A recent example of physical notions not being functions of each other

March 22, 2010

Let me quote John Baez from his recent issue “This Week’s Finds in Mathematical Physics (Week 294)”:

The point of these examples is that most linear resistors let us treat current as a function of voltage or voltage as a function of current, since R is neither zero nor infinite. But in the these two limiting cases – the short circuit and the open circuit – that’s not true. To fit these cases neatly in a unified framework, we shouldn’t think of the relation between current and voltage as defining a function. It’s just a relation!

That is another example of basic notions not being a function of each other.

Maybe that makes my last comment on the relation between ‘price of a good’ and ‘demand for a good’ not being a function of each other more accessible. Between these economic notions there is just a (commutation) relation. They are not functions of each other. I will certainly elaborate on this …