Written by LW user johnswentworth.

This is part of LessWrong for EA, a LessWrong repost & low-commitment discussion group (inspired by this comment). Each week I will revive a highly upvoted, EA-relevant post from the LessWrong Archives, more or less at random

Excerpt from the post:

Claim: the usual explanation of the Scientific Method is missing some key pieces about how to make science work well in a high-dimensional world (e.g. our world). Updating our picture of science to account for the challenges of dimensionality gives a different model for how to do science and how to recognize high-value research. This post will sketch out that model, and explain what problems it solves.

The Dimensionality Problem

Imagine that we are early scientists, investigating the mechanics of a sled sliding down a slope. What determines how fast the sled goes? Any number of factors could conceivably matter: angle of the hill, weight and shape and material of the sled, blessings or curses laid upon the sled or the hill, the weather, wetness, phase of the moon, latitude and/or longitude and/or altitude, etc. For all the early scientists know, there may be some deep mathematical structure to the world which links the sled’s speed to the astrological motions of stars and planets, or the flaps of the wings of butterflies across the ocean, or vibrations from the feet of foxes running through the woods.

Takeaway: there are literally billions of variables which could influence the speed of a sled on a hill, as far as an early scientist knows.

So, the early scientists try to control as much as they can. They use a standardized sled, with standardized weights, on a flat smooth piece of wood treated in a standardized manner, at a standardized angle. Playing around, they find that they need to carefully control a dozen different variables to get reproducible results. With those dozen pieces carefully kept the same every time… the sled consistently reaches the same speed (within reasonable precision).

At first glance, this does not sound very useful. They had to exercise unrealistic levels of standardization and control over a dozen different variables. Presumably their results will not generalize to real sleds on real hills in the wild.

But stop for a moment to consider the implications of the result. A consistent sled-speed can be achieved while controlling only a dozen variables. Out of literally billions. Planetary motions? Irrelevant, after controlling for those dozen variables. Flaps of butterfly wings on the other side of the ocean? Irrelevant, after controlling for those dozen variables. Vibrations from foxes’ feet? Irrelevant, after controlling for those dozen variables.

The amazing power of achieving a consistent sled-speed is not that other sleds on other hills will reach the same predictable speed. Rather, it’s knowing which variables are needed to predict the sled’s speed. Hopefully, those same variables will be sufficient to determine the speeds of other sleds on other hills - even if some experimentation is required to find the speed for any particular variable-combination. (Full Post on LW)

Please feel free to,

11

New Comment
1 comment, sorted by Click to highlight new comments since: Today at 9:09 PM

Credit this post for bringing the LW post to my attention.