I’ve encountered some ideas that are absurdly reminiscent of predominant themes in Scott Alexander’s delightful kabbalahpunk serial novel Unsong, including Adam Kadmon and representing the infinite in the finite.







In mathematics an oracle is a black box that instantly gives the correct yes or no answer to any problem in a certain domain. These are useful e.g. when evaluating what the solution to an open problem would let you do. So a friendliness oracle could look at an AI’s source code and instantly say “Yes, friendly” or “No, not friendly.”

Furthermore, the oracle for any domain of problems whose members you can list can be expressed as a finite real number. For example, if you must go to work only on weekdays, then we can express the oracle for whether to go to work as the number 0.11111001111100…. Each digit after the decimal represents a day, starting with tomorrow (a Monday). Read this number as saying: work, work, work, work, work, rest, rest, work, work, work… and so on. To find out whether you should go to work one morning just count up to the appropriate digit and boom, you instantly know whether to go to work that day.

Of course, you don’t need an oracle for simple problems like this. You need oracles for really hard problems. And the best problem to have an oracle for is the Halting Problem, both because it’s completely impossible to solve, and because you can turn any computable problem into a halting problem. So an oracle for the Halting Problem is a magic item of almost unlimited power, granting its wielder a huge array of mental powers, like the ability to perfectly optimize any well understood system, or to prove any provable finite truth.

You can probably see where this is going.

As it turns out, the members of the halting problem are computer programs. And you can make a list of all computer programs.

Does that mean that all that stands between humanity and the semi-cosmic near-omniscience of the Halting Oracle is simply knowledge of a finite number, waiting for us somewhere between zero and one?

Turns out, yes. It’s called Chaitin’s Constant*, it’s often written as the kabbalistically ominous Ω**, and it’s the closest real life thing to the Vital Name or the Shem HaMephoresh.



We can estimate Ω out to a certain precision, but too much further is literally uncomputable. You can’t get there with any finite computer in any finite amount of time.



And yet.

And yet.

There is apparently nothing preventing you from making a lucky guess. Or being told a particularly interesting string of digits. Or hearing them in a dream.









* technically it’s a family of related constants that all have the same properties because no one can agree on a programming language no I’m not kidding.



** Chaitin also does not seem overburdened with the exigencies of modesty when writing about the importance of his work.. He went on to prove that there are facts about Ω that are necessarily simpler than any proof of them. Chaitin interpreted this to mean that these were facts which were true for no reason.