Which academic subjects examine the efficacy of counting systems?

Question

Which academic subjects examine what the advantages and disadvantages of the various number bases are, e.g. besides base ten: base twelve, base sixteen, base eight, base two and the ways that they can be written and pronounced.

For example, base eight 10001 can be pronounced "one zero zero zero one base eight", "four thousand ninety-six one", "two to the power twelve one", and some other ways, and there is no consensus about which way is best. Would this be a mathematical question, or a cognitive science question, or some other kind of question?

For another example, to what academic subject does the question of how to write thirty-six in base thirty-seven?

Answer 1

First, there is no authoritative taxonomy of academic subjects. As one example, the author of The Professor is In talks about how her research led to job interviews in departments including anthropology, gender studies, and Japanese. Even in the hard sciences, the boundaries between math, physics, chemistry, and computer science are quite blurry.

So how do you know whether topic X falls under discipline Y? The only real way is to see whether there are experts in Y that are working on X. And even this will not yield a one-to-one mapping; there are plenty of perfectly fine subjects that are not being studied at all, and other subjects that are being studied from many disciplines.

Second, there is little interest in developing new nomenclature. Famous physicist Richard Feynman once went down this road, coming up with his own (better, in his opinion) notation for trigonometric functions. He eventually abandoned this effort. From his autobiography:

I thought my symbols were just as good, if not better, than the regular symbols - it doesn't make any difference what symbols you use - but I discovered later that it does make a difference. Once when I was explaining something to another kid in high school, without thinking I started to make these symbols, and he said, "What the hell are those?" I realized then that if I'm going to talk to anybody else, I'll have to use the standard symbols, so I eventually gave up my own symbols.

More generally, there are plenty of places where the nomenclature really could be improved. The names of the quarks, for example, are a bit silly, and the mesons/baryons are not assigned names in any systematic way. Similarly, Dvorak is faster than Qwerty, Python is cheaper than Matlab, and English is more widely spoken than Hungarian. But even if we agree that making these substitutions would be wise, getting large groups of people to invest the time to learn "the new way" is difficult.

Finally, these are not research questions. Developing a new language, or a new software tool, or a new novel, is not usually academic research. Since it is not academic research, it may not fall under the purview of any academic department.

Now computer science researchers who work with binary and octal may find that your tool helps them do research, and that is great if so. But like all tools, researchers will have to judge whether the effort of adopting the tool is worth the benefits the tool can provide. And this can be tough: I put off buying an iPad for years, even though I could afford it, because I just couldn't see what problem it would be solving. More alarmingly, plenty of older researchers still code in Fortran rather than making the effort to learn a modern language. If it is this hard to "sell" a shiny new electric device or to replace a 60-year-old language, imagine how much harder it is to "sell" more marginal improvements. And if the proposed solution seems silly or seems to be solving a non-problem, getting widespread buy-in will be even harder.