Magic and the halting problem

by kingmaker2 min read23rd Aug 201511 comments

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Personal Blog

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?

 

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Answer this question first: Why aren't compasses magic? They are dead objects that move on their own power to point in the same direction no matter where you take them.

Why isn't gravity magic? It's action at a distance.

Why isn't fire magic? It sure must have seemed like magic a thousand years ago.

Somehow, people knew enough not to call these things magic long before we had any explanation for them. Part of the definition of magic seems to include not existing, or not being demonstrable and repeatable.

Let me make a simpler form of this problem. Suppose I flip a fair coin a thousand times, and it just happens to land on heads every time. How do I find out that this is a fair coin, and that I don't actually have a trick coin that always lands on heads? The answer is that I can't. Any algorithm that tells me that it's fair is going to fail in the much more likely circumstance that I have a coin that always lands on heads. The best I can do is show that I have 1000 bits of evidence in favor of a trick coin, update my priors accordingly, and use this information when betting.

The good news is that you will only get a coin that lands on heads a thousand times about 00.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 0000000000000000000933% of the time, so you won't be this wrong by chance very often. In general, you can calculate how likely you are to be wrong, and hedge your bets accordingly.

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.

Nope. The laws of physics are the same in all branches.

Or at least every time someone chants an incantation, by total coincidence, the desired effect occurs.

Those branches would be extremely rare.

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.

I don't find it very obvious how this is related.

So how would a person distinguish between pseudo-magic that will inevitably fail, and real magic that is the true laws of physics?

The pseudo-magic will with large probability fail the next time you test it.

And finally, what if our entire understanding of reality, including logic, is mere deception by happenstance, and everything we think we know is false?

Then you would find out very soon, unless you postulate something to keep the system stable.

Nope. The laws of physics are the same in all branches.

The laws of physics are the same (in MWI, not other multiverse theories.) But there could be a universe where the are are advanced aliens with nanotech, which for some reason decide to mimic magic exactly. Or where, mysteriously, every time someone says "wingardium leviosa", objects happen to levitate, just by chance of random quantum effects.

I do think that both of these universes are so unlikely we shouldn't worry about ever being in them. But I think that is what OP is getting at.

I think that the first universe is sufficiently more likely than the second that you shouldn't assume it's a coincidence, and you should expect wingardium leviosa to keep working.

I agree, but I think OP is referring to the second situation. He's not saying that it's probable, just that it's possible and we can't ever rule it out. These issues go away when you internalize probability, but I understand how people can be confused on issues like this.

[-][anonymous]6y 0

From a Bayesian perspective, it seems very unlikely to be living in such a world.

This line of inquiry is very weird. To address this you'd have to define what you mean by "magic". I believe in this community they call this the "TabbooGame". It's a game where you tabboo the word "magic".

After you tabboo the word magic, then you're just asking if it's possible for laws of physics to exist where you dress as a wizard and wave sticks. It's definitely not possible in our world because I tried and never got any superpowers (damn!!). It's "possible" but it's very lazy for a law of physics for something so complex as dressing as a wizard and waving sticks to exist. [slander against anime and Harry Potter].

Downmodded for the gratuitous anime slam.

Also, I have never heard of a magic system where the magic depends on wearing wizard robes. It's true that wizards are associated with robes, but there's no law of physics which connects robes and spells any more than there is one which connects white coats and being a doctor.

I have never heard of a magic system where the magic depends on wearing wizard robes.

I put on my robe and wizard hat... X-D

It's definitely not possible in our world because I tried and never got any superpowers (damn!!).

Most children trying to do the same proof you did would get the same result in the Harry Potter universe. It's fairly bad as far as a proof goes.