Alex's Adventures in Numberland - Alex Bellos [83]
The astronomically high prices of the early electronic calculators made them luxury business products. The inventor Clive Sinclair called his first product the Executive. One marketing idea involved using geishas to target high-rolling businessmen in Japan. After a night of entertaining, the geisha would whip out a Sinclair Executive from under her kimono so that the host could add up the bill. He would then feel obliged to buy it.
As prices dropped, calculators were seen not only as arithmetical aides but also as versatile toys. The Pocket Calculator Game Book, published in 1975, suggested many recreational activities for the high-tech electronic marvel. ‘Pocket calculators are new to our lives. Unknown five years ago, they are becoming as popular as televisions or hi-fi sets,’ it said. ‘Yet they are different in that they are not a passive entertainment but require intelligent input and definite intention for their use. We are not so much interested in what the pocket calculator can do as we are in what you can do with your pocket calculator.’ In 1977 the bestselling Fun & Games with Your Electronic Calculator included a dictionary of words that can be made using only the letters O, I, Z, E, h, S, g, L and B, which are the LED digits and when turned upside-down. The longest words are:
Seven letters:
OBELIZE
ELEgIZE
LIBELEE
OBLIgEE
gLOBOSE
SESSILE
LEgIBLE
BESIEgE
BIggISh
LEgLESS
ZOOgEOg
Eight letters:
ISOgLOSS
hEELLESS
EggShELL
Nine letters:
gEOLOgIZE
ILLEgIBLE
EISEgESIS
Surprisingly, the list does not include ‘BOOBLESS’ – the word whose use by teenage boys to their flat-chested female classmates is probably responsible for turning a generation of girls off mathematics. Still, Fun & Games with Your Electronic Calculator is probably the only numbers book that improves your English more than your arithmetic.
Enthusiasm for playing with one’s calculator was quickly extinguished as more enjoyable electronic games were introduced to the market. It soon became clear that instead of inspiring love of numbers, calculators would have the opposite effect – bringing about a decline in mental arithmetic skills.
Whereas the logarithm was a brand-new invention made possible by advances in notation, the quadratic equation was an ancient mathematical staple that was spruced up by new symbology. In modern notation, we say that a quadratic equation is one that looks like this:
ax2 + bx + c = 0, where x is the unknown and a, b and c are any constants.
For example, 3x2 + 2x – 4 = 0.
Quadratics, in other words, are equations with an x and an x2. They occur most basically in calculations involving area. Consider the following problem from a Babylonian clay tablet: a rectangular field with area 60 units has one side that is 7 units bigger than the other. How big are the sides of the field? To find the answer we need to sketch the problem, as in the diagram below. The problem reduces to solving the quadratic equation x2 + 7x – 60 = 0.
A convenient feature of quadratic equations is that they can be solved by substituting the values for a, b and c in this one-size-fits-all formula:
The ± means that there are two solutions, one for the formula with a + and one with a –. In the Babylonian problem, a = 1, b = 7 ad c = –60, which gives the two solutions 5 and –12. The negative solution is meaningless when describing area, so the answer is 5.
Quadratics are used in calculations other than those analysing area. Physics was essentially born with Galileo Galilei’s theory of falling bodies, which he supposedly discovered by dropping cannonballs from the Leaning