randomness

[neutrino86]

Just to see if my notion of randomness is relatively correct, i ask, what is randomness?

 

Is it possible to have perfectly random relations in a finite set.

If that sounds uncomfortable, i iterate with modifications,...

Is it possible to have a perfect random number generator.

 

The question arised when in the middle of a conversation about the random generators in programming languages like c, i learnt that these generators generate the so called random numbers by carrying out a finite number of mathematical operations on some time varying variable like say the least significant Integer of the second indicator(For example, take the integer which indicates the seconds, take its cosine,take the first three digits, add two to it, take its logarithm,and so on for a finite number of steps.)

But this isnt RANDOM is it?...we call it random just because the inverse operations would be very very difficult to complete, and is an approximation(i.e the degree of randomness or so, if i may use the term) we all are all happy with.

So about a perfect random number generator?

 

 

thanks in advance.

[matt grime]

Those random number generators are random because they are to all intents and purposes as far as we can see random, in the sense of any output is equally likely as any other output. It is nothing to do with inverse operations, whatever that might mean. And rest of what you say is meaningless. What do you even care to define by random? It is only a loose term, unless you define it properly there is no answer.

[bascule]

i learnt that these generators generate the so called random numbers by carrying out a finite number of mathematical operations on some time varying variable like say the least significant Integer of the second indicator(For example' date=' take the integer which indicates the seconds, take its cosine,take the first three digits, add two to it, take its logarithm,and so on for a finite number of steps.)

But this isnt RANDOM is it?[/quote']

 

No, this is pseudorandom.

 

Pseudorandomness has many advantages in programming. For example, let's say you have a pseudorandom number generator feeding a particular function, and that function is crashing.

 

With a pseudorandom number generator, you're ensured the same sequence of pseudorandom numbers every time. So debugging the function that's crashing becomes much simpler because you know, thanks to the pseudorandom number generator, that your program will crash reliably at the same point every time. With a real random number generator you'd just have to wait and see and hope the events leading to the crash randomly transpire again.

 

 

So about a perfect random number generator?

 

The closest thing you'll get to a "perfect random number generator" is probably a Random Event Generator which uses quantum tunneling in diodes or transistors to create "true" randomness...

[neutrino86]

Those random number generators are random because they are to all intents and purposes as far as we can see random, in the sense of any output is equally likely as any other output. It is nothing to do with inverse operations, whatever that might mean. And rest of what you say is meaningless. What do you even care to define by random? It is only a loose term, unless you define it properly there is no answer.

 

Mr. Grime. Wouldnt you call a stream of numbers random in nature if you were to find no corelation between their appearances and the real number line?

By an inverse operation I meant the inverse of the operations done to get the "random numbers" in a similar fashion to the example i had cited.

I donot feel its looseness, even though i find myself incapable to define randomness with the amount of rigour that could remove a frown on a mathematicians face.

 

 

Since Mr Bascule has enlightened me on a few terms, i shall cite another example highlighting why i doubt anything is random in our world.

 

This is a sentence from http://www.robertnz.net/true_rng.html.

 

"A hardware (true) random number generator is a piece of electronics that plugs into a computer and produces genuine random numbers as opposed to the pseudo-random numbers that are produced by a computer program such as newran. The usual method is to amplify noise generated by a resistor (Johnson noise) or a semi-conductor diode and feed this to a comparator or Schmitt trigger. If you sample the output (not too quickly) you (hope to) get a series of bits which are statistically independent. These can be assembled into bytes, integers or floating point numbers and then, if necessary, into random numbers from other distributions using methods such as those in newran.

 

"

let us now assume thst this true RNG has given us a stream of ten integer numbers, which is produced by having the noise generated by a resistor amplified, and so on as mentioned.

But it should still be possible to formulate the "inverse operations" by ofcourse very very sensitive equipment(to mend the losses due to imperfect instrumentation), and an impossibly vast expanse of time and money(But i should belive that this is not the reason for its unpredictability!!), let alone the fact that the string may appear satisfactorily random to us.

 

Well whatever it be, it should always be possible to predict the output as long as the number of operations done remains finite. Or can it? can there be a perfect RNG?

 

I hope I have made myself clear on this.

[Xyph]

I expect everything is "pseudorandom" at some level.

[Martian]

quantum tunneling in diodes or transistors to create "true" randomness...

 

Hey, thats pretty cool!

[Sisyphus]

I don't think there's any way to have true randomness without looking all the way down to the quantum scale, and even that is not really certain whether its truly random or just deterministic in a way we don't yet understand. Cause and effect is a powerful thing...