Benquo: Even infinitesimal are not equal to zero. You don’t even need infinitesimals in differential calculus. Instead, you can think dx and dy are just variables. You let them approach zero to see what would happen at the limit, but you don’t set them equal to zero. I have always personally found infinitesimals a little disturbing, since one doesn’t really need them anywhere.
I am a little puzzled by this; I don’t know how they teach this stuff in the US, but in Finland, if my memory serves me correctly, they taught how this “proof” is wrong in elementary school. So only complete idiots would be fooled by this “logic”.
I think this argument is flawed with respect to the more technology-oriented questions. Most people do not seriously claim to solve AI problems. What most people (like myself) who are slightly educated in the field (I did an undergrad minor in AI, just very simple stuff) will do is they will suggest an approach that they would try if they had to start working on it. Technical questions also usually yield to evidence very quickly whenever it matters, i.e., when someone would start burning money on an implementation. That is not to say some time and resources are not to be saved by using the maxim outlined here.
OTOH, the part about economists is valid, since most people have very strong ideas (usually wrong ones) about what will work, e.g., as a policy. But then again, most people have no way of wasting (other peoples’) resources based on these faulty ideas.
No, wait...