# Quick wins for improving units

Some of the ideas described in this project are more aspirational than practical, and need adoption by many people in order to be worth switching. In contrast, the entries on this page can be followed right now, with instant benefits!

## Units

### Replace imperial with metric

Imperial units differ between countries, have arbitrary conversion factors, and lots of redundancy. Metric is the same in every country, and doesn’t require conversions (it is coherent).

#### Use metres instead of yards

Those stuck with imperial for compatibility (e.g. in the USA) may find it useful to measure distances in yards rather than feet: since a yard is roughly the same size as a metre, this can build intuition for metric, and rough estimates can be used interchangably.

### Use the SI subset of metric

The metric system has some redundant units like hectares, litres and tonnes. Avoid them, and stick to the subset defined by SI (in those cases: square metres, cubic metres and kilograms, respectively).

### Measure angles in turns

Turns are a direct, intuitive unit for rotation. They are more natural than arbitrary alternatives like degrees (1/360th of a turn) or gradians (1/400th of a turn). For example we can say ‘a quarter turn’ rather than ‘90 degrees’.

### Write turns using τ

Radians are another natural unit of angle, where there are around 6.28… radians per turn; a quantity we represent with the symbol τ. Writing our angles with a τ suffix, like ¼τ, works for both of these units:

• We can interpret τ as ‘turns’, similar to how we interpret ° as ‘degrees’. Hence ¼τ can be read as “a quarter turn”.
• Alternatively, we can interpret τ as a conversion factor between radians and turns, with a value around 6.28… radians per turn. In which case ¼τ can be read as “a quarter of the radians in a turn”, which is about 1.57… radians.

Both of these interpetations are equivalent/interchangable: the syntax we write down is the same for both, how we choose to interpret them is a matter of taste and convenience.

### Replace π with τ/2

The constant π (around 3.14…) is the number of radians in half a turn. Since we already have the constant τ for the number of radians in a turn, we can replace all occurrences of π with τ/2. Whilst the factor of ½ seems annoying, having it appear explicitly in a formula seems preferable to having it be implicit in the definition of π (in fact it is common for formulas to contain 2π, which have the opposite problem!)

Subtraction is redundant and doesn’t behave as nicely as addition: in particlar, rearranging subtractions will change their result (it’s not ‘commutative’ or ‘associative’), e.g. $\left(2-3\right)-7=\overline{8}$, but $2-\left(3-7\right)=6$.
Subtraction requires negative numbers (like the $\overline{8}$ above); in which case, we might as well use them as inputs too. That way we can always use addition, which is commutative and associative, e.g. all of the following are equal $\left(2+\overline{3}\right)+\overline{7}=2+\left(\overline{3}+\overline{7}\right)=\overline{3}+2+\overline{7}=\overline{8}$