Naming Large Numbers
First, Archimedes had to invent a system of naming large numbers. The number system in use at that time could express numbers up to a myriad (μυριάς — 10,000), and by utilizing the word "myriad" itself, one can immediately extend this to naming all numbers up to a myriad myriads (108). Archimedes called the numbers up to 108 "first numbers" and called 108 itself the "unit of the second numbers". Multiples of this unit then became the second numbers, up to this unit taken a myriad-myriad times, 108·108=1016. This became the "unit of the third numbers", whose multiples were the third numbers, and so on. Archimedes continued naming numbers in this way up to a myriad-myriad times the unit of the 108-th numbers, i.e., .
After having done this, Archimedes called the numbers he had defined the "numbers of the first period", and called the last one, the "unit of the second period". He then constructed the numbers of the second period by taking multiples of this unit in a way analogous to the way in which the numbers of the first period were constructed. Continuing in this manner, he eventually arrived at the numbers of the myriad-myriadth period. The largest number named by Archimedes was the last number in this period, which is
Another way of describing this number is a one followed by (short scale) eighty quadrillion (80·1015) zeroes.
Archimedes' system is reminiscent of a positional numeral system with base 108, which is remarkable because the ancient Greeks used a very simple system for writing numbers, which employs 27 different letters of the alphabet for the units 1 through 9, the tens 10 through 90 and the hundreds 100 through 900.
Archimedes also discovered and proved the law of exponents, necessary to manipulate powers of 10.
Read more about this topic: The Sand Reckoner
Famous quotes containing the words naming, large and/or numbers:
“The night is itself sleep
And what goes on in it, the naming of the wind,
Our notes to each other, always repeated, always the same.”
—John Ashbery (b. 1927)
“My weakness has always been to prefer the large intention of an unskilful artist to the trivial intention of an accomplished one: in other words, I am more interested in the high ideas of a feeble executant than in the high execution of a feeble thinker.”
—Thomas Hardy (1840–1928)
“The barriers of conventionality have been raised so high, and so strangely cemented by long existence, that the only hope of overthrowing them exists in the union of numbers linked together by common opinion and effort ... the united watchword of thousands would strike at the foundation of the false system and annihilate it.”
—Mme. Ellen Louise Demorest 1824–1898, U.S. women’s magazine editor and woman’s club movement pioneer. Demorest’s Illustrated Monthly and Mirror of Fashions, p. 203 (January 1870)