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: Draft: Introduction to optimization, published by Alex Altair on March 26, 2023 on LessWrong.

I am posting this draft as it stands today. Though I like it, it does not completely reflect my current best understanding of optimization, and is not totally polished. But I have been working on it for too long, and the world is moving too quickly. In the future, I might aggressively edit this post to become not-a-draft, or I may abandon it entirely and post a new introduction. (Unfortunately, all of the really juicy content is in other drafts that are way less developed.)

[TODO Acknowledgements, AGISF and SERI MATS]

Among the many phenomena that unfold across the universe, there is one that is not immediately evident from an inspection of the laws of physics, but which can nevertheless determine the fate of the system in which it arises. This force which guides the future is statistical in nature. But once it arises, things are not the same. The way that things will go instead is dependent on the exact nature of the force which just so happens to arise.

We will call this phenomenon optimization, which is meant in the most general of terms.

This concept of optimization has a very long and thorough history of discussion on LessWrong. This sequence is built on top of that history. But this first post is written to someone who hasn't necessarily encountered any of it before; it is largely my attempt to distill all the work that has come before. If you are familiar with the previous work, and you have questions or comments about how this framework relates to it, check out this post. [TODO link]

What and why

"Optimization" is a word used both formally and colloquially, and thus it has many uses and connotations, technical and non-technical. You may be coming to this post with one of those other meanings firmly in mind. If you are not a regular reader of LessWrong then it's pretty unlikely that the meaning in your mind matches the meaning in this sequence (though by the end of it I hope you are convinced that I've captured the intuitive notion). And if you are a regular reader of LessWrong, there are a few other concepts that you might think I mean. Take a look at this footnote for some example of what I do not mean.

What I mean by optimization

Our ultimate goal is to formalize an intuitive concept. Sometimes, you can watch something happen and just know that it's basically randomness.

And other times, you watch something and just know that something non-random is happening.

These two patterns are following the same laws of physics. And yet, the latter one is highly conspicuous. The thing that's happening is somehow unusual. Something special. The system is pushing against probability.

An example of optimization is what's called numerical optimization. If you watched a computer performing numerical optimization, you would see it finding values of a function that got closer and closer to the minimum. It might jump around a bit, but it would improve over time. You could tell that it wasn't randomly guessing. Feedback loops, both positive and negative, are other classic examples.

Another is humans. If, from some disinterested perspective, you watched a human for a while, you would see them doing many peculiar specific actions, and then occasionally some big effect would occur. From this disinterested perspective, you would see them doing things like reading a manual, and then driving to a store to pick up a oddly shaped piece of metal. It would not be evident that anything unusual was happening, until a while later, seemingly spontaneously, a huge quantity of corn grows nearby. Without an understanding of the details of the situation, you wouldn't know that they were fixing their tractor. But from the consequences, you could just tell that they had many goals in mind, many ways in w...