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Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Most problems don't differ dramatically in tractability (under certain assumptions), published by Thomas Kwa on May 4, 2022 on The Effective Altruism Forum. Sometimes I hear discussions like the following: Amy: I think Cause A is 300x larger in scale than Cause B. Bernard: I agree, but maybe we should put significant resources towards Cause B anyway, because cause A might be 100x less tractable. According to the ITN framework, we should put 1/3x the resources towards cause B as we do towards cause A. Causes can easily be 300x larger in scale than other causes. But I think Bernard's claim that Cause B is 100x more tractable is actually very strong. I argue that Bernard must be implicitly claiming that cause B is unusually tractable, that there is a strong departure from logarithmic returns, or that there is no feasible plan of attack for cause A. Review of the ITN framework Recall the importance-tractability-neglectedness (ITN) framework for estimating cost-effectiveness: Importance = utility gained / % of problem solved Tractability = % of problem solved / % increase in resources Neglectedness = % increase in resources / extra $ The product of all three factors gives us utility gained / extra $, the cost-effectiveness of spending more resources on the problem. By replacing $ with another resource like researcher-hours, we get the marginal effectiveness of adding more of that resource. In the 80,000 Hours page on ITN, scale ranges 8 orders of magnitude, neglectedness 6 orders of magnitude, and tractability (which 80k calls solvability) only 4. In practice, I think tractability actually only spans around 2-3 orders of magnitude for problems we spend time analyzing, except in specific circumstances. Problems have similar tractability under logarithmic returns Tractability is defined as the expected fraction of a given problem that would be solved with a doubling of resources devoted to that problem. The ITN framework suggests something like logarithmic returns: each additional doubling will solve a similar fraction of the problem, in expectation. Let the "baseline" level of tractability be a 10% chance to be solved with one doubling of resources. For a problem to be 10x less tractable than the baseline, it would have to take 10 more doublings (1000x the resources) to solve an expected 10% of the problem. Most problems that can be solved in theory are at least as tractable as this; I think with 1000x the resources, humanity could have way better than 10% chance of starting a Mars colony, solving the Riemann hypothesis, and doing other really difficult things. For a problem to be 10x more tractable than the baseline, it would be ~100% solved by doubling resources. It's rare that we find an opportunity more tractable than this that also has reasonably good scale and neglectedness. Therefore, if we assume logarithmic returns, most problems under consideration are within 10x of the tractability baseline, and thus fall within a 100x tractability range. When are problems highly intractable? The three outstanding problems in physics, in a certain sense, were never worked on while I was at Bell Labs. By important I mean guaranteed a Nobel Prize and any sum of money you want to mention. We didn't work on (1) time travel, (2) teleportation, and (3) antigravity. They are not important problems because we do not have an attack. -- Richard Hamming Some problems are highly intractable. In this case, one of the following is usually true: There is a strong departure from logarithmic returns, making the next doubling in particular unusually bad for impact. Some problems have an inherently linear structure: there are not strong diminishing returns to more resources, and you can basically pour more resources into the problem until you've solved it. Suppose your problem is a huge pile of tr...