On Thu, February 9, 2012 12:12 "Yuriy Milov" <qdone@xxxxxxxxxx> wrote: (01)
> Engineering and science diverge in regards of principle of openness and
> the big numbers (02)
> For science the infinite ("open") set of natural numbers (1,2,3... so on)
> is the basis of everything ... (03)
> For engineering it's vise versa: 1,2,3 and so on is simple, the 15-puzzle
> is "simplier" than the Rubik's Cube, and ...
>
> Scientific scope: ... an optimal solution is known to be NP-hard. ... (04)
> The "simple" questions devide science and engineering: (05)
> Can the infinite and open world be succesfully "represented" by finit
> number of things (even a "very-very big" number)? (06)
There is no reason to represent the "infinite and open world" for any
application. For a given application, the problem solver should define
the context, and then specify the situation and means of solution within
that context. Of course, as the solver learns more about the situation,
s/he may have to broaden the definition of the context. (07)
You can use small ontologies that are subsets of a larger ontology -- or
are defined in terms of such subsets -- and then restrict reasoning to
the selected ontology components. The reasoner need not know about
the infinite world. (08)
> What is more important - to resolve a puzzle, or to prove that the puzzle
> is NP-hard? (09)
What is more important depends on what you want to do. In most instances
people wish to solve problems, not prove mathematical properties about
them. (010)
Note that an NP-hard problem, may, for restricted input be easy to solve
rapidly. Such solutions can be used and often are. (011)
I remember taking an algorithms course ages ago, in which an NP
algorithm for solving a certain problem was more efficient than a polynomial
solution to the problem for any feasible solution. The cross-over point
only occurred after over a google operations would have been made.
[And no, i do not remember the problem or either of the solutions.] (012)
-- doug (013)
> Have fun
> Yuri (014)
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