I was rereading Three Worlds Collide tonight, and a passage caught my eye:
On screen was the majesty that was the star Huygens, of the inhabited planet Huygens IV. Overlaid in false color was the recirculating loop of Alderson forces which the Impossible had steadily fed.
Fusion was now increasing in the star, as the Alderson forces encouraged nuclear barriers to break down; and the more fusions occurred, the more Alderson force was generated. Round and round it went. All the work of the Impossible, the full frantic output of their stardrive, had only served to subtly steer the vast forces being generated; nudge a fraction into a circle rather than a line. But now -
Emphasis added. The bold part sounds familiar, right?
Beneath the moonlight glints a tiny fragment of silver, a fraction of a line...
(black robes, falling)
...blood spills out in liters, and someone screams a word.
Frankly, I don’t understand either phrase, and I can’t tell by the context if their meanings are at all related. What does “nudge a fraction into a circle instead of a line” mean? In context, it seems to mean to change something but very slightly, yet still to great effect. But I don’t see why the words “nudge a fraction into a circle instead of a line” mean that at all.
Is it a math thing I don’t get? What does it mean? And can it help us understand the MoR prologue, or is it totally unrelated?
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 first means that a fraction of the particles were nudged into a path that was a circle rather than a line. Apparently increasing the chances of fusion. As for the second a “fraction of a line” does not really mean much but it appears to be a comment on the size and form of the glinting thing.
I was rereading Three Worlds Collide tonight, and a passage caught my eye:
Emphasis added. The bold part sounds familiar, right?
Frankly, I don’t understand either phrase, and I can’t tell by the context if their meanings are at all related. What does “nudge a fraction into a circle instead of a line” mean? In context, it seems to mean to change something but very slightly, yet still to great effect. But I don’t see why the words “nudge a fraction into a circle instead of a line” mean that at all.
Is it a math thing I don’t get? What does it mean? And can it help us understand the MoR prologue, or is it totally unrelated?
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 first means that a fraction of the particles were nudged into a path that was a circle rather than a line. Apparently increasing the chances of fusion. As for the second a “fraction of a line” does not really mean much but it appears to be a comment on the size and form of the glinting thing.