hertz
Posts: 1315
Joined: 8/7/2010 Status: offline
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@ Termyn8or ... Exactly. The point is that unless you have a reasonable grasp of mathematics, the numbers are just beyond comprehension. A million, a billion, a trillion - these just sound like three numbers which are each somewhat bigger than the previous number (which of course they are, but with a twist). These are numbers we hear every day in relation to national debt, corporate net worth and so on, but, for the average person, they are pretty well meaningless. quote:
ETA: I'm a bit worried by the people who chose 138x10^whatever, though. Isn't it obvious that the answer has to be the first number you gave times a multiple of ten? I'm not convinced it is obvious. Most people, given a piece of paper and access to the internet and a calculator will, eventually, reach the correct answer. As you suggest, it isn't exactly difficult - it's effectively about adding zeroes. But (and this is the part which you might not grasp because you clearly have a way above average grasp on maths), what those extra zeroes mean, for most people, defies comprehension. And the fact that it is about zeroes is not really implied in the name of the number. For many years it was even possible that a billion might be either of two possible numbers (I think that's all been sorted now). As an aside, I remember reading once that it is difficult for most people to visualise what 8 actually means, let alone a number with six zeroes in it (try it - close your eyes and visualise a person. Now add another person, and another... At some point you will need to count them to keep them in place). I guess that's why counting and numbers were invented - we can't cope with large quantities of objects without having some sort of system to translate the reality of the objects into something more understandable. And that works well for human scale quantities of objects: I can't visualise the difference between 100 and 110 (two groups of people, one containing 100 and the other containing 110 look pretty much identical), but I can easily grasp that 110 is ten more than 100. But at some point it all seems to break down. I find it really hard to grasp the sheer enormity of the difference between a million and a billion, even though I can see the zeroes, without going back the other way and trying to make it into something 'real'. To use Termyn8or's example, the odds of winning the main prize in the lottery in the UK is about 1 in 14 million. People dutifully go off and buy a ticket every week, not considering that: quote:
...your chances of dying in an airplane crash? A one-year risk of one in 400,000 and one in 5,000 lifetime risk. What about walking across the street? A one-year risk of one in 48,500 and a lifetime risk of one in 625. Drowning? A one-year risk of one in 88,000 and a one in 1100 lifetime risk. In a fire? About the same risk as drowning. Murder? A one-year risk of one in 16,500 and a lifetime risk of one in 210. What about falling? Essentially the same as being murdered. And the proverbial being struck by lightning? A one-year risk of one in 6.2 million and a lifetime risk of one in 80,000. And what is the risk that you will die of a catastrophic asteroid strike? In 1994, astronomers calculated that the chance was one in 20,000. However, as they've gathered more data on the orbits of near earth objects, the lifetime risk has been reduced to 1 in 200,000 or more. http://reason.com/archives/2006/08/11/dont-be-terrorized The chances of getting struck by lightning or hit by an asteroid look high in comparison with the chances of winning the lottery. But do we protect ourselves against lightning or asteroids? Hell, no, because that would be crazy, and yet we still go out and buy lottery tickets. And we still look at a national debt figure which is just unbelievably, incomprehensibly huge, and call it 13 Trillion dollars without really getting what that means... This isn't so much about the maths - it's about our understanding of what the maths might mean, and what numbers actually represent. I'm not a mathematician, so I still find this stuff mind-blowingly amazing and awe-inspiring...
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