TAO Posted July 14, 2011 Posted July 14, 2011 In any infinite string of random digits, there would be a series of digits 0,1,2,3,4,5,6,7,8,9 followed by exactly the same series twenty times. There would also be another identical series of twenty strings following that one, but separated from it by the digit 0, and it would be followed by the digit 1 followed by another series of twenty like the first one, followed by 2, and so on.Of course there would be, it is infinite.All totally random.At the top... you said it was 'any infinite string of random digits' already... considering we don't actually have any sets of random numbers... how could this exist in the first place?To give you an idea, pi's digits are not random. If they were random, they wouldn't be calculatable. You can thus, write by as a simple fraction of the Area over square of the radius. Considering you can do this, it isn't actually random, but is called 'pseudo-random'. A truly random number cannot be represented by a fraction, as that means it is definable.You would find the digital representation of pi to the fifteenth decimal place, followed by the digital representation of e to the fiftieth decimal place, followed by the square root of two to the two-hundredth place. Then the whole series would repeat itself, but in mirror image fashion. If these strings did not exist in the number, it would not be random. Of course, its being infinite may mean that you simply could not find them, even though they are there.My friend, you already said in the beginning you were talking about a random set. The problem is, if I can calculate it via a computer, it isn't a random set. I can calculate pi, and I can store pi too. Similarly with e, I can calculate, and store. The reason neither of those is random is because I can calculate them with an equation. A recursive equation, actually. Considering I can do that, it's not truly random, but is based on a non-local variable, wouldn't you say?Randomness and infinity are difficult concepts.Indeed they are. I don't struggle with infinity... it makes sense with my programming. But random does not exist... it is impossible to calculate on a computer. Thus, that is my definition for random... as doesn't random mean 'not based on any variables'.And nah, I don't mean the 'impossible to predict' type of randomness... because that isn't true randomness either. But I have doubts about truly random numbers (numbers that are not based on any variables). Eh, that's the wierd way my mind works.Best Wishes,TAO
asbestosman Posted July 15, 2011 Posted July 15, 2011 Of course there would be, it is infinite.Technically that is incorrect. There is a concept of convergence known as "almost surely". You are correct that the event will happen with probability approaching 1 (100%), but it's technically not certain. Why not? Because there are infinity possibilities of infinite strings, and some of those possibilities never even use some of the digits. Those possibiliites are rare, but they technically exist. If you take a dart and throw it at a number line between 0 and 1, the chance that it hits precisely the spot it does is essentially 0 (infinitesimal) since there are infinity numbers between 0 and 1, yet it happened.Just to blow your mind: did you know there are infinite sequences of rational numbers between 0 and 1 where the sequence always increases? Uncountably many in fact. It turns out that there are also uncountably many infinite sequences of rational numbers between 0 and 1 that do not have this property--precisely as many either way. However, I wouldn't say that both are each equally likely to happen. It may depend on how the sequence is obtained, but if it's generated by continually choosing a random rational number between 0 and 1 repeatedly, The probability quickly converges toward 0 for the sequence always increasing.
Mordecai Posted July 17, 2011 Posted July 17, 2011 Evolution does not concern itself with abiogenesis. http://en.wikipedia.org/wiki/AbiogenesisTrue, but Darwinism does, as in "The origin of species." Just check college textbooks that begin their chapters about evolution with a discussion about abiogenesis. Besides, if you're lucky enough to produce the first life, perhaps that same luck can apply to all the other additions of information. Why not? As noted biologist Giusseppi Sermonti pointed out, "With the first life, we must assume 90% of the work is already done." If 90% was luck, why not have it cover the other 10%? It should very much concern theorists, because both involve the question, "Where does functional information come from?"
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