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A fun talk and paper by

that shows a very useful simple theorem in extreme value theory that should be more widely known. Also a fun application to technological growth models. dnd5e.wikidot.com/cleric:protect

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Chad Jones

@ChadJonesEcon

Jul 20, 2022

Can exponential growth occur if productivity is the best draw from a probability distribution? A video presentation (based on NBER SI) of my paper "Recipes and Economic Growth: A Combinatorial March Down an Exponential Tail." youtu.be/Bl2R63atyAE

7:46 AM · Jul 21, 2022

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The theorem is straightforward. Chad notes it is not new, but it is useful to see the link between number of draws, shape of the tail, and how the maximum behaves.

Anders Sandberg

@anderssandberg

Jul 21, 2022

The basic doubt I have is the ability to search combinatorial tech spaces: clearly we have speed-ups over random search due to knowledge and modularity, but it is not clear they will always outpace the combinatorial growth in every domain.

Anders Sandberg

@anderssandberg

Jul 21, 2022

Linking this to Bostrom's model in nickbostrom.com/papers/vulnera : if usefulness of ideas correlates with potential dangerousness, this model gives reason to think the idea danger distribution could be light-tailed (but combinatorial growth still makes danger growth fast).

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and

Not intended as that, but clearly applicable. Generally D&D probability distributions tend to be rather mild with a "fake" heavy tail ("stubby tail"?) from critical rolls.