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.

She's the 1.66053886(28) × 10-24 moles

Here's a useful google calculator calculation: How many moles is a baker's dozen?. The google calculator will return any dimensionless unit in moles if you ask nicely, such as lightyear/foot (both distances), or kilogram/electron mass (both masses). The former means that a mole of footsteps will transport you millions of lightyears, the latter that a mole of electrons will weigh much less than a bag of sugar.

Google calculator thinks that a mole is just a large number. This is how I would think of it, too. The official definition of a mole is, however, as follows.

1. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is "mol."

2. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.

An amount of substance is "defined to be proportional to the number of specified elementary entities in a sample".

This is of course a load of bollocks (number yet unspecified, but hopefully less than a mole). The phrase "atoms, molecules, ions, electrons, other particles" is ridiculous. Do other particles include cows, donuts, shoes, ships and tins of sealing wax? If not, why not? If so, why not add a couple to the list:

...the elementary entities must be specified and may be atoms, molecules, cows, ions, dildos or other particles.

And don't go all "complex objects" and "elementary particles": an atom isn't elementary in the slightest, and despite the name can be cut open at will.

Why do the SI want to make this distinction between "elementary entities" and everyday objects? Why not use moles to count things? The problem is that the mole is defined in terms of kilograms, and the definition of a kilogram is "equal to the mass of the international prototype of the kilogram." The fact that all known masses are dependent on a lump of metal in Paris staying intact has annoyed scientists for a while. One cow is presently 1.66053886 x 10-24 moles of cows, but if the prototype kilogram loses mass—and in the last century it did—it could in the future be less.

Another problem is that nobody knows quite how many units are in a mole. This is why there is a (28) in the brackets of the title. This means that you could add (or subtract) 28 to (or from) the last two digits (86) and still be within the margin of error. So a cow could as much as 1.66053904 x 10-24 moles of cows, or as little as 1.6605358 x 10-24 moles of cows.

So presuming google calculator and I are correct in treating the mole as a counting unit (and who would wish to doubt this), all scientists don't know how many things they have, and are continously losing/gaining them too, depending on a lump of metal in Paris.

One way out of this crisis would be to count in units (the one), and define the kilogram in terms of electron masses. Thus scientists could again count with with the rest of the population. I don't think the chemists would like it, though.

As a reward for sticking with this post, here is The Answer in moles.

[Disclaimer: The Answer in moles contains error bars and may increase or decrease with time. The author accepts no responsibility for future changes to The answer in moles.]

Some Other Team 3 - Torpedo Entenhausen 1

I joined a football team in the "Spare time league" and made my debut for Torpedo Entenhausen this week. I ran around a lot and caused a bit of trouble for the opposition, who weren't so keen on running but felt that at least one of them ought to run after me. This means that I can play again next week.

I have acquired the ironic nickname the "Kopfballungeheuer", which translates as "The heading monster". Despite being the tallest person on the pitch, I kept missing the ball, and on the occasions when I made contact the ball bounced off my head in a random direction.

Some links:

Elf defence for 'lingerie thief'

Comedy stretcher bearers

I have finally fallen for the google calculator. Calculations with units included are definitely the way forward and cut out many of my mistakes.