101 as the pattern encodes 4 <-relations between 5 elements) which may or may not fulfill at least one condition depending on the relative ordering of non-adjacent elements. But these patterns occure more frequently than 00000 and 11111, representing the strictly monotonic sequences, for example. The {0,1}-encoding omits the relations between those non-adjacent elements.
You can also look at it from a perspective of sorting. There are 5! = 120 permutations for 5 randomly chosen real numbers and we are matching the sorting sequence with 4 (8) partial sorting sequences arising from inequations (i) – (iv): ..1..2..3.., ..1..3..5.., ..2..3..4.., ..3..4..5… (plus all reversed sequences for the >-relations) where (..) is a wildcard for 0 or more indices. The {0,1}-encoding maps 120 permutations non-uniformly to 16 (32) binary patterns. But there are 20 out of 120 permutations where none of the above inequations hold if you choose x1 .. x5 randomly as stated in the theorem. I checked that with some pseudo random numbers and EURJPY data and for the former as well as for data on really small time scales (tick data) the relative frequency converges to 83.33%. On higher time frames, trends seem to be responsible for a stronger ordering which may push the frequency to 93% and above.
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@Anti Could you please point out why you consider 2^5 = 32 binary combinations for proving the theorem? What exactly do they encode?
