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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 inver
by antirez 15y ago
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 "ffaaffaaffaa..." it will be trivial.
Note that this covers a lot of interesting things, for instance PI has a random-looking distribution of digits, but is not random, because from the sequence it will be easy to predict, the observer will see it is PI and will predict the next digits with 100% accuracy.
Actually in this reasoning there is an "observer" that is the one that will try to come up with a model to improve the probability to guess the next item, but still I think it's an interesting way to define randomness, a lot more intuitive than talking about models.
- reizenikker 15y agoHi, Salvatore, Read http://www.amazon.com/Black-Swan-Nassim-Nicholas-Taleb/dp/1400063515 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.
- antirez 15y agoThank you! I'll buy the book, it's a truly interesting subject :)
- reizenikker 15y agoYep, 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_sr_2?pf_rd_p=1278548962&pf_rd_s=lpo-top-stripe-1&pf_rd_t=201&pf_rd_i=1587990717&pf_rd_m=ATVPDKIKX0DER&pf_rd_r=125E5S0W9G3MNNTVP7DP 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
- strictfp 15y agoYou 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.
- kenn 15y agoRandomness 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 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.
- gosub 15y agoThere 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.
- jodrellblank 15y agoIf 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?)
- antirez 15y agoYou 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.