I have been asked several times about how the development of logical induction happened, so I am writing it up.

June 2013 - I write my first Less Wrong Post. It may not seem very related to logical uncertainty, but it was in my head. I wanted to know how to take different probabilities for the same event and aggregate them, so I could take an agent that could maintain probabilities on facts even when facts that it originally thought were separate turn out to be logically equivalent. (I am not sure if all this was in my head at the time, but it was at some point over the next year.)

I make a proposal for a distribution on completions of a theory: repeatedly observe that a set of sentences whose probabilities should sum to one fail to sum to one, and shift their probabilities in a way inspired from the above post. I do not actually prove that this process converges, but I conjecture that it converges to the distribution I describe here. (This post is from when I wrote it up in June 2014; I can't remember exactly what parts I already had at the time.)

December 2013 - I tell my proposal to Abram Demski, who at some point says that he thinks it is either wrong or equivalent to his proposal for the same problem. (He was right and his proposal was better.) At this point I got very lucky; when I told this to Abram, I thought he was just a smart person at my local Less Wrong meet up, and it turned out that he was almost the only person to also try to do the thing I was doing. Abram and I start talking about my proposal a bunch together, and start trying to prove the above conjecture.

April 2014 - Abram and I start the first MIRIx to think about logical uncertainty, and especially this proposal. I at the time had not contacted MIRI, even to apply for a workshop, because I was dumb.

At some point we realize that the proposal is bad. The thing that makes us give up on it is the fact that sometimes observing that $A \to B$ can drastically decrease your probability for $B$ .

August 2014 - Abram and I go to MIRI to talk about logical uncertainty with Nate, Benya, Eliezer, and Paul. We share the thing we were thinking about, even though we had given up on it at the time. At some point in there, we talk about assigning probability $1 / 10$ to a sufficiently late digit of $π$ being 0.

Soon after that, I propose a new project for our MIRIxLA group to work on, which I call the Benford Test. I wanted

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Productivity