A circle is an infinite number of points all equally distant from a single center. That definition came from Euclid, a Greek, although the Greek’s didn’t use zero. Aristotle was afraid to divide by the void because it wasn’t descriptive of the real world.
The Chinese and the Sumerians used placeholders in their counting, adopting different marks for the tens and the 60s digit, since Babylonians used base 60. But they didn’t have a zero.
The Mayans had a zero–they used base 20–which allowed them to produce large astronomical calculations that generated accurate solar and lunar calendars using only sticks. But their isolation prevented trade, which limited their civilization.
The Romans had zero, of course! Nulla. The Romans had sophisticated plumbing and developed roads that lasted for millenia. But Romans disdained to use nulla in their numbering systems, so even though their business records were hierarchical and detailed, they were limited. Growth is limited if a number like 397,654 is CCCXCVMMDCLIV.
The Arabs developed zero; they developed algebra. But the Arabs learned it from the Hindus.
Into the Void
The leap that Hindu mathematicians made, by going from a symbol of nothingness to a circle to a numerical concept, dates to around 500 ACE. The idea of the sacred void, shunya, dates much earlier in Sanskrit, perhaps to 1500 BCE. An Indian mathematician, Bhaskaracharya, showed that taking any number divided by this void (x divided by 0) would equal infinity, and that infinity further divided would remain infinity. The Hindus weren’t afraid of infinity since they could dream of how to divide it.
By 650 ACE, Indian scholars used zero as a placeholder. The placeholder concept was critical to writing and understanding large numbers. Many cultures adopted a decimal-based system–we have ten fingers to count with, after all. What happens when you get above nine? Writing 618 seems like a logical extension of the abacus, but what about 609?
The idea of 1 through 9 plus the 0 are commonly called Arabic numerals, but they may have originated from the Hindus. Yet the Arabs took zero and expanded the void like an opening umbrella over mathematical concepts.
The Qu’ran May Have Pre-Empted Luca Pacioli
While the path of zero until the mid 800s may seem meandering and mercurial, the Arab mathematician al-Khwarizmi grasped all its significance. Others understood negative numbers, but embracing the nothing between the numbers filled in the gap (quite literally) and allowed for new kinds of calculations. His 830 ACE book: al-Kitab al-mukhtasar fi hisab al-jabr wa’l-muqabala (The Compendious Book on Calculation by Completion and Balancing) was comprehensive. It also is the source for that word algebra.
But al-Khwarizmi’s arithmetic had an eminently practical side. For over a century, Arabs of wealth had been grappling with stringent rules in the Qu’ran which dictated inheritance law. What remained in an estate after payment of debts must be strictly divided among wives, sons, and other relatives. The last chapter of The Compendious Book actually covers inheritance accounting using a system of–wait for it–double-entry bookkeeping.
Yep. Luca Pacioli (see Letter “P”) is called the father of double-entry accounting, but it appears that his intellectual daddy was al-Khwarizmi. In fact, most medieval Christians, especially the Italians, considered the Arabs to be heretics and didn’t want anything to do with their evil mathematics. They distrusted zero and its blasphemous origins and were slow to develop accounting linked to the Qu’ran. So it took Europeans longer.
Yet though the Italians were slow adopters, they got there eventually. Marco Polo was credited with bringing many things back. By the late 1200s, zeros and sophisticated business accounting might have come from Arabia, Turkey, India, China, or any number of places along the Silk Road.
Infinity and the Foo Fighters
As with many things in history, some may erroneously gave credit to the Europeans, at least for bookkeeping. Who gets credit is often blurry. People credit Newton with calculus in the 1680s, although Leibniz also generated similar ideas in 1670. (Calculus being essential to economics, thus the bane of many a business student.) Leibniz also pioneered the idea of binary systems, and when Englishman George Boole in 1847 took Leibniz’ algebra of concepts further, he created Boolean algebra. An American student at MIT, Claude Shannon, noticed the similarity between Boolean logic and electric circuits and wrote a 1937 thesis on how computers could be structured, using binary systems.
The pioneering Dutch computer scientist Willem van der Poel said thanks very much, and as early computers were being built, he created in the 1950s what is described as the zero-one-infinity rule. As systems were built, some included arbitrary limitations such as word lengths, data interfaces, and bus lengths. Real world constraints exist; storage has a cost. However, the zero-infinity rule suggested that if there is a problem, the origin might be an arbitrary limitation in the design, rather than an error in code.
American computer science professor Bruce J. MacLennan also described it thus:
Allow none of foo, one of foo, or any number of foo.MacLennan’s version of the zero-one-infinity rule.
The only reasonable numbers are zero, one and infinity.
As computer programmers debate what “arbitrary” means in this rule, it’s clear that not only zero and one but also infinity must be taken into account. Today, the financial language of business has married the digital interface, and the two are now inseparable. It seems therefore fitting to end 26 posts about accounting concepts with rules that absorb zero to infinity, the result of zero divided.
Like the worm ouroborous, zero can stretch back on to itself. Ideas that leave the hearth to expand their journey along the Silk Roads of learning can return home to show the family that there can be placeholders, T-accounts, algebra, Ponzi schemes, binary computers, and numbers in the terabillions. Those of us in the noble profession are unafraid of the void.
As I said in letter “A,” most huge empires and great civilizations thrived because of their accountants. Things really took off when they embraced nothing.
Th-th-th-that’s all folks! Thanks for reading my A to Z Accounting. Drop me a note with any suggestions or thoughts for future A to Z challenges.