Babylonian number
Senkare square table
This is an example of Babylonian mathematics, written in wedge text. With this square table, you can see how Base 60 is put into practice.
has three differences from our numbers
Number of symbols used in Babylonian mathematics
Imagine if all you have to do is learn to write a line like me and a triangle, it would be much easier to learn arithmetic in the early years. This is basically all the things that the ancient Mesopotamians had to do, although they changed them here and there, elongated, rotated, etc.
They don't have our pens and pencils, nor paper. They wrote about the tools used in sculptures because the medium is clay. Whether this is harder or easier to learn than a pencil is a toss-up, but so far they are leading the way in the easy department with only two basic symbols to learn.
cardinality 60
The next step is to throw wrench to the simple department. We use 10 as the cardinality, and the concept seems obvious because we have 10 digits. We actually have 20, but let's assume we're wearing sandals with protective toe coverings to prevent sand in the desert, heat from the same sun, can bake clay sheets and save them so we can find them in a thousand years. Babylonian used this base 10, but only partially used. To some extent, they used a 60-based cardinality, which is the same minute, second and degree of a triangle or circle we see around. They are accomplished astronomers, so this number may come from their observations of the sky. The Base 60 also has a variety of useful factors that make it easy to calculate. Still, having to learn Base 60 is daunting.
In "Salute to Babylon" [Mathematics Bulletin, Volume 76, No. 475, "The Application of Mathematics History in Mathematics Teaching" (March 1992), pp. 158-178], author and teacher Nick Mackinnon said that he used Babylonian mathematics to teach cardinalities other than 10 for a 13-year-old child. The Babylonian system uses 60 as the cardinality, which means it is not decimal, but helix.
Position Notation
Babylonian digital system and our digital system both rely on position to give value. The two systems practice differently, partly because their systems lack zero. The first time trying basic arithmetic, learning the Babylonian position system from left to right (high to low) may not be more difficult than learning our 2-way positioning system. We must remember the order of decimal numbers - increasing from decimals, one, ten, hundreds, and then spreading out on the other side in the other direction, without a column, only one tenth, one hundred, one thousandth, etc.
I will discuss the location of the Babylonian system in the next few pages, but first there are some important numeric words to learn.
Babylonian years
We use decimal quantities to talk about the time period of the year. We have 10 years of ten years, 100 years (10 years) or 10X10 = 10 years squared, and 1000 years (10 centuries) or 10X100 = 10 years cubic. I don't know there are any higher terms than this, but these are not units used by the Babylonians. Nick Mackinnon mentioned a stone tablet of Senkareh (Larsa) by Sir Henry Rollinson (1810-1895)*, used by the Babylonians, not only the year involved, but also the number implied:
- rescue
- Nel
- Sa.
SosnaSussos
Still no decisive: Learning the square sum of cubes from Latin is not necessarily easier than the monosyllable Babylonian term that does not involve cubes but multiplied by 10.
What do you think? As a Babylonian schoolchild or a modern student at an English school, would it be harder to learn the basics of digital?
* Henry's brother George Rawlinson (1812-1902) shows a simplified square copy table in "The Seven Monarchs of the Ancient Oriental World" . According to the category of Babylonian year, the table appears to be astronomical.
All photos come from this online scanned version of a 19th century edition of George Rawlinson's The Seven Great Monarchies Of The Ancient Eastern World.
Numbers in Babylonian Mathematics
Cuneiform Square table
Because we grew up in different systems, the numbers in Babylon are confusing.
at least the number goes from high on the left to low on the right, just like our Arabic system, but the rest may look strange. The symbol of one is a wedge or a Y-shaped shape. Unfortunately, Y also represents 50. There are some separate symbols (all based on wedges and lines), but all other numbers are made up of them.
Please remember that the writing form is cuneiform or cuneiform shape . Due to the tools used to draw lines, there are limited varieties. A wedge may or may not have a tail, and after printing a partial triangle, it is drawn by pulling a cuneiform stylus along the clay.
These 10 are described as arrows and look a bit like stretching.
Three lines can be as high as 3 small 1 (written like Y, shortened tail) or 10 (written like ) gather together. First fill in the top line, then fill in the second line, and then fill in the third line. See next page.
1, 2 and 3 lines
above highlights three sets of cuneiform number clusters
Now, we don't care about their value, but demonstrate how you see (or write) 4 to 9 identical numbers combined together. Three are carried out in succession. If there is a fourth, fifth or sixth one, it will be below. If there is a seventh, eighth or ninth row, the third row is required.
The following page continues to provide instructions on using Babylonian cuneiform for calculations.
Square Table
From what you read above about south—you will remember being Babylonians of 60 years, wedges and arrows—they are descriptive names for cuneiform markers, and see if you can figure out how these calculations work. The dash marker is a number on one side and a square on the other side. Try as a group. If you can't figure it out, check out the next step.
How to decode the square table
cuneiform square table Arabic conversion.
can you figure it out now?
...
has 4 clear columns on the left, followed by a dash-like sign, and 3 columns on the right. From the left, the equivalent of 1s column is actually the 2 columns closest to the "dash" (inside column). The other 2 columns, the outer columns together count as 60s columns.
- 4- = 40
- 3-Ys=3.
- 40+3=43.
- The only problem here is that there is another number behind them. This means they are not units (their place). 43 is not 43 1s, but 43-60 because it is a hexadecimal (cardinality 60) system, and as shown in the following figure, it is in the soss column.
- Multiply 43 by 60 to get 2580.
- adds the next number (2- and 1-Y wedge = 21).
- you have 2601 now.
- that is 51 squares.
The next row has 45 in the soss column, so you multiply 45 by 60 (or 2700) and then add 4 from the unit column, so you get 2704. The square root of 2704 is 52.
Can you figure out why the last number = 3600 (60 squares)? Tip: Why not 3000?
