Often when I read a debate between two great thinkers genuinely searching for truth, I find myself feeling somewhat caught between them, and yet somehow off to the side.
Now, with my better intuitive understanding of the geometry of high dimensional search spaces, this makes more sense to me. Of course as you try your best from your local information to move towards truth you will find yourself moving in a curve. (If the updates were just a straight line, you could take much larger steps and get to the truth faster.) And when other local searchers with similar pursuits compare their trajectories, of course all these paths will together look like decaying orbits. We circle gradually inward, updating a few dimensions at a time. Our attention is too limited to move in every direction needed all at once.
Often when I read a debate between two great thinkers genuinely searching for truth, I find myself feeling somewhat caught between them, and yet somehow off to the side.
Now, with my better intuitive understanding of the geometry of high dimensional search spaces, this makes more sense to me. Of course as you try your best from your local information to move towards truth you will find yourself moving in a curve. (If the updates were just a straight line, you could take much larger steps and get to the truth faster.) And when other local searchers with similar pursuits compare their trajectories, of course all these paths will together look like decaying orbits. We circle gradually inward, updating a few dimensions at a time. Our attention is too limited to move in every direction needed all at once.