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gold Here is some eTCL starter code for calculating the sowing rate of barley and wheat in ancient Sumerian fields. The impetus for these calculations was checking grain sowing rates in a cuneiform text,The Farmer's Instructions or Farmer's Almanac. Most of the testcases involve replicas or models, using assumptions and rules of thumb.
In the Sumerian coefficient lists and literature on clay tablets, there are coefficients which were used in determining the amount of materials and the daily work rates of the workers. In most cases, the math problem is how the coefficient was used in estimating materials and work rates. One difficulty is determining the effective power of the coefficient in base 60. For example, 20 could represent either 20*3600,20,20/60, 20/3600, or even 1/20. The basic dimensions and final tallies were presented in the Sumerian accounts on clay tablets, but the calculations and some units were left off the tablet. At least one approach for the modern reader and using modern terminology is to develop the implied algebraic equations from the Sumerian numbers. Then the eTCL calculator can be run over a number of testcases to validate the algebraic equations.
From a paraphrased translation of "The Farmer's Instructions" , 3 measures will be spent on each 18 iku area. The number 3 is a bare number 3 without units and refers to the amount of seed on a standard surface area of 18 iku. An iku is equivalent to 3.6E3 square meters and 18 iku is equivalent to 1 bur or 6.48 hectares. From this and other texts, the Sumerians reckoned seed or grain quantities in volume units. The unitless 3 could represent either 3*3600,3,3/60, 3/3600, or even 1/3 times some unknown volume unit. The most likely unit is some multiple of the sila, which is equivalent to a liter. The task here is evaluate the unitless 3 in terms of Sumerian or other sowing rates. However, the research would like to find the seeding rate represented by unitless 3 and compare the seeding rates mentioned in other cuneiform texts.
"The Farmer's Instructions" also has a discussion on seed and farrows, which can be used to derive one possible interpretation of the sowing rate in the customary silas per bur. The key phrases are 8 farrows in a ninda and 1 volume gin of seed per ninda. A ninda is length unit of 12 cubits or 6 meters. A gin of seed is about 1/60 of a sila or liter. The numbers set up as a small square plot of 12*12 cubits , 144 square cubits, or 36 square meters, requiring 8 gin or 8/60 sila of seed for 36 square meters. There are 8 farrows in the plot with each farrow of width 12 cubits/8 farrows or 1.5 cubits. A Sumerian bur is 6.48E4 square meters or 6.48 hectares. Setting proportions of (8/60)/36= volume_seed/6.48E4, volume_seed = {(8/60)*6.48E4)} /36 , 240 sila per bur.
From other texts, the sowing rate in Sumer and the Mesopotanian countries ranged from 240 to 360 silas per bur, but 270 silas per bur is closest to an often standard sowing rate. Using proportions, the standard sowing rate reduces as 270 silas per bur, 15 sila per iku, or 9 volume gin per small square plot of 144 square cubits. For comparison, the most quoted modern European rate for barley is 100 kilograms per hectare. The eTCL calculator will convert the silas per bur into kilograms per hectare using the density of barley (0.62 kg/liter) or the density of wheat (0.78 kg/liter). Note that the density of barley and other grains changes with the seed moisture content or humidity, so comparison with kilograms of seed before standard moisture content (1920 etc) can introduce a 2 to 5 percent error. Likewise, some modern countries use different standards of moisture content in their agricultural reports.
For the push buttons in the eTCL calculator, 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. The current result numbers will be cleared on the next solve button. Aside from the TCL calculator display, when one presses the report button on the calculator, one will have console show access to the functions (subroutines).
#pseudocode can be developed from rules of thumb.
#pseudocode: some problems can be solved by proportions (rule of three), to some order of magnitude
#pseudocode: enter quantity1, quantity2, quantity3 and expected output (quantity4) for testcases.
#pseudocode: enter time in years, number of remaining items
#pseudocode: output fraction of (remaining items) over (items at time zero)
#pseudocode: ouput remaining items as fraction or percent
#pseudocode: output fraction of (quantity4 ) over ( quantity1 at time zero)
#pseudocode: output fraction of (quantity2) * (quantity3 ) over (quantity1 at time zero)
#pseudocode: outputs should be in compatible units.
#pseudocode: rules of thumb can be 3 to 15 percent off, partly since g..in g..out.
#pseudocode: need test cases > small,medium, giant
#pseudocode: need testcases within range of expected operation.
#pseudocode: are there any cases too small or large to be solved?| table 1 | printed in | tcl wiki format |
|---|---|---|
| quantity | value | comment, if any |
| testcase number: | 1 | |
| 240.0 : | seed volume silas | |
| 18.0 : | field surface area iku | |
| 0.62 : | seed density kilograms per liter | |
| 240.0 : | seed volume liters | |
| 0.0648 : | answers: surface area square kilometers | |
| 6.48 : | surface area hectares | |
| 240.0 : | seed silas per bur | |
| 22.962 : | seed kilograms per hectare | |
| table 2 | printed in | tcl wiki format |
| quantity | value | comment, if any |
| testcase number: | 2 | |
| 270.0 : | seed volume silas | |
| 18.0 : | field surface area iku | |
| 0.62 : | seed density kilograms per liter | |
| 270.0 : | seed volume liters | |
| 0.0648 : | answers: surface area square kilometers | |
| 6.48 : | surface area hectares | |
| 270.0 : | seed silas per bur | |
| 25.833 : | seed kilograms per hectare | |
| table 3 | printed in | tcl wiki format |
| quantity | value | comment, if any |
| testcase number: | 3 | |
| 360.0 : | seed volume silas | |
| 18.0 : | field surface area iku | |
| 0.78 : | seed density kilograms per liter | |
| 360.0 : | seed volume liters | |
| 0.0648 : | answers: surface area square kilometers | |
| 6.48 : | surface area hectares | |
| 360.0 : | seed silas per bur | |
| 43.333 : | seed kilograms per hectare |
# pretty print from autoindent and ased editor
# Sumerian Seeding Rate Calculator
# written on Windows XP on eTCL
# working under TCL version 8.6.x and eTCL 1.0.1
# gold on TCL WIKI, 10nov 2014
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 {{} {seed volume silas :} }
lappend names {field surface area iku :}
lappend names {seed density kilograms per liter :}
lappend names {seed volume liters (optional):}
lappend names {answers: surface area square kilometers :}
lappend names {surface area hectares : }
lappend names {seed silas per bur: }
lappend names {seed kilograms per hectare :}
foreach i {1 2 3 4 5 6 7 8} {
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 Seeding Rate
from TCL WIKI,
written on eTCL "
tk_messageBox -title "About" -message $msg }
proc break_flag_routine { } {
global side1 side2 side3 side4 side5
global side6 side7 side8
global spares
global testcase_number
set t9 $testcase_number
set product_entries [* $side1 $side2 $side3 $side4 $side5 $side6 $side7 $side8]
if { $product_entries < 0.0 } { puts " warning flag! negative numbers detected in product entries ref. tc$t9" }
foreach item { 1 2 3 4 5 6 7 8 9 10 } {
set error$item 0 }
#{-?\d*(\.\d+)?} regsub -all -- {[^0-9.-]} $input "" number
if { $side1 < 0.0 } { set side1 .000001 ; set error1 1 }
if { $side2 < 0.0 } { set side2 .000001 ; set error1 1 }
if { $side3 < 0.0 } { set side3 .000001 ; set error1 1 }
if { $side4 < 0.0 } { set side4 .000001 ; set error1 1 }
if { $side5 < 0.0 } { set side5 .000001 ; set error1 1 }
if { $side6 < 0.0 } { set side6 .000001 ; set error1 1 }
if { $side7 < 0.0 } { set side7 .000001 ; set error1 1 }
if { $side8 < 0.0 } { set side8 .000001 ; set error1 1 }
if { $error1 == 1 } { puts " warning flag! negative numbers detected, defaulted to positive entries ref. tc$t9" }
foreach item { 1 2 3 4 5 6 7 8 9 10 } {
set error$item 0 }
return 1 }
proc calculate { } {
global answer2
global side1 side2 side3 side4 side5
global side6 side7 side8
global testcase_number
incr testcase_number
set side1 [* $side1 1. ]
set side2 [* $side2 1. ]
set side3 [* $side3 1. ]
set side4 [* $side4 1. ]
set side5 [* $side5 1. ]
set side6 [* $side6 1. ]
set side7 [* $side7 1. ]
set side8 [* $side8 1. ]
break_flag_routine
set barley_density 0.62
set wheat_density 0.78
set grain_density $side3
set side4 $side1
set side5 [/ [* $side2 3600. 1. ] 1E6 ]
set side6 [/ [* $side2 3600. 1. ] 1E4 ]
set side7 [* [/ $side1 $side2 ] 18.]
#set side8 [/ [* [* [/ $side1 $side2 ] 18.] $grain_density] 1. ]
set side8 [/ [* [* [/ $side1 $side2 ] 18.] $grain_density] 6.48 ]
}
proc fillup {aa bb cc dd ee ff gg hh} {
.frame.entry1 insert 0 "$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"
.frame.entry8 insert 0 "$hh"
}
proc clearx {} {
foreach i {1 2 3 4 5 6 7 8 } {
.frame.entry$i delete 0 end } }
proc reportx {} {
global side1 side2 side3 side4 side5
global side6 side7 side8
global testcase_number
console show;
puts "%|table $testcase_number|printed in| tcl wiki format|% "
puts "&| quantity| value| comment, if any|& "
puts "&| testcase number:|$testcase_number | |&"
puts "&| $side1 :|seed volume silas | |&"
puts "&| $side2 :|field surface area iku | |& "
puts "&| $side3 :|seed density kilograms per liter| |& "
puts "&| $side4 :|seed volume liters | |&"
puts "&| $side5 :|answers: surface area square kilometers | |&"
puts "&| $side6 :|surface area hectares | |&"
puts "&| $side7 :|seed silas per bur | |&"
puts "&| $side8 :|seed kilograms per hectare | |&"
}
frame .buttons -bg aquamarine4
::ttk::button .calculator -text "Solve" -command { calculate }
::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 240.0 18.0 0.62 240.0 0.0648 6.48 240.0 22.9}
::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 270.0 18.0 0.62 270.0 0.0648 6.48 270.0 25.8 }
::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 360.0 18.0 0.78 360.0 0.0648 6.48 360.0 43.33 }
::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 Seeding Rate Calculator"
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Please place any comments here, Thanks.