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| Authored by: PolR on Monday, October 15 2012 @ 09:39 AM EDT |
I know. I considered saying something along these lines. But wanted to place the
discussion at a level laymen can follow as much as possible. This requires
omitting details like this one.
The point is to let people know of the difference between a formula and an
algorithm. How many algorithms can arise from a formula is not the point.
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| Authored by: Anonymous on Monday, October 15 2012 @ 03:09 PM EDT |
Had a similar thought, decided that what you're describing
is not quite the same formula. Say you want to find m. First
you solve for m, then you have a new formula that suggests a
straightforward algorithm.
m = E/C^2
In fact, even a single formula like E=mC^2 suggests more
than one algorithm. The most obvious algorithm is to follow
the Fundamental Order of Operations (PEMDAS, with left-to-
right associativity), but you could multiply m, C and C
together in any order.
In many cases a slightly less intuitive order of arithmetic
makes a big difference to performance and/or correctness.
For one thing, computers keep a finite number of significant
digits, and it's surprisingly easy to lose precision when
doing scientific calculations; doing things in a particular
order can help. For another, algorithmic improvements not
evident from the formula can make a vast difference in
performance. As a very simple example, compare calculating
the Fibonnacci sequence with and without dynamic
programming.
Finally, some formulas don't immediately suggest any
algorithm at all. For example, there are plenty of integrals
with no known exact solution. Methods of successive
approximation usually exist, but that requires applying a
whole other formula.
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