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