ORIGINS OF THE MULTIPIER DEFINITION IN MATHEMATICAL CALCULATIONS

(By Judge Navin-Chandra Naidu)

The Sanskrit scholar Pingala innovated the matrameru (mountain of cadence) system of mathematical calculations where the sequence of numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 . . . in which each successive number is the sum of the previous two, and the ratio between the a number and its immediate antecedent tends towards a golden mean (around 1.618).

Leonardo of Pisa, or Fibonacci, introduced this Indian method of mathematics when he published his path-breaking book Liber Abaci (The Book of Calculation) in 1202 where the discounted value today of a future revenue stream could be applied to commercial bookkeeping, to currency conversions, and crucially, to the calculation of interest using the decimal system which came with the matrameru. (See William N. Goetzman, Fibonacci and the Financial Revolution, National Bureau of Economic Research Working Paper 10352 (March 2004).

Usury was outlawed and its practitioners excommunicated in 1179 by the Third Lateran Council. Jews jumped at this opportunity to become money-lenders. But they found a get-out clause in Deuteronomy 23:20 unto a stranger thou mayest lend upon usury; but unto thus brother thou shalt not lend upon usury. Jews were expelled from Spain in 1492. By 1497, Jews were forced to adopt Christianity, and they sought refuge in the Ottoman Empire. In 1516 Venetian businessmen accepted Jews and their money-lending occupations and settled them in a special area of the city upon the site of an old iron foundry called the ghetto nuovo (ghetto means casting).

BANKING began with the Medici family after the 1340s wiped out the Florentine lending houses of Bardi, Peruzzi and Acciaiuoli when Edward III of England and King Robert of Naples defaulted on their loans The Medici were foreign exchange dealers. The Papacy became an important client with all sorts of currencies flowing into their coffers. Giovanni di Bicci de Medici was the pioneer of this business. Geneva, Pisa, London became branches of Medici business.

Bills of exchange (cambium per literas) was an important contribution by the Medici in the Middle Ages to finance trade. Medici drew up and sold the BOE to a bank on discount for cash when a trader could only pay after the transaction was concluded. The bank collected from the trader with interest. The Medici thus circumscribed usury laws frowned by the Church. The Medici made a fortune in banking and finance. Competition came. Gradually, the Medici were phased out.

Amsterdam, London and Stockholm led the next decisive wave of financial innovation. By lending amounts in excess of its metallic reserve, it pioneered fractional reserve banking exploiting the fact that money left on deposit could profitably be lent out to borrowers. Depositors seldom wanted their money out of the bank en masse, and only a fraction had to kept as reserves in the bank (bank policy). The liabilities of the bank thus became its deposits (on which it paid interest) plus its capital; its assets became its loans (on which it could collect interest) plus its reserves.

BANK OF ENGLAND began 1694 primarily to finance war by converting a portion of the governments debt into shares in the bank which brought special privileges to the bank plus a special monopoly for the creation of banknotes (1742) and the usefulness of fractional reserve banking system based on $100.

Example: You deposit $100 (M0) in Bank A. It keeps $10 on reserve and lends $90.00. The borrower takes the $90.00 to Bank B. This bank keeps $9.00 reserve (10%) and lends $81.00.

M0 equals $100.00, but M2 = $271 (100 + 91 + 81) = creation credit = money = FRACTIONAL RESERVE BANKING.