“Life moves very fast. It rushes from Heaven to Hell in a matter of seconds.”
― Paulo Coelho

This week, I was suddenly reminded of a fact I’d been meaning to keep track of, and I was disappointed to discover that even though I always endeavour to remember birthdays and holidays (mainly due to a system of elaborate reminders, notes and excessive list-making), I’d missed a hugely significant anniversary. Shortly after the clock struck midnight on New Year’s eve, I had passed one billion seconds old.

While not one of the usual anniversaries to celebrate, I’d been looking forward to this one – it turns out that one billion seconds works out to somewhere between 31 and 32 years (my ‘just-after-midnight’ statement assumes I know the exact time I was born, which I don’t, but I have a reasonable estimate) . If you’d like proof, here’s a breakdown:

$$\begin{gathered} 1000000000\mathrm{s}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}\mathrm{s}=1000000000÷60\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{u}\mathrm{t}\mathrm{e}\mathrm{s} \\ 16666666.\dot{6}\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{u}\mathrm{t}\mathrm{e}\mathrm{s}=16666666.\dot{6}÷60\mathrm{h}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{s} \\ 277777.\dot{7}\mathrm{h}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{s}=277777.\dot{7}÷24\mathrm{d}\mathrm{a}\mathrm{y}\mathrm{s} \\ 11574.\overline{074}\mathrm{d}\mathrm{a}\mathrm{y}\mathrm{s}=11574.\overline{074}÷7\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{k}\mathrm{s} \\ 1653.\overline{43915}\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{k}\mathrm{s}=1653.\overline{43915}÷52\mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{s} \\ =31.\overline{796906}\mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{s} \end{gathered}$$

This quantity may mildly surprise you – partly because humans in general can be quite bad at interpreting numbers like a million and a billion. We know what the number means, and can calculate with it, but intuition can fail us when trying to put it into context.

It turns out that a second is quite a nice way to contextualise large numbers – for example, here’s an interesting fact I heard about the number of seconds in six weeks:

$$\begin{array}{rcl}6\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{k}\mathrm{s}& =& 6\times 7\mathrm{d}\mathrm{a}\mathrm{y}\mathrm{s}\\ & =& 6\times 7\times 24\mathrm{h}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{s}\\ & =& 6\times 7\times (8\times 3)\mathrm{h}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{s}\\ & =& 6\times 7\times (8\times 3)\times 60\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{u}\mathrm{t}\mathrm{e}\mathrm{s}\\ & =& 6\times 7\times (8\times 3)\times (10\times 3\times 2)\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{u}\mathrm{t}\mathrm{e}\mathrm{s}\\ & =& 6\times 7\times (8\times 3)\times (10\times 3\times 2)\times 60\mathrm{s}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}\mathrm{s}\\ & =& 6\times 7\times (8\times 3)\times (10\times 3\times 2)\times (3\times 5\times 4)\mathrm{s}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}\mathrm{s}\\ & =& 1\times 2\times 3\times 4\times 5\times 6\times 7\times 8\times (3\times 3)\times 10\mathrm{s}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}\mathrm{s}\\ & =& 10!\mathrm{s}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}\mathrm{s}\end{array}$$

The number of seconds in six weeks can be expressed as a product of the numbers one to ten – that is to say, there are 10! seconds in six weeks. Large factorials like this ($10!=3,628,800$) are similarly difficult to quantify, so this is a nice fact to have in your pocket.

A million is a more manageable number; a million seconds is just over 11 and a half days, which might be the length of a single short project you work on in your lifetime, or how long a holiday lasts, or somewhere at the long end of how long you might reasonably expect a banana to keep for (if it was really fresh when you got it).

So my 1 billion seconds = 31 years milestone makes a nice distinction between a million and a billion – a couple of weeks versus a good chunk of my life. Another reason I’m disappointed not to have properly celebrated (I mean, I was celebrating, but not necessarily this) is because this is probably the biggest power of ten I’ll reach in my lifetime. I’ll probably survive to 2 billion seconds, and if I’m lucky maybe even 3 billion, but there’s no way I’ll make it to 10 billion and certainly not a trillion.

But here’s some you might manage:

• 1 year on the planet Jupiter is about 11.86 years
• 10 million minutes (aka 10 MEGAMINUTES) is about 19.01 years
• 1000 fortnights is about 38.33 years
• 1000 months is about 83.4 years, if you’re lucky!

So raise a billion glasses for me, and celebrate your milestones in seconds not years (as long as it doesn’t make you feel too old).