Any sufficiently advanced technology is indistinguishable from magic.
Disproof of Clarke’s Third Law:
Suppose that it is true.
Then there exists a level of advancement such that any technology beyond there is indistinguishable from magic. Call that level “Sufficient.”
Let X be an instance either of magic or of technology Sufficiently advanced or higher.
There is a law of the universe saying that it cannot be determined which X is.
Magic may still be able to distinguish whether X is magic.
By Clarke’s Third Law, anything that can be done by magic can be done by sufficiently advanced technology.
So there must be some technology capable of telling whether X is magic. This contradicts the assumption that X is indistinguishable, and Clarke’s Third Law is therefore false.
The obvious nitpick to make is that “advanced” isn’t linear. But if Arthur Clarke thought it was OK to ignore that, I don’t feel guilty about making the same mistake. It doesn’t affect the Law much anyway.
The correct nitpick to make is about the line saying that magic could distinguish whether X is magic. After all, that violated one of the assumptions. But then you, O fictitious Internet interlocutor, are in the position of saying what magic can and can’t do. It can ignore laws of the universe; that’s sort of the definition.
I can easily imagine a Magical Black Box that distinguishes between magic and not magic, just as easily as I can imagine a Magical Black Box that does anything else. And the point of Clarke’s Third Law is that if magic can do something, there must be some technology capable of doing that, too, just without being a black box.
For a less self-referential argument, consider the speed of light. Maybe some advanced future civilization could use wormholes, warp drives, or whatever to go faster than it. But maybe they can’t. Maybe there isn’t a way around it, and it’s an actual feature of the universe that relativity can’t be beaten, not ever. Then it’s completely independent of how advanced your technology is: no matter how smart you are or what your Kardashev ranking is, you’re still limited by The Rules. (That’d suck.)
And if we live in a universe like that, then there’s totally a way to prove that something is magic: Can it teleport? If relativity always applies, and I can get from Earth to Mars in six seconds (Note: I cannot currently do this), then I’m suspending the laws of the universe.
What might be true is the converse of the Law: any sufficiently analyzed magic is indistinguishable from SCIENCE! In the example up there, being able to prove that teleportation is magic depends on already knowing that you’re in a universe where relativity is inviolate. When you see someone go from Earth to Mars in seconds, you don’t know if you’re living in that kind of universe or not. You don’t know if they’re suspending the laws of the universe or if the laws included an exception that you didn’t know about. So any time you see magic in action, you don’t know if it’s something supernatural or something natural but super.
Technically all this proves is that insufficiently analyzed magic is indistinguishable from technology. But if it’s actually on that side, if it’s actually working by ignoring laws of the universe, then no amount of analysis will let you distinguish it. (Short of magic, of course, or knowing everything about the universe and being able to prove that you do. That’s probably provably impossible to do without magic, but I don’t have a proof handy.) This is pretty much what happens every time you or I use our superpowers. Some philosophers insist that there must be a natural explanation, but whatever. I’ll just keep violating the laws of the universe; let me know if you manage to distinguish it.
Despite being false, Clarke’s Third Law is also extremely awesome. After all, most “magic” you see in fiction is just following some unusually complicated laws of physics. Producing light by saying “Lumos” may be called “magic,” and maybe nobody knows how it works, but magic works by its own set of laws and I bet you don’t know how your television works, either. In your average fantasy book, there is some way that magic works, and if it were some advanced technology, the reader usually wouldn’t notice a difference.
Case in point: Star Wars. I know everyone hates the midichlorians for pretty much precisely this reason, but the prequels did demonstrate that the Force could be unexplained mysticism or bad technobabble and it’s pretty much identical either way. Most fantasy doesn’t actually come out and say the bad technobabble, but they almost always could. (The Lord of the Rings is an explicit exception; I can’t think of many others.)
The other reason Clarke’s Third Law is awesome is its contrapositive. Any technology distinguishable from magic is INSUFFICIENTLY ADVANCED. Think of something advanced enough that you can’t distinguish between it and magic, and how cool it would be if all our technology were as advanced as, say, a human brain.
So keep using Clarke’s Third Law, just as an approximation that’s usually true instead of an enduring and unchangeable law of the universe. It’s still possible to break that law if you want to. You know, like with physics.