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: 3C's: A Recipe For Mathing Concepts, published by johnswentworth on July 3, 2024 on LessWrong.

Opening Example: Teleology

When people say "the heart's purpose is to pump blood" or "a pencil's function is to write", what does that mean physically? What are "purpose" or "function", not merely in intuitive terms, but in terms of math and physics? That's the core question of what philosophers call teleology - the study of "telos", i.e. purpose or function or goal.

This post is about a particular way of approaching conceptual/philosophical questions, especially for finding

"True Names" - i.e. mathematical operationalizations of concepts which are sufficiently robust to hold up under optimization pressure. We're going to apply the method to teleology as an example. We'll outline the general approach in abstract later; for now, try to pay attention to the sequence of questions we ask in the context of teleology.

Cognition

We start from the subjective view: set aside (temporarily) the question of what "purpose" or "function" mean physically. Instead, first ask what it means for me to view a heart as "having the purpose of pumping blood", or ascribe the "function of writing" to a pencil. What does it mean to model things as having purpose or function?

Proposed answer: when I ascribe purpose or function to something, I model it as having been optimized (in the sense

usually

used

on LessWrong) to do something. That's basically the standard answer among philosophers, modulo expressing the idea in terms of the LessWrong notion of optimization.

(From there, philosophers typically ask about "original teleology" - i.e. a hammer has been optimized by a human, and the human has itself been optimized by evolution, but where does that chain ground out? What optimization process was not itself produced by another optimization process? And then the obvious answer is "evolution", and philosophers debate whether all teleology grounds out in evolution-like phenomena.

But we're going to go in a different direction, and ask entirely different questions.)

Convergence

Next: I notice that there's an awful lot of convergence in what things different people model as having been optimized, and what different people model things as having been optimized for.

Notably, this convergence occurs even when people don't actually know about the optimization process - for instance, humans correctly guessed millenia ago that living organisms had been heavily optimized somehow, even though those humans were totally wrong about what process optimized all those organisms; they thought it was some human-like-but-more-capable designer, and only later figured out evolution.

Why the convergence?

Our everyday experience implies that there is some property of e.g. a heron such that many different people can look at the heron, convergently realize that the heron has been optimized for something, and even converge to some degree on which things the heron (or the parts of the heron) have been optimized for - for instance, that the heron's heart has been optimized to pump blood.

(Not necessarily perfect convergence, not necessarily everyone, but any convergence beyond random chance is a surprise to be explained if we're starting from a subjective account.) Crucially, it's a property of the heron, and maybe of the heron's immediate surroundings, not of the heron's whole ancestral environment - because people can convergently figure out that the heron has been optimized just by observing the heron in its usual habitat.

So now we arrive at the second big question: what are the patterns out in the world which different people convergently recognize as hallmarks of having-been-optimized? What is it about herons, for instance, which makes it clear that they've been optimized, even before we know all the details of the optimizati...