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What is random?by Jabbu
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#1
Aug1714, 05:58 PM

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Does "random" have different meaning in classical physic from SR, GR or QM? What is the difference between random, deterministic and probabilistic? Is probabilistic either randomprobabilistic or deterministicprobabilistic, or is probabilistic a truly separate category on its own?
If we flip a coin 100,000 times and the number of heads match the number of tails 5050% every time +/ some tiny variation, then how's that random outcome? Wouldn't it be truly random if we could flip 90% heads at one go and then 20% heads in another go just as easy, and just as easily as 40% heads, 1%, or 72%? 


#2
Aug1714, 06:01 PM

P: 180

Is "random" the same thing as "without cause", or can something have a cause and still be random?



#3
Aug1714, 06:20 PM

P: 21

One working definition of random is something that can't be predicted. In your case each flip of the coin gives a random result, but over time lots of random results give a clear picture about the nature of the coin.



#4
Aug1714, 06:25 PM

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What is random?
I'd give this article a read if you haven't already: http://en.wikipedia.org/wiki/Randomness



#5
Aug1714, 06:29 PM

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Also, note that probability is inherently tied to randomness. A single event (like the flip of a coin) may be random in the sense that you don't know with certainty what side it will land on, but you can say there there is some probability for the coin to land on each side. I think the first part of that last sentence is key here. Any single event is random if we can't say for certain what will happen, even though we can define probabilities for each possible outcome.



#6
Aug1714, 06:31 PM

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You touch many different and interesting concepts here.
First, deterministic means that the outcome of an experiment is fixed before doing the experiment. So even before doing an experiment, there is only one outcome which will happen and (in principle) we can predict this outcome. All of classical physics is deterministic. For example, when I throw a ball, I can (in principle) calculate exactly where it is going to land and how long it is going to take. When I flip a coin, I can calculate (in principle) what side of the coin is going to be up and what side is going to be down. However, the variables involved and the equations involved are so immensly complicated that we can never do these calculations. Furthermore, our measurements can never be done precisely enough to know exactly which state we are in now. This is where probability theory comes in. While flipping a coin, the outcome is predetermined exactly. But the outcome is unkown to us. Probability theory does give us some way of accessing some information about the coin flips. As another example, the number 0.1234567891011121314151617... is called the Champernowne constant. It is completely determined, it is clear to everybody how exactly this number continues. However, if I ask you for the 1000th digit, then you would have to do a tedious calculation in order to find out. So again, the number is determined, but this determination is unknown to us. We can again use probability theory to study the number. So we can figure out the chance of getting a 1 as 1000th digit. This is also the idea behind pseudorandom number generators. True random processes are very difficult to generate and do not exist in classical physics. However, they do come up in quantum mechanics. Whether the processes which come up are actually deterministic in some sense is currently unknown. Probability theory is currently the only tool available to study these processes. You also mention cause. Here you must specify what exactly you mean with cause. The term is rather vague and philosophical. I don't even know if it is a meaningful term in science, but others probably know more. Also, not all processes satisfy the Law of Large Numbers. One famous example is this experiment: "Choose a number at random from ##(\pi/2,\pi/2)## (where all numbers are equally likely). Then shine a light on a wall where the angle between the light and the wall is the number you have chosen. The outcome of the experiment is the place on the wall where the light hits" This experiment has the curious property that the averages do not converge. This means that it does exactly what you described in your post: in one run, the average place where the light hits the wall can be entirely different from the the average place where the light hits in the second run. Even if you make the runs long enough, you will see no pattern in the average place where the light hits. http://www.math.uah.edu/stat/applets...xperiment.html Luckily for us, these types of situations are very rare. 


#7
Aug1714, 06:39 PM

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The blue curve looks almost like a Gaussian centered at 0. 


#8
Aug1714, 06:46 PM

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Also, we see that the distribution is symmetric, and if the expectation value were to exist, then it would be 0. But it doesn't exist. In fact, if you try to calculate it, then you will constantly hit ##\infty\infty## situations which are not welldefined (and which should not be welldefined in this case since the averages don't converge). So from that pointofview, we see that 0 is no more special than any other value. It might be the mode of the distribution and the median, but it is no more special than any other point in terms of expectation value. 


#9
Aug1714, 06:52 PM

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#10
Aug1714, 07:04 PM

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In that sense, tossing a coin is not truly random, it is only pseudorandom, however our lack of knowledge means that it is truly random for all practical purposes. I don't think it is currently known whether something truly random exists or not. 


#11
Aug1714, 07:12 PM

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Maybe a better example would be 0.23571113171923293137.... where the digits are the sequence of all prime numbers. There probably isn't a way to find the n'th digit of that sequence without tabulating a sufficient number of primes. If the underlying distribution was Cauchy, your finite estimate of the variance will always be infinitely wrong http://en.wikipedia.org/wiki/Fattailed_distribution 


#12
Aug1714, 07:15 PM

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#13
Aug1714, 07:26 PM

P: 180

I'm not sure how to define "cause", but I'd say it has to do with limits and constraints, some range or degrees of freedom, where things perhaps can be more or less random rather than just random or not. I think if we could find meaningful and persistent definition for "cause" it would bring us that much closer to some definite answer, even if that answer is that there is no answer. 


#14
Aug1714, 07:31 PM

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#15
Aug1714, 07:46 PM

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There are some interesting proposals of what random means (for example: http://en.wikipedia.org/wiki/Kolmogo...rov_randomness), but I don't really think this is the definition we're looking for. I personally consider a definition of randomness to be closer to philosophy than to science. 


#16
Aug1714, 08:24 PM

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I've always taken random to mean that a phase particle has more than one future, and solutions are not unique.
Its not necessary that a random distribution be Guassian. There are lots of different distribution shapes. 


#17
Aug1714, 08:25 PM

P: 180

It is indeed something more specific to say about randomness, but still far from apparent. With any given supposedly random sequence, I don't think we can say with certainty that there really does not exist a simple recursive function that would actually duplicate it. 


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