Gödel and Daemons – an excursion into literature

Explaining Gödel’s theorems to students is a pain. Period. How can those poor creatures crank their mind around a Completeness and an Incompleteness Proof… I understand that. But then, there are brave souls using Gödel’s theorems to explain the world of demons to writers, in particular to answer the question:

You can control a Demon by knowing its True Name, but why?

Very impressive.

Found at worldbuilding.stackexchange.com, pointed to me by a good friend. I dare to full quote author Cort Ammon (nothing more is known), to preserve this masterpiece. Thanks!!!!

Use of their name forces them to be aware of the one truth they can never know.

Tl/Dr: If demons seek permanent power but trust no one, they put themselves in a strange position where mathematical truisms paint them into a corner which leaves their soul small and frail holding all the strings. Use of their name suggests you might know how to tug at those strings and unravel them wholesale, from the inside out!

Being a demon is tough work. If you think facing down a 4000lb Glabrezu without their name is difficult, try keeping that much muscle in shape in the gym! Never mind how many manicurists you go through keeping the claws in shape!

I don’t know how creative such demons truly are, but the easy route towards the perfect French tip that can withstand the rigors of going to the gym and benching ten thousand pounds is magic. Such a demon might learn a manicure spell from the nearby resident succubi. However, such spells are often temporary. No demon worth their salt is going to admit in front of a hero that they need a moment to refresh their mani before they can fight. The hero would just laugh at them. No, if a demon is going to do something, they’re going to do it right, and permanently. Not just nice french tips with a clear lacquer over the top, but razor sharp claws that resharpen themselves if they are blunted and can extend or retract at will!

In fact, come to think of it, why even go to the gym to maintain one’s physique? Why not just cast a magic spell which permanently makes you into the glorious Hanz (or Franz) that the trainer keeps telling you is inside you, just waiting to break free. Just get the spell right once, and think of the savings you could have on gym memberships.

Demons that wish to become more powerful, permanently, must be careful. If fairy tales have anything to teach is, it’s that one of the most dangerous things you can do is wish for something forever, and have it granted. Forever is a very long time, and every spell has its price. The demon is going to have to make sure the price is not greater than the perks. It would be a real waste to have a manicure spell create the perfect claws, only to find that they come with a peculiar perchance to curve towards one’s own heart in an attempt to free themselves from the demon that cast them.

So we need proofs. We need proofs that each spell is a good idea, before we cast it. Then, once we cast it, we need proof that the spell actually worked intended. Otherwise, who knows if the next spell will layer on top perfectly or not. Mathematics to the rescue! The world of First Order Logic (FOL, or herefter simply “logic”) is designed to offer these guarantees. With a few strokes of a pen, pencil, or even brush, it can write down a set of symbols which prove, without a shadow of a doubt, that not only will the spell work as intended, but that the side effects are manageable. How? So long as the demon can prove that they can cast a negation spell to undo their previous spell, the permanency can be reverted by the demon. With a few more fancy symbols, the demon can also prove that nobody else outside of the demon can undo their permanency. It’s a simple thing for mathematics really. Mathematics has an amazing spell called reductio ad infinitum which does unbelievable things.

However, there is a catch. There is always a catch with magic, even when that magic is being done through mathematics. In 1931, Kurt Gödel published his Incompleteness Theorems. These are 3 fascinating works of mathematical art which invoke the true names of First Order Logic and Set Theory. Gödel was able to prove that any system which is powerful enough to prove out all of algebra (1 + 1 = 2, 2 + 1 = 3, 3 * 5 = 15, etc.), could not prove its own validity. The self referential nature of proving itself crossed a line that First Order Logic simply could not return from. He proved that any system which tries must pick up one of these five traits:

• Incomplete – they missed a detail when trying to prove everything
• Incorrect – They got everything, but at least one point is wrong
• Unprovable – They might be right, but they can never prove it
• Intractable – If you’re willing to sit down and write down a proof that takes longer than eternity, you can prove a lot. Proofs that fit into eternity have limits.
• Illogical – Throw logic to the wind, and you can prove anything!

If the demon wants itself to be able to cancel the spell, his proof is going to have to include his own abilities, creating just the kind of self referential effects needed to invoke Gödel’s incompleteness theorems. After a few thousand years, the demon may realize that this is folly.

A fascinating solution the demon might choose is to explore the “incomplete” solution to Gödel’s challenge. What if the demon permits the spell to change itself slightly, but in an unpredictable way. If the demon was a harddrive, perhaps he lets a single byte get changed by the spell in a way he cannot expect. This is actually enough to sidestep Gödel’s work, by introducing incompleteness. However, now we have to deal with pesky laws of physic and magics. We can’t just create something out of nothing, so if we’re going to let the spell change a single byte of us, there must be a single byte of information, its dual, that is unleashed into the world. Trying to break such conservation laws opens up a whole can of worms. Better to let that little bit go free into the world.

Well, almost. If you repeat this process a whole bunch of times, layering spells like a Matryoska doll, you’re eventually left with a “soul” that is nothing but the leftover bits of your spells that you simply don’t know enough about to use. If someone were collecting those bits and pieces, they might have the undoing of your entire self. You can’t prove it, of course, but its possible that those pieces that you sent out into the world have the keys to undo your many layers of armor, and then you know they are the bits that can nullify your soul if they get there. So what do you do? You hide them. You cast your spells only on the darkest of nights, deep in a cave where no one can see you. If you need assistants, you make sure to ritualistically slaughter them all, lest one of them know your secret and whisper it to a bundle of reeds, “The king has horns,” if you are familiar with the old fairy tale. Make it as hard as possible for the secret to escape, and hope that it withers away to nothingness before someone discovers it, leaving you invincible.

Now we come back to the name. The demon is going to have a name it uses to describe its whole self, including all of the layers of spellcraft it has acquired. This will be a great name like Abraxis, the Unbegotten Father or “Satan, lord of the underworld.” However, they also need to keep track of their smaller self, their soul. Failure to keep track of this might leave them open to an attack if they had missed a detail when casting their spells, and someone uncovered something to destroy them. This would be their true name, potentially something less pompous, like Gaylord Focker or Slartybartfarst. They would never use this name in company. Why draw attention to the only part of them that has the potential to be weak.

So when the hero calls out for Slartybartfarst, the demon truly must pay attention. If they know the name the demon has given over the remains of their tattered soul, might they know how to undo the demon entirely? Fear would grip their inner self, like a child, having to once again consider that they might be mortal. Surely they would wish to destroy the hero that spoke the name, but any attempt runs the risk of falling into a trap and exposing a weakness (surely their mind is racing, trying to enumerate all possible weaknesses they have). It is surely better for them to play along with you, once you use their true name, until they understand you well enough to confidently destroy you without destroying themselves.

So you ask for answers which are plausible. This one needs no magic at all. None of the rules are invalid in our world today. Granted finding a spell of perfect manicures might be difficult (believe me, some women have spent their whole life searching), but the rules are simply those of math. We can see this math in non-demonic parts of society as well. Consider encryption. An AES-256 key is so hard to brute force that it is currently believed it is impossible to break it without consuming 3/4 of the energy in the Milky Way Galaxy (no joke!). However, know the key, and decryption is easy. Worse, early implementations of AES took shortcuts. They actually left the signature of the path they took through the encryption in their accesses to memory. The caches on the CPU were like the reeds from the old fable. Merely observing how long it took to read data was sufficient to gather those reeds, make a flute, and play a song that unveils the encryption key (which is clearly either “The king has horns” or “1-2-3-4-5” depending on how secure you think your luggage combination is). Observing the true inner self of the AES encryption implementations was enough to completely dismantle them. Of course, not every implementation fell victim to this. You had to know the name of the implementation to determine which vulnerabilities it had, and how to strike at them.

Or, more literally, consider the work of Alfred Whitehead, Principia Mathematica. Principia Mathematica was to be a proof that you could prove all of the truths in arithmetic using purely procedural means. In Principia Mathematica, there was no manipulation based on semantics, everything he did was based on syntax — manipulating the actual symbols on the paper. Gödel’s Incompleteness Theorem caught Principia Mathematica by the tail, proving that its own rules were sufficient to demonstrate that it could never accomplish its goals. Principia Mathematica went down as the greatest Tower of Babel of modern mathematical history. Whitehead is no longer remembered for his mathematical work. He actually left the field of mathematics shortly afterwards, and became a philosopher and peace advocate, making a new name for himself there.

(by Cort Ammon)