In flipping coins, is the probability of obtaining the particular sequence tail tail ... tail 100 times inferior to any other sequence of flipping coins 100 times ?<p> Basically, a probability is :<p> number of favorable outcomes<br> ------------------------------------<br> number of possible outcomes<br> <p> Flipping one coin, the probability of obtaining tail is 1/2<br> Flipping two coins, the probability of obtaining tail tail is (1/2)*(1/2)=1/(2^2)<br> Flipping 100 coins, the probability of obtaining tail tail ... 100 times is 1/(2^100)<p> By using the same reasoning the probability of obtaining tail head tail head ... tail head 100 times is exactly the same than obtaining tail tail ... 100 times that is to say the probability doesn't take the order of sequence into account. <br>So Probability concept, which is purely <b>mathematical</b>, is not enough to define the concept of <b>randomness</b>. In 1965 - after the concept of <b>Entropy</b> was introduced by <b>Shannon</b> - <b>Kolmogorov</b> defined the concept of <b>algorithm complexity</b> for a <u>finite bit of strings</u> so that a <b>random string</b> is <u>"incompressible"</u> in the sense that a <u>program</u> would have to be <u>expanded as the serie grows larger</u>. So Kolmogorov, the father of <b>probability axioms</b> in 1933, recognised their limit himself: the use of these <u>axioms</u> only relie on <b>logical correctness</b> - which is <u>purely mathematical</u> - not on their <u>relevance to physical phenomena</u>. <br><b>Walter Shewart</b>, the father of <b>Quality Control</b>, remarked also - well before <b>Kolmogorov</b> - that it was necessary, for use in <u>real world</u>, to define a concept like <b>randomness</b> not only with <b>probability axioms</b> but also <u>operationally</u> by comparing with a <b>physical operation</b> like flipping coins. <b>Kolmogorov</b> somehow had the same idea than <b>Shewart</b> except that he wanted to use a <b>computer</b> or <b>algorithm</b> which is indeed a <b>physical operation or device</b>. Probability FAQs (in construction): http://www.econometric-wave.com/faqs/probability/home.html.html
Random by definition has no pattern. And is not expressible in math....as far as I know. The market is not truly random. It has current and flow. Might be more expressible in physics. Maybe. Truly, the more I look at trading.....it does not have much to do with math at all, but the ability to dance to a rhythm. And spot when everyone else has stopped as they change feet. It has to do with reading the emotional pulse of the market. And math is sorely lacking in the ability to read emotion.
One could also argue that there is no such thing as randomness. If all laws of the universe are deterministic, then it is our inability to take into account all variables to explain what otherwise appears chaotic. However, in the book, "Does God Play Dice with the Universe," the author explains that, no matter how accurately we measure a specific action, movement or process, we are inable to measure it with infinite precision. Anything less than this introduces great unknowns some X time period into the future. I cannot think of one process in the universe that is truly random. Even in quantum physics, both possibilities occur but then split off into other universes.
Aphie....I think thought and emotion are truly random events. Not the process that creates them with the nerves firing....but the actual thought or emotion.
So then you are saying you believe in something beyond the physics of just our neurons firing? I thought you were atheist?
bobcathy1 wrote: This is not true, as you can see studying textbooks on random processes; e.g. diffusion and jump-diffusion processes are both random processes, but have different structures: http://home.cerge-ei.cz/petrz/fm/f400n19.pdf As math stands, the last sentence is certainly true. __________________
Yes, I am an atheist. It does not preclude this sort of thinking. I do not adhere to science as dogma as some of the atheists on this board. I am comfortable with the unexplained.
My goodness, we have a lot of very intellegent people on this board. Bob is very impressed. Not a lot impresses him mind you. Yes, there is no logic to emotion. And math is pure logic.
It's not about the question if randomness exists or not here - although it is interesting in fact crucial question. It's about how to define it, that it exists or not is another question . In fact to answer if randomness can exist or not one must define the thing first, because if one cannot even answer the question of definition one cannot say if the object exists or not since it depends on the definition . Secondly we are not on metaphysical plan. Mathematical object doesn't exist, when a planet is modelised by a mathematical point, of course we know that it is not a point in reality, the same when one use the concept of randomness ... the problem here is once again that the concept of randomness is not even defined so clearly like a point or a line in mathematics. That's why some groups can abuse from this lack of mathematics like the RMH & EMH propagandists see "A summary of EMH by economists" http://www.elitetrader.com/vb/showthread.php?s=&threadid=25863&highlight=EMH . This doesn't mean that by this EMH is invalidated by this sole argument (there are other arguments for that), it only means that their claim is at least shamelessly overexaggerated. This is due to historical reasons but this theory impacts in practice investment behaviors of institutions (and so public money) and regulations which are based on EMH validity. As to come back to Randomness, if you want to say that you roll a "fair" dice, Randomness is clearly the concept that you need. In that sense Randomness "exists" by refering to it by this PHYSICAL OPERATION although you don't define it mathematically. That's what Shewart called "operational definition". Existence doesn't mean something concrete, it can be an abstraction but this abstraction must be defined if not explicitly at least implicitly which is the case here if one refers to a physical operation instead of a mathematical definition which doesn't really exist at least for the moment. The EMH propagandists above doesn't use such operational definition so that their claim ressembles (some even say is) postulate. Their attack on Technical Analysis - at least those that are founded on so called market's action like the existence of patterns - is so much less valid although once again it is enough to pretend that it demonstrates the existence of such patterns, it means that they cannot by a sort of undisputable authority decretes their invalidity. In practice that's what they are doing: they claim that they are undisputable .
harrytrader wrote: Probability (random processes) and (Euclidean) geometry are equally well defined mathematically. But also if the dice-roll process is say an n-th order Markov chain (a random process that could violate EMH).