Updated 2017-03-09 23:27:21 by gold

Sumerian Coefficients at the Bitumen Works and eTCL Slot Calculator Demo Example edit

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Introduction edit

gold Here is some eTCL starter code for calculating materials of ancient Sumerian bitumen. The impetus for these calculations was checking bitumen weights in some cuneiform texts and modern replicas. Most of the testcases involve replicas or models, using assumptions and rules of thumb.

In ancient Sumer and Babylon, there were many terms for bitumen products, but the two primary terms in the Sumerian language were esir a (watery bitumen ) and esir had (dry bitumen), as cited in the Sumerian coefficient lists. Babylon sold 60 liters of construction and waterproofing pitch (esir a) for 1 silver piece and 40 liters (eq. vol) of dry pitch (esir had) for 1 silver piece. At least in terms of shipping, esir had easier to transport. Esir a was a liquid petroleum product and had to be shipped in pottery jars and probably kept sealed. If price is measure of petroleum fractions for the heavy (esir had) fraction and light fraction (esir a), the tar fraction was 40 liters (for a shekel)/ 60 liters (for a shekel) , 2/3, or 40/60 of the heavy esir a fraction. Using modern terms for crude oil, the tar fraction was from 10-14 %, 5.25 kg to 7.3 kg out of 52.5 kilograms of converted barig 60 liter unit.

The texts mention both cooking and (implied) sun dry processing for bitumen. Suppose that the Babylon products were derived from successive cooking or sun-dry processes, then a crude production line or process could be outlined: 100 liters crude oil > 85 liter lamp oil > 60 liters construction & waterproofing pitch > 40 liters dry pitch. Starting with 100 per cent, straining and cooking would remove impurities such as spare water, sand particles, and plant matter. Further cooking would remove the gasoline and naphtha fractions, leaving about 85 percent for lamp fuel (eg. kerosene) and medicine. Additional cooking would remove kerosene and some mineral oil leaving 30 percent of the original crude oil for a heavy oil/pitch fraction (esir a) for waterproofing woven products, construction of floors and walls, and waterproofing bricks. The next stage would cooking or drying the heavy oil/pitch into the 20 percent residue called esir had. The conjecture here is that esir a was the feedstock for esir had. Esir had was used in crafts as a cement or mixed with stone powder as a sort of moldable plastic. Possibly, esir had was used as fuel in brick kilns, smelters, and other industrial processes.

For eTCL calculator, the recommended procedure is push testcase and fill frame, then change the entry for raw bitumen and push solve. The English terms "watery pitch, wet pitch, and dry pitch" appeared in the original English translation by Goetze, Mathematical Cuneiform Texts. They are used in the eTCL calculator for consistency with the original translation. Pushing the report button will print a report in the Tcl Wiki format on the console window.

Table 1, Possible fractions left after cooking or sun dry processes.

possible fractions left at boiling or sun dry processes.
100 liters crude oil > 85 liter lamp oil > 60 liters construction & waterproofing pitch > 40 liters dry
modern fractions, no cracking modern (1870's) modern fraction
product fraction starting zero % starting 100% Babylon 100-% Cuneiform name Bablylon use or comment
gasoline 1.7 98.3 no reported use
naptha 14. 84.3 85 naptum (fire oil)
kerosene 34 50 60 naptum (fire oil)lamp oil, medicine
bunker oil 18 32.3 30 esir a (wet pitch waterproofing,construction
tar,pitch,wax 15 17.23 20 esir had dry pitch
losses 12 5 5
total 100

Table 2 , Sumerian coefficients at the bitumin refinery

coefficient transliterated english possible decimal /fraction
15 igi.gub.esiri.e coefficient refined pitch 15/60
16 igi.gub.esiri coefficient raw pitch 16/60
15 ssa esiri coefficient pitch 15/60
12 ssa esiri coefficient (refined?) pitch 12/60
10 45 06 ssa ina ki-ri-im coefficient (refined?) pitch 0.1794
15 ssa esiri ? coefficient (raw?) pitch 15/60
15 ssa esiri-e-aIt coefficient refined pitch 15/60
2.5 barig (of) esir-e-a price wet pitch 2.5 barig for 1 shekel , URIII
10 gu (of) esir-had price dry pitch 10 gu for 1 shekel , URIII
12 gu (of) esir-had price dry pitch 12 gu for 1 shekel, URIII
4 ban (of) esir-had price dry pitch 4 ban for 1 shekel, Babylon 1900 BC

Note: Some of the coefficient values may appear redundant, however the coefficient lists and price lists for bitumen products appeared in considerably different eras, countries, and languages. To that extent, it is risky to assume that a bitumen product in Babylon (1900 BCE) means the same consistency,price, and product in Sumer (UrIII, 2300 BCE)

Pseudocode and Equations using coefficients

Pseudocode with some Equations
namespace path {::tcl::mathop ::tcl::mathfunc}
pseudocode: answer is mandays of labor or silver pieces +- error
price? = raw materials + labor + profits
price? = raw materials + heat process
price? = raw materials + labor

Testcases Section

In planning any software, it is advisable to gather a number of testcases to check the results of the program. The math for the testcases can be checked by pasting statements in the TCL console. Aside from the TCL calculator display, when one presses the report button on the calculator, one will have console show access to the capacity functions (subroutines).

Testcase 1

T 1table printed in tcl wiki format
quanity value comment, if any
testcase number 1
initialcrude kilograms: 100.
naptum (fire oil) kilograms 85.0
lamp oil (& medicine) kilograms: 60.0
liquid pitch kilograms:: 30.0
dry pitch kilograms : 20.0
heating value of dry pitch, Megajoules: 400.0
price of pitch in silver: 1.0

Testcase 3

T 2table printed in tcl wiki format
quanity value comment, if any
testcase number 2
initialcrude kilograms: 10.
naptum (fire oil) kilograms 8.5
lamp oil (& medicine) kilograms: 6.0
liquid pitch kilograms:: 3.0
dry pitch kilograms : 2.0
heating value of dry pitch, Megajoules: 40.0
price of pitch in silver: 0.1

Testcase 3

T 3 table printed in tcl wiki format
quanity value comment, if any
testcase number 3
initialcrude kilograms: 500.
naptum (fire oil) kilograms 425.0
lamp oil (& medicine) kilograms: 300.0
liquid pitch kilograms:: 150.0
dry pitch kilograms : 100.0
heating value of dry pitch, Megajoules: 2000.0
price of pitch in silver: 5.0

Screenshots Section

figure 1.


  • Cities of the Ancient World: [1]
  • major paper in understandable prose,Equivalency Values and the Command Economy
  • Robert Englund, UCLA [cdli.ucla.edu/staff/englund/publications/englund2012a.pdf]
  • Ur III Tablets in the Valdosta State University, search on cdli
  • Cuneiform Digital Library Journal, search on Equivalency Values
  • Ur III Equivalency Values[2]
  • Especially, the Ur III Equivalency Values for esir a and esir had sections.
  • The Sumerian keywords -bi, esir, and had search on the cdli
  • are very effective, but major size files to download
  • Mathematical Coefficients of Bitumen, Paul BRY NABU(01-2002)7, in French

Appendix Code edit

appendix TCL programs and scripts

        # working under TCL version 8.5.6 and eTCL 1.0.1
        # pretty print from autoindent and ased editor
        # Sumerian bitumen calculator
        # written on Windows XP on eTCL
        # working under TCL version 8.5.6 and eTCL 1.0.1
        # gold on TCL WIKI , 10apr2014
        package require Tk
        namespace path {::tcl::mathop ::tcl::mathfunc}
        frame .frame -relief flat -bg aquamarine4
        pack .frame -side top -fill y -anchor center
        set names {{} {raw bitumen kilograms:} }
        lappend names {answers: naptum (fire oil) kilograms:}
        lappend names {lamp oil (& medicine) kilograms : }
        lappend names {liquid pitch (waterproofing) kilograms: }
        lappend names {dry pitch (construction) kilograms:}
        lappend names {heating value of dry pitch, Megajoules}
        lappend names {price of product in silver: }
        foreach i {1 2 3 4 5 6 7} {
    label .frame.label$i -text [lindex $names $i] -anchor e
    entry .frame.entry$i -width 35 -textvariable side$i
grid .frame.label$i .frame.entry$i -sticky ew -pady 2 -padx 1 }
        proc about {} {
            set msg "Calculator for Sumerian Bitumen                 
            from TCL WIKI,
            written on eTCL "
            tk_messageBox -title "About" -message $msg } 
        proc calculate {     } {
            global answer2
            global side1 side2 side3 side4 side5
            global side6 side7 testcase_number 
            global initialcrude bitumenkg  
            global construction oilcl crude lampoil
            global silverxpr   
            incr testcase_number
            #straining sand,set initialcrude [* $side1 0.98]
            set initialcrude  $side1  
            set bitumenkg $initialcrude
            set side2 [* $bitumenkg .85]
            set side3 [* $bitumenkg .60]
            set side4 [* $bitumenkg .30]
            set side5 [* $bitumenkg .20]
            set side6 [* $bitumenkg .20 20]
            set construction [* $bitumenkg .60]
            set oilcl [* $bitumenkg .30]
            set crude [* $bitumenkg .20]
            set side7 [* $side5 [/ 1. 20.]] 
            set silverxpr $side7
        proc fillup {aa bb cc dd ee ff gg} {
            .frame.entry1 insert 0 "$aa"
            .frame.entry2 insert 0 "$bb"
            .frame.entry3 insert 0 "$cc"
            .frame.entry4 insert 0 "$dd"
            .frame.entry5 insert 0 "$ee"
            .frame.entry6 insert 0 "$ff"
            .frame.entry7 insert 0 "$gg"}
        proc clearx {} {
            foreach i {1 2 3 4 5 6 7} {
                .frame.entry$i delete 0 end } }
        proc reportx {} {
            global side1 side2 side3 side4 side5
            global side6 side7 testcase_number 
            global initialcrude bitumenkg 
            global construction oilcl crude lampoil
            global silverxpr  
            console show;
            puts "%|table printed in| tcl wiki format|% "
            puts "&|quanity| value| comment, if any|& "
            puts "&|testcase number| $testcase_number||& "
            puts "&|initial crude kilograms: | $side1 ||&"
            puts "&|naptum (fire oil) kilograms  | $side2||& "
            puts "&|lamp oil (& medicine) kilograms:| $side3||& "
            puts "&|liquid pitch kilograms::| $side4 ||&"
            puts "&|dry pitch kilograms :| $side5||& "
            puts "&|heating value of dry pitch, Megajoules:| $side6 ||&"
            puts "&|price of labor in silver:| $side7 ||&"
         frame .buttons -bg aquamarine4
        ::ttk::button .calculator -text "Solve" -command { calculate   }
        ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 100. 85. 60. 30. 20. 400.   1.0 }
        ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 10. 8.5 6.0  3.0 2.0 40.  .1 }
        ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 500. 425. 300. 150. 100. 2000.   5.0}
        ::ttk::button .clearallx -text clear -command {clearx }
        ::ttk::button .about -text about -command about
        ::ttk::button .cons -text report -command { reportx }
        ::ttk::button .exit -text exit -command {exit}
        pack .calculator  -in .buttons -side top -padx 10 -pady 5
        pack  .clearallx .cons .about .exit .test4 .test3 .test2   -side bottom -in .buttons
        grid .frame .buttons -sticky ns -pady {0 10}
        . configure -background aquamarine4 -highlightcolor brown -relief raised -border 30
        wm title . "Sumerian Bitumen Calculator "       

Pushbutton Operation

For the push buttons, the recommended procedure is push testcase and fill frame, change first three entries etc, push solve, and then push report. Report allows copy and paste from console.

For testcases in a computer session, the eTCL calculator increments a new testcase number internally, eg. TC(1), TC(2) , TC(3) , TC(N). The testcase number is internal to the calculator and will not be printed until the report button is pushed for the current result numbers (which numbers will be cleared on the next solve button.) The command { calculate; reportx } or { calculate ; reportx; clearx } can be added or changed to report automatically. Another wrinkle would be to print out the current text, delimiters, and numbers in a TCL wiki style table as
  puts " %| testcase $testcase_number | value| units |comment |%"
  puts " &| volume| $volume| cubic meters |based on length $side1 and width $side2   |&"  

News flash:20Apr2015. In an exciting manner, Naval archeology around the S.A. gulf is developing the ground truth for the bitumen coefficients and the cuneiform ship inventory lists. The analysis here noted that some coefficients lead to thick coatings of 3-4 centimeters, much thicker than expected from modern ship paint and coatings. In some ship excavations, it has been determined that vegetable fibers comprise 10 to 60 percent of the bitumen coating on excavated ships. The reported fibers appear to be grass or reed fibers. In most cases, soil or beach contamination over the ages could not account for the vegetable fibers. Hence, some excavated ship coating samples appear to be a composite material of dried bitumen and vegetable fibers, applied as a hot mixture (using modern terms here). The cuneiform texts suggested that some ships were salvaged for the bitumen coating and timbers. Also, reused (crushed) bitumen materials were referenced in the ship inventories. Ship inventories of grass were thought to used for rope and mats, but now the possibility is that some chopped fibers were deliberately added to bitumen at the arsenal (UrIII). Effectively now, there are two types of known Sumerian composites, the bitumen/ vegtable fiber composite used on ships and the bitumen/limestone powder used in sculture.

gold This page is copyrighted under the TCL/TK license terms, this license.

Comments Section edit

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