Dear AGI,

What is the maximal complexity of an environment in which prediction of future 
events in the environment is still computationally feasible?

In most 'realistic' environments prediction of the near future needs to be 
very precise and prediction of the far future can be vaguer, i.e. a large 
class of event types satisfies the prediction, in order for an agi agent to 
achieve its goals. (If prediction on the very long term also needs to be 
detailed and precise the environment is impossible for any agent, not?). 

In a formula, :
(maximal vagueness of prediction that is allowed by agi agent, in order to 
plan and act successful to achieve goals) / (time scale of horizon of 
prediction) =  some constant.

Vagueness of prediction is the number of perception event types that satify 
the prediction. (count the perception event types at bit level).

somewhat equivalent formula:
(number of patterns of about time length l that occur in the environment) / 
(about l) =  some constant

A pattern here is a class of noisy variations on a pattern (10% noise, 20% 
noise? The smaller the constant gets the higher the noise ratio can be.).

How large can those constants be? How complex may the environment be maximally 
for an ideal, but still realistic, agi agent (thus not a solomonof or AIXI 
agent) to be still succesful? Does somebody know how to calculate (and 
formalise) this?

Bye,
Arnoud


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