The numbers we now use originated in India, spread to Syria and Arabia, reached Italy after hundreds of years, and were first ''publicized'' by Leonardo of Pisa in 1203. Recognizing their great superiority over Roman numerals for calculating, European scholars quickly adopted the Indo-Arabic numbers, which led to universal acceptance a mere 300 years later. What a beautiful example of cultural lag! Roman numerals are still used for corner-stone dates of buildings, copyright dates in books, hours on faces of clocks, and the sequence of Olympic Games and Super Bowls.

The symbols: I = 1, V = 5, X = 10,  L = 50, C = 100, D = 500, M = 1 000. The numbers, printed from left to right in decreasing value, are added, except that when a smaller precedes a larger, it is subtracted; for example: XI = 11, and IX = 9; LX = 60, and XL = 40; CX = 110, and XC = 90.

A defect of the Roman system, and of our present system as well, until about 1300 AD, was the lack of zero. A figure that stood for ''nothing'' was repugnant to the ancient Greeks. To hold a place in a long number, however, zero is ideal. To add up segments of a trip,  it makes good sense to call the starting point 0 and the first stop 1. The monk who invented B.C. and A.D. did not know zero, so he omitted year zero, setting up a confusion about the beginnings of centuries and millenia that is still with us. For example, did Augustus Caesar (63BC - 14AD) live to age 76 or 77? It is clear that a number line consists of a zero point with positive numbers extending to the right, and negative numbers to the left.

The binary number system was a 1697 idea of Leibniz. It turned out to be highly useful. Expressed entirely with 1 and 0, the system is based on powers of 2. It starts at the right end with 2⁰ = 1, then 2¹ = 2, 2²= 4, 2³ = 8, and so forth. For example, 1101 = 8 + 4 + 1 = 13, because the 0 indicates that 2¹ is not present. If the meaning of 2⁰ or 2¹ is not clear, review the rules of exponents.  The binary system is especially useful in computers; an electrical switch is either  on or off. There are 10 kinds of people in the world, those who understand binary, and those who don't.

The oldest number system is the sexigesimal (base-60) system used by accountants and astronomers of Sumer more than 5 000 years ago. The figures belong to archaeology, but significant remnants of the system are found in the 60-second minute, the 60-minute hour, the 24-hour day, the 90-degree right angle, l80-degree hemispheres, and 360-degree compass. The beauty of this system is the extraordinary number of factors; 60 is divisible into whole parts by every number up to 12, except for 7 and 11. There is no sign that base-60 will ever disappear.

Fig. 3-1

Roman use of letters to signify numbers apparently came from the Greeks, not from Latin letters. One could say that ideas and reasoning came from the Greeks, and that Rome built an empire by adding a strong army and efficient tax collection. Teaching of the Greek language has virtually disappeared, but it is still useful to know the alphabet. The word alphabet comes from α and β, and an extraordinary number of English words have Greek roots. All 24 Greek letters except for ι (iota) and ο (omicron) are used regularly in math and science. Some standard examples are: the angle θ (theta), λ (lambda) for wavelength, and ν (nu) for frequency. When you go to Athens, and climb the steps of the Acropolis (ακρο [akro] = high, πολισ [polis] = town), you will be able to read the admission ticket (Figure 3-1), and the street signs in the Plaka below.

Some words, like 'υβρισ [hubris] and 'οριζον [horizon], have entered the English language unchanged, except for addition of the letter h, which is not in the Greek alphabet. The elevated comma indicates the ha sound; 'Η' is the letter eta, the long e. All the letters have names, which are used in crossword puzzles, and in naming fraternities and sororities. On the Acropolis ticket and other similar tickets, below the standard numbers are two-letter abreviations of their names.

Some advice, attributed to the priests of Apollo at Delphi: ΜΗΔΕΝ ΑΓΑΝ.

This is literally "Nothing too much", and is found in Latin literature as NIHIL NIMIS, nothing in excess, moderation in all things. Political ΔΗΜΟΚΡΑΤΙΑ originated in Athens. A favorite put-down of the elite is to assign someone to 'οι πολλοι [hoi polloi] = the many, the masses, the common people.

The accepted date for the first Games at Olympia, Greece is 776 BC. All pagan cults were banned in 393 AD. Held every four years, that makes: 1169 / 4 = 292 Games. The modern Games began in 1896, which makes the 2004 Athens Olympiad: 2004-1892 (year zero) = 112 / 4 = XXVIII.