The Appeal of Nought.

It’s strange to think that nought or zero isn’t really a number. Numbering systems go back many thousands of years but as late as the seventh century the existence of zero was argued over. The Hindu-Arabic number system brought to Europe in the thirteenth century by Fibonacci had only the nine numerals 1 to 9 but used a placeholder symbol ‘o’ that as he excitedly put it, “any number may be written.” It’s thought the Olmecs in S America also used a placeholder symbol as early as 50BC and appears in the Mayan calendar, but neither considered it a number. To consider the enormity of this concept consider an empty table and being asked, “There are zero things on the table, what are they?” It’s of course absurd; there could be zero of anything on the table, apples, spaceships or people. In terms of counting quantity, which is why we invented numbers, zero is not an integer or even the smallest fraction of one. As a placeholder symbol it simply allows unlimited counting. The same can be said of negative numbers. “How many negative amounts of things on the table?” Once zero is conceived of negative numbers can also be conceived. What has been built using these concepts is not a quantitative counting system but the whole numerical edifice of mathematics, hugely useful and powerful but not in some basic sense counting. Yet today we count using zero and negative numbers as equally real as the Arabic numerals 1 to 9. We no longer differentiate between quantitative numbers and conceptual numbers. This is no small matter. It’s the difference between reality and illusion. I might even suggest ‘enough’ is a more quantitative number even though it’s not defined numerically. My question is how are we being misled by conceptual numbers? As a simple example we might buy a computer or a car on their impressive stats whilst having little use for the power they provide. A man may strive to acquire wealth a thousand times greater than he could ever spend or become fat from eating twice as much as his body needs. Increasingly our use of conceptual numbers has made numeracy emotive, and apparent quantities dictated by power. How can it be a financial wiz can acquire more in a minute than a bus driver in a year? Because he is at the heart of the economic power that dictates the value of numbers, conceptual numbers that have become real quantities. It’s impossible to argue against because the whole human race has now embedded in its counting system what was introduced as a conceptual placeholder symbol as a real numeral. Try for example this simple mathematical proof.

Let x = y. 
Then x² = xy. 
Take y² from both sides: 
x² - y² = xy - y² that can be written as

(x – y)(x + y) = y(x – y). 
Divide by (x - y) gives 
x + y = y. 
As x = y, this gives 
2 y = y. 
Thus 2=1 or 
1 = 0.

By dividing by (x – y), ie zero as x=y and zero is only a placeholder symbol one gets a spurious result. Such spurious results are our undoing.