metrotable tutorialJesús Cabrera (jccsvq)(*), 2025.
(*) At gmail.com
Python3 command line application based on MesoMath for printing fragments of metrological tables in the style of those used by ancient Babylonian scribes and their apprentices.
The metrological tables showed the correspondence between the additive values of measurements of length, surface, weight, etc. and the abstract multiplicative sexagesimal numbers required by multiplicative arithmetic (calculations of areas, volumes, etc.). A modern analogy would be the following: we have a square with a side measuring one yard, two feet, and five inches (the additive measurement), and we want to calculate its area. We would need to convert the measurement to a homogeneous unit, for example, inches, with 65 inches. With this value, we can calculate the area of the square as 65^2 = 4225 square inches. This value of 65 would be our abstract multiplicative number, and a modern metrological table would show us an entry for the association:
1 yard 2 feet 5 inches -> 65
You need to edit the metrotable.py script and change line 7 so that instead of /home/jesus/Nextcloud/MesoMath the sys.path argument points to the absolute path of your installation directory.
#!/usr/bin/env -S python3
'''Printing of metrological tables'''
# Change the `sys.path.append` argument to the absolute path of the directory
# containing the `mesomath` module ( your installation directory).
import sys, argparse
sys.path.append("/home/jesus/Nextcloud/MesoMath") # <- change this
After this, you can invoke the script as:
$ python3 metrotable.py
If nothing happens and you're returned to the prompt, all is well. You can now try
$ python3 metrotable.py -h
or, if you prefer long options:
$ python3 metrotable.py --help
to get a long list of short and long options:
usage: metrotable.py [-h] [-t {L,Lh,S,V,C,W,SysG,SysS}] [-m MIN] [-M MAX]
[-i INCREMENT] [-w WIDTH] [-f FORCE] [-x {1,2,3,4}] [-n]
[-v] [-r]
Prints an excerpt of a metrological table
options:
-h, --help show this help message and exit
-t {L,Lh,S,V,C,W,SysG,SysS}, --type {L,Lh,S,V,C,W,SysG,SysS}
Type of metrological table to print (Try: -r for a
remainder) (default: None)
-m MIN, --min MIN Minimun value of variable to print, ex: "10 susi"
(default: 1)
-M MAX, --max MAX Maximun value of variable to print, ex:"2 kus", or a
comma separated list "2 kus,5 kus" (default: 10)
-i INCREMENT, --increment INCREMENT
Increment of the variable between table lines, ex: "5
susi" or a comma separated list matching MAX in length
"5 susi,1 kus" (default: 1)
-w WIDTH, --width WIDTH
Sets the reserved width for printing measurement
values to WIDTH (default: 20)
-f FORCE, --force FORCE
Force base unit to number FORCE (default: -1)
-x {1,2,3,4}, --example {1,2,3,4}
Runs an example test (default: None)
-n, --noheader Suppress header printing (for chaining results)
(default: False)
-v, --verbose More information in the header and reciprocals if the
abstract numbers are regular (default: False)
-r, --remainder Lists the available measurement systems and their
units, then exits (defafile:///home/jesus/Nextcloud/MesoMath/tutorial.md
jccsvq fecit, 2025. Public domain.
On Unix-like systems, you can make the script executable:
$ chmod +x metrotable.py
and copy/move/link it to a directory in your system's path. Then, simply:
$ metrotable.py -h
to run it, or, if you rename the file to metrotable, then simply:
$ metrotable -h
Start by:
$ metrotable -r
to take a look at the metrological systems covered by this application:
Remainder of systems and units: Old Babylonian Period
=======================================================
System L: Babylonian length meassurements
Units: danna <-30- us <-60- ninda <-12- kus <-30- susi
Base unit: ninda
System Lh: Babylonian length meassurements (Heights)
Units: danna <-30- us <-60- ninda <-12- kus <-30- susi
Base unit: kus
System S: Babylonian surface meassurements
Units: gan <-100- sar <-60- gin <-180- se
Base unit: gin
System V: Babylonian volume meassurements
Units: gan <-100- sar <-60- gin <-180- se
Base unit: gin
System C: Babylonian capacity meassurements
Units: gur <-5- bariga <-6- ban <-10- sila <-60- gin <-180- se
Base unit: gin
System W: Babylonian weight meassurements
Units: gu <-60- mana <-60- gin <-180- se
Base unit: gin
NPVN System S: Babylonian System S to count objects
Units: sargal <-6- saru <-10- sar <-6- gesu <-10- ges <-6- u <-10- dis
Base unit: dis
NPVN System G: Babylonian System G to count objects
Units: sargal <-6- saru <-10- sar <-6- buru <-10- bur <-3- ese <-6- iku
Base unit: iku
Most interestingly, here are some examples to get an idea of what the program offers:
$ metrotable -x 1
Example 1:
Table: Babylonian length meassurements
ubase: 2 (ninda)
From: 10 susi
To: 2 kus
Step by: 5 susi
Output follows:
Metrological list for Babylonian length meassurements
Base unit: ninda
Meassurement Abstract
=========================================
10 susi -> 1:40
15 susi -> 2:30
20 susi -> 3:20
25 susi -> 4:10
1 kus -> 5
1 kus 5 susi -> 5:50
1 kus 10 susi -> 6:40
1 kus 15 susi -> 7:30
1 kus 20 susi -> 8:20
1 kus 25 susi -> 9:10
2 kus -> 10
or with the -v or --verbose options to obtain a header with more information and a new column with the reciprocals of the abstract numbers if they are regular or "igi nu" ("not regular" in Sumerian) if thei are not:
$ metrotable -x 1 -v
Example 1:
Table: Babylonian length meassurements
ubase: 2 (ninda)
From: 10 susi
To: 2 kus
Step by: 5 susi
Output follows:
Metrological list for Babylonian length meassurements
units: danna <-30- us <-60- ninda <-12- kus <-30- susi
cfact: 1 30 360 21600 648000
Base unit: ninda
Meassurement Abstract Reciprocal
====================================================
10 susi -> 1:40 36
15 susi -> 2:30 24
20 susi -> 3:20 18
25 susi -> 4:10 14:24
1 kus -> 5 12
1 kus 5 susi -> 5:50 --igi nu--
1 kus 10 susi -> 6:40 9
1 kus 15 susi -> 7:30 8
1 kus 20 susi -> 8:20 7:12
1 kus 25 susi -> 9:10 --igi nu--
2 kus -> 10 6
and, in the same way:
$ metrotable -x 2 -v
Example 2:
Table: Babylonian surface meassurements
ubase: 2 (sar)
From: 10 gin
To: 2 sar
Step by: 10 gin
Output follows:
Metrological list for Babylonian surface meassurements
units: gan <-100- sar <-60- gin <-180- se
cfact: 1 180 10800 1080000
Base unit: sar
Meassurement Abstract Reciprocal
====================================================
10 gin -> 10 6
20 gin -> 20 3
30 gin -> 30 2
40 gin -> 40 1:30
50 gin -> 50 1:12
1 sar -> 1 1
1 sar 10 gin -> 1:10 --igi nu--
1 sar 20 gin -> 1:20 45
1 sar 30 gin -> 1:30 40
1 sar 40 gin -> 1:40 36
1 sar 50 gin -> 1:50 --igi nu--
2 sar -> 2 30
$ metrotable -x 3 -v
Example 3:
Table: Babylonian capacity meassurements
ubase: 2 (sila)
From: 1 gur
To: 3 gur
Step by: 3 ban
Output follows:
Metrological list for Babylonian capacity meassurements
units: gur <-5- bariga <-6- ban <-10- sila <-60- gin <-180- se
cfact: 1 180 10800 108000 648000 3240000
Base unit: sila
Meassurement Abstract Reciprocal
====================================================
1 gur -> 5 12
1 gur 3 ban -> 5:30 --igi nu--
1 gur 1 bariga -> 6 10
1 gur 1 bariga 3 ban -> 6:30 --igi nu--
1 gur 2 bariga -> 7 --igi nu--
1 gur 2 bariga 3 ban -> 7:30 8
1 gur 3 bariga -> 8 7:30
1 gur 3 bariga 3 ban -> 8:30 --igi nu--
1 gur 4 bariga -> 9 6:40
1 gur 4 bariga 3 ban -> 9:30 --igi nu--
2 gur -> 10 6
2 gur 3 ban -> 10:30 --igi nu--
2 gur 1 bariga -> 11 --igi nu--
2 gur 1 bariga 3 ban -> 11:30 --igi nu--
2 gur 2 bariga -> 12 5
2 gur 2 bariga 3 ban -> 12:30 4:48
2 gur 3 bariga -> 13 --igi nu--
2 gur 3 bariga 3 ban -> 13:30 4:26:40
2 gur 4 bariga -> 14 --igi nu--
2 gur 4 bariga 3 ban -> 14:30 --igi nu--
3 gur -> 15 4
$ metrotable -x 4 -v
Example 4:
Table: Babylonian length meassurements
ubase: 2 (ninda)
From: 10 susi
To: 2 kus,12 kus,5 ninda
Step by: 5 susi,1 kus,6 kus
Output follows:
Metrological list for Babylonian length meassurements
units: danna <-30- us <-60- ninda <-12- kus <-30- susi
cfact: 1 30 360 21600 648000
Base unit: ninda
Meassurement Abstract Reciprocal
====================================================
10 susi -> 1:40 36
15 susi -> 2:30 24
20 susi -> 3:20 18
25 susi -> 4:10 14:24
1 kus -> 5 12
1 kus 5 susi -> 5:50 --igi nu--
1 kus 10 susi -> 6:40 9
1 kus 15 susi -> 7:30 8
1 kus 20 susi -> 8:20 7:12
1 kus 25 susi -> 9:10 --igi nu--
2 kus -> 10 6
---------------------------------------------------
2 kus -> 10 6
3 kus -> 15 4
4 kus -> 20 3
5 kus -> 25 2:24
6 kus -> 30 2
7 kus -> 35 --igi nu--
8 kus -> 40 1:30
9 kus -> 45 1:20
10 kus -> 50 1:12
11 kus -> 55 --igi nu--
1 ninda -> 1 1
---------------------------------------------------
1 ninda -> 1 1
1 ninda 6 kus -> 1:30 40
2 ninda -> 2 30
2 ninda 6 kus -> 2:30 24
3 ninda -> 3 20
3 ninda 6 kus -> 3:30 --igi nu--
4 ninda -> 4 15
4 ninda 6 kus -> 4:30 13:20
5 ninda -> 5 12
The program needs four pieces of data to calculate a segment of a metrological table:
-t or --type)-t or --min)-M or --max)-i or --inc)For example:
$ metrotable -t L -m '10 susi' -M '2 kus' -i '5 susi'
will reproduce example 1 (add -v at will).
Metrological list for Babylonian length meassurements
Base unit: ninda
Meassurement Abstract
=========================================
10 susi -> 1:40
15 susi -> 2:30
20 susi -> 3:20
25 susi -> 4:10
1 kus -> 5
1 kus 5 susi -> 5:50
1 kus 10 susi -> 6:40
1 kus 15 susi -> 7:30
1 kus 20 susi -> 8:20
1 kus 25 susi -> 9:10
2 kus -> 10
We can subdivide the table into different sections with different increments by entering MAX and INC as comma-separated lists. For instance, by using:
MAX = '2 kus,12 kus,5 ninda'
INC = '5 susi,1 kus,6 kus'
in
$ metrotable -t L -m '10 susi' -M '2 kus,12 kus,5 ninda' -i '5 susi,1 kus,6 kus' -v
we obtain the table from 10 susi to 2 kus with increment of 5 susi, from 2 ku to 12 kus (1 ninda) with increment by 1 kus and from this point to 5 ninda by 6 kus:
Metrological list for Babylonian length meassurements
units: danna <-30- us <-60- ninda <-12- kus <-30- susi
cfact: 1 30 360 21600 648000
Base unit: ninda
Meassurement Abstract Reciprocal
====================================================
10 susi -> 1:40 36
15 susi -> 2:30 24
20 susi -> 3:20 18
25 susi -> 4:10 14:24
1 kus -> 5 12
1 kus 5 susi -> 5:50 --igi nu--
1 kus 10 susi -> 6:40 9
1 kus 15 susi -> 7:30 8
1 kus 20 susi -> 8:20 7:12
1 kus 25 susi -> 9:10 --igi nu--
2 kus -> 10 6
---------------------------------------------------
2 kus -> 10 6
3 kus -> 15 4
4 kus -> 20 3
5 kus -> 25 2:24
6 kus -> 30 2
7 kus -> 35 --igi nu--
8 kus -> 40 1:30
9 kus -> 45 1:20
10 kus -> 50 1:12
11 kus -> 55 --igi nu--
1 ninda -> 1 1
---------------------------------------------------
1 ninda -> 1 1
1 ninda 6 kus -> 1:30 40
2 ninda -> 2 30
2 ninda 6 kus -> 2:30 24
3 ninda -> 3 20
3 ninda 6 kus -> 3:30 --igi nu--
4 ninda -> 4 15
4 ninda 6 kus -> 4:30 13:20
5 ninda -> 5 12
Options -n --noheader suppress the printing of the table header, which can be useful if you want to join table segments by shell scripting.
$ metrotable ... > table.txt
$ metrotable ... -n >> table.txt
$ metrotable ... -n >> table.txt
...
Options -f --force allow the calculation of abstract numbers using any unit as a base unit. For instance:
$ metrotable -t W -m '1 mana' -M '5 mana' -i '1 mana'
Metrological list for Babylonian weight meassurements
Base unit: gin
Meassurement Abstract
=========================================
1 mana -> 1
2 mana -> 2
3 mana -> 3
4 mana -> 4
5 mana -> 5
$ metrotable -t W -m '1 mana' -M '5 mana' -i '1 mana' -f 0
Metrological list for Babylonian weight meassurements
Base unit: se
Meassurement Abstract
=========================================
1 mana -> 3
2 mana -> 6
3 mana -> 9
4 mana -> 12
5 mana -> 15
Options -w --width will change the default of 20 chars width of the meassurement text field
$ metrotable -t W -m '1 mana' -M '5 mana' -i '1 mana' -w 30
Metrological list for Babylonian weight meassurements
Base unit: gin
Meassurement Abstract
=========================================
1 mana -> 1
2 mana -> 2
3 mana -> 3
4 mana -> 4
5 mana -> 5
This software does not use the principal fractions: 1/3, 1/2, 2/3 and 5/6.