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 reasoning. Evidently QTI gives the experimenter the equivalent computing power of a Quantum computer. ie exponential order problems can be solved in linear time. 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]. - David --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com). Version: 6.0.797 / Virus Database: 541 - Release Date: 11/15/2004