Tag Archives: halloween

An AI Apocalypse, but Just for You

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For Halloween, I like to talk about spooky scenarios. And these days, the most trendy one is an AI apocalypse.

You can run into a wild range of ideas for how AI could go wrong, of varying plausibility. They go from hacks shutting down key infrastructure or engineered viruses, to taking over nuclear arsenals and sending out armies of killer robots, all the way to nanotech that devours the world and flawlessly manipulative plans that end up filling space with computers simulating hell at the speed of light.

And of course, on the other end, the possibility that banks suddenly become convinced that the investments underpinning AI companies’ trillion dollar evaluations aren’t going to pay, collapsing the economy.

So, lots of things to be scared of this year!

But in all of those scenarios, at least we suffer together. If civilization cracks like an egg, everyone who survives has to adapt and figure out a new path forward. And if everyone’s dead, well, everyone’s dead. There’s something oddly comforting about that.

That’s not guaranteed, though.

I occasionally see quotes from “100+ reactions to 100+ solutions”, a compilation of thoughts by mathematicians about OpenAI’s recent claim to have solved hundreds of difficult open problems in mathematics. For the most part, these people aren’t writing about an AI apocalypse that sweeps civilization into a new form. They’re writing about what AI seems to be capable of in mathematics, right now, and wondering how they personally will withstand it.

Picture a world where you’ve defined yourself around something. Maybe you’re competitive, someone who wants to be the best in the world. Maybe you just want something of your own, accomplishments that came from you, not anyone else. Either way, it’s something you love, something you chose a strange and difficult path to pursue.

Then, that identity falls apart. For the competitive, you’re not the best anymore, not at the kind of thing you were doing, you’ll never be the best at that again. For the rest, your sense of ownership is less secure. Someone could hear about that problem you’re tinkering with, decide to tackle it on a whim, and jump so far ahead that you’d never be able to catch up on your own merits.

And if there isn’t a wider collapse, you’re facing this on your own. You might have to find a new job, though in a world where universities still need math classes that seems unlikely. But you will have to find a new purpose. You’d have to become a different kind of mathematician, at minimum, one more dedicated to something the AI can’t do and less dedicated to the things that happened to define your style of mathematics. Your friends in other fields will never quite understand. Your friends outside of academia will understand even less.

If we thread the needle between the apocalypses of powerful AI and an economic bubble that pops so hard that companies can’t host the models anymore, we end up with a series of quieter, more personal AI apocalypses, people who feel like their own world is ending, and have to figure out how to go on. For now, that’s the possibility many mathematicians are considering. We’ll see how many others consider it in the years to come.

I Ain’t Afraid of No-Ghost Theorems

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In honor of Halloween this week, let me say a bit about the spookiest term in physics: ghosts.

In particle physics, we talk about the universe in terms of quantum fields. There is an electron field for electrons, a gluon field for gluons, a Higgs field for Higgs bosons. The simplest fields, for the simplest particles, can be described in terms of just a single number at each point in space and time, a value describing how strong the field is. More complicated fields require more numbers.

Most of the fundamental forces have what we call vector fields. They’re called this because they are often described with vectors, lists of numbers that identify a direction in space and time. But these vectors actually contain too many numbers.

These extra numbers have to be tidied up in some way in order to describe vector fields in the real world, like the electromagnetic field or the gluon field of the strong nuclear force. There are a number of tricks, but the nicest is usually to add some extra particles called ghosts. Ghosts are designed to cancel out the extra numbers in a vector, leaving the right description for a vector field. They’re set up mathematically such that they can never be observed, they’re just a mathematical trick.

Mathematical tricks aren’t all that spooky (unless you’re scared of mathematics itself, anyway). But in physics, ghosts can take on a spookier role as well.

In order to do their job cancelling those numbers, ghosts need to function as a kind of opposite to a normal particle, a sort of undead particle. Normal particles have kinetic energy: as they go faster and faster, they have more and more energy. Said another way, it takes more and more energy to make them go faster. Ghosts have negative kinetic energy: the faster they go, the less energy they have.

If ghosts are just a mathematical trick, that’s fine, they’ll do their job and cancel out what they’re supposed to. But sometimes, physicists accidentally write down a theory where the ghosts aren’t just a trick cancelling something out, but real particles you could detect, without anything to hide them away.

In a theory where ghosts really exist, the universe stops making sense. The universe defaults to the lowest energy it can reach. If making a ghost particle go faster reduces its energy, then the universe will make ghost particles go faster and faster, and make more and more ghost particles, until everything is jam-packed with super-speedy ghosts unto infinity, never-ending because it’s always possible to reduce the energy by adding more ghosts.

The absence of ghosts, then, is a requirement for a sensible theory. People prove theorems showing that their new ideas don’t create ghosts. And if your theory does start seeing ghosts…well, that’s the spookiest omen of all: an omen that your theory is wrong.