Version 15 of Babylonian Combined Work Norm Algorithm and eTCL Slot Calculator Demo Example, numerical analysis

Updated 2017-03-01 20:20:14 by gold

Babylonian Combined Work Norms Algorithm and eTCL Slot Calculator Demo Example, numerical analysis

This page is under development. Comments are welcome, but please load any comments in the comments section at the bottom of the page. Please include your wiki MONIKER in your comment with the same courtesy that I will give you. Its very hard to reply intelligibly without some background of the correspondent. Thanks,gold

gold Here is some eTCL starter code for Babylonian combined work norms in calculator shell.

There are a number of Babylonian problems on combined work norms. The method or formula was combined work norm equals 1/(1/norm1 +1/norm2 +1/norm3). Alternately, some Babylonian texts use the formula for combined work norm as 3/(1/norm1 +1/norm2 +1/norm3), where the change is adjusted in the accounting. The modern term for the method is the harmonic mean. For the modern reader, some of the difficulty was that some work norms familiar to the Babylonians have to be constructed from the known corpus of Old Babylonian coefficients. In the Babylonian problems, two to five of the work norms were combined. For the eTCL calculator, there were 3 work norms to be combined. The combined work norm units for the eTCL calculator are normally units per man*workday.

As an example, suppose that Babylonians defined different work norms for making volumes of bricks. The work norm was 10/60 volume units for brick type $aaa, 20/60 volume units for brick type $bbb, and 10/60 volume units for brick type $ccc. Here the volume unit was one sar, equivalent to 18 cubic meters of earth or equivalent to volume of bricks (with the right scale factor or production factor). The harmonic mean formula is 1/((1/$aaa)+(1/$bbb)+(1/$ccc)), substituting expr 1./((1./(10./60. ))+(1./(20./60. ))+(1./(10./60.)))=decimal 0.0666 or ~ 4/60 in base60. The eTCL calculator returns a combined work norm of 3.999/60 volume units. The number of bricks is 3.999*27 or 108.0 bricks.

For example, the difficulty in excavating a canal increases with the depth and the Babylonians defined different work norms at each depth level. The work norm was 20/60 volume units between 1 and 2 cubits, 10/60 volume units between 2 and 3 cubits depth, and 8.5/60 volume units between 3 and 5 cubits. Here the volume unit was one sar, equivalent to 18 cubic meters of earth. Suppose a worker spent equal amounts of the work day at each of the three levels. Then his work norm should be the combined work norm of 20/60,10/60 , and 8.5/60. The eTCL calculator returns a combined work norm of 3.73/60 volume units. In modern terms, the production or excavation volume was (3.73/60)*18 cubic meters, 1.1 cubic meters of earth. This answer is reasonably close, but it appears that some offset scheme or partial fractions are being used also. Ref. canal depths in Sumerian Construction Rates on this wiki.

Pseudocode Section

       # using pseudocode 
       # possible problem instances,  
      initialize algorithm_result = 1.
      check algorithm 
      f(solution) =? initial product
      check_sum = a+b+c+d+e = original real estate
      set answers and printout with resulting values 
      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?

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

table 1printed in tcl wiki format
quantity value comment, if any
1:testcase_number
10.0 :work norm (a)
20.0 :work norm (b)
10.0 :work norm (c)
27.0 :work production factor :
1.0 :optional:
1.0 :optional:
108.0 :answers: production norm:
4.0 :combined work norm

Testcase 2

table 2printed in tcl wiki format
quantity value comment, if any
2:testcase_number
10.0 :work norm (a)
10.0 :work norm (b)
20.0 :work norm (c)
27.0 :work production factor :
1.0 :optional:
1.0 :optional:
108.0 :answers: production norm:
4.0 :combined work norm

Testcase 3

table 3printed in tcl wiki format
quantity value comment, if any
3:testcase_number
20.0 :work norm (a)
10.0 :work norm (b)
10.0 :work norm (c)
27.0 :work production factor :
1.0 :optional:
1.0 :optional:
108.0 :answers: production norm:
4.0 :combined work norm

Screenshots Section

figure 1.

Babylonian Combined Work Norm Algorithm and eTCL Slot Calculator screenshot

References:

Appendix Code

appendix TCL programs and scripts 

        # pretty print from autoindent and ased editor
        # Babylonian Combined Work Norm calculator
        # written on Windows XP on eTCL
        # working under TCL version 8.5.6 and 1.0.1
        # gold on TCL WIKI, 25feb2017
        package require Tk
        package require math::numtheory
        namespace path {::tcl::mathop ::tcl::mathfunc math::numtheory }
        set tcl_precision 17
        frame .frame -relief flat -bg aquamarine4
        pack .frame -side top -fill y -anchor center
        set names {{} { work norm (a) :} }
        lappend names { work norm (b) :}
        lappend names { work norm (c) : }
        lappend names { work production factor :  }
        lappend names { optional:  }
        lappend names { optional:  }
        lappend names { answers: production norm:  }
        lappend names { combined work norm  :} 
        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 Babylonian Combined Work Norm 
            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 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. ] 
            # initialize placeholder answer
            set combined_work_norm 1.
            set production_factor $side4
            set norm_a [/ $side1 60.]
            set norm_b [/ $side2 60.]
            set norm_c [/ $side3 60.]
            set combined_work_norm [+ [/ 1. $norm_a ] [/ 1. $norm_b ] [/ 1. $norm_c ] ]
            #set combined_work_norm [/ 1. $combined_work_norm ] 
            set combined_work_norm [/ 1. $combined_work_norm  ]
            set combined_work_norm [* $combined_work_norm  60. ]
            set side8 $combined_work_norm 
            set side7 [* $combined_work_norm  $production_factor ]
                    }
        proc fillup {aa bb cc dd ee ff gg hh} {
            .frame.entry1 insert 0 "$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 :|work norm (a) |   |&"
            puts "&| $side2 :|work norm (b) | |& "  
            puts "&| $side3 :|work norm (c) | |& "
            puts "&| $side4 :|work production factor : | |&"
            puts "&| $side5 :|optional: | |&"
            puts "&| $side6 :|optional: |  |&"
            puts "&| $side7 :|answers: production norm: |  |&"
            puts "&| $side8 :|combined work norm  |  |&" 
            }
        frame .buttons -bg aquamarine4
        ::ttk::button .calculator -text "Solve" -command { calculate   }
        ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 10.  20.   10. 27.  1.  1. 108.0 4.0}
        ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 10.  10.  20.  27.  1.  1. 108.0  4.0 }
        ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 20. 10. 10. 27. 1.  1. 108.0  4.0 }
        ::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 . "Babylonian Combined Work Norm 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. The current result 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   |&"

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Comments Section

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