Wednesday, April 01, 2009

A Kiddush HaChamma Roundup

  1. An e-book on kiddush hachammah, as a roundup of nice blog posts on the subject. (from SerandEz and Hirhurim)

  2. First, some more on Birkat haChamma. On the last blog roundup, I suggested a nigleh reason for Kiddush HaChama. I may have been hasty in suggesting that particular one, for all sorts of deep, yet surface reasons are plausible. It could be to appreciate Hashem's creating of the sun, or the wonder of the complex yet perfect movements of the stars and planets. Gilui noted in a comment on that post:
    In Pirkei D'Rebbi Eliezer, the discussion regarding the sun is only part of a larger discussion which includes the moon, then moving on to a combined cycle which doesn't mathematically exist of 84 years. I would suggest that one shouldn't try to attach meaning to the ritual until checking out the bigger picture.
    Indeed, he put together a very nice site (link is to Chapter 6, but see it all) all about Kiddush HaChamma, with halachos, and an analysis of the math involved. Check it out.

    I will admit that I do not have the time or patience to want to read through the mathematical and astronomic analysis right now. So I don't know if he is correct or incorrect that this is an entirely and obviously fictional calculation.

    He suggests that Chazal therefore had mystical reasons for wanting to arrive at the number 84, which is the mystical 7 times the mystical 12. Thus:
    Chazal knew this. There is no doubt, due to the arbitrary nature of the inaccuracy. The very plain goal of the entire chapter of Pirkei D'Rebbi Eliezer is to arrive at the number 84. So let us look at the number.


    Chazal wanted to hint at something by creating an 84 year cycle. It hints at its factors, which are cycles of their own: 7 and 12 years.
    It strikes me, if it is indeed inaccurate, that it might be a legitimate mistake. Perhaps a mistake in calculation, which would not be detected readily because of the long time span from the beginning of the cycle to the end. Or a typographical error which cascaded. I would not assume that Chazal would deliberately mess up the calculation, when the goal is presumably to accurately hit a specific time for a halachic purpose.

    Also, as I wrote in a comment on the previous roundup post, are we really taking about Tannaitic Chazal here? After all:
    In terms of Pirkei deRabbi Eliezer, this returns to the question of its date of authorship. If it is Tannaitic, from the Tanna Rabbi Eliezer, then it is giving deeper insight into the meaning of this bracha. If it was composed shortly after 833 CE, then it is post-Talmudic...
    I will add the following here. If this is really Chazal, or whoever the author of Pirkei deRabbi Eliezer is, hinting to us at something with deep mystical significance, then we should not expect other folk to be using this fictional 84 year cycle. And yet, it seems to have been pretty standard even outside Jewish circles. To cite Wikipedia on the lunisolar calendar:
    Rome used an 84-year cycle for Easter calculations from the late third century until 457. Early Christians in Britain and Ireland also used an 84-year cycle until the Synod of Whitby in 664. The 84-year cycle is equivalent to a Callipic 4×19-year cycle (including 4×7 embolismic months) plus an 8-year cycle (including 3 embolismic months) and so has a total of 1039 months (including 31 embolismic months). This gives an average of 12.3690476... months per year. One cycle was 30681 days, which is about 1.28 days short of 1039 synodic months, 0.66 days more than 84 tropical years, and 0.53 days short of 84 sidereal years.
    Maybe we can say that they got it from us. After all, we are talking about Easter calculations, and early Christians. But surely Rome had people skilled at astronomy and mathematics. If it really is entirely fictional and does not accord with any kind of calculations, why would they use it, and not simply discard it?

    Therefore, I would not leap to the conclusion that some deep mystical reason exists for the 84 year cycle.

    (The Julian calendar also uses the somewhat inaccurate approximation of 365 1/4 days, just as in PDE, and not in order to obtain some mystically significant result.)

    Another interesting point: In terms of the fictional cycle, perhaps this is why we no longer do the birchat halevana and for the other signs of the zodiac in their tekufah. The standard reason given is that anan lo bekiin, and that has merit, since even as the world at large has better astronomical knowledge, the particular calculations they did may not accord with our modern calculations; or, we might say respectfully that we are not bekiin, when in truth, it was they who were not bekiin. And since we cannot fulfill the law in accordance with the metzius, we fazed these out. More on this later, perhaps.

  3. Also, the Seforim blog has a nice overview on birchat hachammah.

  4. And Yeranen Yaakov has a post describing how one should look at someone named Avraham when reciting kiddush hachammah, and mentions the Ostravtza Gaon on this kiddush hachammah falling on erev Pesach, though misstating the uniqueness of this event.

    Also, whether or not Rabbi Yehuda's position is that birchat hachamah is avodah zarah.

  5. For the event, JNUL has a bunch of kiddush hachammah material. Check it out. In particular, this poster from Chabad. Perhaps I will discuss it later.

  6. Thanbook on liturgies for blessing the sun.


Ezzie said...

I actually may have found a couple of those through you, so Yiasher Kochacha. :)

גילוי said...

As an aside, Baraita of Shmuel haKatan references the 84 year cycle, saying that he is writing at the completion of x number of cycles.

I recently uploaded a translation of chapter 7.

Here's the relevant part:

The total of the days of the lunar year is 354 days, 8 hours and 876 chalakim. All the hours of the lunar month are 708 hours and two thirds of an hour. All the hours of a lunar year are 8504 hours.

They start the paragraph by telling you that they know the exact value of 29 days 12 hours and 793 chalakim multiplied by 12, and then they finish the paragraph without the chalakim, which creates the cycle brought at the beginning of the chapter. In other words they explain the cycles without the background math at first.

Anonymous said...

I was Just interested do you do the Ten crumbs or is it Just Boogy Woogy for you? I saw that Reb Moshe did not(new Haggadah in Hebrew) Just Something I would Like to Hear your Input on. and if you do do it is it because of Minhag Avosinu Biyadenu

joshwaxman said...

I am not taking an official position on it.

However, the following is my general impressions, from what I've seen.

1) I do indeed have someone put out ten pieces of chametz, following what my father does. The person writes down the places the pieces were put, just so that if I somehow don't find one, we will know where it is.

2) The reason is presumably concern that the bracha would be levatala. If the person really searches, it would not be levatala, even if he did not find.

3) It might also be based on the gemaras talking of a person leaving 10 and finding 9, but as I understand it, that is either reading present practice into the gemara, or else present practice evolved from misunderstanding that gemara. Rather, it is placing them down *after* happening to find them, and then discovering a change in number, I am pretty sure.

4) I am also unhappy with the idea that one may not speak until he finds the first piece of chametz. I don't think this is so. And especially with people grunting rather than saying things necessary for the bedika.

5) While I clean the house as best I can prior to bedika, I am usually very swamped, so there are real chances of finding some chametz anyway during the bedika.

Why do I put it out? A combination of minhag, it doesn't hurt, and that it can be fun for the kids.

But of course, this was all off the cuff. Interesting about Rav Moshe. Thanks.


yaak said...

Great round-up!

Re: misstating the uniqueness, I realize it was misstated, and I have another post on that whole topic.

The Thanbook link has a great link of Nusha'ot that is very cool:

Anonymous said...

By the way since I started I will take it up a level with a Kaf Hachaim on Birchas Illonos on Shabbos.He says you can not make the Bracha on shabbos because of Borer. Now if your like me you say WHAT BORER BY BIRCHAS ILLONOS? so he explains You are separating the Klipos.I discussed this with someone as it makes for good table talk(;he said Lishtosoi you cant eat on Shabbos because you are also Misakin the Klipos with eating? Someone at the table told me see Likutie Torah(Baal Hatanyah) on Chayah Sarah first piece you will have an answer see there for a real Kabbalistic answer which I don't understand. All Those that are interested "PUK CHAZI".I would love to hear your Take on the matter.

Anonymous said...

another Tidbit: Reb Moshe ate Erev Pesach Matzos . I always thought it was a chassidish thing?

גילוי said...

In response to this:

I will admit that I do not have the time or patience to want to read through the mathematical and astronomic analysis right now. So I don't know if he is correct or incorrect that this is an entirely and obviously fictional calculation.

I must say that I find it odd that you make almost an entire blog post about something that you don't have the time or the patience to learn :)

But as far as proving that it is fictional:

Chapter 6 does not discuss the year of Rav Adda, so there is no blaring proof that they knew that 365.25 isn't accurate. Chapters 7 and 8 do mention the Ibbur cycle.

All you need for confirming that the rest is a major kvetch is the paragraph that I posted in an earlier quote, and the last paragraph:

The total of the days of the lunar year is 354 days, 8 hours and 876 chalakim. All the hours of the lunar month are 708 hours and two thirds of an hour. All the hours of a lunar year are 8504 hours.

In three cycles of the sun and four cycles of the moon, 84 years, which is one hour of the day of the Holy One, Blessed be He, the sun and the moon equalize, at the beginning of Tuesday night at the hour of Shabbtai at the hour they were created.

josh waxman said...

"I must say that I find it odd that you make almost an entire blog post about something that you don't have the time or the patience to learn :)
But as far as proving that it is fictional:"

How does the quote prove it is fictional? Is the math wrong, or is it an approximation? Can you elaborate?

I am willing to grant that it is fictional. Or rather, a rough approximation which is good enough, or else that they are trying to fit things into the calculation which don't work. Either way, my point is that "everyone else is doing it too." That is, the Romans also used an 84 year cycle, and so did the Christians. Or are you saying their 84 year cycle is different?

My point is that, as far as I understand it, I don't need to care if the cycle is fictional or not. Other people, not Jewish, used it. So either is actually is accurately counting something, or else it is not accurately counting something but is a good enough approximation for something. Since I would not attribute deep kabbalistic intent to the Romans, why should I do this for Pirkei deRabbi Eliezer?

גילוי said...


I gave you the quote. I will post it a third time.

The total of the days of the lunar year is 354 days, 8 hours and 876 chalakim. All the hours of the lunar month are 708 hours and two thirds of an hour. All the hours of a lunar year are 8504 hours.

There is a phrase in these prakim called Yadot Sha'ah, hands of an hour. If you compare uses, it turns out that they are equal to a third of an hour.

Earlier in chapter 7, it says the length of a month is 29 days, 12 hours, 2 ידות שעה, and 73 chalakim. Here it says 708 hours (which is equal to 29 days and 12 hours) and 2 ידות שעה. In one place precise, the other place, not.

Furthermore, it does acknowledge the difference between the solar year and the lunar year in chapter 7. I would personally find it hard to believe that they didn't know that after 84 years this difference would add up.

Please do not assume that I am attaching deep kabbalistic intent, as you call it, stam.

joshwaxman said...

I am deliberately being dense, because my underlying point is that I don't want this to get into a technical analysis of the math, and I don't think it *should* be a matter of the technical math. Rather, if they are calculating something that others (Romans, Christians) calculate as well, then it is no longer "fictional."

regardless, who says kabbalah existed at the time of PDE, and who says that post-Talmudic PDE reflects the belief of Chazal in formulating the bracha?

I'm about to meet with someone, so bli neder, I'll elaborate on this a bit later, and try to address your specific points.


גילוי said...

For what it's worth, Josh, you might have noticed that we comment on similar blog posts, debunking myths, etc. There is a reason for that, critical thinking on an intellectual level, and hopefully that we're both striving for truth, and point out falsehood where it is. I'm not going to argue about whether or not kabbalah existed, as I don't believe I can easily provide any convincing proof to you, but I am convinced, via proofs, that it did exist.

Regarding your initial point that it should or should not be a matter of technical math: Chazal made it "easy" so that (among other things) you wouldn't have to. I'm talking about the reasoning behind it. The meaning of an 84 year cycle is given as well. I'm pointing out that it is an unneeded drash, as there is a more precise one elsewhere in the work.

joshwaxman said...

To sum up and thus leave it as non-technical as possible, there is an internal inconsistency in PDE, in that in one place it mentions chalakim (=1/18 of a minute, or 1/1080 of an hour), while in another, it omits it.

If the problem is the chalakim, and the precision involved therein, in that 73 chalakim are missing, I would point out the following:

It does not seem that in early Jewish mathematical texts, they used a fractional base 10 system. Indeed here, we have how many days, hours, thirds of hours, and then chalakim. Elsewhere, in terms of calculating vessels of the mishkan, I have seen 1/2's, 1/4s, 1/8ths, 16ths, and so on. And they did not have Microsoft Excel, or calculators, to work with.

Before resorting to a mystical explanation, perhaps we should ask ourselves how much more complicated each line of calculation would be. Multiplication and division were not so simple in those days either. Is it possible that to simplify the calculation, an approximation was used. And they either figured that if there is drift, it does not matter since they are defining a system, or that they did not realize by how much the drift would be over 84 years? This seems eminently plausible to me.

The mark of many conspiracy theories is to show irregularities, and then allege that these must be the result of a conspiracy. But here, perhaps there were other causes -- laziness, the supreme difficulty of the calculations, or an attempt to arrive at the popular and known 84 year cycle.

all the best,

גילוי said...

Chapter 7 talks about intercalation. To say they simply wouldn't realize it seems like a stretch. They knew that 11 days were lost per year.

joshwaxman said...

The fact that there is a difference in 11 days between the lunar and solar calendars is well known, and would be well-known to them. Indeed, you can see the glaring different between the two calendars each and every year, and the difference is major -- 11 whole days.

Meanwhile, multiplying 73 X 12 for one year is hard to do, and then dividing it by 18 (did they have the concept of minutes) to get 44.something minutes is also very hard to do. The result, if you measure in 1/3s of an hour, is very hard to express. Even then, it is not a perceptible difference -- it is less than an hour every year. They would then have to multiply by 84 to get the number of 45 minute differences (or rather, 2 yedot shaa and Z chalakim) in 84 years, then change it into days, hours, minutes, etc. It is a lot of work. And it is not necessarily obvious up front that it would make a difference (even though of course it does -- 2+ days? -- if you want this precision).

Meanwhile, these might be "famous" calculations. The intercalation of lunar to solar years is famous. There might also be famous sources about calculating this "famous" 84 year cycle (and indeed it is famous, used by Christians and Romans), which is based on the approximation given. Was the author of PDE a mathematician, or was he a scholar of Torah and midrash, who was not trying to innovate but rather to give the calculations of the results of the calendar in use?

What if you saw the exact same type of approximation in the words of Aristotle? Such an approximation seems eminently plausible to me. Would you assume that there must be some hidden deep meaning.

The problem, to my mind, is that it is a rabbinic text, and we are trained to look for nuance and hidden meanings in such texts. But sometimes the true meaning is indeed the surface level, and texts of this sort are "flawed."


גילוי said...

So you confirm that the difference of 11 days was obviously well known. They can't multiply 11 times 84?

If 73x12 is difficult, why did they manage it just fine in the paragraph that I have already quoted 3 times? Rather, they introduced the inaccuracy at a level where they could have done more.

Yerushalmi Brachot 1:1 (I forget the location of the corresponding Bavli) has the breakdown of times (and interestingly enough does not include chalakim at all, but rather units that are all 1/24 of the prior unit).

Regarding your last line, you have it backwards. I already learned something somewhere else, and I found confirmation in the midrashim on the cycles of the sun and moon.

joshwaxman said...

you see, now we are getting into the technical mathematical stuff. I didn't, and don't want to make it about the calculations, and double-checking their calculations.

If they are repeating existing calculations (perhaps from *different* sources), then it is explainable without resorting to any sort of deliberate miscalculation, or difficulty of figuring.

Maybe I miscalculated, but how does multiplying 11 times 84 help us? From what you said above, the problem in accuracy was the missing chalakim. The missing chalakim don't add up to 11 days per year; they add up to about 44 minutes per year. That would be multiplied by 84. Are you making a different argument about inaccuracy, or are they somehow related? You see how this is getting complicated? And I don't think the complication in the end is going to be relevant.

So they did manage to multiply 73 by 12. Good *first* step. Notice that the result is not something they need to divide and distribute into days and hours? They leave it as chalakim. Doing multiplication of *that* number, 876, by 84; and then dividing to find out how many days, hours, yedot shaah, and chalakim in *one* 84 year period, and other periods, is not trivial. We are talking about a different way of conducting multiplication and division, as far as I understand it.

And if they got from somewhere else that it is an 84 year cycle, the famous existing cycle in use by Christians and Romans, they might just give the calculation that works to generate the number they know it should be.

In terms of the last line, yes, when a ritual exists, people like to add all sorts of rationalizations for it, and those often supersede, more than merely supplement, the initial, true reason. For example, fish and meat, of course someone suggested a mystical reason for it. But according to the gemara, it is sakanta, or tzaraas. When some halachic sources suggest doing away with the prohibition because the sakanta is simply not present, these added, spurious rationalizations stand in the way, for after all, *this* is the reason. Yes, it is easy to read such a rationalization and then read it into an irregularity in the text. And I admit it is an irregularity. I still don't find it convincing. i would sooner say that the calculation via approximations was deemed acceptable, or that the calculation was simply flawed.

It really comes down to this: What do you have to say about this:
"A cycle was then framed at Rome for 84 years, and generally received by the Western church, for it was then thought that in this space of time the moon's changes would return not only to the same day of the month, but of the week also. Wheatley tells us that, 'During the time that Easter was kept according to this cycle, Britain was separated from the Roman empire, and the British churches for some time after that separation continued to keep Easter according to this table of 84 years. But soon after that separation, the Church of Rome and several others discovered great deficiencies in this account, and therefore left it for another which was more perfect.'—Book on the Common Prayer, p. 40."

Here we have the exact same miscalculation. True, they did not reckon chalakim. But we have apparently the same 84 year cycle, precisely, as far as I can make out. And it is inaccurate. Was this Roman and Christian inaccuracy the result of deep mystical intentions? Or was it the result of miscalculations?

BTW, one of my planned upcoming posts will be whether, given the inaccuracies in kiddush hachamah, saying it nowadays is halachically problematic, as a bracha levatala.


גילוי said...

OK Let me give you a quick overview:

Chazal assert 365.25 solar year, and go on to explain how the sun returns to its position after 28 years.

Chazal assert that a lunar month is 29d12h793ch, that a lunar year is 354d8h876ch, and then that a lunar year is 354d8h, and that this creates a 21 year cycle.

The least common multiple of 21 and 28 is 84. The 84 year cycle is when both realign in the sky. So what I'm mentioning of 11 * 84 is that they knew that the 84 year cycle didn't exist. 84 * 365.25 days is not the same as 84 * 354.33 days, but rather it is 84 * (365.25-354.33).

So to recap, they fudged the numbers to get the 21, and then ignored the ibbur difference.

joshwaxman said...

Assuming this is correct, and they conflated the two year-units, didn't we lose some multi-billion dollar spaceship because some scientist in one place did not convert from feet to meters?

And assuming all this is correct, didn't the Romans perform the *same* fudging, only to eventually discover that it did not work?


גילוי said...
This comment has been removed by the author.
גילוי said...

I am asserting that they knew that they didn't match up when they wrote it. What you wrote about the Romans seems to be that they didn't realize it. The things you quoted in the blog post on lunisolar calendar are far more complicated in comparison to the math I gave.

joshwaxman said...

bli neder, I'll try to respond to you on Sunday. swamped at the moment.

good shabbos,

joshwaxman said...

yachol lihyot. i'm not convinced, as I have made worse errors on simpler calculations. And if he did not have an editor to spot the error, and if people treat it as holy text as opposed to one person's calculations, it is quite possible it would have evaded criticism and correction. Again, they are arriving in the end at an 84 year cycle, which is indeed a famous one.

Meanwhile, check out my latest post, in which I wonder whether these inaccuracies, and that what we will see next Wednesday will not be a Tekufah (vernal equinox), should preclude Modern Orthodox Jews from saying it, as a possible brachah levatalah. Of course, if one treats it all as fictional and mystical, then perhaps one can say this problem does not begin.


גילוי said...


There is what to say that it was inaccurate in the time of the Tannaim.

If you look at the difference between the scientific solar year length and the 365.25 day-solar year, you should be able to calculate back to when the two were in sync. That brings you the early 3400's.

joshwaxman said...

can you clarify what was inaccurate, and in terms of what?

thanks again,

גילוי said...

What do you mean in terms of what?

Perhaps you will find the answer that you are trying to get out of me here:

joshwaxman said...

sorry, it does not help; and while the linked to article is a nice theory, there are all sorts of convolutions that could be hidden in the calculations, or answered by other calculations. this all then approaches mathematical derash. which is why i dislike all sorts of "confusing" math to prove these types of theories.

did anshei knesset hagedolah establish Shmuel's calendar? Why is it attributed to him, and what relevance is there then that he was an astronomer? Is there any evidence that the Anshei Knesset HaGadol established the birchat hachama? Why not attribute it to them, rather than leaving it as an anonymous brayta? Also, this would require reading Abaye's clarification into the original intent of the brayta. Possible, but no means certain.

Is it possible, since this was the established calendar, that it was established by non-Jews, and the Jews signed on to it?

But you are right. It helps clarify that you were saying that the shift of the vernal equinox was already in place. So you are talking about this shift, rather than anything about an 84 year cycle.

What was the shift in the days of the Tannaim? Amoraim? Was it several weeks? Or was it less than a day? Are you saying that even then, it was not the "real" vernal equinox?

the year 3400 means a 2369 years ago. Which means, if we date the Tannaim to the year 70, a span of 300 years. How much shift occurs in 300 years? If my calculation is correct, 0.00462 * 300 is 1.386 days, which *might* not really be perceptible. How were Chazal determining what an equinox was? The days and nights being approximately the same length? Did they second-guess their calendar? Were people in ancient times celebrating the spring equinox in accordance with this rough calendar?

also, that they seem to believe that the sun is coming back to the precise position as maaseh breishis (and thus the 28 year cycle) seems to indicate belief that this calendar *was* accurate for this purpose. Or at the least, Abaye did.


גילוי said...

Measuring the equinox was known, see Eiruvin 56a, also where the inaccurate year length is given.

joshwaxman said...

please qualify the statement for me, rather than leaving it up to me to perform calculations. what exactly do you make of Shmuel's statements about tekufat nissan? Are those correct or incorrect. Short statements without definitive conclusions are not as helpful.

"Measuring the equinox was known"
but was it known by *Abaye*, who seems to be assuming that the calendar of Shmuel is precise??



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