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# Units

The chair is 2 away’ and ‘the popcorn needs 10 more’ make no sense to say. But ‘the chair is 2 metres away’ and ‘the popcorn needs 10 seconds more’ do make sense. A unit is clearly necessary. We have to invent units for our properties.

• We could for instance invent the unit metre1 for position (the ‘where’) and
• the unit second2 for time (the ‘when’).

And what about quantity? While it doesn’t make sense to say ‘how far is it? It is 3 away’, it does make sense to say ‘how many are there? There are 3’ or ‘you two go up the stairs’. We could say ‘3 pieces’ and ‘2 guys’ if we wanted to. But clearly, the unit can be implied and is thus not necessary. So, let’s keep ‘quantity’ unit-less.

The sizes need units as well. Let’s choose

• the unit metre for length,
• the unit square metre for area (since ‘square’ is a word for a 2D shape) and
• the unit cubic metre for volume (since ‘cube’ is a word for a 3D shape).

Since sizes are just ways to talk about chunks of space, it makes sense that their units overlap with the unit for position, the property of space. But while ‘metre’ makes sense for length (it is after all just a difference between positions), how should we understand ‘square metre’ as area and ‘cubic metre’ as volume? Let’s invent a description of these units:

• A square metre can be the space covered by 1 metre lengthwise and crosswise, while
• a cubic metre can be the space covered by 1 metre lengthwise, crosswise and vertically.

Now, after all these inventions, you may be asking: why metre and second?

Of no special reason. We could have chosen anything: ‘The cable is two coffee tables long’, ‘1 sofa length long’, ‘as long as the garden apple tree is tall’ etc. All would be fine as a length unit if we just picked one and stuck to it. Someone picked something back in history and called it the metre. And we have stuck to it ever since. How long that metre was chosen to be was not important as long as something was chosen (and as long as it was measurable).

References:

1. Online Etymology Dictionary’ (dictionary), Douglas Harper, www.etymonline.com