Sunday, August 10, 2014

Millions and Billions

When I was a teenager in Canada there was a time when many people were talking about the concept of a million. People would wave their lottery ticket and talk about how wealthy they would be when they won a million dollars. They talked about government debts that were measured in millions of dollars. People tried to envision what a million of anything would look like.

Recently I have been again thinking of the concept of millions and then I added to this by thinking about billions. We use the word billion a lot more now than we did in the 1970s and we even talk about billionaires in the world.

Yesterday I went out on my relatively healthy lawn and counted blades of grass. In a one centimetre by one centimetre section of the lawn I counted 50 blades. In a ten centimetre by ten centimetre square I scaled up and estimated approximately 250,000 blades. Then, I did some more math. Based on my counting, if the whole lawn was of this same uniform density, then a million blades of grass would take up a space of 20,000 centimetres squared (cm2)  or 2 m2; that is, they would fill a square that is 1.4 metres by 1.4 metres.

Then I did the math for a billion. One billion blades of grass would take up 2000 square metres of land which is equivalent to a square that is 44.7 metres by 44.7 metres. This is a little less than half of the area of a football field.

I found this impressive but still hard to visualize. So I started thinking about ping pong balls. A standard ping pong ball is four centimetres in diameter. Four of them in a square take up a space of eight centimetres by eight centimetres or 64 cm2. Therefore, one million ping pong balls will rest on 1600 square metres of land or 0.16 hectares. This is equivalent to a square that is 40 metres by 40 metres. One billion ping pong balls would take up 160 hectares of land which is equivalent to a square that is 1.265 kilometres by 1.265 kilometres. Let's round up and say that one billion ping pong balls would sit inside a square that is 1.3 km by 1.3 km. This is getting easier to imagine.

Now, hang in there with me for one more visualization. If we say that a penny is 1.5 mm in thickness, then a stack of one million pennies would be 1.5 km tall; provided that the bottom penny was not squished by the weight of the million minus one on top of it. By extension, a stack of one billion pennies would be 1500 km tall and a stack of 25 billion pennies would be knocked over by the moon as it went by in its orbit.

These are interesting concepts and images but where is the practicality in this blog? Well, hopefully it is easier to comprehend large numbers by visualizing a comparative system. For example, I have been trying to visualize how many people are in the world and think about how many of them are in difficult circumstances. There seems to be an excessive amount of war and suffering in our world right now. When I was born, the world population was around three billion people, and today there are over seven billion people on this planet. I wonder how many of those seven billion are suffering right now. Everyone desires that these seven billion might be at peace with themselves and with each other. We try to imagine a world in which this could happen. For my part, I will choose this day to be at peace with the small fraction with whom I come in contact and I call upon you to consider doing the same. Perhaps you and I can start to scale up peace.

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