From 0 to Infinity in 26 Centuries Read Free Page B

right-angled triangle if they knew the length of the other two sides.
    There are, of course, many more far-fetched theories regarding the Ancient Egyptians, including the super-high technology they appropriated from the legendary island of Atlantis (or from aliens,
or time travellers...). I cannot say whether such things were true, but I do know the Egyptians were pretty clever fellows.
    A Tall Order
    The fact about the Ancient Egyptians that I always find most extraordinary is that the Great Pyramid, which was completed
c
. 2560 BC , was the tallest building in the world until the central towers of Lincoln Cathedral were raised in AD 1311 – that’s the best part of 4,000
     years!
    T HE M AYANS
    By the first millennium AD Mayan civilization had reached a level of cultural and mathematical development similar to the Mesopotamians and the
Egyptians. They declined somewhat as time went by, but when the Spanish conquistadores arrived in the early 1500s the Mayans had managed to recapture their previous levels of sophistication.
    Born in isolation
    The Mayans left behind a raft of evidence that demonstrated how they conducted their mathematics, but unfortunately virtually all of it was destroyed when the Spanish invaders
arrived and sought to convert the region’s heathens to Catholicism.
The Dresden Codex
is one of three surviving examples of Mayan writing. Although it was badly damaged during the
Second World War, the book still contains a great deal of insight into the Mayan development of mathematics. Many surviving monuments in modern-day Mexico and Guatemala contain numerical
information, such as dates, inscribed upon them.
    Unlike the cross-pollination that occurred between the Mesopotamian and Egyptian cultures, the Mayans developed in complete isolation. They also failed to fulfil the last two criteria of
‘civilization’: they did not possess the wheel, perhaps because there were no beasts of burden in the parts of Central America where they lived; they also did not seem to be able to
smelt metal. However, despite technically still existing in the Stone Age, the Mayans were able to build great cities, some of which contained populations of over 50,000 people.
    Number crunching
    So, what of their mathematics?
The Dresden Codex
is concerned only with astrology and astronomy, so everything we know about the Mayans’ mathematics is shone
through this lens.
    The Mayans used a base-20 system, within which lay a base-5 system (much like the Mesopotamians’ base-60 and base-10 system).

    Like modern mathematics, Mayan mathematics had a grasp of place value : the value attached to the position of each digit. Unlike modern mathematics, Mayan mathematics
placed numbers in vertical stacks, with the highest place value positioned at the top. Because the Mayans counted in groups of twenties, each level in the stack was twenty times the value of the
level below. From the bottom it went something like this: 1s, 20s, 400s, 8000s, etc. So our number 8577 is one 8000, one 400, eight 20s and seventeen 1s, which in Mayan looked like this:

    The Mayans had a symbol for an empty level in the stack, e.g. they possessed a concept of zero, which avoided the confusion faced by the Mesopotamians. So the number 419 (one
400, zero 20s and nineteen 1s) looked like this:

    The Mayan calendar
    As the information contained in
The Dresden Codex
would attest, the Mayans’ way of life was governed by astrology. Ritual human sacrifice was an integral part of
Mayan culture and was thought to aid the continuation of the Mayan people’s cosmology.
    Tasked with working out which rites were necessary to appeasethe gods, high-ranking priests were responsible for interpreting the positions of the sun, the moon and Venus.
They developed a system of several different calendars, which the Mayans used in parallel. They possessed a 365-days-a-year civil calendar called the
Haab
, which comprised 18 months of 20
days each, plus 5 ‘nameless’