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Bits & Pieces

Morse code is ternary but here is an easy binary code to use next time you’re in prison:

Tap code

Only uses taps and pauses, and never sequential pauses.

The 5×5 grid is a pretty optimal way to keep sequences low which is probably what you want.

Arguably an 8×4 box instead helps if you wanna learn ASCII at the same time since it sorta maps to octal, i.e. “E” would be “tap taptaptaptaptap” But, it’s 1 to 8 instead of 0 to 7.

We used to use just 7 bit ASCII straight up but it’s difficult to count the number of pauses that pass sequentially. An easy finger mnemonic for binary ASCII is to learn to count to four in binary (00, 01, 10, 11) and then use two 0-indexed 4×4 boxes (phalanges of both hands) and the sixth bit from the right sets lowercase.

Speaking of bit, today I learned that it used to be a value of money (a piece of eight) and two bits of a dollar was easy enough to figure out, it’s a quarter. And for odd bits, since there is no 12.5 cent coin people just used dimes. This would’ve worked well if the system was hermetic and you could just define a dime to be half a quarter and two dimes to be a quarter but of course they still had to interface with the larger world. So no one would wanna give you a quarter for two dimes.

Here’s R L Stevenson on the topic, in 1892:

In the Pacific States they have made a bolder push for complexity, and settle their affairs by a coin that no longer exists – the bit, or old Mexican real. The supposed value of the bit is twelve and a half cents, eight to the dollar. When it comes to two bits, the quarter-dollar stands for the required amount. But how about an odd bit? The nearest coin to it is a dime, which is, short by a fifth. That, then, is called a short bit. If you have one, you lay it triumphantly down, and save two and a half cents. But if you have not, and lay down a quarter, the bar-keeper or shopman calmly tenders you a dime by way of change; and thus you have paid what is called a long bit, and lost two and a half cents, or even, by comparison with a short bit, five cents.

This reminds me of how in the Arabian Nights there are dirhams and dinars and they are both in use but it’s not always straight-forward to exchange between them.

It’s a bit odd that binary bits are called bits, i.e. eighths, they should be called halves since binary is a system based on halving. Why the heck’s there eighths?

Solderpunk writes in to add:

I stumbled upon the answer to a question I’d never actually asked before, but in retrospect should have been obvious - why on Earth are octaves called octaves, if “oct” means eight? Okay, sure, eight is a power of two, but why not name them something more directly related to the basic concept, which is all about halving or doubling? The answer, as you may well already be aware, is that when - and only when! - considering a heptatonic scale, you need to go up/down eight consecutive notes to go up/down an octave. The name makes no sense from the perspective of scales of any degree other than seven. Of course, this is by no means the only case of “scale hegemony” in music terminology/notation - just one I hadn’t noticed before and one whose discovery just happened to coincide in time alarmingly well with your post!