QUESTIONS AND PROBLEMS 127the fifte to Venus, the sixte to Mercurius, the seventhe to the mone.
And then ageyn the 8 houre is to Saturne, the 9 is to Jupiter, the 10
to Mars, the 11 to the sonne, the 12 to Venus... And in this manner
succedith planete under planete fro Saturne unto the mone, and
fro the mone up ageyn to Saturne. [Chaucer, 1391, Robinson, p.
553]Chaucer made references to these hours in the Canterbury Tales.^9 Thus, all
this planetary lore and the seven-day week have their origin in the sexagesimal
system of counting and the division of the day into 24 hours, which we know
is characteristic of ancient Mesopotamia. But if the Mesopotamians had used a
decimal system and divided their days into 10 hours, the days would still occur in
the same order, since 10 and 24 are congruent modulo 7.
Questions and problems
5.1. Find an example, different from those given in the text, in which English
grammar makes a distinction between a set of two and a set of more than two
objects.
5.2. Consider the following three-column list of number names in English and
Russian. The first column contains the cardinal numbers (those used for counting),
the second column the ordinal numbers (those used for ordering), and the third the
fractional parts. Study and compare the three columns. The ordinal numbers and
fractions and the numbers 1 and 2 are grammatically adjectives in Russian. They
are given in the feminine form, since the fractions are always given that way in
Russian, the noun dolya, meaning part or share, always being understood. If you
know another language, prepare a similar table for that language, then describe
your observations and inferences. What does the table suggest about the origin of
counting?
English Russian
one first whole odna pervaya tselaya
two second half dve vtoraya polovina
three third third tri tret'ya tret'
four fourth fourth chetyre chetvyortaya chetvert'
five fifth fifth pyat' pyataya pyataya
six sixth sixth shest' shestaya shestaya
5.3. How do you account for the fact that the ancient Greeks used a system of
counting and calculating that mirrored the notation found in Egypt, whereas in
their astronomical measurements they borrowed the sexigesimal system of Mesopo-
tamia? Why were they apparently blind to the computational advantages of the
place-value system used in Mesopotamia?
5.4. A tropical year is the time elapsed between successive south-to-north crossings
of the celestial equator by the Sun. A sidereal year is the time elapsed between two
successive conjunctions of the Sun with a given star; that is, it is the time required
for the Sun to make a full circuit of the ecliptic path that it appears (from Earth)
to follow among the stars each year. Because the celestial equator is rotating (one
(^9) See the 1928 edition edited by John Matthews Manly, published by Henry Holt and Company,
New York, especially the third part of the Knight's Tale, pp. 198-213.