20 Million Cubic Litres

I just sat in a cafe and read the European edition of the guardian, which sadly doesn't have Ben Goldacre's column in it. This week he makes fun of bad usage of numbers and statistics in newspapers. The European edition does, however, have a report on sending music to the stars, with the following excerpt:

Nasa will encrypt the song and beam it into space from its Madrid transmitter on Monday at the start of a 2.5 quadrillion-mile trip (that's 23 zeros for anyone without a large capacity calculator) to Polaris, where it will finally arrive in the year 2439.

The single most useful thing I learned studying physics is that there are almost exactly pi*10^7 seconds in a year. I also learned that the speed of light is almost exactly 3*10^8 m/s. So if you multiply the speed of light with the time of 400 years, there is no way that you're going to get a power of 10 to the 23.

I never learnt what a quadrillion is, as any attemped use usually ends in confusion between the British and American systems, but all these things that end in 'illion' are powers of three. 23 is a prime number, and obviously not a multiple of 3. I worked all of this out in the cafe, but things are a lot easier with a google calculator, which kicks ass, and has room for lots more zeros than needed astronomically.

((2 439 years) - (2 008 years)) * c = 2.53363342 × 10^15 miles

(Rounding to an appropriate level of significance is left as an exercise for the reader)

If all this sounds too mathematical, you can just look up Polaris in Wikipedia, and find out that it is 431 light years from the earth. This means that light will take 431 years to get there, and will arrive in 2439. No miles, no powers of tens to the fifteen, not so much fun.