The base-ten positional numeral system, also called the decimal system, has become so ubiquitous in the globalized 21st century that it’s easy to forget that this method of working with numbers has not always been the preferred, nearly universal method.
Across most of the world, today, Arabic numerals—so-called because the symbols and their associated positional system were introduced to Europeans by Arab merchants, though they called them Hindu numerals having been introduced to them by their Indian mathematician inventors—are the dominant method of displaying numeric information.
There are still quite a few other glyphs in use beyond the 1 2 3 4 5 6 7 8 9 and 0 that many of us who use the Arabic, Latin, Cyrillic, or Greek alphabets are accustomed to—Tibetans, Burmese, and Kannada alphabets all have their own numerical systems, for instance—but the emergence of typesetting in Europe, and the subsequent mass-production of printed works using Arabic numerals meant that these numbers became the de facto dominant representations across much of the world. Their use by merchants and bankers and other numerate professionals—people who were often trained in double-entry bookkeeping by a printed book that used this number system, or someone else who learned from such a book—further solidified these symbols’ hold on the modern world.
Beyond the shape of the glyphs, though, the decimal system that was paired with these figures allowed for new types of math and numerical thinking that, although technically possible with previous methods, was cumbersome and not obvious.
Having a spot for one, ten, one hundred, one thousand, and so on in a figure makes that figure more manipulatable in ways that weren’t initially obvious to folks using other arrangements. But this setup eventually became so useful that even die-hard Roman numeral fans eventually re-learned how to use numbers, and then began to invent things like decimal separators, rational and irrational numbers, and other precursors to modern mathematics that may never have been invented lacking a system that left room for them.
It may seem like such a system was inevitable, either because it seems so obvious to us, today, or because humans typically have ten fingers—so counting would seem to logically lead in this direction.
While true that many cultures based their own, independently developed (or independently iterated from a previous, shared ancestor culture) number systems on base-ten thinking, this is far from the only system humans have developed around the world and across history.
Many cultures have at some point used some type of unary number system, which means using some kind of tally mark for each unit of something you wish to represent, in some cases then developing “bundle” symbols for groups of individual units (called sign-value notation), as is the case with Roman numerals, where one is a single I, two is II, three is III, but five is V, ten is X, and so on. Ancient Egyptians used a similar system.
In Pre-Columbian Mesoamerica, the Mayan civilization used a base-20 system, the indigenous Yuki people in what is today California used a base-8 system, and the Chumashan languages in the same general part of North America used a base-4 counting system.
Some Australian Aboriginal languages use a base-5 number system, some Nigerians use a base-12 system, and the Huli language of Papua New Guinea uses a base-15 system.
All of which is to say that base-10, though very useful in some senses, especially when paired with a standard positional numeral system that allows a small set of glyphs arranged in a particular order to represent even massive and incredibly small numbers to a very precise level, is not the only way to think about and work with numbers.
Which means our mathematical understanding could be quite different, had history gone a different way, spreading a different system via early mass-production methods.
It also means we could discover or develop a new system in the future, allowing us to perceive and work with numerical and mathematical concepts of which, today, we are mostly or entirely unaware.
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