What's "pmC"?
It stands for "percent [of] modern Carbon [14]" and you need to take "modern" as "modern level, but corrected for pre-industrial levels" ...
The main isotope of carbon is carbon 12. They are both isotopes of carbon insofar as they both have six protons. But they are different isotopes insofar as the number of neutrons is different. 6 + 6 = 12, 6 + 8 = 14. Now, the carbon 14 isotope is very rare. However it's even rarer in very old samples of carbon, like fossil fuels. This means that since the Industrial Revolution, carbon 14 levels have sunk.
Sunk because diluted, that is. But there is also a sinking because of decay. Here is how it works. In 5730 years, it sinks from 100 to 50 pmC. Actually that has never ever happened, because 5730 years ago, carbon 14 was not yet 100 pmC. So, it's more like in 5730 years, it sinks to 50 % of original levels. In twice 5730 years, it sinks to 25 %, that is in 11,460 years. And that also has never happened, because the world didn't exist 11,460 years ago. In three times 5730, it sinks to 1/8 or 12.5 %. That's 17,190 years.
So, while years add multiples of 5730 years, carbon levels sink to powers of 0.5. But what about fractions of 5730 years? Well, to roots of 0.5 %.
5730 / 2 = 2865
0.5 1/2 = 0.707* or 71 %.
5730 / 4 = 1432.5
0.5 1/4 = 0.8409** or 84.09 %
And if the original level was 100 pmC, that means that in 2865 years, a sample sinks from 100 to 84.09 pmC. From 839 BC to now, you'll get approximately 70.711 pmC in a sample, and from 593 AD approximately 84.09 pmC in a sample. Because in 839 BC and 593 AD, the atmospheric level, what samples usually start out with, was approximately 100 pmC.
I say approximately, because there have been fluctuations. These are accounted for in normal calibration graphs. Like that very classic one of Minze Stuiver and Bekker, which I have often cited.
Why don't my pmC values match the carbon date?
Example, from my tables***
- 2691 BC
- Eber born
- 2686 BC
- 24.08 pmC, dated as 14,456 BC
From Eber (or Heber) born, you may gather, that the sequence 2691 BC, 2686 BC is the real timeline.
Now, 2686 + 2026 = 4712 years. If the sample was from then, some would expect over 50 pmC. Like 56.552 pmC.
0.5 (4712/5730) = 0.5655°
But if the sample were from 14,456 BC, it would be well below 24.08 pmC.
14,456 + 2026 = 16,482
0.5 (16,482/5730) = 0.13618°° or 13.618 pmC
So, what is "24.08 pmC" doing there?
It's saying what the atmospheric level was back in 2686 BC. Not what the sample is now, but what the atmosphere and therefore the sample was then.
Now take a look a the number of extra years in the carbon level:
14,456 - 2686 = 11,770
So, back then we need a carbon level of ...
0.5 (11,770 / 5730) = 0.2408°°° or 24.08 pmC
Which, as it happens, is what I gave.
How can you know the carbon level back then? You weren't there to verify it.
Sure. Neither was the scientist there to verify the carbon level tens of thousands of years earlier as having been 100 pmC. That the original carbon level of 100 pmC doesn't figure in some versions of the formula, doesn't mean the theory doesn't require it.
These scientists and I agree on the carbon 14 level in the sample in 2686 BC being roughly speaking 24.08 pmC. What we differ is on whether the sample was ancient back then as they think, or recent back then and reflecting the atmosphere back then.
Either way, the current level in the sample will be 13.618 pmC. Don't believe me? Let's check.
24.08 pmC°°° * 0.5655° = 13.618 pmC°°
But back to the question how I know. And how they know. Or are supposed to know.
They presume the carbon level has been roughly speaking 100 pmC over the last 100,000 years. They consider this confirmed by among other things tree ring calibration, which that far back I consider as circular.
For my part, I use Biblical events and compare with archaeological or related finds. The Flood involves an opening of the fountains of the Deep, which would also involve volcanism. Therefore a supervolcano eruption should be from the Flood. One is carbon dated and that is Campi Flegrei, 39 000 BP. The Babel event, in the chronology I use between 350 after the Flood (Noah's death) and 401 after the Flood (Peleg's birth), 40 of the 51 years, involves a certain set of people (not necessarily the entire human population, I think it was the global élite of as yet a one world extended family), a certain set of people removing there from the East and finding a plain inside the general region of Shinear (Mesopotamia). It doesn't say any tower as piece of architecture actually got built and it doesn't say they ceased to try to build whatever it was (I think they finally succeeded with Wernher von Braun), but it does say they ceased to build the actual city.~ Göbekli Tepe is West of the Mountains of Armenia, over 300 km West of Mount Judi which is in the Westernmost Turkish province Armenia, just East of the Tigris. It is in the North edge of a plain, which stretches down to the Syrian border and around Haran. That plain is inside the stretch from Eurphrates to Tigris. And when Göbekli Tepe was deliberately buried in sand, this was a complete cessation of building activity at the site up to when Klaus Schmidt discovered it. Lowest level of GT gives the date 9500 BC (I've also seen 9600), while highest gives the date 8000 BC (I've also seen 8600). And the Genesis 14 war, of which Rob Skiba II used to say he was waiting for archaeological discoveries, actually involves one. In Asason Tamar, the Amorrhites or Amorrheans are attacked, and we know from 2 Chronicles (20:2? Yes!) that Asason Tamar is En Geddi. But being attacked presupposes living there, and the latest or only population of En Geddi that is possible for Genesis 14 is (thank you Osgood), the Chalcolithic. And there was an evacuation of En Geddi ending that, and the temple treasures were buried in a cave and carried there on reed mats. Now reed is a very short lived plant and would have been reflecting the atmosphere just before it was harvested. The reed mats are carbon dated to 3500 BC.
This gives me the equations 2958 BC = 39 000 BP, 2608 BC = 9500 BC, 2557 BC = 8000 BC and 1936 BC = 3500 BC. On my Newer Tables~~ these are the first four main anchor points. And each anchor points gives the carbon level at the time.
37,050 - 2958 = 34,092~~~ so 1.618 pmC #
9500 - 2608 = 6892, so 43.443 pmC #
8000 - 2557 = 5443, so 51.766 pmC #
and
3500 - 1936 = 1564, so 82.763 pmC #
If I know the carbon levels at two different anchor points, and there is no anchor point between them, my one way of knowing the carbon levels between is, modelling a fairly even rise. I divide the stretch between the anchor points into even smaller time spans, I then calculate how much the carbon level rose after each of these, and after the final one I check that the final time stretch results in a carbon level matching the overall time stretch, the anchor point.
There is a clumsy way of doing this, like if I divided the stretch into two, I could divide the difference into two and insert the medium there. This is what I do as a makeshift when checking on carbon dates between those in the tables.
There is also a smart way of doing this, which I did to produce the tables, namely take the speed of production during the overall stretch and multiply it with the production rates as they normally would be
2557 - 1936 = 621 years.
0.5 (621/5730) = 92.763 % ##
1 - 0.92763 = 0.07237 or 7.237 pmC ##
51.766 pmC * 92.763 % = 48.02 pmC ##
82.763 pmC - 48.02 pmC = 34.742 pmC ##
34.742 pmC / 7.237 pmC = 4.8 times faster
621 divides neatly into three substretches of 207 years:
2557 - 207 = 2350 BC
2350 - 207 = 2143 BC
2143 - 207 = 1936 BC
And then we take the normal decay and production for that substretch. Normal decay and production mean how they match now in the "100 pmC era" (which isn't quite one).
0.5 (207/5730) = 97.527 % ###
1 - 0.97527 = 2.473 pmC ###
2.473 pmC * 4.8 = 11.872 pmC ###
48.02 pmC + 11.872 pmC = 59.892 pmC ###
This would give us
- 2350 BC
- 59.892 pmC
For some reason, I found*** instead:
- 2350 BC (!)
- 62.358 pmC, dated as 6254 BC
And how do I get from the pmC at this intermediary point to the carbon date? It's a formula I don't quite understand, I borrowed it from a video on exponential equations, by MathQueen / MathemaTrick, but I have found it to be correct on a few checks. The reason that I put (!) after two years is, I actually found triple sixes among the decimals for the pmC value, and that's why I find probable that Nimrod (an original 666) died around these years, a bit after Shelah died in 2361 and a bit before Sarug was born in 2295 BC.
The reason the values are different is, here I am calculating an a larger stretch, 207 years directly from 2557 BC, on the table I calculated on a smaller stretch of 23 years which itself had been reached over several times this kind of operation, 23 times 9 being 207.
Now, how do I calculate the carbon year from here, as said? What is my formula?
5730 * log(x) / log(0.5) + real year = carbon year
where x is the pmC value in decimal form rather than percentage form
where decimals for carbon year are rounded to nearest integer
This applies to the two different versions for 2350 as follows:
5730 * log(0.62358) / log(0.5) + 2350 = 6254 BC
5730 * log(0.59892) / log(0.5) + 2350 = 6588 BC
If I had instead simply taken the first third of the difference, it would have been:
2557 BC ~ 2350 BC ~ 1936 BC
51.766 pmC ~ x ~ 82.763 pmC
(82.763 pmC - 51.766 pmC) / 3 = 10.332 pmC
51.766 pmC + 10.332 pmC = 62.098 pmC
5730 * log(0.62098) / log(0.5) + 2350 = 6289 BC
In other words, whichever method I take, the carbon date for 2350 BC is in the mid to late 7th Millennium BC.
So you mean Heber was born in the Palaeolithic after the Ice Age Maximum and Shelah died in the Neolithic?
Yes.***
- 2691 BC
- Eber born
- 2686 BC
- 24.08 pmC, dated as 14,456 BC
- 2361 BC
- Shelah died
- 2350 BC (!)
- 62.358 pmC, dated as 6254 BC
And the real distance in time was just 330 years, not 8000 +.
What would prove you wrong?
If a civilisation had watched all this happen and taken it down, and the records could be guaranteed as genuine, that would equate to proving another timeline, possibly the one of the uniformitarian timeline, correct.
However, if we found such records or even inhabitants of a country with such records, very unlikely already, it would still be a huge task to prove that this civilisation was genuine for all of these years into the past. And example of won't do it is say "we know that Australians were there 30 000 years ago, because they recorded a geological shift that happened at that time" where the only reason we "know" the geological shift was back in 30,000 BP is carbon dates.
But pending that, we have a mental and religious civilisation, if not an unbroken material one, in the people of the one God. From Abel and Seth to Noah, from Noah to Abraham. And they took down records, at least transmitting them orally. I'll cite Fr. George Leo Haydock for an even earlier event, the Fall:
Concerning the transactions of these early times, parents would no doubt be careful to instruct their children, by word of mouth, before any of the Scriptures were written; and Moses might derive much information from the same source, as a very few persons formed the chain of tradition, when they lived so many hundred years. Adam would converse with Mathusalem, who knew Sem, as the latter lived in the days of Abram. Isaac, Joseph, and Amram, the father of Moses, were contemporaries: so that seven persons might keep up the memory of things which had happened 2500 years before. But to entitle these accounts to absolute authority, the inspiration of God intervenes; and thus we are convinced, that no word of sacred writers can be questioned. H.
A modern scientist would not express himself as Father Haydock did in 1811 to 1814, while Catholicism was still illegal in England. Pinker said something about both older books and children having a freshness of style, of expression, because they are not encumbered by routine use of scientific terminology. Both C. S. Lewis as well as J. R. R. Tolkien, and I, have striven to emulate this quality.
But this does not mean Father Haydock was less stringent. I have tried to improvise a terminology for what he says as "minimally overlapping generations" ... Haydock used the Vulgate or Masoretic chronology, and has Methusalem as the last generation born before Adam died, in my LXX based one, it's more like Jared is that or his father.
On the other hand, Haydock thinks this was written down first by Moses, but I think even Abraham already started writing it down. This means that overall, despite the longer chronology, I have fewer minimally overlapping generations than Haydock has. The reason why I think Abraham wrote things down is, from chapter 12, Genesis becomes narratives that are more prolix and less easy to transmit correctly orally.
This sets a very high bar for such a potential civilisation. Discovering it would be like discovering the Book of Mormon: a "discovery" is a breaking point in information transmission where fraud and mistakes are clearly possible. If the civilisation were alien, I would say it was demonic, and even if the purported aliens seemed human enough, I'd suspect they were men having been trapped in demonic illusions by abduction. At the very least, these would be reasonable suspicions.
And as the word of God doesn't lie, I would on top of that need a good reason how this is a possible interpretation of the Genesis we have.
A final point: Why do you give the calibration as a series of pmC levels, rather than as a graph?
The graphs by Stuiver and Bekker are very adapted for carbon 14 levels at the origin of samples fluctuating around 100 pmC. If 750 and 450 both carbon date to 550 BC, it's less interesting to note that in the atmosphere 102.449 pmC over wiggles sank to 98.798 pmC. It's more interesting to know a raw number of 2500 carbon years is applicable both for calibrated 750 BC and for calibrated 450 BC. I don't pretend to follow such minor wiggles over very detailed calibration from tree rings, I give a much rougher calibration, and for that one the most interesting thing is how the carbon 14 level rose in the atmosphere.
My original "mission statement" was mostly "prove that carbon 14 could have risen from very low (1—3 pmC) to normal stable levels without the radioactivity needed having to destroy everything except spiders" and if I could on top of that provide a tool for assigning archaeology to the Biblical chronology, that was just a bonus. I think by now my original mission statement is very amply met.
Hans Georg Lundahl
Nanterre University Library
St. Narn of Bergamo
27.VIII.2026
Bergomi sancti Narni, qui, a beato Barnaba baptizatus, primus ab ipso ejusdem civitatis Episcopus ordinatus est.
Other resources than linked in footnotes:
High-Precision Decadal Calibration of the Radiocarbon Time Scale, AD 1950–6000 BC
Minze Stuiver (a1) and Bernd Becker (a2)
https://www.cambridge.org/core/journals/radiocarbon/article/highprecision-decadal-calibration-of-the-radiocarbon-time-scale-ad-19506000-bc/F1AB60097B0184501418D3EAEAD2EA90
Sylvester Joseph Hunter on Genesis, Henry Morris on 15 Cubits
Sunday 5 May 2024
https://creavsevolu.blogspot.com/2024/05/sylvester-joseph-hunter-on-genesis.html
(The term I use in above is "minimal overlaps" and not "minimally overlapping generations")
The Times of Abraham
By A.J.M. Osgood Published 30 Mar, 2006
First appeared in Journal of Creation 2(1) Pages 77 - 87, April 1986
https://creation.com/en/articles/the-times-of-abraham
Footnotes:
* 0.7071067811865475
** 0.8408964152537145285
*** Newer Tables, Flood to Joseph in Egypt
° 0.5655244996321537
°° 0.1361774954058079
°°° 0.2407985781241745
~ This distinction matches Masoretic and Vulgate. LXX says they ceased to build the tower and the city.
~~ See Newer Tables, Preliminaries for all such equations or anchor points. They are numbered I to VIII, and VIII being Fall of Troy, carbon date = historic date, carbon level in the time = has finally reached 100 pmC. I have taken over the numbers from previous tables, "New Tables" from 2020, and two new anchor points, one set arbitrarily and one for the Exodus, have been inserted but slashed for surrounding two anchor points. I/II and VI/VII.
~~~ I had taken 39,000 BP as 37,000 BC, but its actually 50 more since BP is measured backwards from 1950.
# 0.5 (34,092/5730) = 0.0161789498737946
0.5 (6892/5730) = 0.4344336256776197
0.5 (5443/5730) = 0.5176637713737836
0.5 (1564/5730) = 0.8276258493022752
## 0.9276310630766214
0.0723689369233786
0.480200994555716
0.3474248547465592
4.8007455894287776
### 0.9752705146651369
0.0247294853348631
0.1187199676501877
0.5989209622059037
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