Problems for Intermediate Methods in Theoretical Physics Edward F. Redish

Other Vectors

In mathematics class, a "vector" is typically just a set of numbers. In physics, we have a variety of vectors with a variety of characteristics. One example of a possible vector is a set representing someone's "wealth." Let us consider a number of possible sources of this wealth. Assume that the people you are considering may possess:

• funds in US\$, D
• funds in Iranian Rials, R
• funds in Cuban Pesos, P
• a number of acres of (possibly) cultivatable land in North Dakota, A.

The three currencies are only marginally convertable into each other. At some times it has been illegal to convert them into each other except through government offices, but one could do it on the black market at a very different rate. There is presently no market for North Dakota acreage, but it could become valuable in a few years. Is it appropriate to consider the set of these numbers (D, R, P, A) as an element of a linear space? A vector space? Why or why not? Compare this "vector" with a "vector" that we might use in physics.

Problem suggested by T. Bing.