Computers don’t do numbers very well. They don’t do numbers at all. What they do is manipulate sets of symbols according to certain logical rules. We humans connect these symbols with numbers, or some other object of our thoughts. A certain symbol could be a number, a letter from some alphabet, or even a colour chosen from some finite palette. The following was written in 1842 by Ada Lovelace

Many persons who are not conversant with mathematical studies, imagine that because the business of [Babbage’s analytical] engine is to give its results in numerical notation, the nature of its processes must consequently be arithmetical and numerical, rather than algebraical and analytical. This is an error. The engine can arrange and combine its numerical quantities exactly as if they were letters or any other general symbols; and in fact it might bring out its results in algebraical notation, were provisions made accordingly.

She is credited by many as the world’s first programmer. How many programmers today have the same understanding that she did?