The Birkana hexadecimal number symbols

There was a teacher in high school that taught his classes to count in binary on their fingers. It became common for students to flip the double bird at each other in the halls yelling "132!"

In my high school orchestra, I'd count the rest measures on my cello's fingerboard using binary. Usually I'd only need four fingers, but occasionally I'd need my thumb as well if the composer mistook the cello for a bass.

This method is impractical to use due to the way the human hand works. Representing numbers where the middle and ring fingers are in different positions is tricky, and using this method for counting quickly is nearly impossible because it requires the simultaneous movement of multiple fingers up and down.

The method of counting on finger creases, on the other hand, is entirely practical, and I've known people who have used it for more than 50 years.

Coincidentally, I am reading a leading history of mathematics, and just read the section on Mesopotamian math (the source of our base 60 customs, such as time, degrees in circle, etc.).

The Sumerians (of Mesopotamia, as was Babylon) not only used base 60, but also were the first known to use position or place value to indicate power of 60 the same way we do in base 10, a significant invention. For contrast, the Romans did not use position: IV is 4, not 15. Thus 11 (imagine Sumerian characters; sorry I don't know my Unicode well enough) in Sumerian is 61 in our contemporary system, and 563 in Sumerian would be 18,363 today. I'm impressed: Could people work with these numbers in their heads? Did someone doing Sumerian addition and multiplication have to memorize 60 x 60 tables, the way we memorized 10 x 10 tables in grade school? (The historian is silent on this matter.)

> if you point just the joints, not the tips, you get base 12. / If you count multiples of 12 with the five fingers in the other hand, you get to 60. / And this is the reason we have the 12-hour ...

The historian doesn't mention this (and how would anyone know today how the Mesopotamians counted on their hands?), but does say, "There is reason to believe that this choice of 60 rather than 10 as a unit occurred in an attempt to unify systems of measure, although the fact that 60 has many divisors may also have played a role."

Other societies commonly have used base 20 (my speculation: maybe natural if you are barefoot or wear sandals) and base 5. I highly recommend the book, the leader in its time (1987) and maybe still today:

A Concise History of Mathematics, 4th revised Ed., by Dirk Struik

> And this is the reason we have the 12-hour, 60-minute system, and other sexagesimal systems, ever since ancient Babylonia.

> https://en.wikipedia.org/wiki/Sexagesimal

Your phrasing is quite a bit stronger than your source's:

> It is possible for people to count on their fingers to 12 using one hand only, with the thumb pointing to each finger bone on the four fingers in turn. A traditional counting system still in use in many regions of Asia works in this way, and could help to explain the occurrence of numeral systems based on 12 and 60

It was a long time ago; we don't actually know why the Mesopotamians liked cycles of 60, and it's unlikely that we ever will. But the argument "it's easy to divide 60 by 2, 3, 4, 5, and 6" is a lot more parsimonious. We do know that the Romans, despite using a base-10 number system, had money which divided into 12, not 10, subunits, precisely to make money easier to divide. 12 and 60 are technologically superior to 10, and this can explain their use even in societies which we know used base-10 numbers. (Such as... the Mesopotamians, who, as shown in your link, represented the value 47 as 4*10+7.)

Thanks a lot! :)

The shapes are all able to be written in a way that visits points in the corners of the square in the same order (UL, LL, UR, LR). So 0111 and 1110 can be written with the skewed V shape because the 1's are in sequence, while 1011 and 1101 are written with rotated L shapes because they skip one of the middle bits. (Compare also 1111, a backwards N shape).

The actual logic is a bit more benign.

Once upon a time, the digit for 0 was a dot, the digit for 1 was (close to) ι, the digit for 2 was (close to) μ, the digit for 3 was close to w with a leading descender like μ has. The digit for 4 might have been closer to a + sign that eventually morphed to look more like a backwards 2. It was the number of vertical lines which encoded 1, 2, or 3; with 4 and 5 and 6 there was more need to come up with more-abstract symbols.

In Arabic these first 4 digits have actually survived relatively unmolested, ٠‎ - ١‎ - ٢‎ - ٣‎, while the backwards 2 for 4 started hooking down to become a ٤ and some other stuff happened with the next 5 digits.

In English the digits for 2, 3, and 4 all rotated about 90 degrees counterclockwise while the tail disappeared for the 3 and the 4 didn't close up on the top until relatively late.

I get what the parent is saying, though. It's just binary digits on a weird looking vertical number line. Each part of the "digit" may as well be a zero or a 1, because that's all it represents. Position tells us what the value is, 2^0, 2^1, 2^2, or 2^3, no need for different symbols. And while we're at it, let's write it left-to-right MSB first, because that's how other numbers work, and it fits on a line nicely, like so: 0101.

For fun, I have designed a font like that once. Each hex digit was 4x4 grid, and there were (visually distinct and symmetric if possible) patterns of 0-15 filled dots.

I also thought about an extension for having a symbol for each byte value in 16x16 grid. The lower half byte would determine a 4x4 pattern, which would be repeated over the 16x16 grid according to the pattern corresponding to the higher half byte.

This is a good point, but you get the same from standard Hex notation.

But standard Hex notation has the advantage that I can say FF to someone, but how do I pronounce these things? I guess this could have merit, but I just don't have much of an issue using standard Hex notation.

> Either way, 0-F is a lot easier.

Easier for us because it's the conventional way hexadecimal was represented in computer history, and how we learned it.

That rune-like system is more "logical" in the way you can visually read the value by summing the segments/bits value composing the berkanam rune from least significant at top to the most significant at bottom.

I may have made a mistake in assuming that the vertical line, because it was drawn in a different weight, was not part of the symbol. Without the line 1 & 4, 2 & 8 and 3 & 12 would rely on the vertical relationship with other symbols.