Volume 33 Number 39
Produced: Fri Sep 1 6:45:04 US/Eastern 2000
Subjects Discussed In This Issue:
Accuracy of Molad
[Alan Rubin]
Gematria for Pi
[Art Roth]
Gematriot (2)
[Zev Sero, Warren Burstein]
Gematriot-Aleinu Leshabeach
[Gilad J. Gevaryahu]
Hebrew & Roman Calendars
[Jonathan Baker]
Lunar month
[Mike Gerver]
Pi and the Yam Shel Shlomo
[Zev Sero]
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From: Alan Rubin <arubin@...>
Date: Thu, 31 Aug 2000 15:51 +0100 (BST)
Subject: Accuracy of Molad
I would be grateful for an explanation of the accuracy of our tradition
for the time between two moladot and how it relates to the present
calendar.
Russell Hendel wrote:
> the Sinaitic tradition that the exact average lunar month is 29 days
> 12 793/1080 hours. As Prof. Rabbi Sholomo Sternberg points out in his
> book on Celestial mechanics this is correct to the nearest 1080th of an
> hour.
And Yisrael Medad wrote:
> the time between two moladot of the hebrew calendar is 29:12:793, as
> said, but the correct astronomical value is in our time near to half a
> second less
If the molad is calculated with a fixed period of 29:12:793 then over a
period of 1,900 years there should be a cumulative error of 21.8 hours
(based on an error of 1080th of an hour) or 3.3 hours (based on an error
of half a second)
The possibilities are then that either:
There is now a difference of at least 3 hours between the calculated and
observed molad.
or the error is much less than half a second.
or I have not understood how the calendar works and some correction is
made based on actual observation.
Alan Rubin
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From: Art Roth <AJROTH@...>
Date: Mon, 28 Aug 2000 11:49:58 -0500
Subject: Gematria for Pi
From: Daniel M Wells <wells@...>
> Just out of interest the posuk states the circumference was 30 and the'kav' -
> diameter was 10. Kav in the posuk is spelled Koof Vav Heh which is 111 in
> gematria. Next to it is written that the 'Kri'- the pronunciation should be
> Koof Vav without the Heh and thus 106 in gematria.
>
> The circumference is 3 times the diameter
> circumference = 3 * 111/106 = 3.1415 to 4 decimal places.
>
> Amazingly C=Pi*D in mathematics where Pi = 3.1415 to 4 decimal places.
>From our moderator, commenting on the above:
> [Not pi, but as mentioned in submission above, an approximation to pi correct
> to 4 decimal places. Mod.]
The above gematria produces an amazingly good approximation to pi; it
indeed gives 3.1415 to 4 decimal places. However, the true value of pi
(3.14159...) is actually 3.1416 to 4 decimal places. Thus, the
approximation is off by 1 in the fourth decimal place and is hence not
quite correct (as claimed above) to four decimal places.
Art Roth
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From: Zev Sero <Zev@...>
Date: Wed, 30 Aug 2000 18:19:41 -0400
Subject: Re: Gematriot
Gilad J. Gevaryahu <Gevaryahu@...> wrote:
> However, gematria sometimes caused things to be changed. An example
> which come to mind is in tefilat "aleinu leshabeach." The sentence
> "she'hem mishtachavim lahevel varik umitpalelim le'el lo yoshia" was
> erased [by the censor] from most sidurim in the Middle Ages, and lately
> found its way back into many sidurim. The line was censored because of
> the gematria of "varik." "varik" [vav, reish, yod, kuf=316] and so is
> Jesus [yod, shin, vav=316]. The Christians thought that the Jews spit at
> Jesus, since 'rok' means also spittle, and it was customary to spit on
> the ground during the recitation of this tefila.
One tiny little problem: the word is `veLArik', which adds 30 to the
gematria. What's 346 the gematria of?
Zev Sero
<zsero@...>
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From: Warren Burstein <warren@...>
Date: Wed, 30 Aug 2000 14:30:04
Subject: Re: Gematriot
>From: Gilad J. Gevaryahu <Gevaryahu@...>
>However, gematria sometimes caused things to be changed. An example
>which come to mind is in tefilat "aleinu leshabeach." The sentence
>"she'hem mishtachavim lahevel varik umitpalelim le'el lo yoshia" was
>erased [by the censor] from most sidurim in the Middle Ages, and lately
>found its way back into many sidurim. The line was censored because of
>the gematria of "varik." "varik" [vav, reish, yod, kuf=316] and so is
>Jesus [yod, shin, vav=316]. The Christians thought that the Jews spit at
>Jesus, since 'rok' means also spittle, and it was customary to spit on
>the ground during the recitation of this tefila. The double meaning,
>that is Jesus in gematria, and spittle in Hebrew had to do, according to
>some, with the spitting on the ground at that word. The Yiddish
>expression "er kummt tsum uysshpayen" means "he comes at the spitting"
>that is, to describe someone who arrived at the service as late as the
>concluding of the tefila at 'aleinu.' See EJ 2:555-558.
The line would be troubling to the censor without the gematria. The
"they" who "bow before emptiness and nothingness and pray to a god who
doesn't save" refers to the "goyee haaratzot" and "mishpachot haadama"
(nations of the lands, families of the earth) of the first sentence.
The censor, knowing he's part of "they", would have no trouble
understanding that it is his diety which is being spat at, even if he
can't add.
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From: Gilad J. Gevaryahu <Gevaryahu@...>
Date: Thu, 31 Aug 2000 09:19:07 EDT
Subject: Gematriot-Aleinu Leshabeach
Zev Sero was kind enough to send me a copy of his challenge to my post
(MJ v33n33) where I said:
Zev writes: << One tiny little problem: the word is `veLArik', which
adds 30 to the gematria. What's 346 the gematria of?>>
Most siddurim in my collection have "varik". To wit: Rinat Israel
(Jerusalem 1971), Ezor Eliyahu (Jerusalem 1998), Art Scroll, Shabtai
Sofer (Baltimore, MD 199?), Rome (Italiani, Rome 1964), Machazor l'Rosh
Hashanah v'Yom Kippur (Koren, by D. Goldschmidt, Jerusalem, 1970),
Siddur Ras Seadiya Gaon (Jerusalem 1985), Siddur R' Shlomo m'Garmaise
(Hershler, p. 125, n. 54), Keneste HaGedola (Yemenite, Tel-Aviv, 1978),
Siddur Yesod Malchut (Jerusalem). Some of the above are critical
editions.
Only one siddur in my collection has 'lelarik' as indicated by Mr. Sero
and that is Tehilat Hashem (Lubavitch). I suspect that the letter lamed
was added for the very same reason as my original post, that is to cause
the gematria to not equal Jesus, and avert the criticism. Therefore,
this is also a form of "censored" version, albeit a different one.
Gilad J. Gevaryahu
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From: Jonathan Baker <jjbaker@...>
Date: Wed, 30 Aug 2000 00:44:25 -0400 (EDT)
Subject: Hebrew & Roman Calendars
Eli Linas brings the gemara in Shabbos 75a that praises Israel for its
knowledge of astronomy, which ability raises us beyond other nations.
Rambam in Guide 2:11 bemoans our loss of mathematical and astronomical
ability. Granted that one needs some fairly sophisticated mathematics
(by medieval standards) to understand the calendar, what primacy is
Mr. Linas bemoaning? The Jews were never innovators. Our fixed
calendar postdates the Egyptian discovery of the 19-year cycle by 700+
years (ca. 400 BCE -> end of Sanhedrin in 325 CE). The gemara elsewhere
talks about the Jewish view of the Sun returning during the night above
the heavens, contrasted with the Gentile view that it returned under the
earth, and admitted that the Gentile view was more plausible.
Do you have some concrete evidence of Jewish primacy in mathematics or
astronomy beyond that of, say, the Greeks (who really innovated most in
mathematics)?
Daniel Wells says "indecisive much like the Muslim calendar of which
there are two versions: Egypt and Iran." I like the indecisiveness, and
bemoan its loss among us. When I asked a Muslim co-worker, "So, I guess
Ramadan is starting next Tuesday", he said "Or Wednesday, or Thursday,
we have to wait for the court in Mecca to tell us". It brought home to
me the loss of the Sanhedrin, that we no longer can rely on the
Divinely-ordained method for fixing the calendar, and have to rely on
second-best calculations.
By the way, what divergence between Egypt and Iran? "Calendrical
Calculations" by Dershowitz and Reingold only has one Islamic calendar;
the modern Persian calendar is a solar calendar.
As for calendar drift, there's also the 91.25 day tekufah (season-
length) which we use, the Julian season-length, which causes things
linked to the solar cycle to drift, like the switch from veten bracha to
veten tal umatar livracha (mentioning rain in the blessing of years in
the Shmoneh Esreh), which is supposed to switch 60 days after the
autumnal equinox, but really switches 4/5 December, 13 days later.
Jonathan Baker
<jjbaker@...>
Web page update: new divrei torah. <http://www.panix.com/~jjbaker>
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From: Mike Gerver <Mike.Gerver@...>
Date: Wed, 30 Aug 2000 14:06:59 +0200
Subject: Lunar month
>From Russell Hendel, in v33n32,
> the most famous
> is the Sinaitic tradition that the exact average lunar month is 29 days
> 12 793/1080 hours. As Prof. Rabbi Sholomo Sternberg points out in his
> book on Celestial mechanics this is correct to the nearest 1080th of an
> hour. The Talmud based on a verse in Chronicles, praises the tribe of
> Yissachar as "excelling in Astronomy".
What is the source that this value for the lunar month (technically the
synodic month, to distinguish it from the sidereal month which is also
"lunar") is a Sinaitic tradition? I find this extremely hard to
believe. This is exactly the same as the value of the synodic month
given in Ptolemy, the standard Greek astronomy book at the time when the
calendar was fixed by Hillel Sheni. (The time of the first molad after
the creation of the world, the molad of Tishrei in year 2 of the Hebrew
calendar, was rounded off to an exact hour from the value that one would
calculate from Ptolemy, but the time from one molad to the next is
exactly the same as given by Ptolemy.) Ptolemy describes in detail how
he calculated this value, based on Babylonian eclipse observations going
back several hundred years.
The length of the synodic month (expressed in solar days) is actually
changing gradually in time. There are two reasons for this. 1) The
effect of tidal drag, which slows down the rotation rate of the earth
much more than it slows down the revolution period of the moon (hence
steadily decreasing the ratio of the synodic month to the solar day).
2) There is a slow periodic change in the revolution period of the moon,
which has a period of about 80,000 years, and is due to the
gravitational effect of Jupiter and other planets, if I am remembering
this correctly. (There is an explanation in the Encyclopedia
Brittanica.) Right now this periodic effect is decreasing the revolution
period of the moon, so it adds to the other effect. The two effects are
about equal in magnitude. Since the period, about 1900 to 2700 years
ago, when Ptolemy's Babylonian eclipse observations took place, the
synodic month has decreased by about half a second. The value given by
Ptolemy (and used by Hillel Sheni) is just about dead on for the period
when the eclipse observations took place, but is noticeably longer than
the current value.
If the length of the synodic month were a Sinaitic tradition, accurate
at the time of Matan Torah, then we might have expected it to be a
little longer (by 0.25 seconds) than the value given by Ptolemy, though
perhaps that much precision is asking too much. If the time of the molad
were also a Sinaitic tradition, accurate at the time of Matan Torah,
then we might have expected it to be about an hour earlier than the time
given by Hillel Sheni, though I suppose it's possible that Hillel Sheni
adjusted his time of the molad after consulting Ptolemy's book. And of
course, it's possible that the Sinaitic tradition was designed to be
accurate at the time of Hillel Sheni, when it would be needed.
Still, by far the most reasonable explanation is that Hillel Sheni
looked up the numbers in Ptolemy.
Mike Gerver
Raanana, Israel
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From: Zev Sero <Zev@...>
Date: Wed, 30 Aug 2000 14:10:11 -0400
Subject: Pi and the Yam Shel Shlomo
The problem is not with the Tanach, which can easily be understood to be
rounding each dimension to the nearest whole number; the diameter was
between 9.5 and (30.5/pi), and the circumference was between (9.5*pi)
and 30.5.
Nor is the problem with the mishna in Eruvin 1:4, which can likewise be
understood to be endorsing the use of a rule of thumb, even though it is
known to be inaccurate, just as it does when it defines sqrt(2) as 1.4,
and we use this even though we know that it's just an approximation.
The problem is with the gemara on Eruvin 15a, which insists that pi is
*exactly* three, with not even a slight error. It also insists that the
Yam Shel Shlomo was perfectly round, which shoots down explanations that
rely on odd shapes. Tosafot points out the problem, but doesn't suggest
an answer, and I haven't seen anyone else who even mentions it.
Russell Hendel <rhendel@...> wrote:
> As tosafot points out no one in the Talmud really believed that pi=3
Where does Tosafot make such an extraordinary statement? The only
tosafot on the subject that I'm aware of is on Eruvin 15a/b, where it
notes that the gemara *does* seem to be saying that pi is exactly and
precisely 3, and that this is a problem because the mathematicians
disagree. But it does not suggest any answer, let alone one along the
lines of the tosafot in Sukkah that you quote about the rule that
sqrt(2) can be considered equal to 1.4.
Zev Sero
<zsero@...>
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End of Volume 33 Issue 39
