Monday, September 7, 2009

Origins of the Numerals

Origins of the Numerals

Today's numbers, also called Hindu-Arabic numbers, are a combination of just 10 symbols or digits: 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0. These digits were introduced in Europe within the XII century by Leonardo Pisano (aka Fibonacci), an Italian mathematician. L. Pisano was educated in North Africa, where he learned and later carried to Italy the now popular Hindu-Arabic numerals.


Hindu numeral system is a pure place-value system, that is why you need a zero. Only the Hindus, within the context of Ind-European civilizations, have consistently used a zero. The Arabs, however, played an essential part in the dissemination of this numeral system.




Numerals, a time travel from India to Europe

The discovery of zero and the place-value system were inventions unique to the Indian civilization. As the Brahmi notation of the first 9 whole numbers...

Before adopting the Hindu-Arabic numeral system, people used the Roman figures instead, which actually are a legacy of the Etruscan period. The Roman numeration is based on a biquinary (5) system.

To write numbers the Romans used an additive system: V + I + I = VII (7) or C + X + X + I (121), and also a substractive system: IX (I before X = 9), XCIV (X before C = 90 and I before V = 4, 90 + 4 = 94). Latin numerals were used for reckoning until late XVI century!







The graphical origin of the Roman numbers






Other original systems of numeration

Other original systems of numeration were being used in the past. The "Notae Elegantissimae" shown below allow to write numbers from 1 to 9999. They are useful as a mnemotechnic aid, e.g. the symbol K may mean 1414 (the first 4 figures of the square root of 2).

Chinese and Japanese contributions

The Ba-Gua (pron. pah-kwah) trigrams and the Genji-Koh patterns, antique Chinese and Japanese symbols, are strangely enough related to mathematics and electronics. If all the entire lines of the trigrams (___) are replaced with the digit 1 and the broken lines (_ _) with the digit 0, each Ba Gua trigram will represent then a binary number from 0 to 7, and each number is laid in front of its complementary (0<>7, 1<>6, 2<>5, etc...).

Write "a", "b", "c", "d" and "e" under the five small red sticks of each Genji-Koh pattern. By doing so, you will have the 52 manners to CONNECT 5 variables in boolean algebraics. The binded sticks form a "conjunction" (AND, .), and the isolated sticks or groups of sticks form a "disjunction" (OR, +). The pattern at the top left represents: [("a" and "d") or ("b" and "e") or "c"]


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