“If you cannot calculate, you cannot speculate on future pleasures and your life will not be that of a human, but that of an oyster or a jellyfish.” -Plato, Philebus, as quoted by Georges Ifrah in The Universal History of Computing: From the abacus to the quantum computer
Summarizing the History of Mechanical Calculating Devices and My Research Thereupon
This summer, I spent two months on campus focusing on my freshman Monroe research project. Six of the more or less eight weeks I spent in books and articles mining for information about mechanical calculating devices. My project topic is not one covered exclusively or in depth by any one source, so I gathered my data by skimming promising history of math sources for mentions of devices. Although I could probably build an adequate fort using stacks of my books and articles and a blanket (I really wanted to do this at my desk in Swem), the amount of information I gleaned from each resource was disappointingly small. On the bright side, I guess that means my research is pretty original.
I spent the second to last week of July (Week 7) moving all of the books I checked out of Swem to my dorm, writing one and a half blog posts, organizing my thoughts, outlining my essay, and otherwise trying not to run out of steam before I could compose the paper itself. Week 8, I wrote. To clarify, writing for me is a slow process of analyzing the pros and cons of each word and checking each possible source of the fact I want to add and then some others just in case. So, Week 8 consisted of twelve-hour days wherein I alternated between focus and frustration.
At the end of the summer, I have considerably more knowledge than I did at the beginning, as well as research experience, I have an overwhelming amount of notes, and I have about half of a first-draft essay.
To summarize the pure research, let me split it into two categories. First, there are a number of tools, which, because they rely on global principles, can be found in the histories of most peoples. These include knots, tally sticks, finger-reckoning, and abaci. Knots and tally sticks do not technically fit as they were not used to calculate, but merely to count or to record data. I still considered them in my research because they act as evidence for how people in far-flung places tend to approach mathematical challenges in similar fashions. Plus, in one way, counting was the very first computational process, although now “computation” implies more complicated procedures.
Knots and tally sticks have extremely long histories (the Lembombo bone from near Swaziland is a tally stick dating back to 35,000 bc [Joseph, 2000]), but fingers have always been with humans. I like to call them the “default” calculational tool, and you can probably think of a time, maybe even recently, when it just made sense to count something out on your fingers. However, the intuitive idea to use one finger to correspond to one unit of sheep or soldiers or items on your to-do list is not the only way to use fingers. Many systems throughout history have been developed to allow into the thousands on just two hands. For example, one system used in China from at least 1593 until the nineteenth century enabled a person to count up to 99,999 with a single hand and up to 9,999,999,999 using both hands (Ifrah, 2000).
The abacus, as I discussed in my last post, comes in a variety of forms through space and time; however, its underlying principles remain the same as they are fundamental principles of math. Thus, they fall under this first category.
The second category consists of calculating devices specific to a culture. For example, in East Asia, mathematicians used “counting rods”, or small bamboo sticks manipulated on a grid to perform arithmetic as well as to solve systems of equations. (See my first post for more details.)
Although the summer has ended, my project has not. I am not satisfied with my research on European devices (there is just so much on that particular subject), so I intend to investigate that further. More importantly, I have not finished my paper. I am uncertain whether I could publish it, but if only for my own sake, I want to complete it.
Ifrah, G. (2000). The universal history of numbers: From prehistory to the invention of the computer (D. Bellos, E. F. Harding, S. Wood, & I. Monk, Trans.). New York, NY: John Wiley & Sons.
Joseph, G. G. (2000). The crest of the peacock: Non-European roots of mathematics. Princeton, NJ: Princeton University Press. (Original work published in 1991)