August 21, 2012

Horse 1351 - Our Number's Up

Numbers. Billions and billions of them. Billions and billions of trillions of them. Most of us use number in our day without even realising it; numbers like 20, 4 and 47. Take a walk around your local supermarket and you see numbers like 250, 750, 74.67 and 10%.
Numbers are all around us, permeating our lives and even working away quietly in places we can't even see. Few people give thought though to the very scary truth that one day, we just might run out.

In agricultural societies most people only needed small numbers like 6, 7 and maybe if you were a farmer, numbers like 100 or 349. People used to use small numbers in trade and life was more or less simple. In fact the largest numbers which were known to be in use by high ranking officials were only in the millions.
THe ancient Egyptian hieroglyph for one million was this:

This is a man seemingly exasperated or perhaps terrified of the number he now holds. Numbers like one million were know to be so dangerous that normal Egyptian citizenry were not normally allowed to read, lest their brains fall out. It's a strange thought I know, but we shall return here.

The Sumerians used a Sexagesimal number system which instead of the number 10 as its base, used a base of sixty and the Babylonians improved on this by using a base of 360. The Greeks and Romans though who had far more militaristic ends for numbers reverted to a base of ten. They even formed their armies into groups of 100s; calling the officers in charge "hekatontarchos" in Greek and a "centurion" in Roman. Today we only really refer to centuries when talking about groups of years or perhaps runs in cricket.

The Romans though had a distinct problem. Their writing system only allowed them to properly deal with in thousands. The Roman notation for one thousand was a capital M.
This is an interesting aside but Abraham was promised that his "descendants as numerous as the stars in the sky and as the sand on the seashore", and the Pharaoh who would not let them go complained that they were uncountable. Although this is obviously due to there simply being a lot of people, the inability to count large numbers (the Romans could only count 1000s and the Hebrews only had a notation for 900), meant that at least they were aware that there was a problem.

During the Dark Ages, it was Arabic and Indian people who developed our current number system. It wasn't until gold started to return from the fringes of empires which were being built by the European powers that numbers bigger than a million were even required. At first only governments needed millions to deal with sums being drawn on budgets, but soon it became apparent that private parties were beginning to use them.
The American War of Independence started out as a taxation dispute, in which millions of pounds were being argued over. Many many lives were lost and the new nation, forged on the fields of battle still to this day has a national debt which runs into trillions.

Charles Babbage built the first computer (albeit mechanical) for the computation of astronomical and mathematical tables, and as science reached the middle of the 20th century, computers and eventually pocket calculators could be bought to handle ever larger volumes of numbers and calculations.

The problem with numbers being progressively larger is that people's brains simply can not deal with them or take them in. This is evidenced by most people's inability to remember anything larger than their own 10 digit telephone number; most people often can not remember their Tax File Number.
I suspect that if one were to behold all of infinity at once, that they would probably die instantly through shock or at very least be hideously mentally scarred. As it is, most people who work with numbers on a consistent basis, people like scientists, accountants, maths teachers and engineers, are on the whole, not normal. Some people like train spotters and B-road enthusiasts are really quite strange indeed and I wonder if this is further evidence of the hidden and dangerous powers of numbers. Already we have branches of mathematics looking at irrational and imaginary numbers, so this can't be a good sign if even the science of numbers is describing itself like this.

The fact is that we are using numbers so much now that we could be facing eventual calamity. Computers themselves are known as "number crunchers" and reduce millions, billions and increasingly trillions and quadrillions into a stream of 0s and 1s. Somewhere down the line we are going to start losing 0s and 1s and this can already be seen in government accounts and budgets.
Joe Hockey as Shadow Treasurer was accused of having a 70 billion black hole, and numbers smaller than 1000 are routinely dropped from the books of accounts of multi-national corporations.

We are being warned of an impending energy crisis, a future food crisis, climate change, and housing shortages but no-one in the media seems to want to talk about an impending number shortage.
We tell children in school that numbers go on forever but the same thing was said by Allessandro Volta who invented the battery and as we all know, batteries eventually need replacing because they "run out".
The point is that as limited and small beings we are aware that we can not handle very big numbers and we're unaware of how far they go. If numbers and mathematics are contained in one giant set, then we are in danger of using them all up. Crunching numbers means that machines have to be developed to make new ones and even though people do derive fortunes from pushing numbers around spreadsheets and computers, there might come a day when there are simply no more numbers left to use.

Please think of the numbers. Don't waste them.

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