Suppose you have two designs for a system. Both have the same amount of
energy. System 1 duplicates all data, whereas system 2 does not. Clearly,
system 2 will have twice as much capacity for data, although not
necessarily twice as much usefulness. (Both systems would prioritize
resource usage to store the most valuable data first, and therefore system
2's second half would have less value its first, which should be the same
as system 1's total.)
I'm no statistician, but you can figure it out mathematically. You want the
system with the greatest total value over the systems' anticipated
lifespan. The value would be a sum of the values of each datum stored
successfully at each instant in time. If you can figure out the value of
each datum, and the probability of it being destroyed at a given moment,
then you can integrate to get the total value of the system. Better still,
you might find that SOME data is worth duplicating, and some is not. There
would probably be a series of variable "value thresholds", above which
everything is duplicated, triplicated, or more. But how to place a value on
the ability to answer "4" when the question is "2+2"?
I doubt that we have the faintest idea at this time how to measure the
risks, benefits or even the anticipated lifetime in the case of a
super-intelligent system. The very thought of trying to work the equation
out makes me long for the day when I need to make the choice. I never did
get the hang of Calculus. Corporations face the same problem regularly, and
the skill and judgement of the board in approximating these and other
variables is an important part of what determines how much profit they make.
Still, it's fun to speculate.
Regards,
Darren