Austronesian Hebrew/Orthography/Numerals

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AH numbers were sexagesimal, that is, base-60. Undergirding this system, however, was a decimal sub-base. As scribes of various functionaries, many of the texts we have were business registers and logs of transactions.

Writing

1 2 3 4 5 6 7 8 9
𝍠 𝍡 𝍢 𝍣 𝍤 𝍥 𝍦 𝍧 𝍨
10 20 30 40 50 , .
𝍩 𝍪 𝍫 𝍬 𝍭 𐩐 𐩑

AH employed separate symbols for its numerals, at least in administrative texts, though sometimes elsewhere. The system seems to have been a compromise between the Chinese Counting Rods and Akkadian cuneiform. Horizontal lines mean one's. Vertical lines mean 5 when attached to horizontal lines, and 10's when unattached. The word divider (a high, single, solid dot) is used like our comma, to group numbers. A hollow, lower, circle served as a the border between whole numbers and fractions. When fractions begin with zero, and can be determined from context, an initial 'o' is omitted.


Hands

Method of counting to ten on the right hand

AH scribes counted to ten on the right hand and five on the left hand, enable a representation of 0 to 59 on the hands. The following is a lesson to replicate their technique.

Place your hands before you. Your right hand should be palm up and your right elbow close to your body. Turn your left hand palm down, with your left elbow flying out to the left. Stiffen your fingers so that all of them are pointing straight out and not of them are curved. This is position '0'. Flex only your right pinky, which should rotate it 90º and point it at your face. This is '1'. Now bring your right ring-finger down, which will allow you to connect the outer two fingers of your right hand with your palm. This is '2'. Your right middle finger comes down next, to make '3'. Bring your right pointer finger down to make '4'. Finally, your right thumb comes in to make a fist, completely closing your right hand. This is '5'.

'6' requires your right pinky finger to fly back out, and therefore your right thumb must control your other fingers. '7' consists of your right pinky and ring fingers flying out. '8' looks like an "O.K." sign, as three fingers point away from your body, but your right thumb and index finger make an 'O'. '9' has four finger flying up, but your right thumb still curled in. For '10', your right thumb is released, and the pinky of your left hand comes down onto the counting surface (if available). Continue through the teens, bringing your left ring finger down to join your pinky on the table as your right hand completely unfurls for '20'. The process continues until '59' -- where all the fingers of the left hand are down and only the thumb of the right hand is curled -- whereupon '60' appears identical to '0'.

By these methods, AH scribes were able to add, subtract, multiple, divide, square, and square root very large numbers. They used a dot (also the word divider) to divide groups of 60, writing base-10 numbers in between. The "decimal point" or line between whole numbers and fractions, was a small circle. Our notation used colons between groups of 60 and a period as the decimal point. For example:

Counting rod v1.png Counting rod h2.png 𐩐Counting rod v3.png Counting rod h4.png 𐩐Counting rod v5.png Counting rod h6.png 𐩑 Counting rod h7.png 𐩐 Counting rod h9.png = 12:34:56.07:09 = 12 * 602 + 34 * 601 + 56 * 600 + 7 * 60-1 + 9 * 60-2 = 45296.1191666...

They knew pi/π to two sexagesimal places:

Counting rod h3.png 𐩑 Counting rod h8.png 𐩐 Counting rod v3.png = 3.08:30 = 3 + 8 * 60-1 + 30 * 60-2 = 3.141666... (99.9976% accurate)

as well as √(2):

Counting rod h1.png 𐩑 Counting rod v2.png Counting rod h4.png 𐩐 Counting rod v5.png Counting rod h1.png 𐩑 Counting rod v1.png = 1.24:51:10 = 1 + 24 * 60-1 + 51 * 60 -2 + 10 * 60-3 (99.99995764% accurate)

These and other similar values suggest their measurements never exceeded the precision of the "tens" of the third sexagesimal place.

1/n
2 3 4 5 6 8 9 10
30 20 15 12 10 7:30 6:40 6
12 15 16 18 20 24 25 27
5 4 3:45 3:20 3 2:30 2:24 2:13:20
30 32 36 40 45 48 50 54
2 1:52:30 1:40 1:30 1:20 1:15 1:12 1:6:40

History

ANE Number Signs
Word Section Number 1 2 3 4 10 20 50 100 1,000 10,000
Aramaic 𐡗 𐡘 𐡙 𐡚 𐡛 𐡜 𐡝 𐡞 𐡟
Phoenician 𐤟 𐤖 𐤚 𐤛 𐤗 𐤘 𐤙
OSA 𐩿 𐩽 𐩾
Simplified Akkadian vs. Chinese
S.Akkadian 𒀸 𒐀 𒐁 𒐂 𒐃 𒐄 𒐅 𒐆 𒐇
Arabic 1 2 3 4 5 6 7 8 9
Chinese
S.Akkadian 𒌋 𒌋𒌋 𒌍 𒐏 𒐐 𒐑 𒐒 𒐓 𒐔
Arabic 10 20 30 40 50 60 70 80 90
Chinese 廿
?
Arabic 100 1000 10000 100000 million 10 mill.
Chinese

Received Akkadian System

Generic

1,2,3,4,5,6,7,8,9,10,20,30,40,50 = 𒁹, 𒈫, 𒐈, 𒐼, 𒐊, 𒐋, 𒐌, 𒑄, 𒑆, 𒌋, 𒌋𒌋, 𒌍, 𒐏, 𒐐

Length

Same as Generic

Area, Volume, Bricks

1,2,3,4,5,6,7,8,9, 10, 20, 30, 40, 50 = 𒀸,𒐀, 𒐁, 𒐂, 𒐃, 𒐄, 𒐅, 𒐆, 𒐇, 𒐴, 𒐵, 𒐶, 𒐸, 𒐹

Large Length, Area, Volume, Bricks

60, 120, 180, 240, 300, 360, 420, 480, 540 = 𒊹, 𒐣, 𒐤, 𒐦, 𒐧, 𒐨, 𒐩, 𒐪, 𒐫

600, 1200, 1800, 2400, 3000 = 𒐬, 𒐭, 𒐮, 𒐰, 𒐱

3600 = 𒊹𒃲 (𒃲 = GAL cp. Hebrew rab... = 10,000)

Capacity

Same as Generic

Large Capacity

60, 120, 180, 240, 300, 360, 430, 480, 540 = 𒐕, 𒐖, 𒐗, 𒐘, 𒐙, 𒐚, 𒐛, 𒐜, 𒐝

600, 1200, 1800, 2400, 3000 = 𒐞, 𒐟, 𒐠, 𒐡, 𒐢

3600 = 𒊹

Weight

same as area

Dry Measure

1,2,3,4,5,6,7,8,9 =𒑏, 𒑐, 𒑑, 𒑓, 𒑕, 𒁹, 𒑖, 𒑗, 𒐉