In physics, we build models to represent the real world. We find equations to describe falling objects, cooling bodies, and collapsing stars. The equations are really just mathematical models, and when the equations accurately predict the behavior of something, we feel like it has been correctly modelled; at least until we find out differently.

A number of years ago, I spent a great deal of time investigating the true nature of value, aside from modern economic conceptions of the word. Of particular note is that people commonly equate value with money. Yet, if these two really are equivalent, then it follows that the way we model money – the equations we use – should also correctly apply to our observation of value. So what is the evidence for this?

First, let’s consider the summation of money and value. If you begin with twenty dollars and someone gives you another twenty dollars, I think we would all agree that you now have twice the money. But let’s contrast that with something that is not money. If you have a reserved seat on a flight from London to New York, that will have a certain value for you. If someone gives you another seat on that same flight, in most cases your value would not considered to have doubled.

Second, let’s look at the behavior of money and value over time. The financial equations that deal with interest rates, dividends, and account balances do a very good job of modelling money – by definition – but do they correctly model the nature of value? Looking at the equations governing compound interest on money in a bank account, we will use the following formula for continuously compounded interest :

P = C e ^rt

In this equation, P is the resulting value, C is the initial deposit, e is the natural logarithm (a mathematical constant), r is the interest rate, and t is the time over which the interest accrues. For a positive interest rate over a positive time period, the resultant amount of money will always be larger than the initial deposit and it will grow exponentially over time.

But does this equation really represent how value in the world of “things” behaves? Let’s consider some simple examples: If you have an apple and you “bank” it in your refrigerator for a month or two, does the resulting apple have a value greater or less than the initial apple? If you have an automobile and bank it in your garage for a few years, does it have more value when you come back to withdraw it? How about books, or furniture, or clothing, or tools? Does the value of such things go up or down with time? Although there are a few exceptions, such as a vintage bottle of wine or a classic automobile, just about everything loses some or most of its value over time.

The point here is not to say that banks have it wrong. Banks handle money exactly the way we expect it to be handled. The point is simply that money should not be confused with value. They are two very different things and they do not behave in the same ways, nor should they be expected to do so. Any system that correctly models value will show a depreciation over time, dwindling to an ever smaller value. As a result, the above equation only begins to model value when the interest rate is negative.