Sanhedrin 11b ~ The Tekufot

The Jewish leap year

The Jewish year usually contains twelve lunar months. In this page of Talmud we learn the reasons that the rabbis may add an extra month to the Jewish calendar, and proclaim a thirteen month leap year:

סנהדרין יא, ב

תנו רבנן על שלשה דברים מעברין את השנה על האביב ועל פירות האילן ועל התקופה על שנים מהן מעברין ועל אחד מהן אין מעברין

The rabbis taught in a Baraisa. We may intercalate a month and declare a leap year on account of three things: On account of the grain's ripening after the month of Nissan, on account of the fruit ripening after Shavuot, and on account of a season [tekufah] that is scheduled to begin in the wrong calendar month. We intercalate the year if two of these reasons are present, but for just one of these reasons we do not intercalate.

Let's look at the last reason. If the season is scheduled to being in 'the wrong month', the rabbis adjust the length of the year to bring it back into line.  Pesach must always fall in the Spring, so if the 15th of Nissan is part of the season of winter, we add another lunar month to the previous year and so push Pesach into Spring. 

The Solar Year, according to Shmuel

Here is the thinking behind this.  The rabbis of the Talmud, led by Shmuel, believed that a solar year was 365.25 days long, or 365 days and 6 hours. No more and no less. (This is also the length of the Julian calendar, adopted by Rome and all of Europe, including the Catholic Church.  It was the prevailing calendar in Europe, so Shmuel was in good company. ) Shmuel also believed that each of the four seasons was precisely one quarter the length of the solar year, or 91 days and 7.5 hours. Jewish tradition taught that the Sun was created on what would have been a Tuesday at 6pm. This time was also considered by the rabbis to have been the vernal equinox and the start of Spring in the first year of creation. Summer would therefore have started 91 days and 7.5 hours later, and fall another 91 days and seven hours after that.  The cycle repeats itself every 4 years, at which time the start of Spring will once again be at precisely 6pm, though not on a Tuesday. (It takes 28 years for the start of Spring to once again fall on a Tuesday at 6pm - and the next day is when we celebrate the rare event of Birkat Hachama. But I digress.)

Two Problems with Shmuel's Jewish Calendar

The first problem is that the solar year is not exactly 365 days and 6 hours in length. In fact it is 365 days, 5 hours, 48 minutes and 46 seconds - or 11 minutes and 14 seconds shorter than the Julian/Talmudic year. That's a small difference to be sure, but it adds up to three days every 400 years.  As a result of this difference, Spring, as measured by the day of the equinox, kept falling behind. In the days of Julius Caesar it had started on March 21, but by 1582 it had fallen behind and coincided with March 11. To bring the calendar back on track, Pope Gregory XIII knocked ten days out of the calendar, declaring the day after October 4, 1582 to be October 15th.  He also instituted a leap year of one extra day every four years, (except for years divisible by 100).  Shmuel's calendar had no similar fix, and the start of Spring in that calendar is about two weeks away from the actual, measurable Spring equinox.  

Path of the sun as seen over the northern hemisphere. On June 21, the start of summer the sun is at its most northern position. On Dec 21, the start of winter, it is at its most southern position.    

 A second problem with Shmuel's calculation is that he attributed the same length to each of the four seasons, when in fact the seasons are not of equal length. This is because the earth does not revolve around the sun in a perfect circle, but instead has an elliptical orbit.  When the earth is closer to the sun it speeds up, and when it is further away it slows down.  In fact not one of the four seasons are 91 days and 7.5 hours in length. Here are the actual lengths:

Spring - about 92 days

Summer  - about 93 days

Fall - about 90 days

Winter - about 89 days

Shmuel's orderly system has no astronomical basis, and his seasons do not follow an orderly and predictable pattern. If you were to ask, "what happens in the sky at the beginning of Spring according to Shmuel?"the correct answer is nothing.  If you were to ask the same question of the actual day and time on which Spring begins, the answer would be "on that day and at that precise moment, the tilt of the earth's axis is exactly perpendicular to the sun."

Here are the actual start days of the seasons for this coming year, 2025 and their start according to the calendar of Shmuel.  

Start of the 2025 Seasons
Season	Astronomical	Shmuel Times are for Jerusalem
Spring	March 20 5:01 A.M. EDT	April 7 6.39pm
Summer	June 20 10:42 A.M. EDT	July 8 2.09 AM
Fall	September 22 2:19 P.M. EDT	Oct 7 9.39AM
Winter	Dec 21 10:03 A.M. EST	Jan 6, 2026 4.09AM

Shmuel's calendar is pretty accurate, but over time, small discrepancies become larger.  Pope Gregory instituted a fix, but we have yet to do so. By not tweaking our Jewish calendar, the average date of the first day of Pesach is one day later every 216 years compared to the Sun, and one day every 231 years compared to the Gregorian date. This may not seem like a problem now.  But around the year 15,000 CE [sic] the first day of Pesach will occur on June 22, which is clearly not in the Spring. But I guess by then it will be somebody else's problem to fix.

Channukah, From the Talmudology Archives~ What Have the Maccabees Ever Done for Us?

Who could forget that classic scene from The Life of Brian, in which the Judean rebels ask, “What have the Romans ever done for us?”

After much debate, Reg, the rebel leader (played of course by the brilliant John Cleese) concludes “All right, but apart from the sanitation, the medicine, education, wine, public order, irrigation, roads, a fresh water system, and public health, what have the Romans ever done for us?”

We might have asked the same thing about the Maccabees, or as they are known in Hebrew, the Maccabim (spelled either מַכַּבִּים, or מַקַבִּים), the heroes of the story of Chanukah. They gave us Chanukah to be sure, and their name: Maccabi Games and Maccabi Tel Aviv Football Club,and Maccabi Haifa and Maccabi Petach Tikvah, and more. But really, aside from a stunning military victory, a few decades of peace, freedom to worship in the Temple, and some naming opportunities, what have the Maccabim ever done for us? Actually, a lot more than you might have thought. They might have given us everything.

CHANUKAH in a nutshell

As a reminder, Antiochus had set his sights on conquering Alexandria in Egypt but was prevented from doing so by the Romans, who ordered him to withdraw or consider himself to be at war with the Roman Republic. Recognizing when he was defeated, he turned his army north. According to the Second Book of Maccabees (5:11–14), here is what happened next:

Raging like a wild animal, [Antiochus] set out from Egypt and took Jerusalem by storm. He ordered his soldiers to cut down without mercy those whom they met and to slay those who took refuge in their houses. There was a massacre of young and old, a killing of women and children, a slaughter of virgins and infants. In the space of three days, eighty thousand were lost, forty thousand meeting a violent death, and the same number being sold into slavery.

As described by the Jewish historian Josephus (who was not an eyewitness, but lived about a century later), here is what caused the Jewish revolt:

Now Antiochus was not satisfied either with his unexpected taking the city (Jerusalem), or with its pillage, or with the great slaughter he had made there; but being overcome with his violent passions, and remembering what he had suffered during the siege, he compelled the Jews to dissolve the laws of their country, and to keep their infants uncircumcised, and to sacrifice swine's flesh upon the altar; against which they all opposed themselves, and the most approved among them were put to death.

The Maccabim, led by Mattathias (Mattisyahu) and his five sons, waged a guerilla campaign against their Greek oppressors, which culminated in a military victory and the re-dedication of the Temple in Jerusalem. Of course there may have been a miracle, something to do with oil (though the Rambam makes no mention of it, as we have discussed elsewhere), but the real miracle was the restoration of an independent Jewish state under the Hasmoneans, until civil war and an intervention by the Romans ended it all in 63 BCE.

By any account this would be enough for which to thank the Maccabim (well, not the civil war, but certainly the rest). But it turns out that perhaps we owe the Maccabim a great deal more than this.

a search for the terminus ante quem

In 2022, the Israeli archeologist Jonathan Adler published The Origins of Judaism, in which he asked a simple question: what is the earliest archeological evidence for Jewish practice? Adler was not primarily interested in textual evidence (though he cites a fair amount), but with the lived experience of individuals, on their practice and not on their beliefs. Adler focussed on epigraphic and archeological discoveries, to arrive at a terminus ante quem, “the boundary of time when or before which the particular element of Judaism under examination must have first emerged.”

…the date of the earliest available evidence demonstrating that Judeans knew something resembling the Torah and were observing its laws will serve as the terminus ante quem for the earliest emergence of Judaism. That it to say, Judaism must have emerged at this time or earlier. Lacking further evidence, this is the most we can determine with any degree of confidence (18).

I know what you are thinking, and Adler addresses it:

Absence of evidence is not evidence of absence. It is possible, for example, that the Judeans commonly knew of the Torah and were observing its laws for decades or even centuries prior to our established terminus ante quem, and that for whatever reasons no evidence has survived (ibid).

Adler’s conclusion, based on a “data-driven analysis” is that “we possess no compelling evidence dating to any time prior to the middle of the second century BCE which suggests that the Judean masses knew of the Torah and were observing its laws in practice. This will establish the middle of the second century BCE as the overarching terminus ante quem for the initial emergence of Judaism.” Which is to say, the Hasmonean period. Here is just some of that data.

1. Kashrut

   As we have discussed elsewhere on Talmudology, Adler analyzed the makeup of fish remains at 30 sites throughout the southern Levant from the Late Bronze Age through to the end of the Byzantine period (ca. 1550 BCE to 640 CE). They found that “the consumption of scaleless fish— especially catfish—was not uncommon at Judean sites throughout the Iron Age and Persian periods.” In other words, Judeans likely ate catfish, which are not kosher. [You can read a criticism of this claim from Bar Ilan’s Joshua Berman and Ari Zivotovsky here.] Pig remains suggest that by the Roman era, Judeans were not eating pork. “But here the trail of evidence ends. Prior to the second century BCE, there exists no surviving evidence, whether textual or archeological, which suggests that Judeans adhered to a set of food prohibitions or to a body of dietary restrictions of any kind…it is only from the Hasmonean period onward that we may claim to know of Judeans adhering to a set of dietary restrictions of any kind.” (49)

2. Ritual Purity

   Josephus describes two stories set in the second half of the first century BCE that relate to ritual purity. The Dead Sea Scrolls, composed some time in the second or first century BCE are of course full of laws that address this area. And they are mentioned in the Apocrypha and Pseudepigrapha, dated to a similar time. The Maccabim themselves are described (2 Mac 12:38) as having purified themselves “according to the custom” before making camp for Shabbat. Beyond this, the Hebrew Bible provides “little evidence” that the laws of tumah and tahara were known before the second century BCE. For example, although the complex rituals around purification after touching a corpse (tuma’at met) or contracting a skin disease (tzara’at) are mentioned in the Torah, there is not “even one passing allusion to anyone putting these rites into practice elsewhere in the Hebrew Bible.” In addition, although there are many mikva’ot (ritual immersion pools) that date to the Hasmonean period, no stepped mikva’ot have yet been dated “to any time earlier than the late second century BCE” (82).

3. Visual Art

   There is a Torah ban on making a graven image, but the earliest imageless coins were minted in Judea in 131 BCE. In contrast, all the surviving coins minted in Judea in the fourth century BCE display human and animal images. The Persian era Judean authorities included figural images on all their minted coins and exhibited “no signs of regard for any such Pentateuchal prohibition.” Adler suggests that it was only from the Hasmonean era onward “that there is a never before seen aversion to figural art among Judeans” (111).

4. Tefillin and Mezuzah

   We have yet to unearth any tefillin and mezuzot artefacts that predate the second century BCE, though, to be fair, these objects are made of perishable organic material. (Remember, Adler is focussed on the lived experience of the Judeans, not what may have been written in the Torah. The latter certainly predates this.) Fun fact: perhaps the oldest archaeological witness to tefillin or mezuzah is the Nash Papyrus, dated to mid-second century to the mid-first century BCE. But there are many finds that demonstrate that by the first century CE tefillin and mezuzah existed as Judean ritual practices.

5. The Menorah

   “A single golden, seven-branched menorah as prescribed in the Pentateuch certainly stood in the temple prior to its destruction in 70 CE, and both texts and archaeological finds suggest that Judeans living in both the first century CE and the first century BCE were well aware of both its existence and its general appearance. Prior to the mid-first century BCE , not a single example has been found of a seven branched menorah depicted in Judean (or Israelite) art, and earlier texts that speak of either a single or multiple golden or silver lampstands in the temple provide little correspondence with Pentateuchal prescriptions” (167).

Menorot in Judean art only appear from the Hasmonean time onward. From here.

Judaism as a way of Life emerged during the Hasmonean Period

Adler provides more evidence, from the observance of Shabbat and Yom Kippur and Sukkot, to the establishment of the synagogue. You will have to read that for yourself, or listen to a talk in which he outlines his thesis.

Our resolute conclusion has been that some point around the middle of the second century [BCE] should be regarded as our terminus ante quem, the time during or before which we ought to seek the emergence of Judaism….we would be remiss not to regard as at least suggestive the fact that all of the many practices and prohibitions analyzed throughout this book first come into historical focus precisely during the course of the Hasmonean period. Is it possible that Judaism as a way of life followed by Judeans at large first emerged only around this time?

It turns out that the Maccabim have done a lot for us. Way more than you might have once thought. They either (i) left us with the earliest cultural artefacts that belong to a Judaism we might recognize as our own, or (ii) were the first to practice it. Either way,

…it would not be wrong to view Judaism as having emerged out of the crucible of Hellenism, which dominated the cultural landscape of the time. In a poetic way, it seems only fitting that our English word “Judaism” itself is the result of a Hebrew/Greek hybrid, rooted etymologically in the Greek rendering of the Hebrew “yehudayah” merged with the Greek suffix'“-ismos”. (236)

Now that is a something worth saying Hallel for.

אחינו כל בית ישראל
הנתונים בצרה, בצרה ובשביה
העומדים בין בים ובין ביבשה
המקום ירחם ירחם עליהם

ויוציאם מצרה לרווחה
ומאפלה לאורה ומשיעבוד לגאולה
השתא בעגלא ובזמן קריב
ואמרו אמן

---

More Talmudology for Chanukah:

Rashi and Why Women Light the Menorah

Was there a Chanukah Miracle?

Bava Basra 167a ~ Torture & Coerced Testimony

In today’s page of Talmud we read of three incidents in which torture (or according to some, the threat of torture) was used to obtain a confession of a crime. In the first two, Abaye suspected that bills of sale had been forged. "כפתיה ואודי" - Abaye  bound the suspects to a post, and they confessed. In the third case it was Rava who suspected that his own signature and that of the elderly Rav Acha bar Adda had been forged. Rava too, bound the suspect to a post, after which not only did the suspect confess to forging both signatures, but he went on to explain how he had forged that of the elderly Rav Acha, whose hands had a tremor. 

 אנחי ידאי אמצרא ואמרי לה קם אזרנוקא וכתב

I placed my hands on the rope of a bridge while signing. Others say he stood on a skin bottle and signed.

Other cases of coerced Confessions

We first encountered coerced confessions when we studied Bava Metzia. There, we read that Mar Zutra The Pious had coerced a student to confess to his crime.

בבא מציא כד, א

מר זוטרא חסידא אגניב ליה כסא דכספא מאושפיזא חזיא לההוא בר בי רב דמשי ידיה ונגיב בגלימא דחבריה אמר היינו האי דלא איכפת ליה אממונא דחבריה כפתיה ואודי

Mar Zutra the Pious was involved in an incident in which a silver cup was stolen from his host. Later, Mar Zutra saw a certain student wash his hands and dry them on his friend's garment. Mar Zutra said: "this is the one who stole the cup, for he has no consideration for his friend's property. Mar Zutra bound the student to a post and coerced him, and he confessed to the crime (Bava Metzia 24a).

For completeness, we should note that there is a fourth passage in the Talmud (Niddah 25b) that also uses the language of כפתיה ואודי.  In that passage, a man was accused of having intercourse with his wife when she was ritually impure. He too was bound and confessed, though it is not clear who was ordering the binding.

He was bound and he confessed

Courtesy of Wikimedia.

The phrase that is used in all four cases is כפתיה ואודי "they bound him and he confessed." The root of the word to bind is כפת, which is used in rabbinic literature to mean to tie or to bind. Rabbi Asher ben Yechiel (Germany ~1250-1327), known as the Rosh, is certain that the suspect was tortured. In his commentary on the passage in Bava Metzia, he wrote וכפתיה בשוטי עד דאודי "he flogged him with rods until he confessed." (As in חושך שבטו שונא בנו ואהבו שחרו מוסר "spare the rod and spoil the child," from Proverbs 13:24.) Rabbi Betzalel ben Avraham Ashkenazi (Israel ~1520-1594) in his commentary to Bava Metzia called Shitah Mekubetzet agrees that coercion was used, although he is unsure if it was physical or psychological:

כפתוהו ואודי. יש מפרשים כפתוהו על העמוד והלקוהו בשוטים. ויש מפרשים כפתיה בדברים שנדוהו אם לא יודה האמת

Some explain that he was tied to post and flogged. Others explain that he was verbally coerced (and threatened with excommunication) until he confessed.

False Confessions

In a 2010 paper published in the Stanford Law Review, Brandon Garett notes that DNA testing has now exonerated over forty people who falsely confessed to rapes and murders. He wonders how an innocent person could convincingly confess to a crime he never committed. For example, in 1990  Jeffrey Deskovic, a seventeen-year-old, was convicted of rape and murder. Deskovic was a classmate of the fifteen-year-old victim, had attended her wake, and was eager to help solve the crime. During one of several police interrogations he “supposedly drew an accurate diagram,” which depicted details concerning “three discrete crime scenes” which were not ever made public. "In his last statement, which ended with him in a fetal position and crying uncontrollably," wrote Garrett, "he reportedly told police that he had “hit her in the back of the head with a Gatoraid [sic] bottle that was lying on the path.” Police testified that, after hearing this, the next day they conducted a careful search and found a Gatorade bottle cap at the crime scene."

“Scholars increasingly study the psychological techniques that can cause people to falsely confess and have documented how such techniques were used in instances of known false confessions.”

— Garrett, B.L. The Substance of False Confessions. Stanford Law Review 2010. 62 (4): 1051-1119.

Deskovic was convicted of rape and murder and served more than fifteen years of a sentence of fifteen years to life. Then in 2006, new DNA testing not only exonerated him, but also matched the profile of a murder convict who subsequently confessed and pleaded guilty. So how did Deskovic know all the details of the crime to which he confessed? Here is what the District Attorney noted in the post-exoneration inquiry:

...Given Deskovic’s innocence, two scenarios are possible: either the police (deliberately or inadvertently) communicated this information directly to Deskovic or their questioning at the high school and elsewhere caused this supposedly secret information to be widely known throughout the community.

Another paper, this time in the North Carolina Law Review, analyzed 125 cases of "proved interrogation-induced false confessions, which, the authors note with some pride, is "the largest cohort of interrogation-induced false confession cases ever identified and studied in the literature." It makes terrifying reading.  

It is of course really hard to study in the laboratory the psychological effects of torture and coercion and how they produce false confessions.  But scientists try anyway. For example, a 2016 paper from a team from the New School for Sociological Research in New York and the University of California studied the effect of sleep deprivation on false confessions.  When compared to those who had rested, participants were over four times more likely to sign a false statement if they were deprived of one night's sleep.  In another recent peer-reviewed paper, (Constructing Rich False Memories of Committing Crime) psychologists used suggestive retrieval techniques on some rather nice Canadian undergraduates. They found that up to 70% of those interviewed 

were classified as having false memories of committing a crime (theft, assault, or assault with a weapon) that led to police contact in early adolescence and volunteered a detailed false account. These reported false memories of crime were similar to false memories of noncriminal events and to true memory accounts, having the same kinds of complex descriptive and multisensory components.

They continue: 

Our finding that young adults generated rich false memories of committing criminal acts during adolescence supports the notion that false confessions and gross confabulations can take place within interview settings. The Innocence Project has shown that about 25% of false convictions are attributable to faulty confession evidence...The kind of research presented here is essential in the quest to help prevent memory-related miscarriages of justice.

False Memories Become Real

In an article in The New Yorker, Rachel Aviv reported on the remarkable story of how DNA evidence exonerated six convicted killers. Despite this, two of them had detailed memories of the killing that they didn't commit. One was a woman named Ada Taylor who confessed to a woman’s murder in 1989 and for two decades believed that she was guilty.

She served more than nineteen years for the crime before she was pardoned. She was one of six people accused of the murder, five of whom took pleas; two had internalized their guilt so deeply that, even after being freed, they still had vivid memories of committing the crime. In no other case in the United States have false memories of guilt endured so long. The situation is a study in the malleability of memory: an implausible notion, doubted at first, grows into a firmly held belief that reshapes one’s autobiography and sense of identity.

Of course murder is not the same as forging a document, but the lesson for those in criminal justice is the same. People confess to all sorts of things - especially when they are coerced or tortured- and can even forge false memories of the crimes of which they were accused.  

Permitted Coercion in Jewish Law

In the Code of Jewish Law, the שולחן ערוך, the passage in Bava Basra is the basis for the legal right to extract a confession from a person suspected of forging business documents.

שולחן ערוך חושן משפט מב, ג

ואם צריך לכוף בעל השטר ולהכותו כדי שיודה יעשה כדי שיוציא הדין לאמיתו

If it is necessary, the owner of the document (who is suspected of forgery) may be beaten in order for him to confess and the truth to come out...

This certainly made me feel uncomfortable, but let's put this into some context. Torture has been a part of many judicial systems, and was a feature of  Roman law.  Perhaps most notoriously it was used by the Inquisition, after Pope Innocent IV issued a papal bill Ad extirpanda in 1252 which authorized its use by the Church.  Closer to home, the US has recently grappled with, and condemned, cases in which the Central Intelligence Agency tortured prisoners, as the Senate Select Committee on Intelligence (partially) revealed in 2014. But among the thousands of legal decisions in the Babylonian Talmud, there are only four rabbis who are named as having tortured or coerced a suspect to confess. And that low number, though it is not zero, should provide us with some solace.  

Bava Basra 155b ~ Delayed Puberty in Boys

In today's page of Talmud we read about the treatment for the delayed onset of puberty:

כי אתו לקמיה דרבי חייא אי כחוש אמר להו זילו אבריוהו ואי בריא אמר להו זילו אכחשוהו דהני סימנין זמנין דנתרי מחמת כחישותא וזמנין דנתרי מחמת בריותא

Whenever people came to Rabbi Hiyya [with a case of a man who had not developed pubic hair]  he would tell them, if [the man was] thin, ‘Let him gain weight’; and if they were overweight he would say ‘Go lose weight’; for these signs [of sexual maturity] are sometimes delayed as a result of emaciation and sometimes  as a result of obesity.   (Yevamot 97a)

Rabbi Hiyya probably lived in the second half of the second century, and the treatment he suggested is one of the earliest examples associating nutritional status and delayed puberty.  Elsewhere in the Talmud we find this statement attributed to Rava, who died around 350 CE. But whoever suggested it first, I have found nothing in the works of Hippocrates, Aristotle and Galen that address this issue, so this association does not appear to have been a widely held belief in antiquity that was simply being echoed in the Talmud. 

There has been some discussion of what appears to be the increasingly earlier onset of puberty in girls. In fact, menarche, (the age of a girl's first menstrual period) has been steadily decreasing by a consistent three years per century of record keeping. However, R. Hiyya was addressing not the early onset of puberty in girls, but its delayed appearance in boys.  He noted that this delay was sometimes related to extremes of nutritional status, and so in these cases, was amenable to intervention.

“R.Hiyya may have been the first first to report an association of obesity and delayed puberty in boys.”

R.Hiyya was on to something. He (or Rava) may in fact have been the first to report an association between obesity and delayed puberty in boys.  This association has been confirmed by several studies which found that obesity has different effects on puberty in boys and girls. In girls, obesity is associated with earlier puberty, while in boys it has the opposite effect, and delays sexual maturation. But it was not until 2010 this association was confirmed by a longitudinal population-based study. This reported that a "higher BMI z score trajectory" (i.e. obesity)  during early to middle childhood may be associated with later onset of puberty among boys. 

The finding that puberty may be delayed in boys who are underweight has also been confirmed. As far as I can tell, none of the researchers has credited Rava (who died around 350 CE.) or Rabbi Hiyya for being the first to notice these associations. But they were first, and firsts count for something in science.