Origins 17(2):5665 (1990).
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WHAT THIS ARTICLE IS ABOUT
The biblical constraints on a time scale are combined with the constraints provided by carbon14 data in the formulation of a mathematical relationship for conversion between C14 age and real time. This relationship is developed for convenient adaptation to varied interpretations of the biblical time constraint specifications, and is presented by an equation of exponential terms, a tabulation of useful data points, and a graph.
INTRODUCTION
Among individuals who have a concern regarding the validity of the
historical and chronological data in the book of Genesis, there has been a desire for a
reliable conversion between radiocarbon age and realtime age that extends over the full
range of biblical specifications. Such a conversion would be an aid in the formulation and
testing of models for earth history. The object of this treatment is to summarize the
constraints to such a conversion that are provided by data in the biblical text and by
C14 age data, and incorporate these constraints into a compatible mathematical
relationship.
The era with which this treatment is primarily concerned dates from the
beginning of the refashioning of Earth's geology, geography, climate, and ecology that
resulted from the universal catastrophe described in the seventh and eighth chapters of
the book of Genesis — the Flood.
BIBLICAL CONSTRAINTS
According to the text of the Bible that was the universal standard
among Christians for the first six centuries, the Flood occurred 5352 years BP (Brown
1990). (BP refers to years before AD 1950, the zero reference time for C14 age.) Since
the Authorized Version (King James) of AD 1611 Western European Christianity has favored a
biblical text according to which the Flood may be dated at 4472 BP (Shea 1979). For a
treatment that encompasses both of these traditions I can take as the biblical
specification for the date of the Flood the approximation 5000±500 BP (a simplification
of the straightforward 4950±450).
Some interpreters contend that the dates for the Flood given in the
preceding paragraph should be reduced by 215 years. This view is based on the presumption
that the Apostle Paul's statement in Galatians 3:17 overrides the testimony of Moses.
Considering two statements made relatively close to an event, and speaking directly to
that event (Genesis 15:13 and Exodus 12:40, 41; also quoted in Acts 7:6), to be more
definitive than a passing allusion made fifteen hundred years later, I conclude that the
Hebrew nation lived in Egypt for 430 years prior to the Exodus, not merely 215 years as
may be inferred from Galatians 3:17. This view places Galatians 3:17 in the category
specified in 2 Peter 3:16.
I prefer to place the Flood at 5350 BP, rather than the 5000 BP which I
will use in the following mathematical treatment. This preference is based on the evidence
that the chronological data in the fifth and eleventh chapters of Genesis as given in the
scripture used by the early Christian church (the LXX) are much closer to the values
specified by Moses than are those in the Masoretic text (MT) of the ninth century AD. As a
set of numbers related to human genealogy, those given in the LXX are much more reasonable
and internally consistent than those in the MT. The MT data in Genesis 11 are more
difficult to fit into a reasonable treatment of historical data, ethnographic
considerations, or C14 data. There is substantial evidence that a source for the MT gave
numbers in the fifth and eleventh chapters of Genesis that had been systematically reduced
from the values in the primary source (Zurcher 1959).
What motivation could there have been for such reduction? The
millennial concepts that were held among both Jews and Christians at the beginning of the
Christian era (Fox 1986, pp. 265267; Taylor 1855) (i.e., belief that the coming of the
Messiah would occur before or at the conclusion of six millennia following creation, with
a seventh millennium of universal idealistic conditions) would give determined opponents
to designation of Jesus of Nazareth as the Messiah strong motivation for removal of
evidence that they were nearing the close of the sixth millennium since Creation. This
objective is accomplished by the difference between the MT and the LXX of about 1500 years
for the time since Creation Week. Anyone who wishes to investigate this consideration more
fully should consult Zurcher's treatment (Zurcher 1959). On page 42 of his monograph he
says: "For about fourteen centuries, almost all the theologians thought there had
been a subtraction made by the Jews of Palestine ..."
CARBON14 CONSTRAINTS
Agreement of C14 age with realtime historical age can readily be
established as far back as the middle of the second millennium BC (3500 BP) (Libby 1955).
Correlation beyond 4000 BP must be based on models that involve assumptions, due to lack
of objects that can be precisely dated from historical records. The most successful model
has been the Bristlecone Pine dendrochronology developed by C. W. Ferguson (1968). Dr.
Ferguson arranged specimens of dead Bristlecone Pine wood from the White Mountains in
California into an approximate sequence according to their C14 age, and then "fine
tuned" this sequence by growthring matching. His correlation between
dendrochronology and C14 age won reluctant acceptance from anthropologists, Quaternary
geologists, and other scientists whose models had required much greater ages than were
given by C14 (Gladwin 1976, Lee 1981). The latest refinements to the dendrochronologic
age versus C14 age relationship are given by Stuiver et al. (1991). According to the
dendrochronologic model there was an increasing C14 concentration in the biosphere with
increasing age beyond 3000 BP (C14 age increasingly less than the corresponding realtime
age).
Due to its characteristic complacent growth ring patterns, Bristlecone
Pine wood from the White Mountains is not well suited for the development of a
dendrochronology standard. This difficulty was emphasized by Dr. Ferguson in a letter to
Herbert Sorensen, dated 3 March 1970, by the statement: "I am often unable to date
specimens with one or two thousand rings against a 7500year master chronology, even with
a 'ballpark' placement provided by a radiocarbon date." (Sorensen 1975). There is
need for a demonstration as to whether an equally good, if not better, master growthring
sequence can be established with Bristlecone Pine specimens preliminarily arranged in a
sequence of realtime age such as would be obtained from the correlation relationship
developed in this paper.
The retrograde increase in biosphere C14/C12 ratio between 3500 BP
and 7000 BP required by the Ferguson Bristlecone Pine dendrochronology reaches about 10%
over the present value. A further increase up to about 50% going back to 20,000 BP has
been proposed on the basis of recent dating of corals by both the uraniumthorium (UTh)
method and the C14 method (Bard et al. 1990). In my judgment, a correlation of real time
with UTh age has even greater uncertainty than with C14 age.
There is increasing evidence that organic specimens which can be
established confidently as fossils of material that was involved in the Flood (e.g., coal)
have C14 ages in the 40,000 year range (Brown 1988b). This constraint, together with
placement of the Flood at about 5000 years BP, specifies that at the beginning of the
Flood the biosphere had no more than about 1/100 of the C14/C12 ratio
that has characterized it over the past 3500 years. (A 1/100 ratio
corresponds to a C14 age slightly greater than 38,000. An added 5000 years of real time
would give such material a present C14 age of 43,000.)
A MODEL FOR CORRELATING C14 AGE WITH THE BIBLICAL TIME SCALE
With the preceding background on constraints provided by the
chronological data in the Bible and by C14 data, we can now proceed to the task of
correlating these constraints. The correlation developed will be an interpretation, and
should be based only on fundamental data, not on other interpretations such as the
Bristlecone Pine dendrochronology model or the UTh age model. It is to be compared with
these other interpretations, but to be kept distinct from them.
For the major readjustment period following the Flood we can presume
that radiocarbon levels in the atmosphere may be represented by Equation 1:
A = A_{1} (1  e^{at}).
In Equation 1, A represents C14 level, either as the ratio of C14
to C12, or as C14 spontaneous transformations per unit of time per unit mass of carbon;
A_{1} represents the equilibrium level of A; e is the base of the natural
logarithms — 2.718... —; a is a parameter which is related to the rate at which
A reapproaches equilibrium after a disturbance from its equilibrium value A_{1};
and t is real time measured from zero at the end of the Flood. The value of A for plant
tissue will be essentially the same as for the CO_{2} in the air from which it
obtained its carbon. In animal tissue A will represent the average for the food supply
which furnished the carbon in that tissue.
The large amount of organic material, and probably some of the
carbonate sediment, buried during the Flood and now existing only as fossil material
indicates that prior to the Flood the world inventory of C14 was associated with a much
larger amount of C12 than has been the case since the Flood. This is in agreement with
the evidence that A for this material was about or less than 1/100 of the
present value (equal to or less than 0.01A_{1}). For simplification, Equation 1
treats A as having zero value at the end of the Flood. To obtain a significant comparison
in the time immediately following the Flood a constant in the vicinity of 0.005, and
within a range of uncertainty that might extend to 0.01, should be added to the exponent
at.
The parameter a in Equation 1 is determined by the rate at which CO_{2}
is taken out of the atmosphere by the reestablishment of vegetation over the Earth's
surface after the Flood, and by the cooling of the oceans associated with glaciation and
the development of frigid climate zones. (The solubility of CO_{2} in water
increases with a lowering of temperature.) An effective change in the parameter a would be
produced also by a change in the rate of formation of C14 by interaction of
cosmic rays with nitrogen in the upper atmosphere. The proportion of the cosmic rays from
outer space to interact with Earth's atmosphere and produce C14 is determined by the
strength of the geomagnetic field. Fluctuations in the geomagnetic field are to be
expected during stabilization following the crustal disruption associated with the Flood.
A decrease in the geomagnetic field (increasing the production of C14), or a lowering of
the ocean surface temperature (reducing the amount of atmospheric CO_{2}), would
contribute to an increase in the value of a.
Equation 1 is based on the assumption that the combined effect of all
the factors influencing the rate at which the level of C14 in the atmosphere changed from
its preFlood value to its postFlood equilibrium value can be satisfactorily represented
by a firstorder exponential function with a single exponential constant. To the extent to
which this assumption is inadequate and there has been fluctuation of A about a smooth
simple exponential trend toward an equilibrium value, there will be uncertainty in a
realtime age equivalent based on Equation 1.
The relationship in Equation 1 will be easier to work with if time is
measured from the present, rather than from the beginning of the postFlood era. This is
accomplished by setting t = (FT), with F equal to a biblically based BP date for the
Flood, and T representing real time BP, as in Equation 2:
A = A_{1} [1  e^{a(FT)}].
To evaluate the parameter a in Equation 2 we can presume A was equal to or better than 0.9 A_{1} at T equal to 4000, since C14 ages based on interaction with the atmosphere have a better than 95% agreement with realtime historical age over the range of T from zero to 3500. To obtain a trial value for a we can set
0.95 A_{1} = A_{1} [1  e^{a(F  T)}]
at T = 4000, which gives
e^{a(F4000)} = 0.05,
or
e^{+a(F4000)} = 20;
from which
a = 2.996/(F4000).
With this value for a, the activity at T years BP as given by Equation 2 becomes (3):
A = A_{1} [1  e^{2.996(FT) / (F4000)}].
Since we are not making observations at time T, but at the present (T = 0), we need an expression for the activity now (zero BP), A_{n}, of a specimen that had activity A at T years BP. After T years ago the C14 activity will have decreased exponentially at the rate given by the mean life of a C14 atom. For simplification we can use 8300 years for the mean radiocarbon life, since this value differs by less than ½ of 1% from the correct value 8267 (halflife 5730 years divided by the natural logarithm of 2). Accordingly A_{n} = A e^{T/8300}, with A given by Equation 3. Equation 4 is:
A_{n} = A_{1} [1  e^{2.996(FT) / (F4000)}] e^{T/8300}.
The activity now, A_{n}, is interpreted to indicate a C14 age R by the relationship (5):
A_{n} = A_{l} e^{R/8300}.
Combination of Equations 4 and 5 gives Equation 6, a relationship between T and R for a specified F:
e^{R/8300} = e^{T/8300} [1  e^{2.996(FT) / (F 4000)}].
Equation 6 is not useful for values of T within about ten years of a value for F, or values of R greater than about 35,000 years, because A has been inaccurately assumed to be zero for T = F.
QUANTITATIVE CORRELATION BETWEEN BIBLICAL MODEL REALTIME AND C14 AGE
For a treatment that is a median between various views of biblical chronology we can use 5000 years for F (I have already given my reasons for preferring 5350 years to be the "correct" value) to obtain Equation 7:
e^{R/8300} = e^{T/8300} [1  e^{2.996(5000T)/1000}].
For the calculation of relations between R and T Equation 7 may be reduced to either Equation 8 or Equation 9.
(8) e^{R/8300} = e^{T/8300}  (3.121×10^{7})
e^{+2.876T/1000}
(9) R = T + 8300 ln [1  e^{2.996(5000T)/1000}]^{1}
(ln designates "the natural logarithm of".)
The relationship between R and T for representative values of R is
outlined in Table 1. A graphical representation of these data for F = 5000 is given in
Figure 1.
TABLE 1. Representative Values for the Relationship Between Biblical Model RealTime Age T and Radiocarbon Age R. The R subscript indicates assumed date of the Flood. Estimates of relationship are not warranted for values of T within about ten years of the date for the Flood, or radiocarbon ages greater than about 35,000.
T R_{5,500} R_{5,350} 0
1,000
2,000
3,000
3,500
4,000
4,250
4,500
4,550
4,600
4,650
4,700
4,750
4,800
4,850
4,900
4,950
4,975
4,990
5,000
5,100
5,200
5,300
5,340
5,3500
1,000
2,001
3,021
3,593
4,426
5,177
6,600
7,046
7,580
8,231
9,038
10,064
11,414
13,284
16,116
21,321
26,794
34,230
(infinite)
———
———
———
———
———0
1,001
2,005
3,045
3,638
4,426
5,006
5,865
6,091
6,342
6,622
6,938
7,295
7,702
8,170
8,713
9,352
9,715
9,949
10,113
12,186
15,673
24,004
37,038
(infinite)
FIGURE 1. Conversion plot for RealTime Age T Versus C14 Age R. Presumed date for the Flood set at 5000 BP real time.
This conversion between C14 age and real time resolves the enigma of the 7000±2000 C14 age difference between hair and muscle for a musk ox carcass that was presumably frozen in Alaskan muck about 17,000 C14 years ago (Stuckenrath and Mielke 1970). The correlation represented in Equation 7 places death of the animal in the vicinity of 4900 years ago (from C14 age of hair), and suggests a life span within ten years of 50, rather than in the range between 5000 and 9000. Other examples of similar nature have been presented by the author previously (Brown 1987, 1988a, 1990).
CONCLUSIONS
There appears to be a basis for a quantitative correlation of C14
ages over the range between zero and the vicinity of 35,000 years BP with realtime ages
that are in conformity with biblical guidelines. Because the buildup of C14 in the
biosphere from less than 1/100 to the full zero BP reference standard level
over the time between the Flood and about 3500 BP probably did not proceed with monotonous
uniformity, some anomalies are to be expected in realtime ages derived from C14 ages by
means of a mathematical model for such correlation. Since the buildup of C14 from levels
associated with C14 ages in the mid40,000 years range to levels associated with a C14
age of about 35,000 years evidently occurred over only a few years of real time,
correlation with realtime for C14 ages greater than 35,000 is highly uncertain. For C14
ages in the range between 4000 and 30,000 years the associated realtime age probably may
be significantly placed within a range of less than ±100 years.
It is the hope of the author that this treatment will contribute to
confidence in the biblical chronological data, and increase the effectiveness with which
that data may be utilized in scientific research.
ACKNOWLEDGMENTS
Appreciation is due Harold G. Coffin and reviewers for the improvements in clarity and effectiveness of this treatment that have resulted from their suggestions.
REFERENCES
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