Now that's quite an irrational essay (and not irrational in the same mathematical sense that pi is irrational). First the author suggests that this understanding is something that the "Lord" revealed to him.
A claim that an understanding was a "revelation from the Lord" doesn't make this understanding necessarily irrational. An understanding should be taken by the validity of its content, not by what the author believes about it. I don't agree with the correlation you make between irrationality and claim of "divine revelation". Of course such a claim should be treated with skepticism but it doesn't follow that the essay is already judged as "irrational" because of it.
Of course we should be extra careful when people insist on having recieved special revelations from a superior "source," but on the other hand we should not be fall into temptation to poison the well when an argument that may turn to be valid is accompanied by such claims.
By the way, it could be said in favor of the author that he affirms: "In this case, the Lord ultimately brought to our attention some subtleties usually overlooked in the Hebrew Text." He doesn't seem to be making any special claim of being a special "reciever" of supernatural communications but seems to express himself in typical Evangelical style that attributes to "the Lord" all things good that they are favored with. It is a little like when an unbeliever says "thank God".
Then the ketiv/qere system of emendation is taken to be as a cypher for a hidden meaning without supplying any examples or evidence that this can be the case and not that it is an instance of what the system elsewhere always indicates, namely, the pronunciation of a word that is written differently than how it should be pronounced.
The khetiv/qere system is used for a specific purpose in Hebrew texts, but ancient Rabbinical traditions often assign "hidden meaning" to linguistic phenomena. Ketiv/qere can thus be taken as a "cypher" for this sytle of exegesis. So the scribe who recorded the variation in 1 Kings 7:23 may have not had the intention to encode this pi thing in the manuscript, but the style of interpretation that is assumed by the author is definitely not foreign to Jewish interpretive tradition.
Simply the fact that a qere is provided is apparently enough for the author to claim: "This appears to be a clue to treat the word as a mathematical formula".
The fact that a qere is provided may not be enough to establish a link with math formulas by itself, but there are traditions spanning millenia that do exactly that. That's how the minds of religious Jewish interpreters work. "What is the gematria of that word?" is one the first things that they think of when they find things like textual variations or strange and/or hard Scriptural sayings. So resorting to mathematical formulas is not a big hermeneutic jump, but a natural way of reading the text in these "conditions of pressure and temperature."
Then the author devises an arbitrary non-intuitive means of computing a value for the circumference that would agree with the value of pi (at least resolved to a handful of places).
It is not arbitrary in face of historical and traditional Jewish interpretation. It is the natural, intuitive, path to follow, in line with the spirit of countless works of Rabbinical exegesis (and, it seems to be unbeknownst even to the author that the link is so tight).
See, if a person trained in Jewish thought and tradition would come across this variation (qav and qaveh) when reading the text in question, he would probably think, among other things, in terms of the symbolic meaning of the letter that is added, in terms of gematria, in terms of typology, etc. If that person also had a little talent with math, the line of thought when reading the verse in question could follow like this:
"Well, this is a nice scriptural verse because it mentions that the molten sea in the temple had a circular shape. Jewish theology teaches that the temple is a blueprint of the cosmos, a microcosmos. And Scripture teaches that in Creation G'd "drew a circle on the surface of the deep." (Proverbs 8:27) It is all coherent.
But the verse also captures the interest because it implicitly mentions the Number Pi, the number of the circle! It is a rare appearance of a mathematical concept in a Scriptural context.
I know that in the real world pi is always used by approximation. In 1 Kings 7:23, it is 3, which is fairly good approximation to a religious text. I wonder if there's something more if I go deeper (as usual)...
When I compare the value in the verse to a better approximation of pi, I can measure the accuracy of the value of pi in the text. Thus:
3 / 3.141592654 = 0.954929658 → 95.4929658 % accuracy.
Now, I also see that there is a word in the verse - "(measuring) line" - that has two important features:
1. It is a word that encapsulates the meaning of the subject matter at hand (pi, circumference)
2. It is a word that has a textual variation (qav and qaveh).
This really sounds like a hint to something more. Well, first thing I should do is to check the numerical values of these words as I'm used to.
Qav = 106
Qaveh = 111
Hey, I begin to see something here. 106 is fairly close to 111. Is there any relationship between...?
106 / 111 = 0.954954954 → 95.4954954 % accuracy.
That's it!
3 / pi → 95.4929658 % accuracy.
106 / 111 → 95.4954954 % accuracy.
That's just too much. It is not everyday that you find such a precision in a pattern! 3 is to pi what one spelling of "line" is to the other (106 to 111)! How could that be? Maybe it just a big coincidence, but I know that "coincidence is not a kosher word". Well, this is either an amazing trick of a smart scribe or the hidden Hand of the Almighty leaving His Fingerprints into the text!"
So, this is just a summary of what could go on inside the mind of someone who is used to Rabbinical interpretation. It is not non-intuitive. It fits perfectly with their traditional approach to sacred texts of looking for patterns. It doesn't mean that we have to necessarily recieve it as divine. It means that this is not irrational. The accuracy is too high.
This is non-intuitive in part because if there was a problem with the rounded value of the circumference ("thirty cubits"), the obvious qere would have been for that number. Moreover, if one looks the verse up in the BHS, one would see that the qere is the shorter qav, not the longer qaveh. The qere is the revision, so why is the author revising the circumference upward from 30 cubits to something larger? It should be the opposite. He should be revising the value down from 30 to a shorter length, as the gematria of the qere should yield a shorter number than the ketiv. But that would ruin the amazing "discovery" that he seeks to find.
I totally understand what you mean. But that's not the way the Jewish-styled interpreter would approach the text. For him, the measure of the circumference doesn't need to be "revised". It is not a "problem" at all. He accepts the implied value of pi in the text as valid and acceptable in a theological document such as the Book of Kings. He is just looking for something "more" that reinforces the wisdom of the text, as he is used to do. Therefore the high level of accuracy obtained in the comparison between the values of pi and the values of "line" speaks louder to him than the fact that the "3 / pi → qere/khetiv" correlation goes to opposite directions. He reads it in a "poetical" kind of way, just like he wouldn't reject the validity of chiastic paralellism in Hebrew poetry in contrast to standard paralellism just because in the former case the parallelism is introvert.
The essence lies on the the fact that there are two different spellings of "circumference". This variation could be better presented if the author pointed to the phenomenon of parallel passages in sacred texts instead of strictly focusing on the "qere/khetiv" in 1 Kings. 2 Chronicles 4:2 records the same content of 1 Kings 7:23. It comprises a repetition of the molten sea's description, but it reads qav instead of qaveh! Just a little hey that makes all the difference! To a Jewish exegete, this is like a neon sign telling him to dig deeper. Maybe the path he would take to detect the pi pattern would be first to compare qav/qaveh (106/111) and then to move on to the examination of the value of pi in face of this variation, reversing the direction of the hypothetical line of thought that I offered above.
Rabbi Mattityahu Munk was probably the first to document this pattern in his work The Halachik Way for the Solution of Special Geometry Problems. In it he also offers another insight: the description of the circumference that begins in the letter qoph in qaveh ("a line of thirty cubits compassed it round about") has 22 letters, whereas the value of the diameter has 7 letters ("ten cubits"). And 22/7 is a very common approximation of pi! (22/7 = 3.142857) There's also a college paper by Shlomo Belaga examining this qav/qaveh variation: On The Rabbinical Exegesis of an Enhanced Biblical Value of Pi.
Now, the big thing concerning these approximations of pi expressed through fractions is that they aren't just any kind of approximations. They couldn't be any better.
What do I mean? Well, any real number can be expressed in terms of a continued fraction.
![Continued fraction expansion](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Continued fractions are a useful tool to give a series of "best" estimates for an irrational number. (Check out an online "continued fraction" calculator.) Each term of the sequence is called a convergent.
The following is the infinite continued fraction expansion of the Number Pi:
![Continued fraction expansion of Pi Continued fraction expansion of Pi](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
The first "best approximation" of pi is 3. The second is 3 + (1/7). The third is 3 + (1 / (7+1/15)) and so on. It gets closer and closer to the actual value of pi.
Now, as we turn back to our case, we find that the value of pi implicitly provided in the surface text of 1 Kings is 3, which coincides with the first convergent of the continued fraction expansion of pi. That is not striking in itself, but the second convergent also coincides with an estimate of pi derived from the text of 1 Kings! The second convergent is 3 + (1/7), which is the same as 22/7, the estimation of pi that we found by counting the number of letters in the descriptions of the circumference and the diameter! (Curiously, the text of 2 Chronicles 4:2 gives us 21 letters instead of 22 because of the missing hey and so the fraction 21/7 yields the first convergent of the pi series.)
It gets even "worse". The third convergent also coincides with the remaining estimation of pi derived from the text! The third convergent is 3 + (1 / (7+1/15)), which is the same as 3 x 111/106. 111 and 106 are the numerical values of the word "circumference" found in the parallel verses describing the molten sea. That's simply staggering. Words fail to describe it. All three approximations of pi that can be extracted from the text are exactly the same numbers in the fraction expansion of pi (which is a perennial set of data)!
And there's a unifying guiding principle in this correlation: the deeper we move into our Jewish-fashioned exegesis of the text, the better is our approximation of pi! The estimation of 3 is derived from the mere surface reading of the passage. The estimation of 3.142857... is found by the less simple method of letter count in the description of the measurements in the Hebrew text. Finally, the best estimation of pi (3,141509...) is obtained from numerical values of the letters of the word "circumference". Gematria is reputed by Jews as a deeper form of exegesis.
That cannot be categorized as any other thing than a "pattern", regardless of how it came to be.
As a last and least note, Jewish interpretation would also look for assigning meaning to the defining hey that makes all the difference. Hey has the value of 5, and the approximation of pi given by the qav/qaveh relation coincides with pi in fivesignificant digits (3,141509...) and even the digit sum of these numbers adds up to five (3+1+4+1+5 = 14 → 1+4 = 5). Moreover, the letter hey is considered by the Rabbis the Letter of Revelation (which in Hebrew is connected to the idea of roundness, rolling; galah), because the letter literally means "hey!", "behold!".