Idea 2: Changing the Number System for Currencies (Part I)
One of my first interactions with decimal-point representations occurred the first time I wanted to buy something with my childhood piggy-bank savings (That “something” was roller blades!). At the time, I was able to understand and accept at face value the types of values that money could have and how to manipulate them in basic ways. It did not occur to me that money could take negative values. Here’s a timeline of my life with respect to understanding of currency values:
Ages ~5-~8: Money has positive values. When those values are fully written out, they are represented by expressions of the form …abc.xy. You can add, subtract, multiply, and divide these values, but you have to be careful about always rounding to the second decimal point value, even if manual or calculator results first give you a non-terminating value.
Ages ~8-~18: Money can take on negative values! The sign of a monetary value encodes the direction of monetary flow within a monetary reference system. For example, if your net worth is negative, more money has flowed to you than you have contributed to the currency system in which that net worth is defined. If you want to put a label on the types of numbers that are allowed to represent monetary values, they are rational numbers that terminate at the second decimal digit. I’m going to idiosyncratically refer to this set as “Q.2”. My concerns about money were very simple and limited in this period and I had lots of time and energy to get philosophical about it.
Ages ~18-28: I simply focus on making my net worth increase mostly monotonically from $0.00.
Ages 28-31: Temporarily satisfied with my net worth, I again begin to indulge in philosophy, as follows.
I’m going to completely ignore the historical context and rationales for the development of number systems for representing currencies; I’m interested not in why the dice have fallen the way they have but instead that they have fallen different ways throughout history and in what could be achieved if we were to adopt a different system. To me, this is a compelling question because of the social interactions and structures that are enabled by the changes that have indeed actually happened throughout the development of monetary systems. So, the first idea is that we could once again refine our concept of what money represents and use a different number system to model that concept.
If we want to explore beyond the set Q.2, what menu of options does mathematics have to offer us? In Part II of this topic will be dedicated to the second main idea of exploring which options are available given the state of mathematics today and what some implications of each of those options might be.