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I’m reading about math. More specifically, I’m reading Zero: The Biography of a Dangerous Idea by Charles Seife, a distinguished mathematics professor and writer. For those unfamiliar, the book chronicles the development of the mathematical idea of zero, along with its scientific and social implications.

In the beginning, there was nothing. Yet in mathematics, this truth is almost paradoxical: early systems lacked the numeral zero, meaning that early math was devoid of a numerical representation of nothing. In Zero, Seife describes the reason for this.

The first evidence of human math is a 30,000-year-old wolf bone that was found in Czechoslovakia in the late 1930’s. Inscribed upon this bone is a series of notches that are undoubtedly human-made. Though it is unclear what this object was used for, it was a tool for counting. Seife points out, however, that this sort of tool excludes a need for zero. At this time, most cultures had not a precise idea about any numbers at all, let alone zero. In fact, most only held a distinction between “one” and “many”. Even still, languages such as those of the Siriona Indians of Bolivia and the Brazilian Yanoama people lack words for anything larger than three. Instead, they use the word for “much.” This simplicity demonstrates the small need  for numerical precision in many societies.

The lateness of zero’s creation can be partially explained by a lack of necessity. Seife explains this, writing that, “You never need to keep track of zero sheep or tally your zero children. Instead of ‘We have zero bananas,’ the grocer says, ‘We have no bananas.’ You don’t have to have a number to express the lack of something, and it didn’t occur to anybody to assign a symbol to the absence of objects. This is why people got along without zero for so long. It simply wasn’t needed. Zero just never came up” (8).

When zero finally did come up, it ironically arose out of necessity. Early number systems, sans zero, worked similarly to tally marks. For instance, a number such as six would be linguistically represented as “two and two and two.” As systems advanced, they began to use the place of numbers as an indicator of values. For instance, the number 128 works as follows. 1 in the third place means one hundred, two in the second place means 20, and 8 in the first place means simply eight. However, without zero to use as a placeholder, this type of number system doesn’t work. A number with two eights could mean eighty-eight, eight hundred and eight, eight thousand and eighty, etc. The zeros in this number are what make it clear (88, 808, 8080). Thus, zero arose as a placeholder and came to have significance.

So far, I’ve been thinking about possible topics for the research paper. A section of the book that I found particularly interesting describes how Pythagoras, the famous Greek mathematician, believed that all numbers must be rational, or numbers that can be expressed as the quotient of one integer (...-2,-1,0,1,2…) and another. As he toyed with a monochord, a type of one-stringed instrument, he found that the most pleasing tones were produced when the string was pressed down so that the two lengths formed were in whole number ratios. After reading this, I began to think about the connection between numbers and music, specifically the number zero. This prompted a possible topic: the varying use and function of rest (silent space) in music throughout history.