Today I was discussing the nature of number systems with a former seminary professor from Erskine Seminary. At first it seems strange that I would be discussing such a "mathematical" idea with a seminary professor, however, the idea is not as strange as it seems. What one will find through a discussion like this, that is, a discussion about number systems with a non-math person, is that number systems stretch far beyond mathematics. This is exactly what I discovered through my conversation with this former professor. The two main ideas that came out of this conversation were that: There is reasoning behind each number system, and, The uniqueness of each number system.
First, our conversation started with the origins of the current number system that we use here in the United States. Though it is up for some dispute, it is pretty generally accepted that our number system spawned from ancient Arabic numbering systems. Other than origins, is there a meaning behind the number system and, more importantly, what is the meaning? What came up in our conversation is that there is, in fact, a meaning behind our current number system. Although the numbers that most of us write daily do not display the following characteristics, they find their purpose in the traditional style of these numbers. There is a meaning! What is it? So we see, even in this common typeface that the number one, 1, is not just a line, but has a small tic or downslope at the top. It turns out that this is not simply the product of a sloppy writing, greasy teenager, but rather, is the remnant of the intentional meaning. Traditionally, the number 1 is written more like this ^, minus the superscript. We find actually that many countries still write the number 1 this way (Germany and other European countries). The traditional 2 is written more like Z, the traditional 3 is written more like a sideways W. Anyhow, what we notice about these numbers is vertices! Yes! As it was originally written, for the most part, the number of vertices or changes in direction signified which number it was. a 1 has one vertex, a 2 has
2 vertices, etc. This is something that I, and I assume, many other people, even mathematicians, have not thought about. What does this have to do with the role of a number system?
The answer to the previous question came, for me, in the furthering of our discussion about these unique properties in each number system. This will also serve to outline the role of our current number system. This discussion was not as in depth as you might think, in fact, it was pretty basic. Sometimes the most prolific understandings of an idea or concept. The main topic of our conversation revealed itself in Roman numerals. The professor outlined that in his current career as a superintendent, he works with young students teaching Greek from time to time and, in relation to that conversation, talked about Roman numerals with the students. On the one dollar bill, he explained, 1776 is printed on the bill in Roman numerals. He simply explained that the number is nearly 9 characters long. The students, naturally found this very confusing. We then talked about how incredibly difficult it would be to do any type of meaningful mathematics using that number system. It really brings into perspective, the incredible mathematical achievements by ancient mathematicians using number systems that were, basically horrible. What does this mean for the role of our number system? It means that it makes mathematics more accessible, meaningful, and more quickly progressing than ever before. Without our current, concise, and easily understood numbering system, mathematics would be slowwwww. It would be like doing internet research with dial up. Or eating rice with a single chopstick. Our current number system effectively eliminates the single chop stick rice eating of math.