
The Birkana hexadecimal number symbols - yawaramin
http://yawar.blogspot.com/2016/10/the-birkana-hexadecimal-number-symbols.html
======
david-given
Fun fact: you can count to hexadecimal on the fingers of one hand.

The way it works is that each of your four fingers has four well-defined
places on them: the three joints, plus the tip. You use your thumb to point at
one of these. The first finger represents 1-4, the second 5-8, the third 9-12,
the fourth 13-16. You count up and down by moving your thumb.

Also, because you use the thumb of the same hand for pointing, you can count
two different hexadecimal numbers if you use both hands --- which means you
can count to 256.

(I don't know anybody limber enough to do this with their toes.)

As a special bonus: if you point to the fleshy pads of the fingers instead of
the joints, you can use the same system for base 12.

~~~
daeken
Counting in binary gets you even further. If each finger is one bit, you can
easily count to 2^10-1 == 1023. I frequently use this to keep track of running
totals over 10.

~~~
lern_too_spel
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.

~~~
yorwba
There is quite some variation in the way the human hand works. I can move my
middle and ring fingers completely independently, but when I stretch my left
middle finger, my left pinky tries to extend, too. I can prevent this by
pressing its tip against my palm.

Except for this difficulty, simultaneously moving multiple fingers is no
problem for me. For binary counting you just need to flip a group of fingers
inward and extend the next one. There are instruments that require more
difficult movement patterns to play.

I just timed myself repeatedly counting to 32 as fast as possible on my left
hand, and I averaged at 13 seconds. That seems entirely practical to me.

~~~
lern_too_spel
Now try counting to 32 using the creases method. You'll beat that time without
any practice. I can count on my creases faster than I can count in my head,
and it requires little mental effort, which is why you would use an external
counter in the first place.

------
pygy_
The bibi-binary notation is somewhat similar (16 === 2^2^2). It was patented
in 1968 by Bobby Lapointe, a French variety singer, but didn't get much
traction AFAICT. Bibi-binary also has a custom pronunciation for hex digits.

The article is in French[0], but the main illustration that describes the
system is self-explanatory[1].

0\. [https://fr.wikipedia.org/wiki/Syst%C3%A8me_Bibi-
binaire](https://fr.wikipedia.org/wiki/Syst%C3%A8me_Bibi-binaire)

1\.
[https://upload.wikimedia.org/wikipedia/commons/a/a0/Table_de...](https://upload.wikimedia.org/wikipedia/commons/a/a0/Table_de_correspondance_entre_le_Bibinaire_et_les_autres_notations.svg)

~~~
blahedo
I just translated the article to English; see
[https://en.wikipedia.org/wiki/Bibi-
binary](https://en.wikipedia.org/wiki/Bibi-binary) .

~~~
lccarrasco
Thanks a lot! :)

------
FoeNyx
It could also interestingly be mixed with reflected binary code [1] with only
one segment changing between two successive values.

> Theoretically, the Unicode Consortium could decide to add the Birkana
> symbols to the Unicode specification and some enterprising font designer
> could come up with a set for general use.

There are already some runes encoded in unicode, but most of the symbols of
the birkana system does not match any existing historical runes though.

Yet, there is something in unicode that is somehow visually close [2]: braille
patterns (2 columns of 4 rows of dots). But sadly the braille dots are not
ordered in the same way because it was extended from 6 bits (from top to
bottom : left column 123, right column 456) to 8 bits (from top to bottom :
left column 1237, right column 4568).

\--

[1]
[https://en.wikipedia.org/wiki/Gray_code](https://en.wikipedia.org/wiki/Gray_code)

[2]
[https://en.wikipedia.org/wiki/Braille_Patterns](https://en.wikipedia.org/wiki/Braille_Patterns)

------
lucb1e
What I find the neatest is that it's not just showing hexadecimals, but the
binary representation at the same time. In the Birkana symbol for 9 it's very
easy to recognize the binary 1001: it has the top and bottom 'bits' set.

It also made me aware that I never thought about the symbols we use for
numbers. Our digits 0 through 9 suddenly seem very arbitrary, looking at
Birkana. Though ten digits are more difficult than sixteen to represent this
way, they could certainly have had logic in them.

~~~
yawaramin
As for the logic behind our decimal digits, there was an explanation going
around for it, but at best it's probably reaching very hard. I'll let you
decide:
[http://message.snopes.com/showthread.php?t=49183](http://message.snopes.com/showthread.php?t=49183)

~~~
drostie
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.

------
zenobit256
Huh, you could use a double-sided version of this for a byte.

~~~
jl6
I like it! Comes with a built-in eternal holy war over whether 0x16 goes top
left or bottom left.

------
ajb
The geomantic figures
([https://en.wikipedia.org/wiki/Geomantic_figures](https://en.wikipedia.org/wiki/Geomantic_figures))
can also represent 4 bit values. Unfortunately they aren't in unicode either.
The Ba gua
([https://en.wikipedia.org/wiki/Bagua](https://en.wikipedia.org/wiki/Bagua))
are, but can only represent 3 bits per symbol.

~~~
porges
The Tài Xuán Jīng symbols are, however. A subset can be used like:

𝌆𝌇𝌉𝌊𝌏𝌐𝌒𝌓𝌡𝌢𝌤𝌥𝌪𝌫𝌭𝌮

So Unicode has Bagua (3 bits), Tài Xuán Jīng (4 trits), and I Ching (6 bits,
but incomplete).

------
xupybd
That's just binary? I find hex notation much easier to use and to communicate
verbally.

~~~
nabla9
There are 16 symbols, so it's hexadecimal.

The symbols themselves neatly match the binary representation of 4 bits, so
you can look at the numbers and see them as binary numbers in groups of four
if you wish.

These would be great hexadecimal symbols for programmers.

~~~
Gracana
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.

------
todd-davies
> AMONG number systems, the hexadecimal system of counting (or 'radix') has a
> special place in the hearts of programmers, being closely related to binary,
> the fundamental number system used by all modern computers.

Could somebody explain how hexadecimal is more closely related to binary than
any other base is? My only conclusion is that one hexadecimal digit is
equivalent four binary digits.

~~~
maaaats
Bases in 2^n can be easily converted between, as you can consider each
group/symbol independently when converting.

------
szc
I think there is a problem with this notation - it is not self aligning.
Meaning that if you hand wrote these you could then easily mis-read the
values. It would probably be okay in printed form or if you were using lined
paper, using the ruled line as a centre point.

~~~
OMGWTF
Can you provide an example that could be misread?

I think its quite easy to judge whether a downwards accent starts at the top
of the line or at the middle, similarly for the upwards accent if it starts at
the middle or at the bottom.

~~~
szc
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.

------
userbinator
It somewhat reminds me of this:
[https://en.wikipedia.org/wiki/File:Bruce_Martin_hexadecimal_...](https://en.wikipedia.org/wiki/File:Bruce_Martin_hexadecimal_notation_proposal.png)

I've also seen various notation for writing numbers in hex used by some
reversers/crackers/demosceners mostly from Eastern European countries, who
probably used hex enough to develop something similar to a stylised form of
0-F but distinctly different from those letters/numbers for easier reading and
writing. (This was when home computers were still relatively new, and it was
usual to make great amounts of handwritten material when working with them.)

------
fatihpense
I had reinvented these symbols, without knowing Birkana, for one of my hobby
alphabets at high school. I had given a lot of thought with my high-schooler
leisure time and haven't been able find more simple system with enough data
capacity. I think readability suffers from similarity though.

They also look like some symbols from Old Turkic alphabet, If I recall
correctly it was my source of inspiration:
[https://en.wikipedia.org/wiki/Old_Turkic_alphabet](https://en.wikipedia.org/wiki/Old_Turkic_alphabet)

------
igaray
I like the 12480 script
[http://www.omniglot.com/conscripts/12480.htm](http://www.omniglot.com/conscripts/12480.htm)

------
sharkjacobs
it would be nice, just generally, not to introduce another character which is
just a plain vertical line, even if 99.9% of the time it is identifiable by
context

