Tom McCabe wrote:
From whence do you get the idea that there is no
relationship between the low-level mechanisms and the
overall behavior? Even if the relationship is
horrendously confusing, it must exist if the entire
thing is to be described as a "system"; if there is no
relationship between the mechanisms and the overall
behavior, then the mechanisms could be destroyed by
H-Bomb and the behavior would continue unchanged, in
which case the mechanisms aren't really mechanisms. As
for the existence of a mathematically analyzable
relationship, I presume that we're talking about
systems implemented in atoms, and the physicists have
already proven that all known relations between atoms
are mathematically analyzable.
- Tom
What?!
You are missing something here: this argument is about complex systems.
It might be useful if you were to pick up some background on that
before wading in with your comments, because at the moment you are
interpreting some of the language of that field in strange ways.
Physicists, for example, make no such claim as the one you cite above.
The idea of "no relationship" between different levels of description
refers to "no practical way to solve the equations and predict high
level behavior, even if we do have the equations (or whatever) that
describe the low-level mechanisms".
Consider the set of all cellular automata like John Horton Conway's Game
of Life, for example. Define a parameter that describes the "fecundity"
of a given automaton, which is the quantity of viable, reasonably
long-lived 'creatures' that exist in each system. I bet that if I put a
few thousand examples of such systems in front of people, they would be
able to produce a subjective measure of the 'fecundity' of the various
examples.... and all I need for my purposes is that this subjective
parameter would be pretty much agreed by this group of people.
Now: can you write down a formula that would allow the 'fecundity' to
be predicted from the rules of each automaton? You must feed the rule
definition into the formula and out will pop the level of fecundity for
that system. The formula is not allowed to simulate the system: it
must be some kind of mathematical, analytic formula or algorithm that is
not equivalent to a simulation.
Such a thing is widely agreed to be a virtual impossibility. The
formula probably does not exist, and even if it did, it could easily
take more than the lifetime of the universe to find it.
When you understand the impossibility of that formula, and then the
relevance of this analogy for AGI, you'll be in the same ballpark as my
argument.
Richard Loosemore.
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