---
title: Improving our units and notation
---
Many of the systems and ideas we use every day, like the way we count and
measure things, were developed over centuries. They have managed to "stand the
test of time", which is certainly an advantage; but they also suffer a form of
"historical inertia", which can prevent subsequent insights from gaining
traction.
For example, we still talk about 90°, 120° and 180° instead of ¼, ⅓ and ½ turns;
essentially because the Babylonians didn't have fractions 5000 years ago. We
also have redundant units like the tonne (Megagram) and litre
(milli-cubic-metre); we waste time learning tricky, niche concepts (like
subtraction and pseudovectors) rather than more elegant, general alternatives
(like negatives and rotors, in the cases mentioned).
These pages are my ongoing attempt to find such situations, where we can replace
complicated approaches with simpler ones; combine a bunch of ad-hoc choices into
some smaller set of consistent rules; and avoid some notions entirely (turning
them into niche historical curiosities, rather than foundational curricula
taught to every child).
Note that the truly important parts, the underlying ideas, are generally *not*
my own; although their unorthodox presentation will include some originality,
e.g. to avoid historical baggage and focus on coherence. Many of these are whole
subjects which *will not* be described in full detail, or with the level of
rigour some might desire; this is largely due to my own ignorance, but also to
focus on equipping individuals (mostly myself!) with a 'core' of good ideas,
which can be taken further if desired. I'll include links to Wikipedia, etc. for
those who are curious for more!
Each idea should be mostly stand-alone, although they will be *presented* in a
cohesive way (for example, long-subtraction uses the notation from negatives);
I'll try to cross-link such cases.
## Categories ##
[Quick wins](quick_wins.html) lists some ideas which are relatively easy to
adopt right now. More specific, in-depth pages are collected below, into rough
categories.
### Units of Measure ###
[The metric system is far better than the various 'imperial'
systems](metric.html), although
[not for the reasons usually given](metric_red_herring.html).
We can make life even simpler by limiting ourselves to the SI subset of metric,
although [that could also be improved](improving_our_units.html).
### Numbers ###
['Minus signs' are ambiguous](minus.html) and should be avoided. Instead,
[over-bar notation composes better](negative_bar_notation.html), and facilitates
[negative digits](negative_digits.html) which let us
[avoid subtraction](subtraction.html).
Unfinished:
- [Extending to place-value notation](place_value.html)
- [Joining matching parentheses](parentheses.html).
- [Vectors and PGA](projective_geometric_algebra.html)
- [Projective geometry](projective.html)
- Finding [the difference between values](diff.html)
It can be useful to distinguish between *absolute values* and the *relative
differences between them*. This is pretty straightforward in one dimension, and
lets us find the difference between Natural numbers (resulting in an Integer).
This is closely related to vectors, and [extends](extents.html) to signed areas
(bivectors), signed volumes (trivectors), etc. in higher dimensions. Those
concepts are core to Geometric Algebra, but also appear in fields like Algebraic
Calculus. I'm not sure if they're directly compatible, but it would be
interesting to find out!