This entry is a short excursion into elementary number theory, an area of mathematics that would appear to have little to do with financial data, but which, in fact, lies at the heart of very heart of the process of keeping financial records.
Historically, numbers have represented magnitudes. The quantities of sheep in a flock, fish in a basket, or wives belonging to a rich husband were all magnitudes that required the invention of numbers to communicate. As a number, quantities were expressed simply as amounts, volumes, or other positive magnitudes. They had no meaning other than as positive amounts and they could only be combined with other positive amounts to produce new positive amounts, or compared with positive amounts, resulting in a ratio that was always positive.
All magnitudes can be fully expressed as positive numbers. The number zero is not needed because there is no such thing as a non-quantity. In a like manner, negative numbers are not needed to express magnitude because there simply is no such thing as a negative quantity. Historically, this purpose of expressing magnitudes defined what numbers were and determined the boundaries of numbers that made sense.
Eventually, the number zero was added as a place holder when larger numbers became expressed with a positional notation that aligned them in columns. This first occurred in India and eventually spread to Europe and became our modern number system. However, for centuries, only the concept of zero was added to positive numbers as they continued to only represent the magnitude of quantities.
Numbers continued to exist as positive expressions of magnitude until the nineteenth century when numbers, including integers, fractions (rational numbers), and amounts exacted with decimal points (“real” numbers), all morphed into something that has both a magnitude and a direction, a very elementary one-dimensional form of what engineers refer to as a vector. Today’s numbers have the magnitude that is expressed as the size of the number and a direction that is expressed as the number’s “sign.” A modern number has a sign that designates it as a positive or negative value, the negative values being those that are less than zero.
The significance of the revolution that gave the modern number a direction to go with its magnitude is that it is far more flexible and powerful to use. Where it once could only measure positive quantities and be combined and compared to other positive quantities, it can now be used to combine and compare opposition. The electrical engineer can use formulas that work with electricity of both positive and negative charge; the structural engineer can find the resulting force that is composed of both a left and right component, and the mathematician can find a valid answer when a larger sum is subtracted from a smaller. The modern idea of a number has given our industrial society a technical sophistication that was not possible with the numbers used by Isaac Newton and Galileo.
But, in the area of financial analysis, the idea of a number remains locked in its ancient manifestation as a magnitude without direction. The numbers that move our equity markets and shake our governments are the balances of accounts that are without a sign (until when a loss is reported to a general public that fully comprehends the negative direction of a number). Financial numbers come from obfuscating algorithms that are only necessary to compensate for the lack of numeric direction and that only accountants understand. The simplest and most intuitive business concepts are made difficult and obscure because modern accounting was invented before we gave numbers direction and they remain unchanged because of traditions and practices that are long past rendering a service to the world of information.
A credit is a withdrawal and is the negative of a debit that represents a deposit. Given its proper representation as a modern number the financial balance becomes a simple and intuitive concept that opens a whole new world of information to the information starved decision-maker.
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