Volume 19 Number 17 Produced: Wed Apr 5 22:54:41 1995 Subjects Discussed In This Issue: Codes [Mike Gerver] Uses of Mathematics ? [Sylvain Cappell] Vav DeGichon: A Flawed Numerology? [Mechy Frankel] ---------------------------------------------------------------------- From: <GERVER@...> (Mike Gerver) Date: Wed, 29 Mar 1995 3:38:04 -0500 (EST) Subject: Codes Harold Gans' use of the Heisenberg uncertainty principle, chaos theory, and Godel's incompleteness theorem to show that it is impossible to predict the future (and that the results reported by Witztum et al therefore show the divine origin of the Torah) reminds me of a story I heard from Prof. Binyamin Frankel of Hebrew University. Prof. Frankel's father was Prof. Avraham Frankel, a mathematician who made important contributions to set theory in the early part of this century (e.g. the Zermelo-Frankel axioms). When he was growing up, Binyamin Frankel would hear his father and colleagues arguing about _why_ one plus one is two. Binymain thought this was such a ridiculous question that he resolved not to go into pure mathematics, or any field close to it. He ended up going into experimental applied physics, and made a very successful career of it. Now I am not entirely sympathetic to Binymain Frankel's point of view in this story. Although I am an applied physicist myself, I enjoy reading popular articles on set theory, Godel's proof, chaos theory, foundations of quantum mechanics, etc. I don't consider the questions dealt with in these articles as ridiculous or insignificant. Indirectly, applied physics often depends on statistical mechanics, whose foundations depend on chaos theory, and applied physics always depends on arithmetic, which depends on set theory and the Zermelo-Frankel axioms. On the other hand, I think Binymain Frankel would justifiably think it peculiar if he were giving a talk on x-ray diagnostics for tokamaks and someone in the audience made a comment on it, using the Zermelo-Frankel axioms to prove a point. The results reported by Witztum et al in the Aug. 1994 issue of Statistical Science raise real questions about whether and how these results can be explained without invoking miracles and the divine origin of the Torah. These questions have about as much to do with Heisenberg, Godel, and chaos theory as set theory has to do with x-ray diagnostics. By bringing up Heisenberg, Godel, and chaos theory, Gans is distracting people from dealing seriously with the real issues. Having said this, I really ought to explain what I think the real issues are. I will do this briefly, but like Gans, I cannot go into any detail in the space available. (This is not just an excuse for being too lazy to write it up. I did try writing it up a couple of months ago, but couldn't get it into less than 23K. Evidently this was too long for mail-jewish, since it was never run.) I will be happy to provide more details, off-line, for anyone interested. The paper by Witztum et al actually has two separate surprising results. 1) The distribution of c(w,w') is far from uniform in the interval (0,1), being instead heavily skewed toward low values, when w is a name from the list of famous rabbis and w' is the yahrzeit date of that person. 2) The distribution is much less skewed when the lists of names and dates are randomly permuted. In order to explain these results without invoking miracles, we need a "natural" explanation for both (1) and (2). Several possibilities come to mind, and I plan to check them out and see if they work. Result (1) might be explained if there were long range order in the distribution of letters in the text of Breishit [Genesis]. For example, suppose that certain letters of the alphabet are more likely to occur in even positions in the text (letter #2, #4, #6, etc.) while other letters are more likely to occur in odd positions (letter #1, #3, #5,...). This will make certain words more likely to occur as unperturbed ELS's in the text (i.e. (x,y,z) = (0,0,0)) than as perturbed ELS's (with other values of x,y,z), while other words will be less likely to occur as unperturbed ELS's. If both the name w and the date w' are from the set of words that are more likely to occur as an unperturbed ELS, and if w and w' both span a significant fraction of the text of Breishit, then c(w,w') will tend to be closer to zero than to one. If w or w' is from the set of words that is less likely to occur as an unperturbed ELS, then it may not occur at all, and c(w,w') for his pair will be eliminated from the distribution. The resulting distribution of c(w,w') for all the names and dates would then be skewed toward low values, even if there is nothing special about the names and dates. The effect would go away if the words or the sentences were randomly scrambled, since this would destroy the long range order. I do not know if the text of Breishit has this kind of long range order, but I hope to find out. If it does, this would be an interesting fact, but it would not be evidence for the the divine origin of the text, since it would be quite possible for a human being to create such a text without the use of a computer. Result (2) seems at first to imply that the author of the text could predict the future, that the text "knows" which rabbis would die on which dates. A more reasonable way to look at it, though, is that the rabbis in the list were not dying on random dates, but were preferentially dying on certain dates, depending on their names. Actually, it is clear that the yahrzeit dates on the list are not randomly distributed. Memorable dates such as Rosh Chodesh, Yom Tov, Chol Hamoed, Chanukah, etc. make up about one third of the dates on the list, although they only make up about one sixth of the dates on the calendar. Most likely this is because memorable yahrzeit dates are more likely to be remembered, and because a yahrzeit date that is close to Rosh Chodesh, for example, may get changed to Rosh Chodesh if it is passed on as an oral tradition before being written down. This particular effect does not seem to depend on the person's name, but there may well be other effects that do. For example, I have found that of the 11 people on the list who are known as "Ba'al ha..." followed by the name of a sefer they wrote, 7 of them died in Shevat or Adar, while you would only expect this to be true of 2 of them. A possible non-supernatural explanation for this might be that people who devoted all of their energy to writing one major sefer would be more likely to neglect their health, or to neglect their parnassa [making a living] and not have enough money for food and fuel, and be more likely to die in the winter. I don't know whether patterns of this sort are enough to account for the results reported by Witztum et al, but I hope to find out. Again, I apologize for the terse explanations in the last two paragraphs, which are probably incomprehensible to anyone who has not spent a lot of time working on this problem. I will be happy to send a more lengthy explanation to anyone who wants it. I must add that I find some of Sylvain Cappell's comments on the codes (also in v18n95) unreasonable, although he may well be right about the sociology of codes enthusiasts. Surely it is not relevant what the reputation of "Statistical Science" is for publishing questionable papers, or how many emininent professors agree or disagree with the paper. The only things that are relevant are whether the results reported in the paper are correct, and whether there is a non-supernatural explanation for them. These questions can only be answered by verifying the results, and by thinking of possible explanations and testing them. The fact that the paper was published in a refereed journal is relevant only in that it makes the paper plausible enough that it is worthwhile to check it out, rather than to dismiss it as a crank paper or a fraud. Of course, investigating these things is no substitute for studying the content of the Torah. But the results reported by Witztum et al are so surprising, if true, that they cry out for an explanation, like any other surprising physical or mathematical phenomenon, and it is in that spirit that I am drawn to investigate them. Mike Gerver, <gerver@...> ---------------------------------------------------------------------- From: <cappell@...> (Sylvain Cappell) Date: Mon, 6 Mar 95 23:46:31 EST Subject: Uses of Mathematics ? Subsequent to my posting refering to the two new contending systems of mathematically reading texts, there have been many postings and I have also received curiously analogous emails from afficinados of both the "topological codes" and the "statistical codes." These generally argued that their own distinctive way of creating an innovative approach to religion and text is based on a valuable use of mathematics, while the other is devoid of scientific interest. While I had not disputed, analyzed or compared the contrasting claims of either of these systems of mathematical approaches to religious insight, I am afraid that I really am not yet able to see all the sharp contrasts between the "topolgical codes" and "statistical codes" that both groups seem to insist on. Indeed, enthusiasts for opposed escoteric systems are often prepared to explain how their particular novel methodology merits special consideration and is to be totally and absolutely distinguished from what they view as the other's pseudoscience, whose fallacies are all too apparent to them. Both systems, after all, while making some references to historical Rabbinic Judaism, do in fact share being based upon radically new departures in religious epistomolgy, in both cases based on mathematically inspired methodologies or languages which may, at least in principle, be applied or adapted to the texts of many religions. In both the "topolgical codes" and "statistical codes" groups I indeed have some good and deeply valued mathematical friends who may be involved, or more precisely, are perhaps just intruiged or attracted by the astonishing vast claims being asserted for the power or novelty of their respective speculative mathematically based approaches to religion and texts. Indeed, in the case of the "topological codes" ( which I have looked at further and which despite being a researcher in topology still can not personally understand anything of ) there has been interest expressed by a mathematical friend who is a recognized expert in topology. However, supporters of the "statistical codes" feel that in assessing scientifically the claims of the "topological codes" this is perhaps not really relevant, as in the final analysis, apparently it was not in any case argued that these notions of geometrically reading novel meanings into religious texts bear any direct relation to conventional topology as commonly practiced by mathematicians. The "statistical code" novelties, on the other hand, while it has intruiged several fine pure mathematical friends, has not apparently seriously interested any leader in statistical research, a subject deservedly famous for having all too often trapped even distinguished nonspecialist scientists, and the only very distinguished and disinterested academic researcher on statistics that I know of who has examined this gives it no credit. Some writers referred to the publication of a paper in a peer-reviewed journal as demonstrating the absolutely superior claim of "statistical codes" to be a scientifically based approach to religion, unlike the "topological codes". This doesn't really seem quite fair, as it is commonly known to all serious scientists, that the mere publication of a paper in one of the several hundred thousand peer-reviewed scientific journals currently in print does not imply that the paper is correct or that it represents even the presumptive currently accepted scientific consensus. ( As a particularily widely discussed example of this commonplace, recall the controversy a few years back when the editor of Nature, one of the great journals of science, published a paper on th claims of the pseudoscience of homeopathy. ) Some colleagues doing research in statistics have said that, alas, that is notoriously true of some papers that appear in the journal containing the paper on which the adepts of the "statistical codes" base their claim to have a more scientificly based approach to religious texts. In any case, to be fair, the proponents of the "topoogical codes" may analogously also come to seek the "confirmation" of trying to get a scientific publication. There are of course important epistomological differences immediately apparent between the two schools of applying mathematics to religion. To the perhaps mystically or artistically inclined devotees of the "topological codes," it may seem to offer practitioners new cosmic meanings ( perhaps related to those some have usually sought in some other Eastern religions and religious traditions ), however apparently alien to conventional Judaism or standard science. The "statistical codes" approach, on the other hand, by its nature tends rather to, in effect, deprecate the traditional centrality ascribed to meaning in Jewish texts. ( In this connection, some respondents expressed concerns about what may ensue when "statistical codes" come to be invoked by propagandists for some other religions, who perhaps, as they may have greater funding, will use even bigger computers in developing statistical "proofs" of religious points. Indeed, I have been told by Russian colleagues that statistical "proofs" had earlier been used by Russian Orthodox Christian mathematical mystics in the former Soviet Union, though at the time they did not have access to poweful computers. Happily, it should not prove necessary to invest in ever bigger computers to defend Judaism from any"statistical attacks"; a powerful dose of Jewish humor should suffice. ) Of course, conventional mathematics is hardly likely to be damaged by all this, or even to ever take notice of any disputes between these two mathematical approaches to religion and texts. Both these novel approaches to applying mathematics to religion and texts do, in fact, raise some perplexing and deeply disturbing sociological questions. Some of these difficult sociological problems will, in the Jewish context, no doubt be the focus of some serious academic researches: Why at this particular time are some apparently favoring radical innovations in place of the traditional centrality of meaning in the texts ? Are some sadly reduced to viewing texts as formal or mathematical cribs ? From whence do some get the novel feeling that the texts are somehow in need of scientific endorsements or expansion in outlook or of the "prestige" of invoking fancy sounding mathematical terminology ? Is there no basis for concern that intelligent, well-educated and sensitive Jews sadly unfamiliar with Jewish texts may be repelled from even looking at them when turned off by what they may view as formalistic, boring, puerile or profoundly nihilistic interpretations ? To ask again, as none of the many replies and postings from either school responded to this: Why shouldn't we be confident that the reasons for becoming interested in Jewsh texts can be drawn, as always, from their uniquely profound and exciting ideas, legal codes, traditions, history, stories, poetry, wisdom and values ? Those are all things that mathematics, wonderful and beautiful as it is, can make no claims of providing. Professor Sylvain Edward Cappell Courant Institute of Mathematical Sciences, New York University 251 Mercer Street New York, N.Y., 10012 <cappell@...> ---------------------------------------------------------------------- From: Mechy Frankel <frankel@...> Date: Tue, 28 Mar 1995 11:57:05 -0500 (EST) Subject: Vav DeGichon: A Flawed Numerology? 1. As I was leining last week's parsha, i was reminded of a problem which i've not found a satisfying solution for and wondered whether anybody else might have run across a decent explanation. 2. When reading parshas Shimini, we notice on that the vav in the word "gichon" in Vayikra 10:42 is written extra large because, as many chumashim note on the spot, it marks the halfway point, by letter count, of the full torah text. Of course this simply follows a practice prescribed by the post-talmudic composition, Meseches Sofirim (ch 9) which directs a graphical marking of this numerical milestone. Meseches Sofirim, in turn, is simply iterating the gemara Kedushin 30a which uncontestedly asserts, amongst other things, that the vav of gichon is the halfway point. 3. The problem with all this of course is that the vav of gichon is most assuredly not the the torah's halfway point. In fact its not even close, being almost 5000 places off the true letter count midpoint (to be found in the entirely unremarked Vayikra 8:28) So what's going on here? To scale this error in perspective we should consider that the torah overall has a bit over 300,000 letters - so we're talking of a 1.6% error, and for a simple counting problem, this (as we say in DC) should not be considered close even for government work. 4. Some possible solutions include the following: a) The gemara in Kedushin 30a records a tradition in the name of R. Yosi that "inhu bikei bechaser veyeser veanan lo bekieanun" i.e. that already in talmudic times people were apparently not completely certain of the maleh and chasers (plene and defectives). Thus the text the gemara is referring to could have had a much different distribution of vavs and yuds than our modern chumash, and thus the vav of gichon could have been the real halfpoint of their text, but not ours. This, however, is quite problematic since i) Why should the author of Meseches Sofirim written close to, or in, the period of prime activity by the Tiberian Massoretes, and thus presumably had a version of the torah pretty similar to ours (hard to believe there would be 5000 chaser-maleh differences by that point) repeat this incorrect assertion which must have disagreed with the text now before him? ii) Meseches Sofirim also repeats the gemara Kedushin 30a assertion that the words "darosh dorash" in Vayikra 10:16 mark the halfway point in the torah by word count (and is so noted in many chumashim today). This too is manifestly incorrect, since the real halfway word is "mizbeach" in 8:15) being off by about 900 words (actually about 61 pesukim and guestimating a 15 word average). And this inconsistency could not be explained away by appealing to uncertainty in chaser-maleh since that would have no effect at all on the word count. iii) Even the general talmudic uncertainty of chaser-maleh is by no means a given since R. Meier testified in Sotah 20a that he himself was quite expert on these matters ("lo mibaieh bichaseros veyeseiros debaki ana"), and the very notion that that the talmud would inform us that vav of gichon was the halfway point, or expound the halacha that a sefer torah which had a maleh writen as chase or the reverse was pasul (a halacha cited in Menachos 29b and surprisingly enough articulated by the very R. Yosi who declared "anan lo bekianin' above, so clearly something is going on here) would indicate that chazal in fact had a firm grasp of the text. b) The text of the gemara in Kidushin 30a is simply corrupt from a very early period, and Meseches Sofirim was mislead by the corrupt text. This solution was offered by R. Y. Shor (Mishnas R. Yaacov, ch.4) but it's difficult to accept that Maseches Sofirim would so slavishly repeat a corrupt girsah when there was such a wide and obvious disagreement with the text which must have been in front of him at that point. c) R. Eliyahu Posek (in Piskei Eliyah, chelel 3, siman 1) suggests that the halfway of letters in Kidushin 30a doesn't refer to all letters but only the "different" or problematic ones. i.e. if we look only at letters involved in maleh-chaser, kri-kesiv, special large or small letters, etc. then vav of gichon will be halfway through that list, similarly the word pair "darosh dorash" is halfway through a list comprising only remarkable words, (such as tishagalna-tishcavneh). This purely pilpulic response is not very convincing and in any event does not explain why the vav in gichon should be any more the midpoint of such a list than any other letter in the word gichon. d) R. Reuven Margolis (in Hamikra VeHmesorah, and where I also initially found the last two references) suggests that it is necessary to also count blank spaces in the torah text, which are also prescribed by tradition. e.g. spaces are prescribed between "open" and "closed" parshas, within the text of the various shirim, etc. and the vav of gichon would mark the halfway point in prescribed letter spaces, some of which are unoccupied. This argument is made by its author somewhat more persuasively than I've summarized it here but, aside from its pilpulishe flavor, ultimately fails entirely to explain the "darosh dorash" word count problem. 5. There are also problems with the talmudic (Kedushin 30a again) count of the number of pesukim at 5885 which is off by about 40 from the current arrangement. This, however, has long been remarked by chachamim (see e.g. gilyon hashas to Berachos 7a, also the Yalkut Shimoni to Ekev 247 has a girsa referencing a 8455 pasuk count) who seem willing to entertain a talmudic textual emendation here. In any event, this generally would not seem to be as a big a problem as the letter or word count discrepency since there are already indications from the talmud itself that different communities split up some pasukim differently, with different counts. e.g. kidushin 30 "ki asa R. Acha.. amar bimaarava paskei leih lihai kera litlasa pisukei" ("when R. Acha came he said in Israel this pasuk is split into three separate pesukim.."). 5. So there you have it. I'm stuck. Any good references or ideas? Mechy Frankel H: (301) 593-3949 <frankel@...> W: (703) 325-1277 ----------------------------------------------------------------------

End of Volume 19 Issue 17