The Value of Pi, The Mysteries of Pi and e and the Bible.

by Chalam 55 Replies latest watchtower bible

  • Narkissos
    Narkissos

    Neo,

    I'm surprised that in such an elaborate post you didn't address my simple objection, namely that the same ketiv / qere' variation (qwh / qw)occurs in passages which have nothing to do with circles and circumferences (not surprisingly, since the term basically means "cord" or "measuring-line," as can be used for all kind of linear measures, straight, circular or other).

    More generally, I think that a rational approach of Jewish literature and exegesis (from Torah to Qabbalah) cannot dispense with a historical perspective. The writing and rewriting of the Biblical texts expanded over a relatively long period during which the Hebrew language naturally (i.e. culturally) evolved, allowing for a number of lexical and graphical variations to happen and get "caught" in the texts. The correction from 1 Kings 7:23 (K) to 2 Chronicles 4:2 clearly indicates the direction of this evolution -- btw, the writer(s) of Chronicles most likely didn't expect his(their) work to be compared with that of Samuel-Kings. The rewriting was meant to replace the older account. When (much later) both the canon and the text were considered fixed, it was "too late" to harmonise the texts through correction: then came the time for pointing the existing variants (between parallel texts as well as between archaic and later forms of the same Hebrew terms, as in the ketiv / qere' system). Even later came the time for interpreting those variants.

    Using late middle-ages Jewish gematria as a key to interpret the original meaning of Biblical texts shortcuts the 1,500 year historical process which produced, fixed, pointed the textual variations on which late rabbinical and qabbalistic interpretations developed. This is only possible from a transhistorical perspective (such as that which ascribes the integrality of the oral Torah to Moses) which makes critical and rational assessment impossible.

  • Chalam
    Chalam

    A claim that an understanding was a "revelation from the Lord" doesn't make this understanding necessarily irrational.

    I agree!

    What is the bible for to the believer? To reveal God to us.

    What does the Holy Spirit do for the believer? Reveal God to us.

    What does God do throughout the bible to mortal men? Give revelation.

    When I first started looking into the JW beliefs and the Holy Spirit told me to go an read John 1:1 in the NWT. Now that was a revelation!

    Of course, I later found that this is a key verse for JWs and non JWs alike.

    I am amazed that there are individuals that spend a lifetime reading and researching the bible but never actually believe what it says :(

    All the best,

    Stephen

  • Neo
    Neo

    Neo,

    I'm surprised that in such an elaborate post you didn't address my simple objection.

    Hi there Narkissos! I'm sorry that I didn't address your post. I don't want to avoid anything. I just concentrated on a larger post (Leolaia's). I'll address your objection in detail.

    ... namely that the same ketiv / qere' variation (qwh / qw)occurs in passages which have nothing to do with circles and circumferences (not surprisingly, since the term basically means "cord" or "measuring-line," as can be used for all kind of linear measures, straight, circular or other).

    I also copy your previous post for convenience:

    What about Jeremiah 31:39 and Zechariah 1:16, where the MT has exactly the same qere' / ketiv variant, qw / qwh?

    To these comments, I reply:

    First, and less importantly, please note that in my post above I showed time and again that I understand that qaveh/qav means "(measuring) line". I repeatedly rendered the word as "line" (though a couple of times I called it "circumference" for convenience). So it is clear to me that the word qaveh/qav does not mean circumference.

    Second (and also less importantly), your objection may arise from the insistence of the author of the original article quoted in the opening post on the association between qaveh and the word "circumference." Your objection most likely doesn't arise from this, but I'll comment it just in case.

    The author states: "The common word for circumference is qav. Here, however, the spelling of the word for circumference, qaveh, adds a heh (h)."

    By this he either meant one of two things:

    1. The Hebrew word qav/qaveh means circumference.
    2. The underlying Hebrew word rendered as "circumference" in his translation of 1 Kings differs from the usual spelling of that Hebrew word.

    In the first case he obviously would be wrong. But chances are that he was fully aware that this is not the literal meaning of qaveh, since his article was very short and to-the-point and thus he was probably not much worried to explain this distinction to the reader. And even if he believed that qav/qaveh means "circumference," it wouldn't constitute a fundamental mistake in his thesis anyway.

    That leads us to what I believe is the focus of your objection. Qaveh doesn't mean "circumference," so what about the other khetiv/qere occurrences of the same word? The answer is simple. There is no need for the other verses (Jeremiah 31:39 and Zechariah 1:16) to follow the exegesis of 1 Kings 7:23. In this examination, the word qav/qaveh has three distinct attributes that matter: spelling, denotation and connotation. In all three the denotation is the same (line, cord), the spelling is the same (qav/qaveh variation), but in 1 Kings the connotation differs from the other two. The "line" there is used as a tool to measure the circumference of a circular object, thus identifying in that specific context the object called "line" with the concept of circumference (since a measuring line assumes the shape of the object that is measured). The connotative value of "line" in 1 Kings is not carried over to the other verses just because the same word is used.

    The interpretation related to pi in 1 Kings 7:23 that is unfolded by the spelling variation can only be applied to that limited context. Each case obviously should be examined on its own merit. Your question is incorrectly blending the contextual significance of qaveh in 1 Kings 7:23 with its ontological meaning.

    Please let me know if that clears up this particular issue before we move on to the other points.

  • Narkissos
    Narkissos

    Hi Neo,

    Thanks for your reply. I didn't (and still don't) mean to engage in a lengthy discussion about this actually. But as you seem to misconstrue the implicit argument underlying my first post on this thread I probably ought to make it clearer.

    In briefly pointing to the other instances of the same spelling variation in the MT, I didn't mean to suggest that the "special exegesis" of qw(h) in 1 Kings 7:23 could or should apply to them. I meant to question whether any "special exegesis" is called for anywhere in the first place.

    In the OP -- as well as yours -- the variant spelling is taken first as a clue that some "special exegesis" is in order, then as the key to the "special exegesis" to be applied. Now whether it is unique or not certainly has a bearing on whether the whole reasoning is warranted or not. It definitely has in common semantics which depends on corpus usage: words mean what they use to mean unless a clear contextual indication calls for an unusual meaning substituting to or combining with the usual one (allusion, pun, double entendre, etc.). If a text makes sufficient sense without any extraordinary meaning it is highly likely that the alleged extraordinary meaning was not meant in the first place (still one of the best applications of Occam's razor). Otherwise you are positing an "author" writing so as to be misunderstood except by the chosen few -- a hypothesis which indeed cannot be proven wrong because it is logically unfalsifiable: you have cornered yourself out of rational discussion.

    Actually the necessity for some "special exegesis" doesn't arise from the text, which makes perfect sense as a non-specialist approximation. It arises from the confrontation of the text with a new readership which has learned the basics of theoretical geometry in grade school.

    (Btw, even semi-rational thinking distinguishes between the rule and the exception, as well as between frequent, rare or unique exceptions: it's no chance if four-leaf, not three-leaf clover is taken as a "sign" of something.)

    So I think it is very disingenuous on the part of the semi-rationalist apologist not to point to the other instances where the same phenomenon occurs, getting the reader to believe that it is unique and henceforth more likely to be taken as a clue and then as a key to "special exegesis".

  • Neo
    Neo

    Hey there, Narkissos! I'm sorry for the delay, time has been short.

    Now I hear your argument! Thanks for being much clearer. You are of course correct in showing that, if it is claimed that the variation is unique or that "it must mean something," the honest and correct path for the apologist to take is to show how often the same phenomenon occurs elsewhere. I share the sentiment of your comments. Note that I'm taking a different approach from the one we find in the OP, as I conveyed in my first post. It is highly unlikely that scribes envolved in the composition of 1 Kings 7:23 (or even 2 Chronicles 4:2) had this "pi pattern" in mind when they penned the text, since it involves forms of interpretation that reached a developed state only long after the composition period. What I was showing was what kind of approach an interpreter of the text could take, in particular the one who follows the historical and traditional age-old Jewish fashion of interpretation. It could be anyone living, say, in the 17th, 19th or 21st century, for the matter.

    The OP's quoted article seems to lead us to think that, since there is a qere/khetiv variation, it should be taken as a clue that will lead us to find the pi pattern. It also seems to suggest that this was encoded by either the original author(s) or, most likely, the scribes that copied the earliest manuscripts. Moreover, the article appears to be an apologetic effort to "explain" this apparent "wrong value" of pi in the Bible.

    I do none of that. The implied value of pi in the text doesn't need to be defended. It is just an estimation that suffices for the context of a religious work. The text doesn't demand anything else for the reader to aprehend its content and meaning. It is fully satisfying as it stands.The occurrence of the qere/khetiv phenomenon in 1 Kings 7:23 doesn't mean that a "special exegesis" is in order.

    I'm showing the path the Jewish intepreter takes if he is looking for "something more". The passage gives him much more than he could ever hope for! Those who are familiar with Jewish mystical exegesis know the Jews believe the biblical text has different "levels" of interpretation. The pious Jewish student of Scripture believes that, if he digs deeper into the text, he will be generously rewarded with gems of wisdom lying beneath the surface. So when he approaches 1 Kings 7:23 (or actually any other passage of their sacred writings), he knows that the description of the molten sea means what it says. But he believes that if God was the author of Scripture, he might as well have encoded additional layers of meaning in the passage.

    Therefore his trained mind will look for understandings that go beyond the plainest meaning of the text. The question is: will he find anything in 1 Kings 7:23? The question is even more significant because, in a sense, that verse is not an ordinary one. Jewish interpretation places great emphasis on the symbolic significance of numbers and geometry. Number symbolism suffuses Jewish mystical thought. And 1 Kings 7:23 just happens to be a very rare passage in the Jewish Bible (the only one I can think of at the top of my head) that deals with geometric and engineering calculations, because of the implied value of pi. It naturally lends itself to being interpreted beyond its surface meaning. It is not just another "average verse". The bets are high. Will he find anything meaningful there?

    It is only in this context that the spelling of qaveh appears as a clue-key. If he is searching the verse for a hint that will lead him to a deeper insight, the spelling of qaveh will no doubt quickly catch his trained eye (either by means of the qere/khetiv occurrence or the variation in the 2 Chronicles parallel passage). And that's where he would find the beauty of it: the spelling variation is a rather ordinary, non-unique phenomenon. To him it would follow precisely as his belief claims: God reveals himself in small things like in the letters of the sacred writings.

    One of the traditional practices in Rabbinical Judaism is counting the number of letters in a given text. If he follows the clue given by qaveh and, beginning with this word, counts the number of letters that form a self-contained sentence describing the circumference of the molten sea ("a line of thirty cubits did compass it round about"), he will find 22 letters. Twenty-two letters describing a circumference -- that wil pick his curiosity, suggesting that he is on the right track, because for him the mere mention of a set of "22 letters" evokes the Hebrew alphabet, which has exactly 22 letters. And a very ancient Jewish tradition states that God used the 22 letters to shape the cosmos, saying that he "placed them in a circle." (Sepher Yetzirah 2:4)

    In this tradition, the letters are the agents that delimit the shape of the world that was a primeval chaos before creation, according to Genesis. (Compare Sepher Yetzirah 1:11) The waters of the deep are thus delimited by God's creative word, integrating with the declaration that "he set a circle upon the face of the deep" (Proverbs 8:27,29), which in turn is imaged by the molten sea in the temple (reputed by Jewish thought as a typological representation of the cosmos). This a-circle-and-22-letters motif thus results in a very tight, unexpected and impressive integration between Jewish mysticism and 1 Kings 7:23.

    And so it goes as I explained in detail in my first post: the alternate spelling of qaveh omits the "revealing" letter hey and that reduces the letter count from 22 to 21. The 22/21 ratio thus adjusts the estimation of pi to a better value. Similarly, using a "deeper" practice of Jewish interpretation - gematria - gives us two values for the qv(h) word - 111 and 106. And the ratio 111/106 adjusts the estimation of pi to an even better value.

    Three estimations of pi:
    3
    3 * (22/21) = 3.142857...
    3 * (111/106) = 3.14150943396226...

    It is very important to draw attention to the significance of this. One could say that "numbers can mean anything," to excuse himself to think a little about the significance of the pattern. A person can "search for patterns" in a given text and may even find something "meaningful" like a "pi pattern" if he looks hard enough. But that is definetely not what is going on in this passage. There are countless "approximations of pi," but the three approximations of pi above (3, 3.142857... and 3.14150943396226...) are EXACTLY the first three elements in the sequence of convergents of pi (which is by definition a sequence of better and better approximations)! This mathematical sequence (like the prime number sequence or the repdigit sequence, for instance) is a fixed set of data. The approximations just couldn't be any more significant.

    And there's no force-fitting whatsoever: the student is limited to resorting to standard historical Jewish interpretational practices - textual variation, letter count and gematria -, doing so with much grace and simplicity. And more: it possesses internal harmony: the "deeper" the style of exegesis gets (plain text reading → letter count → gematria), the better the approximation is, all the while integrating grade-school geometry with Jewish theology and cosmogony. There is pattern and coherence in what was supposed to be a sea of chaos. That's a top-level phenomenon and it is impossible to remain indifferent to the pattern once you see it. It is mind-boggling.

    What do you think?

  • Narkissos
    Narkissos

    Thanks for your reply Neo. It does clear up a few ambiguities as to the historical dimension of the problem: above all, that the interpretive method involved at the very least cannot be shown to be -- and probably is not, as far as probability goes -- contemporary to the writing of the texts.

    From a rational perspective this is more than sufficient to "debunk" the apologetic agenda underlying the "demonstration" -- that such a pattern can be read in(to) the text using late medieval to modern Jewish methodology is, in principle, utterly irrelevant to the ancient history of mathematics.

    Btw there is no small irony in seeing fundamentalist Christian apologists resorting to Jewish methodology when they think they can, when you consider that both interpretive systems -- early Christian-Orthodox-Catholic-Protestant and Pharisaic-Rabbinical-Qabbalistic -- have developed against one another as much as independently. It seems like Christianity is fond of revisiting its so-called "Jewish origins" from time to time to see what is left, or more exactly what has grown since last visit, to plunder. First Christianity built itself mostly with the Jewish Hellenistic tradition (especially the Septuagint). Then in Jerome's time it claimed the hebraica veritas and the proto-Masoretic Hebrew text. Then the MT in late middle-ages, Renaissance humanism and Reformation. Why should that stop?

    I suppose the force of the (de-)monstration (monstratio, "showing") depends on your mindset; if you cringe from the notions of "chance" or "coincidence," if your desire for potentially meaningful patterns outweighs the sense of arbitrariness, if you have constructed your "sacred text" as a magical labyrinth where anything is possible -- except "chance" and "coincidence" precisely -- then I understand it can look quite impressive.

    Side thought: in Western, Christian and post-Christian culture the meaning of Latin inventio has developed from "finding" to "invention". I find (!) it to be symptomatic. The emphasis has shifted from unveiling what is (and was prior to the unveiling) to creating what was not. And the more artificial our life the less we trust artifice to make meaning. As much as we embrace meaninglessness there is a hidden nostalgy for truth as "original" and "unfabricated" which paradoxically fuels modern criticism of any truth as secondary and fabricated. This may be our curse but it is ours (mine, at least).

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