[lmm]

> Example, the value that money represents is a single value. But why is it a scalar and not a vector? For example, why isn't everything priced with a value and a carbon cost? That would make prices vectors instead of scalars. In fact people value things across many dimensions and have to come up with a price, a single value. Imagine playing a video game where, instead of 3d vectors, everything is represented as the length of the vector. That's a lot of information that is just thrown away.

The whole value of monetary prices is that they're fungible - rather than having to compare the value of things in x different dimensions, you reduce everything to that scalar concept of value.

> In fact, markets have a known flaw called externalities. This flaw is created partly from the fact that value is a scalar. This flaw is so severe that major pollution has been created by economic activity (global warming, ozone, etc) that risks all life on this planet.

On the contrary, having value be a scalar is the solution, because it allows us to make tradeoffs between value and pollution. Cap and trade works (it worked for acid rain); the missing part is the will to actually do it.

All that said, you might be interested in China's "social credit" system - that's the main example I know of this concept of "vector value", because it exists to impose a standard of behaviour on individuals that's not tradeable and fungible.