I must admit, I’m disappointed. [Even more so with the response… see update at bottom.]
When Rabbi Adlerstein and I started Cross-Currents, I used to read various critical responses to my essays on several blogs. It was not long, though, before I realized that to read them was foolish — there are some bloggers who will quite reliably insist that the sun rises in the west simply because an observant Rabbi has said otherwise. [This is the same reason Rabbi Avi Shafran declines to publish comments to his essays.] Since then, people have occasionally written to ask why I offered no response to various online critiques and rebuttals, and “a waste of time” has been my inevitable answer.
There are some, though, of whom you expect more. And last night, someone asked me to look at a post by a moderately well-known writer and blogger. You’ll all know who he is, but I’m not going to link to the post for a different (yet similar) reason than I didn’t link to the viral video of yesterday — I hope he’ll regret posting it, because he should, even if he doesn’t yet.
This is personally disappointing because we used to be friends, and I persisted in believing that we were. On one of his early trips to Baltimore to talk about zoology and Torah, he stayed in our house. His best line was when my wife said that “bats aren’t bugs,” and he immediately recognized the source: “I am expert on two things. Zoology, and Calvin and Hobbes.”
Even after his books were condemned by Gedolim, he remained a client — our work for other Jewish organizations led to doing commercial web hosting, and although I have sold my interest, I believe he’s still using that service. So whether or not I agreed with him, we were hosting his rejection of the ban. This remained true even after I was asked by Rav Aharon Feldman, shlit”a, to review Rav Meiselman’s book, “Torah, Chazal and Science,” for the journal Dialogue.
Now although Rav Meiselman doesn’t name names, it was obvious to whom he was referring when he wrote in his preface that:
A spate of books and articles and a nonstop discourse in the blogosphere have attempted to introduce a radical new theology and proclaim it compatible with classic Jewish belief. Most of this literature has been sophomoric at best. In general it has not been written by people trained simultaneously in Torah and science, whereas the topics dealt with often involve complex issues, calling for expertise in both.
So I understand why he wasn’t too pleased with the book, and that he probably wouldn’t enjoy my favorable review. But you know, that’s how things are sometimes, and the truth is best served when we don’t involve our personal animus or emotions.
As it happens, my review included addressing criticisms found in two other reviews, both critical of Rav Meiselman’s position. One of those critical reviews was written by the person who took over publication of the banned books after they were dropped by their previous publisher, and with whom I’ve collaborated on several matters. I carefully expressed my feeling that “when a person starts off with such an obviously negative perspective, it is that much more important to base criticism upon clear errors or contradictions, and reference other, more neutral sources to support his position.”
And in that case, we apparently succeeded in avoiding personal conflict. That reviewer wrote to me that he welcomes criticisms of his writing and looks forward to future cooperation in the many important areas where we largely and/or entirely agree.
Not so, apparently, when it comes to the blogger’s opinion of my review. There is no reason for disagreements to involve falsifications or straw man arguments, of course, but what upset my friend were the personal attacks. I may indeed be a “charedi polemicist,” but in context it didn’t seem that he meant that as a compliment. And what ended up happening is that in his effort to make me look foolish, he either falsified my words or those of Rav Meiselman, or mocked the words of the Rambam — all of this in a post entitled “Adulating Dishonesty.” One is reminded of the old adage found in the Gemara about projecting one’s own defects onto others: Kol HaPosel, B’Mumo Posel, all who invalidate use their own defects to do so.
In the first paragraph, the blog asserted that Dialogue “coincidentally” has Rabbi Meiselman on the editorial board. This is incorrect, and the blogger cannot use a non-fact to imply collusion or censorship (the word “coincidentally” can only be read in context as insinuating that this was anything but coincidental). While Rabbi Meiselman was a member of the Rabbinic Board governing previous issues, and was so listed on the inside front cover of those issues, he is no longer listed — for he left the board prior to the compilation of the current issue. He had no input or control regarding any part of my submission. His former membership of the Rabbinic Board cannot serve to impugn the credibility of a review written after his departure.
The second paragraph, though, was what surprised me. I will address this in detail, so that the reader may see for him or herself. Here is the paragraph in question from the blog post (minus the last sentence, which transitions to the main sections):
Some 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!
There are no additional words related to this subject in the blog post; this quote is both complete and entirely in context. The clear implication of his words is that Chazal presented Pi as being three, and that I or Rabbi Meiselman (or both) suggested that it “must have been” that Chazal knew that Pi was an irrational number — projecting current mathematical knowledge back into the distant past in order to excuse a coarse estimate, and then using that very projection to tout Chazal’s prescience. This, of course, would be ludicrous, and an apt target for rich mockery. And that is indeed his point, to use this as an example of “hilarious” adulation.
Yet here is what I actually wrote:
The author [Rav Meiselman] cites many similar cases in which Chazal possessed knowledge of the physical world beyond what was known to other cultures. For example, the ratio of the circumference to the diameter of a circle (pi) is an irrational number, meaning it cannot be expressed as a ratio of integers. This was only established by contemporary mathematicians in 1768, but the Rambam explains that the reason why Chazal used the approximation of 3:1 is because the actual ratio cannot be stated definitively in any case (p. 154).
Nowhere did I suggest that it “must have been” that Chazal knew that three was merely an approximation of Pi, which they knew to be an irrational number. What I wrote is that the Rambam said that this was so. And the Rambam, of course, said this many centuries before mathematicians achieved the same understanding.
And here, further, is the referenced passage from page 153-154 of Rav Meiselman’s book:
Let us begin with the example of Pi, which we referred to in the course of an earlier discussion. This number, which is both irrational and transcendental, is the ratio of the circumference of a circle to its diameter. It seems that one of the first definitive statements of its irrationality in recorded history is that of the Rambam in his Peirush Hamishnyos. In contemporary mathematics this fact was only established by the German mathematician Johann Heinrich Lambert in 1768.
The Rambam gives no source for his information. 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.
Again, the idea that Chazal knew three to be a rough estimate for Pi, which they further knew to be an irrational number, is attributed directly to the Rambam. Rav Meiselman provides extensive footnotes throughout his book, and includes the text of the Rambam’s Pirush HaMishnayos, Eruvin 1:5, which shows the attribution to be accurate, in two notes on page 154. Note that as the Pirush was originally written in a Judeo-Arabic dialect and later translated, there are minor differences between the text of Rav Meiselman’s footnotes and the text as found in the back of Maseches Eruvin in a Vilna Sha”s. But please don’t believe my translation, you are invited to do your own of either version:
You must know that the ratio of the diameter of a circle to its circumference is unknown, and impossible to express precisely. And this is not due to our lack of understanding… [rather] it is by its nature unknown, and cannot be fully known… but it is possible to estimate… The best estimate used by academic scholars is a ratio of one to three and 1/7… And since this will never be entirely understood except by approximation, they (Chazal) took a large number and said that anything that has three in its circumference has a diameter of one, and they relied upon this in what was required for measurements in the Torah.
If we translate his language to that used by mathematicians today, the Rambam said that Pi is an irrational number, as Rabbi Meiselman wrote — “a real number that cannot be expressed as a ratio of integers, i.e. as a fraction… irrational numbers, when written as decimal numbers, do not terminate, nor do they repeat.” [Pi is the paradigm used in the Wikipedia article.] It can never be fully known. Supposedly mathematicians have reached 12.1 trillion digits.
So here is why I am disappointed:
Did I say that Chazal presented Pi as being three, because “this must have been” because they knew it was an irrational number? Of course not. Did Rabbi Meiselman? Once again, of course not — and we know the blogger has Rav Meiselman’s book, because he says himself that he is “steadily working through” its contents.
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.”
So the author of the statement found so “hilarious” by the blogger is: the Rambam.
The reader of the blog post in question is led to mock the very idea that Chazal knew Pi to be an irrational number — in other words, to mock the words of the Rambam.
I cannot speculate upon whether the blogger actually read and comprehended this portion of Rabbi Meiselman’s book before erecting his straw man and leading the reader to mock a profoundly insightful statement of the Rambam. I don’t see, though, why it is relevant. Whether deliberately or through negligence, he led the reader to mock Divrei HaRambam!
What I can say is that I hope this 2000-word exercise is helpful and enlightening to some readers, and at least explains both my disappointment and why I will decline to address such things in the future. It’s clear at this point where the dishonesty lies.
[His response is yet more saddening and revealing. First, the writer posts a picture of Voldemort with a caption reading “he who must not be named.” Even some of his supporters termed his initial post attacking me “rabid,” but because I did not want to descend to his level, and condemn him while naming names, I’m apparently to be criticized for that too. It’s no surprise, really.
In his latest essay, he makes unsourced claims about Greek and other knowledge in order to portray the Rambam’s statement about Pi as a common insight: “But it was known to be irrational long before” Lambert proved it, he says.
History says otherwise. Lambert’s colleague Leonhard Euler believed that Pi was irrational, but could not arrive at a proof. It was Euler who got Lambert a position at the St. Petersburg Academy of Sciences. Later, Lambert arrived at a proof for Euler’s belief. So the blogger’s claim is simply not correct.
The Rambam, on the other hand, says categorically that it is impossible to arrive at an exact value of Pi, 600 years earlier.
And once again, the blogger does not read the Rambam. He says “Rambam surely didn’t get it from the Gemara, or he would have said so.”
I’m sorry, but this is simply breathtaking. I know that he has no formal training in any scientific field, but I did think he possessed a yeshiva-level familiarity with Jewish sources. Yet everyone at that level knows that the Rambam in particular was unlikely to provide source references, even in Halachic matters. This is true even in the Mishnah Torah, and all the more so his Pirush HaMishnayos. No one who has read even a few Perakim of Rambam could support this blustering assertion.
But furthermore, the Rambam quite clearly states that Chazal knew that Pi was irrational, independent of the question of the Rambam’s source for this information — although, once he tells you that Chazal knew it, there is no longer much of a question. He says: “and since this will never be entirely understood except by approximation, they (Chazal) took a large number.”
In order to avoid this, he offers another demonstration of his penchant for straw man arguments:
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.
That is correct, and no one said otherwise. The Rambam says that Chazal knew it to be irrational and therefore used three. That is what Rav Meiselman wrote, and what I wrote.
Understand that Chazal were not afraid of fractions. In order to indicate the length of lunar months, an hour is divided into 1080 portions, because a lunar month is 29 days and 12 + 793/1080 hours. Note that 792/1080 is 11/15 — but Chazal needed greater precision!
It is as the Rambam says, and as Rav Meiselman understands him: in this particular case, there is no precise value. No matter what estimate one uses for Pi, it will remain an estimate. Anyone with a piece of string can tell that Pi isn’t 3 — on the contrary, had Chazal used a more precise estimate such as 3 and 1/7, people like this blogger would have held it up as evidence that Chazal didn’t know math.
Yet further evidence of Chazal’s wisdom!
I think we’re done here.]
If this sort of distortion/straw-man is news to you, then you have obviously not followed this fellow’s previous posts on Torah Chazal and Science. It seems to me that with regards to this topic, he is incapable of rational thought.
The difference between what the Rambam wrote and what R. Meiselman (and you) wrote is the following: the Rambam wrote that Chazal used pi = 3 because pi is irrational. However, the Rambam did not say or imply that their use of pi = 3 PROVES that they knew that pi is irrational. It is R. Meiselman who makes that leap, and it is quite a leap.
There is no evidence that, if challenged to prove that Chazal had unusually advanced scientific knowledge, the Rambam would have responded by quoting their approximation of pi. He may well have conceded that alternative reasonable (though, in his opinion, incorrect) explanations could be advanced for Chazal’s approximation, which would negate such a proof.
It appears that you have adopted his strawman argument which I mentioned in my update. While he 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.
Didn’t RMM say that? Quoting from above:
He writes that Chazal use an approximation for Pi rather than a fraction because it is irrational… The very fact that Chazal did so indicated to him that they knew it to be irrational.
See the entire paragraph. The Rambam already knew this to be true, and of course Chazal knew it as well. You could nitpick about RMM’s language but he is not saying that using 3 for Pi is simply a standalone proof that they knew it to be irrational. The Rambam’s language is specific and very different: since it could not be done precisely, Chazal took a round number.
The Rambam conjectured, but did not know that pi is irrational, since he had no proof and nothing is known in mathematics without a proof. It is very likely that Archimedes (and many, many others) also though pi to be irrational given that he bothered to calculate upper and lower bounds to pi to about 0.2% of its value using the method of exhaustion and 96-sided polygons.
More importantly, the Pythagoreans actually proved the surprising (at the time) fact that square root of 2 is irrational, with great consequences for subsequent development of mathematics. Based on Rabbi Meiselman’s reasoning, this is evidence that the Pythagoreans were given access to a divine revelation on mathematics.
The bottom line here is that it does seem very odd to try to prove that Chazal were ahead of their times because they used a very crude estimate of pi. The Rambam is trying to explain why Chazal used such a crude estimate when better estimates were available. He is not in any way making a claim that they were ahead of their time in mathematics. This is Rabbi Meiselman’s chiddush and I’m not sure why it should be immune to criticism just because he is attempting to use a statement of the Rambam to make his point.
David, let me guess… you’re not expert in the Rambam, am I right? I say that because the Rambam said what he did as a definitive fact, that “this thing from its very nature cannot be determined and in its essence cannot be known.” And you reduce that to “conjecture.” To him it was like knowing the day is 24 hours long, it was just a fact.
Your second paragraph is a non sequitur, and the third adopts the strawman argument I mentioned in my piece, as I’ve pointed out elsewhere. Chazal were ahead of their times because they knew Pi was irrational, plain & simple.
I don’t see the issue, personally.
The Rambam “knew” that the exact calculation of Pi was beyond the ability of Chazal to use for practical halacha, whether the number was “rational” or “irrational”. As we know in halacha, after a certain point differences in size or measurement become immaterial (for example, your Tefillin needing to be perfectly square). Therefore Chazal chose to use an approximation that works in Halacha.
Even had the 12 billionth decimal place been repeating (and Pi been “rational”), Chazal and the Rambam would have come out with the same result and statement.
P.S. I see the shittos of Rashi and Tosfos in Bava Basra, Daf 102a to be more typical of secular knowledge awareness at the time. If they were not aware of the Pythagorean Theorem, and did not bother to check their calculations by taking out a ruler, why should we think Amoram 700 years earlier would have a different knowledge basis and a different method of proof?
The Rambam’s language is very specific — by its very nature, the value of Pi cannot be known. He did not offer a “conjecture” as David said, nor did he say “it’s immaterial.” He said it can’t be done. That’s the definition of an irrational number.
“Why should we think?” Because the Amoraim were 700 years closer to Sinai. The idea that Chazal lost other types of knowledge faster than Halacha certainly makes sense, and if so we have no idea what was lost when. But again, I don’t see that as relevant. Even if they did not know the Pythagorean Theorem, the Rambam says they used an approximation for Pi because it cannot be known precisely. That was an astounding statement even in the Rambam’s day.
Rabbi Menken is correct that he likely intended that pi is irrational. A repeating decimal can be represented as a finite fraction.
However Rabbi Menken is wrong that this was an astounding statement. The discovery of both irrational numbers and pi occurred well over 1000 years before the Rambam. Even in Chazal’s time, no one with any knowledge of mathematics would have been surprised that pi is irrational given that no one could find an equivalent fraction for pi. What was lacking was a proof, and the Rambam had no proof either, which is why his statement remains nothing more than a conjecture. Again, greatness of mathematics consists of supply novel proofs, not fairly conventional conjectures.
David, again — Lambert’s colleague Euler believed it to be irrational. That obviously tells us that this was by no means known.
And you are mistaken because you think the only way to know something is via a mathematical proof. The idea that it might be revealed by G-d in the Torah isn’t on your radar — but of course, it should be! The Rambam did not need a mathematical proof, and that is what makes his statement so astounding. He told us that he knew it, and implied clearly that Chazal knew it, and none of them had a mathematical proof.
Mathematicians don’t run the world. “If you didn’t prove it mathematically, you don’t know it” simply isn’t true.
Dear Rabbi Menken
I am a fairly frequent reader (and slightly less frequent commenter) on both this and RNS’ blog. I really must say that to an outsider such as myself this all looks like a case of two Rabbis bickering with no substance to the discussion. Neither of you appear to give any real thought to the possible correct interpretation of each other’s words, but merely assume that the other is in the wrong and then interprets their words as such.
Case in point. You never clearly said that the Gemara’s phrasing “proves” that Chazal knew that Pi is irrational, but RNS seems to have assumed you meant such. RNS never said that to assume that Chazal did not know that Pi was irrational is “hilarious” however you seem to assume such.
So basically you both agree that the Rambam believed Chazal to have known that Pi is irrational, you both agree that that may well have been the case. Case closed… or it should be.
Most any argument could, of course, be considered that way, but I simply used this as an example of why even his factual statements cannot be trusted, much less his depictions of what others say! There’s a reason why he resorted to the tenor he did, and called me a “charedi polemicist” as if that were somehow relevant.
I confess that I am not understanding in what way you are equating his use of a straw man argument with something that I said. I quoted him precisely: “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!” That is what he called “hilarious,” in black and white.
And that is a straw man, as neither RMM nor I ever asserted that Chazal’s use of three simply “must have been because they knew” and proved their wisdom. The Rambam, on the other hand, says this as a factual matter, not to prove anything to anyone. Since it can’t be known, he said, they used three. It is the Rambam’s confident assertion that the value of Pi cannot be known that is extraordinary.
Thank you for your response.
You are being somewhat vague. I agree that you did not state that because Chazal say Pi=3 that proves they knew it to be irrational. I also agree that (from your quote) the Rambam seems to have believed that Chazal did know that Pi was three and that is why they did not attempt to quote it accurately.
What you are not clear about is whether you think the Rambam believed that the fact that Chazal wrote Pi=3 proves that they knew it to be irrational. Is this something you believe?
I think it is pretty clear (again only from the quote you provide, I am no maimonidean scholar) that there is no reason to assume such. It could well be that despite the fact that the Rambam believed Chazal both to know Pi to be irrational and that to be the reason of their quoting Pi=3 that the fact they quote Pi=3 is not a proof that they knew Pi to be rational.
That A caused B does not imply that B is proof of A. Many things could cause B it just happens to be in our case that it was A that caused it.
If you agree that the Rambam does not imply that there is a proof from the statement Pi=3 that Chazal knew it to be irrational then you have erected a straw man against RNS by implying him to find the Rambam hilarious. He does not find the Rambam (or in fact you) to be hilarious, he finds a straw man to be hilarious. I personally find them to be more tiresome than hilarious but there you are.
You’re moving the clauses around in a way that neither the Rambam nor the writer did — at least, not until I called him for terming the Rambam “hilarious.” That is when he erected a straw man: “Yet Rambam does NOT say, however, that the fact of Chazal using three proves that they knew it to be irrational.” No one said otherwise. That would require that Pi being irrational is the only possible explanation for estimating Pi as three, and no one has offered or defended that assertion. That appears prima facie to be an untenable position — there’s no other, plausible, workable explanation for why they used three for Pi? But that’s not what the Rambam said, nor is it the position that the blogger chose to ridicule.
Let’s return to what they actually said, and work from there.
What the Rambam says, and this is all I have said all along, is since the value of Pi cannot be determined precisely and will always remain an approximation, they took a round number. See Pirush HaMishnayos, Eruvin 1:5. That’s a reasonably precise translation if we understand Mispar Gadol to mean round number, which, in context, I believe we agree that it does.
I think it obvious from this statement that the Rambam both knew Pi to be irrational, and believed that Chazal knew Pi to be irrational. How else could we understand his words, if not that Chazal used a round approximation because it’s impossible to be precise? Note, again, that he does not say that writing Pi=3 proves it’s irrational, it’s that their choice of such a gross approximation (rather than the much more accurate 22/7, which was apparently well known) is because no one will ever produce the precise and final value. The obvious implication, of course, is that they knew that.
This conforms precisely to what the writer held up as “hilarious:” “Chazal … presented Pi as being three, because this must have been because they knew it was an irrational number and cannot be expressed exactly.”
Then, when I called him on it, he erected the straw man that you are asking if I support, which, of course, I never did, and do not. Capiche? Atah Kolet?
Rabbi Menken: Ramba”m, unlike Rabbi Meiselman, is not suggesting that Chaza”l knew anything their contemporaries didn’t. He is, after all, addressing the question of why Chaza”l chose to use 3, rather than the well known and much more accurate 22/7 as an approximation (by the way, what you have translated literally as ” a large number” would be better translated into modern terminology as “the integer part”–3 after all is not usually considered a large number). While there was no proof that pi was irrational until the eighteenth century it was widely suspected by the Greek mathematicians–it is related to the notorious problem of “squaring the circle”; i.e. constructing a square with the same area as a given circle with straightedge and compass. While the Greeks had no proof of impossibility, it was well known that even their best mathematicians didn’t know how to do it. For example, Archimedes, who died 45 years before the Maccabean revolt, wrote that he thought it was impossible, and offered rational approximations closer to pi than 22/7, and his works were well known in the time of Chaza”l.
Mike, the Rambam isn’t saying anything at all about others. He’s simply saying a fact unknown outside the Jewish world. Others dispute your assertion about Greek mathematicians, they discovered the concept of irrational numbers but did not know that Pi was one. As I point out in an update to my piece, Lambert was inspired to prove it irrational by a colleague who believed it to be so. This clearly indicates that it was not a common belief, much less common knowledge, of mathematicians even in the eighteenth century.
I agree with you about “large number,” but that is the literal translation of Mispar Gadol or Cheshbon Gadol. I was going to use “round number” but figured someone would complain. He means a coarse, rough estimate number.
Rabbi Slifkin claims Rav Meiselman distorted and misquoted Rav Soloveitchik’s “words” from The Emergence of Ethical Man. I was wondering if you or someone else could address Rabbi Slifkin’s claim.
Additionally, in your review, you do not respond to Dr. Aviezer’s criticism that Rav Meiselman failed to cite the retraction of the CERN study about the speed of light. Additionally, Rav Meiselman claims the Big Bag Theory made no predictions that have been confirmed. Dr. Aviezer points to the background energy in the Universe. (I learned of this discovery at least a decade ago and always heard it as confirming the Big Bag Theory.) You say that Rav Meiselman is not trying to put down science but is trying to show the greatness of Chazal. But nonetheless, Rav Meisleman cites the original study and makes his claim about the Big Bag Theory. Should he not have cited the retraction of the CERN study and addressed the question about background radiation?
I use “words” in quotation as not everything necessarily came from the Rav, or maybe it was edited. (Rav Meiselman believes that these books should not have been published. Dr. Tova Lichtenstein, the Rav’s daughter, was in charge of the series, and that serves to counter Rav Meiselman’s opinion. Only at techiyas hameisim will we know who was correct.) Rav Meiselman however does try to work with the book and thus we can question whether he presented the views in it accurately.
When an individual demonstrates that he’s not a rational actor, that he’ll resort to straw men and distortions in lieu of a sober conversation, rational people move on. You should know that Rav Meiselman is not difficult to find if you would like his response on any issue.
I no longer have a copy of Dr. Aviezer’s piece in front of me. As you know, it takes much less time to make a statement than to consider and rebut it. But I don’t see the relevance. Rav Meiselman did say that we “don’t know how this will bear out,” implying he was unaware of the retraction. But he was making a larger point about the transitory nature of scientific theories. That is not “putting down” science — it is the “nature of science” that new discoveries upend old theories. As you know, in my review I found that Dr. Aviezer seemed to overreach to try to avoid this reality even on tangential issues, such as whether general relativity “invalidated Copernicus” or Newton’s Law of Gravity — where quotes from Einstein himself confirmed he agreed with the view espoused by Rabbi Meiselman.
Rav Meiselman himself points out that the discovery of the background radiation in 1964 is what gave the Big Bang theory traction (p. 268). Again you would have to ask him what he meant about predictions.
Is this to say that we can’t come to any conclusions when Chazal say something that does agree with science? After all, it is the nature of science that new discoveries upend old theories, and we may discover something that contradicts what we previously thought.
It’s a good question. I have heard that Rav Meiselman doesn’t have much interest in the Big Bang theory for this reason. Personally, I can’t read the Ramban on Breishis 1:1 without seeing a description of the Big Bang in rabbinic language. But if they decide the Big Bang was wrong tomorrow, will that change our Emunah? That’s the key issue, really.
Rabbi Menken, the words of the Ramban in the first chapter of Bereshis are firmly esconsed in ancient Greek science, the valiant efforts of Dr. Schroder to read Big Bang theory therein notwithstanding. The Ramban is clearly talking about physical spheres which surrounded the Earth, which were opaque at one point, and the “light elements” thereof concentrated in one place on day three allowing external light to shine through. This is a far cry from Big Bang, although it does demonstrate the creativity needed to bridge the gap between the model of science one assumes to be most correct (in Ramban’s case the Greek model) and the Torah. That creativity can serve as a model for bridging the gap with modern scientific ideas, so long as doing so is not in of itself defined as heretical.
Eli, I don’t know what you mean, and have not read anything Dr. Schroeder says on the topic. I think you’re looking at a different element of a very long Ramban — part of which sounds incredibly familiar to anyone who knows about the Big Bang: a small dot with no physical matter, just pure energy to create things, and from that one dot everything was formed. It sounds far more like the Big Bang than it sounds like Vayehi Ohr, yet the Ramban says this is exactly what the pasuk means.
The fact that the Rambam said he (and, according to him, Chazal) “knew” that pi was irrational has nothing to do with proving it formally and mathematically, which is what Lambert accomplished in the 1700s. There are a lot of scientific ideas that were discussed as a being “known” before they were technically and formally proven. Put another way, the Rambam saying he “knows” something doesn’t mean he was familiar with the absolute mathematic proof discovered 600 years later.
As long as we’re quoting peirush hamishnayos, it’s ironic that in the Introduction the Rambam himself famously states that he freely took ideas from philosophers and secular sources throughout his peirush, but didn’t indicate where so that they would not be disregarded, and that one should accept the truth regardless of its source!
(For what it’s worth, the Rambam’s answer does seem a little strained – that chazal used a less accurate figure (3) rather a widely known far more accurate one (22/7) because the exact number to the millionth decimal point is unknowable?)
I think you haven’t been reading! The scare quotes around “knew” are foolish. The Rambam said he knew, full stop. He also said Chazal used three precisely because this was so.
You are obviously right that this is different than proving it mathematically, but then you jumped to saying that “lots of things” were known before they were proven. Please reread the post and comments, because it is clear that in Lambert’s day it was not known that Pi is irrational. One of his colleagues believed it to be true, and later Lambert proved it.
Given that it was not known even in Lambert’s day, it is certain that this has nothing to do with philosophical ideas used by the Rambam. And of course, he indicated that this fact was so obvious to Chazal that it was the reason they used three.
And I would say on the contrary, the fact that 3 1/7 was commonly known means Chazal used three for a reason — the Rambam gives the reason. Again, “since the value cannot be known precisely, they used a round number approximation.” The point is that no matter how many digits past the decimal point you use, you’re still using an estimate.
Remember they are talking about using rods or poles one tefach wide for Eruvin, which are D’Rabbonan. So they say a rod with a circumference of three tefachim qualifies for their purposes.
“As long as we’re quoting peirush hamishnayos, it’s ironic that in the Introduction the Rambam himself famously states that he freely took ideas from philosophers and secular sources throughout his peirush, but didn’t indicate where so that they would not be disregarded, and that one should accept the truth regardless of its source!”
The rambam says no such thing in his introduction to mishnah. He says this in his introduction to his shemonah perakim before pirkei avos in reference to ethical statements made by philosophers. If anything this militates against you- if he specifically mentions this by his shemonah perakim regarding avos the clear implication is that for the rest of peirush hamishnayos he stuck to Jewish sources.
This is a perfect example of someone being totally confident yet totally ignorant.
I support aspects of RNS’s ideas, but believe R. Menken is correct on the names point. There was a similar issue which Prof. Marc Shapiro conceded to R. Gordimer(I believe R Avi Shafran likewise avoids names at times for this reason):
“He (A. Gordimer) not only attacks the Open Orthodox rabbis but also shows his contempt for them by generally refusing to even mention their names. Instead, he refers to an unnamed Open Orthodox rosh yeshiva or rabbi and you don’t know who he is speaking about until you click on the link. I realize he doesn’t respect these figures, but to even deny them the simple courtesy of mentioning their names, as if to do so is muktzeh mehamat mius, is in my opinion simply disgraceful (albeit a common writing style in the haredi world).”
“With all due respect, Dr. Shapiro has it completely wrong. My essays are about ideas, not people, and I thus attempt to leave out names to the greatest extent possible. Omission of names is not a form of contempt; on the contrary, it is a way to show that the discussion is about ideology and not personalities.”
Dr. Shapiro conceded the point in the comments.
(“Response to Dr. Marc Shapiro: Good Shot, but Wrong Target”, Cross Currents, 2/19/16).
BTW “He Who Must Not Be Named” is a reference to a pro-slifkin blogger from 10 years ago who collated different sources; google “He Who Must Not Be Named and torahandscience.blogspot.com”
I hope that I will not be accused of restating what has been already stated but I think that we should remind ourselves that the conflicting points made in these arguments are really at their core restatements of the arguments between the Anti-Maimonidians and the Maimonidians.
Perhaps we should remember the sad conclusion when according to Rabbenu Yonah, z”l, who deeply regretted anti-Maimonidian stridency when he saw the destruction of twenty-four wagon loads of Gemorahs in the same place where the Rambam’s seforim had been burned by the French saw the destruction of the previous wagon loads of Shasim as a divine judgment. ( I don’t know when he wrote his Shaarei Teshuvah but in that sefer there is what appears as what I think is a unique prescription for a possible way to attenuate a Chillul HaShem by performing an act of Kiddish HaShem.)
The modern descendants of the Anti-Maimondians attempt to deligitimize their opponents and the modern Maimonidians sometimes respond vehemently.
I think that this debate is really about Sociological boundaries within Orthodox Judaism and whether those who do not accept that Chazal had advanced scientific knowledge through Ruach HaKodesh (and behind this all is the issue of the place of Kabbalah in Judaism) are “true” Orthodox Jews. (However it is a somewhat lop-sided debate as the Maimondians do not seek to deligitimize the Anti-Maimondians.) The Maimonidian viewpoints were ascendant in the recent past and the Anti-Maimonidians seem to be currently ascendant. However only G-d knows the truth and the debate will not be resolved by bullying or by incivility and deligitimization of fellow Yirai Shamayim.
What you refer to as the “Maimonidians” in the present discussion is the side trying to tear down a clear statement by Maimonides.
Someone pointed out to me that if you think your “Maimonidians” do not seek to deligitimize [sic] the “Anti-Maimonidians” then you didn’t read the blog in question much, or have an interesting way of defining delegitimize. If you did not recognize him attempting “to diminish or destroy the legitimacy, prestige, or authority of” either myself or Rabbi Meiselman, something is amiss with your reading or comprehension.
Regarding what you said about incivility, yes. I was very disappointed, as I said, and much as I think he is wrong, I have attempted to demonstrate that his attacks upon me were false — and ended up encouraging people to belittle a statement of the Rambam — without returning the falsehoods and ad hominems.
I want to point out one more aspect of the Rambam’s statement which is inconsistent with the blog post. The premise of this post is the the Rambam stated that he knew something that others of his time did not know. However, the Rambam himself says the opposite in part of the commentary that Rabbi Menken ellided. He says:
“You must know that the ratio of the diameter of a circle to its circumference [pi] is unknown. It is impossible to state its value precisely. This is not due to ignorance on our part, as the foolish think, but because by its nature it cannot be known and it is impossible to know.”
So the Rambam himself says that the knowledge he is imparting here is only disputed by the foolish and known to any intelligent person. This contradicts the entire thesis of Rabbi Meiselman and Rabbi Menken.
David, you’re being persistent beyond what my time allows, but I’m glad you pointed it out because it is quite the opposite. “Ignorance” is not a correct translation for “chesaron yediah,” which means “lack of knowledge.”
At what level is a “fool” who spends his time pondering mathematical proofs? If this were known to any intelligent person, why would the Rambam bother to mention “foolish” exceptions?
Without the mistranslation, the Rambam’s intent is obvious: “this is not due to lack of knowledge on our part, as the foolish think.” That implies that this foolishness was the common belief among educated people, who were trying to determine its value.
Note that in the Vilna Shas the translation from Judeo-Arabic does not say “foolish” but “the group called Gahaliy’ah.” This appears to be the Arabic word Jahaliyyah which the translator did not comprehend. It is an Islamic term meaning “ignorance of divine guidance” or “the state of ignorance of the guidance from G-d.” To Arabs, it meant the entire Arab world pre-Islam. So what would a religious Jew mean when he meant “those ignorant of divine guidance?” Who among the non-Jews of his day would not qualify as “ignorant of divine guidance?”
You opine that the blogger mocks the Rambam’s claim that Chazal understood pi to be irrational. Not at all: he’s mocking inferences like “Chazal possessed knowledge of the physical world beyond what was known to other cultures,” a claim the Rambam citation does not make.
The Rambam clearly implies that Chazal knew this. The fact that most others did not is an historical fact, and David Ohsie pointed out the passage in which the Rambam says all the Jahaliyyah don’t know this to be true.
I have no quibble with the idea that Chazal knew (lacking only a rigorous proof) that pi is irrational. I have a hard time believing that between them, the Arabs, and the Greeks, that they were the sole possessors of this knowledge. Sources, anyone?
I hope your bar mitzvah was a success.
R. Slifkin has asked me to post a correction: what he is mocking is the assertion that you can use Chazal’s statements in this topic to PROVE that they knew Pi to be irrational, which assertion can be inferred from R. Meiselman’s words: “The very fact that Chazal did so (approximated Pi) indicated to him (Rambam) that they knew it to be irrational.” R. Slifkin takes issue not with the Rambam, but rather with what R. Meiselman infers from the Rambam.
Thank you. For those who don’t know, the back story is that after a dialogue in the comments to this article on my Facebook page, I told NS early on Friday that I could not discuss it further that day due to the Simcha, and please wait for Monday. He refused, and called it a “cop out” that I would not continue discussing it right then. I repeated that he was rehashing and again said the dialogue would have to wait. And again he persisted. Finally I warned him that if he persisted again I was going to have to ban him off my wall, and of course he persisted. Elly what I cannot comprehend is why you would be his lackey.
In any case, I see nothing here that isn’t found in your comment of May 27, 2016 at 10:57 am, except a modest change in what it is you claim he is mocking — from the general statement that “Chazal possessed knowledge of the physical world beyond what was known to other cultures” to the specific example.
We are not discussing a mathematical proof, but whether the Rambam knew a fact about the natural world centuries before mathematicians came to the same conclusion, and whether the Rambam implies that Chazal also knew this to be the case. Both of these are obviously true.
We understand that people say things like “I know Hillary will never be president” when they don’t know, they only have a guess. But in an academic context when someone says “given that X is true” and then goes on to derive other things from that fact, it is quite certain that the person does know that information, or is deluded.
Only in the case of the Rambam does he insist that the Rambam doesn’t know what the Rambam says he knew!
Was that remarkable? Yes. As stated earlier, it is quite clear from the historical record that Pi‘s irrationality was not common knowledge at the time Lambert proved it, and certainly not when the Rambam confidently stated that it was so.
The field of mathematics did not leap forward in the centuries between the Gemara and the Rambam. It stretches credulity to imagine that Chazal made a rough estimate for no known reason, the fact that Pi is irrational then became common knowledge, and the Rambam then projected this common knowledge back upon Chazal. Yet the Rambam clearly says SINCE Pi is irrational, Chazal chose a round number.
NS is trying to walk back his mockery to something which might actually make sense. He is failing because it’s impossible to read the Rambam any differently. Perhaps mockery was a bad idea to begin with?
At the end of the day — why are you trying to bring his irrational “rationalist” silliness and mockery to a journal intended for mature adults?
RMM quotes other scholars (one of whom was contemporaneous with the Rambam) in his footnotes, who also declared that is irrational. Was their knowledge also divinely inspired?
Why the snide question? There was, as RMM specified, a singular source, the mathematician al-Biruni, who also stated clearly that it cannot be specified as a fraction. There is also speculation that an Indian scholar five centuries earlier said the same. But it was by no means a common belief or conclusion, and the Rambam takes it for granted both that Pi is irrational, and that Chazal knew this. According to the Rambam, the reason Chazal used such a round number approximation was that one could not specify it precisely. Not a speculation, a statement of fact.
Note also RMM’s footnotes also include the following: “while I have quoted the Rambam, many other Rishonim say the same thing independently, and it is taken for granted in many rabbinic sources.” A select few mathematicians were debating this, yet the contemporary Rabbinic world took it as established fact.
“You’ll all know who he is, but I’m not going to link to the post for a different (yet similar) reason than I didn’t link to the viral video of yesterday — I hope he’ll regret posting it, because he should, even if he doesn’t yet.”
It’s quite obvious that he’s not taking anything down. Why not just end this silliness and post his name anda link? I personally have found the discussion about the Rambam’s take on Chazal’s take on Pi quite stimulating. But I have had to wade through pages of ad hominems and insinuations to try to get it.
I am not blaming anyone or claiming that one side or the other is responsible for the silliness. I’m simply saying that not naming Dr Slifkin and linking to his blog post has had the effect (irrespective of whether it was intentional) of making it harder to gain clarity on the substantive subject at hand.
I agree in retrospect that some readers perceived the omission differently than I intended, although I stated my intent in my original post. But the cows having left that particular barn, I don’t feel now is the right time to go back and change it.
Are you saying that when the Rambam says that he and Chazal know Pi to be irrational, he means he knows it as a fact (i.e. as if it were proven), but when he refers to the mathematicians in the very same paragraph, he means that they just believed it, like Euler? That is certainly a chiddush, even without considering the Rambam’s rationalist worldview. It is much more likely that the Rambam, as well as the mathematicians, believed that Pi was irrational, in the sense that a mathematical proof had not been established at the time.
I quote Rambam’s reference to the mathematical scholars below:
It’s not a chiddush at all, it’s what the Rambam says. You mistranslated the first phrase of the passage about scholars: “But it is possible to know by approximation, and the scholars of…”
So they were trying to get more and more accurate figures. The Rambam says explicitly that the foolish (Jahaliyyah, perhaps non-Jews) believe it to be a lack in our knowledge, whereas in actuality Pi cannot be known precisely. He says that as a fact, and says the fools believe otherwise.
Dear Rabbi Menken,
I very much appreciated your review of Rav Meiselman new book in Dialogue. I’m glad to see I was “mechaven” to some of the criticisms you raised with the previous published negative reviews.
I sincerely regret the unwarranted abuse and defamation you received as a result. The mere fact that you made any positive reference to Rav Meiselman and his book made you a target of unmitigated on-line put-downs and insults. Welcome to the club!
I also very much sympathize with your innocent attempt to clarify matters and defend yourself from the most egregious misattribution, in the face of vitriol and personal animosity unleashed against you by Dr. Slifkin. It was as if the very mentioning of the personal nature of his unwarranted attacks made you even more of a target for him to act out further.
I am trying to clarify matters on my blog as well and posted the following:
This refrain of the question, “is there proof…?” is already buying into Dr. Slifkin’s clever straw man.
Rabbi Menken never claimed there was a proof, nor did Rav Meiselman.
The following points are being made:
The Rambam knew with certainty that pi was an irrational number and that the number given by Chazal — 3 — is not at all the value of pi.
But instead of attributing a gross geometric error to Chazal, the Rambam turned it around and attributed to Chazal that same definitive knowledge the Rambam had — that pi is an irrational number.
As another commenter pointed out, the Rambam took it completely for granted that 1) Chazal would not make such a gross error and 2) he also took for it granted that Chazal possessed knowledge that we, today, would consider quite advanced for Chazal’s time.
Notice the term “proof” or “proved” was not invoked once in that entire paragraph.
Now if you a) trust the Rambam’s attribution to be accurate (as most traditional Jews would) and b) knowing the history of mathematics and the almost complete lack of documented certainty regarding the true nature of pi, then that combination, for us, is an impressive claim the Rambam is making about Chazal.
Obviously, the evidence is “internal” — meaning, you wouldn’t use the Rambam’s statement about Chazal’s knowledge to convince a skeptic. Rabbi Menken emphasized in his review of “Torah Chazal and Science” that it was written for ma’aminim Bashem UbaTorah.
But Rav Meiselman now goes another step and speculates that perhaps the Rambam himself only felt convinced of the irrationality of pi because Chazal chose to employ an approximation.
Rav Meiselman speculates that the fact that Chazal did not supply an exact number may have indicated (not proved) to the Rambam that the value of pi cannot be an exact number in principle.
In other words, The Rambam may have felt — for whatever reason — possibly halachic — that if Pi had a specific value, Chazal would have certainly used it instead of an approximation.
So if one were to understand that the Rambam’s own basis for the definitive knowledge that Pi is irrational comes from this inference (not proof) of Chazal’s use of an approximation, then again, from our perspective (not the skeptic’s) this would push the earliest documented knowledge of the irrational nature of Pi back to Chazal’s time instead of the Rambam’s.
The takeaway for me personally is a) seeing how the Rambam took it so much for granted that Chazal could not make a fundamental error in geometry and b) how much credit the Rambam gave Chazal regarding their knowledge of advanced mathematics — regardless if they were the very first or not.
I think Dr. Slifkin would do well to adopt the “Rationalist Rambam”‘s approach in granting Chazal the benefit of the doubt.
The source of the problem here with this whole back-and-forth I believe (beyond the obvious unresolved psychological issues he has with Rav Meiselman), is that Dr. Slifkin reflexively goes into “krum kiruv-bashing mode” whenever he even suspects something that sounds like a proof of Chazal’s Divine Wisdom is being claimed by a Kiruv rabbi.
He has apparently been so thoroughly jaded by the on-line skeptics he has unsuccessfully debated over the years that he now actively argues on their behalf against anything that even smells like a proof.
Those who have been reading J-blogs for a while know that Rabbi Menken was a favorite target of the “krum kiruv-bashing” crowd from way back when. How utterly sad that Dr. Slifkin has apparently been recruited by them to do their on-line Kiruv bashing and has adopted their crass, derisive mode of expression.
“He has apparently been so thoroughly jaded by the on-line skeptics”
It’s not just skeptics, but a legitimate dispute(R. Adlerstein wrote in the recent Klal Perspectives, “A rebbi who uses approaches developed by the kiruv movement decades ago might later learn that their effectiveness has long since waned or disappeared”.).
In R. Menken’s August, 2015 post(“Different Problems Require Different Solutions”), I’ve quoted both people who are in favor of proofs(R. Yaakov Salomon from Aish who himself is in favor, but says the dispute has been going on for hundreds, if not thousands, of years), and those who disagree(R. Moshe Benovits of NCSY, R. Jonathan Sacks). I imagine there is some nuance, for example, presenting something as an “argument”, as I mentioned there from R. Adlerstein.
I would argue that this “dispute” was driven (by people in the field, mind you) not so much by their pursuit of more intellectually rigorous proofs, but primarily because these proofs were criticized by the skeptics for their shoddiness and now those proofs are considered an embarrassment.