A mathematical formula that can guarantee lottery winnings, revisited

It's been almost a decade since I first posted about the scam going around that a mathematical formula can guarantee lottery winnings. Well, I just found out that I was wrong--sort of--and I'm back to make an apology.
Joan Ginther was a math whiz as a kid, graduated at the top of her class at a small Texas high school, and went on to get a PhD in mathematics, with an emphasis on statistics, at Stanford. She then dutifully spend the next sixteen years teaching maths at small colleges in the Western US, but all that changed when she won a $5.4 million share of the Texas Lotto in 1993. Like most lotto millionaires, she quit her job. And like most lotto millionaires, she kept right on buying lottery tickets.
But here is what made Joan Ginther different: she actually HAD found a mathematical formula to guarantee lottery winnings, and she used her initial windfall to keep playing in such a way that she went on to win big two more times in the next 15 years--enough millions to keep up her lotto habit without having to borrow against future payouts. She'd found a way to lower her odds of winning from one in tens of millions down to about one in hundreds--which means that, given the right time and place, buying out her hometown Texas store's supply of lottery tickets produced better than even odds of hitting the jackpot. This she finally did in 2006, winning $10 million from one of a stack of $50 Extreme Payout tickets she'd gotten someone to purchase for her. She also allegedly hired an attorney to come to Texas, pick up the winnings, and return them to her Las Vegas hideout.

Once Texas Lottery officials realized this mega-winner obviously had some formula for buying winning tickets, they launched a full-on investigation of her. This turned out to be quite difficult to do, as she had stopped coming to Texas in person to buy the tickets, so there wasn't much to investigate. They tried to get the FBI involved, but once the FBI learned that she was using publicly available information--published by the Lottery Board itself--and legal proxy buyers, they had to patiently inform the Lotto officials that if researching ticket distributions was legal, and ordering publicly available information was legal, and hiring someone to buy and redeem tickets in your name was legal, then there was no crime to investigate.

Joan Ginther, though, never attempted to sell her forumla. Why would she? It was working fine for her. But after she cashed in for the fourth time, the ensuing investigation resulted in changes to the distribution of tickets that basically rendered her formula useless.
In 2010.
So by the time "Jared" started trying to sell me his mathematical secret to winning the lotto--if "he" had in fact managed to break into the Sanford Archives and get "his" hands on her dissertation from the early seventies (allegedly on the way winning lotto tickets were distributed)--it was already obsolete. So I do apologise for scoffing at the idea that it could be done--but I note that in the decade since I made that claim, every multiple lottery winner has turned out to be relying on fraud and inside access--not a mathematical formula. So yeah, it's not much of a mea culpa, because it doesn't have to be.

I also need to give credit due to Nathaniel Rich and Peter Mucha, the reporters who broke the story. According to Mucha, she never stopped buying Texas Lottery tickets, even after her big win, but the fifth big payout eluded her. As for me, I'm happy to go to my grave at a ripe old age never having purchased a single one.

A life not wasted on education

There's been a bit of a buzz recently regarding a ground-breaking discovery by a young mathematician who goes by the name Hannah Cairo. You won't read anything about it in the linked article, but this teenager who is generally regarded as female is actually an imposter in that role, having started out life as a male whose Christian name has been so effectively wiped from the record that I will just be referring to him in this article as Cairo (in that, at least, I have literary company).
What interests me the most about this story is not that a teenager was able to solve a 40-year old problem in higher mathematics, but that doing so was able to propel him over several of the barriers that have been erected to keep free-thinking individuals out of higher education. Cairo, you see, will be entering a doctoral program in mathematics at the age of seventeen. What’s so unprecedented about this is that he not only doesn’t have a master’s degree in the field, the usual prerequisite for embarking on a doctrinal program—-he doesn’t even have an undergraduate degree. And for what it’s worth, he’s never even been to high school; he went directly from homeschool to taking advanced college math classes.
Now, the vast majority of universities to which Cairo applied did turn him down, citing the usual standards of their gatekeepers. But he was accepted by the graduate schools of Johns Hopkins and the University of Maryland, who were somehow able to make enough exceptions to their enrollment policies to squeeze him in.
Decades ago, I noted the irony of Lynn Conway bragging about being the only woman in her electrical engineering graduate program at MIT, when in fact Conway was a man named Robert at the time (it's also very interesting to note that Conway went on to become a tenured professor at the University of Michigan, without having jumped through the requisite hoop of first obtaining a doctoral degree). Now, I note the irony that an alleged female math prodigy can’t be celebrated as such because it would only bring attention the fact that he’s actually a male. The article can only emphasize Cairo’s youth as an unusual aspect of his accomplishment, not his alleged gender. And I have to wonder whether Cairo would have stood any chance of hurdling over the entrance barriers to the PhD program he’s now entering had he not been granted special handling due to self-inclusion in the protected class of transgender.
What does it tell you that, as a male, Cairo would have been sent back to high school to jump through dozens more hoops on his way to eventual stardom, but as a female, he found the hoops magically disappearing before him? The movie Some Like it Hot seems eerily prophetic on this note.

Gödel’s Incompleteness Theorem falsifies Atheism (something I found online)

Gödel’s Incompleteness Theorem states:

“Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory.”

To briefly state the implications of this:

All predictions about the future are inductive. Outside the circle. In Gödel’s language they are “undecidable propositions.” It’s probable you’ll still have your job next week… but maybe you don’t.

All scientific laws are based on inductive reasoning. All of science rests on an assumption that the universe is orderly, logical and mathematical based on fixed discoverable laws.

You cannot PROVE this. (You can’t prove that the sun will come up tomorrow morning either.) You literally have to take it on faith. In fact most people don’t know that outside the science circle is a philosophy circle. Science is based on philosophical assumptions that you cannot scientifically prove. Actually, the scientific method cannot prove, it can only infer.

(Science originally came from the idea that God made an orderly universe which obeys fixed, discoverable laws – and because of those laws, He would not have to constantly tinker with it in order for it to operate.)

All closed systems depend on something outside the system.

You can always draw a bigger circle but there will still be something outside the circle.

Whatever is outside the biggest circle is boundless. So by definition it is not possible to draw a circle around it.

If we draw a circle around all matter, energy, space and time and apply Gödel’s theorem, then we know what is outside that circle is not matter, is not energy, is not space and is not time. Because all the matter and energy are inside the circle. It’s immaterial.

Whatever is outside the biggest circle is not a system – i.e. is not an assemblage of parts. Otherwise we could draw a circle around them. The thing outside the biggest circle is indivisible.

Whatever is outside the biggest circle is an uncaused cause, because you can always draw a circle around an effect.

If you visit the atheist website Infidels, you will find the following statement:

As defined by philosopher Paul Draper, naturalism is "the hypothesis that the natural world is a closed system" in the sense that "nothing that is not a part of the natural world affects it."

But according to Gödel’s theorem, every system is dependent on something greater being outside the system. Draper's hypothesis cannot be correct. Because the universe is a system, it has to have an outside cause. A cause that is not bound by time, matter, or energy, because it is outside of all those, and they are subject to its control. A cause that cannot itself have any cause, because it is outside the widest circle. A cause that is infinite in every way, because it's not a system that can be encircled. You can call that what you want; I call it God.

Atheism's denial of God flies in the face of a basic law of mathematics.

A review of David Instone-Brewer's Bible Contexts Series - Chapter 20: Cain's "wife"

Dr. David Instone-Brewer is an eminent Bible Scholar in England, one of the experts responsible for the last tranche of changes to the NIV. He knows a lot more than I do about a lot of things, and since he makes it easy to access most of what he writes, I follow him to my advantage--especially in the area of Old Testament Studies, which is his specialty. What I've learned from him, however, are generally facts and insights I hadn't been exposed to before. I don't sit at his feet for much of what he weaves into his teaching, which are just standard tenets of atheism (although I admit, some of them are new to me as well). For although he identifies as an evangelical, he nonetheless looks to atheist scholars and their disciples to inform his interpretation of the Scriptures--and is thus oft led astray.

Dr. D is greatly hampered in his ability to gain insights from the book of Genesis, believing as he does that it was composed as a sort of religious fiction during the Babylonian captivity to inspire Jews not to lose hope in their present situation, or something along those lines. He doesn't believe that it is even intended to be a serious historical record, and certainly not that it was compiled from written eyewitness accounts. There is therefore no apparent limit to the imaginations his mind can supply from a reading of this section of the Scriptures, guided by the speculations of the atheists which lie behind much of his theology. And since he drinks deeply at the font of those who have no access to absolute truth, he all but admits that what he sincerely believes to be true today may be ridiculed a decade or a century from now, as atheist philosophers discard old and unworkable alternative explanations for how the world works, and imagine new ones yet to be disproven. This approach leads him far astray from orthodox understanding. 

Take, for example, his chapter on Cain's Wife. He already reinterprets the first two chapters of Genesis in an atheistic framework, starting with a random humanoid whose ancestral line went back to stardust. He then departs from the atheist narrative just a bit to give God credit for taking this human-looking animal, the pinnacle of billions of years of random evolution, miraculously granting him a human spirit, and then--in a most unusual departure from his involvement of the previous billions of years, and in a biological process we can hardly imagine, much less explain scientifically--splitting off a half-clone which became the first human woman. He then set the newly enlightened couple in special walled enclosure he called Eden and commanded them not to eat a certain fruit. They did so regardless, and as a result they were cast out of Eden to resume their evolutionary progress without any life-sustaining access to the fruit of the tree that conveyed some sort of immortality. And here enters Cain's Wife, who he proposes was a non-human, implying along the way that the host of present mankind must be descended from her.

I hesitate to critique Dr. D in any area of actual OT Studies, as he is an acknowledged expert in both the Hebrew language and rabbinical literature. But here he has left far behind anything directly related to the Hebrew Scriptures to dabble in Evolutionary Biology, in which he is no expert--leaving me on much firmer ground to dispute him. [Edit: he does claim biological expertise based on his undergraduate studies, but then, so could I, having sat for General Science in Bible College.]

I will be interacting in this post with Chapter 20 of his book Bible Contexts which, at least for now, can be found at his website http://www.biblecontexts.com/. He introduces the chapter as follows:

If Cain married someone living outside Eden, this would explain some strange details in Genesis. It would also explain how our gene pool contains so much variation.

---

His book is all about explaining strange details in Genesis with even stranger speculations. He sees a problem with God selecting just two humanoids--really, only one--to begin the human family tree. Although his God is capable of many amazing feats, Dr. D seems constrained by his acceptance of atheist teaching to place the Laws of Nature at a higher tier on the hierarchy than that occupied by Nature's God. The God who could split the first man in half at the sub-cellular level to produce the first woman was nonetheless stumped at providing this pair's descendants with enough genetic variety to produce the four blood types, so He needed to pull in some genes from the neighboring humanoids to pull it off. Thus, Cain's Wife. 

Now Mrs. Cain was not a Neanderthal, mind you--Cain had already inherited those genes from his long-dead humanoid ancestors. What she provided instead was access to the "rich gene pool" that had resulted from millions of years of primate evolution. Dr. D uses a modern analogy to explain why this was not only sufficient, but necessary, if humanity were to survive The Fall:

 Cain could, of course, have married his sister – though the Bible doesn’t say this happened. It is difficult to imagine her wanting to marry a brother (especially the nasty brother who murdered the nice one). Presumably this incest wouldn’t be dangerous like it is today because God could have made sure there weren’t any dangerous recessive genes in Adam’s chromosomes. However, our human race would be very weak if the entire gene pool had been limited to just Adam’s chromosomes. Restricted gene pools often cause problems in overrefined agricultural animals or crop lines because this makes them vulnerable to pests and changes in the environment. This is solved by interbreeding with wild species to reinvigorate the gene pool by introducing more variety.

Here he makes a mistake commonly perpetuated by pseudoscientists, assuming that a genetic bottleneck always results in a dangerously depleted gene pool. The reason modern agricultural crops and animals have depleted gene pools, and wild varieties don't, is precisely the result of human intervention to breed out unwanted variation. Absent that unnatural selection, a fairly robust set of genes will continue to be passed on, even in a small population. But racism is a powerful and primordial urge, such that organisms resist hybridisation and generally seek to mate with creatures most like themselves, resulting in further speciation, as any organisms that depart from the standard in the same direction tend to seek out each other for breeding, leaving an even more depleted genome to their descendants. Were it not for the balancing act of another primordial urge--that of men, having gone forth to conquer, seeking and finding sexual release amongst the females of the conquered races--humans would be much more genetically depleted than we are. 

If I were to hypothesize myself, I would say that God created Adam with two completely different sets of chromosomes, with each of the millions of gene pairs consisting of different alleles. Thus Eve was far more distant from Adam, genetically, than any two humans are today; at the time she was split off from him, she only shared 50 per cent of his genetic material. And if God were powerful enough to pull off forming yet another haploid set for the rest of Eve, then he only shared half of her genome--providing far more diversity than Cain could have brought into the young race by impregnating a distant descendant of the Neanderthals and Denisovans. Adam could well have carried one haploid gene for Type A blood, and one for Type B. We don't even have to split that in half again to get all three of the blood types just among their children, provided that Eve possessed the same. And if, post-Fall, any two of their children ended up with an allele that lacked the information for producing either the A or B antigen, Type O could emerge as early as their grandchildren's generation. It's a stupendous pity that Dr. D, with all his learning, didn't see how God could accomplish this without having Cain interbreed with a non-human. 

       Mutations occur very rarely, unless there are carcinogens present. This is good, because most mutations are dangerous – as seen by the effects of carcinogens. Reproductive cells are protected from mutations by DNA repair mechanisms, which make sure that accidental mutations are rarely passed on to our children. A few do get through – on average sixty-four mutations – though this is tiny compared to the three billion base pairs that are copied perfectly.⁴ However, some of these are so harmful that they result in miscarriage – about 10 percent of pregnancies end this way. So even a small increase in mutation rate would result in a lot more miscarriages.

Dr. D goes on at length to describe just how humanly impossible it would have been for God to actually get the human race going with just two people. Okay, and where does the book of Genesis imply that God can't do anything humanly impossible? This cognitive dissonance would be laughable, did he not with such sincerity lend credence to the atheist hypotheses. Of course, the way heredity works now, in our currently depleted human population, where any two humans on the planet share at least 99.9 per cent of the same genome, does not necessarily speak to how things would have worked back when they shared barely half of that. We don't really have any idea what a genuinely rich gene pool looks like, as the nature of genetic recombination means that some genes go missing with each successive generation, and after several thousands of years, every genome has become depleted to one extent or another--unnatural selection greatly accelerating the process. And since this goes against the collective wisdom of Evolution--which imagines, contrary to all evidence, the gene pool at large becoming progressively richer over time--Dr. D. just isn't going to hear this from his atheist mentors or their disciples.

So whom DID Cain marry? Well, as all scholars have noted, Genesis doesn't say. And why should it? If humanity began with only one man and one woman, and no ape-men to "enrich the gene pool," then of course he married his sister. Anyone with even half a human brain could figure that out with just a little help; there's no need to state the obvious. All we need is the succinct statement of the compiler of Genesis 3 that Eve was "the mother of all living." That leaves no room for any previous races to insert their alleles into the human genome, period. 

Dr. D should have stuck with interpreting and explaining the Bible, and left fairy-tale speculations to those who reject the Genesis account out of theological necessity. 

Does χιλια ετη mean a thousand years?

As promised in my last post, here is a critique of Peter Hoover's view of the Millennium. In an email broadcast on August 12, he wrote briefly of his fling with premillenialism, and subsequent revocation:

I dropped all popular theories, all names that would identify me to this school of thought or another, and I chose to cling to Jesus' Gospel and the Scriptures themselves. Nothing more. Nothing less. With only this in mind, these became my conclusions. My passion. My goal:
 1. Building on the right foundation, Jesus Christ (1 Corinthians 3:11). "No one can lay any foundation other than the one already laid, which is Jesus Christ." Whatever we build on, whatever we use, whatever we teach must come from Jesus. Everything else is unsafe and will not stand in the end. If Jesus and his apostles did not teach it, if Jesus' example does not match with what we are promoting, we are in the wrong. Plain and simple.
 2. Choosing the Narrow Way (Matthew 7:13-14). The broad way, the way of the crowd, the popular way is dangerous. The narrow way, the way of Jesus, is the only right and safe one. How shall we find it? From Jesus and his apostles alone. Not from any modern organisation or religious group. Not, particularly, from any church. The real Church of Jesus Christ, the Church that truly follows him on the narrow way, is the fellowship of all who listen carefully, who follow, and obey. Why is it narrow? Because few choose it. It is the Way of the Cross.
 3. Following the Context and Flow of Scripture (2 Timothy 2:15). Using the Scriptures responsibly includes its context and how they were presented to us, one after the next. That is how we need to use all information anywhere. To use the Scriptures in a game of "fast and loose," pulling out bits and pieces here and there, while cobbling them together again through all kinds of ingenious ways, is not only dangerous. It is dishonest. It takes serious study (like they did in Beraoea) and the help of the Holy Spirit. It is not safe for us to use the Scriptures unless the Lord Jesus has already freed us from human prejudice and a pre-established agenda.
 4. Not Adding, not subtracting from prophetic Scriptures (Revelation 22:18-19). "I warn everyone who hears the words of the prophecy of this scroll: If anyone adds anything to them, God will add to that person the plagues described in this scroll. And if anyone takes words away from this scroll of prophecy, God will take away from that person any share in the tree of life and in the Holy City, which are described in this scroll."
How seriously have we taken these sobering words at the end of John's Revelation? I am amazed. Of all Scriptures used by Christians, anywhere, none of them have been tampered, twisted and added onto more than this one itself. An absolutely massive world-wide movement, involving millions upon millions of people, entire political parties and shocking wars have revolved around what is read "between the lines" of Revelation 20:1-10.
 But, seriously, have you ever carefully read this chapter yourself? Stunning in its simplicity!
 There is not one word, not even the minutest suggestion of any "restoration of Israel," or of any flesh and blood Jews, or of any earthly nation governed by Christ, in this passage.
Neither is there any suggestion in the entire Scriptures of any "pre-tribulation rapture," or of any restoration of animal sacrifices that glorify God, or of a return to the laws of Moses.
 In fact, the "thousand years" is one of the most poorly translated pieces of the entire New Testament in our North European languages. The Greek word (check it out in Strongs, or wherever you wish) is the word "chilioi," not singular, but plural. In other words, it already includes "thousands of years," instead of just one clearly defined millennium. But even the word "thousands" is not totally accurate.
 "Chilioi" is not the word that Greek speakers would use to describe "thousands." Instead they use the word, "chiliades." Chilioi, as used by the Apostle John is a vague term, used basically for a "long long time." An age.
And this brings us right back into the rest of all the teachings of Christ, the simple Gospel that tells us nothing more than to be ready at all times for the day of judgement. Not adding. Not subtracting, is a key to understanding Bible prophecy. If the Lord wanted us to know more, he would have told us more. And in the meantime, while we are still waiting, I rest every night in total peace. The Lord is in control. Not me. And this is why I refuse to latch onto any "ism" or humanly constructed line of thought: premillennialism, amillennialism, postmillennialism, etc. Who needs it if we have the Gospel of Jesus in our hearts and hands? 

 I wanted to give the full context of his claim regarding the meaning of  χιλια ετη, the term Revelation 20:2 uses, because he is so totally wrong about this that I can't address it without making him look really stupid. And he's not stupid, he's just way out of his league here, casting judgment on basically every Bible ever translated in English. Yes, Strongs uses the transliteration 'chilioi' for G-5507, which is its nominative singular lemma form. But not even Strong translates it as 'thousands', but 'a thousand'. This shows how a little knowledge is a dangerous thing; being able to look up a word in Strongs does not qualify one to evaluate Bible translations.

It gets worse, when he assays to read the mind of the modern Greek. I actually don't know modern Greek, but I do know that when Google or Bing attempt to translate Biblical Greek as if it were Modern Greek, the result in English is usually hilarious, but never accurate. Google, however, perfectly rendered either χίλια χρόνια (its Modern Greek translation of 'thousand years') or χίλια ἔτη (the Koine equivalent). So all the talk about how a Greek speaker would say it is nothing but ignorance strutting as erudition; at least at first blush, it's 'chilia' either way.

If Peter Hoover wants to accuse a Bible translator of mistranslating 'thousand', he need look no further than Acts 21:20, where many Bibles have the elders telling Paul that "thousands" of Jews had come to faith, when even Strongs could tell him that the number is actually that of the next order of magnitude, 'myriads'.

And how is χίλια ἔτη used elsewhere in the Bible? Well, it is only used twice elsewhere, and both times it is used proverbially to refer to a long time, like me saying in English, "Never in a thousand years would I expect such a scholar and historian as Peter Hoover to make such a blunder." But this is not proverbial language here--it's narrative, with terms like, "And when the thousand years are ended," which is pretty specific.

It's not as if John didn't know how to express large numbers: in the majority text of Revelation 9:6 he speaks of a number of horseman so large as to be inconceivable in his day, a thousand myriads (the two largest Greek numbers put together). Then in 5:11, he gives up counting the heavenly host after running clean out of big numbers: myriads of myriads, and thousands of thousands. But he is able to divide 144,000 by twelve and come up with the right number; and when it comes to telling time, he is twice able to count up to one thousand, two hundred, and sixty days. It sure seems to me like John considers χίλιοι to mean 'a thousand'.

Could χιλια ετη refer to a long time, rather than exactly 12,000 months? Well, it does every other time it's used in the Bible, so I would have to answer "possibly," given that Revelation is a highly symbolic book anyway. But let's at least be honest about the evidence, and stick with what we have rather than making it up. And we are certainly not on firm ground to assume that it does, and build our theory on that.

P.S. In the interests of fair use, I should note that you can receive your own free subscription to Peter Hoover's emails by so requesting in an email to detention.river@gmail.com.

How many metres in a cubit? The answer may astound you.

Dear Readers,
I know it's only been a day since I edited my last post (if you haven't read it yet, I highly advise it), but I just have to share what I learned today about the Egyptian cubit. If you watch the relevant minute of the referenced video, you will see that the most ancient Egyptian cubit is a function of the ratio of pi and phi in metres, out to four or five digits (.52356) over the precise 230,366½-millimetre width of each of the Great Pyramid's four sides.
This would indicate that the most ancient Egyptians were aware of the relationship of geometry to base ten out to five digits--a metre is the distance from the equator to the pole, divided by ten thousand--as well as the irrational numbers of higher mathematics. As later generations of Egyptians lost this knowledge, it stands to reason that their cubits became less and less precise--ranging as much as a centimetre off the ancient standard (and even more so by the time we get to the TNIV).
If the Egyptians at the dawn of history were capable of manipulating such abstract numbers to such precision, it lends credence to the idea that the numbers in Genesis chapter five--even more ancient--are the result of equally complex calculations. Note that in each of the nine generations enumerated, the age at which the son was begotten always ends in zero, two, five, or seven--as do the lifespans of the first seven generations. This is regardless of whether one follows the Hebrew, Greek, or Samaritan numbers. And as it turns out, two and five are among the factors of phi squared; it appears that some complicated mathematical formula was at work in producing ages that always ended in one of these two factors of phi squared, or the sum of them. And it appears that we are only now finally coming to the point in our understanding of ancient mathematics to be able to transcribe these numbers into something more useful to our purposes, which is establishing the time span between Creation and the Flood.

Added on August 19:
This video shows a tablet from ancient Babylon now understood to contain formulas of higher mathematics used to construct triangles from an entirely different perspective than has been used for the past 2500 years. Clearly Ancient Man was much more intelligent than materialist paradigm has been willing to accept. Perhaps more on that, in a later post.

An Upside-down Christmas Tree in China

In an earlier post, I pointed out that national fertility rates tend to fall wherever national income rises. While such is indeed the case in China, the drop is further exacerbated by the national One-Child Policy, which went into effect in 1979. Not surprisingly, there's now a big drop in the 30-34-year-old cohort of the Chinese population. As China's population growth slows to a crawl, there's some talk of eliminating the policy, or at least cutting it back further (only about a third of Chinese couples are currently subject to the restriction).

But actually, it's already too late. The pre-policy Chinese couples are already fast heading out of their peak childbearing years, so for an entire generation to come, the reproductive potential of the Chinese is going to be severely curtailed.

In order do their part to keep China's population from dropping, every couple consisting of two only grandchildren (the 'little emperors') would have to first produce six children just to replace themselves and their parents; then another eight to replace their grandparents! Obviously, that is not going to happen. Instead, as the larger cohorts of the population die off, the population will peak, then start a long and continuous decline--even if the birth rate doubles or triples among the remaining cohorts as they come of childbearing age.

That results in an Upside Down Christmas Tree.

The Old Math: Nominal Figures and Biblical Numbers

100269 I have touched on the topic of Biblical Numbers in earlier posts; in this one I shall attempt to wrap up the entire topic as it relates to the supposed accuracy of Bible Translations.

 I once worked in a factory where one of the items we handled was an electrical device with an "8-ft" cord. Now everyone knows that an 8-foot cord is longer than a 6-foot cord and shorter than a 9-foot cord. But do they know that it is exactly 96.0 inches? Well, no. Electrical cords of that length could easily be stretched by the major part of an inch, but for purposes of reaching the nearest electrical outlet, precision right down to the tenth of an inch really isn't necessary. So I had to chuckle when I saw, on the Spanish side of the box, the measurements of this same 8-ft cord given as 244 cm. Now that does happen to be 8.0 feet, but I really doubt that anyone ever got out a tape measure and measured that cord right down to the nearest centimetre. What they basically had was a 2½ metre cord; they just didn't realise that for their purposes of measurement, that was equal to 8 feet.

Take an even more obvious example of round numbers in measurement. Ever heard of a 2 by 4? If you live in a single-family house in North America, it's most likely that you have. It is the standard size piece of lumber for wall construction. But it's not 2 by 4 inches, or even 2 by 4 centimetres; it's actually 1-1/2 x 3-1/2 inches, to the nearest quarter-inch. To avoid false advertising, lumber stores have to note that all lumber measurements are given in "nominal sizes," but everybody already knows that to be accurate, they have to subtract 1/4 to 3/4 of an inch from the nominal size. Even though the lumber is planed to greater precision, it's just not practical to name any more precise a measurement than the nearest inch.

And thus we come to Biblical numbers. Ever notice that Bible measurements are always given in whole numbers, rounding off to more and more zeros as the numbers get bigger? You'll never find a hundred and one or a million and two of anything in the Bible [UPDATE 2018: although I must admit that 1 Kings 4:32 comes uncomfortably close--UPDATE 2021: but only in the Masoretic text, and translations thereof].

Take Job's wealth as a fine example. Do you really think he had exactly 7000 sheep, 3000 camels, 1000 oxen, 500 asses, and 10 children? Well, we do know about the children, because there were 7 sons and 3 daughters. But obviously the other numbers were rounded off to the nearest hundred--or maybe even the nearest thousand.

The most precise figures given in the Scriptures are always for the ages of Biblical figures. Methuselah, for example, lived 969 years. That's obviously not rounding off to the nearest thousand, hundred, ten, or even five. Rounding off to the nearest year gives us a known level of precision for calculating the age of the earth, but after ten generations, we can't be precise to the year any more; ten years is more like it. So in giving broad chronological timespans, note that the Bible always rounds off to the nearest decade or even the nearest century:

-Your descendants will be strangers in a country not their own, and they will be enslaved and mistreated four hundred years.
-For three hundred years Israel occupied Heshbon, Aroer, the surrounding settlements and all the towns along the Arnon.
-Now the time that the children of Israel lived in Egypt was four hundred thirty years.
-This was four hundred and eighty years after the people of Israel were rescued from their slavery in Egypt.

These are nominal figures. Sometimes they indicate more precision than is evident; sometimes they don't. Abraham's and Sarah's ages seem to have just happened to both end in zero when Isaac was born, for example. But when the Bible is showing a higher level of precision than is evident, it has ways of saying so:

And he said to them, "I am a hundred and twenty years old today; I am no longer able to come and go, and the LORD has said to me, 'You shall not cross this Jordan.' --Deut. 31:2 (this verse is probably the source of the Jewish tradition that a prophet always died on the anniversary of his life beginning)

And at the end of four hundred and thirty years, to the very day, all the hosts of the LORD went out from the land of Egypt. --Exodus 12:41

And the number of days that David dwelt in the country of the Philistines was a year of days, and four months.  --1 Samuel 27:7

And there came out from the camp of the Philistines a champion named Goliath of Gath, whose height was six cubits and a span. --1 Samuel 17:4

Aha. This is actually the only time anyone in the Bible was given a height in partial cubits.  Really??? It may seem incredible to not be any more precise than the nearest 20 inches when giving someone's height, but consider:

Which of you by taking thought can add one cubit unto his stature? --Matthew 6:27

How think ye? if a man have an hundred sheep, and one of them be gone astray, doth he not leave the ninety and nine, and goeth into the mountains, and seeketh that which is gone astray?--Matthew 18:12

Perhaps the British can serve us an an example. Before succumbing to the metric system, they typically weighed things in stone rather than pounds (pounds being reserved for referring to their specie). Now, the nominal weight of a stone is fourteen pounds. Obviously saying that a newborn baby weighed one stone would be meaningless unless the number were in fact precise to the pound; in that case one would have to say something like "the baby weighed an entire stone!" But for purposes of giving the weight of an adult a stone was not exactly fourteen pounds; it only represented an approximate range. So an eighteen-stone man was one of considerable size or girth--about 250 pounds.

Since height was typically measured in cubits, one would go from being three to four cubits tall as soon as he crossed that threshold--adding, in nominal terms, one cubit to his stature.

So, back to Goliath. For some reason his height is given more precisely than any other person in the Bible (although the Ark of the Covenant was also measured down to the half cubit). By the way, Ishbi-Benob is actually the only other person in the Bible whose height is given (five cubits, which may then have been in the same range as Goliath's), but Christian History tells us that the Apostle Paul was only three cubits tall. Many are the commentators who leap to the conclusion that Paul was therefore 4' 6", but they are committing the fallacy of overprecision. Not only is their cubit itself too precise, they aren't even rounding to the nearest cubit. Since 3½ cubits is the normal height for a person, all we can say for sure is that Paul was about 10 inches shorter than normal, give or take several inches. He could well have been five foot even.

So for Goliath, we have a more precise measurement for his height: to the nearest five or so inches. Since other giants of antiquity are listed at seven cubits, even his 6½ cubits kept him out of the record books. Were he two cubits less than that, however, the half a cubit by which he was shorter than Ishbi-Benob would definitely put him in the junior league of giants. Only if he were a particularly short giant would it make sense to add that extra half cubit--even as a 4½ year old is careful to add that extra half year, it representing as it does a whole eighth of his lifespan. This would also make more sense, given that King Saul, as a tall short man, must have been pretty close in height to Goliath, a short tall man. Yet even though he had his own suit of armor and a sword, he was willing--the coward--to send a shepherd boy, who had neither, up against Goliath.  It would also make sense that David could find Goliath's sword, although obviously bigger than normal, to be of some use to him; perhaps it was more like a dagger to Goliath.  When David said "There is none like it" he could well have been referring to its patented forging, rather than its unique size.

One last note: An Egyptian text gives an interesting height to the giants of Canaan:

"The face of the pass is dangerous with Shasu, hidden under the bushes. Some of them are 4 or 5 cubits, nose to foot, with wild faces."

Note that "four cubits and a span" falls right in the middle of that range. And that "six cubits and a span" puts Goliath way out of it.

The New Math: The NIV and Sarah's Three Measures of Flour

"And Abraham hastened into the tent unto Sarah, and said, Make ready quickly three measures of fine meal, knead it, and make cakes upon the hearth."                   --Genesis 18:6 KJV

Okay, so the inquiring reader may want to know just how much is "three measures." How about turning to that bastion of contemporary scholarship, the 1978 NIV?

So Abraham hurried into the tent to Sarah. "Quick," he said, "get three seahs[a] of fine flour and knead it and bake some bread."
 [a] That is, probably about 20 quarts (about 22 litres)           --NIV78

Dear me. Like the ill-fated Mars Mission of 1999, which overshot its goal, the CBT suffered from an inability to correctly convert to metric. Twenty quarts is in fact less than 19 litres. Kind of embarrassing for something billed as "The First Truly International English Version." Ah well, this one certainly didn't get past the revision of 1984, surely.

So Abraham hurried into the tent to Sarah. "Quick," he said, "get three seahs[a] of fine flour and knead it and bake some bread."
[a] That is, probably about 20 quarts (about 22 litres)              --NIV84

Dear, dear me. The CBT's scholarship isn't looking so scholarly here, is it.  Well, the TNIV was the epitome of scholarly scholarship, correcting all the gross outdated language of that childish project, the NIV. It reads:

So Abraham hurried into the tent to Sarah. "Quick," he said, "get three seahs[a] of the finest flour and knead it and bake some bread."
[a] That is, probably about 36 pounds or about 16 kilograms  --TNIV04

Oh. A measure, then, is now twelve pounds, rather than thirteen and a third cups (the way modern people actually measure flour). So we have now moved from ill-fated scholarship to pedantry. Are we really expected to believe that Sarah used up most of a 50-pound bag of flour just to slap together a meal for her husband and his three visitors? Come on! If they aren't even sure of the amount, why guess such a large number?

Well, the TNIV was a source of embarrassment alright, but its faults, thank heaven, have now been rectified once and for all in the NNIV of 2011. Right?

So Abraham hurried into the tent to Sarah. “Quick,” he said, “get three seahs[a] of the finest flour and knead it and bake some bread.”
[a] That is, probably about 36 pounds or about 16 kilograms --NIV2011

EDITED ON MARCH 27-28, 2012
Okay, so the CBT don't turn out to be quite so stupid after all, but scholarly. VERY scholarly. What they were using here were DRY quarts. A 'dry quart' is one thirty-second of a bushel, or 67.2 cubic inches. In other words, more than a litre, rather than less. Cripe! Someone reading the NIV because the KJV was too hard to understand is not going to know that flour is OF COURSE always measured in 'dry' rather than 'liquid' quarts. Especially since anyone who ever measures out four cups of flour for a recipe uses a 'liquid' cup measure to do so. Furthermore, anyone turning to the more detailed notes under the "Table of Weights and Measures" in the back of the 1985 NIV Study Bible will be told that a dry quart and a liquid quart are, respectively, LESS and MORE than a litre.

If late 20th-century recipe books that actually called for a quart of flour didn't use dry quarts, and if the NIV editors couldn't even keep straight which was which, why ever would the New International Version use them?

END EDITS.

On a related note, there is one other place in the Scriptures where "three measures" is mentioned:

Another parable spake he unto them; The kingdom of heaven is like unto leaven, which a woman took, and hid in three measures of meal, till the whole was leavened.                          --Matthew 13:33 KJV

Well, we already know what "3 measures" were in 1978 over in Genesis. What were they in 1973 in Matthew?

He told them still another parable: “The kingdom of heaven is like yeast that a woman took and mixed into a large amount[a] of flour until it worked all through the dough.” [a] Greek three satas (about a bushel)

Okay, I guess this is another measurement entirely; a bushel is 37 quarts [32 DRY quarts--ed.] or 35 litres. But where's the metric? Oh, it must not have come along until 1978:

He told them still another parable: “The kingdom of heaven is like yeast that a woman took and mixed into a large amount[a] of flour until it worked all through the dough.” [a] Greek three satas (probably about 1/2 bushel or 22 litres)                                              ---NIV78,84

Good Grief! We've cut our bushel in half! Not quite in half, though, as 22 litres is  62 per cent of 35. More like two-thirds of a bushel, but who's keeping track?  Sigh. Let's see what improvements came along in 2001:

He told them still another parable: “The kingdom of heaven is like yeast that a woman took and mixed into about sixty pounds[a] of flour until it worked all through the dough.” [a]Or about 27 kilograms --TNIV, NNIV

Okay, so now everything is in weight rather than volume (did the CBT really commission somebody to go weigh a litre of hand-ground flour for this project?), with a litre of flour weighing 1227 grams.

Back to Genesis:
16 kilograms = 22 litres. That's 1375 grams per litre, pretty close when you're rounding off. But since when did half a bushel, or even 62% of a bushel of flour, weigh sixty pounds? By my calculations a whole bushel of flour (as if anyone ever measures it in bushels) should come up to only about 25 kg or 55 pounds.  Oh, I know. It all depends on whether Sarah measured it before sifting, or after! Maybe she measured it all in heaping teaspoons, and added some "for good measure."

Actually, all this misses the point of converting significant figures. Trying to specify, down to the litre or pound, how much flour was involved is taking literal translation to its extreme--something proponents of the NIV said we should never, ever try at home. The point is that Sarah prepared a huge amount of bread for Abraham's guests, and that it's possible to leaven a huge amount of flour just by putting a little active yeast in it to grow. But by trying to prove how scholarly they were, the CBT ended up with dunce caps on their heads.

More information on this subject is available in a subsequent post.

UPDATE JULY 2014
In this post I pointed out that the NIV's translation of kikkaroth (KJV cakes) conveys the wrong image to today's young person. Going back over this post, I see the same thing--except here the Hebrew word is 'ugowt. That's a plural word, so it should convey more the image of a huge stack of pancakes than a few loaves of bread.
When an English speaker makes pancakes or tortillas, he would never say that he is "baking bread," yet that is how the NIV has conveyed Sarah's action to the English reader.

Three Levels of Numerical Precision in Published Report

Headline: "Libyan forces pound Misrata, 1,000 evacuated by sea"

Dateline: "BENGHAZI, Libya (Reuters) – A chartered ship evacuated nearly 1,000 foreign workers and wounded Libyans from Misrata on Monday"

Copy: "The Ionian Spirit steamed out of Misrata carrying 971 people, most of them weak and dehydrated migrants mainly from Ghana, the Philippines and Ukraine, heading for the rebel stronghold of Benghazi in eastern Libya."

Thus we see three accepted levels of precision, all in the space of a single article. We could go even further and count the exact number of souls on board, which would include all those in utero. Interestingly enough, this would probably be within the range already outlined; a different number from the third listed, equally precise, yet both perfectly accurate.

This is something to keep in mind when dissecting the Four Gospels.

Cracking the Google Bar Code

It's been more than 20 years since I sat down one day with a pile of envelopes and cracked the Zone Improvement Plan bar code. Excited, I then turned my hand to cracking the Universal Product Code, but soon gave up in frustration. The series of thick and thin bars seemed to carry no information corresponding to the digits beneath them.

Well, today on the 57th anniversary of the official recognition of the bar code, I finally did it. The key turned out to be that the thick and thin spaces between the bars also carry information, and, even more importantly, there are extraneous digits at the beginning, middle, and end of the code. Furthermore, there are always an odd number of digits (in order to begin and end the series with a bar rather than a space), so in the last half of the code the numerals begin with a space rather than a bar.

This all came about because today the GOOGLE logo is a bar code. I haven't been able to crack it yet, but I've gone to all the work of teasing out the digits. I don't know yet whether they are base-2 or base-4 binary, but nothing I've tried so far has worked. I welcome suggestions!

Here are the digits:

2112142113131341111341111221142211141122141221142331112

There are 55 digits, which to me probably signifies that 211 and 112 are the beginning and ending markers (which is more ZIP code than UPC code), and that the central digit, 1, marks the middle. That leaves 12 numerals of 4 digits each. They can't be read as UPC code numerals, which always consist of 4-digit sequences that add up to seven. How that is supposed to spell Google, I don't know. Maybe instead it's a date: 10-07-1952/2009.

Or, the end markers could just be the digit 2 and there are 13 numerals. Please help!

Added on October 8th:
Well, I was on the right track. The end marker '2' is only there to allow the code to end in a bar; barcodes for that reason always have to have an extra digit as long as the characters contain an even number of digits. This particular code is rather consistent, in that all other characters contain six digits. So I was a bit short on the end-markers; the symmetry of their outside digits was only coincidental.

But the extraneous 'g' truly is a mystery. In the science of textual criticism, this would be referred to as dittography, but of a rather unusual kind.

The entire barcode translates as follows:
-begin sequence-Googleg-end sequence-.

I don't see that it would have been all that hard to decode only 49 characters instead of 55, especially given that the key was freely available online. And the notion of a checksum doesn't seem to fit, as it is only used with numeric codes like UPC.

I'll check back in if anyone can solve the mystery. And yes, a malicious website in China (forexbids.cn) has hacked into many of the sites discussing this mystery!