# Happy Birthday to me

“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:

$1000000000\ \mathrm{seconds} = 1000000000 \div 60\ \mathrm{minutes}\\ 16666666.\dot{6}\ \mathrm{minutes} =16666666.\dot{6} \div 60\ \mathrm{hours}\\ 277777.\dot{7}\ \mathrm{hours} =277777.\dot{7} \div 24\ \mathrm{days}\\ 11574.\overline{074}\ \mathrm{days} =11574.\overline{074} \div 7\ \mathrm{weeks}\\ 1653.\overline{43915}\ \mathrm{weeks} =1653.\overline{43915} \div 52\ \mathrm{years}\\ = 31.\overline{796906} \ \mathrm{years}$

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:

$\begin{eqnarray} 6 \ \mathrm{weeks} &=& 6 \times 7 \ \mathrm{days}\\ &=& 6 \times 7 \times 24 \ \mathrm{hours}\\ &=& 6 \times 7 \times (8 \times 3) \ \mathrm{hours}\\ &=& 6 \times 7 \times (8 \times 3) \times 60 \ \mathrm{minutes}\\ &=& 6 \times 7 \times (8 \times 3) \times (10 \times 3 \times 2) \ \mathrm{minutes}\\ &=& 6 \times 7 \times (8 \times 3) \times (10 \times 3 \times 2) \times 60 \ \mathrm{seconds}\\ &=& 6 \times 7 \times (8 \times 3) \times (10 \times 3 \times 2) \times (3 \times 5 \times 4) \ \mathrm{seconds}\\ &=& 1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8 \times (3 \times 3) \times 10 \ \mathrm{seconds}\\ &=& 10! \ \mathrm{seconds}\\ \end{eqnarray}$

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).

• #### Katie Steckles

Publicly engaging mathematician, Manchester MathsJam organiser, hairdo.

### 3 Responses to “Happy Birthday to me”

1. Dani Poveda

Happy Birthday, Katie! I’m having mine next week!

I’m turning a semiprime number of days, $4931 \times 2 = 9862$ days, which are $852076800$ seconds.

In this year, $2017$, I’m turning ${3}^{3} = {\lfloor\pi\rfloor}^{\lfloor\pi\rfloor} = {\lfloor\frac{852076800}{{\pi}^{17}}\rfloor}^{\lfloor\frac{852076800}{{\pi}^{17}}\rfloor} = 27$ years old on Pi Day! :D