Quick wins for improving units
Part of my units pages
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 by individuals right now!
Easy 🟢🟡🟠🔴 Hard
Units
🟢 Use metric rather than imperial
Imperial units differ between countries; metric is the same everywhere.
Imperial units have arbitrary conversion factors, and lots of redundancy; metric is coherent.
Metric is already the standard in most of the world (although the UK needs to sort out its road network, but that’s a whole other issue!).
🟢 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: 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 the hectare (ten kilo square metre), litre (milli cubic metre) and tonne (megagram). Avoid those, in favour of the subset defined by SI.
This also includes using Kelvin for temperatures, which is the same as Celsius but 273 higher.
🟠 Use more logical names
The base unit of mass is called the “kilogram”, which is an inconsistent use of the prefix “kilo” (it’s a thousand grams; but grams aren’t our base unit). The archaic name “grave” doesn’t have this problem.
The base unit of time is called the “second”, which is an inconsistent use of the ordinal “2ⁿᵈ” (it’s a sixtieth of a sixtieth of an hour; but hours aren’t our base unit). The abbreviated name “sec” doesn’t have this problem.
The downside is maybe having to explain what these mean to others.
🟢 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 interpretations 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.
Numbers
🟢 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!)
🟢 Add negatives instead of subtracting
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. , but .
Subtraction requires negative numbers (like the 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
🟠 Use binary prefixes
If we don’t mind numerical changes we can switch from base-10 prefices “kilo”, “mega”, etc. to base-2 “kibi”, “mibi”, etc. since they’re close enough, and the base is more sensible. Thankfully these are standardised, and the meaning should be mostly clear: perhaps listeners would think we have a speech impediment, but they’d get the right order of magnitude. It should go without saying, but we should not do this when being misinterpreted would have bad consequences!
🔴 Use a different base
Using a highly-composite numerical base, like dozenal; or a simpler base like binary (or adjacent systems like hexadecimal, common in computer languages).
These may be useful individually, but the widespread use of base 10 would likely counteract most of the advantages they offer in teaching, learning, calculating, etc.