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What is randomness? Nobody knows..

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Re: What is randomness? Nobody knows..

#31

Post by bgilroy26 »

pdhborges wrote: post #11
dsthysd wrote: post #5

Randomness is an equal chance that one of a number of events occur. Is he arguing that we do not know what randomness is? Or that we have not found anything truly random?

No. There are plenty of random variables without non-uniform distributions. Plus an event in probability theory is not what you think it is. An event can be any subset of the sample space.

The behaviour that dice and spinners and coins are trying to emulate is precisely what dsthysd said. In each case you hope that the faces of the die, sections of the spinner, and sides of the coin are equally likely each time.

I don't think I'm being unrealistic, how can learning more about probability theory change the conventional definition of random?

Isn't the real difficulty in trying to make a non-deterministic system out of a computer, since all we ever do with computers is feed instructions into them?

Re: What is randomness? Nobody knows..

#32

Post by strictfp »

antirez wrote: post #26

I think there is very good, and at the same time trivial , definition of how much random something is. Given any source of data, you define randomness the inverse of the ability of somebody observing the output sequence to guess what the next item will be. For instance in a stream of random bytes the observer will not be able to guess with more probability than 1/256 what the next byte will be, but if the sequence is…

You can in the same way argue that PI was random, but is not anymore now that it is known. The same could be said about any random sequence, like the tables of random numbers in calculus books or known PRNGs with known seeds.

Re: What is randomness? Nobody knows..

#33

Post by reizenikker »

antirez wrote: post #29
reizenikker wrote: post #28

Earlier quoted context omitted.

Hi, Salvatore, Read http://www.amazon.com/Black-Swan-Nassim-Nicholas-Taleb/dp/14... this book, Nassim discover and explore for most of people the true meaning of randomness, and actually he show useless of "Mathematical true randomness" in real life. Highly recommend this book. And Yep, u are absolutely right, the random effect, is totally depends on how to look at it.

Thank you! I'll buy the book, it's a truly interesting subject :)

Yep, exactly! Especially u can look on more common topic like success, and part of probability in it.

And sorry, they already have a second edition: http://www.amazon.com/gp/product/081297381X/ref=pd_lpo_k2_dp... ,

after this book, i highly recommend read his another book: fooled by randomness

Re: What is randomness? Nobody knows..

#34

Post by kenn »

antirez wrote: post #26

I think there is very good, and at the same time trivial , definition of how much random something is. Given any source of data, you define randomness the inverse of the ability of somebody observing the output sequence to guess what the next item will be. For instance in a stream of random bytes the observer will not be able to guess with more probability than 1/256 what the next byte will be, but if the sequence is…

Randomness is an interesting topic indeed.

For instance, up until 2012 introduced with Ivy Bridge, a true hardware-based random number generator hasn't been available to the masses. (http://en.wikipedia.org/wiki/RdRand)

what we believe to be random may not be, and I've seen UUIDs generated on cheap mobile devices can easily collide when their clock battery is dead.

Re: What is randomness? Nobody knows..

#35

Post by gosub »

antirez wrote: post #26

I think there is very good, and at the same time trivial , definition of how much random something is. Given any source of data, you define randomness the inverse of the ability of somebody observing the output sequence to guess what the next item will be. For instance in a stream of random bytes the observer will not be able to guess with more probability than 1/256 what the next byte will be, but if the sequence is…

There is also a measure of deegre of accuracy: if we have a sequence that is repeat(1..100), a predictor that always says 100 will be 1% accurate, while a prediction of repeat(2..101) will never be accurate but alway off just by one.

Re: What is randomness? Nobody knows..

#37

Post by jodrellblank »

antirez wrote: post #26

I think there is very good, and at the same time trivial , definition of how much random something is. Given any source of data, you define randomness the inverse of the ability of somebody observing the output sequence to guess what the next item will be. For instance in a stream of random bytes the observer will not be able to guess with more probability than 1/256 what the next byte will be, but if the sequence is…

If I give you the sequence 3.14159265, you will glance at it and say "Pi" and predict 35 as the next digits.

If I give you 7, 5, 8, 5, 9, 13, 6, 10, 9, you may not see the pattern at all, when it's "digit of pi + 4", and therefore is as predictable.

Your definition seems to depend on the intelligence of the observer. Is that measuring "how much random something is" or "how clever the viewer is"? (And, is there a difference?)

Re: What is randomness? Nobody knows..

#38

Post by stcredzero »

pygy_ wrote: post #15
toisanji wrote: post #7

Earlier quoted context omitted.

they are related, what is free will?

You could be conscious and live under the illusion of free will... That's unlikely, though. See http://www.ams.org/notices/200902/rtx090200226p.pdf

I keep reading that sentence. I guess I had no choice in the matter. What is free will?

Re: What is randomness? Nobody knows..

#39

Post by antirez »

jodrellblank wrote: post #37
antirez wrote: post #26

I think there is very good, and at the same time trivial , definition of how much random something is. Given any source of data, you define randomness the inverse of the ability of somebody observing the output sequence to guess what the next item will be. For instance in a stream of random bytes the observer will not be able to guess with more probability than 1/256 what the next byte will be, but if the sequence is…

If I give you the sequence 3.14159265, you will glance at it and say "Pi" and predict 35 as the next digits. If I give you 7, 5, 8, 5, 9, 13, 6, 10, 9, you may not see the pattern at all, when it's "digit of pi + 4", and therefore is as predictable. Your definition seems to depend on the intelligence of the observer. Is that measuring "how much random something is" or "how clever the viewer is"? (And, is there a diff…

You can simply assume the cleverest observer, but actually it's not just about smartness (ability to compute / recognize) but also the amount of data the observer has access to. For instance in a PRNG where I use some kind of source of entropy, like delay between user keystrokes, an observer that is able to watch the user typing can predict the sequence, another can not.
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