Consider the following experiment...
On a computer we generate a million numbers at random, and we write a
program that tests whether the numbers are stored in ascending order, and if
not causes the experimenter to be killed.
A device that measures the polarisation of photons from a light source is
used to generate a random bit string, stored on the computer to be executed
as a program to attempt an in-place sort of the million numbers. After the
program terminates (by executing a HALT instruction) the test procedure is
run to validate the program.
Assuming QTI the experimenter will always find that a "sorting algorithm"
was generated. Often this will work on *any* list of numbers - not just the
one that it was "trained" on.
An interesting question is whether there will be a tendency to discover
short and concise algorithms. In any case, the experiment could be repeated
many times to allow the experimenter to seek short programs - by giving it
less space to work in.
Some really difficult problems could be solved with this technique - eg
"Find a proof to ...", and the test code simply validates the line of
Evidently QTI gives the experimenter the equivalent computing power of a
Quantum computer. ie exponential order problems can be solved in linear
Perhaps the US should build such a machine, making use of its nuclear
arsenal so the whole world can share in the benefits of such enormous
computing power [tongue in cheek].
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