Copyright © 2002 by Creation Research Society. All rights reserved.
The Earth’s Magnetic Field is Still Losing Energy
D. Russell Humphreys
CRSQ Vol 39 No 1 pp 1-11 June 2002
Abstract
This paper closes a loophole in the case for a young earth based on the
loss of energy from various parts of the earth’s magnetic field.
Using ambiguous 1967 data, evolutionists had claimed that energy gains
in minor (“non-dipole”) parts compensate for the energy loss
from the main (“dipole”) part. However, nobody seems to have
checked that claim with newer, more accurate data. Using data from the
International Geomagnetic Reference Field (IGRF) I show that from 1970
to 2000, the dipole part of the field steadily lost 235 ± 5 billion megajoules of energy, while the non-dipole part gained only
129 ± 8 billion megajoules. Over that 30-year period, the net loss of energy
from all observable parts of the field was 1.41 ± 0.16 %. At that rate, the field would lose half its energy every 1465
± 166 years. Combined with my 1990 theory explaining reversals of polarity
during the Genesis Flood and intensity fluctuations after that, these
new data support the creationist model: the field has rapidly and continuously
lost energy ever since God created it about 6,000 years ago.
1. Introduction
Three centuries later, William Gilbert (1600), Queen Elizabeth’s
personal physician, carefully compared observations of the earth’s
magnetic field with the field of a lodestone sphere. He found them very
similar. The field of the earth is indeed close to being that of a dipole,
though the dipole’s axis tilts about 11.5° away from
the earth’s rotational axis. However, the actual field in some
places can deviate from that of a purely dipole field by as much as
10% in direction and intensity.
Early in the nineteenth century, Carl Friedrich Gauss (1833; 1839) used
many measurements from all over the world to characterize the earth’s
field. Using what is now called “spherical harmonic analysis,”
he mathematically divided the field into dipole and non-dipole
parts.
The non-dipole parts of the earth’s field have more than two poles.
For example, the quadrupole part has a four-pole shape, such
as a square of four bar magnets would produce (Figure 2b). A cube of
bar magnets, having eight corners and eight poles, would produce an
octopole field (Figure 2c), and so forth in multiples of two.
One name for each part of the field is harmonic. Another is “mode.”
Figure 2. Dipole and non-dipole magnetic fields from bar magnets: (a) dipole, (b) quadrupole, and (c) octopole. Each source can have various orientations relative to the coordinate axes. The actual sources of the fields in the earth’s core are various distributions of electric current.
Of course, the actual cause of the earth’s non-dipole field is not
bar magnets, but simply small irregularities in the electric current
in the earth’s core. For example, suppose the doughnut-shaped flow
of current I mentioned above were not lined up exactly with the earth’s
center, but offset a bit northward above the center. Then the resulting
field would have most of the non-dipole parts we observe in the earth’s
field (Benton and Alldredge, 1987).
The strength of the source of each part of the field is called its moment,
such as the “dipole moment” and the “quadrupole moment.”
Gauss found that the earth’s magnetic dipole moment is an order
of magnitude stronger than any of the non-dipole moments.
Scientists after Gauss continued to make global measurements of the field.
Three decades ago, Keith McDonald and Robert Gunst (1967; 1968) published
the first systematic analysis of such measurements, covering the whole
period from 1835 to 1965. They drew a startling conclusion: during those
130 years, the earth’s magnetic dipole moment had steadily decreased
by over eight percent! Such a fast change is astonishing for something
as big as a planetary magnetic field. Nevertheless, the rapid decline
remained relatively unknown to the public, a “trade secret”
known mainly to researchers and students of geomagnetism.
2. The Geomagnetic Wars
In the context of Dalrymple’s emphasis on past polarity reversals
and intensity fluctuations in the field, he seemed to be placing his
hopes on a conjecture: that energy from the dipole part of the field
is not being dissipated as heat, but is instead being stored up in the
non-dipole part. Later it would be converted into a new dipole field
with reversed polarity.
Dalrymple also claimed that some energy from the dipole part was going
into an unobservable “toroidal” part of the field, in which
the lines of force wind through the earth’s core in the east-west
direction. Because such lines of force would remain within the core,
they would only reveal their presence indirectly, by currents traveling
outside the core in the earth’s mantle and crust. Shortly after
Dalrymple made that claim, several Bell Laboratories scientists found
that such currents are very small (Lanzerotti et al., 1985).
Barring very improbable structure (alternating layers of conductors
and insulators) in the earth’s mantle, their result implies that
the toroidal part of the earth’s magnetic field is small, removing
such fields as a significant reservoir for energy disappearing from
the dipole part.
Barnes (1984) replied to Dalrymple by asserting that the non-dipole components
are merely irrelevant “noise.” He did not calculate non-dipole
energies.^{ } As for
past magnetic polarity reversals, he cast doubt on their reality, citing
a number of papers.
After surveying the evidence for geomagnetic polarity reversals for myself,
I concluded that they had indeed occurred. I proposed that they took
place rapidly during the Genesis flood (Humphreys, 1986). I outlined
a “dynamic decay” theory generalizing Barnes’s free-decay
model to the case of motions in the core fluid. I suggested that if
such motions were fast enough, they could cause magnetic polarity reversals.
Also, I predicted the paleomagnetic signature rapid reversals would
leave in thin, rapidly-cooling lava flows.
Dalrymple had an opportunity to be an official reviewer for my paper,
and to have his review published. He did not take advantage of the opportunity.
In my response to the other reviews of my paper, I made note of Dalrymple’s
silence (Humphreys, 1986, p. 126).
Shortly after that I published a review of the evidence for past polarity
reversals, reaffirming their reality (Humphreys, 1988). Then I developed
my dynamic-decay theory further, showing that rapid (meters per second)
motions of the core fluid would indeed cause rapid reversals of the
field’s polarity (Humphreys, 1990). I cited newly discovered evidence
for rapid reversals (Coe and Prévot, 1989), evidence in thin lava flows
confirming my 1986 prediction. Since then, even more such evidence has
become known (Coe, Prévot, and Camps, 1995).
The reversal mechanism of my theory would dissipate magnetic energy,
not sustain it or add to it, so each reversal cycle would have a lower
peak than the previous one. In the same paper (Humphreys, 1990, p. 137),
I discussed the non-dipole part of the field today, pointing out that
the slow (millimeter per second) motions of the fluid today could increase
the intensity of some of the non-dipole parts of the field. However,
I concluded by saying the total energy of the field would still decrease.
Despite these creationist answers, skeptics today still use Dalrymple’s
old arguments to dismiss geomagnetic evidence. Much of that is probably
due to ignorance of our responses, but some skeptics are still relying
on the non-dipole part of the field. They hope that an energy gain in
the non-dipole part will compensate for the energy lost from the dipole
part.
I said, “hope,” because it appears that since 1967, nobody has
yet published a calculation of non-dipole energies based on newer and
better data. So that is what I will do below. It turns out that the
results quash evolutionist hopes and support creationist models.
3. The International
Geomagnetic Reference Field
First, we need more accurate data than what was available in 1967. Figure
3 shows why. This figure reproduces the McDonald and Gunst figure [1967,
p. 28, Figure 3(e)] on which Dalrymple based his claim. It shows a curve
depicting the “mantle” energy (from the top of the core to
the surface) as first decreasing and then increasing. However, the data
for the latter part of the curve have a lot of scatter, deviating widely
from the curve. For example, in 1965, two points are 1.2 and 1.6% below
the curve, while the two others are 1.6 and 6.4% above the curve. A
data spread of 8%, four times greater than the 2% upswing the curve
alleges, should not give anyone great confidence in the trend.
Figure 3. Reproduction of Figure 3(e) from McDonald and Gunst (1967, p. 28), showing “Total poloidal field energy in mantle,” which is the total observable magnetic field energy between the top of the earth’s core and the earth’s surface, not including the energy above the surface. In their graph each energy unit, 10^{24} ergs, corresponds to 10^{17} joules, or 100 petajoules (1 PJ = 10^{15} joules).
McDonald and Gunst (1967, p. 30) explain the large scatter as being caused
by “errors of analysis of higher degree terms. [In extrapolating
surface data down to the top of the earth’s core] small errors
in the harmonic coefficients are unduly amplified.” They add, “Likewise
in Fig. 3(e) we have not been able to enter meaningful information from
the analyses of epoch 1965.”
In 1968, perhaps in response to the above kinds of issues, the International
Association of Geomagnetism and Aeronomy (IAGA) began more systematically
measuring, gathering, and analyzing geomagnetic data from all over the
world. This group of geomagnetic professionals introduced a “standard
spherical harmonic representation” of the field called the International
Geomagnetic Reference Field, or IGRF. Every five years, starting in
1970, they have published the dipole moment and higher moments of the
field out to the 10^{th} harmonic.
Using old data, the IAGA also extended the model back to the year 1900.
They now have a standardized set of geomagnetic data spanning the whole
twentieth century, 21 epochs of 120 coefficients each. Several journals
have concurrently published the most recent version. You can download
it free of charge as an ASCII file, a table of over 2500 numbers, from
several sites on the Internet (Mandea et al., 2000). One of the
Internet sites has an article listing the estimated accuracies, which
I have used here (Lowes, 2000). The IGRF is the best set of global geomagnetic
data available, accurate enough to give reasonably good values for the
non-dipole energies, especially from 1970 until now. Table
I shows the data for that period.
4. Calculating the Energy in the Field
In this section, I show how to use the IGRF data to calculate the electrical
energy stored in the earth’s magnetic field. If you do not wish
to know the mathematical details, just skip to the next section. If
you want to study basic electromagnetics, or refresh your memory of
it, I recommend Dr. Barnes’s very clear undergraduate textbook,
Foundations of Electricity and Magnetism (1965).
The magnetic flux intensity B at a location in space tells us
how strongly and in what direction the field would compel a compass
needle to point. (Bold font denotes a vector, and all quantities are
in SI units.) In regions where there is no electric current, which is
approximately true outside the earth’s core, we can represent the
magnetic flux intensity as the gradient Ñ of a magnetic scalar potential F:
(1)
The IGRF model gives a spherical harmonic expansion of the magnetic scalar
potential for a given date. I define F_{n} as the component
of potential associated with the n^{th} harmonic, so
the total magnetic potential becomes
( 2)
The integer n labeling a harmonic is called the degree.
Taking the gradient of this equation, we can write the total magnetic
flux density as a sum of components:
(3a,b)
The IGRF specifies the n^{th} component of the magnetic
potential as a sum of n + 1 terms:
(4)
Here a is the mean radius of the earth, 6371.2 km; r is
the radial distance from the Earth’s center, f
is the longitude eastward from Greenwich, q
is the geocentric colatitude (90° minus latitude),
and
is the
associated Legendre function of degree n and order m normalized
according to the convention of Schmidt (Merrill and McElhinny, 1983,
p. 24). The numbers
and
are called the Gauss coefficients. The
IGRF model truncates the expansion at the tenth harmonic, N=10.
As many textbooks show, the energy density (joules per cubic meter) stored
in the magnetic field B at a given point is
(5)
The dot represents the scalar product, and m _{0} is the magnetic permeability of the vacuum (which is essentially the
same as the magnetic permeability of the earth). To obtain the total
energy E contained in the magnetic field outside the Earth’s
core, we must volume-integrate Equation (5) from the radius of the core,
b = 3471 km, out to infinity:
(6)
Now examine in more detail at the energy density u which goes
into this integral. Expanding B in Equation (5) by using the
sum in Equation (3a) gives us:
(7)
In the first summation, B_{n} is the magnitude of the
vector B_{n}. The second summation contains the
cross-terms resulting from squaring the sum in Equation (3a). In doing
the angular part of the volume integral of Equation (6), we find that
the cross-terms drop out because of the orthogonality of the spherical
harmonic functions chosen for Equation (4) (Merrill and McElhinny, 1983,
p. 24). That leaves us with a much simpler expression,
(8)
where each of the energy components is
. (9)
Using Equation (4) to expand Equation (9), and using orthogonality to
eliminate cross-terms in m, we get the energy E_{n}
of the n^{th} harmonic in a useful form:
(10)
where we recall that a and b are the radii of the earth’s
surface and core, respectively, and where G_{n}^{2}
is the sum of the squares of the Gauss coefficients for the n^{th}
harmonic:
(11)
McDonald and Gunst [1967, p. 27, Equations (3.7), (3.8)] give this result
in a slightly different form. First, to change from their Gaussian units
to our SI units, we must replace their relative permeability m with m_{ 0}/4p. Second, we must change their R_{e}
to my a, and their r _{e} to my a/b. Third, we must add their
equations (3.7) and (3.8) to get the total energy for all harmonics.
When we sum my Equation (10) over all harmonics as in Equation (8),
we get the same result.
As another check, the numerical values of my results using IGRF data
agree, within five percent, with the graphs of McDonald and Gunst for
the period in common having the least scatter, 1915 to 1925. The small
disagreement is due to differences of several percent in the Gauss coefficients
in the two data sets. The differences arose from different ways of analyzing
the raw magnetic data. For example, McDonald and Gunst for practical
reasons truncated their analysis with N = 6, whereas the IGRF
went out to the tenth harmonic. Since the difference in data accounts
for the difference in results satisfactorily, the approximate agreement
is further support for equations (10) and (11).
The factor a/b in Equation (10) is the ratio of the earth’s
surface radius to the radius of the core. Since the equation raises
this factor, 1.835, to the power 2n + 1, the higher harmonics
have much more weight relative to the lower harmonics. That is why it
is very important to secure accurate data for the higher harmonics.
Equations (10) and (11) give the total magnetic energy outside the core
radius, r=b. Although magnetic fields and energies also exist
in the core as well as outside it, observations of the field outside
the core cannot determine the field in the core. Different distributions
of electric currents, fields, and energy in the core can give the same
field outside the core. Furthermore, “toroidal” fields could
exist entirely within the core. However, indirect evidence indicates
toroidal fields are small, as I mention in section 2.
A spherical harmonic expansion of fields inside the core would invert
the radial factors, so that they would be of the form (r/b)^{
n + 1} [Smythe, 1989, Section 7.12, Equation (5)]. That
implies that field intensities in the core should not be drastically
different than those at its surface. Since (r/b) ≤
1 in the core, the lower harmonics should dominate. These considerations
suggest that the ratio of non-dipole to dipole energy would not change
much if we could somehow include the contribution of fields in the core.
Anyway, we can do no better than to use the fields we can measure. Thus,
the E of Equation (8) is the total observable energy.
Benton and Alldredge [1987, p. 266, Equations (2), (3)] give the energy
only above the earth’s surface, r=a. They define G_{n}^{2}
with a multiplying factor that I have instead placed into the final
energy equation. If we put (a/b) = 1 into my equations,
the result agrees with theirs.
A final caveat is that extrapolating the IGRF model down to the top of
the core does not account for electric currents in the mantle and magnetization
in the crust. However, the electrical conductivity of the core is much
greater than that of the mantle or crust, and evidence suggests that
magnetic sources outside the core are relatively small. For example,
it appears that crustal magnetization only affects harmonics higher
than the tenth (Benton and Alldredge, 1987, p. 271, Figure 2).
5. Results and Accuracy
Table II and Figure 4 show the energies contained
in the earth’s magnetic field from the years 1900 to 2000, according
to the IGRF data (of which Table I is a sample)
and equations (8), (10), and (11). The dipole energy is E_{1},
the non-dipole energy is the sum of E_{2} through E_{10},
and the total energy E is the sum of E_{1} through
E_{10}. The last row shows Lowes’s (2000) estimates
of rms error in B averaged over the earth’s surface. The
rows labeled with sigmas (s) show the corresponding errors in the various
calculated energies.
Figure 4. Dipole, non-dipole, and total energies computed by Equations (10) and (11) from the International Geomagnetic Reference Field (IGRF) for the entire twentieth century. Energy units are exajoules (1 EJ = 10^{18} joules = 1000 PJ). From 1970 onward, the non-dipole data are more accurate than for earlier years. Sections 5 and 6 discuss the “pulse” in the non-dipole energy during 1945 and 1950. Lines are least-squares exponential fits that include the points from those two epochs.
The most important thing to notice in these numbers is the great loss
of energy from the field. According to the IGRF data, the total
observable energy decreased over 2.6% during the twentieth century.
This loss of 180 ± 34 petajoules (1 petajoule = 1 PJ = 10^{15}
joules = 1 billion megajoules) amounts to 50 billion kilowatt-hours
of electrical energy - enough to power over five million U.S. households
for a year.
Notice that the energy loss was steady except during two epochs, 1945
and 1950. Between 1940 and 1950, according to the IGRF model, total
energy jumped up by a remarkable + 4.7%. Then from 1950 to 1955, the
total energy plummeted even more rapidly by almost the same amount (-
4.2% of the 1940 value), to a value about equal to what the century-averaged
trend (curve fit in Figure 4) would give for 1955. In other words, though
there may have been a temporary “pulse” of energy that decade,
it disappeared and left no lasting impression on the long-term energy
trend.
Moreover, all of the pulse came from the non-dipole component.
Notice that during the period in question, the dipole energy continued
its steady decay and suffered no corresponding pulse in the negative
direction. However we interpret the pulse, the steady dipole decay contradicts
Dalrymple’s conjecture: that increases in non-dipole energy ought
to be fed by losses in dipole energy.
The pulse of non-dipole energy may not be real. It turns out that essentially
all of the pulse comes from a roughly 300% rise and fall in the energy
of the 9^{th} and 10^{th} harmonics alone. According
to McDonald and Gunst (1967, pp. 29-30), harmonics higher than the 6^{th}
had errors large enough during that period to cause problems. As Figure
3 shows, the energy data have a large scatter during that time.
Figure 5 shows the estimates I mentioned above by
one of the IGRF authors (Lowes, 2000) of the rms errors in B
predicted by the model during the twentieth century. Notice that there
is a large bump in error at the same time as the alleged pulse. This
casts more doubt on the reality of the pulse. However, if it is real,
I offer a possible explanation in the next section.
Because of the efforts of geomagnetists after 1968 to measure and characterize
the field more systematically, the data from 1970 to 2000 are much more
accurate than the earlier data. That is especially so in years when
satellite data added greatly to the precision.
Figures 6 and 7 show the dipole and non-dipole energies during the accurate
period. The straight lines in the figures are least-squares exponential
curve fits. The fits show that during those 30 years the dipole lost
235 ± 5 PJ, whereas the non-dipole part gained only 129 ± 8 PJ. Contrary
to Dalrymple’s hope, the sum of the two energies decreased.
Figure 8 shows the decline of the total (dipole plus non-dipole) observable
energy from 1970 to 2000, again with an exponential curve fit. The fit
gives an energy decay time of 2113 ± 239 years, or an energy half-life
of 1465 ± 166 years. That means the net loss of energy during the 30-year
period was 96 ± 11 PJ. In 30 years, 1.41 ± 0.16 % of all the observable
magnetic energy disappeared.
Figure 5. Estimated root mean square error in the IGRF magnetic
field intensity B at the earth’s surface (Lowe,
2000), in nanoteslas. |
Figure 6. Dipole energy decrease from 1970 through 2000. |
Figure 7. Non-dipole energy increase from 1970 through 2000. |
Figure 8. Total energy decrease from 1970 through 2000. |
6. Where the Energy
Went
As far as we know, natural processes cannot destroy energy, so the energy
lost from the observable magnetic field had to go somewhere. Either
(1) it went into magnetic fields hidden from our view inside the core,
or (2) the processes in the core converted it into some other form of
energy.
Possibility (1) is unlikely, because several natural processes expel
magnetic flux (lines of force) upward out of the core (Humphreys, 1990,
p. 131). These are transport, buoyancy, and diffusion
of magnetic flux lines. First, according to Alfven’s theorem
and observations (Shercliff, 1965), upward flows of the electrically
conductive fluid in the core sweep magnetic flux up with them to the
surface, as Figure 9(a) shows. Second, magnetic buoyancy (Parker, 1983;
Wissink, et al., 2000) tends to prevent flux from going back
down with downward flows of the fluid. Third, magnetic diffusion pushes
flux upward out of the core into the less conductive mantle rock, Figure
9(b). Thus, flux tends to emerge from the core, not disappear back into
it.
Figure 9. A magnetic line of force emerges out of the earth’s core. (a) An upflow of the electrically conductive core fluid pushes a section of the line up to the outer surface of the core, and magnetic buoyancy keeps much of the line from descending with downflows. (b) The line of force diffuses upward out of the core.
My 1990 paper shows that as upwelling core fluid expels magnetic flux,
it also generates loops of new lines of force in the reversed direction.
If the motions are fast enough to generate new flux lines faster than
dissipative processes (discussed below) can destroy them, then eventually
the new flux loops can combine and emerge from the core as large loops
of flux of reversed direction from the previous field. However, as I
showed in the paper, the new flux is never as great as the old flux,
because of dissipative processes. Thus, the new reversed (mostly dipole)
field could never have as much energy as the previous field.
The only demonstrated possible core process I know of which might add
energy to a magnetic field is the stretching-out of lines of force (by
differential rotation of the fluid) into a “toroidal” east-west
direction, as possibly happens on the Sun (Humphreys, 1986, p. 116).
The energy for the stretching comes from the motions of the fluid. However,
as I pointed out in section 2, observational evidence weighs against
strong toroidal fields existing now in the earth’s core.
One process we can be certain about is ohmic dissipation or “joule
heating.” Because the core is not a perfect electrical conductor,
its electrical resistance will continually be eroding the electrical
currents in the core, converting magnetic field energy into heat. As
I mentioned in section 2, the observed rate of loss of magnetic energy
is quite consistent with observed electrical resistivity of likely core
materials under core conditions. Thus, the missing field energy is most
likely to have become heat in the earth’s core.
What about the general increase of non-dipole energy? My model would
suggest it is simply due to the motions of the fluid “chopping
up” dipole flux lines of force into smaller loops of flux, which
will then dissipate their energy faster. McDonald and Gunst (1967, p.
25, italics mine) agree:
This [nondipole energy increase] leads us to
conclude that the zonal dipole field is being driven destructively to
smaller values by fluid motions which transform its magnetic energy
into that of the near neighboring higher-order modes [harmonics] rather
than expend it more directly as joule heat. The joule heating rate
associated with the original dipole energy necessarily increases,
however, since the free decay period decreases monotonically with increased
degree of mode.
In other words, the smaller loops of flux will dissipate their energy
as heat even faster than the larger loops do. So presently fluid flows
are converting some of the dipole energy to into non-dipole energy.
However, rapid ohmic dissipation of the non-dipole energy is continually
destroying much of the non-dipole energy even while the fluid flows
are generating it.
According to both my model and the picture given by McDonald and Gunst,
the rate of conversion from dipole to non-dipole energy should be proportional
to the amount of dipole flux. For example, if there were no dipole flux,
no energy would be added to the non-dipole parts. In the future, when
the dipole flux will be weaker, the conversion of dipole to non-dipole
energy will slow down. But the ohmic dissipation of non-dipole energy
will proceed unabated. At some time, dissipation will exceed production.
After that time, even the non-dipole energy will decrease.
It is interesting that Dalrymple did not seem to perceive the implications
of the McDonald and Gunst quote above. If he had, he would have had
less reason to hope for the long-term preservation of magnetic energy.
What about the pulse of magnetic energy in the 9^{th} and 10^{th}
harmonics in 1945 and 1950? If it was real, it may have been caused
by the expulsion of a medium-sized loop of flux completely out of the
core into the mantle, as Figure 10 shows. Since the electric currents
maintaining such a loop would be entirely within the low-conductivity
mantle, the magnetic energy of the loop would dissipate quickly, not
contributing to the accumulation of non-dipole energy. However, it may
have had some effect on the rotation of the earth’s mantle, perhaps
eventually resulting in the “geomagnetic jerk” observed in
1969 (Courtillot and Le Mouël, 1984).
Figure 10. Medium-sized magnetic lines of force move completely
out of the core into the mantle. Possibly such an event caused the
non-dipole energy “pulse” of 1945-1950. |
Conclusion: the Earth’s Magnetic Field is Young
The trend in the IGRF data from the most accurate period, 1970 to 2000,
is very clear. During that period the total energy - dipole plus non-dipole
- in the observable geomagnetic field decreased quite significantly,
by 1.4%. Though the data over the previous part of the century are less
accurate, there was still an overall decrease of total energy. According
to my geomagnetic model, whose general features agree with paleomagnetic
and archeomagnetic data, the total field energy has always decreased
at least at today’s rate, and it will continue to do so in to the
future (Humphreys, 1990).
Today’s energy decay rate is so high that the geomagnetic field
could not be more than a few dozen millennia old. Moreover, during the
rapid polarity reversals of the Genesis Flood, and during the large
fluctuations of surface field B for millennia after the Flood,
the rate of energy loss was much greater than today’s rate. That
shortens the age of the field even more. In the absence of any workable
analytical theory (or data) to the contrary from the evolutionists,
these data are quite consistent with the face-value Biblical age of
the earth, about 6000 years.
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