Wednesday, August 26, 2009

A Note on Zero
Part I

Zero

One of the most important intellectual feats of all time was the invention of the Zero. Now “0” is what enabled the creation of a place system of writing numbers and in fact seems to absolutely necessary for higher mathematics aside allowing the use of numbers in a significantly less cumbersome way.

Now the “0” is a symbol meaning “nothing” and indicating non existence and as such the idea of something representing “nothing” can be a bit of a stretch especially if you figure out that this “nothing” is in fact a real number and not simply “nothing”.

Now the concept of Zero, as a number, since it is not obvious seems to have been invented only three times. In Ancient Babylonia, Mesoamerica and India.1 In each case the invention seems to be independent. So called uses of Zero like symbols in Egypt etcetera do not count in that they seem to have been used to indicate that nothing of X remained and not to have been used as a true number to count with. A dash in list by an item is also today commonly used to indicate nothing.2

Babylonian Zero

Now I mentioned above although a Zero represents “nothing” this nothing is still in mathematical terms a real number so that thinking of Zero as simply being nothing misunderstands what it is.3 This being the case any symbol representing nothing is not necessarily a Zero. In order for a Zero to be a true Zero it must be used in a numerical system and must be understood to be a number like other numbers.

Now to get to the point of what do I mean about a Zero being a “true number” perhaps one can look at the following problem:

6789 divided by 0 = ?

If you don’t treat Zero like a real number you get the answer “0”. If you treat Zero like a real number you get the answer infinity. In other words zero goes into 6789 an infinite number of times.4

Now the other use of Zero indicating that it is viewed as a “true number” and not simply an indication of nothing is if you use it in ordinary ways to number things. For example the Maya had Zero days, and years indicating that they understood Zero as a true number.5

Mayan Zero

It is strange that the Greeks and the Romans had a hard time with the idea of both infinity and the void and that this led them to avoid using a Zero. To put it simply the idea that there could exist “nothing” was thought impossible by most Greeks and Romans and further the idea that something could be infinite further bothered them has being both absurd and horrible.6

The Mathematicians of India however had no problem at all with either the idea of a void “nothing” or the idea of infinity. The result was that they devised a Zero and place system of writing numerals.7

Indian Zero

The Zero is one of these inventions that only seems obvious in retrospect. In fact it seems that the idea of using something to represent nothing and that that “nothing” is in fact something is simply counter intuitive.

Later I might write some more about the Zero but this is it for the time being.

1. Seife, Charles, Zero, Penguin Books, London, 2000, p. 12-19, 63-71, Ifrah, Georges, The Universal History of Numbers, John Wiley & Sons, Inc., New York, 2000, pp. 148-156, 308-311, 438-439.

2. See web page on Egyptian Zero. Lumpkin, Beatrice, The Ancient Egyptian Concept of Zero and the Egyptian Symbol for Zero, Here Page provides some interesting material but fails to prove that the “Zero” is a Zero at all.

3. Seife, pp. 19-23, 131-156.

4. See Seife p. 71, Ifrah, p. 440, and Wikipedia, Division by Zero, Here. I should note that this answer does not solve all division by Zero problems and that this result can lead to mathematical paradoxes etc., if your not careful. See Wikipedia article for more info.

5. Ifrah, pp. 312-316.

6. Seife, pp. 19-62.

7. Ifrah, pp. 356-440, Seife, pp. 63-82.

Pierre Cloutier

No comments:

Post a Comment