From: Matt Mahoney (matmahoney@yahoo.com)
Date: Fri May 02 2008 - 10:03:07 MDT
--- William Pearson <wil.pearson@gmail.com> wrote:
> 2008/5/1 Matt Mahoney <matmahoney@yahoo.com>:
> > If two symbiotic agents with unequally sized saturated memories
> > communicate, then both agents must change state at the same rate,
> > as measured by conditional algorithmic complexity.
>
> If and only if they send each other no redundant or useless
> information. Which is unlikely even between subsystems of the same
> agent.
I accounted for both in my analysis. In general, a message will be
longer than the amount of state change in the receiver. We may regard
any information from sender A that is ignored by the receiver B as
having not been communicated. If the remainder is x, then in general
|x| >= K(x) >= K(x|B(t1)) = K(B(t2)|B(t1)), x may be more redundant to
B than any intrinsic redundancy in x itself.
The most efficient distribution of information in A and B is the one
that minimizes the redundancy due to shared knowledge,
K(A)+K(B)-K(A,B). If A and B cooperate then they can achieve this by
communicating x whenever B can store it more efficiently than A, i.e.
K(x|B(t1)) < K(x|A(t2)).
> > Now suppose that A is a human and B is a calculator. This is a
> > reasonable division of labor because the calculator can do
> arithmetic
> > faster and more accurately than I can. But I can completely
> change the
> > state of the calculator's registers much faster than it can change
> me
> > into a different person. This is also the case with all nonhuman
> > agents in existence today. But if B was a superhuman AI, then the
> > situation could be reversed.
>
> No, because we are not exactly like calculators and other nonhuman
> agents. We can resist state change, as long as things don't send
> tweak
> our motivational systems as well (pain, pleasure). Just look at how
> slow academic fields are to change.
I used a calculator as an example because there is little shared
information, as in the ideal case. Another example would be a
notebook. After you write down something like a phone number, you can
forget it. After you read and memorize it, you can throw away the
note. It is your choice, of course, but having a notebook to outsource
some of your memory changes your behavior slightly vs. not having one.
Humans resist rapid change because we have a long term memory rate of
about 1 bit per second, not because we want to. Slow change still
happens.
> Do you consider the visual cortex as trying to change you to a
> "different person"? If not why not? Why is it not separate?
If you didn't have one, you would be very different.
-- Matt Mahoney, matmahoney@yahoo.com
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