On 26 Jan 2015, at 04:56, John Clark wrote:
On Sun, Jan 25, 2015 'Chris de Morsella' via Everything List <everything-list@googlegroups.com
> wrote:
> The very simple operation of defining the square root of two
generates an -- (as far as we know infinitely extending) – number
stream that is characterized by a high degree of randomness.
That would only be pseudorandom. Algorithms are deterministic, and
random means a event without a cause. There exists a short algorithm
that can produce the decimal value of digits the square root of 2 to
any desired degree of precision so it can't be random. PI also has
such a algorithm, and so does e and so does any real number you can
name, so none of them can be random.
However Turing proved in 1936 that the vast majority of numbers on
the real number line have no name and no algorithm can produce them,
or rather the only "algorithm" to produce a true random number
would be just as long as the as the number itself; for example the
only "algorithm" that could produce a sequence of truly random
digits would just be a list of those digits. That's why no program
can compress random white noise. To produce true randomness you'd
need a physical random number generator, something involving
radioactive decay or photons of light hitting a polarizing filter
would do the trick.
Turing also proved that while the computable numbers are
denumerable, that is countably infinite, the non-computable
(random) numbers belong to the next higher class of infinity.So if
you had a dart with a infinitely sharp point and threw it at the
real number line there is a 100% chance it will hit a non-computable
number and a 0% chance it will hit a computable number.
By the way I think Alan Turing was one of the giants of 20th century
science, the current movie "The Imitation Game" is about his non-
scientific but very important work breaking the German Enigma Code
during the second world war. I loved the movie.
> Now say you are an observer from a parallel universe who somehow
gets akind of sample set through some absurd imaginary portal that
deluges the poor fellow with reams upon reams of seemingly random data
By "seemingly random" I assume you mean it came from a algorithm.
Or by iterated self-duplication or self-superposition.
We cannot generate algorithmically a random sequence, but we can
generate algorithmically all random sequence, thanks to the fact that
the in the sequence
0
and
1
we already generate the correct digit "0" of the 2^aleph_zero random
sequences beginning by 0, and the correct digit "1" of the other half.
Then we proceed,
00
01
and
10
11
and we continue in that way, we generate in that way all finite
initial segments of all sequences. If we make a product of this with
the body of a person, the vast majority of those person are confronted
to a random stream, indeed, most of them algorithmically incompressible.
That is why the Universal Dovetailer generates not only the behavior
of all programs on all finite inputs, but also on the infinite input
streams.
Now, no programs can individuate itself in one computational
histories, it belongs, below its substitution level, to a continuum of
computations (with and without Oracles (in Turing sense), and that is
why we have to justify physics in term of statistics on infinities of
computations.
The miracle is that incompleteness provides the answer why there is
some physical winner, and that his trick consists on adding a phase
allowing the subtraction of the "white rabbits".
Bruno
> each one of them, let’s give it a data dimension say a KB, MB, GB
doesn’t matter, but constrained to a given chunk or window size.
These inter-dimensional data packets unfortunately arrive to our
observer in a scrambled order
How is the data stream scrambled, by another algorithm or a physical
random process such as radioactivity decay?
>The data deluge arrives for eternity… but will the recipient ever
be able to derive the function from the data.
In other words will the recipient ever be able to predict what the
next digit will be?
If you had a large enough sample and true randomness was not used
then you could at least in theory predict what the next digit will
be ( assuming you don't run up against the limit on the number of
computations the universe says can be performed in it), but if true
physical randomness was involved at any point then it would be
hopeless.
John K Clark
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