multiplication essentially a distributive ("grouped") operation
alphabetic notation led to "gematria" -- e.g. 666, the number of the beast; "AMEN"=99; or Pompeii graffiti "I love her whose number is 545." (What was her name in Ionic greek?)
The sad story of George Friedrich Grotefend (1775-1853)
Persian Cuneiform
1802 -- results presented to the Academy of
Science in Gottingen
Henry Creswicke Rawlinson (1810-1895)
Behistun
Inscription, erected by Darius the Great in 516 BCE, in Old
Persian, Elamite, and Akkadian. Old Persian was cracked first.
"Thanks to Rawlinson's remarkable efforts... the
vast records of Mesopotamian civilization were now an open
book." (p. 23)
A timeline
that I'd like to develop, with your help. What I'll need from
you are dates and descriptions of important moments missing
from the timeline.
Babylonian meaning "...the alluvial plain between the twin
rivers, the Tigris and the Euphrates. The Greeks called this
land 'Mesopotamia,' meaning 'the land between the rivers.'"
Differences in geography between Babylon and Egypt meant
that, whereas Egypt was safe from invasion, Babylon was overrun
time and again! (Interesting dynamical system described on page
21).
Gottingen
(now Germany). "Some of the most famous mathematicians in history, Carl Friedrich Gauss, Bernhard Riemann and David Hilbert were professors at Gottingen."
Babylonian pictographs (about 3000 BC) turned into
Cuneiform
Technology implies limitations ("materials chosen for
writing imposed special limitations of their own", p. 21)
cuneiform = wedge
Orientation of the wedge is important, implying that they
understand the rudements of angles.
Out of cuneiform arose the Babylonian positional number
system
sexagesimal system (confirmed in 1854 -- p. 24 --
Senkerah, on the Euphrates). Speculation on its origin:
Year has about 360 days
60 has many divisors, making lots of
fractions nice (terminate).
Interesting that they used base 10 to make their set of 59
symbols making up their sexagesimal digits. (p. 24)
Had subtraction sign (p. 24)
Absence of zero meant that "position" was relative: "one
could only rely on context to relieve the ambiguity." (p. 25)
300 BC, a "divider" was introduced, indicating an empty
space -- used only medially and not at the end.
"Babylonians of antiquity never achieved an absolute
positional system." (p. 26)
In fact, our author claims that "The Babylonians
were the only pre-Grecian people who made even
a partial use of a positional number system."
(p. 23), then contradicts himself on p. 27, re
the Chinese.
The Mayan system is also called positional (#13,
p. 30, and see p. 7), and they had a zero!
"Fractions that had non-terminating sexagesimal expansions
were approximated by finite ones...." (p. 26)
Babylonian fractions beat Egyptian ones, because the
Egyptians felt obliged to express fractions as sums of
unit fractions (p. 26).
Ancient Chinese sources don't exist, primarily due to
differences in climate and writing materials (bamboo
and cord, bark, or silk, p. 21 and 27).
No mathematical texts survive from India, BCE (p. 27).
Shih Huang-ti (China, 221 BC) tried to destroy all books
of learning.
There is a misconception that the Chinese developed a lot
of important theoretical mathematics. Actually they were mostly
focused on the calendar, and the claim is that, as of the 16th
century, studying mathematics on one's own was forbidden under
pain of death (p. 28).
