I just imagined it so that means it must be imaginable (e.g. you have a head that can contain arbitrarily many happy implants and because of their particular design they all multiply each other’s effect). It doesn’t seem very realistic, though, at least for humans.
Yes. y = log(x) is convex globally. A logarithmic utility function makes sense if you think of each additional dollar being worth an amount inversely proportional to what you have already.
How in jubbly jibblies did this get voted down? The obvious way to resolve the ambiguity in “convex” and “concave” for functions is to also specify a direction.
This can explain locally convex curves. But is it imaginable to have a convex curve globally?
It’s imaginable for an AI to have such a curve, but implausible for a human having a globally convex curve.
That’s what I think. Anything is imaginable for AI.
I just imagined it so that means it must be imaginable (e.g. you have a head that can contain arbitrarily many happy implants and because of their particular design they all multiply each other’s effect). It doesn’t seem very realistic, though, at least for humans.
Yes. y = log(x) is convex globally. A logarithmic utility function makes sense if you think of each additional dollar being worth an amount inversely proportional to what you have already.
No, your example is concave. The above posters were referring to functions with positive second derivative.
The mnemonic I was taught is “conve^x like e^x”
I learned “concave up” like e^x and “concave down” like log x.
How in jubbly jibblies did this get voted down? The obvious way to resolve the ambiguity in “convex” and “concave” for functions is to also specify a direction.
It might be downvoted because it specifies “concave up” and then “concave down”.