
What is randomness? Nobody knows.. - gnosis
http://www.johndcook.com/blog/2012/04/19/random-is-as-random-does/
======
antirez
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
Hi, Salvatore, Read [http://www.amazon.com/Black-Swan-Nassim-Nicholas-
Taleb/dp/14...](http://www.amazon.com/Black-Swan-Nassim-Nicholas-
Taleb/dp/1400063515) 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
Thank you! I'll buy the book, it's a truly interesting subject :)

~~~
reizenikker
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...](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)
,

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

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danmaz74
_The right question isn’t “is this system random?” but rather “is it useful to
model this system as random?”_

I couldn't agree more on this. As George E.P. Box put it, "Essentially, all
models are wrong, but some are useful".

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jpdoctor
I love when financial types talk about a "20% chance" of X happening (like
earnings miss, default, etc) If you are familiar with the postulates of
probability, you realize that they are talking out of their butts, and are
trying to sound oh-so-precise-and-mathematical.

Much of the financial world is about the appearance of quantitative thinking
and not actual quantitative thinking.

~~~
ryandvm
It is better to be wrong than to be vague. --Freeman Dyson

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pierrebouchet
I think one of the most widely accepted definitions of randomness in
mathematics was given by Martin-Löf.

Basically it says that a process is random iff it doesn't exhibit any
_atypical_ property that you can test with an algorithm.

In other words: if there is no computable way of proving that it's not random,
then it is random.

~~~
jasomill
How does this not trivially exclude everything (the first definition, not the
circular restatement)? Considering that, say, a sequence of coin flips either
has the property of "beginning with heads" or "beginning with tails," it
certainly appears to.

~~~
pierrebouchet
My bad, I was being too vague - sorry for that.

I meant "any atypical property" instead of "any property".

An "atypical property" being a property that _almost no sequence_ has, i.e the
set of sequences which exhibit this propery is a measure-zero set.

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gosub
Randomness should be a function of both a numeric series and an agent. It
should measure the ability of a given agent to predict the next element in the
series.

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bo1024
Good article. I liked the points made, especially the comparison to continuous
variables.

The argument about "true" randomness versus psuedo-randomness is very
interesting. As the dilbert comment posted elsewhere points out, it's
impossible to really know how "random" something is, because if it matches
your expectations, then it isn't.

So it's hard even to compare "true" random number generators and psuedo-ones.
You might even argue that PRNGs are better in some cases because you can make
provable statements about the distribution of their output. (Of course, those
statements might depend on the seed being "random"....)

Anyway, I guess the takeaway is that, as the author says, randomness is poorly
understood; instead, we can only make statements about random numbers and
probabilities and do our best to reconcile those with what we have to work
with in real life. This seems like poor comfort to academics who rely on some
formal notion of randomness that is unachievable, but on the other hand
randomness seems to always work "well enough" in practice.....

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Symmetry
I tend to think of randomness as a quantitative measurement of our ignorance
of the world.

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powertower
Randomness has at least one property... It can't be compressed.

That is, it has no pattern.

~~~
Teapot
Sometimes randomness spits out what we call patterns. 123456 seems like a
pattern to us, and our beloved compression algos we wrote. But 123456 is just
as random as any combo. I think. Right?

Related thinking, Sean Carroll on TED- Arrow of Time
<http://y2u.be/WMaTyg8wR4Y> He says there's 'more' or 'less' entropy, but is
there _really_ such a thing? Rolling 6666666 on a dice, and we scream luck!
But rolling 3164536 should be just as likely/unlikely.

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dsthysd
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?

~~~
pdhborges
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.

~~~
bgilroy26
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?

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Herring
That's how science works. If you keep asking why & digging deeper, you
eventually reach something that hasn't been "explained" in terms of something
else.

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givan
nothing is really random in an absolute way, when we have stuff that is very
complex or hard to compute and we can't figure out what it is we call it
random

~~~
philwelch
Well, maybe quantum indeterminacy.

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stcredzero
Reminds me of the question of consciousness.

~~~
toisanji
they are related, what is free will?

~~~
pygy_
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>

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

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bcjordan
Relevant xkcd: <http://xkcd.com/221/>

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BlackShirt
Reminds me of the delbert comic: <http://dilbert.com/strips/comic/2001-10-25/>

