A followup to Contra Hoel On Aristocratic Tutoring:
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:
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Early scientists should make more (and larger) discoveries than later scientists.
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Early scientists should be relatively more likely to be amateurs; later scientists, professionals.
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Early scientists should make discoveries younger (on average) than later scientists.
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These trends should move more slowly for the most brilliant scientists.
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These trends should fail to apply in fields of science that were impossible for previous generations to practice.
Going one-by-one:
1: Early scientists should make more (and larger) discoveries than later scientists
In our model, a forager spends her day walking some distance away from camp, then foraging there. Her success depends on how far from camp she is, and how depleted the food supply is in the area she tries to exploit. For example, if she has twelve hours of daylight, she might walk for six hours, then spend six hours foraging.
The very first forager can walk zero hours, then forage a 100% virgin terrain. Suppose this is worth 100 points per hour, and she spends all twelve hours foraging. She can get 1200 points.
Suppose that as time goes on, areas immediately outside camp are 100% depleted, areas 6 hours from camp are 50% depleted, and so on. A forager might choose to walk 6 hours from camp and spend the next six hours foraging in 50% depleted terra
