From: Matt Mahoney (matmahoney@yahoo.com)
Date: Thu May 01 2008 - 16:58:37 MDT
--- William Pearson <wil.pearson@gmail.com> wrote:
> Nothing has free choice, however not all information channels have an
> equal affect on the state of the systems involved. I think it
> possible
> to create computer systems that have a symbiotic relationship, but a
> much less ability to change a human than the human does it.
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. However if by "change"
you mean the percentage of information affected, then the smaller
agent will change faster relative to its size.
Suppose that A and B are saturated agents and algorithmic complexity
K(A) > K(B). Consider a message x from A to B, where we don't count
any bits ignored by B. Then K(B(t2)|B(t1)) = K(x|B(t1)), where t1 is
the time before the message and t2 is after. A can forget x (since A
can always get it back from B), so K(A(t1)|A(t2)) = K(x|A(t2)).
By symbiotic, I mean that communication tends to minimize K(A) + K(B),
an ideal division of labor. If K(x|B(t1)) < K(x|A(t2)) (B can remember
x more easily than A could have), then B should keep x, or else send it
back.
If A and B are both saturated and symbiotic at equilibrium, then
information is conserved. Both agents must change state at the same
rate. There must be equal amounts of information flowing in each
direction because neither agent can hold any more.
This relation holds even if the agents perform lossy compression. If
one agent transmitted information faster than the other, then the other
receiver must discard some of it to make the rates equal. To
generalize the above argument, let x be the part of the message that is
not ignored by the receiver. The sender, of course, must continue to
remember the ignored part.
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.
The agents need not be symbiotic. By a simpler argument, the maximum
change K(A(t2)|A(t1)) is min(K(A), K(B)), i.e. transfer all of the
information from B to A until A is full. Then B can change A into a
different person only if K(B) >= K(A).
But given the rate of human long term memory, it would take many years.
-- Matt Mahoney, matmahoney@yahoo.com
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