On 31 May 2016, at 02:33, Russell Standish wrote:
On Mon, May 30, 2016 at 02:58:43PM +0200, Bruno Marchal wrote:
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.
He is alluding to complexity in the eye of the observer. It is related
to KCS complexity, without being identical to it, hence my follow up
comment on learning processed (quoted below).
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.
Hmm - the "output" of the UD (ie UD*) is a very low complexity
object. The complexity you refer to is actually UD* seen from the
inside by a computationlist observer. That complexity has indeed
arisen through an evolutionary process: mutation via the FPI,
?
selection via the fact that observers do not see all of the UD*,
OK.
But using the Turing equivalent view of the UD* as theorem in Robinson
(or Peano Arithmetic), you can see that such complexity exists for
aritrhmetical reason, unrelated to the observers. Indeed the view from
inside can be defined in arithmetical term thanks to such existence.
but
just one single history and heredity via the fact that only consistent
continuations count.
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.
The counting algorithm produces a simple object. Complexity is
generated by selecting some subset of that simple object, and it is
the selection which creates the complexity.
Like in quantum mechanics. But the complexity must be present before
we can observe it, and it is mathematically present, like all branches
of Everett Universal Wave.
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.
To restate above, you are confusing the complexity observed by a
putative internal observer (which by computationalism assumption must
exist), and the complexity of the UD*. The former is generated by an
evolutionary process, and high, the latter is low (being equal to the
KCS complexity of the UD).
I just use Blum complexity. It exists without the introduction of any
observer. Also, in the UD, there is no mutation, and no Darwinian
selection. Only a measure on the existing computations.
Of course, all this list is based on the idea that the overall theory
should be simple (like RA), but even without notion of observers, such
simple theory admit a rich third person theory of complexity.
The point is that such complexity can be derived from the elementary
assumptions, and we don't have to invoke physics or evolutionary
biology to get its existence. We might need to evoke evolutionary
biology to justify *our* (human) apprehension of it.
Bruno
--
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Dr Russell Standish Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Senior Research Fellow hpco...@hpcoders.com.au
Economics, Kingston University http://www.hpcoders.com.au
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