From 0 to Infinity in 26 Centuries Read Free

described.
However, drawing decent images in thick wet clay is tricky, so they took to using the end of a wedge-shaped stylus (a rod-like implement with a pointed end) to make marks.
    Number system
    The Mesopotamian’s number system was base 60 (also referred to as sexagesimal ), which means they counted in blocks of 60 rather than in blocks of 10, as we do
today. Lots of numbers go into 60 (mathematicians would say 60 has many factors), which makes it a convenient number with which to do arithmetic. We still see a few reminders of it today – 60
seconds in a minute and 60 minutes in an hour hark back to the Babylonians.
    Cunningly, their number system contained only one symbol, made using the end of a stylus:

    They would use up to nine of these symbols. They would show a 10 by rotating the stylus by 90 degrees to get a slightly different symbol:

    So the number 47 would look like this:

    The Mesopotamians could write up to the number 59 in this way, using a sub-column for each of the tens and units digits. To write numbers larger than 59, they would write a new
number alongside the tens and units (just as we can go as high as 9 in one column before we have to move on to the next one). Whereas our columns follow the pattern units, tens, hundreds,
thousands, etc., according to our way of thinking the Mesopotamians’ columns went units, sixties, three-thousand six-hundreds, two-hundred and sixteen-thousands. A Mesopotamian would think of
our number 437 as being 7 lots of 60 (7 × 60 = 420) plus 17, which they would write like this:

    Zero interest
    Although this seems like a pretty decent number system, not unlike our own, there were a couple of problematic areas. The first problem was that until
c.
500 BC the Mesopotamians had no symbol for zero, which means they had no way of showing an empty column. For example, if I write down 205, the zero tells you that I mean two-hundred and
five, and nothing else. The Mesopotamian number system was flawed because empty columns in the middle or at the end of a number were missing. For example:

    This looks like 60 + 10 = 70. But there could be an empty column in the middle, in which case the number would be 3600 + 0 + 10 = 3610. Or there could be an empty column at the
end, in which case we would have 216000 + 60 + 0 = 216060 – quite a large difference. Apparently, Mesopotamians tended to rely on the context in which the numbers were used in order to read
them in the most reasonable way.
    Early Arithmetic
    Many people consider the abacus to have been the ancient world’s version of the electronic calculator. In fact, the counting frame with beads
     – which most people think of when they hear the word abacus – is a relatively modern piece of technology, first made popular in China after AD 1000.
    The word ‘abacus’ is thought to come from the Hebrew word for ‘dust’, and the first abacuses were simply that – a board or level surface
     strewn with dust that could be used as a scratch pad for calculations. Eventually the dust was replaced by a board with tokens that could be placed in columns to allow for the addition of large
     numbers without having to be able to count higher than ten.
    Later, the Romans used pebbles or, in Latin,
calculi
(from which we get the words calculus and calculation). In England, we called the tokens
     ‘counters’, which is why shops had a counter-top to put their counting board on.
    Multiplication madness
    The second problem arose when the Mesopotamians tried to multiply numbers together. Whichever way you multiply using our decimal system, you need to have memorized your times
tables up to 9 x 9 (because 9 is the highest digit we have). However, according to the Mesopotamian system, you neededto know your times tables up to 59 x 59! We think they
used a few key times tables, written on small tablets, to help, but even so their times-table tests at school must have been a nightmare.
    Archaeologists have found many hundreds of clay