Why notation matters

In his book “The Fabric of Reality”, David Deutsch considers notations to be theories of their own because they postulate symbols and relations according to how conveniently they are able to emulate the behavior of what they represent.

In this sense, some formalisms in certain contexts are indeed more valid than others, similarly to how different programming languages are better suited to one purpose than another.

It is quite trivial to realize that Deutsch’s hypothesis is correct, because the different mathematical notations used throughout history have indeed allowed calculations to be performed more intuitively and efficiently.

Just think of the nightmare it would be to do mathematical calculations using Roman numerals instead of Arabic ones.

Roman numerals represent only addition and subtraction efficiently, unlike the positional system of the Arabic numerals, and today are only used almost as decorative numbers.

But for certain tasks, even Arabic numerals can be outclassed. There is a numbering system invented by the order of Cistercian monks in the 13th century, which is able to represent very large numbers with an ingenious system.

A vertical straight line acts as an axis dividing the plane into four quadrants, each representing one of the four digits: the upper right…