Some of Rabbi Menken’s eager adulations of Rabbi Meiselman’s book are hilarious. Rabbi Menken notes that an example of Chazal’s advanced knowledge of the natural world is that they presented Pi as being three, because this must have been because they knew it was an irrational number and cannot be expressed exactly!Rabbi Menken agrees that it would indeed be ludicrous to project current mathematical knowledge back into the distant past in order to excuse a coarse estimate, and then use that very projection to tout Chazal’s prescience. However, he claims, neither he nor Rabbi Meiselman said any such thing:
Rather, it was the Rambam who said so, 600 years before modern mathematicians reached this same conclusion. In the Rambam’s time, this statement was hardly projecting “current knowledge” back onto Chazal, because even then the nature of Pi remained unknown. On the contrary, the Rambam’s statement itself is evidence that “Chazal possessed knowledge of the physical world beyond what was known to other cultures.”He quotes Rabbi Meiselman as explaining how Rambam demonstrated that Chazal knew Pi to be an irrational number:
The Rambam gives no source for his information (that Pi is irrational). Scholars have presumed that he deduced it from Talmudic passages in which it is implied. In fact, the Rambam seems to say so almost explicitly. He writes that Chazal use an approximation for Pi rather than a fraction because it is irrational. This seems to imply that if Pi were rational there would be no justification for instituting a legal approximation rather than the appropriate fraction. The very fact that Chazal did so indicated to him that they knew it to be irrational.Accordingly, concludes Rabbi Menken, the Rambam’s statement itself is evidence that “Chazal possessed knowledge of the physical world beyond what was known to other cultures.” He is shifting responsibility away from himself and Rabbi Meiselman and instead onto Rambam. And he thus accuses me of mocking the words of Rambam.
Now, let's see what's actually going on here.
First of all, Rabbi Menken's claim that Rambam described Pi as an irrational number 600 years before anyone else is not true. What happened 600 years later was that Pi was proved to be irrational. But it was known to be irrational long before that. It seems that the early Greeks also hinted to Pi being an irrational number. Besides, where does anyone think that Rambam got the idea from that Pi is irrational? R. Meiselman quotes "scholars" as saying that he got it from the Gemara, but he suspiciously does not reference these scholars. Rambam surely didn't get it from the Gemara, or he would have said so. So presumably he got it from the mathematicians of his era, or worked it out himself. (In yet another ludicrous argument, Rabbi Menken takes this as further proof that Chazal knew Pi was irrational, because there is nowhere else that Rambam could have gotten it from!)
But what about the Gemara? Rambam says that Chazal knew that Pi was irrational, and therefore used an approximation. This is a reasonable position. Yet Rambam does NOT say, however, that the fact of Chazal using three proves that they knew it to be irrational. Rabbi Meiselman presents a highly speculative argument to this end: "This seems to imply that if Pi were rational there would be no justification for instituting a legal approximation rather than the appropriate fraction. The very fact that Chazal did so indicated to him that they knew it to be irrational." But there is simply no such implication in Rambam.
And there is a reason why Rambam would not make such an argument. That is because even if Chazal thought that Pi was rational, there would indeed be a justification for using an appropriate fraction. Perhaps Chazal thought that it was a complicated number, and therefore simply rounded it off (as many Rishonim indeed hold). One cannot prove from Chazal using the value of three that they knew it to be irrational.
And there is another possibility, too: that Chazal thought Pi was actually equal to three. Tosafos (Eruvin 14a) points out that, based on the context, the Gemara does not seem to be giving an approximation. Of course, there are various apologetics which argue otherwise, but Tosafos apparently didn't find them convincing. Thus, if someone wants to believe that the Gemara did not mean this, they can do so, but one cannot use the topic of Pi to prove that Chazal had superior knowledge of the natural world, unless one is willing to categorically dismiss Tosafos and Tosafos' arguments.
Furthermore, the Mishnah (Ohalos 12:6) says that "A square is greater than a circle by one-fourth," referring to the perimeter of each when the circle is drawn to the height of the square. This is true if Pi is assumed to be 3, but given a more accurate value of Pi, the perimeter of the square is actually closer to one-fifth longer than that of the circle.
(Some readers will doubtless find it hard to accept that Chazal believed Pi to be 3. The question is whether there is basis for their disbelief, and an analysis of the Gemara and Rishonim reveals that there were much more basic mathematical errors committed by some (but not all) of Chazal. Tosafos (Eruvin 76a) says that Rabbi Yochanan and the Gemara in Sukkah misunderstood a statement by the judges of Caesarea to mean that the diagonal of a square is equal to twice the length of its side. Tosafos states that Rabbi Yochanan subscribed to this understanding of the judges of Caesarea, and that the Gemara in Sukkah rejected it precisely because it is mathematically inaccurate. Rashba expresses surprise at Tosafos attributing a simple mathematical error to Chazal, and he gives an alternate explanation, but he does not deny that Tosafos does indeed say this! Ran likewise expresses surprise that the judges of Caesarea erred in a simple mathematical matter, and cites an alternate explanation of Rabbi Yochanan’s misunderstanding of what the judges of Caesarea were saying, which somewhat lessens the error, but still leaves Rabbi Yochanan making genuine errors of both interpretation and mathematics. Tosafos HaRosh states similarly.)
So, to conclude: We have a Rambam that does not say or imply that the fact of Chazal using Pi=3 proves that they knew it to be irrational. We further have other Rishonim who understand this Gemara as saying that Pi is a rational but complicated number, or that Pi does indeed equal three. So, yes, for Rabbi Menken/Meiselman to present this Gemara as proof of Chazal’s advanced knowledge of the natural world is indeed ridiculous. And, since Rambam did not say this, I am not mocking Rambam (though Rabbi Menken is indeed dismissing Tosafos and other Rishonim).
(Please note that I am currently in the middle of the jungle in Zimbabwe, and tomorrow I am heading to Botswana, so my internet access is sporadic!)
(The full series of critiques of Rabbi Meiselman's book is at this link)
R' Natan, perhaps you handed R' Menken an unwitting opening for an attack. I'm sure you can find other examples where hilarity doesn't get you involved with the Rambam. As you pointed out, the notion of irrational numbers was known from ancient times by Greek mathematicians - among others. The Rambam merely stated something he presumably knew from secular sources since he was well versed in Arabic mathematics. His argument is weak, however, when it comes to the Talmudic approximating pi as 3. While an exact representation is impossible (the meaning of 'irrationality' in such a number), a much better approximation, 22/7, was commonly used in classic sources. As the Tosafot in Eruvin 14a note, the Gemara there is under the impression that the verse in Kings I relating the ratio of the circumference of the great temple basin to its diameter (30/10 amot) was to be considered as denoting an accurate relationship rather than a rough approximation (the large cast vessel was probably not perfectly circular so that there may have been a range of diameters). Nor is pi the only irrational number involved in halachic material considered by the sages. the ratio of the diagonal of a square to the side, sq. rt 2) is another common example. The sages (except possibly, R'Yochanan) knew to represent that ratio as 7/5 (1.4) rather than 2. That approximation is only 1% off the more accurate commonly used value of 1.414 (as compared to the 4.5% error in taking pi as 3 - using 22/7 involves only a 0.04% error). Tosafot in Eruvin 76b and Succah 8 demonstrate beautifully that 7/5 is a bit too small an approximation, but still serviceable. The point is that there is no evidence that the sages were aware of a better value for pi, and the fact of irrationality is irrelevant. Nor does R' Menken comment on any other point in the critique of his review. Neither his review, nor his response to the critique can be considered a sign of intellectual honesty - to say the least.
ReplyDeleteY. Aharon
Y. Aharon
I suggest that, whatever the reason, Rabbi Menken's not mentioning ANYONE by name, when he makes it absolutely clear that he is referring to that person, is clearly objectively unprofessional.
ReplyDeleteI also think that it is obnoxious, but I refrain from suggesting that this is an objective statement, since I suppose that it could reasonably be assumed to be something other than obnoxious.
Catriel Lev, Ramat Bet Shemesh Alef
Perhaps he still holds by the cherem Rav Slifkin was put in and won't name him for that reason?
DeleteI think that the Rabbiner Doktor title was the last straw.
DeleteNS,
ReplyDeleteI think that you are the fuzzier of the two. (Slifkin vs Menken)
Also, Menken admits that he is a "polemicist". I wouldn't care to read anything that Menken writes about, but I think I would find Rabbi Meiselman's writing to be worthwhile. He has a good overall reputation, is considered a legit Rosh Yeshiva and he has a bona fide PhD in Mathematics. The Soloveitchik stuff is just meant for amusement and to be a tyne in the eye of the likely critics and detractors.
Rabbi Meiselman is not my messiah, but rates on my "worthwhile" list. (Haven't gotten the book yet, though.)
By the way, I am connected to the society of accomplished mathematicians, and almost universally, if your PhD isn't in mathematics, you are considered to be no more than a truck driver (or maybe a zookeeper). So the math cred is definitely cool.
Come back when you have your PhD in pure math.
As hominem reasoning at its finest. But of course you can ignore the scribblings of a mere CS guy like me.
DeleteRabbi Slifkin, lacking a phd in math, has nonetheless done an impressive job of destroying rabbi Meiselman's arguments. So what's your degree in math worth again?
DeleteHow about you come back when you have a degree in basic Midot? A little skill in logical reasoning wouldn't hurt either.
DeleteI was misunderstood (my fault.
DeleteA) I am not a mathematician. I am married into GENERATIONS of mathematicians.
B) These people (mathematicians) tend to think that other disciplines are lower and less learned (or at least less honest or rigorous).
C) My real point was to point out that Rabbi Meiselman's math cred, along with his Rosh Yeshiva cred, along with his (FWIW)Sololveitchik cred, makes him more credible than this blogger who has none of the above.
D) SO I checked on one of slifkin's claims that RMM "distorted" something, and upon discovering that NS actually did the misrepresenting, I realize that the Rosh Yeshiva cred is actually worth something. I need to wait until a legit Rosh Yeshiva criticized Rabbi Meiselman's book. There are several who definitely can. NS is not the one to be the messenger.=, and also has no credibility. Probably even less than Menken, the admitted polemicist.
Good day
> By the way, I am connected to the society of accomplished mathematicians, and almost universally, if your PhD isn't in mathematics, you are considered to be no more than a truck driver
DeleteSo mathematicians think that mathematicians are the smartest people. So what?
David: You're thinking too small. It was also a fine example of "Appeal to Authority."
DeleteDaniel
@Daniel: True.
DeleteSnowbird your lack of intelligence is not something to show off, the subjects being discussed are not too hard to grasp if instead of listening to what both sides have to say you decide who is correct based on credentials (and award cred points for family name to boot) you are either completely lacking critical thinking skills or are trying to hide from having to concede that Dr slifkin is right
DeleteA degree in mathematics gives you zero credibility in other unrelated scientific fields. Physics, sure. But even then we have seen time and time again how religious math & physics academics feel compelled to make convoluted claims in their attempt to reconcile Bible and modern science even justifying absurd notions like young earth creationism.
Deletesnowbird - your critique has no credibility.
DeleteSend your spouse to the blog, or go get your PhD in pure math.
Dear Rabbi Voldemort,
ReplyDeleteRabbi Menken's article would appear to be empirical proof that he is in fact a squib. Agree?
Do people such as Mencken and Meiselmann truly believe what they write?
ReplyDeleteDo they actually think that not believing in the inerrancy of Chazal is Keira. Do they think that the Badatz or any other Kashrut organizatio checks that all or even most of its Mashgichim believe in the inerrancy of Chazal.
Do they trust any hashgochos or only eat what they grow in their own gardens and are otherwise strict Vegans?
What happened 600 years later was that Pi was proved to be irrational. But it was known to be irrational long before that.
ReplyDeleteQuibble: nothing in known in mathematics until proven. So Rambam seems to have conjectured that pi is irrational and others probably did also, but no one knew that it was irrational until it was proven.
That's a modern day definition. The status at the time was probably good enough for the Rambam.
DeleteAs discussed in the other comment thread, this is incorrect. Greek Geometry used and required proofs which meet modern day standards. Euclid's proofs are accepted and taught today (except for a few mistakes). If he thought otherwise, then he would have been behind the times. And if he thought he had a proof, he was mistaken.
DeletePresumably, he conjectured, as many others no doubt did, that there was no exact rational corresponding to pi because no one had discovered one yet.
> Quibble: nothing in known in mathematics until proven.
DeleteYou're using a technical definition of "known," while R' Slifkin is using the usual definition.
You're using a technical definition of "known," while R' Slifkin is using the usual definition.
DeleteCan't agree. The Rambam stated his conjecture in a perhaps overly definitive manner. That is not the same as knowing even in the conventional sense.
My main point is that the Rambam suspected that Pi was irrational (probably) which he thought was the conjecture pretty much every other person familiar with mathematics as well as Chazal. It's possible he was mistaken and though that this was actually known, but then he is behind the times and not ahead.
OK, here is the thing Dave. What makes you so sure that the Rambam (or even some of his gentile buddies from med school) had no PROOF that pi is irrational? And even if you "highly doubt it", why is it so whacky for a religious mathematician/rabbi/Soloveitchikel to believe it was likely???
DeleteRabbi Meiselman doesn't claim he had proof. The Rambam doesn't claim he had a proof. But the best evidence of a lack of proof is that the proof would have been a major achievement and would have been publicized and become part of the history of mathematics. But it didn't. Secondarily, the mathematics needed to prove the irrationality of pi had not yet been invented.
Delete"…but still leaves Rabbi Yochanan making genuine errors of both interpretation and mathematics."
ReplyDeleteAs the Me’ri points out, if we assume R’ Yochanan and the Rabbis of Caesarea are talking about area, with their normal assumption of pi = 3, they are exactly correct in both Sukkah and Eruvin. That appears to leave the gemara with a bad quote from R’ Yochanan and then, based on the text they had, they then try very hard to get close to the reality (but don’t not quite make it, see appendix B of my paper below).
I have written a paper that has an annotated diagram and explanation of the math. It is available at An Approach to Rabbi Yochanan and the Rabbis of Caesarea
Any comments would be appreciated.
Avraham, sorry, but whatever the merits of your paper on the subject, your current argument is incorrect or misleading. While R' Yochanan in Succah may well have been thinking of the area of a circular succah that could accommodate 24 people taking up the space of 1x1 amot each, that is clearly not the interpretation of the Gemara there who immediately assumed (also in the conclusion)that he was referring to a circular perimeter that could accommodate 24 1 ama wide people sitting at its outside (just a way of stating that a minimum circular succah, according to R' Yochanan, must enclose a minimal 4x4 ama square according to Rebbe and have a circumference of 24 amot). They appear to consider this case a perfect analog of R'Yochanan's view in Eruvin of a minimum circular opening in a wall separating 2 yards to allow an Eruv Hatzeirot (except that the dimensions there are in tefachim rather than amot). In Eruvin, however, the language used clearly implies a circumference of 24 tefachim rather than an area. The argument of the Tosafot in both Masechtot is that the sages of Caesaria who stated the geometric rule that a circle is 50% larger than the enclosed square refers to areas rather than perimeters. This is correct taking pi as 3. It is incorrect when it comes to perimeters and was never intended to be so used. The Tosafot have no problem with stating that R' Yochanan misinterpreted those sages and implied that he takes a diagonal as the sum of the sides of a square.
DeleteY. Aharon
…your current argument is incorrect or misleading.
DeleteSorry I was not clear. I agree the Gemara in both Succah and Eruvin are talking about circumference my point was while they recognize if you assume the 24 refers to circumference you get “too large” an error, which they assume R’ Yocahnan would not make. So they go through machinations to make it closer, but still with an error. My position is the Amoroim did not know the Rabbis of Caesarea were referring to area, and to quote from my conclusion
“Based on the Me'iri, who says so explicitly, and Tosafos and the Ritva, from whom we can derive it, Rabbi Yochanan is talking about area and is correct in both Succos and Eruvin. Rabbi Yochanan's statement that “the circumference of the Sukah must be large enough to seat 24 people in it” does not mean that the circumference must be 24 Amos, but that there must be room for 24 people occupying 24 square Amos inside the circumference - - in other words, the area of the circle must be 24 square Amos!”
I would say the Gemara and Tosafot did not understand R’ Yochanan and R’ Yochanan was correct.
He doesn't mention your name:
ReplyDeleteA. He doesn't want to call you "Rabbi" so the easy way out is to not refer to you directly at all.
B. Omitting your name implies that those with names are more worthy interms of their arguments. Those with names are winner, those without are losers.
C. Super immature, which already shows the mentality of those whom you're dealing with.
D. I appreciate how the Voldemort idea flew over their heads for what it meant in all its glory.
E. LONG LIVE THE SA!
In Rabbi Menken's latest update, he writes that he did not mention my name "because I did not want to descend to his level, and condemn him while naming names." Can anyone explain to me what on earth this is supposed to mean? I've never heard of anyone (and certainly not a charedi rabbi) refrain from naming the person that they are condemning because they do not want to descend to his level! I'm going to proceed with the explanation that it was because he didn't want to give me even that minimal degree of honor and validation.
ReplyDeleteYour comment about "honor and validation" smacks of childishness. That is to say: You sound like a little child pouting in the corner that mean Rabbi Menken made you feel bad. If you really are the "rationalist" that you claim to be, then act like a grown up rationalist. -Moshe Averick RBS
DeleteMaybe Rabbi Menken meant that he wanted the person disagreeing with him to remain anonymous (well, maybe not, because there are so many indirect references, that only someone who doesn't know anything about Rabbi Slifkin's work for the past 15 years would not be able to identify about whom he's speaking), whereas Rabbi Menken is mentioned explicitly.
DeleteHe attempts to marginalize you, hilariously, as a "moderately well-known writer and blogger." He, of course, believes himself a world renowned sage and opinion-maker. Very nice, Yakov Menken. You're a representative of the "Torah world"? I want no part of that world if so. What a chillul hashem.
DeleteHe also claims, disingenuously, that Avi Shafran ducks his critics because they only criticize him because he is "an observant rabbi." Unbelievable. Straight out of the "anyone who criticizes Clinton is a misogynist" school of thought, an opinion Shafran actually subscribes to.
Look, Menken's commentary is pure ignorance, and probably shouldn't even be addressed. The man simply doesn't know enough to comment in the public sphere. He's the typical Aish Ha-Torah product (regardless of what kiruv seminar he actually went to) - spoon-feed them a few grade school basics, give them a "smicha", and send them back on to the streets to rope in more people. It works great for Jews who were like him, young and easily convinced with gimatriyos and starry-eyed over exotic creatures with beards that they never encountered in their reform synagogues. For FFB Jews, it doesn't work so well.
And the ugly nastiness for sure doesn't work well. What's with all the attacks, Yakov Menken? Always attacking someone - the only way to raise yourself up is by knocking others down? Zero ahavas yisrael.
Nastiness and Ignorance. Not a good combination, and both cause chillul Hashem. Do yourself and everyone else a favor, and leave the commenting on your website to professionals.
I did not realise he was an american Baal teshuva, this explains a lot of questions I had about what Menken wrote and his "tone" (whenever I use that word I remember those heady days in Manchester 10 years ago when Iwas told there were a lot of problems with slifkin's books, but even if you could shlog them all up here was a problem with his "tone").
DeleteThis is precisely how charedim fight: no respect for the opponent: they are never named, their ideas are worthless because they propound them, etc. childish? You bet.
ReplyDeleteThe ancient Greeks proved that pi lies between 3-1/7 and 3-11/71 but this does not mean that they thought that it is an irrational number although Hippasus did postulate that some numbers, such as the square root of 2, are irrational - and aroused the ire of the Pythagorans, who attributed his drowning to this "heresy". However, Rambam states it as a fact and not a theory. No one has been able to prove this without calculus (the Greeks used geometric figures). What is interesting is that the baalei Tosafot did not know that and stated the popular view that it exactly 3-1/7 as a difficulty with the Mishna.
ReplyDeleteAvi, the ancient Greeks did not "postulate" that the square root of 2 was irrational. They proved it and it changed the course of the history of mathematics. If being the first to prove that something is irrational indicates divine providence, then the Greeks must have had Siyata Dishmaya.
DeleteThe Rambam stating it as a fact and not a theory doesn't put the Rambam ahead of his time. At best he was conjecturing, since he didn't actually know that pi was irrational. Undoubtedly many ohters also conjectured it given that no one had found an rational equivalent to pi (which is all the that the Rambam probably meant anyhow; his goal in that statement was to defend the seemingly primitive use of 3 as an approximation by Chazal).
Avi, where did you find Tosafot asserting that pi was exactly 22/7? It's not in the Tosafot on Eruvin 14a. There they only state that the Gemara in question as well as that of Bava Batra 14a appear to take 3 as an accurate value of pi whereas secular scholars agree that pi is greater than 3.
DeleteDavid, the Rambam may have been thinking of the calculation of pi by Archimedes who laboriously calculated the perimeter to radius ratio of regular polygons with increasing number of sides to approach the value of 2*pi. The procedure generated a series of numbers that were increasingly better approximations of pi but didn't reach a constant value. In any case, his argument is weak since, as Tosafot remark, the Gemara's argument assumes that 3 is the accurate value for pi. If a reasonable approximation is needed for practical halacha, 22/7 is a far superior value. Perhaps the argument should be that if the writer of Kings I felt that 3 was a good enough representation for pi, why do the sages need to be any more accurate? There is apparently no corresponding verse relating the diagonal of a square to its sid. Hence the sages went with the then generally accepted value of 7/5 (although R' Yochanan appears to have used 2, i.e., the sum of the sides to approximate the diagonal).
Y. Aharon
Y. Aharon, I agree that the use of the method of exhaustion by Archimedes shows that he probably considered Pi to be irrational. I actually cited this as an example in a comment on Rabbi Menken's article which he may or may not publish.
DeleteDavid, why not? Hashem's hashgacha is on all people. As for Rambam, if he was conjecturing hewould have said "it seems to me". However, he stated it as a fact.
DeleteAnonymous, you a re right. I confused their statement with Rambam's. BTW, the Gra points out that in the relevant pasuk the word for "line" is unusually spelled "קוה". If you divide its gematria by the gematria of "קו" and you get a very close approximation of pi divided by 3.
Even in modern times, many people have believed pi to be 3. In fact, there was an attempt to pass a law to that effect in one of the states of the USA in the early 20th century. Fortunately, the law did not pass...
ReplyDeleteThat's actually a myth. Look it up.
DeleteNot a myth. perhaps a hoax? I have seen the "record".
DeleteYou are referring to Alabama attempting to pass a law that Pi equals 3.
DeleteIt was April Fools humor and you can read about it here: http://www.snopes.com/media/notnews/pi.asp
Shalom is probably referring to this, which is mentioned in the snopes article:
DeleteThough the claim about the Alabama state legislature is pure nonsense, it is similar to an event that happened more than a century ago. In 1897 the Indiana House of Representatives unanimously passed a measure (House Bill no. 246, introduced by Rep. Taylor I. Record) regarding the calculation of the area of a circle that assigned various values to pi other than 3.14. (The bill died in the state Senate.)
It happens to be very easy to show that pi is greater than 3.
ReplyDeletePerhaps the answer to "when will they ever learn" may be found here:
ReplyDeletehttp://mobile.nytimes.com/2012/03/25/books/review/the-righteous-mind-by-jonathan-haidt.html?post_id=541078949392304_626677897499075#_=_
KT
Joel Rich
This is great. I'm mamash loving this.
ReplyDeletePerhaps you can both agree that the Rebbe is melech hamashiach now? ��
This thing about not naming someone being criticized seems to be quite popular in certain religious circles. I once heard a Rav in the US give a whole lecture saying why the audience shouldn't eat in a particular kosher restaurant. He never said the name of the restaurant but described it in such a way as to make it clear which one he was referring to.
ReplyDeleteI also noted, at least in the US, that if a Rav was asked if it was possible to rely on a certain hechsher, they often wouldn't give a straight answer. Is all of this done in order to supposedly avoid speaking "lashon hara" even though the hints come through loud and clear?
Many times it is not perfectly clear which one they are talking about, unless the listener is immersed in gossip to some extent. That really bothers me. "That certain restaurant/show/book/letter writer/property owner, etc."... No, I DON'T know who you mean!
DeleteI tend to just tune it all out.
Have you ever seen the comments policy over by Cross-Currents?
ReplyDelete"Comments must be civil and collegial, in both tone and choice of words. Shrill language, attack words, excessive negativity and cynicism can be taken to other blogs. The harshest, most trenchant criticism can still be phrased in a more gentlemanly fashion. Address the audience rather than the target of your criticism. Close your eyes and imagine that you are in the Oxford Debating Society of a century ago. Ask questions, rather than pontificate."
I always felt there was kinda a double standard at Cross-Currents because if somebody was even slightly hyperbolic they'd not let the comment through, but Yaakov Menken's posts tend to be pretty nasty to anybody who disagrees with the haredi theology that's politically correct in his community (I wouldn't say the same about any of the other writers there, even though I disagree with them on the color of the sky). And I dunno, I think folks at the Oxford Debating Society a century ago were fine talking with their opponents directly and if they weren't using peoples' names, they were prolly using honorifics like "the honorable gentleman" or something.
Cross Currents allows shrill language, attack words, etc. as long as you're agreeing with them.
DeleteThe commenting policy differs by poster. Rabbi Gordimer lets in pretty much everything. Rabbi Menken will let in only comments that he thinks that he can immediately rebut. Rabbi Adlerstein lets in most but only after he provides his rebuttal in []. At least that has been my experience.
DeleteThe only suggestion I can find that pi is irrational that predates the Rambam is from 7th century India. I would guess that the Rambam conjectured it independently, based on what he knew of the Greeks' computations.
ReplyDeleteI wonder what Rabbi Meiselman has in mind when he refers to "Talmudic passages in which it is implied."
Dear Rabbi Slifkin
ReplyDeleteI really don't get this one. In your post of yesterday you assumed that R Menken (RM) was trying to "prove" that Chazal knew that Pi was irrational from the fact that they stated it as 3. In his rebuttal RM effectivly said that that was not what he meant, but merely that the Rambam assumed that Chazal knew this. You accept that to be the case. So what are you arguing about?
On a related note, do you (or any reader) have a source for the assertion that it was known that Pi was irrational "long before that"?
In a nutshell, the argument is about what the term "know" means. The short version is that secular mathematics requires a more rigorous standard in order to say that something is known compared to Rabbis Meiselman and Menken. Therefore a strict comparison isn't comparing apples to apples.
DeleteThe long version is like this. In the mathematical sense, knowing something means being able to prove it for nearly all cases using logical statements. Lambert showed this by proving that pi is an infinite continued fraction and therefore must be irrational.
In contrast, the Rambam's statement isn't a proof but rather a conjecture. Therefore, he may have believed that pi was irrational, but he didn't know it. We only say that you know something if you can prove it, and neither Rambam nor Chazal wrote an actual mathematical proof (or at least, I certainly haven't seen one).
The problem is that Rabbi Menken and Rav Meiselman appear to use this as a case where Rambam and Chazal were far more advanced than the secular knowledge of their time and that they possessed knowledge of the physical world beyond what was known to other cultures. But that's largely due to different definitions of the word to 'know' or 'proof'. Secular mathematicians weren't able to prove that pi was irrational until 1768 but there may have been conjecture that it was irrational prior to 1768.
Rabbi Slifkin believes that the Greeks had also made this conjecture. This is certainly a reasonable hypothesis and highly likely to be correct, but I'm not familiar with any evidence of this.
Rabbi Meiselman tries to prove that Chazal were ahead of their times in mathematics because they used 3 to estimate pi. You can make the argument as sophisticated as you like and cite as many authorities as you like, but the argument remains "irrational", if you will.
DeleteIt was not known in ancient times that pi is irrational. It was probably widely conjectured, since all concrete values for pi were estimates only (which is probably why the Rambam thought it irrational). The Rambam's statement is an interesting footnote in the history of Mathematics, but no more than that.
Oren: I think you are oversimplifying it. While the Rambam may have not had a mathematical proof that pi is irrational, he writes very definitively that the value of pi is not only unknown but is inherently unknowable, and that it can never be known, only approximated. The Rambam supplies this as the reason Chazal gave an approximate number. So the essential question is if there are any secular sources from the time of Chazal, or even the time of the Rambam, that state definitively that pi is an irratonal number?
DeleteYehoshua: I agree that the Rambam wrote very definitively that the value of pi can only be approximated. I would also agree that it is reasonable to say that Rambam was saying Pi is irrational. We're in full agreement on those points.
DeleteI don't know the answer to your essential question, and therefore can only concede the point. I suspect R' Slifkin is correct that the Greeks figured it out, but that's not proof.
Where we disagree is about the importance of a mathematical proof. I feel that a mathematical proof is more valuable then a definitive statement. Sort of like how a link to a study is more valuable then just a reasonable argument. By definition, the study is evidence. But plenty of reasonable arguments are wrong.
Here, suppose you asked a layman how a car works. He could probably tell you how to drive and maybe make a few repairs. You'd be fine with him being on the road. But that probably wouldn't be good enough to become a mechanic. Or to build cars from scratch.
The amount of knowledge necessary to drive a car is different then the amount of knowledge necessary to build a car. And therefore, the answer to the question of 'whether you know how a car works' is different for the car builder and driver. And the amount that they can do with their knowledge is different also. I mean, it's great that the driver can drive, but what does he do if he can't get access to a car? The car builder can just build a new one. And in the same vein, you can build on a mathematical proof but not a declarative statement.
Or, to perhaps give a better example, suppose a Rabbi and a student are discussing a gemara. Suppose the Rabbi makes a definitive statement about the gemara. If the Rabbi's statement isn't disproven, that's probably going to be the accepted understanding. But if the student is able to find a Tosafot that references another gemara that supports his point, then the student is going to win the argument (presuming the other rishonim say nothing). And this is because a proof trumps a definitive statement.
Likewise, Lambert brought a proof that clearly demonstrated Pi is irrational. Rambam made a statement that strongly suggested that Pi was irrational. Both people are in agreement with each other. But Lambert's argument is stronger because he was able to determine a proof. Just like the student would win against his Rabbi if he found a Tosafot supporting him.
I still maintain it's about how you define "know".
Oren: I think you are oversimplifying it. While the Rambam may have not had a mathematical proof that pi is irrational, he writes very definitively that the value of pi is not only unknown but is inherently unknowable, and that it can never be known, only approximated.
DeleteThis shows that he was either mistaken or else used strong language in his conjecture. It doesn't demonstrate being ahead of his time in Mathematics.
The Rambam supplies this as the reason Chazal gave an approximate number. So the essential question is if there are any secular sources from the time of Chazal, or even the time of the Rambam, that state definitively that pi is an irratonal number?
It is obvious to anyone with mathematical understanding the pi was likely irrational since no one was able to pin it down to a fraction. The Rambams speculation was interesting, but the result was unsurprising.
David: With all due respect, I really don't get you here. I will readily concede that the Rambam did not have a mathematical proof that pi is an irrational number. But you are making assumptions concerning what is in fact the entire debate here, thereby ending up with a predetermined outcome. As I understand you, your position is that since there was no mathematical proof for the irrationality of pi until fairly recently, when the Ramban writes as definitively as can be that he knows, and that Chazal knew, that pi is an irrational number, he was in fact speculating and exaggerating his claim. In addition to being somewhat offensive to the Rambam in accusing him of being wholly imprecise in his wording, this also presupposes that the only way the irrationality of pi could be known is by means of mathematical proof. If one believes that Chazal had any information transmitted from Sinai about the natural world (not that all their natural-world knowledge was from Sinai, but that any of it could be), then the Rambam can be taken at face value, that both he and Chazal knew this to be a truth. To me, what would be convincing here is a statement asserting the irrationality of pi with the same definiteness as that of the Rambam from at least the time of the Rambam and preferably from the time of Chazal.
DeleteThe fact that someone states something definitively is not evidence that he has any greater knowledge of that claimed fact. Also, the Rambam himself did not claim to have a proof, nor did he claim to have a Mesorah.
DeleteBut we can cut this short very easily by noting that the Rambam makes some very definitive statements that turned out to be false. In the Sefer Hamitzvos that spontaneous generation is a reality and that anyone that denies it hasn't studied science. He also makes definitive statements about the four elements and the spheres, neither of which exist.
1) Never try to teach a pig to sing. It wastes your time and annoys the pig.
ReplyDelete2) In a time without calculators, writing paper and ball point pens, assuming Pi to be three would save a lot of time, ink and costly parchment when trying to figure things out.
3) Apple Pi is the best kind, as long as it's Pas Yisroel
Whilst in this case I agree with everything you wrote, I still genuinely don't understand why you need to debase yourself with bringing pictures of movie characters in connection with your work.
ReplyDeleteI don't believe that can be considered professional under any circumstances. I don't see serious rabbis and, lehavdil, judges and politicians who wish to be taken seriously associating themselves with these things. It simply provides ammunition for those who attack you.
...and to be brutally honest, maybe the ammunition is justified.....
Deleteie you? Because nobody else has ever bought it up.
Delete...Well, maybe that says something about Rabbi Slifkin's followers...
DeleteShow me a serious academic (unless it's a doctorate in TV studies), professional, judge etc and lehavdil rabbi who does such things. Even the great rationalist MO RZ rabbis don't use movies as their props.
************: You are completely wrong. Cultural references abound in high level academia as well as in judicial opinions. They are a way to pack a lot of information into a short reference as well as something to grab the attention of the audience. Rabbis do or don't depending on their personality and their congregation. And Harry Potter is as well known a cultural reference as anything in Shakespeare at this point.
DeleteRabbi Avraham J. Twerski wrote an entire book based around Charlie Brown comic strips. Does that count?
Deletehttp://www.amazon.com/When-Do-Good-Things-Start/dp/0312132123
David,
DeleteI read judicial reference fairly often and I have never seen any references. And even if true that classics are quoted on occasion in any event I dispute your assertion that Harry Potter is a culteral reference akin to Shakespeare or the classics. It isn't, it is kid's fiction and a load of rubbish actually. When it is studied in academia and universities I will revise my assertion. But that won't be for some 500 years, by definition if at all.
But if Rabbi Slifkin believes his audience requires Harry Potter references and suchlike to be understood, so be it. I thought that they were made of more intellectual stuff!
JD
DeleteCharlie Brown is a lot deeeper and cleverer interpersonal relationship wise than Harry Potter which is a load of rubbish.
David
DeleteI normally like to talk gently but it seems you don't get it.
If Rabbi Slifkin considers himself a serious manhig or leader in klal yisroel with a serious message to teach and give over,than he should act as dignified rabbonim do and not bring kiddy stories and characters as props. Period.
And the fact that you might be able to find some young rabbi trying to engage his young not particularly serious congregation in some mussar by also quoting superman or batman or harry potter is neither here nor there.
Charlie Brown is a lot deeeper and cleverer interpersonal relationship wise than Harry Potter which is a load of rubbish.
DeleteSorry, now your are trolling :).
It's the difference between chochma b'goyim and rubbish b'goyim.
DeleteIn any event Rav Twerski used it as a tool, not just random name dropping. It's completely non comparable.
You guys have guilted me into looking up the Wikipedia article on "Proof that Pi is irrational", and other references.
ReplyDeleteIt seems to me (MA physics, not math) that the Greeks proved that sqrt(2) was irrational. But I haven't found any source that says they proved that _Pi_ was irrational. If they had done so, Lambert (1761) wouldn't get the credit for it.
The Greeks knew, perfectly well, what "proof" meant (in their culture, and in all of mathematics until 20th century work on foundations and formalization).
. . . So they might have _conjectured_ that pi was irrational,
. . . but they would have known that they didn't _know_ (that is,
. . . that they couldn't _prove_) that pi was irrational.
So, if Rambam said that he _knew_ that pi was irrational (quoting the Greeks), he was confusing "know" with "conjecture" -- a serious mistake.
Forgive me if I misunderstand the argument.