Tianguis is a Mexican word that comes from the Nahua or Aztec language, for an open public market. The word has been used to describe markets where most of the vendors are indigenous Mexican farmers and craftsmen; however the use of the word has expanded to flea markets and outdoor bazaars. The major problem encountered by these sellers and their customers was that many or both were not fluent in the other's language. This led to frequent arguments and hand signals to affect an exchange.
The Arabs were the masters of mathematics during their ascendency, until their great works were destroyed in the crusades. One still finds many who use the abacus, a system of sliding beads on strings. They, and the Mayans, and the Hindi all held a special place for zero, but it was left to the Silicon Valley graduates to develop the calculator.
Time was when every engineering student carried a long, tan pigskin oblong object on his belt. Inside was a ten-inch device called a slide rule, more familiarly called a slip stick. That was not so long ago, you will recall. In order to understand that phenomenon, and the events leading up to it we need to understand a few basic principals of mathematics. We won't go into the various systems, other than to mention that the primary ones in use today are the binary; basically ON or OFF, and the base 10, or Decimal system. Logarithm, in mathematics, the exponent or power to which a stated number, called the base, is raised to yield a specific number. For example, in the expression 102 = 100, the logarithm of 100 to the base 10 is 2. This is written log10 100 = 2. Logarithms were originally invented to help simplify the arithmetical processes of multiplication, division, expansion to a power, and extraction of a root, but they are now used for a variety of purposes in pure and applied mathematics. They enabled mathematicians to use addition of numbers rather than multiplication to calculate, leading to the invention of the slide rule.
Slide rules came in several different forms. Usually they were the ten-inch one favored by engineers. They were accurate to three decimal places, which was sufficient for most engineering estimates. There were also circular slide rules that were handier to carry, and equally accurate. My father worked in budgetary estimation, where more accuracy was needed. He had a ten-foot slide rule in his department that was accurate to four decimal places, and was frequently used by the engineers when higher accuracy was required.
In 1967 a team of three engineers from Texas Instruments, Inc. invented the portable, electronic, handheld calculator. Jack Kilby, widely known as the inventor of the integrated circuit (IC), or computer chip, along with Jerry Merryman and James Van Tassel, built an IC-based, battery-powered miniature calculator that could add, subtract, multiply, and divide. This basic calculator could accept 6-digit numbers and display results as large as 12 digits. The prototype of this device is now displayed in the Smithsonian Institution, based in Washington, D.C.
The process was acquired by a division of Rockwell International, based in Anaheim, California, and not too long afterward was licensed to a Japanese consortium. The Japanese began selling these hand-held calculators for a tenth of what they were bringing on the open market, and the slide rule was gone, replaced by the hand-held calculator.
Pocket calculators always produce the same results when proper entries are made, and their accuracy is as great as the number of digits on the display screen. The development of the battery-powered hand-held calculator brought about tremendous furor in the academic, shopping, and banking communities. Schools, banks, even the tiangues of Lakeside were affected. Teachers did not know whether to ban their use or encourage them. Would discourage students from learning basic mathematics? Others thought that students needn't learn the basics because calculators were universally available. At first, when only the lucky few had them, calculators were forbidden in examinations. When at last they were permitted, the invigilators examined them with suspicion. They were checked to see they held no cribs, and that their capabilities did not make the mathematics too easy. Left with paper, pencil, and time few students today can perform even simple long division, and root extraction is an impossibity. But now, we do not have the conflicts about prices at the tianguis.
