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The History of Business and Financial Mathematics (part 2)


III-) The Value and the Currency

At a time when men lived in restricted communities, taking from nature all the products they needed, there must no doubt be very little communication between the various societies. But with the development of handicrafts and culture and due to the unequal distribution of the various natural products, trade has gradually become necessary.

The first type of trade was barter, a formula whereby goods and commodities corresponding to raw materials or objects of great necessity are exchanged directly (and thus without the intervention of a "currency" in the modern sense of the word).

Sometimes, when it came to groups that entertained unfriendly relationships, these exchanges were in the form of a silent barter. One of the two parties deposited, at a previously established place, the various goods with which it wished to exchange and, on the following day, found in its place (or beside them) the products offered by the other partner. If the exchange was considered convenient, the products would be taken, or returned the next day to find a larger quantity. The market could then last several days or even end without exchange when the two parties could not find ground for understanding.

Scenes as such could be observed for example among the Australian aranda, the Ceylon vedda, the Bushmen and African pygmies, the botocudos of Brazil, as well as in Siberia and Polynesia.
With the intensification of communication between the various groups and the increasing importance of transactions, the practice of direct barter has quickly become a hindrance. Goods could no longer be exchanged at the whim of such an individual or by virtue of a use consecrated to the price of endless discussion.

There was therefore a need for a relatively stable system of evaluations and equivalences, based on a principle (neighboring that of the base of a numbering system) giving the definition of some fixed units or standards. In this system it is always possible to estimate this or any value, not only for economic operations but also (and perhaps above all) for the regulation of important legal problems, and all sorts of utilitarian products, materials or objects served on that occasion.

The first barter unit admitted to pre-Hellenic Greece was the ox. It is no coincidence that the Latin word pecunia means "fortune, currency, money": it comes, in effect, from pecus, meaning "cattle, flock"; moreover, the proper meaning of the word pecunia corresponds to "having in oxen".
But in ancient times the barter operation, far from being a simple act, should instead be surrounded by complex formalities, most likely linked to mystique and magical practices. It is in any case what the ethnological analysis of contemporary "primitive" societies reveals, which has been confirmed by a number of archaeological discoveries. It can therefore be assumed that in pastoral cultures the idea of ​​a standard bull (blood coin) succeeded the idea of ​​a "sacrificial ox" itself linked to the estimated intrinsic value of the animal.

By contrast, in the Pacific Islands goods were estimated on pearl or shell necklaces. After a certain period, it began by exchanging strips of fabric for animals or objects. The fabric was the coin; the unit was the span of the ribbon two times eighty wires wide.
Such methods, however, presented serious application difficulties. Thus, as trade developed, metals played an increasing role in trade, ultimately becoming the preferred "currency" of sellers and buyers. And the valuations of the various commodities began to be made quantitatively by weight, each referring to a kind of standard weight for one metal or another.

Also in Pharaonic Egypt, genres and commodities were often treasured and paid for in metal (copper, bronze, and sometimes gold or silver), which was initially divided into nuggets and straws. The assessment was also made in the form of ingots or rings, the value of which was then determined by weighing.

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So far we are not only dealing with a simple barter, but also a true economic system. From then on, thanks to the metal pattern, the goods were no longer exchanged at the mere pleasure of the contractors or according to often arbitrary consecrated uses, but because of their "fair price".

Until then, it was merely a matter of introducing into transactions and legal acts a kind of standard weight, the unit of value to which the price of each commodity or stock in question was referred. On the basis of this principle, such a metal or other could then serve at all times as "salary", "fine" or as "exchange value", and in the case of "fine" some kind of primary interest calculation was used to get a certain value for it.

By learning to count abstractly and group all kinds of elements according to the base principle, man has thus learned to estimate, evaluate, and measure various quantities (weights, lengths, areas, volumes, capacities, etc.). He also learns to reach and conceive ever larger numbers even before he can master the idea of ​​infinity.

He was also able to elaborate various operative techniques (mental, concrete, and later written) and to raise the first rudiments of an initially practical arithmetic before becoming abstract and leading to algebra - where today we have widely developed Financial Mathematics.

It was also opened the way for the elaboration of a calendar and astronomy, as well as for the development of a geometry initially structured in measures of length, areas and volumes, before being speculative and axiomatic. In a word, the acquisition of this fundamental data has gradually allowed humanity to try to measure the world, to understand it a little better, to put at its service some of its many secrets and to organize its economy to develop it.

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