Scott Alexander on the argument from low-hanging fruit [stagnation, redux]

Scott Alexander, The Low-Hanging Fruit Argument: Models And Predictions, Astral Codex Ten, April 1, 2022.

It begins:

Imagine scientists venturing off in some research direction. At the dawn of history, they don’t need to venture very far before discovering a new truth. As time goes on, they need to go further and further.

Actually, scratch that, nobody has good intuitions for truth-space. Imagine some foragers who have just set up a new camp. The first day, they forage in the immediate vicinity of the camp, leaving the ground bare. The next day, they go a little further, and so on. There’s no point in traveling miles and miles away when there are still tasty roots and grubs nearby. But as time goes on, the radius of denuded ground will get wider and wider. Eventually, the foragers will have to embark on long expeditions with skilled guides just to make it to the nearest productive land.

Let’s add intelligence to this model. Imagine there are fruit trees scattered around, and especially tall people can pick fruits that shorter people can’t reach. If you are the first person ever to be seven feet tall, then even if the usual foraging horizon is very far from camp, you can forage very close to camp, picking the seven-foot-high-up fruits that no previous forager could get. So there are actually many different horizons: a distant horizon for ordinary-height people, a nearer horizon for tallish people, and a horizon so close as to be almost irrelevant for giants.

Finally, let’s add the human lifespan. At night, the wolves come out and eat anyone who hasn’t returned to camp. So the the maximum distance anyone will ever be able to forage is a day’s walk from camp (technically half a day, so I guess let’s imagine that everyone can teleport back to camp whenever they want).

This model can explain some otherwise confusing observations about the history of science:

1. Early scientists should make more (and larger) discoveries than later scientists.
2. Early scientists should be relatively more likely to be amateurs; later scientists, professionals.
3. Early scientists should make discoveries younger (on average) than later scientists.
4. These trends should move more slowly for the most brilliant scientists.
5. These trends should fail to apply in fields of science that were impossible for previous generations to practice.

Scott then goes on to elaborate on each of those five.

I've presented a somewhat more abstract version of this argument that takes a 1992 article by Paul Romer, Two Strategies for Economic Development (gated), as its point of departure: Stagnation, Redux: It’s the way of the world [good ideas are not evenly distributed, no more so than diamonds]. That blog post makes up the second part of my working paper, What economic growth and statistical semantics tell us about the structure of the world, August 24, 2020, 19 pp, https://www.academia.edu/43938531/What_economic_growth_and_statistical_semantics_tell_us_about_the_structure_of_the_world.

Here's the abstract from that working paper:

The metaphysical structure of the world, as opposed to its physical structure, resides in the relationship between our cognitive capacities and the world itself. Because the world itself is "lumpy, rather than "smooth" (as developed herein, but akin to "simple" vs. "complex"), it is learnable and hence livable. Machine learning AI engines, such as GPT-3, are able to approximate the semantic structure of language, to the extent that that structure can be modeled in a high-dimensional space. That structure ultimately depends on the fact that the world is lumpy. It is the lumpiness that is captured in the statistics. Similarly, I argue, the American economy has entered a period of stagnation because the world is lumpy. In such a world good "ideas" become more and more difficult to find. Stagnation then reflects the increasing costs the learning required to develop economically useful ideas.