Magic and the halting problem

It is clear that the Harry Potter book series is fairly popular on this site, e.g. the fanfiction. This fanfiction approaches the existence of magic objectively and rationally. I would suggest, however, that most if not all of the people on this site would agree that magic, as presented in Harry Potter, is merely fantasy. Our understanding of the laws of physics and our rationality forbids anything so absurd as magic; it is universally regarded by most rational people as superstition.

This position can be strengthened by grabbing a stick, pointing it at some object and chanting “wingardium leviosa” and waiting for it to rise magically. When (or if) this fails to work, a proponent of magic may resort to special pleading, and claim that as we didn’t believe it would work it could not work, or that we need a special wand or that we are a squib or muggle. The proponent can perpetually move the goalposts since their idea of magic is unfalsifiable. But as it is unfalsifiable, it is rejected, in the same way that most of us on this site do not believe in any god(s). If magic were to found to explain certain phenomena scientifically, however, then I and I hope everyone else would come to believe in it, or at least shut up and calculate.

I personally subscribe to the Many Worlds Interpretation of quantum mechanics, so I effectively “believe” in the multiverse. That means it is possible that somewhere in the universal wavefunction, there is an Everett Branch in which magic is real. Or at least every time someone chants an incantation, by total coincidence, the desired effect occurs. But how would the denizens of this universe be able to know that magic is not real, and that everything they had seen was by sheer coincidence? Alan Turing pondered a related problem known as the halting problem, which asks if a general algorithm can distinguish between an algorithm that will finish or one that will run forever. He proved that one could not for all algorithms, although some algorithms will obviously finish executing or infinitely loop e.g. this code segment will loop forever:

while (true) {

//​do nothing


So how would a person distinguish between pseudo-magic that will inevitably fail, and real magic that is the true laws of physics? The only way to be certain that magic doesn’t exist in this Everett Branch would be for incantations to fail repeatedly and testably, but this may happen far into the future, long after all humans are deceased. This line of thinking leads me to wonder, do our laws of physics seem as absurd to these inhabitants as their magic seems to us? How do we know that we have the right understanding of reality, as opposed to being deceived by coincidence? If every human in this magical branch is deceived the same way, does this become their true reality? And finally, what if our entire understanding of reality, including logic, is mere deception by happenstance, and everything we think we know is false?