Bob Mottram wrote:
On 30/04/07, *Mike Tintner* <[EMAIL PROTECTED]
<mailto:[EMAIL PROTECTED]>> wrote:
Best example I can think of is William Calvin saying something
like: "the conscious mind is clearly designed to deal with
problematic decisions, where existing solutions won't work. The
smartest mind is the one that can find the correct answer to those
problems." Well, that's a definite self-contradiction. There is
no correct answer to problematic decisions, only a calculated gamble.
When dealing with probabilities there may be no single correct answer,
but a variety of possible answers with probabilistic weightings
assigned to them (the calculated gamble). For example, when you have
a robot navigating around using its senses the raw sense data is
always subject to some degree of noise or quantisation. Over time the
exact same sensory input could correspond to multiple possible
positions of the robot, but some will be more probable than others.
The uncertainty in sensing and the movement of the robot can be
modelled using mathematical curves called probability density
functions. Much of the time the functions used to represent the
uncertainty are gaussian ("normal") distributions, although this isn't
always the case.
More generally, in problems of a very common type (possibly several
different types) the optimal solution is computationally intractable,
even when it is precisely definable. In such cases the practical
choices are between "good enough", "almost optimal", and "not getting
the answer in time to use it". "Good enough" is frequently so much
quicker to calculate that it's the best choice for a quick reaction.
"Almost optimal" generally requires careful analysis of the problem,
which means that you had better have predicted that the problem was
going to show up ahead of time. "Optimal" is generally a very poor
choice, even for library code...though occasionally it is the best choice.
Well, reading this over it seems that "optimal" has been given a rather
poor definition, when viewed in the context of these classes of
problems, but that's the term used by my Linear Programming professor a
few decades ago. Also note that "good enough" isn't defined, but has to
be a judgment call in every particular case. A *quick* judgment call.
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