
The Quest for Randomness - ot
http://www.americanscientist.org/issues/pub/2014/3/the-quest-for-randomness
======
0x0
There's a challenge posted online to compress a file of one million presumably
random digits, and it's been running for 10+ years without anyone claiming the
prize:

[http://marknelson.us/2012/10/09/the-random-compression-
chall...](http://marknelson.us/2012/10/09/the-random-compression-challenge-
turns-ten/)

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EzraVinh
If it was generated by a physical process, it might be possible that the
signal has lower entropy than a truly random signal. It would be interesting
to look at n-gram frequencies.

First you would have to extract the original digits. Since log(10) * 10^6 /
log(256) = 415241.01, and the binary file contains 415241 bytes, I assume that
the binary file is produced by converting a million digit number to binary.

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j2kun
I wrote a more rigor-oriented article on Kolmogorov complexity a while back.
HN readers might enjoy: [http://jeremykun.com/2012/04/21/kolmogorov-
complexity-a-prim...](http://jeremykun.com/2012/04/21/kolmogorov-complexity-a-
primer/)

I too love Aaronson's writing style, so my work is no substitute for his
insights.

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Xcelerate
Darn, the article stopped right before it got to the interesting part in my
opinion.

I love Scott Aaronson's writing and way of explaining things though. I was
thinking how well this article was written before I looked at the author.

Randomness is a subject that fascinates me, as I've been studying how it
relates to quantum mechanics. I've arrived at the conclusion that a more
useful word that "random" is "unpredictable".

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zhaphod
Scott writes very well. And he writes some of the lengthiest technical posts I
have read. I find writing one paragraph of technical writing akin to chewing
diamonds. Don't know how he does it. I have been lurking on his blog for some
time and I have learned a great deal.

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cyborgx7
At an intellectual level I have accepted that quantum mechanics truly are
random, but in a small corner of my mind I still believe that the universe is
deterministic.

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HCIdivision17
I think it's fair to say that's a reasonable coping mechanism for staying
sane. QM notoriously has no everyday analog, whereas determinism holds up
reasonably well in daily life!

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cortesoft
I feel the opposite... determinism does NOT fit with my day to day observance,
because my perception is that I have free will. If I accept determinism, I
also have to accept that I actually don't have free will, and that seems
contrary to my perception of myself.

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beloch
So, what if some omnipotent trickster/adversary/god designed a deterministic
universe specifically to fool you into thinking you have free will?

I tend to believe in free will myself and I _hate_ the above argument because
I don't know of any way to refute it. As far as I know, the question of free-
will vs determinism is unanswered. Even tests of randomness using Bell
inequalities requires an assumption of free choice. It's... _disquieting_.

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cortesoft
My point wasn't that the world COULDN'T be deterministic BECAUSE I have free
will... I was saying that the world NOT being deterministic fits better into
my own perception of how the world works, since it appears to me that I have
free will.

As far as I know you are correct; there is no way to distinguish if I actually
have free will or not.

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PavlovsCat
Not trying to tell you what you should think about your own free will, but
here's what I think about mine:

What I consider as me, my consciousness, is getting fooled in so many ways to
think it made decisions it pretty much just observered... that particles
making up my grey matter can go this way or that way, randomly, without "me"
actually taking any conscious influence on them, doesn't really make a
difference to me. It's like the difference between a truly random random
number generator, and one that just spits out a pre-determined list; "I" don't
get to pick the numbers either way.

When I was younger, I tried to "see where my thoughts come from", and it
always seems like they come around some corner, out of some blind spot. I
never meditated but I, but I always liked the phrase "watching thoughts
arise", because that's how it seems, they come into view of my inner eye so to
speak, but the inner eye does not make them, not originally. I can add 2+2,
but I can't _make_ me get the idea to add 2+2. Well, actually, I can make
myself get the idea to add 2+2, but I can't make myself get the idea to make
myself get the idea to add 2+2... and so on. Is it possible to talk about
these things without it sounding like esoteric gibberish?

Anyway, I kinda don't think we have free will, not to the degree we like to
believe, anyway - but I can't help treating myself and others as if we did. I
think life would seem kind of pointless otherwise, certainly anything beyond
bacteria and plants, so it might be a necessary illusion for us "higher" life
forms.

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kaa2102
I've done some work with monte carlo and discrete event simulation. The
runs/iterations produced utilize psuedo-random number generation. Many
discrete-event simulation software platforms reproduce exactly the same
numbers on a given run. Also, monte carlo simulation software like @Risk and
CrystalBall enable users to select psuedo-random number generation methods.
For instance, utilizing the Latin Hypercube method will sample more evenly
from a Gaussian distribution rather than pulling more from the peak and tails.

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mrcactu5
so much for i.i.d. random variables.

we don't know if the variables are random and have no way to tell - definitely
- if they are independent or identically distributed.

i was always confused when cryptography textbooks only talk about
pseudorandomness. probably `import random` is not sufficient for them

and I was also confused by ergodic theory textbooks, which qualify levels of
randomness like "equidistributed" or "3-fold mixing" but we can find dynamical
systems which only go so far.

that would be an interesting experiment to see what happens to the law of
large numbers if the randomness bits are correlated.

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throwaway21
I think the guy working on TempleOS is basing his concept on the idea that
computers can provide some sense of "randomness".

Not really related, but I thought it was an interesting connection.

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azth
> As a first step, we could check whether the digits 0 through 9 appeared with
> approximately equal frequency, among, say, the first million digits. Passing
> such a test is clearly necessary for randomness...

Why is that the case? This just means that the digits are uniformly
distributed. Why can't they have a different distribution and still be
"random"?

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j2kun
I think he is appealing to intuition here, where randomness means you can't
predict the next drawn value with accuracy better than uniform.

But you're right, you can draw randomly according to a different distribution.
However, if you allow any distribution in your definition of "random" then you
get the constant distributions. It's not very intuitively random anymore. So
the question becomes, how do you pick which distributions are allowed and
which aren't?

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Ono-Sendai
Kolmogorov complexity as a measure of randomness / information content has
problems in my opinion:
[http://www.forwardscattering.org/post/7](http://www.forwardscattering.org/post/7)

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j2kun
I think your contention (if you're the author of this post) is misguided. In
particular, the "languages" you define have the string hard coded in their
definition, and are hence at least as long as the string you want to encode.
In other words, your additive constant is not universal.

The definition of Kolmogorov complexity is not with regard to whatever machine
you want. You fix one and only one universal Turing machine U at the
beginning, and then you measure the Kolmogorov complexity of a string using a
different language with respect to U. Using your notation, K(x) is defined as
K_U(x), and you can relate it to K_perl(x) by K_perl(x) + |perl interpreter
written in U| = K_U(x). If you wanted to redefine all of Kolmogorov complexity
using your L_{perl, i} language, you could do that just fine, but then it's
_your bad definition_ that makes the interpretation silly.

Besides, if you pick an otherwise "random" string and single it out as being
special, doesn't that intuitively make it no longer random?

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Ono-Sendai
Thanks for the detailed reply, I'll ponder upon it and reply in a bit :)

