Bingo. You took the words out of my mouth, er, the concepts out of my
skull, or something like that.
Similarly, quantum computers (or analog) computers can require elaborate
mechanisms to yield digital results. So, for some problems, a quantum
computer may take only a few steps where a digital computer may require,
say, 10^15 steps, yet a digital computer may require only 10^4 steps (ok,
maybe 10^6) to balance my checkbook, where a quantum computer might require,
say, 10^12 steps.
There's a class of problems that are easily solved by digital methods, a
class easily solved by analog methods, and there will be a class of problems
easily solved by quantum methods, and a class easily solved by genetic
methods. All of which can be solved by other classes of methods, with
enough time and resources (the question of resource existance is beyond the
scope of this e-mail).
Some problems clearly fit into particular classes. Others fit in multiple
classes. Future mathematicians/information scientists/whoever will figure
out how to classify--and solve--other problems. It is not obvious to me how
a number factoring problem can be solvable with a quantum computer, but I've
done enough high level math to know that weirder things have been
discovered, and I have a vague sense that the regularity of the problem
(i.e., a prime # cannot be divided by any other prime number less than the
square root of it) could tie in with wave functions.
The classification scenario is sort of like NP-complete problems. One way
of catagorizing algorithms is as to whether they can be solved in polynomial
time (i.e., as more variables are added, the time/steps to solve it
increases as a polynomial function), or non-polynomial time (i.e., time
increases exponentially).
The classic traveling salesman problem (i.e., find the shortest path
visiting x nodes, each only once) is non-polynomial since the number of
steps increase exponentially with the number of nodes. However, it is
amenable to genetic techniques which involve billions & billions of tagged
DNA sequences floating around in a soup, linking up in billions of ways, one
of which represents the best possible solution.
I cannot imagine balancing my check book with a genetic technique (well,
maybe my checkbook before my wife took over the bookkeeping, but sort of
thing has been discussed in the Hitchhiker's Guide to the Universe.)
Anyway,....it's all very fascinating, but it still seems like quite a
stretch to say that quantum computation techniques proves a multiworld
universes.
Grace & peace,
Dennis Sweitzer