The History of Mathematics: A Brief Course

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38 2. MATHEMATICAL CULTURES I

considerable work had been done earlier on the codex by another director of the
Dresden library, a philologist named Ernst Forstemann (1822-1906), who had 200
copies of it made.
The work consists of eight separate treatises and, according to the experts,
shows evidence of having been written by eight different people. Dates conjectured
for it vary from the thirteenth to the fifteenth centuries, and it may have been
a copy of an earlier document. The first 15 folios are devoted to almanacs and
astronomy/astrology, while folios 16 23 are devoted to the Moon Goddess. Both of
these sections are based on a 260-day calendar known as the Tzolkin (see Chapter
5). It is believed that these pages were consulted to determine whether the gods
were favorably inclined toward proposed undertakings. Folio 24 and folios 46-50
are Venus tables, containing 312 years of records of the appearance of Venus as
morning and evening star. Such records help to establish the chronology of Maya
history as well as the date of the manuscript itself. The pictures accompanying
the text (Plate 3) seem to indicate a belief that Venus exerted an influence on
human life. These pages are followed by eclipse tables over the 33-year period from
755 to 788 CE. Folios 25-28 describe new-year ceremonies, and folios 29-45 give
agricultural almanacs. Folios 61-73 give correlations of floods and storms with
the 260-day calendar in order to predict the end of the next world cycle. Finally,
folio 74 describes the coming end of the current world cycle. The Maya apparently
believed there had been at least three such cycles before the current one.
The mathematics that can be gleaned from these codices and the steles that
remain in Maya territory is restricted to applications to astronomy and the calen-
dar. The arithmetic that is definitely attested by documents is rudimentary. For
example, although there is no reason to doubt that the Maya performed multiplica-
tion and division, there is no record showing how they did so. Undoubtedly, there
was a Maya arithmetic for commerce, but it is very difficult to reconstruct, since
no treatises on the subject exist. Thus, our understanding of the achievements
of Maya scientists and mathematicians is limited by the absence of sources. The
Maya documents that have survived to the present are "all business" and contain no
whimsical or pseudo-practical problems of an algebraic type such as can be found
in ancient Chinese, Hindu, Mesopotamian, and Egyptian texts.


Questions and problems

2.1. Does mathematics realize Plato's program of understanding the world by con-
templating eternal, unchanging forms that are perceived only by reason, not by the
senses?


2.2. To what extent do the points of view expressed by Hamming and Hardy
on the value of pure mathematics reflect the nationalities of their authors and
the prevailing attitudes in their cultures? Consider that unlike the public radio
and television networks in the United States, the CBC in Canada and the BBC
in Britain do not spend four weeks a year pleading with their audience to send
voluntary donations to keep them on the air. The BBC is publicly funded out of
revenues collected by requiring everyone who owns a television set to pay a yearly
license fee.


2.3. In an article in the Review of Modern Physics, 51, No. 3 (July 1979), the
physicist Norman David Mermin (b. 1935) wrote, "Bridges would not be safer if
only people who knew the proper definition of a real number were allowed to design

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