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thinking about numbers… May 22, 2009

Posted by aquillam in Astronomy.
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A few weeks ago I was at an astronomy lecture Second Life. I went exploring the island latter, and happened to run into a couple of the other avs who had been to the lecture.  One of them said they had difficulty believing the Universe could only be a mere 13.7 billion years old. It’s such a small number. I wondered when “billion” became a small number…

I remember learning about the age of the universe in college.  I remember thinking how increadably young the Sun is compared to the age of the Universe. At 5 billion years, the Sun is roughly old enough that the very first sun-sized stars would have been dying as our Sun was born. It does sound very young when you think of it in terms of solar lifetimes.

But then I looks at the young earthers.  They believe the Earth is only about 4000 years old, and some of them say that they simply can’t believe that the Earth could possibly be billions or even millions of years old (just google “young earth”, you’ll get dozens of hits.)

In fact, most societies came up with an age of the Earth that falls into the thousands of years.  Dalrymple has a nice table in his book The Age of the Earth, and he also talks about how people arrived at the present age.  In some early cases, expirimental results were delayed from publication because people simply couldn’t believe the results they were getting.  I’m kind of wishing I had the book here so I could give you a specific example… Only a century ago, millions of years was inconcievably long!

Now recently I’ve heard people  talking about”billions of dollars” in industry and government as if it was chicken feed. People have become billionairs, so a billion dollars doesn’t mean much at the institutional level.  It’s gotta be a trillion to mean something. All this has me wondering if people have any idea what these numbers actually *mean* because I barely do, and I deal with huge numbers on a daily basis.

So I thought I’d run through an illustration I used to do for my astronomy class. One they tended to forget about within a week or so, I think because the concept was just too hard for them to concieve. And here’s hoping I’ve done my math right…

One sheet of US standard letter paper is 8.5 x 11 inches, and is about 0.1 mm thick.

One ream (500 sheets) of paper is 8.5 x 11 inches and stands 2 inches tall.

1000 sheets of paper would therefore make a stack roughly 4 inches tall.

One million is a thousand thousand, so a million sheets of paper would stand 4000 inches tall.  That’s 333 feet  or about the length of a football field, minus one end zone.

One billion is a thousand million. The stack analogy is kind of silly at this point: it’s 4,000,000 inches tall, or 63 miles.  If you stacked the paper on the floor of the football field (including both end zones), you would need to make each stack 11,273 pieces of paper high. Thats 22.5 reams of paper in every stack, with the stacks packed together to cover the football field – almost 4 feet of paper.

Now for a trillion. If a billion makes a stack about 63 miles tall, a trillion would make a stack 63 thousand miles tall.  This could wrap around the earth 2.5 times, or fill a football field 3/4 of a mile deep. Or cover a thousand football fields 4 feet deep.  That is a lot of paper…

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