def: oracle: see http://en.wikipedia.org/wiki/Oracle_machine Question: wouldn't an oracle violate the law of conservation of energy or second law of thermodynamics, by creating a device similar to the Maxwell Demon? In other words, would being able to get information without actually computing it or acquiring it experimentally violate the second law (or first)? Note that "computing it" or "acquiring it" are correlated but different, in the first case you could use the oracle, for example, in this way: you measure position and velocity of all the molecules, then you use the oracle to "cheat compute" their new positions and velocities without actually spending a bit of energy. In the second case, you don't even care of measuring the initial conditions of the experiment, you just ask the oracle what you need (this would be a "physical oracle"). As far as I know, it seems to me that the answer is positive: oracles cannot exist in this universe, as we know it, (i.e. with the current laws that we know). From Wikipedia Maxwell demon: """Szilárd pointed out that a real-life Maxwell's demon would need to have some means of measuring molecular speed, and that the act of acquiring information would require an expenditure of energy. Since the demon and the gas are interacting, we must consider the total entropy of the gas and the demon combined. The expenditure of energy by the demon will cause an increase in the entropy of the demon, which will be larger than the lowering of the entropy of the gas. [...] In 1982, Bennett showed that, however well prepared, eventually the demon will run out of information storage space and must begin to erase the information it has previously gathered. Erasing information is a thermodynamically irreversible process that increases the entropy of a system. Although Bennett had reached the same conclusion as Szilard’s 1929 paper, that a Maxwellian demon could not violate the second law because entropy would be created, he had reached it for different reasons."""