[b-hebrew] Ktiva & Kria

belaga at math.u-strasbg.fr belaga at math.u-strasbg.fr
Fri Nov 2 13:54:12 EDT 2007

> Edward:
> Interesting article. I have two questions:


> Seeing as this deals with a rabbinical practice, what relevance does
> it have to practice near the beginning of royal succession (second
> generation)?


> While the 10 cubit measurement referred to an external measurement of
> the vat, did the circle of 30 cubits refer to an external measurement,
> or to an internal one (external minus the thickness of the metal)? If
> to an internal one, how close would it be to pi?


> I had never heard before that this was only an approximation for legal
> purposes, but it makes sense as a way to explain the Biblical data.
> Karl W. Randolph.

Dear Karl,

Thank you for you kind appreciation.

Before trying to answer your query (which I have divided above into  
three distinct questions, A-C), let me tell you about the reliability  
(one of your requirements during the recent Academic debate) of what I  
am presenting in the article:

(1) On the negative side, there is no proof that the discrepancy  
"Ktiva versus Ktiva" in question has been intended for the purpose  
stated in my article.

(2) Also on the negative side, there is no proof that the  
interpretation of the discrepancy presented in my article is of  
ancient origins.

(3) On the positive side, there is no doubt that King's architects and  
engineers knew the number Pi with a good precision: in the case of the  
King's Shlomo sea (or vat), the difference in the circumference would  
be about one meter;

(4) Also, the excellent precision of the proposed value (this was an  
original mathematical analysis of mine - Ein Chacham Ke'Baal  
HaNissayon, No one is as wise as he who has experience) contributes  
positively to, but still does not prove, the idea that this  
approximation was intentionally coded by the discrepancy "Ktiva versus  
Ktiva"; this was the reason that the mathematical community at large  
took it rather seriously.

(5) Besides, methodologically, the situation fits perfectly into the  
multi-layer semantic structure of the Hebrew Bible; as in the PaRDeS  
rabbinical scheme, Pshat->Remez->Drash->Sod (Plain meaning -> Hint->  
Interpretation -> Mystery), here, too, we have a simple,  
straightforward opinion about the value of Pi, for everybody man (it  
is used, for example, in Mishnah, in the Massehet Shabbat), and we  
have then a scholarly opinion.

(6) According to this scheme, there is a high probability that more  
advanced opinions existed - in my article, I am quoting Rambam on the  
subject, who almost thousand years ago informally introduced the idea  
of an irrational if not transcendental number - discovered at the end  
of the 19th century ! In other words, methodologically, I did learn  
from this paradigm: Ezehu Chacham ? Ha-lomed mi-kol adam - Who are  
wise? Those who learn from all people [human beings].

Now your questions:

(A) Relevance. Anybody acquainted with the Mishnaic and Talmudic  
traditions knows that all rabbinical comments were driven by a very  
few basic motivations. One of the most nobles of them was the search  
for rational explanations (the aspect very clearly presented in our  
Academic Debate by Yitzhak Sapir), for precision and, as we would call  
it today, for scientific integrity - just for the sake of it.

(B) This question is seriously debated in some other papers on the  
MATHEMATICAL discrepancy presented above (3).

(C) Cf. my (5) above.

Thank you for the careful reading and good questions.

Edward G. Belaga
Institut de Recherche en Mathématique Avancée
Universite Louis Pasteur
7, rue René Descartes, 67084 Strasbourg Cedex, FRANCE
tel.: 333 90 24 02 35, FAX: 333 90 24 03 28
e-mail : edward.belaga at math.u-strasbg.fr

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