I have always hated math. I could see its use in for example programming, but I could never appreciate math and numbers for what they are. This changed after we had to guestimate how long it would take to evacuate all 32 million people in the Tokyo area. And after that the number of drops of water in the North Sea. I loved this experience and told enthusiastically to my fellow students that these guestimations would be the only reason I would do math and like it.

A lot of them liked it a lot less. “You can’t do this to math problems”, they explained. “10 is not of the same order as a 100”. So how come that the same experience can provoke such a different emotion. I think this has to do with the concept we have of math. We see it as accurate with only one good solution. For a lot of problems this true. The engineer that build a skyscraper can’t be off by a factor of 10. In the math exams I did in high school it was not allowed to be off by a factor of 10.

So how can you in these guestimations be off by a factor of 10? This is because of why you are doing it. If you do it for designing a skyscraper, you do the math for the safety of the people who are going to live or work in it. If you do a math test you do it to show your skill in a field of math. So why do you do the guestimations? I think you do them for yourself. To understand how much a billion dollars is. How many molecules are in a can of coke? The answer to this question is; It is in the same order of number of drops of water in the North Sea. Or if the monucules where the size of autodropjes(a Dutch licorice) the number to cover the whole earth with one kilometre of those. This makes it possible for me to reason with these big numbers. And as Phil Plait put it beautifully: “Teach a man to reason, and he will think for a lifetime”

So coming back where we stared is the order of a factor 10 useful. I think it is. If you see a number in the paper or hear it on TV and radio. You can check it. You should not worry if your off by a factor of 10. If you are off by a factor of 10 you should do some research. Are your guestimations or is the number wrong? For this purpose the order of 10 is useful for other goals more accurate numbers are useful. And if this factor 10 provokes sceptical interrogating number we otherwise would have taken for granted, it can’t be wrong way of doing math. Because science is exactly that the sceptical interrogation of our universe.

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