Re: comparing two randomizers

On Oct 10, 9:22 am, BrainDumb <vortex...@xxxxxxxxxxx> wrote:
The topic is old. If there are answer(s) somewhere, please point me
there.

At random.org, author claims 'true random numbers to anyone'. From
reading a few sources,

1. I understood it's impossible. Is it true?

2. 'True random' appears to be a well written algorithm/data source
that is harder to guess and pass most statistics tests. It seems that
a few people called it 'chaotic' to indicate complex nature of process
and intractability of the problem. So is hard to guess implies random.

3. If indeed true random was possible than I couldn't say this
algorithm was better than another. In other words, there is no degree
of quality once true randomness is achieved?

4. We are told (on wikepedia) that expansion of Pi produces random
digits. Yet there are simple series for Pi. A few years ago, a bunch
of mathematicians produced a formula that calculates any digit of Pi,
without calculating previous ones.
a. If numbers after decimal point are random, why are we able to
tell a digit with 100% accuracy. This was pointed by Dave H. in one of
the posts.
b. If expansion were random, why is there short formula. This seems
to connect w/ Wolfram's ideas.

5. In general, is it possible to produce a truly random value from a
combination of deterministic values. Somehow, I am thinking about
central limit theorem.

"random" in these circumstances
is regularly defined in a complexity-theoretic manner

complexity is a measure relative to
some computation specification language L
and in particular
the complexity_L(C) of a collection C
is defined as the length(M) of a minimal specification M in L
suchThat M produces C as output

then a collection C is said to be random
if complexity_L(C) >= |C|

for finite collections
the random ones are the incompressible collections relative to L

for infinite collections
the random ones cannot have a finite specification in L
ie. they are the "noncomputible" sequences in L

pi is not random in this definition
for any turing complete specification language L

no physical processes can ever be proven to be random

what these sites are talking about
is something that should probably be called "hopefully random"
which is only a heuristic and not in any way rigorous or sound
( in fact - for any such heuristic
it is easy to prove there will be nonrandoms
selected as random by the heuristic
the proof is also complexity-theoretic )

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=--=-=-=-
galathaea: prankster, fablist, magician, liar

.

Relevant Pages

  • Re: comparing two randomizers
    ... tell a digit with 100% accuracy. ... for finite collections ... for any turing complete specification language L ... no physical processes can ever be proven to be random ...
    (sci.math)
  • Re: comparing two randomizers
    ... tell a digit with 100% accuracy. ... ie. they are the "noncomputible" sequences in L ... claim to offer "true random numbers" ... in the sense of infinite sequences ...
    (sci.math)
  • comparing two randomizers
    ... author claims 'true random numbers to anyone'. ... 'True random' appears to be a well written algorithm/data source ... tell a digit with 100% accuracy. ... If expansion were random, ...
    (sci.math)
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