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Big Numbers

Entry 917, on 2008-12-31 at 23:06:20 (Rating 2, Science)

Over the last few days I have been discussing big numbers with a friend who is also a blogger. His original subject was how numbers involved with amounts of money are represented by the news media. Especially when it comes to contentious issues like the recent financial bail out of the banks and other institutions, millions, billions and trillions seem to just all disappear into the category of "a lot" to many people.

He has a good point. I think that many people would have trouble writing down those numbers because they might not know how many zeros are involved with each. If you are wondering, a million is 1,000,000; a billion is (usually) 1,000,000,000 and a trillion is 1,000,000,000,000. In science big numbers are usually written in an exponential form where the number of zeros is included, for example a trillion would be 10¹² which is a lot more manageable for really big numbers.

For example, there are about 10⁸⁸ particles in the observable universe. That's 10 thousand trillion quadrillion quadrillion quadrillion. That's a lot, isn't it? But would it surprise you to know there are 10²⁵ (10 quadrillion) particles (molecules in this case) in a glass of water? So there are 10⁶³ cups of particles in the universe!

Small numbers can be fun too. Here's one of my favourite examples of a small number: The first radio astronomy was done by Karl Jansky in the 1930s. Since then the total power collected by every radio telescope in the world is less than the energy of one rain drop hitting the ground. Notice that I didn't mention any numbers, but consider that there would be millions of hours of observations from the hundreds of radio telescopes in the world in that time.

Another amazing fact which shows the size of the universe without using big numbers is this: A single photo from the Hubble Space Telescope's Deep Field camera covers an area of the sky the size of a single dot on your screen at normal viewing distance. In that area there are 3000 galaxies! Imagine how many dots it would take to cover the sky, and how many galaxies there are in total if each dot contains 3000! And remember that galaxies typically contain 10 billion to 10 trillion stars each (OK, so I couldn't help throwing in some big numbers there).

Another way to explain how big the universe is is to compare it to something most people are familiar with. I ask them to think about going to a beach and picking up a handful of sand and thinking about how many grains of sand there are in that handful, then how many are on the whole beach, and then on every beach on the planet. That's a lot of sand, right? (most estimates put it at around 10²² or 10 billion trillion grains. But there are more stars in the known universe than that! (at least according to some estimates because the two numbers are very similar).

So maybe it would be better to present money wasted on the Iraq war or on saving the financial institutions using these sorts of techniques. There are 300 million people in the USA so a trillion dollars equates to $3,300 each. Whether that's more or less that what most people expect I don't know, but at least it gives an understandable figure to base their response on.

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