One nice feature of resource theories is that they enable us to measure things like "general welfare" or "well-being" using preorders that are subtler than the set of real numbers. I keep thinking a lot of problems with our society are due to "flattening" preorders to total orders that can be embedded in the real numbers, in order to give everything a worth in dollars. When we do this, everything becomes interconvertible with everything else. This is very convenient but I think it's _wrong_, both morally and conceptually. Will future societies laugh at us for having money that's 1-dimensional?

I haven't developed these thoughts very much; it's hard for me to know exactly what to do with them. But both von Neumann–Morgenstern and Tobias have nice theorems about when preorders can be embedded in the real numbers, so I may talk about those in a future lecture. This lets us see which of the hypotheses of these theorems don't apply in real life.

I haven't developed these thoughts very much; it's hard for me to know exactly what to do with them. But both von Neumann–Morgenstern and Tobias have nice theorems about when preorders can be embedded in the real numbers, so I may talk about those in a future lecture. This lets us see which of the hypotheses of these theorems don't apply in real life.