MichaelDickens's Shortform

by MichaelDickens24th Sep 20202 comments
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"Are Ideas Getting Harder to Find?" (Bloom et al.) seems to me to suggest that ideas are actually surprisingly easy to find.

The paper looks at the difficulty of finding new ideas in a variety of fields. It finds that in all cases, effort on finding new ideas is growing exponentially over time, while new ideas are growing exponentially but at a lower rate. (For a summary, see Table 7 on page 31.) This is framed as a surprising and bad thing.

But it actually seems surprisingly good to me. My intuition is that the number of ideas should grow logarithmically with effort, or possibly even sub-logarithmically. If effort is growing exponentially, we'd expect to see linear or sub-linear growth in ideas. But instead we see exponential growth in ideas.

I don't have a great understanding of the math used in this paper, so I might be misinterpreting something.

Bloom et al. do report exponential growth of various metrics, but I don't think these metrics are well-characterized by 'ideas'. They are things like price-performance of transistors or crop yields per area.

If we instead attempt to measure progress by something like 'number of ideas', there is some evidence in favor of your guess that "ideas should grow logarithmically with effort". E.g., in a review of the 'science of science', Fortunato et al. (2018) say (emphases mine):

Early studies discovered an exponential growth in the volume of scientific literature, a trend that continues with an average doubling period of 15 years. Yet, it would be naïve to equate the growth of the scientific literature with the growth of scientific ideas. [...] Large-scale text analysis, using phrases extracted from titles and abstracts to measure the cognitive extent of the scientific literature, have found that the conceptual territory of science expands linearly with time. In other words, whereas the number of publications grows exponentially, the space of ideas expands only linearly.

Bloom et al. also report a linear increase in life expectancy in sc. 6. I vaguely remember that there are many more examples where exponential growth becomes linear once evaluated on some other 'natural' metrics, but I don't remember where I saw them. Possibly in the literature on logarithmic returns to science. Let me know if it'd be useful if I try to dig up some references.

ETA: See e.g. here, number of known chemical elements. Possibly there are more example in that SSC post.