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# Symbols & equations

Saying ‘the chair is 2 metres away’ or ‘the position of the chair is 2 metres away’ works. But writing it becomes exhaustingly long. Let’s invent a shorter way to write it, such as:

$$s=2\,\text{metres}$$

Here we gave ‘the position of the chair’ a simple symbol: $s$,1 and we chose the symbol $=$ to mean ‘is’ or rather: ‘equals’. This way of writing – this “language”2 – is called mathematics.3

The $=$ symbol – the ‘equal sign’ we might call it – now tells us that what is on its right side is the same as what is on its left side. This is surely also the case if they were switch around:

$$s=2\,\text{metres}\qquad 2\,\text{metres}=s$$

So, the order doesn’t matter. Whenever such ‘equal sign’ is involved, let’s call it an equation. Now, let’s give a symbol to the other properties we have so far:

• Position can be symbolised $s$ as we just did,
• time $t$ and
• quantity $n$.4
• For the sizes, length/distance can easily be symbolised $L$,5
• area $A$ and
• volume $V$.

Sentences such as ‘the area of the trampoline is 6 square metres’, ‘the volume of the hay stack is 3 cubic metres’ and ‘the fall lasts 10 seconds’ can now be written shorter as

$A=6\;\text{square metres}\quad$ , $\quad V=3\;\text{cubic metres}\quad$ and $\quad t=10\,\text{seconds}$

The units are also long, though. Let’s shorten them down as well:

• The second can be shortened to $\mathrm s$, while
• the metre can be shortened to $\mathrm m$,
• the square metre to $\mathrm m^2$ and
• the cubic metre to $\mathrm m^3$.

The square metre and cubic metre were just the metre in 2 and 3 directions, so $\mathrm m^2$ and $\mathrm m^3$ feel fitting.6 Our sentences are now nicely compact:

$A=6\,\mathrm{m^2}\quad$ , $\quad V=3\,\mathrm{m^3}\quad$ and $\quad t=10\,\mathrm{s}$

The symbols could have been anything – letters are easy. If we run out of letters in the English alphabet, we can use other alphabets as a supplement, such as the Scandinavian ones with their $æ$, $ø$ and $å$ or the Greek with its $\alpha$, $\beta$, $\pi$, $\rho$ etc. See an overview of some alphabets in Resource: Alphabets.

Note that we have chosen to use italic symbols for properties and non-italic, straight-up symbols for units. Because, why not? It makes it easy to see them apart.

References:

1. Sapiens. A Brief History of Humankind’ (book), Yuval Noah Harari, Penguin Random House UK, 1st ed., 2014, www.penguin.co.uk/books/109/1097846/sapiens/9780099590088.html, ISBN 9780099590088, page 140
2. Online Etymology Dictionary’ (dictionary), Douglas Harper, www.etymonline.com