Anthony J. Pennings, PhD


Lotus Spreadsheets – Part 5 – Numeracy and the Power of Zero

Posted on | February 17, 2015 | No Comments

Previously, I explored the electronic spreadsheet as a meaning-making application that was central to the financial explosion of the 1980s and its Apple II running VisiCalc spreadsheet economic aftershocks. Spreadsheets framed and produced information and meaning consequential to monetary and organizational practices as they became part of the daily routines of information workers.

In my last post, I explored the importance of symbolic representation systems, mainly writing, in the workings of a the spreadsheet. Written alphanumerical symbols have had a historic role shaping modern Western society and with the invention of ASCII characters, the facility of the PC-based applications, including the spreadsheet. In this post, I will focus specifically on the power of numeracy, with a special emphasis on the role of zero. The zero is an extraordinary cognitive invention that has been central to the rise of modern capitalism and that peculiar manifestation, the modern corporation.

Although still used on occasion for style, Roman numerals have been mathematically obsolete for several hundred years. Initially based on scratching or tallying systems for sheep and other items, Roman numbers most likely represented hand figurations or gestures. For example, the number 10 or X probably represented two thumbs crisscrossed. Addition and subtraction were relatively straightforward, but division and multiplication were not as “easy or obvious.” Roman numerals included thousands (“M”) but they never developed a representation for million or beyond.

The modern system of numeration is based on representations using ten different digits 0, …, 9 imported from the Middle East and Asia and will be called Indo-Arabic in this post. These numerals are said to have been designed based on the number of angles each numeral contained and over the years the way they are written have rounded out. The Arabian interest in Indian numerals based on zero arose to solve practical problems such as inheritances, purchases, sales contracts, tax collection and wills. Indo-Arabic numerals moving from India to the Middle East and finally to Europe were crucial for accounting and financial systems that have since become global standards and key ingredients in spreadsheet formulations.

Evidence dates the zero (also known as the naught, or nil) back some 2000 years to the Angkor Wat civilization in Cambodia; although it is generally recognized that India refined its use around 500AD, and it came to Europe in the early 1200’s from Arabia. Muhammed ibn-Musa al-Khwarizmi, or “Algorismus,” as his name was Latinized, was probably one of the most influential mathematicians in the transfer of this knowledge to the West. The Persian scholar taught in Baghdad sometime between 800 and 850. He wrote a book on the Hindu number system that was translated into Latin as De numero indorum or “On the Hindu numbers.” He later wrote another seminal book, Al-jabr w’al muqabalah, which became known in Europe as Algebra, based on the author’s Latin name and is the root of the English word “algorithm.”

One of the mathematicians who introduced these numbers to Europe was Leonardo of Pisa or Leonardo Pisano, famously known as “Fibonacci.” It is short for filius Bonacci, the son of Bonaccio. In his book, Liber abaci (Book of the Abacus or Book of Calculating) completed in 1202, he showed how the Indo-Arabic numbers could be used. The book was divided into four parts. The first introduced Indo-Arabic numbers, especially zephirum, which became zefiro in Italian, zero in the Venetian dialect. The second section showed how calculations dealing with currency conversions, compound interest, and the determination of profit could benefit businesses. The third and fourth sections addressed a number of mathematical problems including irrational numbers and the Fibonacci sequence that the author is most known for today. The video below introduces his relevance to commercial activities.

It was the development of the zero and the related positional system that made modern “Western” calculation systems so effective. It has become necessary for a variety of mathematical purposes including decimals, sets, and quite significantly, the mathematical systems that makes it easier to work with larger quantities. Using the place holding system, nine numbers plus zero can represent an infinity of figures. The same symbol, such as 7, takes on different meanings (7, 70, 700, etc.) depending on its location within the representation of the number. The positional base-10 system using ten different digits 0, …, 9 has been globally accepted as the primary mathematical standard for human calculation.

The base-10 positional system probably emerged from counting on our fingers, but it is adequately suited to arithmetical computations as it needs only ten different symbols and uses the zero to mark the place of a power of the base not actually occurring. Think of a car’s odometer that every ten miles causes the dial to turn and milestones such as 10,000 and 100,000 are markers of a car’s age that we often subscribe significance.

One of the strengths of the spreadsheet is its ability to combine complex calculations with human understanding of the base-10 mathematical system. While the “alien intelligence” of computers can now handle more complex base systems such as the duodecimal (base-12) and sexagesimal (base-60) place-holding systems used in time and geographic calculations, base-10 is useful because, quite frankly, humans are used to it. Although computers use a base-2 system with nearly infinite combinations of 1s and 0s, the positional base-10 system has been globally accepted as the mathematical standard for human calculation and a key component of spreadsheet usability.

The calculative abilities of zero and other Indo-Arabic numbers brought new levels of certainty and confidence for commerce and eventually science in the West. By 1300, zero-based accounting and other numerical techniques were being adapted by the merchant classes. Double-entry accounting techniques emerged first for tracking resources and checking for errors, but later resulted in the conceptual separation of a business from its owner, a precursor condition for the emergence of the modern corporation. The spreadsheet drew on this history of numerical innovation to become a tool of organizational productivity and power.





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