Suppose a machine at each time step outputs a 0 or a 1, then inputs a 0 or a 1
from an unknown environment.  The goal of the machine is to predict the next
input bit.

This goal is precisely defined.  It is also consistent with some popular
definitions of intelligence.  For example, if the source of bits is English
text, then there is currently no known algorithm that can score a lower error
rate than the average human.

However, this by itself is not a useful definition of intelligence.  Different
algorithms will rank differently depending on the environment.  For example,
if the action of the environment is to take the output bit b and feed back
1-b, then all algorithms will rank equally (un)intelligent.

Now consider a ranking that does not depend on a choice of environment.  Two
machines, A and B, are connected so that the output of each is connected to
the input of the other with a small delay (less than 1 time step). 
Furthermore, the connection from A to B is inverted.  Both machines try to
predict simultaneously what the other will output.  If the outputs match, then
A wins a point.  If they differ, then B wins a point.  Can we say that the
machine that wins the most points is more intelligent?


-- Matt Mahoney, [EMAIL PROTECTED]

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