Volume 18 Number 43 Produced: Mon Feb 13 22:50:43 1995 Subjects Discussed In This Issue: Archeology and Shiurim [Stan Tenen] Meru - MNZPK [Stan Tenen] Uses of Mathematics [Stan Tenen] ---------------------------------------------------------------------- From: Stan Tenen <meru1@...> Date: Mon, 13 Feb 1995 09:44:40 -0800 Subject: Archeology and Shiurim Does anyone know what natural angular measures where in use in the time of Moshe? We know that the "Babylonian" 360-degree division of the circle was known in even earlier Sumer (so Abraham would have known of it) and likely throughout the patriarchal through First Temple periods, but I am looking for a purely Torah based measure of angles. It is interesting to note that there are 13-lunar months of approximately 28-days in a 364-day year. (The 13-months form a "13-Petaled Rose".) 364 (or 365) being very close to 360 means that a 27-day (star) or 28-day (earth) month would occupy about 28 or 29-degrees of arc on the yearly solar cycle circle. Our natural unit of angular measure is the radian. One radian is approximately 57-degrees - about twice the extent of the monthly 28-day lunar arc on the 360/364/365-day solar cycle. In other words, it appears that while our current natural measure is one-radian, the ancient natural measure may have been approximately 1/2-radian. Either choice is also supported by the ease of marking a circle in 60-degree or 30-degree sections with a compass. But this is speculation. Does anyone know? The reason that this is important is that it appears that the exact shape of the idealized hand - Tefillin strap that generates the Hebrew letters is in part determined by whatever the natural angular measure was. I have been trying to decide between 1-radian, which is natural to us, and 1/2-radian, based on the reasoning outlined above. Thanks, B'Shalom, Stan ---------------------------------------------------------------------- From: Stan Tenen <meru1@...> Date: Wed, 8 Feb 1995 21:50:40 -0800 Subject: Meru - MNZPK For the past several years while Rabbi Fleer has been visiting with us, he has proposed various challenges in an effort to test and evaluate the Meru conjectures. One consisted of requesting an explanation for why the final letters are often listed in "M'Nun-Z'PaK" order (Finals: Mem, Nun, Zadi, Fe, Kaf) instead of in the standard alphabetical/gematria order (Finals: Kaf, Mem, Nun, Fe, Zadi). We now have an explanation for this special order. The final letters are said to refer to redemption, so I have always searched for some way in which the final letters could complete or return the other letters in some way. As it turns out, when the letters of the full 27-letter alphabet, with the finals, in standard alphabet/gematria order at the end, are written out on the umbilic toroid form we found in B'Reshit, the final letters form the final tip of the last turn. Interpreted geometrically, this places the final letters around the "ovaries" of the idealized fruit (the Continuous Creation model) formed by the letters of B'Reshit. (The exact same umbilic toroid simultaneously displays the AT-BaSh symmetry of the 22-letter alphabet AND the Base-3 or ternary symmetry of the full 27-letter alphabet. I believe that this construction is unique - except for topological equivalents, there is likely no other way to show the symmetry of the 22 and the 27 letter alphabets on the same form simultaneously and without ambiguity.) Now all of the models we have found in B'Reshit are models of self-organization based on an idealized embryonic growth cycle - as modeled by our idealized fruit or Continuous Creation topology. And our theory also applies explicit operational meanings (that closely parallel the traditional meanings of each letter's name) to each letter. We can read these meanings off of our previously developed table of meanings. When we combine these two sets of findings, the unusual order for the final letters makes sense. The embryonic model suggests the following stages of growth in this order: 1. Seed (in ovaries at center of the idealized fruit) 2. Stem (or sprout emerging from the seed) 3. Maximal growth of leaves & branches at the highest part of the tree 4. Opening of the tree to heaven, opening of all leaves, opening of buds 5. Holding the fullness of the new fruit The final letters in their special order are: 1. Mem Womb and Ovaries, thus geometrically at the center. 2. Nun Connection, prince, thus a "stem" erupting from the center 3. Zadi "Righteous", Upright, Tree, thus the maximum height of the "fruit tree yielding fruit whose seed is inside itself." 4. Fe "Mouth", thus puffing, filling and opening up, at the maximum fullness of the new fruit 5. Kaf Holding the whole fruit in the palm of our hand Now, to those who are not familiar with the topology and the geometry, the above may make little sense or it may seem arbitrary or forced. When you compare the each of the letter's meanings directly with the geometry of the Continuous Creation / Idealized fruit model, you can not only see how the descriptions apply but, even more surprisingly you can see the outline of each of the modern final letters arrayed on the Continuous Creation / Idealized fruit model. There is some confirmation of this in the traditional gematria equivalents. MNZPK = 280 = 10 = 1. The 10 may refer to the 3,10 torus knot and/or to the 10 s'pherot that make up the model. The 1 refers to the Unity of HaShem alluded to by the unity and coherence of the model. Traditional references to the Continuous Creation / idealized fruit model compare it to a "bull" and to a "fruit". A "bull" is Pe-Resh, and a "fruit" is Pe-Resh-Yod. The gematria of Pe-Resh is also 280 - as was pointed out to me by Rabbi Fleer - so the comparison with MNZPK makes sense. Anyone who would like to see my sketches of this, should ask and send us your postal address. B'Shalom, Stan ---------------------------------------------------------------------- From: Stan Tenen <meru1@...> Date: Mon, 13 Feb 1995 09:43:47 -0800 Subject: Uses of Mathematics A recent technically trained poster pointed out that those who cannot follow the mathematical discussions should know that he cannot follow them either. This is to be expected. I cannot speak for the statisticians, but with regard to my work I have tried to make it clear that unless you see the illustrations and drawings that go with the discussion it is generally not possible to understand what I am describing. It is thus a bit disingenuous to complain about a lack of understanding when that was explicitly stated as likely. This is not entirely due to my limitations. One of the most important reasons why the materials I have been presenting have been lost to us is that we have not retained any images or models. This was likely because they might have become the objects of idolatry, so it is understandable that we do not have surviving models, but it does limit understanding. Now that formal computer languages are so common, it is easier to understad that not everything of importance in our reality can be communicated with phonetic words alone. (Over reliance on the efficacy of words alone to convey information can become, in this mathematician's opinion, a form of hubris.) I have previously posted an evaluation of my work by Rabbi Gedaliah Fleer, a recognized expert in kabbalah. Here is an eminent mathematician's evaluation of this work: COMMENTS ON THE MERU PROJECT by LOUIS H. KAUFFMAN, PROFESSOR OF MATHEMATICS University of Illinois at Chicago, 2 April 1991 The Meru Project (initiated by Stan Tenen) proposes to study the text of Genesis, as written in Hebrew, through the hypothesis that this text is an integral whole whose structure and meaning can be understood at all levels of its projection. One usually reads a text at the level of the sentences and paragraphs, in a context of message or story. Even when pursuing this approach, the form of the text (lettering, arrangement, illustration, or physical form of the work itself (scroll, bound book, illuminated manuscript...)) is an integral component of the meaning that is transmtted. In the case of the text of Genesis, the Hebrew language has deep roots, so deep that an analysis even at the level of the letters and form of the letters may be required. The Hebrew letters are also symbols for numbers, and so this language and its alphabet are particularly intertwined with the numerical, mathematical, algorithmic basis of language and thought. It is the intent of the Meru project to take the text of Genesis, and to subject it to a search for structures that indicate the nature of mechanisms of production. A religious tradition (Kabalah) has engaged this kind of study with the intent of understanding/experiencing creation itself. Meru's admittedly more secular mode has the similar aim of coming into contact with the creativity of the text, and with structures/algorithms/patterns that illuminate relations between this study and mathematics and natural science. In the Meru viewpoint a remarkable combination of geometry/sign/symbol underlies the coherence (is the coherence) of the text of Genesis. Investigation of these patterns involves a combination of mathematics, graphics, history and linguistics. By far the most remarkable feature of Stan Tenen's work is his highly creative use of the geometry/topology of the third and higher dimensions. He has seen that the coherence of the text can be mapped by lifting fragmented lower dimensional structures into higher dimensional counterparts that project the lower structures. Alphabets on tetrahelixes, letters as shadows of a hand-held flame, flat yantras as projections of networks of lines in space, creative process and recursion in the twisting pattern of the seven color map on the torus, pattern seeds unfurling into weaves and spirals and metaphors of relationship, the text itself wrapped and mapped in and out of these geometric structures. This unfurling is the creative center of the Meru Project and its greatest promise. In attempting to unfold the text of Genesis, Stan Tenen has created the beginnings of a wonderful geometric language - using real and deep mathematical structures. The language is a new alphabet, an alphbet of geometric forms that may solve the riddle of Genesis. The geometric alphabet is itself not only of great artistic and conceptual value, but I believe that it will be seen to hold a key for many other questions in language and science. This project brings together the old and fascinating questions about origins of language and the self with the rigorous traditions of modern geometric thinking and mathematical imagination. (signed) LOUIS H. KAUFFMAN Department of Mathematics, Statistics and Computer Science The University of Illinois at Chicago Box 4348 Chicago, IL 60680 Professor Kauffman is one of the foremost topologists and authorities on knot theory. Besides the above evaluation, Prof. Kauffman, as editor of the series, "Knots and Everything," has asked his publisher, World Scientific, to have me to write a book on the topology of the Hebrew alphabet for this series. Also at Prof. Kauffman's invitation I recently presented a paper on my findings to the Knot Workshop at the Univ. of Minn., Minneapolis, Geometry Research Center. (It was well received.) Besides Prof. Kauffman, Prof. Ralph Abraham, past chair and recently retired from the mathematics department at UC Santa Cruz, endorses this work, and Prof. Jay Kappraff, (Mathematics, NJIT) is currently drafting a chapter on my findings for his new book. This work has also been favorably evaluated by several well-known (and not so well-known) physicists and cosmologists (Sirag, Rauscher) and computer scientists (Moulton, Wolff). Anyone who is interested can check on our work by calling one of the several dozen respected professionals on Meru Foundation's board of advisors which is printed in our introductory booklet. My work is entirely independent of the "codes in Torah" work, yet it appears to offer an explanation for the codes that is consistent with Torah and with science. So, please, dear mail-jewish reader, take my findings as a serious work-in-progress with potentially important implications. I need the help of the Torah community to do this work and to make best use of the findings. I especially need the help of the very persons who are naturally the most skeptical and the most critical - mathematicians and scientists who care about Torah. I openly state my limitations not so that it will be easy for those who are not interested in these matters to put down this work or repeat my limitations back to me, but so everyone will know where my findings and opinions can be trusted and where they cannot be trusted. These are important findings for the Torah world. They have been examined by recognized Torah and secular experts. They are not easy to understand at first, but they are very easy to understand once you get it. They depend only on technology we know was available in Moshe's time - such as calendar-making and weaving (what we might over-impress ourselves by calling "knot theory"). Even really intelligent persons are not likely to understand this work without seeing the illustrations. These findings propose one explicit solution. No statistics are involved. These findings resolve many conflicts and ambiguities in Talmud and in Kabbalistic texts. These findings are testable and refutable; they are, according to others, good science and they are, according to others, consistent with and respectful of Torah Judaism - which they strongly support. I cannot do this work alone - both because I cannot read Hebrew or Aramaic well enough and because I do not have sufficient mastery of modern formal mathematical notation. B'Shalom, Stan ----------------------------------------------------------------------

End of Volume 18 Issue 43