On 30 May 2016, at 02:52, Russell Standish wrote:
On Sun, May 29, 2016 at 05:38:59PM +0200, Bruno Marchal wrote:
On Friday, May 27, 2016 at 3:58:11 AM UTC+10, John Clark wrote:
Richard Dawkins said "The theory of evolution by cumulative
natural selection is the only theory we know of that is, in
principle, capable of explaining the existence of organized
complexity."
This is just ridiculous. Elementary arithmetic leads to all possible
levels of complexity, from computable linear and polynomial to the
degrees of unsolvability (sigma_i, pi_i, delta_i, i = 0, 1, ...).
Some percolation process, some universal cellular automata, or
simply the Mandelbrot set, illustrate also how complexity can arise
from very simple iteration of very simple number (natural, or not)
number relations.
I am ambivalent on this. Technically, measuring complexity by means of
a Turing machine, as in Kolmogorov-Chaitin-Solomonoff complexity, an
algorithmic process such as your examples above cannot lead to an
increase of complexity.
The only way we can say that the aforementioned examples lead to an
increase in complexity is if the algorithmic process in question
remained forever cryptic to the observer measuring the complexity.
But Kolmogorov-Chaitin-Solomonoff complexity is only one sort of
complexity among many others. Here I am alluding to the program
solving complexity like the Blum measure for learning, or like the
usual P/NP and the arithmetical hierarchy. When Clark mention
organized complexity, he cannot allude to Kolmogorov complexity, but a
more structural type of complexity which can be deep, but have low
Kolmogorov complexity. Indeed, biological and mathematical complexity
is fill of redundancies making them highly compressible.
I don't any form of proof that a learning process cannot learn the
underlying algorithm of say the evolution of a Mandelbrot set.
Indeed. The DU itself is quite learnable by simple algorithm. And it
generates all the complexity of the kind we can encounter in a brain.
On the other hand, if the process involved were genuinely random, and
even your FPI satisfies this, then evolution operating on it will
generate plenty of complexity.
Such randomness plays some role for having the right measure on what
is already complex. But it does not add structural types of
complexity, (usually it can even destroy it). Structural complexity,
well even Kolmogorov complexity is already generated by the simple
counting algorithm in base 2 or bigger. The counting in base two
generates all incompressible finite and infinite strings. If that play
a role in evolution, that will play a role in arithmetic. But the
existence of such role is still speculative.
It is a reasonable hypothesis, though
by no means proven, that evolution is the only possible sort of
process that can create complexity.
It might be the only possible way carbon life could generate the
actual, relative to us human, form of bio-complexity we know. But it
should be obvious that the UD generates all life form complexity
without using carbon, even if for the bio-complexity we know, such
carbon atoms behavior will be generated itself before the biological
process is proceeded. The simulation of the Milky way, at all levels
of description, is among what the UD does, soon or later.
Bruno
Cheers
--
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Dr Russell Standish Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Senior Research Fellow [email protected]
Economics, Kingston University http://www.hpcoders.com.au
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