On Wednesday 27^{th} November 2013, friend of The Aperiodical and standup mathematician Matt Parker tweeted a link to his latest YouTube video.

[youtube http://www.youtube.com/watch?v=r7x-RGfd0Yk]

In the video Matt apologises for some remarks on the imperial number system that he made in an earlier Number Hub video about the A4 paper scale. He then goes into some of the quirkiness of the many imperial number units used for measuring length. It is an unusual ‘apology’, although very entertaining.

This got me thinking about how I think about lengths, and I tweeted that I often think in ‘metric-imperial’ units of length, or multiples of exactly 25mm in my job as a civil and structural engineer – a metric inch, if you like. Colin Wright suggested the name ‘minch’ for these units; there are then two score *minch* to the metre.

I went on to say that similarly you could have a metric pound, the *mound*, of exactly 450g. These units are actually pretty accurate approximations to their imperial origins – a minch is within $1.6\%$ of an inch, and a mound within $0.7\%$ of a pound. They have the advantage that they are “useful” everyday amounts. In effect the pound has already been rounded (more crudely) in many grocery purchases, becoming 500g. That’s often about as much as you need of something (e.g. the 500g of seedless raisins that is currently in our baking cupboard).

I went on to think about an equivalent unit of time. Colin Beveridge suggested a *piyear* of about 100 megaseconds, but I felt that the current way of defining time in relation to distance using the speed of light^{1} should be used._{
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So I came up with the complementary unit of time being the time taken for light to travel one billion minches. This turns out to be remarkably close to one-twelfth of a second ($\frac{1}{11.99169832}$ to be a little more precise). I thought of the name ‘mec’ for this unit, but Colin proposed the far more satisfactory *light-gigaminch*.

I thought about extending the idea to these other units, and there is a lot of interesting reading about how the definition of fundamental units is evolving on Wikipedia:

When it comes to the other SI units (temperature, charge, molecular amount and luminous intensity) you quickly get into considering other fundamental constants like the Boltzmann Constant (with units of $\frac{ML^2}{T^2}$^{ }K).

But in the end I decided this was only a bit of fun, and perhaps I was stretching a point. After all a change in temperature of $1$°F is just a change in temperature of $\frac{9}{5}$°C or °K and it’s hard to see how you could make that very much simpler.

And so here are the proposed set of ‘metric-imperial’ units:

Mass | mound | = | $0.45$ kg | ≈ | $1$ pound |
---|---|---|---|---|---|

Length | minch | = | $0.025$ m | ≈ | $1$ inch |

Time | light-gigaminch | = | $\frac{1}{11.99169832}$ s | ≈ | $\frac{1}{12}$ sec |

Any further thoughts or ideas are very welcome.

- Actually in the latest definition of the SI units this is the other way around: time is defined first based on a frequency property of a caesium atom, and length is then defined from time using the speed of light. [↩]