Guest Post: An Origin of Numbers

Drew Peterson recently earned a BS in physics from Weber State University. He is currently an instructor at AcerPlacer.

Start counting: 1…2…3…4…5… hopefully you can take it from there. Did you start from one like me? Maybe zero? Why didn’t we start at negative one, or even negative one thousand? It’s estimated that humans have been writing down numbers for at least the past 40,000 years (Ifrah, 2000). It’s really impossible for us to grasp how old this really us, but it really leads me to ask: Why have we been counting and writing numbers down for so long?

Let’s think back to the ancient world – I’m trading in a market place, and I need to know how many bushels of wheat to buy. I know how much I need to make a loaf of bread, it’s… that much. Visually, then, I can determine this from experience. Then the person I’m selling to needs to figure out how to charge me. She can see how many bushels I’ve taken but needs more rigidity — she needs to count how much I’ve taken. So the seller counts, maybe with her fingers, certainly not using the number system we think of now (one, two, three). Of course I don’t have zero bushels, in fact in that time I would ask how you could even see or think of zero of anything – let alone the wheat.

So by necessity we count, and by lack of necessity we didn’t need zero. Think of how bizarre an experience it would be to attempt an explanation of negative numbers to an ancient person, who only counts the things in front of them. I find it hard to put those shoes on, so I’ll produce an analogy: Imagine you’re building a shed, and you need to figure out how wide to make it. Your neighbor, who’s helping you, thinks he knows how long the shed should be. “Negative 10 feet!” he says. Of course, you stare in confusion as this answer makes no sense. How could you possibly have negative length?

Eventually, with the rise of currency, humans gained the need to measure nothing and negative of something, specifically when dealing with loans or any sort of deficits. For example, I’m back in my ancient trading market buying seeds to plant for my farm. I really need some seeds today to plant them in time. Unfortunately, I don’t have enough money, but the seller is kind enough to give them to me anyway. Now I owe her some money; I have a debt that needs to be paid. This is the idea of debt that we are commonly used to today, although our ancient people may not have thought of those as negative numbers.


Resources:

Ifrah, G. (2000). The universal history of numbers: From prehistory to the invention of the computer (D. Bellos, EF Harding, S. Wood & I. Monk, Trans.).
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