loved reading this; when you are at a peak you don't really know you are in one, you can almost never get there analytically and almost certainly have to do that computationally, meaning you have approximations of a peak (or a troughs) but you don't always know precisely where you are on the gradient
also - what are our equations? can we describe the mountain? and how do we describe our direction of travel where nothing is analytical and everything is computational / discrete? love the thinking!
Great questions! I agree. We navigate the mountain's paths empirically / computationally. When we slide in any direction we move, we are "sufficiently close" to a peak. Though, we can't rule out that some analytic continuations makes sense...
loved reading this; when you are at a peak you don't really know you are in one, you can almost never get there analytically and almost certainly have to do that computationally, meaning you have approximations of a peak (or a troughs) but you don't always know precisely where you are on the gradient
also - what are our equations? can we describe the mountain? and how do we describe our direction of travel where nothing is analytical and everything is computational / discrete? love the thinking!
Great questions! I agree. We navigate the mountain's paths empirically / computationally. When we slide in any direction we move, we are "sufficiently close" to a peak. Though, we can't rule out that some analytic continuations makes sense...