Tuesday, March 25, 2014

A Family Tree of all Mankind - part 9

Biblical numbers for the Patriarchs.
      Note that "the" Bible gives 2 streams of numerical data: 1.) Age of patriarch when he begets first child. 2.) The length of time thereafter until he dies. The total age of a patriarch is calculated only indirectly by adding the two within our base 10 system, which has some adverse effects on what info we can validly extract from the data. What I mean to say, is that you can't necessarily simply add them and retain full fidelity of the original info. To see that at least something fishy is going on with the numbers, you can crack open even the Bible on your shelf right now and still see lingering syntactical remnants of some kind of previous numerical translation. For example, I'm reading Genesis 5:6 "And Methuselah lived after he begat Lamech seven hundreds and eighty and two years" which is indicative of an additive numerical system, perhaps similar to greek numerals. For example, as recently as the 1860s, we have things like the Gettysburg Address saying, "Four score and seven years ago our fathers brought...etc". Our forefathers used the additive unit of a score which of course is 20 years. Or in the French language today, the number for 90 is still quatre-vingt-dix which translates to four twenties plus a ten. Humans have used all kinds of various additive systems in the even recent past, so we would be foolish to think that whomever originally recorded the numbers in Genesis thousands of years ago understood counting and math the same way we do today. And we'd be equally foolish to assume the various iterations of translations along the way from then until now were all done correctly. More on this later, but for now all I'm saying is lets preserve the two given data streams separately in case some mathematical principal is at work making it invalid to simply add them. Although we'll add them too to see something interesting.
      And here is my attempt at sorting out what all the different versions of the Bible have to say about the numbers given for the patriarchs. (click to enlarge)



      So taking these numbers all together and scrutinizing them, it seems apparent to me that the Septuagint V. version is much more reasonable than the other data. For your convenience and reference, here's a copy of the Septuagint translated into English. I'm not saying it is "reasonable" per se, I'm just saying that they are the least unreasonable, and most internally consistent. From Adam to Noah they stay pretty constant in the 900s like so: 930, 912, 905, 910, 895, 962, 365, 969, 753, 950, 600 And from Noah to Abraham they go like: 600, 535, 460, 460, 404, 339, 339, 330, 304, 205, 175. Now many people (creationists) have focused on the fact that the postdeluvial numbers follow a pretty smooth exponential-ish decline, and have made the argument that because the decline is so smooth men could not possibly have contrived them, therefore it's divine. But you can forget about that nonsense straightaway. Man is pretty ingenious in ancient times, and understanding the exponential to the extent we do today isn't necessary. But also that is just totally irrelevant - This is not true data. We already established that humans don't live for 900 years. Because Science. These numbers are nominally fallacious.

      For good measure let's consider a lesser known mathematical tool: Benford's Law (aka Newcomb's law). The IRS is using Benford's Law right now to determine statistically if you've been cheating on your taxes. Look it up, and apply it to the first digit of the Patriarchs' data from Noah to Adam.



      It turns out that real measurements taken in the real world have a Benford distribution of the leading digits. This is even true independently of base - whether you're counting in binary or decimal or hexadecimal etc.  Age is not usually the best example for this because to really approach Benford, data should span multiple orders of magnitude, so in this case where we are talking about ages in the ballpark of 1000 years, we should most definitely see a Benford-approximated distribution, but instead we see the exact opposite - about as wrong of a distribution as one could possibly have! You couldn't make it worse if you tried! Purely random numbers should have an even uniform distribution of the leading digits, and real world data has a Benford distribution, which is to say 1 should be the leading digit about 30% of the time. And 9 should occur the least. I won't go into the math details, but the reason this is so, has to do with logarithms needing to be equal, and if you're curious about the subject, I assure you it is very interesting and you can read up about it here or here or here or here or here.
      What does this say about the patriarch ages? Nothing we didn't already know - and that is that they are not literally true, but that's hardly useful. The important question is WHY and HOW is the data wrong?
Benford's law is a seriously powerful tool, and I already mentioned that the IRS uses it to determine fraudulent data. Let me show you what it looks like when people artificially contrive numbers and/or cheat on their taxes:



     Humans are chock-full of all kinds of biases and heuristics that they're not even aware of. One such bias is that we prefer certain numbers to others. Because you and I count and think in base 10, we anthropocentrically prefer 5's and 10's. We tend to round numbers off to these, and our currencies reflect this, and the stock markets tend to get hung up around nice round numbers like 1000 or 15000 and paint psychological formations in the technicals that peak or turn around at these levels, and totally deviate from the fundamentals. So in the modern age, an artificial data set will have a lot of 5's. For the patriarchs' ages we obviously have a preposterous amount of 9's. Here's what the Bible (LXX) is trying to claim the distribution looks like from Adam to Noah:



      Riiight. So the signature is different than what we might expect if the numbers were contrived today, because the original authors didn't count the same way we do. What's up with all the 9's then? Some would say 9 has always typically been a "divine" number for various civilizations across the millenia. It's a sign of respect for your deceased ancestors, or a symbol of the Gods. The Vikings for example revered the number 9 by sacrificing 9 of this and 9 of that to their Gods (and 9 humans), and the infamous 666 is really ultimately the antithesis of 999. Now we're getting into much less-than-scientific territory than I prefer, so I'm going to leave it at that for now, and say, while this is indeed intriguing, this is clearly not the whole correct explanation, but I think it is a part of it. 9 is a special number in the eyes men. If you are curious about the possible historical divine significance of 9 please feel free to investigate further.

      So were the men that wrote the old testament lying to us deliberately in some grand across-the-centuries conspiracy? No, I don't think so. Did God write the Bible or deliberately guide the hand of humans who wrote it, and he made the data that way for whatever incomprehensible reason? No. Did God write the Bible at all? No. Did men who are susceptible to all kinds of human errors and biases write the Bible out of their own human volitions? Yes. Did men live at radically different times throughout history and copy and re-copy and re-re-copy manuscripts written by other men? Yes. Did these re-copyings accrue errors both intentionally and by mistake? Yes. And perhaps the most overlooked, under-rated, and important thing of all that you've probably never really contemplated before reading this article is:

DID THESE MEN ALL USE THE SAME BASE 10 ARABIC-NUMERAL COUNTING SYSTEM THAT WE USE TODAY?
(Hint: No.)

      This is a hugely significant question to realize about the Bible. This is not only important in regards to patriarchs of Genesis, but to all other numerical quantities given by the Bible too (40 day flood eh?). The bible was written a very long time ago, while we and our European ancestors have only used base 10 Arabic Numerals for a mere ~1000 years. Before that, we used Roman numerals. Numerical systems are similar to biological organisms in evolution. They arise with variation, and they survive with selection (and Bibles too!). The best mathematical systems tend to survive, while cumbersome awkward systems like Roman numerals go extinct. You can't even really do calculations in Roman numerals without an abacus - there is a reason Arabic Numerals out-competed them memetically. (We actually have India to thank for the invention of base 10 numerals, but we now call them Arabic Numerals because we were introduced to them by the Arabs during the crusades).

      So let's summarize: The Bible on your shelf is written in base 10 Arabic Numerals. The Mesoritic Texts are written in Roman Numerals. The Septuagint is written in ancient Greek Numerals. Then before that there were the Hebrews. The ancient Babylonians used a kind of blend between base 10 and base 6 called sexagesimal. The Genesis account would have had to pass through the Sumerian civilization as well. Adam and Noah and the patriarchs lived awhile back even before then. And somewhere along the pathway of all that, the concept of zero as a placeholder was invented by different civilizations at different times.
      To really get a grasp and understand how significant this is, we just about need to dig in at least a little ways - I'll at least just scratch the surface of how some of those different systems worked... and I know math isn't everybody's favorite topic.

Arabic Numerals: We're very familiar with these.. This is what we use. Like it or not, you and I right now are viewing the world, not truly objectively, but seeing through a "lens" of base 10 thinking. We're culturally biased, and predisposed to all kinds of other filters too.

Roman Numerals: I'm sure you're probably familiar with these too. Adding sucks, multiplication sucks. You certainly wouldn't want to calculate a cosine on an abacus. Although I will concede that the abacus is a surprisingly ingenious tool, and when I was reading Surely You're Joking Mr. Feynman, I enjoyed his discussion about a man he encountered who learned math on the abacus, and there were certain aspects of mental computation that man could perform easily that Feynman could not. And visa versa. So while I could not claim the abacus is always ubiquitously inferior to modern arithmetic, I think it's self evident that Roman Numerals suck. (but easily translatable, as you should have noticed above that every KJV number is identical to its ancestor in the Mesoretic Texts.)

Greek Numerals: An additive system that uses symbols from the Greek alphabet to also represent numbers in a somewhat similar way to Roman Numerals. One of the problems with classic Greek Numerals is they did not have a zero. Here's a place you can get a feel for them if you want. Arithmetic was hard, multiplication was even worse. I recall reading somewhere also that the numbers aren't all unique - that is to say it's difficult to tell the difference between 34 and 304 and 3400 without context clues. Or something to that effect.

Babylonians: A positional system that used a mixture of base 6 or 60 and base 10. Some relics of their math persist today, like 360 degrees in a circle and 60 seconds in a minute. The Babylonian culture existed right in the heart of the fertile crescent roughly around 1500-2000 BC, so their math is relevant concerning Genesis's pathway from origination to the present day. (Before Babylonia and in the same region, were the Assyrians who used essentially this same math, and invented it.. going back to say 2500 BC)

Sumerians: This empire occurred before the Assyrians, in modern day Iraq. Sumerian math was also a sexagesimal system (base 10 and 6 or 60). It's not the first mathematical system known, but the math of the Sumerians/Babylonians is actually surprisingly superior to that of the later Greeks and Romans! Sumerians were able to divide fractions, multiply into the millions, calculate roots, and raise numbers to several powers. Here and here are some good links about them and their math. It was at the nascent stages of the Sumer civilization when the original Genesis account may have been written.

      So let's grant the supposition that Adam and Noah and the patriarchs existed. But who in their right minds honestly insists you can interpret those numbers sitting there on your shelf literally? Sadly many do. The original data hasn't even the slightest remotest chance of surviving to the present day un-corrupted and true. We know this, and we've known it for a long time. Simply take a look at the different bibles to see the numerical mutations. For the longest time, I used to think the real true data was somehow "encrypted" so to speak, within the numbers we see in the KJV through all the mis-translations (accidental and intentional) throughout the ages of men translating copies of copies. I returned to that same approach on and off over the course of my understanding's evolution, and tried to decrypt the signal out from the noise for this data, and was never really able to solve it to my satisfaction. The noise is just too great, and the signal too small, and I figured no one on Earth knows the complete decryption algorithm, although many have tried.
      There are plenty of theories that are very compelling for explaining certain aspects of the differing data streams of Genesis. There's the missing decimal point theory which recognizes that we've taken for granted the concept of zero as a placeholder. So essentially you divide by 10, and this could be coupled with the interesting observation that the units digit (last digit) of the data is very statistically significantly usually a 0, 2, 5, or 7. This suggests to some that those digits could represent a quarter year, like a season.  Here's a quick histogram of the units digits from Adam to Abraham:



      Personally I no longer believe this is the right explanation, but I used to, and it is indeed one of the better ones out there. There are other similar variants like this where you simply hypothesize that years = months so you just divide by 12. Another good analysis is this one here. I don't think any of these are the right answer either; in fact there is no single process to decrypt the data to arrive at a robust answer.

      Without further ado and beating around the bush, let's just get to the spoiler already. This is how old the patriarchs lived in reality. Take a look at that pdf, and this is the best explanation I know of. So this is perhaps something of a let-down from the approach I articulated earlier about discovering some algorithm to decrypt the data streams to isolate the original signal from the noise, but it's the truth. It now looks as though the original data was never written to be taken literally even in the first place and the numerical data wasn't ever even there at all. It's all noise with no signal.

      No, I'm sure those with the Ken Ham level of pig-headedness will still insist on finding a way to believe the bible literally, most likely with some of their favorite biases like confirmation bias and cognitive dissonance. And all the others. But ultimately it doesn't really matter how old exactly the patriarchs were. Their ages most certainly aren't relevant to determining the age of the Earth the way Bishop James Ussher did in the 1600s. But we do still have their names and their relations to each other. Let me state what I personally believe regarding Adam and Eve: Evolution.

      However. The Fertile Crescent in Mesopotamia was the Cradle of Civilization where the agricultural revolution began at the end of the last Ice Age ~10,000 years ago. It was the birthplace of the wheel and the plow, and all the whole time previously, writing had not yet been invented. Humans communicated to each other via oral spoken language for a long time, and at some point writing was invented. And by mathematical proof and simple logic, there must necessarily be some person who is the first person to be recorded and remembered by written history. I believe Adam is that person. Adam is the first person remembered by written history - it's as simple as that. Suppose we had never heard of Adam or the Bible before, and we had to speculate about what the historical record might tell us from back at our beginnings of written history. The reality we observe is pretty much exactly what we would expect in that case - numbers that don't make a lot of scientific sense, shrouded in ambiguity and uncertainty. Written records of Kings' names are highly likely to precede the written records of their ages, at least insofar as the evolution of that into an over-popularized creation myth goes.
      Another perspective can also be made though that writing and counting originated out of economic necessity, so numbers on clay tablets describing wheat and grain tallies and such should perhaps come along stronger at the beginning than names on king's lists. But a grain inventory isn't going to evolve into a creation myth now is it! Adam and the patriarchs are such a king's list. If they existed at all, they were the kings and rulers of their peoples in the fertile crescent. As anyone who's done deep-genealogy knows: history remembers kings. As a scientist, we know Adam was not the first human being to ever live. He was not divinely created by God, nor was Eve. Eve is much less likely than Adam to have existed, and could just be part of the creation fabrication. If they existed, their names they would've called themselves wouldn't have been Adam and Eve (I've read that Adam means "man" in Hebrew). Obviously they had parents and grandparents, same as every other human that's ever lived. Dur!
      As an agnostic/atheist I've always felt it's so painfully obvious that the Bible isn't to be taken literally, along with astrology or any of that other superstitious nonsense. It truly pains me to explain all this pedantic crap with a straight face, but I know so many people just fail to ever consider these things.
      I want to be clear I do not reject the Bible out of hand entirely. There is a ton of real history to be gleaned from the Old Testament that is more or less correlated with archaeology and anthropology. Like King David and Goliath and Jericho - Those were real historical things (minus any mentions of God of course) that happened. But the dates are a bit off, so we have to calibrate the old testament with archaeology. And we definitely have to keep up our guard of skepticism constantly, because humanity's most precious written record from throughout the ages has been corrupted and influenced by religion. So I will seriously grant that there is a likely chance Adam (and maybe Eve) may have really existed in real history, in some capacity. If so, he was a tribal Chief or King in Mesopotamia, probably close to somewhere about 3100 BC +/- 50 years.

      In my tree now, I've entered a higher-precision speculation that Adam may have been born 3113 BC, right around the end of the Uruk Period. It seems intuitive enough to me he may have been the founding father of that dynasty or regime during the Jemdet Nasr period. As I continue to learn more as time goes on, I've become increasingly convinced that this is right. If so, that would make him our ~200th great grandfather (along with the rest of the whole PCD of say 175th to 225th). Although he is included in my family tree software as 186th great grandfather according to KJV dates, the number of generations is unaffected by the dates, so my number of 186 is plausible. But my tree is somewhat sparsely populated around 2500-2900BC. The reason for 3100 BC is because the great river flood in Mesopotamia is carbon dated to occur around 2900 BC, and since Adam is 10 generations back (or more precisely, 10 back on the kings list), then that is surely more robust than my 186 count. 3100 BC correlates beautifully with the observed average temporal distance of 25 years per generation. It's a much needed calibration for my tree, and if one were to get mathematically motivated, one could take a more exact longevity chart (like I have on page 7) and from it create a more accurate generational period that is a function of time, rather than the constant 25 years. Then integrate it between today and 5100BC. I may do this later. Bottom line is Adam is our ~200th ancestor.

      It's noteworthy indeed that the Jemdet Nasr period began in 3100 BC and ended in 2900 BC, and that the antedeluvial patriarchs list is just perfectly long enough for that period. Archaeologically, the artifacts we're finding there show distinct differences from that which came before. Specifically I think Noah (Ubara-tutu) was the last king of the City of Shuruppak in the land of Caanan (modern day Tell Fara, Iraq) and Adam (Alulim) my have been the first king of the City Eridu in the land of Shulon. And the generations in between correspond to that given by the Sumerian Kings list here.

      So the mystery of Adam and Eve has been solved scientifically. Noah and the flood too (<-- don't skip over this link, it is "the droid you are looking for"). It rained for ~6 days, not 40. Also the Ark was round if it existed. There was indeed a flood that happened locally in Mesopotamia, but in spite of the Epic of Gilgamesh and others, a flood hero and an ark may really still be a myth. The ark may have been a pre-existing barge used for commerce up and down the Euphrates, with some of the local common commercial animals on board. There's no reason to suppose it was one single mono-hull boat, but maybe a conglomeration of lots of boats roped together. Mount Ararat in Turkey is nonsense - that's only been introduced to the story around 1100 AD. The word shadu was the same for both mountain and hill, so it was confused and exaggerated as stories tend to do. There is no chance that any of the Ark survives to the present. Noah's alter has also not survived, but I've heard that the site of the alter may be a real place that's been excavated by archaeologists and is described in chapter 5 of this book which I have not read. Noah may have been also called Ziusudra by some of his descendants which etymologically could be the possible origins of the god Zeus. But that is just a speculation.

But back to what's important, let's not forget that we share common ancestry with all of these too; as well as bananas and lettuce and grasshoppers and bacteria and plants and fungi and dinosaurs... and everything else under the Sun made of DNA:




Checkmate Biblical Literalists.


page 1,2,3,4,5,6,7,8,9 page


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