Estimating things, Avogadro
After reading the book Innumeracy years ago, I've tried to estimate different things and to visualize big numbers. Today, while putting the kid to bed (it takes an hour or two, usually) I started thinking about Avogadro constant, that is, the number of particles in a mole. The number is about 6.022 * 10^23, which is very much beyond our usual numbers.
(Explanation of scientific notation.)
I started tackling this number by first thinking of something that would be big, but comprehensible. There are some 6 * 10^9 people on Earth, so it's a good number to start with. This means that everybody on Earth has just 10^14 of... something. Next I thought of something that would be in the billions (10^9, I play an American here) - that is just 1000 * 1000 * 1000, so it's not really that big. It occurred to me that sugar cubes could be approximated by cubes one centimeter a side, and it would just be that 1000^3 for a billion of them. That's a cube ten meters a side, composed of sugar cubes.
This means that if everyone has a ten-meter cube of sugar cubes, it would account to 6 * 10^18 sugar cubes. We're still somewhat short of the original 6 * 10^23, but now we're left with only 10^5 to account for. In the bed I made a mistake about the number, I thought it would be 6 * 10^22, so I thought of what could sugar cubes have that would number ten thousand. Quick mental third root and some checks later I had the answer: if each sugar cube consists of cube sugar crystals and there are 22 crystals per side, there are about 10^4 crystals in each cube. (10648 to be exact, but this is just an estimate).
This means that the number of sugar crystals when each sugar cube has 10,000 crystals and each person on the Earth has a ten meter cube of these sugar cubes, is about 6 * 10^22. To account for the last factor of ten, one might imagine that everyone has a tower hundred meters tall, ten meters a side, consisting of said sugar cubes. Then we at last come to the conclusion that there would be Avogadro's constant worth of sugar cubes.
That's a log of sugar. One would imagine that the Earth would be covered in them, at least in cities. (Exercise: how deep would these sugar cubes be if they were evenly spread on all the available ground? What if you used water, too?)
What is the really numbing thing about this is that this is the number of atoms in about 12 grams of regular carbon. It is very very hard for me to imagine all those sugar crystals, but it's still possible. Trying to relate this to the fact that there are quite a lot more atoms around here is just ming-boggling.
So, I thought it was a nice exercise. Sometimes I feel like I should be a scientist again.
(Explanation of scientific notation.)
I started tackling this number by first thinking of something that would be big, but comprehensible. There are some 6 * 10^9 people on Earth, so it's a good number to start with. This means that everybody on Earth has just 10^14 of... something. Next I thought of something that would be in the billions (10^9, I play an American here) - that is just 1000 * 1000 * 1000, so it's not really that big. It occurred to me that sugar cubes could be approximated by cubes one centimeter a side, and it would just be that 1000^3 for a billion of them. That's a cube ten meters a side, composed of sugar cubes.
This means that if everyone has a ten-meter cube of sugar cubes, it would account to 6 * 10^18 sugar cubes. We're still somewhat short of the original 6 * 10^23, but now we're left with only 10^5 to account for. In the bed I made a mistake about the number, I thought it would be 6 * 10^22, so I thought of what could sugar cubes have that would number ten thousand. Quick mental third root and some checks later I had the answer: if each sugar cube consists of cube sugar crystals and there are 22 crystals per side, there are about 10^4 crystals in each cube. (10648 to be exact, but this is just an estimate).
This means that the number of sugar crystals when each sugar cube has 10,000 crystals and each person on the Earth has a ten meter cube of these sugar cubes, is about 6 * 10^22. To account for the last factor of ten, one might imagine that everyone has a tower hundred meters tall, ten meters a side, consisting of said sugar cubes. Then we at last come to the conclusion that there would be Avogadro's constant worth of sugar cubes.
That's a log of sugar. One would imagine that the Earth would be covered in them, at least in cities. (Exercise: how deep would these sugar cubes be if they were evenly spread on all the available ground? What if you used water, too?)
What is the really numbing thing about this is that this is the number of atoms in about 12 grams of regular carbon. It is very very hard for me to imagine all those sugar crystals, but it's still possible. Trying to relate this to the fact that there are quite a lot more atoms around here is just ming-boggling.
So, I thought it was a nice exercise. Sometimes I feel like I should be a scientist again.