I'm pretty sure I know the meaning (or at least, so to speak, the structure of the meaning) of the phrase in TWC. Imagine first of all that you have some process that generates energy (from some source, such as the fusion of hydrogen into helium) and that's just about self-sustaining. Now, suppose you can arrange for some small fraction of the energy that was being generated and radiated out into the world (in, as is the habit of light, straight lines) to be fed back into the system (so it goes around "in a circle" instead). Then the energy content of that system will build up: slowly at first, but at an increasing rate. Eventually it'll go boom. Initially-small change, positive feedback, large eventual result.
Does this have any connection with the intro to HPMOR? For what it's worth, I'm guessing not. (Except that maybe that phrase was drifting around in Eliezer's unconscious and influenced his exact choice of wording.) It's by no means impossible, but without the extra context in TWC I don't think there's any way for "a fraction of a line" to be interpreted to mean anything like "a fraction of something that would have been radiated outward, instead captured to produce positive feedback", so it would be (so to speak) quite unfair. I expect that whatever the "fraction of a line" before HPMOR chapter 1 is, it can at least be described briefly to people without a mathematics/science/engineering background in such a way that "a fraction of a line" makes sense.
The next discussion thread is here.
This is a new thread to discuss Eliezer Yudkowsky’s Harry Potter and the Methods of Rationality and anything related to it. This thread is intended for discussing chapter 85. The previous thread has long passed 500 comments. Comment in the 15th thread until you read chapter 85.
There is now a site dedicated to the story at hpmor.com, which is now the place to go to find the authors notes and all sorts of other goodies. AdeleneDawner has kept an archive of Author’s Notes. (This goes up to the notes for chapter 76, and is now not updating. The authors notes from chapter 77 onwards are on hpmor.com.)
The first 5 discussion threads are on the main page under the harry_potter tag. Threads 6 and on (including this one) are in the discussion section using its separate tag system. Also: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15.
As a reminder, it’s often useful to start your comment by indicating which chapter you are commenting on.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: