Random theory?
- Thread starter Nanoman
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Surely randomness just boils down to the fact that every event has a near infinite amount of variables which we cant effectively consider/compute to an accuracy that would mean the outcome would always be known error-free?
Theres always something unknown or that cant be measured exactly...
ps3ud0
Theres always something unknown or that cant be measured exactly...
ps3ud0
No, we just don't know whether "random" truly exists yet.
Soldato
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Surely randomness just boils down to the fact that every event has a near infinite amount of variables which we cant effectively consider/compute to an accuracy that would mean the outcome would always be known error-free?
Theres always something unknown or that cant be measured exactly...
ps3ud0
No; that's the whole point. Quantum mechanics says there are things which cannot be predicted, regardless of how much you know about the system beforehand
Of course, knowledge is limited by the HUP anyway…
Soldato
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Well we can use mathematical statistics to "prove" that certain processes are random. In the sense that with certain random number generators the emperical distribution of the random numbers it genrates will approach the theoretical distribution. So as the number of trails you do tends to infinity it's accuracy to the "true" distribution will increase.
In reality it's the only practical way of handling data. It's what every statistician does, fit a model and make sure that whats left over is as random (normal, chi-squared, or whatever) as possible.
Soldato
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Empirical proof of randomness is impossible. It can be observed that the output of some generator seems to tend to some distribution as the number of trials approaches infinity, but this does not eliminate the possibility of the generator's output being governed by a deterministic process.
To use your example of tossing a coin or a die, the process can be described macroscopically by a uniform distribution, but the system is in fact deterministic (again, ignoring quantum effects). This is called pseudorandomness.
A better example of a pseudorandom process is that of random number generators as used in computers, e.g. the Mersenne twister. The algorithm takes a seed value and produces an output based on that seed that follows a uniform distribution, but the algorithm is in fact not random at all, as giving it the same seed will produce exactly the same chain of output values.
I'm going to go and do something productive now
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Soldato
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Empirical proof of randomness is impossible. It can be shown that the output of some generator tends to some distribution as the number of trials approaches infinity, but this does not eliminate the possibility of a deterministic process underlying the generator's operation that can be described by such a process.
To use your example of tossing a coin or a die, the process can be described macroscopically by a uniform distribution, but the system is in fact deterministic (again, ignoring quantum effects). This is called pseudorandomness.
A better example of a pseudorandom process is that of random number generators as used in computers. The algorithm takes a seed value and produces an output based on that seed that appears to follow a uniform distribution, but the algorithm is in fact not random at all, as giving it the same seed will produce exactly the same chain of output values.
I'm going to go and do something productive now
Of course your right, it's not a proof of randomness but it's a proof that the output of some process does statistically approach some distribution.
With any form of statistics you can do no better than using mathematical statistics to test devaiation of your samples from a given distribution.
Randomness is to mathematics is what rationality is to economics. They are concepts that assist in modelling observable data, they will never be proved in a hard sense.