Rabbi Menken once again responded to my post (see the update to his original response) and, once again, only attempts to respond to part of it. His response to the Pi topic is to issue a stream of seemingly contradictory statements that have left many people confused. Here is a selection:
"Chazal were ahead of their times because they knew Pi was irrational, plain & simple."
"...[Natan Slifkin] implied that either RMM or I said “their use of pi = 3 PROVES that they knew that pi is irrational,” this is nonsense. No one said that."
"It is the Rambam’s confident assertion that the value of Pi cannot be known that is extraordinary."
"The Rambam’s statement itself is evidence that Chazal possessed knowledge of the physical world beyond what was known to other cultures.”I think that he's trying to say that Rambam's statement about Pi being an irrational number could only have come from Chazal and therefore proves that Chazal were ahead of their times. However, the claim that Rambam's description of Pi as an irrational number could only have come from Chazal (who said nothing more than that Pi equals three!) is rather staggering and requires proof. Rabbi Meiselman provides nothing other than a weak argument that I refuted in the previous post. Furthermore, as I pointed out in the previous post, the other Rishonim clearly did not understand the Gemara that way. Rabbi Menken does not respond to my pointing out that he and Rabbi Meiselman are (yet again) categorically dismissing Tosafos and all the other Rishonim and Acharonim. And nor, of course, has he responded to anything else in my critique of his review.
"...because I did not want to descend to his level, and condemn him while naming names."Can anyone tell me what on earth this is supposed to mean? What "descent to my level" is there? I might have been overly strident in describing his writings as being ludicrous and dishonest, but he went considerably lower in approvingly citing a description of my writings as "rabid"! Furthermore, Rabbi Menken has had no problem mentioning the names of people at Women Of The Wall or the Reform Movement in his condemnation of them. So how is it "descending" to any level in mentioning names?
Of course, it's all nonsense. The reason why he can mention the names of WoW or Reform is that they are not a serious threat to people in his circle. But I am, and that is why he is afraid to dignify me or give me any credibility by mentioning my name. It's similar to how the characters in Harry Potter are afraid to say Voldemort's name. Likewise, Rabbi Menken won't link to my posts (and gives the silly excuse that the reason is that he hopes that I will change my mind and remove them).
Yet as Dumbledore points out, refusing to say the name of Voldemort actually gives him more power. Likewise, virtually nobody is fooled by Rabbi Menken's excuses for not giving my name, and they are disgusted by both his refusing to mention my name or link to my posts, and his false excuses for it. So, ironically, his technique to try to devalue the opposition ends up having the opposite effect!
This is all starting to get a bit tiresome.
ReplyDeleteFirst, the next time you critically review a book full of religiously nonsensical peudoscientific bafflegag, simply don't mention the name of the book or the author and Mencky will not be forced to issue ludicrus statements in defense of that book and author.
Secondly, really who cares anymore? So Rav Meiselman believes that Chazal were secretly demigod-like superheros with nigh-infinite knowledge and probably understood how Caramilk gets the creamy caramel into the middle of the Caramilk bar. So what? Why does that bother you? Conversely, you believe Chazal were rational men with a great knowledge of Torah and a decent scientific knowledge commensurate with the times they lived in. Why can't he live with that?
Ay-men!!!!
DeleteBecause if you say Chazal were secret demigods who knew everything, there is an inference that the rabbi today has a reflection of this gd-like nature. He can grant absolution, if he tells you to do something that you know is against halacha you must do it anyway.
Deleteits called daas torah...
and these rabbis depend on this logic in order to exist!
Regarding the "descending to your level" part:
ReplyDeleteI think what he means is that when you criticize a respected Rabbi in your posts, you mention them by name, and are therefore speaking Lashon Hara - and he refuses to stoop to your level and do the same to you. I'm not opining on whether it is Lashon Hara or not, but I think that's his point. I could be wrong.
Although I'm not sure what not mentioning your name accomplishes here because it is obvious who he's talking about.
So no debate or meaningful dialogue is allowed?
DeleteI think MK wants to say that you debate and discuss the idea--there is no need to mention names. What difference does it make who said it? (One of the unwritten rules on this blog is that arguing from strength of authority has no weight--e.g., if Rabbenu Ephraim says something that indicates that he believed in werewolves, we don't have to accept that werewolves exist.)
DeleteThere might be some merit to that, even though Rabbi Menken is clearly talking about Rabbi Slifkin, as MK mentioned.
Rabbi Slifkin is insulted b/c Rabbi Menken won't mention his name.
DeleteMK is offended b/c Rabbi Slifkin does mention names.
Oh well.
Isaac and Yitz -
DeletePlease read my comment more carefully. I was simply stating what I think Rabbi Menken's point was. I did not say whether I agree with him or not:
"I'm not opining on whether it is Lashon Hara or not, but I think that's his point. I could be wrong."
"Although I'm not sure what not mentioning your name accomplishes here because it is obvious who he's talking about."
Yehuda P - If it was only meant to discuss the idea, then there were plenty of things in Rabbi Menken's article that didn't need to be written.
MK - go ahead and state it. Do you agree with him or not?
DeleteAh, the old tennis match resumes! Such fun! You should sell tickets!
ReplyDeleteProof that no one is fooled can be found in the fact that the first (moderated) comment to his first post mentions you by name. If Rabbi Menken is concerned not to descend to your level, he apparently doesn't mind if other people do in his own moderated space.
ReplyDeleteI had speculated his refusal to name you was based on the pasuk 'let the name of the wicked rot' which has been used in the past to justify posting quotes or other information from 'wicked' people without citing them as the source. See Saul Lieberman and the Orthodox by Marc Shapiro for a whole slew of examples. http://amzn.to/1XxYUJW
ReplyDeleteWould you rather be referred to as you are in some other posts (not by Menken) by only your last name "Slifkin", in stark contrast to the use of "Rav" whenever Meiselmann is mentioned?
ReplyDeleteI don't know what R Dr Slikfin wants, but I would find it less absurd.
DeleteHis reason for not linking to your posts is obvious. As you point out he ignores most of your points and tries to cherry-pick a very few points to respond to. If he linked to your posts, people would see how weak his position is.
ReplyDeleteSorry, but you are missing the point on this one. You write:
ReplyDeleteI think that he's trying to say that Rambam's statement about Pi being an irrational number could only have come from Chazal and therefore proves that Chazal were ahead of their times. However, the claim that Rambam's description of Pi as an irrational number could only have come from Chazal (who said nothing more than that Pi equals three!) is rather staggering and requires proof.
The issue is not how the Rambam himself knew it is an irrational number, but that the Rambam asserts quite plainly that Chazal knew it is an irrational number, and that is why they gave the approximate value of 3. So even if you could show a clear secular source pre-Rambam for that knowledge, it would not help, as what you really need is a parallel source from the time of Chazal that states with certitude that it is an irrational number.
Yehoshia, with respect, you are missing the point. It is not significant that Rambam says that Chazal's reason was that it is irrational.
DeleteThat seems to me to be this whole argument. The question is, if Rambam did not have a tradition (he claimed to be descended from Jews who were expelled from Yerushalayim, which was the seat of the Sanhedrin) how did he know and why did he ascribe this knowledge to Chazal? It cannot be proven, at least yet, without calculus. Did Rambam or one of his predecessors invent calculus and keep the knowledge secret?
DeleteSo proof of chazal's infallibility requires the assumption that the Rambam was always correct in his interpretation of the Gemora? Even Rav Meiselman doesn't claim that, seeing as that would involve denying any Rishonim ever argued.
DeleteI don't understand you. The sentence that started this entire brouhaha was:
DeleteSome of Rabbi Menken’s eager adulations of Rabbi Meiselman’s book are hilarious. For example, 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 responded that the Rambam himself writes that Chazal chose to use the approximation because they were aware that pi is irrational. Now, I will certainly grant that other Rishonim provide other explanations as to why Chazal chose 3 as pi. That said, the words of the Rambam, taken at face value, state that Chazal knew for a fact that pi was irrational way earlier than this was accepted as fact by the world at large. If one accepts that Chazal knew this for a fact despite there being no mathematical proof for this, that would be an indication that they had some type of access to knowledge about the natural world that did not come from contemporaneous science. You could counter this by showing that even secular scholars from the time of Chazal stated definitively that pi is irrational, or you could counter this by saying that the Rambam didn't mean it when he said that he and Chazal knew this, and he just meant that it was a well-grounded assumption. But absent proof of the former, or a decent textual reason for the latter, I think that the point is very significant.
Yehoshua, you are missing the crucial point. You wrote "If one accepts that Chazal knew this for a fact..." But that's exactly the point! Why would one accept that Chazal knew this? The Rishonim say that they didn't or don't say that they did. Rambam says that they did, but offers no evidence for it.
DeleteI see we are getting nowhere, so I will close with this: You ridiculed the idea that Chazal's usage of 3 for pi can be seen as an indication of their early knowledge that pi is irrational. The Rambam says that Chazal's usage of 3 for pi is because they knew that pi is irrational. Unless you are willing to claim that either: The Rambam did not mean "knew" when he said "knew" or that pi being irrational was known to other scholars at the time of Chazal, you have essentially ridiculed a statement that derives straight from the Rambam. [Not that the Rambam claims that Chazal knew this from Sinai, as he may have thought that it was common knowledge at their time. But we, who (as far as I know) are aware that this is not the case, would arrive at that "hilarious" conclusion.]
DeleteYehoshua, you are still not getting it! I am not making either of those two claims!
DeleteLet me try again.
Rambam said that Chazal's usage of 3 for pi is because they knew that pi is irrational. He might be correct, he might not; we have no way of knowing. But Rabbi Meiselman (and Rabbi Menken) are going much further than Rambam. They are saying that Chazal's usage of 3 for pi PROVES that they knew that pi is irrational!
I disagree with your characterization of what they claim, and anyone who wants can go read the article on Cross-currents and decide who they think is portraying their position correctly.
DeleteNatan, you are the one who is not getting it. Neither of them said that.
DeleteYes, they did indeed say that. I quote:
Delete"Chazal were ahead of their times because they knew Pi was irrational, plain & simple."
And another:
Delete"The Rambam’s statement itself is evidence that Chazal possessed knowledge of the physical world beyond what was known to other cultures.”
The entire context of their discussion is providing proofs that Chazal were ahead of their time!
DeleteTo make this simpler, Rabbi Meiselman thinks that he can prove that Chazal was ahead of their times, possibly with divine assistance. The only way to prove that Chazal knew something is by own their statements. Any later commentary by the Rambam or anyone else is just an aid to interpretation.
DeleteWhat did Chazal actually say? Pi is 3 in halacha. There is simply no way to get from there to where Rabbi Meiselman wants to go.
Knowing that it isn't three =/= knowing that it's irrational. You don't need calculus to know that pie isn't 3.
DeleteIt's pure nonsense like menckens that drove me out of the charedilite camp and straight to modern orthodoxy. Thank Gd i found an intellectual home I can live in.
ReplyDelete"Yet as Dumbledore points out, refusing to say the name of Voldemort actually gives him more power."
ReplyDeleteThis reminds me of the 'nittel night' custom. By refraining from learning Torah etc attests in a roundabout if not direct manner concerning the 'reality' of JC.
To clear up your confusion:
ReplyDelete"Chazal were ahead of their times because they knew Pi was irrational, plain & simple."
The Rambam writes that they knew this, so if one accepts what the Rambam wrote, they were ahead of their times.
"...[Natan Slifkin] implied that either RMM or I said “their use of pi = 3 PROVES that they knew that pi is irrational,” this is nonsense. No one said that."
Neither R' Menken or RMM said that it proves that they knew it, the Rambam says that they knew it and that is why they gave an approximation.
"It is the Rambam’s confident assertion that the value of Pi cannot be known that is extraordinary."
The Rambam lived hundreds of years before the irrationality of pi was mathematically proven, so if one is willing to take him at his word that he knew this to be a fact, it is extraordinary.
"The Rambam’s statement itself is evidence that Chazal possessed knowledge of the physical world beyond what was known to other cultures.”
This could be worded slightly better and should say that based on what the Rambam believed Chazal knew, coupled with what we know other cultures of Chazal's time knew, it turns out that Chazal possessed knowledge of the physical world beyond what was known to other cultures.
All better now?
You're still missing the point. Yes, according to Rambam, Chazal knew that Pi is irrational. But what evidence is there that Rambam is correct? Especially since all the other Rishonim and Acharonim understand the Gemara differently! I'm not saying that Rambam is definitely wrong - he might be correct, but we have no way of knowing, and thus this Gemara is not proof that CHazal knew Pi to be an irrational number.
DeleteThank you - I was bothered by some of the same points. One point, though - even though there is no "evidence" that the Rambam is correct, we still do see that he himself, for presumably valid reasons, DID believe that Chazal knew that pi was irrational. That itself is, I believe, significant.
DeleteNot really. He also thought that [some of] Chazal, and the Neviim, were also fluent in Greco-Muslim philosophy.
Delete"Muslim"???
DeleteWhy is it significant that the Rambam thought that Chazal knew that Pi was irrational? If he thought this was a fact or a very likely conjecture, then he would presumed that all educated people knew it. He doesn't say the irrationality of pi is a great secret known only to those with the right mesora. If he assumed that pi was irrational because no one had come up with a fraction to represent pi, then he would also have assumed that all other intelligent people would make the same deduction.
DeleteWhat is interesting is that he doesn't state that pi IS unknown, but that it can NEVER be known exactly. That is certainly not an obviously apparent fact - I find it hard to believe that the Rambam thought that all intelligent people would necessarily be aware of that fact.
DeleteEr - is this Nekama then, R Natan?
DeleteIf I wanted to do nekamah, then I would be motzi shem ra on him, as he did to me.
DeleteWhat is interesting is that he doesn't state that pi IS unknown, but that it can NEVER be known exactly. That is certainly not an obviously apparent fact - I find it hard to believe that the Rambam thought that all intelligent people would necessarily be aware of that fact.
DeleteAt the risk of the nth repetition:
1) Rambam conjectured it, but didn't know it since he didn't have a proof.
2) Mathematicians would have conjectured it too, since they couldn't find a rational that corresponds to pi.
3) The Rambam explicitly states that only foolish people think that the reason pi has not been stated exactly is because of a lack of knowledge. Everyone else knows it is irrational.
I don't know if your points or correct or not, and it isn't all that important to me. But is does strike me that your aggressive, no holds barred, put down style of writing is not becoming of either a rabbi or a doctor.
ReplyDeleteWell, if you knew more about Rabbi Meiselman, and what he did to me, and if you knew more about Rabbi Menken, you might understand.
DeleteI would say, if you were familiar with Halachic Responsa literature, you would see that R' Dr Slifkin is quite restrained.
Delete@Yosef Cornfeld:
DeleteYou are entitled to your opinion, but do you think that R Menken's style is better, worse or similar to that of R Slifkin.
As to what Kira wrote--As I practical example: It's true that the Shach in Yoreh Deah speaks rather harshly in his glosses (Nekudas HaKesef) on the Taz--and it's rather surprising that such a genius like the Shach would have to resort to such language. But at the same time, the Shach writes in his introduction to his commentary to Nekudas HaKesef that the Taz was his guest, and they spoke together at length, and the Taz was so impressed with the Shach that he rose and kissed the Shach on his forehead!
DeleteBut I don't think Rabbi Slifkin will get a kiss on the forehead from either Rabbi Meiselman or Rabbi Menken any time soon.
Rabbi Slifkin uses logic and shows transparently that his opponents are very deficient in their reasoning, despite their obfuscations. I also find that Rabbi Slifkin is often quite magnanimous. His opponents use tar and feathers and slime. I have never read them being magnanimous or menschlik. They make me ashamed to be associated with a community that tolerates and encourages them.
DeleteSo, on the one hand, Rabbi Slifkin is clearly correct.
ReplyDeleteOn the other hand, as illustrated by many comments on this blog and elsewhere, people without a strong math background will be unable to see why he's correct. Without appreciation for the difference between a proof and a declarative statement, his argument appears to be nothing more than about semantics. Unfortunately, most people don't have a strong background, and therefore will be confused by his argument. As such, while correct, this argument is one he can't win.
From a rational perspective, it makes sense that a statement proven by logic is stronger then a declarative statement. My boss wants logic and proofs from me and not mere statements. I have to say not just what but rather why.
But from a more mystic perspective, it makes no difference whether I can prove something via natural means or whether I can learn it from Ruach Hakodesh. Especially if Ruach Hakodesh can be used to teach me other laws and not specifically just one.
Many comments on this blog also demonstrate that they are unable to accurately read the Hebrew of Peirush Hamishnayos. See this link, decide for yourself
Deletehttp://www.wired.com/2013/03/medieval-insights-into-the-irrationality-of-pi/
All the best
Dave, you take the cake. Do you seriously mean that you are judging how well the readers of this blog understand a Rambam based on how some writer in Wired magazine conveyed a second-hand translation of a second-rate version of the Rambam?
DeleteNo, he just has the Hebrew text :)
DeleteSo does anyone with a Talmud Bavli in their home, although that version of the Rambam is not known for its accuracy.
Delete"Tribalism", to use your word, RNS, is of course the reason why R. Menken disagrees with you. הגע עצמך - how is it that the Charedi/Yeshivah world have invented dozens of new minhagim, and revamped dozens of long-ignored halachas, yet all of a sudden with TECHELES, they have a problem? Anyone who believes the halachic arguments concocted against it is simply a fool. It is tribalism and no other. Techeles came from the mizrachi and centrist orthodox world, not theirs, and thus they cant adopt it.
ReplyDeleteSame with hetter mechira, of course. The Torah says you cannot have chametz in your house on Pesach, yet they have no problem conducting a seder 10 feet away from a closet full of chametz that they "sold" to a goy. Same with running business on Shabbos by "partnership" interests to goy. Same with getting out of the problem of bechor beheimah. Same with a million other things. But hetter mechirah, a Zionist initiative - OH NO, *that* can't be done.
These examples can be multiplied a dozen times over. It's not a personal or individual thing, its just a reality. The charedi world has convinced themselves that they, and only they, are the "authentic" repositories of Torah, and hence by definition, anything related to Torah that didn't emanate from them must perforce be treif. That's the way they think. If I wanted to get political, which I don't, we could illustrate this same way of thinking by use of political parties as well.
היתר מחירה is by no means a 'zionist' initiative. A little history would tell you that it was backed by many of the leading rabbonim in Europe.
Delete@DF, you're correct that tribalism is a big factor in the charedi halakhic process, (although, to be perfectly honest, politics does make its way into the decisions of zionist poskim as well), and you could name more cases than just techelet. However, heter mechira is not a great example. There was already a historical debate in the charedi world itself if heter mechira is valid, and most of the original Matirim allowed it only in dire circumstances.
DeleteFurthermore, there are many more halakhic issues wrt to heter mechira than with chometz et al. E.g. if selling the land itself suffices to remove the kedusha, if selling land in such a manner is even permissible. And, wrt to chametz, one only needs to rely on one's own mental conviction (גמירת דעת) that the sale should indeed be final, whereas by heter mechira, people are uncomfortable relying on the conviction of an unknown farmer that his land will indeed be sold.
Personally, I instruct people to wear techelet but not to use heter mechira except in circumstances where certain criteria is met.
R Stefansky
For the record a significant number of e chareidim are aware of the issues with mechiras chometz and avoid it if possible.
DeleteThe big push for hetter mechirah arose oncurrently with the Zionist initiative. (I am not saying they are the same, I am saying they arose concurrently.) That there may have been isolated rabbis here or there that discussed it beforehand is not relevant. It was not something of importance for the rabbis back in Europe, but it was something of importance for the Zionists. That, and only that, is the reason for the "problems."
DeleteI could also have pointed out how translations were always considered a "crutch" when I was young, and we weren't supposed to use them. But all of a sudden when Artscroll - basically an arm of the Agudah - came along, now we have translations even in yeshivahs. No longer such a big "crutch" apparently.
Come on, now. Let's not fool ourselves. This is all politics, and nothing more.
I have the perfect solution.
ReplyDeleteRefer to yourself in the 3rd person when you write. This way you will be criticized in a "stooped down" version- first person.
Libby Ba'mizrach
Tau, 2*Pi (6.28...) is the true circle constant that shows up frequently in the physics and math that describe the Creator's world. See www.tauday.com
ReplyDeletePi (3.14...) is mathematically irrelevant - why would "ruach hakodesh" have pointed to this misleading number which, when you boil it down to basics, describes half a circle? "Language of Man" perhaps?
The formula for area of a circle is much uglier with tau than pi. Some things are simpler with pi, others tau. To make a big argument out of it is simply being immature.
DeleteAnd that's ignoring the problems With the rather unsophisticated philosophical statement you made...
There's plenty of reasons why r' menkin's claims are crazy, but that's not one of them.
The manifesto was pretty good. Reminds me of the suggestion in Feynman that when you measure distances in the unit of light-seconds you go from E=mc^2 to E=m which is really what Einstein taught us.
DeleteThe point of Pi vs. Tau is to show that Chazal used the best math and science of their time, as would be expected of any great scholar. It's an innovation more radical than Reform to suggest - or worse, to insist - that Chazal had magical knowledge of undiscovered math or science. The magical focus also steals the spotlight away from their observational science and their insights into human behavior.
DeleteBeauty is, of course, in the eye of the beholder, but it is my personal opinion that the "pi" area formula for a circle is a classic example of "sheker hachen v'hevel hayofi" because its simplicity is an accident of multiplying 1/2 * 2pi * r^2, while 1/2 * tau * r^2 is beautifully consistent with how the area of *any* regular polygon is 1/2 * perimeter * apothem. There's a similarly deceptive charm to e^pi*i+1=0. See http://spikedmath.com/fact-005.html
There's plenty of reasons why r' menkin's claims are crazy, but that's not one of them.
DeleteYou may be over-estimating the seriousness of Robert's argument. Especially given the triviality of the following statement: Tau is rational iff Pi is rational.
I couldn't get past the title of this post -- it should be Me, not I!
ReplyDeleteI think that Steven Pinker's rationale as to why "me and John went to the store" is grammatically acceptable applies here as well. Both "me and john" and "I, voldemort" are new nouns of their own right. 😀.
DeleteAnyway I'd better go into hiding before the grammar police arrive...
R Natan - You'd come over far better if you acknowledge the those points on which you were correctly taken to task. For example, R Menken is certainly correct about your assertion that if Rambam's source was the gemara, he would have said so. Namely that your assertion is not only false but patently so, given that he famously doesn't state his sources most of the time, and that a whole literature exists to fill this gap.
ReplyDeleteEqually, R Menken would do well to acknowledge your accurate claims, but I'm on your blog right now.
Similarly, you are simply not dealing with the fact that a) Rambam unequivocally states that Pi is irrational b) he attributes the same knowledge to Chazal c) No other known source from Rambam's time or earlier expresses this confidently.
You need to address whether or not Rambam is consistent elsewhere in expressing conjecture as fact. This would make all the difference to the current discussion.
If Rambam is known to express presumption as fact then you have a point. If not, then Menken's closer to the mark.
All else is prevarication.
The search for emes is looking particularly sloppy today.
In response to your points:
Delete1. OF course Rambam does not mention his sources in the Mishneh Torah. However, here he is DIRECTLY DISCUSSING the relevant Gemara. IF this was his source for the idea that he is discussing, presumably he would say so.
2. How is it relevant that Rambam attributes this knowledge to Chazal? The only relevant point is whether we can PROVE from Rambam that Chazal knew it. Rabbi Menken says that we can. I say that is nonsense.
As for your point #1, your "presumption" is baseless. The Rambam does not often give sources in peirush hamishna either. As to your point #2, once again you are wrong. R' Menken doesn't say that we can prove from the Rambam that Chazal knew it; he says that we see that the Rambam believed that Chazal knew it. You seem unwilling or unable to appreciate this distinction time and time again.
DeleteYou need to address whether or not Rambam is consistent elsewhere in expressing conjecture as fact. This would make all the difference to the current discussion.
DeleteIf Rambam is known to express presumption as fact then you have a point. If not, then Menken's closer to the mark.
All else is prevarication.
Rambam confidently asserts the existence of spontaneous generation and considers anyone who disagrees to be ignorant of science.
Checkmate.
[Actually, this isn't important because the Rambam is conjecturing. The only way to know that Pi is irrational is with a proof which he didn't have. But my first method is easier.]
David, you are begging the question. You write: "The only way to know that Pi is irrational is with a proof which he didn't have." That assumes that Chazal were not privy to Divinely revealed knowledge about the natural world, which is the entire subject of this discussion.
DeleteYou've got it backwards. R Meiselman is trying to prove from this very example evidence of advanced knowledge. The starting point,is the claim that the Rambam made "an astounding statement". If the Rambam had given a proof the irrationality of pi, that would have been astounding and another reason to celebrate the Rambam today. Instead he stated, without proof, something that any intelligent person of his time believed was very likely (say 90% likely). Thus his statement is not astounding and there is no reason to think that either he or Chazal had a mesora on this.
DeleteHis statement was akin to someone looking at the weather forecast with a 90% chance of rain, and declaring the he knows that chance of rain is 100%. If it then rains, is the person's statement "astounding"? Of course not.
Generally, the fact that the Rambam stated something as a fact is no evidence at all that he had special knowledge of this fact. He stated that spontaneous generation definitely exists and derided those who thought otherwise as ignorant of science. All it means is that he thought it was true.
In all probability, the Rambam know that pi is an irrational from some ancient source that got lost in the mists of time.
ReplyDeleteFor example, Wikipedia states (lightly edited, no change in content):
“In 6th century (CE) India, mathematician Aryabhata calculated the value of pi to five significant figures (62832/20000, which is 3.1416). Aryabhata stated that his result "approximately" (āsanna "approaching") gave the circumference of a circle. His 15th-century commentator Nilakantha Somayaji has argued that the word means not only that this is an approximation, but that the value is incommensurable (irrational).”
As R' Slifkin has argued, since the Rambam knew this to be true, he assumed that Chazal also knew it to be true. Although the Rambam often argues with the science of Chazal, in this case he felt no reason to do so.
One last point: To use the Rambam as proof that Chazal had perfect knowledge of science is silly, because the Rambam himself says that Chazal were deficient in their knowledge of science.
Tom, well said! Especially "In all probability, the Rambam know that pi is an irrational from some ancient source that got lost in the mists of time" and "since the Rambam knew this to be true, he assumed that Chazal also knew it to be true."
DeleteTom, I fully agree with what you said, up until the last sentence. Even if one grants your understanding of that line of the Rambam and applies it in a broad sense, that does not mean that they were always deficient in their knowledge of science.
DeleteI'm saying that it's absurd to use the Rambam as proof that Chazal had infallible, perfect knowledge 100 % of the time (as Rabbi Meiselman claims), when Rambam explicity says that that was not the case.
DeleteYehoshua,
DeleteAlthough you misunderstood Tom's point, it still shifts the burden of proof onto the one who claims that the Rambam, without making any specification, believed that Chazal had a divine source for the irrationality of Pi. And not only does he not make any specification, but he constantly refers to essays written by mathematicians and wise people about it:
"...but it is known by approximation and the scholars of Mathematics have already written essays about this to know the approximate ratio of the diameter to the circumference."
"And the approximation that is the guideline that is relied upon by the scholars of applied wisdoms..."
"I'm saying that it's absurd to use the Rambam as proof that Chazal had infallible, perfect knowledge 100 % of the time (as Rabbi Meiselman claims)..."
DeleteTom, R' Meiselman does NOT claim this. He claims that all knowledge is, in principle contained in the Torah, but that few were ever capable of extracting all of it, and that even Chazal were limited in this area. He only claims that whatever definitive statements they made were based on Torah, and these must therefore be assumed to be correct. Read the book.
And Rambam accepted this ancient source - forcefully asserting that it is irrational and disdainfully rejecting those who thought otherwise - based on...?
ReplyDeleteBecause Rambam investigated the reasoning behind the ancient source and agreed with it.
DeleteIt's all a matter of mathematics and logic. No special technology is required.
I'd like to make another point. If Lambert worked it out in 1761 (again, without advanced technological instruments), then Rambam or Chazal could also have worked it out. This would be proof that Rambam/Chazal were mathematical geniuses, but it would not prove that they had knowledge from a supernatural source or that it was taught at Sinai.
So you're saying that Chazal in the time of the Mishnah, and Rambam in the medieval era, had the mathematical genius of some of the top mathematical minds in history, and further spent the time necessary to reach an emphatic conclusion that pi is irrational, which is based on advanced trigonometry, and somehow this knowledge escaped everyone else until the eighteenth century. Got it.
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DeleteYour sarcasm is not warranted.
Deletea) According to Rabbis Meiselman, Menken and their ilk, Chazal were indeed outstanding geniuses in every field of knowledge.
b) Knowledge of trigonometry was indeed very advanced in those times.
c) "Somehow this knowledge escaped everybody until the eighteenth century." Well evidently it did! Rambam was absolutely sure that pi was irrational (he must have known the proof himself or he trusted a source that he thought was reliable). And yet this knowledge was lost and had to be proved again in the 18th century.
In any event, your objections are relevant only to the second approach I suggested. The far more likely explanation is my first one. The Rambam knew from another source which got lost in the mists of the time that pi was irrational. (In fact, as I wrote above, a 6th century Indian mathematician was understood by a 15th century scholar to have reached that conclusion.) The Rambam then assumed that Chazal knew the same thing.
Since this explanation is at least plausible, it cannot be derived from this Rambam that Chazal received knowledge of the natural world from Sinai.
Back to basics for a moment. There are two sources of knowledge - empiricism/logic and revelation. Rambam knew Pi to be irrational. The only question is which of these were his source. R Natan, David et al appear to be assuming there was no knowledge of maths or science through revelation, which is why they are searching, slightly desperately you might say, for his source. Menken et al assume the opposite, that vast amounts of scientific knowledge were revealed. Much of Menken's view has been adequately disproven.
ReplyDeleteI don't see the basis for R Natan's view either though, and don't understand why he is so convinced that he can't accept the possibility that some scientific knowledge was in the hands of Chazal through revelation. The
I am not at all asserting that it is impossible for Chazal to have had scientific knowledge through revelation. I just haven't seen any examples, just lots of claimed examples that turned out to be false!
Delete1) Just to simplify, you can't prove something in math through empirical methods. So it is logic vs. revelation.
Delete2) The issue is not that math could not be revealed through revelation. The issue is that there is not a speck of evidence that the irrationality of pi was ever revealed in such a way. The fact that Rambam conjectured pi to be irrational in writing (with no proof) is an interesting footnote in the history of mathematics, but not particularly astonishing. In fact Rambam himself says that only fools disagree.
3) And to speak more generally, the best explanation for the science of the both the Torah and Chazal is that it was consistent with what what generally known with no special revelation needed or evidenced.
4) Even if someone could convincingly claim that God revealed the answer to some difficult open math problem (e.g. P != NP), but without the proof, then this would not be considered an acceptable solution. In math, you need the proof or you don't "know" the answer. The point in math is to show the proof relationship between the axioms and the theorems. The theorem alone doesn't help.
@David Ohsie This recalls the academic debate as to whether a proof "revealed" by a computer algorithm is worthwhile, since it doesn't give any insight into why the result is true. Nature highlighted this last week.
DeleteI compliment you on a series of remarkable posts over the last few days, and your detailed, clear and thorough critique of Rabbis Meiselman and Menkin.
ReplyDeleteThe fact that you have been able to write them, whilst out on your Africa trip is yet more amazing. You are clearly a Sofer Mahir, someone who besides anything else is a very gifted writer. I often wonder if those who originally put your works in Cherem regret what they have unleashed /created!
Please ignore the critics in the comments who whilst supporting your Hashkafa, or claiming to do so,question why your posts or ongoing Facebook conversations/battles are needed, or somehow think that there is something petty in tenaciously challenging every Sheker. They are missing the point.
In my opinion, Halachicly and ultimately for the survival of Yiddishkeit (as dramatic as that sounds), there is an absolute Chovah to write, and to not let go unchallenged those who pervert history and our Torah. It is wonderful that you can use the Beracha of the Internet on this way, and that you have a forum to fight back.
The detailed Massa U'Mattan is exactly what is needed for the most thoughtful readers who try to take the sugya seriously, and ultimately it does have an effect on people, as my own personal story testifies.
Thank you - YeYasher Kochacha!
EG
This has descended into 2 men with big egos having a hissy fit. Yawn.
ReplyDelete