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Appendix V.   Five Lunar Months?   Further Doubt




Answers to reader questions

Two pivotal questions have been presented by readers of Chapter 1:  Seeking an Actual Date for the Flood.



Reader question 1

(Paraphrasing)  How can February be 'the second month', when the Bible already defines when the second month is?


Author's answer

1.  The Bible demonstrates some degree of flexibility in its selection of time-measurement systems.  Consider the abrupt, unannounced switch to Roman hours in John 19:14; or the distinctly Gregorian tally of 153 days over five months, in 2011.   ( 5-21 to 10-21 )

2.  The Bible, at times, redefines its own concepts:  e.g. "Sabbath"; "fasting".

3.  Even the most reliable Bible teachers have assented to distinctly non-Hebrew months in Genesis 7 & 8, by assuming the need for an extra-Biblical '30-day-month' calendar to explain the 150-days-over-5-months dilemma.

This '360-day calendar' theory receives special scrutiny in  Chapter 1, Sec. 5  for its unnecessary acceptance as the only solution.



Reader question 2

(Paraphrasing)  Your book claims the inability of a lunar-based calendar (i.e., Hebrew) to encompass 150 days in exactly five months.  Enclosed are two examples showing how it can be done.


Author's answer

Steps:

I.   General proofs of lunar-model's unsuitability:  Show that five lunar months cannot reach beyond 149 days to the required 150.

II.  Analyze reader-provided examples of lunar-model's suitability.



I.  General proofs against lunar-model

Approach

Generate the highest possible daycount over a span of five Lunar months, to overcome these months' brevity (avg. ~29.5 days) compared to other calendars' months.  Thus we will assume the most generous pattern of five lunar months:  [30, 29, 30, 29, 30], 
rather than [29, 30, 29, 30, 29].

By painstakingly demonstrating the inability of even this most generous lunar count to reach the required 150 days, the supposed 'lunar solution' to the dilemma [150 days = five months] will be cast in doubt, lending further appeal to this site's Gregorian solution to the same question.



Proof 1

Count dayspans from 17th to 17th, over each lunar month:

lunar month #
    \
     ii     iii      iv      v       vi     vii 
   -----   -----   -----   -----   -----   -----
  |1... | |1... | |1... | |1... | |1... | |1... |
  | 17  | | 17  | | 17  | | 17  | | 17  | | 17  |
  | ..30| | ..29| | ..30| | ..29| | ..30| | ..29|
   -----   -----   -----   -----   -----   ----- 
     \______/\______/\______/\______/\______/
        30      29      30      29      30
       /
dayspans |       |       |       |       |
         |       |       |       |       |
         |       |       |       |       |
   add: 30   +  29   +  30   +  29   +  30  =  148



Dayspan                                     =  148

 ...the "date difference": The days that 
 must be added to ii-17 to reach vii-17 



Dayspan inclusive                           = (dayspan + 1)

 ...all the calendar days that belong       = (148     + 1)
 to the interlude [ii-17] to [vii-17]       
                                            =  149


Proof 2

Dayspan inclusive,  [ ii-17 ] to [ vii-17 ]  can be expressed by  (A + B + C),  where:


   A  =   days in:  partial month   ii

   B  =   days in:  whole months    iii, iv, v, vi

   C  =   days in:  partial month   vii

   ________________________


   A  =   ii-17  to   ii-30
                                    
   B  =   29 + 30 + 29 + 30   
                                    
   C  =   vii-1  to  vii-17

   ________________________


   A  =  {17 18 19 20 21 22 23 24 25 26 27 28 29 30}
           .  .  .  .  .  .  .  .  .  .  .  .  .  .
           .  .  .  .  .  .  .  .  .  .  .  .  .  .
   count:  1  2  3  4  5  6  7  8  9 10 11 12 13 14

   Set A  has  14  members    =   14 x 24-hr periods



   B  =  (29 + 30 + 29 + 30)  =  118 x 24-hr periods



   C  =  {1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17}

   Set C  has  17  members    =   17 x 24-hr periods    
          (not 18, as claimed)

   _________________________________________________

                                      
  (A + B + C)  =     14

                    118

                  +  17
                  _____

                    149  24-hr periods (i.e., incl)


II.  Analyze reader-provided examples of lunar-model's suitability

Reader-provided example 1

One reader of this book shares with us his own rendering of the Lunar months for 4990 BC.  These he has expressed in terms of a version of the Gregorian calendar that has been adjusted for long-term calendar-drift (a concept not recommended by this website).

Here is what the reader states (blue box):

"Using a computer program called LunaCal the New Moon dates and lunar month durations were calculated for the years 4990 and 4989 BC.  The results were then overlaid onto the Gregorian Calendar*.
* Dates have been corrected for the one day error that occurs in the Gregorian Calendar every ~3300 years.


The length of the months and first day of each month of 4990 are as follows:
           1st month  =  29 days - Mar 31
           2nd month  =  30 days - Apr 29
           3rd month  =  29 days - May 29
           4th month  =  30 days - Jun 27
           5th month  =  29 days - Jul 27
           6th month  =  30 days - Aug 25
           7th month  =  29 days - Sep 24
           8th month  =  30 days - Oct 23 
           9th month  =  30 days - Nov 22
          10th month  =  29 days - Dec 22
          11th month  =  29 days - Jan 20
          12th month  =  30 days - Feb 19


Based on the above information the following observations can be made:
(1) The 17th day of the 2nd month in 4990 began on Friday, May 15

(2) The 17th day of the 7th month began on Oct 10 and ended on Oct 11

(3) There are 150 days inclusive from May 15 to Oct 11"



Interpretation of the reader-supplied data of Example 1


Given    Given                 
Lunar  | Gregorian     |Given    Actual|  17th 
month #| month-spans   |count    count |  day= 
-------|---------------|------   ------|--------
i      |  3-31 -  4-29 |  29       29  |  4-16
ii  2nd|  4-29 -  5-29 |  30       30  |  5-15 [A]
iii    |  5-29 -  6-27 |  29       29  |  6-14
iv     |  6-27 -  7-27 |  30       30  |  7-13
v      |  7-27 -  8-25 |  29       29  |  8-12
vi     |  8-25 -  9-24 |  30       30  |  9-10
vii 7th|  9-24 - 10-23 |  29       29  | 10-10 [B]
viii   | 10-23 - 11-22 |  30       30  |   --
ix     | 11-22 - 12-22 |  30       30  |   --
x      | 12-22 -  1-20 |  29       29  |   --
xi     |  1-20 -  2-19 | *29*     *30* |   --
xii    |  2-19 -   --  |  --       --  |   --

By the chart above,
  [A]   ii-17  '2nd mo, 17th day'  =   5-15

  [B]  vii-17  '7th mo, 17th day'  =  10-10

Using the Bible-calculator's dayspan counter–  which adheres strictly to all Gregorian rules–  we find that for the two dates  [5-15] and [10-10] , in any given year ...



Dayspan = Days from Start-date to End-date   .......  = 148 days


    0         1         2            146       147       148
    |-------->|-------->|---- ... --->|-------->|-------->|
 _______   _______   _______       _______   _______   _______
|       | |       | |       |     |       | |       | |       |
|  5-   | |  5-   | |  5-   | ... |  10-  | |  10-  | |  10-  |
|  15   | |  16   | |  17   |     |   8   | |   9   | |  10   |
|_______| |_______| |_______|     |_______| |_______| |_______|





Dayspan inclusive = Days from First minute to Last ... = 149 days


0      1|        2|        3|          147|      148|      149|
|------>|  ------>|  ------>| ...  ------>|   ----->|   ----->|
|_______   _______   _______       _______   _______   _______
0       2 |       | |       |     |       | |       | |       2
0  5-   3 |  5-   | |  5-   | ... |  10-  | |  10-  | |  10-  3
0  15   5 |  16   | |  17   |     |   8   | |   9   | |  10   5
1_______9 |_______| |_______|     |_______| |_______| |_______9



Thus the most generous pattern for  [five lunar months],  {30 29 30 29 30},  falls short of spanning  [150 days],  using either counting method:
                 Dayspan:         (148 < 150)
 
                 Dayspan incl.:   (149 < 150)


Illusory extra day?

This questioner claims to have discovered a way in which 149 Hebrew days can be understood as "150 days", after the terminology of Genesis 7 & 8.  Closer scrutiny of his Observations 1, 2 & 3 above may indicate a resourceful origin for this apparent 150th day.

The core of this suspected accounting method stems from a well-known discrepancy:

  • Gregorian days stretch from Midnight to Midnight.
  • Hebrew days stretch from Sunset to Sunset  (referred to Biblically as "evening-mornings").
  • True, he seems to have found a "150th day" in his Hebrew-calendar version of the Flood story.  However, he does this by counting Gregorian-calendar dates.

    The underlying logic here reduces to this:  It takes a canvas of 150 Gregorian "dates" (not days) upon which to paint the entire Flood-storyboard of 149 evening-mornings.

    For the simplest illustration of this extra-day-'trick', visualize one single Hebrew day, spanning 24 hours from (for example):  [sunset May 15] to [sunset May 16].
            The (Hebrew) span of days:  = 0
            Hebrew daycount:            = 1
            Gregorian dayspan:          = 1
            Gregorian daycount:         = 2
    
    

    Though only one day (24 hours) exists, this one Hebrew day by necessity occupies parts of two Gregorian "dates".  Thus an extra day seems to materialize, yet not one extra minute has been added to the period under measurement.


    Below is a diagram of how the questioner turns 149 days into 150:

    
       150 Gregorian calendar days-------------------------|
    
              149 Hebrew evening-mornings--------------|
    
              _________________________________________
             |                                         |
             |                                         |
       ______|  ii-17   ...ii-18 - vii-16...   vii-17  |___
      |      |                                         |   |
      |      |_________________________________________|   |
      |  May 15  |                              |  Oct 10  |
      |          |                              |          |          
      |__________|                              |__________|
    
      |\\\\\\|                                         |\\\|
    
      0.75 days,          <-  Biblically               0.25 days,
      pre-ii-17               disallowed  ->           post-vii-17
    
    

    Biblical conflict

    While 150 Gregorian dates can be argued, the addition of any extra Gregorian "padding" time (partial days) at either end is not justifiable Biblically.


    Partial day, left

    The first 3/4 of Gregorian-Day-1 (0001-1800), before Hebrew-Day-1 exists.  The Hebrew date is still ii-16.

    Per Genesis 7:11, no rain or flooding is reported on ii-16:

    Genesis 7:11(b)  ...in the second month, the seventeenth day of the month, the same day were all the fountains of the great deep broken up, and the windows of heaven were opened.

    Partial day, right

    Partial day, right:  The last 1/4 of Gregorian Day 150 (1800-2359), after Hebrew Day 150 ceases to exist.  The Hebrew date here is ii-18.

    In Genesis, the 150 days seems to stretch no longer than vii-17:

    Genesis 7:24  And the waters prevailed upon the earth an hundred and fifty days.
    Genesis 8:3  And the waters returned from off the earth continually:  and after the end of the hundred and fifty days the waters were abated.
    Genesis 8:4  And the ark rested in the seventh month, on the seventeenth day of the month, upon the mountains of Ararat.


    Reader-provided example 2

    A reader of this book claims to have a modern-day example of five Hebrew months equalling 150 days, adding that such examples are in fact quite common.

    Here is what the reader states (blue box):

    "Example of 150 days over five lunar months:

    AD 1988

  • 17th day of the 2nd month began on May 3
  • The Astronomical New Moon was on Apr 16 at 15:01 Jerusalem time.
    The following day, April 17 at sunset, was the beginning of this Biblical month.
    This month began one day + ~3 hours after the astronomical event.

  • 17th day of the 7th month began on Sept 28 and ended on Sept 29


  • The Astronomical New Moon was on Sep 11 at 06:50 Jerusalem time.
    The following day, Sept 12 at sunset, was the beginning of this Biblical month.
    This month began one day + ~11 hours after the astronomical event.

    From [May 3] to [September 29], 1988 are 150 days inclusive."




    Interpretation of the reader-supplied data of Example 2

    Approach

    Plot times given for  [Start ii-17],  [End vii-17],  and New-moons

    Display  [Gregorian date] and [Hebrew date]  side-by-side

    Follow count day-by-day to  [vii-17] and/or [Day 150]

    
    __________________________________
    
    Greg.     Hebrew day-of-the-month,
    date      shown at each 1/4 day   
    ----      -------
              0001-0600
              | 0600-1200
              | | 1200-1800
              | | | 1800-2359
              | | | |
    4-16      -,-,-,N          N = "astronomical New moon"
             
    4-17      N,N,N,ii-1
     
    4-18   ii-1,1,1,2
    
    4-19      2,2,2,3
    
    4-20      3,3,3,4
    
    4-21      4,4,4,5
    
    4-22      5,5,5,6
    
    4-23      6,6,6,7
    
    4-24      7,7,7,8
    
    4-25      8,8,8,9
    
    4-26      9,9,9,10
    
    4-27      10,10,10,11
    
    4-28      11,11,11,12
    
    4-29      12,12,12,13
    
    4-30      13,13,13,14
    
    5-1       14,14,14,15       
                           
    5-2       15,15,15,16     
                          
    5-3    ii-16,16,16,17
                        1* --> Start 17th - to - 17th
                               daycount (inclusive*).
    5-4       17,17,17,18
      1**      1  1  1  2    * Each number in this count
                               (1, 2, 3, etc.) says that
    5-5       18,18,18,19      there are This many Hebrew
      2        2  2  2  3      days touched by this
                               17th-to-17th span, so far.
    5-6       19,19,19,20      As soon as the span touches  
      3        3  3  3  4      another Hebrew day, one more  
                               whole day is added to the  
    5-7       20,20,20,21      count inclusive... no matter
      4        4  4  4  5      how much of that Hebrew-day
                               is spent before stopping
    5-8       21,21,21,22      the clock.  This records the
      5        5  5  5  6      maximum amount of time which
                               the span can claim.
    5-9       22,22,22,23  
      6        6  6  6  7   ** Inclusive count, at nearest
                               Greg. date, which starts 1/4-
    5-10      23,23,23,24      day after Hebrew date starts.
       7       7  7  7  8      Shown as a reference scale to
                               the adjacent Hebrew dates.
    5-11      24,24,24,25
       8       8  8  8  9
    
    5-12      25,25,25,26
       9       9  9  9 10
    
    5-13      26,26,26,27
      10      10 10 10 11
    
    5-14      27,27,27,28
      11      11 11 11 12
    
    5-15      28,28,28,29
      12      12 12 12 13
    
    5-16      29,29,29,30  
      13      13 13 13 14
                                 NEW MOON:  ends a 30-day month
    5-17      30,30,30,iii-1 
      14      14 14 14 15
    
    5-18   iii-1, 1, 1, 2 
      15      15 15 15 16
    
    5-19       2, 2, 2, 3
      16      16 16 16 17
    
    5-20       3, 3, 3, 4
      17      17 17 17 18
    
    5-21       4, 4, 4, 5
      18      18 18 18 19
    
    5-22       5, 5, 5, 6
      19      19 19 19 20
    
    5-23       6, 6, 6, 7
      20      20 20 20 21
    
    5-24       7, 7, 7, 8
      21      21 21 21 22
    
    5-25       8, 8, 8, 9
      22      22 22 22 23
    
    5-26       9, 9, 9,10
      23      23 23 23 24
    
    5-27      10,10,10,11
      24      24 24 24 25
    
    5-28      11,11,11,12
      25      25 25 25 26
    
    5-29      12,12,12,13
      26      26 26 26 27
    
    5-30      13,13,13,14
      27      27 27 27 28
    
    5-31      14,14,14,15
      28      28 28 28 29
    
    6-1       15,15,15,16
      29      29 29 29 30
    
    6-2       16,16,16,17
      30      30 30 30 31
    
    6-3       17,17,17,18
      31      31 31 31 32
       
    6-4       18,18,18,19
      32      32 32 32 33
    
    6-5       19,19,19,20
      33      33 33 33 34
    ...*                    ...*|The pattern being established,|
    6-12      26,26,26,27       |accelerate the count to weekly|
      40      40 40 40 41
                                 NEW MOON:  ends a 29-day month
    6-19    iv-4, 4, 4, 5
      47      47 47 47 48
    ...
    6-26      11,11,11,12
      54      54 54 54 55
    ...
    7-3       18,18,18,19
      61      61 61 61 62
    ...
    7-10      25,25,25,26
      68      68 68 68 69
    ...                          NEW MOON:  ends a 30-day month
    7-17     v-2, 2, 2, 3
      75      75 75 75 76
    ...
    7-24       9, 9, 9,10
      82      82 82 82 83
    ...
    7-31      16,16,16,17
      89      89 89 89 90
    ...
    8-7       23,23,23,24
      96      96 96 96 97
    ...                          NEW MOON:  ends a 29-day month
    8-14     vi-1,  1,  1,  2
     103      103 103 103 104
    ...
    8-21        8,  8,  8,  9
     110      110 110 110 111
    ...
    8-28       15, 15, 15, 16
     117      117 117 117 118
    ...
    9-4        22, 22, 22, 23
     124      124 124 124 125
    ...
    9-11       29, 29, 29, 30
     131      131 131 131 132
    ...                          NEW MOON:  ends a 30-day month
    9-18    vii-6,  6,  6,  7
     138      138 138 138 139
    ...
    9-25       13, 13, 13, 14
     145      145 145 145 146
    ...
    9-27       15, 15, 15, 16
     147      147 147 147 148
    
    9-28   vii-16, 16, 16, 17
     148      148 148 148 149
                                 Note:  vii-17 ends with:
    9-29   vii-17, 17, 17, 18
     149      149 149 149 150    Total days (incl)   = 149
                                 Dayspan = (149 - 1) = 148
    9-30       18, 18, 18, 19
     150      150 150 150 151
    
    10-1       19, 19, 19, 20
     151      151,151,151,152
    
    10-2       20, 20, 20, 21
     152      152,152,152,153
    

    Day 149  does 'touch'  Day 150.  But the days-timer ended when the 17th ended.  No part of  Day 150  (vii-18)  belongs to the span  [ii-17 - vii-17]  (incl).



    Conclusion

    The lunar-based (or Hebrew) calendar fails to provide a five-month span encompassing 150 days, even when optimal conditions are provided.

    This agrees with the assertions made in the first chapter of this book (Seeking an Actual Date for the Flood),  which were the focus of the above questions.


    Thanks go to the readers who supplied these valuable questions.

    John O'Leary / Biblecalculator.com