Aswers Research Joural 9 (016):57 6. www.aswersigeesis.org/arj/v9/biblical-lifespas.pdf A Expoetial Decay Curve i Old Testamet Geealogies Philip M. Holladay, Departmet of Mathematics, Geeva College, Beaver Falls, Pesylvaia. Abstract Scholars routiely look with suspicio o the dates ad ages give i the early chapters of Geesis. Several passages are cofusig, multiple textual traditios have bee preserved with differig umbers, The umbers give i the various texts of the Scriptures will be take at face value. Others ca worry about the validity of the umbers. The goal is to show that the lifespas of Old Testamet people bor after the Flood reveal a umerical patter kow as a expoetial decay curve. Thus, the purpose of this paper is to derive a mathematical equatio that predicts, with reasoable accuracy, the lifespa of people bor after the Flood, give the umber of years that they were bor after the Flood. This is true for all of the texts examied. It will further be show that oly the Masoretic text predicts that the huma lifespa will level off to approximately 70 to 75 years. Keywords: textual traditios, Masoretic, Septuagit, Samarita Petateuch Itroductio A equatio of the form y = Ae Bx is called a depedig o whether B is positive or egative. This is crucial to the uderstadig of this paper, so a few are ot mathematicias. Suppose a certai tow has 1000 people ad is growig at 10% a year. I a year it will have 1000 plus 10% of 1000, which is 100, residets ad 1100 plus 10% of 1100, which is 110, residets ad 1100 + 110 = 110. Notice that it added more people growth. Now suppose the tow of 1000 people is losig 10% a year. The after a year it will have Most people are familiar with the mathematical umber very famous umber, but oly with those who study mathematics, is e cosider the tow of 1000 with a growth rate of 10% per year. The equatio y = 1000e 0.10x, with x beig the umber of years ad y beig the umber of residets, models this growth. Thus, i two years (x = ) oe would have y = 1000e 0.0 a calculator). This disagrees with the 110 foud above. Why? Suppose that the calculatios are doe mothly. Dividig the 10% yearly growth betwee the 1 moths, each moth the tow would grow 10 1%. two years. If it is compouded daily for two years, there will be 11.37 residets. If we compoud every agreemet with the equatio. The equatio, y = Ae Bx, assumes that the growth is cotiuous (compouded for the tow it is ot the case that there were 1000 growth is beig added daily, or cotiuously. year (y = 1000e -0.10x) ), but here the lifespa is gettig (y = Ae Bx ) will have a egative B value growth curves have a positive B value.) This patter ave observed this patter. time goes by the predicted lifespa will get closer may residets will there be i 100 years?) It was apparet from the start that oe eeded a equatio of the form y = Ae Bx + C, with B equatio x represets the umber of years a perso y is their predicted lifespa. A, B, ad C preset. Now, as time passes, Ae Bx will approach Ae Bx + C will approach C. This meas that the equatio predicts that the huma lifespa will level off to the value of C. The oly problem with ISSN: 1937-9056 Copyright 016 Aswers i Geesis, Ic. All cotet is owed by Aswers i Geesis ( AiG ) uless otherwise idicated. AiG cosets to ulimited copyig ad distributio of prit copies of Aswers Research Joural articles for o-commercial, o-sale purposes oly, provided the followig coditios are met: the author of the article is clearly idetified; Aswers i Geesis is ackowledged as the copyright ower; Aswers Research Joural ad its website, www.aswersresearchjoural.org, are ackowledged as the publicatio source; ad the itegrity of the work is ot compromised i ay way. For website ad other electroic distributio ad publicatio, AiG cosets to republicatio of article abstracts with direct liks to the full papers o the ARJ website. All rights reserved. For more iformatio write to: Aswers i Geesis, PO Box 510, Hebro, KY 41048, Att: Editor, Aswers Research Joural. The views expressed are those of the writer(s) ad ot ecessarily those of the Aswers Research Joural Editor or of Aswers i Geesis.
58 P.M. Holladay the equatio y = Ae Bx + C is that the mathematics are values of the costats A, B, ad C for ay set of data. The questio the arises as to what is meat by the very best values of A, B, ad C. Suppose Isaac was Now for ay values of A, B, ad C oe ca let x y (usig the equatio). o values of A, B, ad C will give perfect results for differece betwee the predicted age (y) ad the be calculated for all the people ad oe could add up all these differeces (the sum of all the errors). The best value for A, B, ad C would be those values is still a problem as oe error (predicted age mius actual age) might be 10 years ad aother might Mathematicias get aroud this by the method of A, B, ad C that will yield the smallest total of the squares of the errors, here 10 = 100 + 100 = 00. Notice A, B, ad C small as possible ivolves material usually covered i Calculus III. The derivatio will be covered i this paper, but c best values of A, B, ad C to ma squares of all the errors as small as possible, with trust i the mathematicia. The Advaced Math best values of A, B, ad C. Data will be stored i the form (x i, y i ), where x i represets the umber of years y i represets A, B, ad C i such S i the equatio: S ( Ae Bx i C y ) i. i1 Note that Ae Bx i i is predicted age mius actual mmig the errors, is the umber of people. Also, the errors are squared so that positive errors ad egative errors do t cacel each other out. The goal is to S. This is a stadard calculus problem ad leads to the equatios: A= ad B xi yie e yi xe i xe i e i= 1 i= 1 i= 1 i= 1 i= 1 i= 1 e e x iyie x ie yi i= 1 i =1 i= 1 i= 1 i= 1 yie e yi i= 1 i= 1 i= 1 e e i=1 i=1. for B B, the other equatios yield A ad C directly. (All calculatios were doe by computer, of course. Ideed, this probably would have bee impossible to solve before the computer era.) Statisticias have created a method of evaluatig the Let where y ave is the average of the y values. cc = correlatio coefficiet = T S, T where S have S = 0, ad hece cc = 1. Thus, we desire cc to be close to 1. Data from the Masoretic Text The followig umbers are geerally easy to derive this paper. Thus, Terah was bor years after the age of 05 (Table 1). 1 C= y i Ae i= 1 i= 1 T= y y i i= 1 Name Bor Died Lifespa Arpachshad (Ge. 11:10) 440 (Ge. 11:13) 438 Shelah 37 (Ge. 11:1) 470 (Ge. 11:15) 433 Eber 67 (Ge. 11:14) 531 (Ge. 11:17) 464 Peleg 101 (Ge. 11:16) 340 (Ge. 11:19) 39 Reu 131 (Ge. 11:18) 370 (Ge. 11:1) 39 Serug 163 (Ge. 11:0) 393 (Ge. 11:3) 30 Nahor 193 (Ge. 11:) 341 (Ge. 11:5) 148 Terah (Ge. 11:4) 47 (Ge. 11:3) 05 Table 1. purpose of this paper.,
A Expoetial Decay Curve i Old Testamet Geealogies amely whe was Abraham bor ad whe did the is also cofusig because of overlappig reigs, but fortuately these are fairly well established. I the of Scholarly Sources, a table of reasoed dates is give, from which oe ca see that the differeces will have miimal effects o this paper. Geesis 11:6 will be used to establish the year of the birth of Abraham (Table ). A differet date ca old whe he became the father of Abraham, which 70, ad Abraham was bor later, i agreemet with Stephe.) Table. Name Bor Died Lifespa Abraham 9 (Ge. 11:6) 467 (Ge. 5:7) 175 Sarah 30 (Ge. 17:17) 49 (Ge. 3:1) 17 Ishmael 378 (Ge. 16:16) 515 (Ge. 5:17) 137 Isaac 39 (Ge. 1:5) 57 (Ge. 35:8) 180 Jacob 45 (Ge. 5:6) 599 (Ge. 47:8) 147 I the secod year of the famie (after seve good (Table 3). Table 3. Name Bor Died Lifespa Joseph 543 (above) 653 (Ge. 50:) 110 was from the promise to Abraham util the givig of 59 Abraham was 99, the this is the year 391. Thus, the cocludes (). Table 4. The years of Aaro ad Moses. Name Bor Died Lifespa Aaro 99 (Ex. 7:7) 105 (Num. 33:39) 13 Moses 93 (Ex. 7:7) 105 (Deut. 34:7) 10 Table 5) Table 5. Name Bor Died Lifespa Joshua 97 (Joshua 14:7) 108 (Joshua 4:9) 110 also says that this was the fourth year of Solomo s to be the year David died oe has: (see Table 6) Table 6. The years of David. Name Bor Died Lifespa David 1418 ( Sam. 5:4) 1488 (above) 70 well established. I a chroology table the New America Stadard Master Study Bible r Steima (011), ad Thiele (1965) vary slightly, i 971 most the cause of death simply is t stated. Thus the year of birth oe establishes (see Table 7).
60 P.M. Holladay Table 7. Name Bor Died Lifespa Rehoboam 1487 (1 Kigs 14:1) 1545 58 Jehoshaphat 155 (1 Kigs :4) 161 60 Joram 1573 ( Kigs 8:17) 1613 40 Uzziah 1675 ( Kigs 15:) 1743 68 Jotham 1684 ( Kigs 15:33) 175 41 Ahaz 1704 ( Kigs 16:) 1740 36 Hezekiah 1705 ( Kigs 18:) 1759 54 Maasseh 1760 ( Kigs 1:1) 187 67 Summary of Fidigs As demostrated above, there were two poits The details (above) oly give oe versio, but the followig four possibilities: 1. Abraham s birth years. was from the promise to Abraham util the givig of the law. This gives us four possible variatios o the umbers. Agai, x is the umber of years that the y is the perso s cc), 1 is perfect. Therefore, usig the possibilities listed above. Table 8. 1. Usig 1a ad a:. Usig 1a ad b: 3. Usig 1b ad a: 4. Usig 1b ad b: y = 398.979e 0.0057141x + 73.80, cc = 0.9444 y = 397.83e 0.00506664x + 70.4089, cc = 0.9461 y = 388.459e 0.0049511x + 75.5548, cc = 0.9395 y = 386.6480e 0.00473604x + 7.780, cc = 0.9409 ye x cc Note that there is some variatio i all the it is impossible to argue that oe is truly better tha aother. Also, the lifespa will level off towards the should level off somewhere betwee 70 ad 76, a reasoable umber. This is cosistet with to stregth, eighty years... 101), the people who outlived their predicted lifespa died at least 10% before their predicted lifespas were the error betwee the predicted lifespas ad the actual lifespas seems to be related to God blessig Testamet was ot cosidered. The same verses ca Septuagit, with differig umbers, thus: Vaticaus: y = 616.15e x cc ye x cc = 0.9756 predict that the huma life spa will become covered that agrees with Stephe i Acts 7. Does this say aythig about Stephe s source, or the origial ye x cc = 0.9613
A Expoetial Decay Curve i Old Testamet Geealogies ye x cc = 0.935 from our usual 70 76. This is cosistet with Geesis 6:3, The the Lord said, My Spirit shall ot strive with days shall be oe hudred ad twety years. Also, usig the Septuagit (Vaticaus) with the ye x cc This is iterestig as the umbers chaged quite predicts that the huma lifespa will become egative, Coclusio curve of the form y = Ae Bx + C, ad this is true for Iterestigly, the two versios of the Septuagit have too far outside of the give data set. The Samarita ad o predicted lifespa. Lifespa 500 450 400 350 300 50 00 150 100 50 0 0 00 400 600 800 1000 100 1400 16001800 Number of ears from the Flood to heir irth Fig. 1. 61 That the various sets of umbers follow equatios graphs that are early idetical to this oe. The idividuals. Summary of the Data for Versio Oe of the Masoretic Text earest year, the huma lifespa had leveled off to 73 years by David s day (Table 9). Table 9. Years or fter the Flood Actual ifespa Predicted ifespa Name (rouded to the earest year) Arphaxad 438 468 Salah 37 433 40 Eber 67 464 353 Peleg 101 39 307 Reu 131 39 73 Serug 163 30 4 Nahor 193 148 17 Terah 05 197 Abraham 9 175 159 Sarah 30 17 154 Ishmael 378 137 18 Isaac 39 180 14 Jacob 45 147 110 Joseph 543 110 96 Aaro 99 13 76 Moses 93 10 76 Joshua 97 110 76 David 1418 70 73 Rehoboam 1487 58 73 Jehoshaphat 155 60 73 Jehoram 1573 40 73 Azariah 1675 68 73 Jotham 1684 41 73 Ahaz 1704 36 73 Hezekiah 1705 54 73 Maasseh 1760 67 73 Ackowledgmets This study bega as a paper preseted at the
6 P.M. Holladay would ever have rise above a bit of mathematical curiosity. Refereces I The Expositor s Bible Commetary Th Caopy Master Study Bible New America Stadard Nashville, Teessee: Old Testamet Israel Academic. Creatio Research Society Quarterly The Mysterious Numbers of the Hebrew Traslatio Compared with the A Illustrated History of The Holy Bible Appedix of Scholarly Sources Year of Death NASB EBC MKH KP HI David 970 970 971 971 971 Rehoboam 913 913 913 913 913 Jehoshaphat 847 848 848 848 848 Joram 846 841 841 841 841 Uzziah 716 739 740/39 740 740 Jotham 734 736 73 731 731 Ahaz 719 75 716/15 715 715 Hezekiah 700 697 687/86 686 686 Maasseh 63 64 643/4 64 64 NASB: New America Stadard Bible. EBC: The Expositor s Bible Commetary (Gleaso 1979, pp. 368 371). MKH: The Mysterious Numbers of the Hebrew Kigs (Thiele 1965, p. 05). KP: Kigdom of Priests (Merrill 008, pp. 61, 337). HI: A History of Israel: From the Broze Age Through the Jewish Wars (Kaiser 1998).