One billion. Rather big number isn't it? Try and imagine for me one billion pennies? Very hard to visualise as were not used to dealing with such large quantities, but what if i said that i can picture it in two very different sizes?
First we have this
Some wishing well
owner's going to get rich off you.
But then we have this
Even bigger.
Thanks to Alan Taylor of The Mega Penny Project for the pictures.
If you think that's strange then you're probably normal because it is strange. But it does get stranger. By the end of this article I hope you will understand that you can't know which picture is correct just by looking. It takes a little more work than that.
Now, how many times have you counted to one billion? If we count at an average of three numbers per second and i told you that counting to one billion would eat up either 10.56 or 10,560 years, would you believe me? Would you believe that some people, counting at the same speed, would take longer to count to one billion than others? Impossible?
Well actually no. The fact is that counting to one billion is not counting to a specific number, it is counting to a word with an ill defined numerical value, as is the way with all very large numbers.
The problem with these very large numbers is the name of certain numbers depends on where you live..
..Kind of.
It starts with one billion. One million is 1 with 6 zero's wherever you are unless you live a fantasy world where dogs walk their people, men wash the dishes etc. But one billion is different.
In the U.S.A, one billion is 1 with 9 zero's (1,000,000,000 or 10^9). In the UK it is traditionally 1 with 12 zero's or a million million (1,000,000,000,000 or 10^12), whereas 1 with 9 zero's is a thousand million or a milliard.
So we have a diagram.
What is this telling us really? It is telling us the rate of which the population of planet earth is increasing in billions. But what kind of billion are they using? Without implicit numerical data we have to assume the numerical figure or do further research.
But that's simple right? If you're in the UK it's one thing, if your in the U.S it's another, but that just can't work. If i had one billion pennies and traveled to Florida, where do the extra 999,000,000,000 pennies go? Anything physical, such as the world population or pennies, cannot be dynamic in it's 'real' number according solely to man-made borders of spatial dimension. It's just unfeasible and unworkable.
How about then if the above diagram was made in the UK. Then we can surely assume that they are using 10^12 as a billion or 10^9 if it was made in the USA. We have become used to many regional differences in the english language, postman - mailman, trousers - pants, pants - underwear and that's fine. We have no trouble discerning and accommodating the difference in abstract concepts such as language but with numbers, which are 'real' as in 1+2=3 no matter where you are, we have a different story.
A lot of UK residents have adopted the US system of 9 zero's for one billion, the BBC have adopted 10^9 as the billion, as have the government themselves and as such there is an ambiguity as to how many zero's are in a billion when it is written in english instead of number form. For example, 'A Brief History Of Time' was written by Stephen Hawking, a professor of mathematics at Cambridge University. The use of billions in his line of work is very common i'm sure but wherever he writes the word 'billion' what exactly does he mean? This could be the difference of a thousand times
Consider the following example. You are getting ready for work with the news on in the background. As you pull on yesterdays boxer shorts you hear that an asteroid 1.8 billion nanometres in size is heading toward earth. Just as you turn to watch you stumble and fall down the stairs. You are worried that you may have a broken back, but are equally worried that a close encounter of the armageddon kind is imminent. Are you right to be worried? Should you risk permanent damage by getting to your feet and running around in a panic?
On the one hand, 1.8 billion nanometres could be equal to 1.8 metres, the height of a tallish man.
Nothing to worry about there. It will undoubtedly break up in our atmosphere before it even gets close to the ground, But there is always the chance that it is made of an unknown material which is about to get extremely intimate with your crotch.
On the other end of the scale, this 1.8 billion nanometres could be equal to 1.8 kilometres or 5.5 Eiffel Towers. This is huge.
Granted, 1.8km is not exactly apocalyptic but it is going to hit the earth somewhere and as we already know, it's coming for you.
This problem is a big problem for people like me who explain everything in inhumane measures and it continues upwards with higher numbers in multiples of one million. A trillion in the US is a million million or 10^12. In the UK a trillion is a million billion (in UK billions) or 10^18 which would be one quintillion In the USA. This is now the difference of a million times. To most people, i'm sure that this won't make a difference. How often are the numbers billion, trillion and quintillion used by most people? But while comprehending maths or physics books, you need some perspective and absolute amounts.
Imagine yourself back at the bottom of those stairs. Instead of worrying about 1.8 billion nanometres, let's instead worry about 1.8 trillion picometres. Once again this could be the size of a tall man (or woman), but at the other end of the scale the Eiffel Tower would now be eclipsed by a 1,800km asteroid. If you can't imagine how big that is, find something 1,800km in size. It's that big! Approximately half the size of the moon or just a little smaller than Pluto.
This is the reason that i believe it is time for a worldwide standard. Imagine if the number four had several values. Would you pay £4 for an ex-rental dvd? No me neither, i would be too scared that i would lose my life's savings.
Imagine, if you would, sitting a maths exam. the question is thus:
Q.4
Etho can equal 12 or 71
Atho can equal 2 or 972
What is the sum of Etho and Atho?
...................
Well, i expect you either got that answer correct or you didn't. Who am i to judge? I hope that this example highlights the importance of numbers having absolute value, otherwise they are as abstract and meaningless as the words that describe them.
Another real world example:
Imagine that you hear on the news that the government needs an extra 2 billion pounds per year for some crackpot venture. They say that every living person regardless of age or wealth has to 'donate' the same amount over the course of the year. According to the C.I.A World Fact Book the population for the United Kingdom is an estimated 60,776,238, so we need to work out 2 billion divided by 60,776,238 to see how much i would have to pay.
If for some crazy reason the UK government decides to use the traditional UK billion of 10^12, i would be paying £32,907.60p per year. That's £2,742.3p per month. I'm sweating already. According to National Statistics Online, the average annual wage for a full time employee is £23,244. So i would need an extra 1.4 full time jobs to pay this new tax.
If the word billion was used to describe 10^9 however, i would be paying £32.91p per year, that's about £2.74p per month. I think i could just about stretch to that.
Some other countries have 10^3 as a thousand, 10^6 a thousand thousand, 10^9 as a million and 10^12 as a trillion. Admittedly these are non english speaking countries (at least english is not the 1st language), but we are scaring them away from using the word billion altogether. Do we really want to be responsible for this? Even Stephen Hawking is scared of numbers now, considering he has an international reputation to uphold. I quote from the updated tenth anniversary commemorative edition of 'A Brief History Of Time' (p.31).
"..in the case of the most distant object that we have seen, the light left some eight thousand million years ago. Thus, when we look at the universe, we are seeing it as it was in the past."
Is he saying eight thousand million because he is extremely English? I myself refuse to acknowledge 10^9 as anything but a thousand million but one has to ponder Hawking's motivations.
(p.41/42) "The nearest star, called Proxima Centauri, is found to be about four light-years away...or about twenty-three million million miles."
Million million miles people. We should be ashamed.
