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Facts of the Matter Richard Brill |
Breakthrough concept of
zero took centuries to evolveNobody knows when we first learned to count, but we do know that it wasn't done using numerals.
Bones dating from nearly 40,000 years ago have been found in Africa with 29 orderly marks on them, perhaps remnants of our most ancient ancestors tracking the moon cycle. The oldest surviving counting board, a precursor to the abacus, dates back only 5,000 years to ancient Sumeria. In those intervening 35,000 years, people most certainly kept track of things, but there are few records of it.
Numbers are not the same as counting, although we do use numbers to count and numerals to represent numbers. There are great conceptual leaps involved in generalizing from five oranges to five "things" to the abstract idea of just "five." Counting, numbers and their representation as numerals are steps in the development of technological tools that are the cornerstone of our own civilization just has they have been throughout the history of their development.
The simplicity and utility for calculations of our current decimal place-value system make it one of mankind's greatest inventions. It seems so simple and so natural that it may be hard to believe that it came into use rather late in history, and only through a long series of adaptations and modifications.
The Arabic numerals in use today developed from the ancient Indus civilization by way of the Middle East. The earliest Indian system was a decimal place-value system that was used as early as 2000 B.C., but the use of zero did not appear until 2,500 years later.
Zero is not the same as nothing. Nothing means the absence of anything. Zero indicates an empty space. It's the difference between having an empty mailbox and having no mailbox at all. Use of the zero as a place holder in an empty column allows for the unambiguous representation of large numbers, and represents a huge technological advance.
The ancient Babylonians also developed a place-value number system around 3000 B.C., but theirs was a base-60 system, convenient for record-keeping, but awkward for calculations. The most ancient Babylonian tablets portray large numbers, but out of context their meaning is ambiguous. For example the numbers 104 and 14 would both be written the same, as 14. If referring to the birth of a young boy as opposed to an event that happened a "long time ago" there would be no ambiguity because the context of usage defines the size of the number.
It took the Babylonians more than 2,500 years to get the idea of a place-holder. By 400 B.C. they were using a symbol much like our quotation marks to indicate the empty space, With that system 104 would have been written as 1"4, but the "double wedge" was never used for the final zero.
The number 100 would not have been written as 1"", but simply as 1. For some reason, it didn't catch on and the idea was never expanded upon.
Ancient Greek astronomers used the Babylonian system, having adopted the concept of the space-holder after seeing it in Babylonian tables of astronomical data, although there was no place-holder concept in the Greek number system generally.
The Greeks, brilliant philosophers and mathematicians that they were, had an awkward system of numbers that was based on their alphabet, not on numerals. They also used a different system for cardinal (counting) and ordinal (sequential) numbers, which made it even more difficult to do arithmetic, let alone to conceptualize the abstract quality of "number."
Ptolemy, the most famous of the ancient astronomers, wrote the definitive compendium of astronomy that stood as the authority on the subject from the time of its writing in the middle of the second century A.D. until the advent of modern science in the 17th century. He used a symbol much like the zero both between digits and at the end of a number, but it is likely that he considered it more of a punctuation mark than as a number.
It's not clear whether the use of the zero in India derived from Ptolemy's influence, or if it arose independently. It is clear that the zero came into use in India before the middle of the 7th century. Also of note is that the ancient Maya people, who developed a sophisticated culture in Central America long before the arrival of Europeans late in the 15th century, also used zero as a number. Unfortunately they did not influence others with their discovery.
The Indian number system, including the zero, was passed back to the Middle East where the current numerals gradually evolved over 200 years. The first Arabic text that explained the Indian numbers was written early in the 9th century A.D. The concept was also passed eastward, the first text using the zero appearing in China in the late 13th century around the same time that it made it to Europe.
A mathematician named Fibonacci is credited with introducing the Arabic numbers to Europe. As a youth Fibonacci traveled with his father, a customs official who traveled with merchants all around the Mediterranean.
In his travels, Fibonacci came in contact with and recognized the advantages of many different number systems. Upon completion of his travels he compiled various problems and principles of mathematics and published a mathematical textbook in 1202 A.D. using zero as a number in its modern context.
The concept met resistance but was gradually adopted and spread throughout Europe, where it would contribute to the rush of learning in the Renaissance and ultimately to the scientific revolution. Today we transform back and forth between various base number systems such as binary and hexadecimal with ease and have learned how to represent anything from text to sound, pictures, and video as a string of zeros and ones, a use of numbers never anticipated by those distant ancestors.
We could all be a little smarter, no? Richard Brill picks up
where your high school science teacher left off. He is a professor of science
at Honolulu Community College, where he teaches earth and physical
science and investigates life and the universe.
He can be contacted by e-mail at rickb@hcc.hawaii.edu