Numbers that limit us

The first big number that I remember learning about was Avogadro’s number, N, which is 6.022 x 10²³ and represents the number of molecules in one gram-molecule of oxygen. My first chemistry teacher at school, Mr Horkan, was Russian-born and I remember he had a distinctive way of pronouncing ‘Avogadro’, with a heavy guttural accent. We loved to imitate him saying ‘Avogadro’s number’. Occasionally he would deviate from the curriculum slightly and devote a lesson to Russian history rather than chemistry. I recall that he pronounced ‘Novgorod’ with a similar inflection to his ‘Avogadro’. He was an interesting man and I owe my interest in both maths and chemistry to his teaching.

The speed of light is another big number that I learnt at school, though I remember it as 186,000 miles per second which is more manageable than the SI version (299,792,458 metres per second). Nothing can go faster than that, we were told, and it seemed a reasonable idea. If motorways have a speed limit of 70 miles per hour then a universal speed limit of 186,000 miles per second seems generous enough.

Then my education moved on into the world of quantum physics and I encountered Planck’s constant. This is the other end of the scale, unimaginably small at 6.626068 x 10^-34 m² kg / s. Its minuscule value is a reminder that quantum weirdness is very far removed from the scale of everyday life.

This musing on numbers large and small and the limits they impose on us was provoked by a tweet from Andy Powell yesterday. His tweet mentioned the term Yobibytes (YiB), which was new to me but he helpfully included a link that explained what it means: 1 Yib = 2⁸⁰ bytes. That is quite a scary number. Andy’s tweet referred to a short blogpost which asked if anyone had an estimate of “quantitative data on the current deployed storage estate” in the UK higher education sector. It cited various large numbers relating to data storage volumes. During the panel discussion on data at Science Online London last month Tim Hubbard, from the Sanger Institute, told us that Sanger are having to double their storage capacity every 6 months. Currently they are at 12 Petabytes. I wonder whether there will ever come a day when we will have to stop doing science because there is nowhere left to store the data?! Or perhaps Yobibyte-sized USB sticks will become commonplace?

That was quite a thought-provoking tweet from Andy, and all in just 140 characters. Now, that is a limit that I bump up against rather more than the speed of light, or a Yobibyte. I was recently tweeting a large number of links and was very grateful to whoever invented link-shorteners. Without them there would have been no room in my 140-character tweets for any text but the link. URLs seem to have got longer and longer. In the early days of the web they were very simple and short but as websites got bigger and more complex so have URLs. I wonder if anyone has gathered data on the changing length of URLs over the last 20 years, since the web began?

Anyway, I think I have reached my word limit for this rambling blogpost so I will end there.