Scott Garrabrant’s discovery of Logical Inductors.
I remembered hearing about the paper from a friend and thinking it couldn’t possibly be true in a non-trivial sense. To someone with even a modicum of experience in logic - a computable procedure assigning probabilities to arbitrary logical statements in a natural way is surely to hit a no-go diagonalization barrier.
Logical Inductors get around the diagonalization barrier in a very clever way. I won’t spoil how it does here. I recommend the interested reader to watch Andrew’s Critch talk on Logical Induction.
It was the main reason convincing that MIRI != clowns but were doing substantial research.
The Logical Induction paper has a fairly thorough discussion of previous work. Relevant previous work to mention is de Finetti’s on betting and probability, previous work by MIRI & associates (Herreshof, Taylor, Christiano, Yudkowsky...), the work of Shafer-Vovk on financial interpretations of probability & Shafer’s work on aggregation of experts. There is also a field which doesn’t have a clear name that studies various forms of expert aggregation. Overall, my best judgement is that nobody else was close before Garrabrant.
The Antikythera artifact: a Hellenistic Computer.
You probably learned heliocentrism= good, geocentrism=bad, Copernicus-Kepler-Newton=good epicycles=bad. But geocentric models and heliocentric models are equivalent, it’s just that Kepler & Newton’s laws are best expressed in a heliocentric frame. However, the raw data of observations is actually made in a geocentric frame. Geocentric models stay closer to the data in some sense.
Epicyclic theory is now considered bad, an example of people refusing to see the light of scientific revolution. But actually, it was an enormous innovation. Using high-precision gearing epicycles could be actually implemented on a (Hellenistic) computer implicitly doing Fourier analysis to predict the motion of the planets. Astounding.
A Roman author (Pliny the Elder?) describes a similar device in posession of Archimedes of Rhodes. It seems likely that Archimedes or a close contemporary (s) designed the artifact and that several were made in Rhodes.
Actually, since we’re on the subject of scientific discoveries
Discovery & description of the complete Antikythera mechanism. The actual artifact that was found is just a rusty piece of bronze. Nobody knew how it worked. There were several sequential discoveries over multiple decades that eventually led to the complete solution of the mechanism.The final pieces were found just a few years ago. An astounding scientific achievement. Here is an amazing documentary on the subject:
I think Diffractor’s post shows that logical induction does hit a certain barrier, which isn’t quite diagonalization, but seems to me about as troublesome:
As the trader goes through all sentences, its best-case value will be unbounded, as it buys up larger and larger piles of sentences with lower and lower prices. This behavior is forbidden by the logical induction criterion… This doesn’t seem like much, but it gets extremely weird when you consider that the limit of a logical inductor, P_inf, is a constant distribution, and by this result, isn’t a logical inductor! If you skip to the end and use the final, perfected probabilities of the limit, there’s a trader that could rack up unboundedly high value!
Scott Garrabrant’s discovery of Logical Inductors.
I remembered hearing about the paper from a friend and thinking it couldn’t possibly be true in a non-trivial sense. To someone with even a modicum of experience in logic - a computable procedure assigning probabilities to arbitrary logical statements in a natural way is surely to hit a no-go diagonalization barrier.
Logical Inductors get around the diagonalization barrier in a very clever way. I won’t spoil how it does here. I recommend the interested reader to watch Andrew’s Critch talk on Logical Induction.
It was the main reason convincing that MIRI != clowns but were doing substantial research.
The Logical Induction paper has a fairly thorough discussion of previous work. Relevant previous work to mention is de Finetti’s on betting and probability, previous work by MIRI & associates (Herreshof, Taylor, Christiano, Yudkowsky...), the work of Shafer-Vovk on financial interpretations of probability & Shafer’s work on aggregation of experts. There is also a field which doesn’t have a clear name that studies various forms of expert aggregation. Overall, my best judgement is that nobody else was close before Garrabrant.
The Antikythera artifact: a Hellenistic Computer.
You probably learned heliocentrism= good, geocentrism=bad, Copernicus-Kepler-Newton=good epicycles=bad. But geocentric models and heliocentric models are equivalent, it’s just that Kepler & Newton’s laws are best expressed in a heliocentric frame. However, the raw data of observations is actually made in a geocentric frame. Geocentric models stay closer to the data in some sense.
Epicyclic theory is now considered bad, an example of people refusing to see the light of scientific revolution. But actually, it was an enormous innovation. Using high-precision gearing epicycles could be actually implemented on a (Hellenistic) computer implicitly doing Fourier analysis to predict the motion of the planets. Astounding.
A Roman author (Pliny the Elder?) describes a similar device in posession of Archimedes of Rhodes. It seems likely that Archimedes or a close contemporary (s) designed the artifact and that several were made in Rhodes.
Actually, since we’re on the subject of scientific discoveries
Discovery & description of the complete Antikythera mechanism. The actual artifact that was found is just a rusty piece of bronze. Nobody knew how it worked. There were several sequential discoveries over multiple decades that eventually led to the complete solution of the mechanism.The final pieces were found just a few years ago. An astounding scientific achievement. Here is an amazing documentary on the subject:
I think Diffractor’s post shows that logical induction does hit a certain barrier, which isn’t quite diagonalization, but seems to me about as troublesome: