Depression Angles
By William Gewirtz

Introduction:

Depression angles measure the level of darkness or illumination prior to sunrise and, in a parallel fashion, after sunset.

There are two halakhic disagreements that might appear to relate to the use of depression angles. First, there is a long-standing argument about what defines the transition from one day to the next and what is (merely) an indicator that the transition has occurred. Some consider the appearance of three stars as the basis of a definition, while others assume that darkness is defining, with the appearance of three stars merely being an indicator that a specific level of darkness has already occurred. However, this dispute is not consequential to the use of depression angles. Even though depression angles relate directly to (the level of) darkness, since darkness levels and the appearance of stars occur approximately simultaneous, the argument is primarily of theoretical interest. As a result, the disagreement does not influence the use or the operation of depression angles.[1]

Second, a present disagreement is particularly consequential. Do we adopt fixed zemanim, e.g. 42 or 72 minutes after sunset or one hour before sunrise, or variable zemanim that change based both on location and day of the year? In Talmudic literature, physical events like the first appearance of light across the eastern sky, the ability to differentiate between blue and white, the sky’s apex and the eastern horizon appearing equally dark, the appearance of 3 medium stars, etc. all describe events whose occurrence vary at different locations and during different days of the year; they cannot be specified by a single fixed interval. As a result, I have a strong preference for variable versus fixed zemanim.[2] In spite of this being a still active dispute, I will assume that the argument is settled, and will not address the issue further in this paper. Clearly, depression angles are (largely) irrelevant to those who determine zemanim using fixed intervals. Therefore, this paper provides an explanation focused on depression angles themselves, as a methodology to formalize the use of variable zemanim. In what follows, I will explain the use of depression angles, the scientific method that has emerged over the last 150 years that makes use primarily[3] of both latitude and season / date to calculate various zemanim.

How this disagreement between using fixed versus variable zemanim developed would require its own detailed historical study, which I believe has not yet been attempted. Absent such a study, three factors appear to have had some bearing on the issue.

First, from the 12^th through the 18^th century, most observant Jews followed what is referred to as the opinion of Rabbeinu Tam, which equated the length of the intervals

• between sunset and the end of Shabbat and
• between alot hashaḥar and sunrise.

Because the length of the interval between sunset and the end of Shabbat was never lengthened, logic dictated that the (assumedly) equal interval between alot hashaḥar and sunrise be left invariant as well.[4]

Second, Pesaḥim 94a was (surprisingly)[5] read as implying that the time to walk a four milin interval applied year-round.

Third, in his forceful rejection of the opinion of Rabbeinu Tam, the Vilna Gaon proposed both seasonal and latitude-based variation with respect to both the intervals between sunset and the end of Shabbat and between alot hashaḥar and sunrise. While his view gained broad acceptance with respect to the end of Shabbat, its implications for variation based on both latitude and the time of the year with respect to alot hashaḥar, were (and still are) often ignored.

Without further attention to detailed halakhic issues, we will concentrate on the functional aspects of depression angles, (without requiring familiarity with spherical trigonometry on which they are formally based.) But first, we begin with a brief summary of some fundamental elements in the area of zemanim, which will help anchor the discussion.

Zemanim:

Two areas dominate the study of zemanim:

• First, how is the length of the 12 halakhic hours of every daytime period, which begins at alot hashaḥar, to be calculated given variation in the length of the daytime period during the different times of the year? Do we calculate from the daytime period’s halakhic beginning at alot hashaḥar or from the point of sunrise?
• Second, how do we determine the precise delimiters of a day of the week,[6] which almost all agree concludes approximately at the end of the of the bein ha-shemashot period in the evening?[7]

Avoiding the many disagreements in the halakhot of zemanim, we will assume without loss of generality that:

• The amount of time by which alot hashaḥar precedes sunrise, in the Middle East and around the spring and fall equinox when both the daytime and nighttime periods are equal, is 72 minutes.[8]

• The transition point between the days of the week and most critically, the end of Shabbat follows the opinion of the geonim (as opposed to Rabbeinu Tam.)[9]

Addressing primarily only alot hashaḥar and the end of Shabbat is sufficient to illustrate how depression angles can be used in halakha. In many communities, the methods used to determine the end of Shabbat versus alot hashaḥar are different and demonstrate concretely the issue that we will address. In those communities, alot hashaḥar is always a fixed 72 minutes before sunrise and the calculation of alot hashaḥar in those communities does not involve use of depression angles. On the other hand, the number of minutes after sunset at which 3 stars appear or a requisite level of darkness has been achieved varies considerably depending on where you are and the time of the year as well. As a result, very often the end of Shabbat is (either explicitly or implicitly) calculated using depression angles or a near equivalent.

Clocks:

Before addressing depression angles some background on the introduction of clocks into the halakhic literature is required. Beginning at the turn of the 16^th century, about two centuries after the first introduction of mechanical clocks in Europe, clocks were first mentioned in the halakhic literature; at that time, knowledge of the impacts of latitude and season was still non-existent. Throughout the entire period of the rishonim, time intervals were typically referred to not by the number of minutes on a clock, but primarily as estimated intervals. Clocks added a mechanism that allowed various opinions previously specified in terms like the time required to do X, to be translated into a precise, easily specified interval of time.

Clocks began to proliferate almost 200 years before the first recorded reference to either the impacts of latitude or season appear in the halakhic literature. Those impacts were included by R. Avraham Pimential in his comprehensive sefer on zemanim, Minhat Kohen, written during the 17^th century.[10]

The first mention of a clock in the halakhic literature was by R. Yosef ben Moshe, a student of R. Yisroel Isserlein, in Leket Yosher appearing around the turn of the 16^th century;[11] it appeared more than a century earlier than Minhat Kohen. During the 14^th through 16^th century clock making accelerated, well before the nature of variances between zemanim at different locations and during different times of the year were appreciated.

Unfortunately, the precision that clocks provided may have resulted in their increased prominence at the expense of observation. Precision and accuracy are often confused. Clocks provide precision for measurements that may or may not be accurate halakhically. If someone tells you that Shabbat ends at a specific time, that assertion may be very precise but totally inaccurate. Clocks also provided a level of precision that may have been overly seductive. What is yet more disconcerting, clocks allowed pesak to be rendered independent of observation. With an assumed reduced reliance on observation, it is likely that critical halakhic definitions became more subject to disagreement. Examples abound in the halakhic literature:

1. distinguishing between levels of darkness,
2. differentiating between medium and small stars, or
3. establishing the amount of illumination necessary to recognize a friend after dawn

are three clear examples. In each of those three cases, posekim’s opinions often varied significantly and/or recommended caution based on a level of acknowledged doubt.

In the 19^th century, as personal timepieces proliferated and greater uniformity between clocks in different locations became necessary with the growth of the railroads, time took on a yet greater role, something we note but do not address further.

Variation by the time of the year and location/latitude:

In the entire period of the rishonim, instead of time-based measures, most mitzvot dependent on zemanim were performed based on the observation of natural events. The effects of latitude and the time of the year were incorporated implicitly by the use of observation. The occurrence of darkness or the appearance of stars varied naturally between locations regulated by a yet unknown science. How zemanim differed at different locations was largely immaterial; as far as I know, prior to the 17^th century there is no discussion in the halakhic literature comparing zemanim at different locations.

After a significant interval where clocks proliferated, depression angles first appeared in the halakhic literature at the end of the 19^th century. A depression angle[12] measures how far below the horizon the sun appears at a specific moment, providing an accurate measurement of the level of illumination; a larger angle indicates that the sun is further below the horizon with less discernable light coming from the sun. If a depression angle of X degrees occurs at 4:40AM in London and 5:10AM in New York on the same or different days, then one can be certain that the amount of light from the sun is the same at those two times.

If alot ha-shaḥar is defined by the degree of illumination from the sun, to determine alot ha-shaḥar across different latitudes and times of the year, one can[13] utilize depression angles. The first step is to establish the number of degrees below the horizon the sun is located 72 minutes before sunrise in the Middle East around the spring / fall equinox. The second step is to use that same number of degrees to determine alot ha-shaḥar elsewhere and during other times of the year. The 72-minute interval commonly accepted for alot ha-shaḥar corresponds to the sun being approximately 16 degrees below the horizon.

In Israel around the spring / fall equinox, scientists consider the sun to provide no measurable light until approximately 80 minutes before sunrise corresponding to a depression angle of approximately 18 degrees.[14] As the halakhah often disregards miniscule, non-visible quantities, this provides observational support for the standard pesak tacitly assumed that alot ha-shaḥar precedes sunrise by 72 minutes.

From everything I can determine, depression angles capture the halakhic notion of the degree of darkness and light accurately; no alternative for “measuring” ḥashekhah or alot ha-shaḥar has ever been formulated, nor has anyone ever proposed any problem that depression angles might create. Depression angles naturally adjust zemanim based on latitude and the time of the year. Clearly, we may not need such precision; observation was adequate for generations. Nonetheless, a depression angle is to darkness / illumination what a watch is to time.

A small depression angle corresponds to a significant amount of illumination coming from the sun even though the sun is below the horizon. After sunset the level of illumination decreases in a mirror image to the way the level of illumination increases as we approach sunrise. At a depression angle of around 5 – 6 degrees, the halakhic end of a day as specified in the Talmud occurs;[15] at a depression angle of around 11 – 12 degrees we arrive at the point of misheyakir. In between, at a depression angle of 8.5 degrees, Shabbat, as typically practiced currently, concludes. Translating a zeman into a depression angle is neither always straightforward nor undisputed. For certain zemanim, alot hashaḥar for example, the basis is clear: the level of illumination at the beginning of the daytime period, in the Middle East around the spring or fall equinox corresponding to an average time to walk 4 milim. To determine the transition point between days of the week and the end of Shabbat according to the geonim, both biblically and in practice incorporating various ḥumrot, is more complex. Fortunately, following R. Yeḥial Miḥal Tukatzinsky’s calendar for Jerusalem, the practiced end of Shabbat is almost universally accepted by those who rely on depression angles to equate to an angle of 8.5 degrees. Very few posekim following the geonim are more stringent; the practice of the overwhelming majority of 19^th century posekim for whom we have calendars (from which depression angle equivalents can be inferred) were more lenient. However, the earlier point of ḥashekha or 3 medium stars, absent any ḥumrot, is still disputed.[16]

Given the earth’s circular shape, tilt, and rotation, computing depression angles involves spherical trigonometry, which is fortunately not needed for purposes of this paper. Similarly, albeit without the precision, Ḥazal used terms like mi-she-yakkir, hikhsif ha-elyon, the appearance of small/medium stars, etc. all of which relate to the degree of darkness or equivalently the amount of residual illumination from the sun. As noted in the introduction, there is a long-standing halakhic dispute pitting the primacy of darkness against the appearance of stars; which is defining, and which is just a useful indicator? I am strongly biased in the direction of darkness as defining; darkness was already recognized as causing the visibility of stars in geonic times. Since the level of darkness and the appearance of stars are strongly correlated, the dispute, as noted in the introduction, is not consequential to this short paper.[17]

Latitude, the time of the year and depression angles:

For any halakhik zeman, besides the level of darkness specified by a depression angle by which it is defined, two additional variables – the location’s latitude and the date of the year – must also be provided to calculate the time at which that halakhik zeman occurs. The intuition is important. To determine the time (after sunset or before sunrise) at which a level of darkness is achieved, we must know

1. where you are, defined only by your distance from the equator,
2. where the sun is, which can be calculated knowing the exact time of the year, and
3. the level of darkness required.

The former two inputs are just unarguable facts; the latter requires a halakhic determination.

Those mathematically inclined, should think of this as a function of three variables: 1) latitude, 2) date, and 3) darkness level, where those inputs generate a number, the value of the function. That number equals the length of time before or after sunrise or sunset, respectively, at that latitude, on that day, when the degree of illumination expressed by that depression angle is achieved.

Both the latitude and the date play a critical role. However, until latitudes exceed 40 degrees, the seasonal variation for alot hashaḥar is less than about 20 minutes. For ease of explanation, the impact of the date, i.e. the seasonal variation, will be covered separately in the next section. To better understand the impact of latitude, the following discussion focuses on an arbitrary but specific day. The critical inputs in addition to that one day selected are 1) the latitude of the location and 3) the desired level of darkness, specified by a depression angle. I can input, for example, 1) latitude: 30 degrees and 3) the degree of darkness associated with a depression angle of 10 degrees.

For that specific day, given the latitude and a specified depression angle, the function calculates how many minutes before sunrise or after sunset the degree of darkness associated with that depression angle is achieved.[18] If you go further away from the equator, getting dark takes longer. What takes 42 minutes in Jerusalem takes approximately 50 minutes in New York. But things are a bit harder. Mathematicians will describe the result as non-linear, something that equates to “it is not simple.” For a depression angle of 8.5 degrees, it takes 8 minutes longer to reach that level of darkness in New York, situated about 9 degrees further from the equator than Jerusalem. If things were simple, i.e. linear, you might guess that it takes about 8 minutes more for every 9 degrees further from the equator that you are located. If you go 18 degrees further north of Jerusalem, you might expect having to wait (only) another 8 minutes, 16 minutes longer after sunset than the time it took to reach that level of darkness in Jerusalem. However, when we go 18 degrees further north of Jerusalem to Prague, an equivalent level of darkness is achieved 26, and not (a linear) 16 minutes, later.

Prague is further south than the locations of most European Jews who lived in Poland and Russia, about 48 to 56 degrees north latitude where change based on latitude accelerated. Additionally, depression angles have a second complicating factor. Instead of varying latitude, let us hold latitude fixed at say 50 degrees, the latitude again of Prague. Compare, for example, the number of minutes after sunset that it takes to reach a depression angle of 8.5 versus 16 degrees, the latter number being less than twice the former. On a day in early May those times for Prague are 58 and 130 minutes respectively, the latter being more than twice the former; a second non-linearity.

As both latitudes and desired level of darkness change, either very careful observation or scientific knowledge is required. It is not all that surprising that such precision was not always exhibited in the halakhic literature. Note that at latitudes further from the equator and at greater levels of darkness, the degree of seasonal variation increases as well, as we will see in the next section.

Dealing with seasonality

Posekim deal appropriately with seasonality in one of two fundamentally different ways:

1. Some use a simple upper bound for a zeman where use of a such a number does not create significant inconvenience. Some treat R. Moshe Feinstein’s 50-minute zeman for the conclusion of Shabbat in the New York area that way.
2. Alternatively, a posek can use depression angles; R. Yisroel Belsky adjusted R. Feinstein’s 50-minute zeman using depression angles to vary the conclusion of Shabbat between 40 and 50 minutes after sunset during different times of the year.[19]

To begin with, it is important to recognize that the magnitude of seasonal variation increases (non-linearly) both for:

1. Locations further from the equator (thus greater variation in Montreal than Miami.)
2. Greater degrees of darkness (thus greater variation in misheyakir than in the end of Shabbat.) (The average depression angle for misheyakir is approximately 3 degrees greater than the currently prevalent depression angle used to compute the end-time for Shabbat.)

For example, the seasonal variation for the end of Shabbat in Jerusalem is only 6 minutes, from about 36 minutes after sunset near the spring or fall equinox to about 42 minutes after sunset near the summer solstice. On the other hand, the variation in alot hashaḥar in Lithuania is “infinite.” Alot hashaḥar is 102 minutes before sunrise at the spring equinox, 120 minutes before sunrise at the winter solstice, and set to halakhic midnight during periods of the summer. In periods during the summer, the requisite level of darkness equating to a depression angle of 16 degrees does not occur; it never gets that dark during the night, something the Gaon observed.[20] Said differently, illumination from the sun never diminishes to that level either in the evening or equivalently in the morning. The extent to which this was neither recognized by posekim prior to the Gaon nor followed even after the times of the Gaon would require its own (lengthy) essay to illustrate.

The impact on the point of misheyakir provides another interesting topic for study. Pesakim from the Middle East tend to have an earlier point of misheyakir, often equating to a depression angle of between 13 and 11.5 degrees; pesakim from European posekim tend to use 11.5 degrees or less.[21] It suffices to say, posekim from northern Europe need to be read with care in discussions of this issue. Their views on alot hashaḥar and misheyakir are obviously linked; a delayed point of alot hashaḥar would likely delay the point of misheyakir as well.

Those following the 72-minute approach of Rabbeinu Tam should behave equivalently with respect to the end of Shabbat and alot hashaḥar, a practice rarely observed. It is alleged that R. Chaim of Brisk made havdalah Sunday morning, recognizing that Shabbat ends at (halakhic) midnight, coincident with alot hashaḥar and after the time he had already gone to bed. Such practice was rare. Interestingly, in Vilna, using a depression angle of 8.5 degrees to compute the end of Shabbat, a prevalent practice today, even the approach of the Gaon requires waiting 95 minutes after sunset to end Shabbat during the weeks around the summer solstice.

Unfortunately, many incorrect alternatives remain prevalent. Depression angles confirm that the shortest intervals occur in the spring or fall close to either equinox. The longest intervals occur around the summer solstice. Surprisingly to many, the interval around the winter solstice is longer than the interval in the spring or fall, but shorter than the interval in the summer. Because this was not properly understood, an error, going back to R. Pimential[22] persists until today.

While acknowledging that intervals vary by the time of year, in place of depression angles the error links variation in the interval with variation in the length of the period between sunrise and sunset. With this mistaken approach the summer interval is lengthened as it should be, but the variation is calculated imprecisely. In the winter the interval is shortened as opposed to lengthened, a very consequential error.

Interestingly and for reasons I can only suspect, posekim advised against using the implied wintertime reduction in time when it creates a leniency; perhaps the observed result did not conform to expectations or, as some might suggest, their counsel is another example of siyattah di-Shemayah.

A large and well entrenched group chooses not to make any seasonal adjustment. If done to promote simplification, as noted, that is a reasonable approach where implemented with care, (particularly for the end-time for days of the week at latitudes under 45 degrees.)

Often the implementation is entirely indefensible (most often for alot hashaḥar,) very often in combination with an equally poor approach to latitude, and often challenged by careful) observation. The clearest and most prevalent example is given by those who insist that alot hashaḥar is always 72 minutes before sunrise. Using this approach, one can easily end up with misheyakir visibly occurring before alot hashaḥar, a halakhic absurdity of the first order.

Conclusions:

The use of depression angles allows the determination of various zemanim without the need for observation. Given that the observation of various zemanim has become less widely understood and potentionally subject as well to various human frailties, it is likely that depression angles should become (yet more) widely accepted.[23]

The Gaon’s Impact on the Interpretation of both Primary Sugyot in Zemanim

By William Gewirtz

Unquestionably, almost all ḥiddushim in the understanding of the vast literature on zemanim have halakhic implications. My intent is not to influence what has become minhag Yisroel; my focus is on establishing more precise halakhic definitions and theoretical innovations in sugyot that are central to the study of zemanim. Competent poskim can implement any changes in halakhic practice, which they determine that these innovations support.[1]

Two areas dominate the study of zemanim:

• How to determine precise delimiters for the day of the week, which concludes at the end of the period of bein ha-shemashot.[2]
• How to calculate the hours of the daytime period, which according to all opinions begins at alot hashaḥar.

Interestingly, in both Hebrew and English, the words yom and day denote both the daytime period and the day of the week. Our focus is on:

• the Gaon’s impact on the interpretation of two key aspects of Shabbat 34a-35b, which examines the transition between days of the week, and
• a key aspect of the Gaon’s clarification of Pesaḥim 94a focused on the daytime period.

The approach to the above sugyot were radically changed by the Gaon’s observations.[3] However, only the impact on the former sugyah in Pesaḥim is usually recognized.

As I strongly indicated in a paper on errors in halakhic reasoning, I do not believe that attempts to deal with the critique of Rabbeinu Tam’s position by the Gaon have ever been fully effective. In this paper, however, the focus is not on the extensive halakhic literature written primarily in the period of the aḥaronim, but on the text of the gemara itself and its interpretation by rishonim. The conclusions reached are very different.[4]

The first two sections address areas in the gemara beginning on Shabbat 34a where a significant modification to an earlier reading of the gemara, often associated with rishonim aligned with Rabbeinu Tam, is strongly preferred, but only when assuming a slight modification to the presumed opinion of the geonim / Gaon.[5] In a similar vein we suggest a modification to how the bein hashemashot interval is to be used, something I believe to be independent of the positions of Rabbeinu Tam and the Gaon.

The third section addresses the Gaon’s innovative reading of the gemara in Pesaḥim 94a, a reading that is strongly supported by both elementary logic and astronomy. Included in the Gaon’s reading is a concept that was never made explicit in rabbinic literature prior to the Gaon, to the best of my knowledge. As will become clear, that observation forms the basis for the Gaon’s challenge to the opinion of Rabbeinu Tam.

My observations are not intended to be judged as controversial, although concluding a sugyah may not have been correctly understood (or at the very least properly explained) until the 18^th century might be jarring.  It is beyond my focus or competence to deal with the implications of that observation; observations addressing that point would be welcomed.

Section 1: The endpoints of the period of bein ha-shemashot

The dispute between the geonim / Gaon and Rabbeinu Tam revolves around the placement of the interval of bein ha-shemashot, within the interval between sunset and tzait (kol) ha-kokhavim, whose length is (almost always) assumed to be the time needed to walk 4 milin.[6] The length of the bein ha-shemashot period is universally assumed to be the time needed to walk ¾ of a mil. It is normally assumed that

• the opinion of the geonim / Gaon places the bein ha-shemashot period at the start of that interval, while
• Rabbeinu Tam places it at its end.

Those two alternatives represent opposite extremes.  Two adjustments seem reasonable.

• First, separate the dispute between the geonim / Gaon and Rabbeinu Tam into two distinct components:
  • The first concerns the beginning and the second the end of the bein ha-shemashot period, subject to a constraint that the length of the bein ha-shemashot interval must equal the time to walk ¾ of a mil.
• Second, assume that there are multiple hybrid / intermediate positions, situated between the two generally assumed alternatives.^[7]

This allows for

• an interpretation of the gemara in Shabbat similar (or according to some identical) to the overwhelmingly compelling position of the geonim / Gaon relative to the end of the bein ha-shemashot period,
• while defining the beginning of the bein ha-shemashot period using the textual approaches of many rishonim, albeit employing a significantly earlier point in time, much closer to sunset.

While I have not seen this conceptualization explicitly formulated^[8] in the classic halakhic literature, practice and several pragmatic opinions are supportive of this approach.  More importantly, the challenges raised to the opinions of both Rabbeinu Tam and the Gaon are, without exception, directed at the late ending of the Shabbat according to the opinion of Rabbeinu Tam and at the early beginning of the Shabbat according to the opinion of the Gaon.[9] This approach sidesteps the challenges to both opinions. Additionally, this approach absolutely disputes the view that

• Anyone who rejects the start of Shabbat precisely at or even a few minutes after sunset must embrace the approach of Rabbeinu Tam,

an assumption that does not follow logically, though it is occasionally found in the halakhic literature.[10]

There are numerous arguments in support for this position. We cite several of the strongest:

1. The term mi-she-tishkeh ha-ḥamah: Ramban in Torat Ha-Adam[11] and the many ḥakhemai sforad who adopted his position stress that the meaning of the term mi-she-tishkehha-ḥamah unquestionably implies not sunset but a point after A simpler phrase shikiat ha–ḥamah would denote precisely sunset. Of course, mi-she-tishkehha-ḥamah does not imply any specific time but only that the time follows sunset by some number of minutes. The only change required is to assume that mi-she-tishkeh ha-ḥamah is referring to a point much closer to sunset, something that appears more reasonable than a point over 50 minutes later according to the (theoretical) view of Rabbeinu Tam. In other respects, the gemara is read like the numerous rishonim who assumed that mi-she-tishkeh ha-ḥamah cannot refer to sunset proper.
2. Tosefet Shabbat:[12] Ramban argues that tosefet Shabbat could only begin after sunset during an interval that is still a part of the daytime period. Ramban does not consider tosefet Shabbat prior to sunset as meaningful, equating it to the value of illumination from a candle during daylight.
3. The sugyah in Shabbat applies year-round, not only during a specific season or seasons: The gemara in Pesaḥim 94a, which equates the time needed to walk 40 milin with the daytime period, must assume an average day around either the spring or the fall equinox. In the Middle East, during a winter day of approximately 10 hours or a summer day of approximately 14 hours, the distance covered in one day would vary considerably. However, unlike the gemara in Pesaḥim 94a that can only apply to a 12-hour daytime period, the gemara in Shabbat, defines the end of Shabbat using terms like ḥashekhah, hiḥsif ha-elyon ve-hishveh le-taḥton and the appearance of three stars, all of which apply (nearly) uniformly throughout the year.^[13]

At both the fall and spring equinox, the sun appears in the same place over the equator and you might expect Shabbat to begin and end at the identical time.  Certainly, regardless of how one measures darkness, it is equivalently dark any number of minutes after sunset at those two times.  However, in Jerusalem and other parts of the Middle East, unrelated to the degree of darkness, stars first appear a number of minutes later (after sunset) in the fall than they do in the spring.[14]Advantaged by the early appearance of Sirius and Canopus in the spring but not the fall, the Gaon restricts the focus of the gemara to the spring only.

Note that:

1. All rishonim who choose to comment on the sugyah in Pesaḥim 94a state that the day in question occurs only around the spring (or fall) equinox.
2. Not a single rishon makes an analogous comment, restricting the gemara beginning on Shabbat 34b to any specific time of year.

4. Shmuel’s unchallenged statement:[15]With Prof. Levi’s table (provided in the appendix) as background, examine Shmuel’s unchallenged statement on Shabbat 35a, according to the position of the geonim / Gaon.[16] After discussing the appearance of the horizon and the length of the bein ha-shemashot period, the gemara states the opinion of R. Yehudah in the name of Shmuel who asserts: “one star – daytime, two stars – bein ha-shemashot, and three stars – night.”[17] This is followed by the opinion of Yosi (bar Adin) asserting that the stars in question are neither stars that appear in the day (i. e., large stars[18] or planets) nor small stars that only appear well after the time of tzait ha-kokhavim, but medium stars. How might Shmuel’s statement be reconciled with the previous discussion in the gemara?

• First, exclude the implausible suggestion that R. Yosi bar Adin’s assertion that Shmuel’s statement is referring to medium stars applies only to the third part (or second and third parts) of the text. Under this interpretation, the first part of Shmuel’s statement concerning one star, includes not only medium stars but also large stars or planets that are on occasion visible before sunset.  Were that the case, the statement would be informing us that the appearance of a planet before sunset does not indicate that the bein ha-shemashot period has begun. In addition to being forced to argue that the different parts of Shmuel’s statement refer to different types of stars, such an assertion would hardly be necessary; the gemara gives no hint that the bein ha-shemashot period begins before sunset.[19]
• Second, because R. Yosef begins bein ha-shemashot at the time walk 1/12^th of a mil later than R. Yehudah, some[20] align Shmuel’s statement and even pasken like R. Yosef, assuming that R. Yehudah start to bein ha-shemashot precisely at sunset, cannot be reconciled with Shmuel’s statement. Prof. Levi’s chart challenges that approach, since a delay of at most 2 minutes[21] (after sunset) provides no benefit; the first medium star cannot be seen until at least 6 minutes after sunset.
• Third, there are other (implausible) solutions that align Shmuel with Rabi Yosi only, some going so far as identifying the amora Yosi (bar Adin) as the tanna Rabi Yosi. To follow a sugyah focused on Rabi Yehudah, with an uncontested statement that accords only with Rabi Yosi is dubious, at best. Furthermore, Shmuel’s statement, which refers to the non-instantaneous, successive appearance of stars, is difficult to align with an opinion that the bein ha-shemashot interval is instantaneous.

The most plausible suggestion, like the view of R. Ḥaim Volozhin below, is that the bein hashemashot begins at least 6 minutes after sunset.[22]

5. Seeing stars so early (even if only in the spring) is practically impossible:

If the start of the period of bein ha-shemashot for the geonim / Gaon is precisely sunset, there has been considerable effort^[23] to align the appearance of three stars within the time it takes to walk ¾ of a mil after sunset. The only solution provided is to assume that the time needed to walk ¾ of a mil applies only around the spring equinox[24] ^[25] and, even then, to make yet further assumptions to arrive at so short an interval.  Particularly if the time needed to walk ¾ of a mil is 13.5 minutes and even if it is a bit under 17 minutes, three stars can rarely be seen so soon after sunset and then

• only with great difficulty,
• by experts, perhaps aided by telescopes, and
• in a pristine environment absent urban sources of light, like the Judean desert.

Under no circumstances, is 13.5 minutes possible, and 16.85 minutes is almost equally unreasonable.^[26]

6. Multiple opinions that begin bein ha-shemashot slightly after sunset:

• 4 to 5 minutes: The minimum time reported as the custom of Jerusalem^[27] as well as the opinion of R. Shneur Zalman of Liadi,^[28] the point when the sun is no longer visible even from the highest elevations around Jerusalem.^[29]
• Greater than 6 minutes: The opinion of R. Ḥaim Volozhin based on Shmuel’s statement concerning the appearance of a single star that is visible in the spring to an expert observer at that time.[30] The fact that R. Ḥaim Volozhin disagrees with his Rebbe, strongly suggests that the Gaon’s position that Shabbat starts at precisely sunset was only promulgated le’migdar miltah.
• 7 to 15 minutes: These views are supported by a variety of sources mentioned previously including R. Kapach’s view of Rambam and R. Posen’s view of the opinion of the geonim. A time around 10 minutes is implied by many Sephardi poskim who mention that until the call of the Moslem mugrab for their fourth prayer service, it is still day thus allowing for the performance of a brit on that day for a baby born in those few minutes after sunset on that same day one week earlier.

When linked to the times given in Prof. Levi’s charts, various alternatives from 6 – 16 minutes after sunset can be plausibly suggested.  The next section on how the bein hashemashot interval was intended to be used will shed further light in determining how many minutes after sunset might still be considered daytime.

Section 2.  Before or after

One aspect of the Gaon’s interpretation of Shabbat 34b, often assumed without further examination, is that bein hashemashot is calculated by adding its length to the beginning of the beginning of bein hashemashot period.  That assumption will now be challenged.  Though not conclusive as to how the sugyah should be read, some seforim of near contemporaries[31] of the Gaon assume the opposite approach, subtracting the length of the bein hashemashot interval from the end of Shabbat. The arguments below attempt to demonstrate that this approach may have been standard before the writings of the Gaon proliferated years later in the middle of the 19^th century.[32] While some may argue that counting forward from sunset versus backward from nightfall is somehow tied to the fundamental makhloket of the geonim / Gaon and Rabbeinu Tam, there does not appear to be any logical, textual or halakhic basis for such an assertion.

The fundamental question is:

What possible value could there be in introducing (especially in an era before clocks) a time-based approximation that is a lower bound, season dependent, rarely applicable, and then only under rare, idealized conditions, at best? In what context would such information be useful?

Thus, I propose that the time needed to walk ¾ of a mil should be interpreted differently than the Gaon proposed and instead we will attempt to demonstrate that

• The time to walk ¾ of a mil is to be subtracted from the end of the bein ha-shemashot period as opposed to being added to its beginning.
• The period is not a minimum (that occurs only around the spring equinox), but a maximum (that occurs around the summer solstice). Thus, the entire sugyah is applicable year-round providing a conservative upper-bound to the length of the bein ha-shemashot

The arguments for both assertions are interrelated and are presented concurrently.[33]

1. The gemara in Shabbat is primarily focused on Friday night and determining when the bein ha-shemashot period begins, as opposed to when it ends. The gemara assumes that the end to the period of bein ha-shemashot is known; each of the disputants are addressing when the period of bein ha-shemashot begins on Friday night. However, if the time needed to walk ¾ of a mil were meant to be added to the time of sunset, it would be addressing the end of the bein ha-shemashot period and not the beginning.
2. The three fractions (each expressed as the time needed to walk a part (1/2, 2/3 and ¾) of a mil,) given as alternatives for the length of the period of bein ha-shemashot would then all have identical semantics; each of the three fractions (of the time to walk a mil) is counting back from the assumed point of ḥashekhah, to calculate the beginning of the bein ha-shemashot Given Prof. Levi’s chart, under no circumstances could anyone imagine that the time to walk either ½ of a mil after sunset could be the point at which Shabbat ends. The amoraim, R. Yehudah and R. Yosi, are quantifying the opinion of Rabi Yehudah in contrast to Rabi Nehemiah’s interval, whose period of bein ha-shemashot is only the time needed to walk ½ of a mil.
3. If someone were countering the position of Rabi Yosi, who says the period of bein ha-shemashot is instantaneous, it is more likely that he would say that it can be “as long as” opposed to “as short ”
4. The significant issue raised previously of never seeing stars as early as at the time needed to walk ¾ of a mil after sunset becomes entirely moot.
5. The period of bein ha-shemashot has some practical consequence providing a potentially useable, conservative upper bound as opposed to a purely theoretical lower bound, which is of limited to no use.

6. As noted earlier, rishonim, who limit the gemara in Pesaḥim to the equinox periods in the fall and spring, make no such assertion with respect to the gemara in Shabbat. One might presume from the lack of commentary that rishonim assumed that the sugyah applies year-round.

Treating the gemara in Shabbat like the gemara in Pesaḥim as referring only to days around the spring (but not the fall) equinox^[34] is unnecessary when thinking of the interval as a practical upper bound.  All the other descriptions in the gemara, either the appearance of the sky / horizon or the visibility of three stars, apply year-round.

Now examine the three elements in combination:

• The various opinions of rishonim on the time to walk ¾ of a mil – 13.5, 16.85 and 18 minutes.
• Levi’s chart indicating that 3 stars are visible to a careful observer 30[35] minutes after sunset in the summer.
• The two suggested interpretations that
• delay the beginning of bein hashemashot to a point slightly after sunset, and
• view the sugyah as subtracting the length of bein hashemashot from its end to find its beginning.

We can then assume that Shabbat begins from 12 (subtracting 18 from 30) to 16.5 (subtracting 13.5 from 30) minutes after sunset.[36]  However, given

• very natural and expected stringency that occurs even today but certainly are to expected in an era before (widely available and accurate) clocks, and
• the need for tosefet Shabbat

practiced times for starting Shabbat between 5 and 10 minutes after sunset ought not be surprising.

Section 3. The Gaon’s approach to Pesaḥim 94a.

The Gaon’s approach to Pesaḥim 94a is premised on an incontrovertible astronomic and logical fact. Assuming that alot hashaḥar approximates the first light of the day, then its evening counterpart, tzait ha-kokhavim, must occur when the sun’s illumination has (next to) no remaining effect.^[37]  At both of those times, all stars that are in position to be seen are not obscured by illumination from the sun. As a result, the Gaon adds the word kol to differentiate tzait ha-kokhavim, which throughout the Talmudic literature refers to the appearance of 3 stars, from tzait kol ha-kokhavim, the appearance of “all the (potentially visible) stars.” Of course, this point demolishes^[38] Rabbeinu Tam’s interpretation that is predicated on the assumption that the meaning of the term tzait ha-kokhavim occurring in both Pesaḥim 94a and Shabbat 35a is the same. Slightly reformulated the Gaon asks how could the time of the appearance of only three stars and the time of alot hashaḥar, when (almost) all the stars are still visible, be separated by intervals of identical length from sunset and sunrise respectively?  The pre-dawn counter point to the time after sunset when (only) three stars are first visible cannot be alot hashaḥar when (almost) all stars are still visible.^[39]

This ḥiddush is not unexpected, even though the gemara in Pesaḥim is the primary sugyah used throughout halakhic history to provide a source for determining the time of alot hashaḥar.  Despite that halakhic application, the sugyah is focused primarily on geography and astronomy. Thus, harmonious use of the term tzait ha-kokhavim with its use elsewhere in Talmudic literature, which Rabbeinu Tam assumed, need not be presumed.

Since the notion of tzait kol ha-kokhavim is new, it is also not surprising that the Gaon did not specify, to the best of my knowledge, any halakhic uses for the notion of tzait kol ha-kokhavim. Of course, those who followed Rabbeinu Tam’s position had no reason to even consider a point in the evening after tzait ha-kokhavim.

However, that changed with the arrival of what we colloquially call the Brisker methodology. Talmudists of that school have produced potential halakhic implications. For example, it is not difficult to differentiate between:

• halakhot tied to a specific day or those that are to be performed every day,
• from those that have no connection to any specific day but are restricted to being performed only during the daytime period.

Presumably, the construction of the Beit HaMikdash is a straightforward example. While there is a daytime requirement,^[40] there is no constraint on which day of the week that construction should take place. Another example, which does not comport with the above ḥiluk, has been proposed by R. Moshe Soloveitchik. He suggested the use of tzait kol ha-kokhavim as a delimiter for tosefet Shabbat according to those following the Gaon.  While Shabbat ends at the time of tzait ha-kokhavim, R. Soloveitchik proposed that tosefet Shabbat is meaningful only until tzait kol ha-kokhavim.

While these examples^[41] are noteworthy, the lomdus of a yartzeit shiur by R. Joseph Soloveitchik was astonishing. Effectively, but not explicitly, R. Soloveitchik disregarded both historic interpretation and practice when he transformed Rabbeinu Tam into an early supporter of the notion of tzait kol ha-kokhavim.^[42]  As presented in that shiur, though expressed slightly differently, the dispute between the Gaon and Rabbeinu Tam revolves around whether Shabbat ends at tzait ha-kokhavim or tzait kol ha-kokhavim.^[43]

In R. Soloveitchik’s formulation, the Gaon defined a critical point along a continuum beginning at the point of sunset, when there is almost complete exposure to the sun’s illumination, and ending at the point of tzait kol ha-kokhavim when no noticeable impact from the sun’s illumination can still be detected. That critical point occurs roughly when 3 medium stars first become visible and marks the transition point between days of the week according to the geonim / Gaon.  Rabbeinu Tam, however, according to R. Soloveitchik’s formulation, defined the transition between days of the week at the point when the sun’s impact has ended entirely, a point corresponding to the end of the continuum, at tzait kol ha-kokhavim.^[44]

A possible approach that R. Soloveitchik did not employ is that the Gaon and Rabbeinu Tam decided differently based on two conflicting sugyot in Shabbat and Pesaḥim, respectively. Of course, that would be at variance with Rabbeinu Tam’s normal methodology for resolving conflicting sugyot.  Rabbeinu Tam tends to distinguish between sugyot, something he does explicitly with respect to these sugyot, as opposed to declaring sugyot in conflict and deciding between them. The principal motivation for even raising such a possibility is R. Soloveitchik’s complete avoidance of any mention of the challenges to Rabbeinu Tam’s position from the sugyah in Shabbat. This leads me to wonder if in R. Soloveitchik’s ahistorical reformulation of Rabbeinu Tam, and for reasons entirely unstated, R. Soloveitchik gave the sugyah in Pesaḥim prominence and preference over the sugyah in Shabbat according to Rabbeinu Tam.

Conclusions:

It is not at all usual to treat a ruling of the Gaon as le’migdar miltah.  However, three things increase my confidence that I am correct in this instance.

1. The reality as described in the epistle of the Ba’al ha’Tanya referenced earlier, who lived at the same time and in the same general area, clearly describes people working beyond 30 minutes after sunset, something that the Gaon would be motivated to prevent as resolutely as possible.
2. The opinion of R. Ḥaim Volozhin, in open disagreement with the Gaon’s stated position, demands a reconciliation of views.
3. The textual arguments made by rishonim, the halakhic writings and positions of noted aḥaronim, and the various arguments that I have formulated appear convincing.

What should be noted is the Gaon’s interesting ability to impact not just pesak, but the way we (perhaps even unconsciously) approach the study of sugyot.

Appendix

Prof. Levi’s Table

The three times listed in each cell of the table correspond to how difficult it is to see a star.

• The shortest time noted is when an expert who knows exactly where to look can observe a star.
• The intermediate time noted is when a star can be seen with great difficulty.
• The third time noted is when a careful observer can see a star.

The time when stars are visible to a casual observer, is yet later.

[1] My assumption is that poskim may find the innovations useful in exceptional situations as opposed to more typical ones.
[2] According to the vast majority of rishonim, the day ends when bein ha-shemashot ends or at most 2 minutes later.
[3] Familiarity with both sugyot is assumed to fully assess this essay.
[4] See my article in Hakirah spring 2019 for more detail on the Gaon’s convincing attack on Rabbeinu Tam’s position.
[5] A version of that reading is presented in Ohr Meir as the opinion of the geonim, who R. Posen seeks to demonstrate conflict with that of the Gaon.  What the Gaon felt mei ikar ha’din can be disputed as will be illustrated.  Even if one were to reject any variation of the Gaon’s stated position, this paper can also be considered to apply to the less specific view of the geonim.
[6] Both 72 or 90 minutes are increasingly assumed to apply only in the Middle East around both equinoxes and require adjustment (using depression angles) to account for variation by season and latitude.
[7] These positions are more properly characterized as variants of the position of the geonim / Gaon as they are all much closer to their normally assumed period of bein ha-shemashot.
[8] Throughout R. Kapach’s commentary on Mishnah Torah, however, he asserts that this is the position of Rambam. See R. Posen’s view as well, mentioned in footnote 5.
[9] This seminal point was made explicitly by R. Chaim Sonnenfeld in teshuvah 33 (an approbation to a sefer on zemanim) in a recently published volume of his teshuvot.  His reaction, as might be expected, was to be maḥmir, and fulfill the stringencies of both opinions. I argue that the strengths of both opinions lead to the opposite and more probable conceptual position, adopting the leniencies of both positions.
[10] See Vol. 2 of HaZemanim BeHalakha by R. Ḥaim Benish, page 360, especially footnote 58.
[11] Pages 251 – 252, Chavel edition, Mossad Ha-Rav Kook.
[12] This argument is included due to its ancient provenance; it is easily challenged given that it is normally assumed that tosefet Shabbat can begin at plag ha’minḥah, which precedes sunset.
[13] Note as well, that the gemara in Pesaḥim 94a applies to

• a day of average length,
• which occurs around both the spring and fall equinox.

However, the days that would be referred to in Shabbat 34b would be

• a minimum, as opposed to an average, and
• restricted to those days when the appearance of three stars occurs within the time needed to walk ¾ of a mil after sunset. For astronomic reasons such days occur only in the spring and not in the fall.

While neither of these two differences is itself convincing, both lend further support to the thesis developed.
[14] See the chart by Prof. Levi provided in the attachment.
[15] A more extensive analysis of Shmuel’s statement will appear in a future issue of the Torah u’Maddah journal.
[16] This section assumes detailed familiarity with the sugyah on Shabbat 34b-35b.
[17] Prepositions have been omitted from the statement in order not to bias the semantics.
[18] Large stars are defined as kokhavei lekhet, moving stars, currently called planets. Other approaches to dividing stars into categories are much less likely and not considered.
[19] The isolated opinion of R. Eliezer mi’Mitz, who begins the bein ha-shemashot period before sunset, is difficult to reconcile with Shmuel’s statement, in any case.
[20] See the last two paragraphs on page 358 and especially footnote 50 in Vol. 2 of HaZemanim BeHalakha.
[21] The time to walk 1/12 of a mil is between 1.5 and 2 minutes.
[22] While normally I would assume Prof. Levi’s third entry matches Shmuel’s assertion, since this statement might mean seeing a star does not mean bein ha-shemashot has necessarily begun, it might mean just an accidental sighting, which may occur at the earliest time possible when normally only an expert, knowing exactly where to look, can locate a star.
[23] R. Benish, R. Willig, Prof. Levi among many others struggle with this issue.
[24] In the spring Sirius and Canopus can both be seen around 15 minutes after sunset.
[25] Having seen no earlier discussion of this issue anywhere in the halakhic literature, I believe this interpretation originated with the Gaon in O. Ḥ. 261. The alternative under discussion, delaying the start of bein ha-shemashot by some small number of minutes after sunset, eliminating the hypothesis that bein ha-shemashot begins precisely at sunset, which leads to such questions.
[26] Perhaps one can assume some worsening of atmospheric conditions, as a result of pollution, slightly decreasing visibility.  I spoke with a chemist in my synagogue, Dr. Irwin Goldblatt, who verified this as a possibility.  I have no basis to determine how accurate this observation might be, but it is hard to imagine that it is consequential.
[27] See Minhagei Eretz Yisrael by R. Gliss, pages 102 and 282.
[28] Seder Hakhnosat Shabbat, found towards the end of every Ḥabad siddur, specifies 4 minutes. He reverses the position he took in Shulḥan Arukh HaRav, which supported Rabbeinu Tam.
[29]See Zemanim Ke’hilkhatam by R. Boorstyn, chapter 2, section 3, where he summarizes different 19^th and 20^th century posekim in the Middle East who supported times beyond 4 to 5 minutes and up to approximately 10 minutes after sunset.  The rationale he and many of these posekim used is varied often relying on the notion of sea level and / or visibility from higher elevations, a topic of continued debate.
[30] See the addition to Maaseh Rav section 19.  Six minutes is expressed as 1/10^th of an hour to be applied in both the morning and evening, although Shmuel’s assertion of “one star – daytime” is given as the reason for the slight delay after sunset. How R. Ḥaim Volozhin determined this precise time that equals the time at which an expert can see Sirius remains a mystery.
[31] R. Adler, R. Loerberbaum, and R. Sofer all subtract the length of the bein hashemashot interval from the end of Shabbat, see my article, Zemannim: On the Introduction of New Concepts in Halakhah, in the TuMJ 2013.
[32] It goes without saying that the instantaneous communication that characterizes of our current environment cannot be anachronistically assumed in a prior period. This impacts the assumptions made about when some of these sources are read / known, a topic not pursued further.
[33] A set of arguments based on the statement of Shmuel about 1, 2 and 3 stars are not included and will be incorporated in a future paper examining both Shmuel statement and Rambam in multiple sections of Mishnah Torah, based on their mastery of astronomy as it was known in their times.
[34] First suggested by the Gaon in O. Ḥ. 261, this approach is widely assumed in recent halakhic literature. Note that the gemara in Pesaḥim assumes an average day, which occurs in both the spring and fall around the equinox.  However, the Gaon’s argument assumes, not an average interval, but a minimum interval and one that occurs only in the spring, but not in the fall; stars are not visible as early in the fall as in the spring.  On the other hand, as suggested, a maximum would apply year-round.
[35] Prof. Levi uses a depression angle normalization to spring, which we will not explain.  His use of 28 is in fact closer to 30 minutes, as normally defined by clock-time.
[36] 12 – 13 minutes is consistent with the many rishonim supporting a time to walk a mil of 22.5 minutes.
[37] There is no reason to debate whether the underlying science favors either of the two most common halakhic definitions, which sandwich current technology’s identification of the point at which the first light of the sun is visible. Expressed as depression angles the 72- and 90-minute intervals equate to depression angles of approximately 16 and 20 degrees, respectively. With the best available equipment, light from the sun can be observed at a depression angle of approximately 18 degrees. One can then argue that 16 degrees is when the amount of light is visible to humans, while 20 degrees is when one arises in anticipation of emerging light. Both are reasonable positions for defining alot hashaḥar.
[38] So strong a word is intentional given the “bombe” kasha of the Gaon; see immediately below.
[39] R. Moshe Sofer might be trying to deal with this point about a symmetric point to the appearance of three stars in his commentary on Shabbat 34.
[40] See Rambam, Hilkhot Beit Ha’Beḥirah (1:12). Rambam’s formulation is originally stated in the negative, which raises possible questions that might be analyzed in this context.
[41] Other possible examples include the operation of a beit din, the laws of aveilut, particularly the first day, etc.
[42] The philosophical underpinnings that would enable such ahistorical ḥiddushim is beyond the scope of this article. Despite an accusation of partiality, one cannot dismiss the assumption that R. Soloveitchik was aware of the various challenges to his ḥiddush. Despite bringing support from the period of the rishonim, I believe the Rav was establishing what he knew to be a restatement of Rabbeinu Tam’s position, based on the undeniable accuracy and correctness of the Gaon’s notion of tzait kol ha-kokhavim. In my own mind, I have played out a long and imagined conversation with R. Soloveitchik on this subject.
[43] For any number of reasons, it is difficult to imagine the perspective presented was that of Rabbeinu Tam. Rather, it might represent Rabbeinu Tam’s position updated and enhanced by what is now known scientifically.
[44] What I also do not understand is why R. Soloveitchik referred to the mathematical notion of continuity as opposed to any astronomical knowledge, which I think would have been more relevant.

Introduction: Arguments about eating in the sukkah on Shemini Atzeret outside of Israel have a long and somewhat baffling history.[1] While not the only example of practice in opposition to the Shulchan Aruch, it appears to be among the most argued. The gemara, Rambam, the Tur and the Shulchan Aruch, written in many locales, all seem to be as unambiguous as possible in requiring one to eat in the sukkah. The Gaon, incensed by the spreading Chassidic custom to eat outside the sukkah, perhaps lemigdar miltah, went so far as to mandate sleeping in the sukkah on the night of shemini atzeret, in opposition to the Maharil, the Magen Avraham and normative custom. Despite consensus among all major decisors to require eating in the sukkah, an undercurrent of opposition has existed from at least the times of the early rishonim. Support for that opposition has been based on a number of apparently legitimate points. However, despite some early and consistent opposition, despite the logic and halakhic rationale of those who did not sit in the sukkah, and despite the problematic nature of the gemara (as explained below), I hope to explain the basis for the concluding and declarative statement in the gemara: “we sit but do not make a berakha.” In fact, the assumption, explicitly found[2] as far back as the times of the rishonim, that the declarative ruling was interpolated at a later point, is fundamental to explain both sides of the controversy. Some, as early as the times of the rishonim, argue that we can discount such geonic interpolations in deference to the original text which, as will be demonstrated, concludes not to sit in the sukkah. My goal is to explain why the interpolation is to be followed despite its ostensible opposition to the remainder of the text. The major thesis proposed is that one has to differentiate between a period of doubt as existed in both the yerushalmi and bavli when rosh chodesh was declared based on the observation of witnesses and a later period when rosh chodesh was determined using a fixed calendar. The geonic interpolation into the text of the gemara occurred at that later point; its rationale and inconsistency with the texts of the gemara needs to be addressed from that perspective. If I am correct, then in the period when rosh chodesh was declared based on the observation of witnesses, as in the times of Rav Yochanon and Rav,[3] sitting in the sukkah was not always required. However, when the fixed calendar was in use, the rabbis (eventually) decreed that sitting in the sukkah on Shemini Atzeret was obligatory. It may well have been more akin to a gezairah required at their time versus a continuation of historic practice. The remainder of the paper focuses on:

• An analysis of the primary texts of the gemarot that demonstrates opposition to sitting in the sukkah on Shemini Atzeret.
• A conjecture that the level of doubt in the times of the gemara was minor.
• Possible objections to sitting in the sukkah on Shimini Atzeret when not required and why they were perhaps considered overriding particularly given the level of doubt. Additionally, there are critical factors that differentiate Shemini Atzeret from other cases of yom tov sheni.
• The interpolation by the geonim, and their insistence on sitting in the sukkah despite earlier halakhic rulings.
• The objection to the gemara’s conclusion by some early authorities and their different practices.
• Reasons that would exempt you from sukkah in general, would certainly exempt you on Shemini Atzeret; mitztayer and kabbalat penai rabbo are analyzed as bases for not sitting in the sukkah.
• A summary and a modest proposal.

Section 1 – An analysis of the primary text of the gemarot demonstrates opposition to sitting in the sukkah on Shemini Atzeret. The sugya in the bavli masechet sukkah beginning on 46b contains three parts:[4] A. The disagreement of Rav Yochanon and Rav. R. Judah the son of R. Samuel b. Shilath citing Rav ruled: The eighth day which may be the seventh is regarded as the seventh in respect of the sukkah and as the eighth in respect of the benediction. R. Yochanon, however, ruled: It is regarded as the eighth in respect of both. B. Two approaches to interpreting the disagreement. FIRST APPROACH: That one must dwell [in the sukkah on the eighth day] is agreed by all, they only differ on the question of the benediction. According to him who regards the day as the seventh in respect of the sukkah, we also recite the benediction [of the sukkah], while according to him who holds that it is regarded as the eighth in respect of both, we do not recite the benediction [of the sukkah]. R. Joseph observed: Hold fast to the ruling of R. Yochanan, since R. Huna b. Bizna and all the notables of his age once entered a sukkah on the eighth day which may have been the seventh, and while they sat therein, they did not recite the benediction. But is it not possible that they were of the same opinion as he who laid down that once a man has recited the benediction on the first day, he has no more need to recite it? — There was a tradition that they had just come from the fields. SECOND APPROACH: (the ikka de’amri) There are some who say that the ruling that one must not recite the benediction [of the sukkah] is agreed upon by both, and that they only differ on the question whether one must sit [inthe sukkah]. According to him who ruled that it is regarded as the seventh day in respect of the sukkah, we must indeed sit in it thereon, while according to him who ruled that it is regarded as the eighth day in respect of both, we may not even sit in it thereon. R. Joseph observed: Hold fast to the ruling of R.Yochanan. For who is the authority of the statement? R. Judah the son of R. Samuel b. Shilath [of course], and he himself sat on the eighth day which might be the seventh outside the sukkah. C. A declarative ruling that “we sit but do not make a berakha.” And the law is that we must indeed sit in the sukkah but may not recite the benediction. A. The disagreement of Rav Yochanon and Rav: Rav states that Shemini Atzeret is treated as the seventh for “this” and the eighth for “that.” Rav Yochanon states it is the considered as the eighth for “this” and “that.” The two approaches differ as to what “this” and “that” refer.[5] B. Two approaches to interpreting the disagreement: The first alternative assumes that all agree that sitting in the sukkah is obligatory; the argument concerns whether to make a berakha. In this approach Rav is asserting that one makes a berakha “leishev ba’sukkah.” The phrase “the seventh for this” refers to this obligation for a berakha on sitting in the sukkah. “The eighth for that” refers to the fact that the other prayers of Shemini Atzeret – kiddush and tefillah – mention only the eighth day and make no mention of Sukkot. Rav Yochanon asserts we make no reference to Sukkot, making no berakha when sitting in the sukkah on the eighth. It is the eight for “this” refers to sitting in the sukkah without a berakha; “the eighth for that” is interpreted identically to Rav. According to both opinions, “this” refers to whether or not a berakha is made when sitting in the sukkah on Shemini Atzeret. According to both opinions, “that” refers to the mention of only Shemini Atzeret in the prayers of the eighth day. This reading is rather forced in that there does not appear to be any disagreement about what holiday ought to be referred to in the various prayers and blessings of the eighth day. While the word “this” is informative, the word “that” is not. Stating both Sukkot and Shemini Atzeret in one prayer/blessing would be contradictory; declaring a day to be both Sukkot and Shemini Atzeret was never even raised as a possibility and for good reason. The first approach then quotes practice that supports the view of Rav Yochanon, suggesting that we are to follow the opinion of Rav Yochanon. The second approach assumes not making a berakha on sitting in the sukkah is undisputed; the argument is about even sitting in the sukkah. Thus the second part of the phrase – the eighth for “that” states that common view of both Rav and Rav Yochanon omitting a berakha on sitting in the sukkah. “This” refers to the obligation to sit in the sukkah. Rav maintains for “this” it is considered the seventh and hence one is obligated to sit in the sukkah. Rav Yochanon maintains it is the eighth for “this” as well with no obligation to sit in the sukkah. Note that in this approach of the ikaa de’amri, both parts of the sentence are informative. The second approach then also quotes practice that supports the view of Rav Yochanon, suggesting that we follow the opinion of Rav Yochanon Were the sugya to end at this point, the conclusion would be clear for two reasons. Each reason itself is two-fold, resulting from both a general principle as well as a detail present in this specific case.

• First, generally, where there are two alternative approaches, the second, the ikaa de’amri, is assumed normative.[6] As well in this specific case, as indicated, the phrase of both Rav and Rav Yochanon is more informative in the formulation of the ikka de’amri.
• Second, when there is a dispute between Rav and Rav Yochanon, we generally follow Rav Yochanon.[7]As well, in this specific case the text in both alternatives immediately includes an example of practice that follows the opinion of Rav Yochanon.

Taken together, we would assume to follow the second alternative and the opinion of Rav Yochanon – and not sit in the sukkah on Shemini Atzeret. According to many readings, this conclusion is made even more strongly by the yerushalmi.[8] While the bavli addresses the obligation to sit in the sukkah, the yerushalmi notes that one may not sit in the sukkah while making kiddush but one may enter the sukkah afterwards if he so desires. While some rishonim quote this yerushalmi as opposing the psak of the bavli,[9] others claim[10] that the yerushalmi is addressing a region of Israel where there was no doubt about what day the courts declared rosh chodesh. Rabbi Schacter, in support of the former opinion, observed that the yerushalmi uses the expression “leilai yom tov achron;” the plural, “leilai” is only relevant if there is a yom tov sheni on the ninth. Given this interpretation, the yerushalmi is making a rather strong point of equating the nights of the eighth and ninth, dismissing any possibility of an obligation to eat in the sukkah on the eighth.[11] C. A declarative ruling that “we sit but do not make a berakha:” Despite the reading of the gemara as outlined, the bavli concludes that “we sit but do not make a berakha.” This opinion is that of both Rav in the second alternative and Rav Yochanon in the first alternative. This ruling corresponds to two of four opinions quoted; the two alternative opinions – not sitting at all or sitting and making a berakha – are only supported by one amora and only according to one alternative. Despite that, this ruling is contradicted by the normal principles of psak where we would follow Rav Yochanon’s opinion in the second alternative, as well as the yerushalmi. The language of the gemara “shemini safek shevii,” and in particular the various amoraim cited, place the gemara not in the period of calculation based on a fixed calendar, but still during a period where rosh chodesh was declared based on observation. During that period, yom tov sheni was observed because of real doubt and also, at some point, as a precaution even during those years where doubt did not exist. Given the establishment of a fixed calendar in 359 CE by Hillel II, it is not entirely clear in exactly what era yom tov sheni was firmly established and, more importantly, when it was extended to include sitting in the sukkah on Shemini Atzeret. It is entirely plausible, that this declarative ruling obligating sitting in the sukkah on Shemini Atzeret followed the period debated in the gemara by multiple centuries. This resolves the apparent contradiction in the text. Why this was not stated explicitly in the gemara is only problematic if one does not assume it was obvious. Section 2 – A conjecture that the level of doubt in the times of the gemara was minor. Returning now to the period of real doubt over which day was declared rosh chodesh, the question of why was sitting in the sukkah not considered mandatory? We will deal with a number of reasons that would argue against sitting in the sukkah in the next section. However, there are two factors that would reduce the level of doubt in the times of declaration based on observation.

• First, atmospheric conditions in the Middle East around the beginning of Tishrai are normally excellent and the ability for a new moon crescent to be observed is very high.[12]
• Second, the beit din had flexibility to reduce any doubt around Rosh HaShana. When necessary, the beit din could delay declarations of rosh chodesh Elul to guarantee that a moon’s crescent would always be present to be observed on the evening following the 29th of Elul.[13]

These two factors lowered the level of doubt considerably. In addition,

• the late date in the month when Shemini Atzeret occurs and
• the effort to determine Yom Kippur

would likely reduce the level of doubt even further. After fasting only on the 10th day of Tishrai as Yom Kippur, it is entirely possible that in spite of observing yom tov sheni on the first days of sukkot, the level of doubt was minimal and insufficient to overcome the objections covered in the next section.[14] Section 3 – Possible objections to sitting in the sukkah on Shemini Atzeret when not required and why they were overriding particularly given the level of doubt. Additionally, one can differentiate Shemini Atzeret from the more usual case of yom tov sheni on multiple grounds. There are two potential issues with sitting in the sukkah on Shemini Atzeret, tarti de’sasreh, acting in a contradictory manner[15] and violating the prohibition to add to a mitzvah, by adding an additional day of sukkah observance, particularly on Shemini Atzeret where sitting in a sukkah is not part of the observance.[16] In the case of sitting in the sukkah, a potentially neutral act, neither is violated if some aspect of performance is compromised; however, the degree of compromise required may be in dispute. Regardless of which of the two reasons[17] is invoked, in a case of limited doubt, one or the other or both may have been sufficient to make sitting in the sukkah on Shemini Atzeret either not obligatory or perhaps not even permitted without some restrictions. Both the yerushalmi and various opinions in the main text of the bavli, support this conclusion. At some point after a fixed calendar was established in the fourth century, a second day of yom tov was formalized (or maintained.)[18] As Rav Soloveitchik explained, an additional level of kedushat yom tov was applied to either an ordinary day (the day after a yom tov, isru chag) or the first day of chol hamoed because of sefaikah de’yoma. This additional level of kedusha, automatically invoked obligations for kiddush, tefillah, sippur yetziat mitzraim, etc. as well as prohibitions from work. Of course, such an approach could not be applied to Shemini Atzeret; it was already a holiday and one could not add to its kedusha, only change it. This was not done; note that we do not mention Sukkot nor do we observe the mitzvah of lulav. We simply sit in the sukkah without a berakha, something that is both different from a halakhic perspective from other observances of yom tov sheni that derive from the changed status of the day, and in Rav Soloveitchik’s opinion, less than satisfactory conceptually. He said, perhaps half-seriously, that despite his unwavering adherence to normative halakha, the position of the chassidim makes more sense. In any case, sitting in the sukkah is a unique observance with textual, historical and conceptual challenges. Section 4 – The interpolation by the geonim[19], and their insistence on sitting in the sukkah despite earlier halakhic rulings. I do not know the precise history of yom tov sheni. However, both reciting berakhot during yom tov sheni against normal halakhic practice,[20] as well as the assumed halakhic interpolation by the geonim requiring sitting in the sukkah on Shemini Atzeret may both have similar origin – the need to reinforce the observance of yom tov sheni. As Dr. Haym Soloveitchik points out,[21] the case of sukkah on Shemini Atzeret proves the wisdom of insisting on a berakha; the one mitzvah of yom tov sheni for which we do not recite a berakha, resulted in widespread non-observance. It seems more than likely that this interpolation was recognized as “outside the norm” if the practice during the period of doubt did not include sitting in the sukkah on Shemini Atzeret. Like berakhot, it may have been viewed as necessary particularly following a single day observance of Yom Kippur to strengthen the observance of yom tov sheni. One can only assume that the ruling’s discontinuity from the remainder of the text of the gemara was recognized and did not need elucidation; when first written, a then contemporary reader would recognize the change in practice. Section 5 – The objection to the gemara’s conclusion by some early authorities and their different practices. Given universal acceptance of the observance of yom tov sheni in the times of the rishonim, one would not have expected any deviation from the gemara’s definitive conclusion. Rabbi Schacter and Dr. Soloveitchik highlight a number of sources that illustrate the lack of universal acceptance of the gemara’s conclusion by Rashi’s rebbe and members of his family,[22] a distinguished member of the Maharil’s community,[23] and by a member of the Kolonymous family.[24] Citing the core sugya in the bavli and the yerushalmi, while certainly relevant does not in and of itself justify deviating from a clear conclusion even if it is of geonic origin. What is universally conjectured is that the cold climate of Northern Europe motivated a change. For the geonim omitting a berakha constituted enough of a heker to obviate either objection – either a tarti de’sasreh or violating a prohibition to add to a mitzvah by adding an additional day of sukkah observance. In a temperate climate, eating outside without a berakha renders sitting in the sukkah a more balanced act – clearly not a complete fulfillment of the obligation to sit in the sukkah, but, nonetheless, still honoring the institution of yom tov sheni shel galyot. However, in the cold climate of Northern Europe, even absent a berakha, either objection would, as it did in the times of real safek, make sitting in the sukkah (at least during kiddush) problematic. Note as well that the custom of returning to the sukkah during the day is consistent with this logic. During the day:

• the temperature is milder,
• there is no tarti de’sasreh from the recitation of kiddush, and
• having been absent from the sukkah at night, as Rav Soloveitchik pointed out, creates a discontinuity of performance that renders sitting in the sukkah the following day a non-violation of adding to the mitzvah.

What is perhaps most surprising is that even after the period of the Tur and Shulchan Aruch, Rav Yosef Yuzpa, the dayan in Frankfurt am Mein around the end of the 16th and beginning of the 17th century, when Rav Isaiah Horowitz, the Shelah HaKadosh, was Rav, in his sefer Yosef Ometz was still able to state that a family, descendant of Troyes, who does not sit in the sukkah, “has on what to rely.”[25] Section 6 – Reasons that would exempt you from sukkah in general, would certainly exempt you on shemini atzeret; mitztayer and kabbalat penai rabbo are analyzed as bases for not sitting in the sukkah. Mitztayer would exempt one from sitting in the sukkah not just on Shemini Atzeret but also on Sukkot proper. However, mitztayer is likely not binary. At one extreme, by living unnaturally in the sukkah one may not even fulfill one’s obligation, regardless of intent, as would be the case in extreme cold or very rainy weather. If, however, it is somewhat uncomfortable given the elements, sitting in the sukkah may no longer be obligatory, while it would still remain a fulfillment of one’s obligation. It seems logical as well to differentiate further the notion of mitztayer as it might apply to Sukkot versus Shemini Atzeret. Perhaps a yet lesser degree of mitztayer, not sufficient to allow eating outside the sukkah on Sukkot, might nonetheless, be more than sufficient to override and invalidate the level of heker made by not reciting a berakha. I have not seen any discussion of this notion by poskim, despite its apparent logic.[26] By analogy, one might not be legally drunk, but nonetheless it would be wise not to drive a car. Similarly, one might argue for eating outside the sukkah on Shemini Atzeret in conditions that do not meet the halakhic definition of mitztayer on Sukkot proper. Thus, cold temperatures that might not justify eating outside the sukkah on Sukkot could nonetheless justify, and indeed perhaps mandate, not eating in the sukkah on Shemini Atzeret. Rav Soloveitchik, in an attempt to justify Chassidic practice, noted the importance of the night of Shemini Atzeret, following the “guten kvitel” that Kabbalists associated with the day of Hoshana Rabbah. Like the exemption accorded to the celebration of sheva berachot even on Sukkot, when the sukkah does not comfortably provide adequate room, one can argue that the large celebrations by Chassidim where they are mekabeil penai rabbom, would similarly provide an exemption. I would add that here as well, a lesser degree of need might again be seen as voiding any heker provided by just omitting a berakha. Of course, while this explains why a tisch was held outside the sukkah, it does not in any way justify a general practice of avoiding the sukkah that has become widespread in many Chassidic circles.[27] Section 7 – A summary and a modest proposal. The discussion in the gemara covered a period of history where there was real doubt about the declaration of rosh chodesh, although in the case of Shemini Atzeret, that doubt was minimal. In the face of minimal doubt, the reasons not to sit in the sukkah prevailed. The geonim, perhaps in order to strengthen the notion of yom tov sheini, instituted the practice that “we sit but do not make a berakha.” It is not my intent to give halakhic advice; some might suggest that perhaps we ought to not even ask a local rabbi as much as follow family practice. In any case, for those who eat in the sukkah, I would consider situations of partial mitztayer that might arise, where eating in the sukkah may not be appropriate. On the other hand, given widespread laxity, one might argue that the stringencies of the geonim and the Gaon might again be particularly relevant. Of course, most fundamentally for those whose ancestors ate outside the sukkah in Warsaw, conditions are rather different in Miami,[28] or even in Baltimore or Boston.

This is the last of four posts based on a forthcoming monograph by Dr. William Gewirtz that addresses the period of bein hashemashot, the most fundamental area of dispute in the area of zemanim.

The previous post summarized the main sections of the monograph; this post summarizes some of the areas of innovation and is followed by concluding observations.

Much of what was proposed tacitly made two basic assumptions:

 First, both halakhic practice and its conceptualization were influenced by the migration of Jews from the Middle East to Central and Northern Europe during a period when the impact of latitude on zemanim was not yet understood.
 Second, with the subsequent growth of clocks, increasingly, halakhic practice was specified using time in preference to observation of natural events.

It is probable that both of these factors were consequential. (Increasingly, time replaced observation as the basis for specifying halakhot. Preference for a time based halakhic rule (72 minutes, for example) over the underlying event from which the interval of time was derived has become increasingly common. More subjectively defined phenomena like misheyakir or the approximate boundary between a medium and a small star were less often utilized and, as a result, became less well understood.)

The PDF of the entire epilogue is attached. The epilogue includes a complete list of the innovations that have been proposed and a more extensive version of post 3. A subset of the innovations proposed and a concluding example and remarks follow below:

1. The dispute between the geonim and Rabbeinu Tam revolves around placing the interval of bein hashemashot, whose length is the time to walk ¾ mil, within the interval between sunset and tzait (kol) hakokhavim whose length is the time to walk 4 mil. It is normally assumed that:

 the opinion of the geonim places bein hashemashot at the start of the interval, while
 Rabbeinu Tam places it at its end.

Those two alternatives represent opposite extremes. Two modifications were suggested throughout:

 First, separate the dispute between the geonim and Rabbeinu Tam into two distinct components; the first concerns the beginning and the second the end of the bein hashemashot period, subject to a constraint on the length of the bein hashemashot interval.
 Second, assume that there are multiple hybrid / intermediate positions, bracketed by these two alternatives. (These positions might be more properly characterized as variants to the position of the geonim as they are all much closer to their bein hashemashot interval.)

This allows:

 an interpretation of the gemara in Shabbat similar or more likely identical to that of the overwhelmingly compelling position of the geonim relative to the end of the bein hashemashot period,

 while defining the beginning of bein hashemashot using a variant of the textual approach of the Shulchan Aruch and Rabbeinu Tam.

While I have not seen this conceptualization formulated explicitly (Throughout R. Kapach’s commentary on Mishneh Torah, however, he asserts that this is the position of Rambam.) in the classic halakhic literature, practice and a number of pragmatic opinions are supportive of such an approach. This approach impacted sections 5 – 8 and is central to many of the suggested innovations. The opposite implication:

 Anyone who rejects the start of Shabbat precisely at or even some number of minutes after sunset must embrace the approach of Rabbeinu Tam

which does not follow logically, is often found in the literature.
2. It is preferable to read the gemara in Shabbat assuming that all opinions vary insignificantly concerning the end of Shabbat; this is the opinion of almost all rishonim and independent of the position of Rabbeinu Tam. The gemara’s focus is primarily on the beginning of bein hashemashot on Friday evening, and that point is in dispute.

3. Modern practice, contemporary halakhic literature, as well as colloquial idiom, typically refers to time intervals calculated from sunset. Assuming that way of thinking when reading specific sources, we fail to consider that the gemara, various rishonim and achronim (we referenced R. Lorberbaum, R. Adler and R. Sofer) refer to intervals of time counting backward from the end of Shabbat as well, not always counting forward from sunset.

4. Rabbah’s interval, the time to walk ¾ mil, is more likely an upper bound on the length of bein hashemashot (the length of bein hashemashot in the summer) counting back from the point of chashekha versus a lower bound (the length of bein hashemashot in the spring) counting forward from sunset. Treating the gemara in Shabbat similar to the gemara in Pesachim as referring only to the (fall and) spring equinox is unnecessary when thinking of the interval as a practical upper bound. (First suggested by the Gaon in OC 261 and widely assumed in recent halakhic literature. Note while the gemara in Pesachim assumes an average that occurs at both the spring and fall equinox, the Gaon’s argument assumes, not an average, but a minimum and referring only to the spring, but not the fall equinox. No rishonim, who limit the gemara in Pesachim to the equinox periods in the fall and spring, make any such assertion with respect to the gemara in Shabbat. A maximum, as opposed to a minimum, would apply year round, as one might also conclude from the lack of commentary.) All the other measures in the gemara of chashekha, the appearance of the horizon, or the visibility of three stars apply year-round. Some of the arguments in favor of such a position include:

 The gemara in Shabbat is discussing Friday night and the beginning of bein hashemashot, as opposed to its end. If the time to walk ¾ of a mil were a minimum, counting forward from the beginning of bein hashemashot, it would address the end of bein hashemashot and the end of Shabbat, as opposed to its beginning.
 The three fractions of the time to walk a mil that are given as alternatives for the length of bein hashemashot would all have identical semantics counting back from the assumed point of chashekha.
 The interval of bein hashemashot is of practical consequence providing a useful upper-bound as opposed to a theoretical lower bound.
 If someone were countering the position of Rabi Yosi, who says bein hashemashot is instantaneous, it is more likely that he would say that it can be as long as opposed to as short as.

5. Shmuel’s assertion about 1, 2 and 3 stars is likely to mean that one star can still occur during daytime, but two stars only (If we assume that bein hashemashot begins 14 -15 minutes after sunset then “only” should be replaced with “almost always.” Though proposed by R. Kapach in his interpretation of Rambam, it would make Shmuel’s assertion slightly less useful. The suggested meaning of Shmuel’s statement is more elegant if we assume that bein hashemashot starts at most 12 – 13 minutes after sunset in the Middle East.) appear after the beginning of bein hashemashot (whose start may also precede the appearance of the first star) and three stars confirm that the transition to the next day has occurred.

6. Moving the beginning of bein hashemashot forward from sunset even according to Rabbah, a variant of the generally assumed opinion of the geonim, successively solves the following issues:

 at 4 – 5 minutes, the minimal time reported as the custom of Jerusalem as well as the opinion of R. Shneur Zalman of Liadi, the point when the sun disappears from the highest elevations around Jerusalem, Shmuel is consistent at least in a limited sense with R. Yosef while remaining completely inconsistent with Rabbah.
 at 6 minutes, the opinion of R. Chaim Volozhiner and the appearance of a single star in the spring to an expert observer, Shmuel is more easily consistent with R. Yosef but consistent with Rabbah only in a limited sense.
 at 7 – 15 minutes depending on a variety of factors, Shmuel is entirely consistent with Rabi Yehudah and the time to walk ¾ mil can be easily considered a practical upper bound.

7. While many equate and then struggle to resolve Rambam’s approach to Shabbat and Kiddush Hachodesh; I assume they are dissimilar. (Why so obvious an approach was not considered may be related to the assumption that safek chashekha and bein hashemashot are coincident. Though the two notions may be practically coincident, they are certainly not conceptually the same. For those following an opinion akin to the geonim for the end of Shabbat, they may not even be practically coincident. Within the halakhic literature there are differing opinions about the relationship between safek chashekha and bein hashemashot.) In both instances, Rambam considers chashekha as defining the end of a day. For a beit din declaring the beginning of a new month, Rambam sees no necessity to impose an interval of bein hashemashot. Thus, Rambam in hilkhot Kiddush Hachodesh states the halakha in (2:8) and then the recommended practice in (2:9). However, in hilkhot Shabbat, as noted in our opening paragraph, when dealing with a community, Rambam utilizes a notion of bein hashemashot, an interval that he defines practically as opposed to theoretically.

8. While the appearance of the horizon and the visibility of stars are difficult to reconcile with the opinion of Rabbeinu Tam, the argument between Abaye and Ravah, looking east and west at the same point in time, is most challenging. I cannot conceive of anyone in the Middle East detecting any change looking at the eastern sky 50 – 60 minutes after sunset. This is perhaps the greatest challenge to Rabbeinu Tam’s definition of the end of Shabbat.

9. It is probable that R. Adler’s 24/35 minute period of bein hashemashot is computed counting back from Rabbeinu Tam’s conceptual end of Shabbat. The alternatives, either counting back from the time that the Frankfurt community typically observed as the end of Shabbat or counting forward from any point in time, are less plausible. While this formulation faces textual challenges, other attempts to explain R. Adler’s opinion including that assumed by the editors referenced by Dr. Leiman as well as multiple suggestions of R. Benish face far more difficulty.

10. A number of recent essays on zemanim, including those by R. Kotler and R. Willig, suggest specific dependencies linking

 the dispute between the geonim and Rabbeinu Tam,
 the dispute whether shaot zemaniot are calculated from sunrise or from alot hashachar,
 and in the case of R. Willig even the time to walk a mil.

I see no such logical dependency and found that custom and / or authorities supported almost every possible combination of alternatives.

11. It is puzzling that when calculating the opinion of the Magen Avraham / Trumat Hadeshen attention to the impact of latitude and/or seasonality is rarely taken into account. In addition to morning zemanim, like the latest time for kriat shema, being earlier, this approach would also provide an alternative for plag haminkha (that many communities in US latitudes might find useful.) Similarly, adjusting alot hashachar would often imply an earlier start for those fast days that start at daybreak (particularly the 17th of Tammuz.) (While not a Magen Avraham specific issue since alot hashachar is applicable according to all opinions, invariance of the 72/90 minute interval is likely inherited from similar practice applied to the position of Rabbeinu Tam with respect to the end of Shabbat which then influenced the calculation of shaot zemaniot according to the Magen Avraham. (See summary for category 3. where this is further explained.) Though conceptually challenging in both contexts, a fixed 72/90 minutes does not create obvious observational issues, except for alot hashachar and only at latitudes further from the equator, like northern Europe.) That would avoid a practice that allows eating on the morning of a fast as late as (or even after) the time of misheyakir.

A concluding example:

The migration of Jews from the Middle East to other locations required adjustment in practice that often necessitated creating concrete concepts in areas that might have otherwise been left unexplored. That process contributed to a wealth of material with which many poskim have had to grapple. Both the categorization and the new approaches that have been proposed should make this vast halakhic literature more understandable.

As I mentioned in the preamble, criticism within the rabbinic literature has been muted, (There are a few very notable and important exceptions.) and potential inaccuracies have often not been identified and discussed adequately. As a result, it is impossible (perhaps even for great poskim who are unacquainted with astronomy or the impacts of season and /or latitude) to read the literature without intense effort.

Let me illustrate using the most widely followed posek of our times, and conclude with a few words, which I hope will be taken as they are meant. I choose R. Feinstein because I assume that many will conclude that if his responsa illustrate my concerns, I could have easily chosen any number of other poskim.

Consider five decisions of R. Feinstein:

1. In the New York area, Shabbat ends 50 minutes after sunset even in accordance with Rabbeinu Tam.
2. One can pray as early as 90 minutes before sunrise under special circumstances.
3. Perform a brit the following week on Wednesday, for example, for a baby born late Wednesday afternoon until 9 minutes after sunset.
4. In the New York area, allow specific activities forbidden only at a rabbinic level on the Shabbat until 40 minutes after sunset on Friday.
5. Unlike other zemanim, chatzot is always at the same time (that varies by location) and does not vary throughout the year.

Summarizing issues discussed previously, these tshuvot are challenging in six (R. Feinstein’s mention of the time to walk 4 mil as 96 minutes while given no practical consequence is also problematic.) different areas:

1. Like R. Pimential approach to Holland, R. Feinstein’s derivation of 50 minutes for New York, reasons by analogy on the appearance of stars, using Lithuania as his base for 72 minutes. Were R. Feinstein to have used Babylonia, certainly a more logical choice, he would undoubtedly have reached a radically different conclusion. R. Willig expresses a similar point, albeit less directly. (This issue was raised directly in a recent sefer by R. D. Heber, Shaarei Zemanim, page 90.) Generally, this psak is quoted without hesitation or comment. (Perhaps new meaning for the term chassid shoteh can be ascribed to the publishers of a sheet I picked up at the Kotel, that provide R. Feinstein’s 50 minute zman for New York for use in Jerusalem.)
2. As R. Feinstein is following the conceptual approach of Rabbeinu Tam, then the end of Shabbat and the time for alot hashachar ought to be treated identically. Instead, R. Feinstein:

 relies on a 22.5 versus 18 minute time to walk a mil for alot hashachar but never even suggests a 22.5 minutes based stringency for Shabbat,
 adjusts only Shabbat’s end but not alot hashachar based on latitude (R. Feinstein does briefly mention the possibility of latitude adjustments for alot hashachar in the tshuva but chooses not use it.) and
 never addresses the relationship between his rulings that, according to the opinion of Rabbeinu Tam that he is following, are conceptually linked.

3. Adjusting zemanim based on latitude to correlate to a physical occurrence like the appearance of stars or the degree of light is strongly supported. However, directly adjusting the time to walk a mil whose length is linked neither to latitude nor to season by location, has no logical basis and leads to conclusions that are in fundamental conflict with observation. (While there exists imprecise language in the literature prior to R. Feinstein that talks in terms of such adjustments, using it as a basis for a psak that reduces / equates 13.5 minutes to 9.375 minutes is inexplicable. As we have noted, this is logically equivalent to asserting a watch that moves 72 minutes in Lithuania, only moves 50 minutes in New York.)

4. Deriving the beginning of bein hashemashot by subtracting from the time that Shabbat ends is common in psak and rooted in the text of the gemara. However, it requires that the end of Shabbat be accurately established. The time that R. Feinstein uses for the end of Shabbat is his (and R. Y. M. Tukitzinsky’s) calculation that is among the most stringent methods for calculating what is already a stringency based on three small stars and not the point that the gemara uses, three medium stars. This is further impacted by R. Feinstein’s use of a “truncated / adjusted” time to walk ¾ mil of 9.375 minutes (as opposed to 13.5 minutes) for the New York area, resulting in a significant leniency. To be concrete, as opposed to the 40 minutes (50 minutes and subtracting 9.375 minutes for bein hashemashot) after sunset that R. Feinstein derives, three medium stars are visible approximately 27 – 32 minutes after sunset, safek chashekha and certainly bein hashemashot precedes that point by some number of minutes. Of course, R. Feinstein, operating within the framework of Rabbeinu Tam, may not consider 50 minutes as a stringency.

5. Chatzot varies slightly day to day (given the tilt of the earth in its orbit) according to the all methods for calculating the hours of the day; the variation is approximately 20 minutes in the New York area.

6. At a very fastidious level, R. Feinstein calculates adjustments based on latitude without regard for the non-linear relationships that exist between the duration of different sub-intervals of bein hashemashot.

In all but the third item above, R. Feinstein had an extensive literature from which to derive support. As was noted, R. Soloveitchik carefully recast the opinion Rabbeinu Tam to avoid these and other issues. However, he ended up with a conceptual approach to Rabbeinu Tam as well as a personal chumrah, which is almost unheard of in the halakhic literature and widely divergent from practice. However, given that this is an area with a long tradition of practice, great poskim, of which R. Feinstein is a unique example, exhibit an impeccable sense (In addition to or perhaps as a result of siyatta di’shemaya.) that guides them in how to decide. I remain struck by the accuracy of the psakim, independent of their problematic rationale. Let us reexamine the five decisions and how they might be alternatively justified:

1. Shabbat ends 50 minutes after sunset in the New York area. Despite this not being the conceptual opinion of Rabbeinu Tam, as R. Feinstein assumes, it is precisely the opinion of the geonim as calculated by R. Yechial Michal Tukitzinsky, the first major contemporary figure to write extensively on this topic combining knowledge of both halakha and astronomy. (R. Belsky’s (re)interpretation of R. Feinstein makes this correspondence precise. See the commentary supporting the www.myzmanim.com website.)
2. One can pray as early as 90 minutes before sunrise in special circumstances. A latitude and seasonal adjustment of 90 minutes provides a basis for yet greater leniency. Beyond the reliance on a 22.5 minute mil, 90 minutes in New York is close to both the scientific point of first light (approximately 90 to 120 minutes), and, more importantly, a latitude/season adjusted 72 minutes (approximately 80 to 110 minutes). The fact that R. Feinstein was willing to rule so differently on the end of the Shabbat and alot hashachar aligns with tradition, albeit in conflict with the conceptual viewpoint of Rabbeinu Tam.
3. Perform a brit the following week on Wednesday, for example, for a baby born late Wednesday afternoon until 9 minutes after sunset. Clearly, this psak is in perfect alignment with the views developed and similar to the tradition of Jerusalem over the generations that assumed that a baby born a few minutes after sunset has his brit on the same day the following week. (See Minhagei Eretz Yisrael by R. Yaakov Gliss, pages 102 and 282 who mentions 4 – 5 minutes and Zemanim Kehilkhatam by R. Boorstyn, chapter 2, section 1, footnote 7, who claims that R. Shmuel Salant, would rule that a baby born after sunset but before the call of the mugrab, seven to ten minutes after sunset, has his brit on the same day the following week.) Even rejecting Rabbeinu Tam’s late end of Shabbat based on the overwhelming arguments of the Gaon and others, a start to a day a few minutes after sunset is supported by generations of practice. Even R. Feinstein’s reliance on Rabbeinu Tam for a slightly delayed beginning to bein hashemashot is often rejected.
4. Allow specific activities forbidden only at a rabbinic level on the Shabbat until 40 minutes after sunset. Perhaps the most challenging given the undisputed assumption that the gemara meant bein hashemashot to extend back from three medium stars (a depression angle of about 6 degrees) versus R. Feinstein’s roughly 8.5 degrees and R. Feinstein’s use of a “truncated / adjusted” 9.375 minutes to walk ¾ mil. Nonetheless, being exceedingly liberal with respect to a rabbinic prohibition, especially, in the face of need, has a long tradition. Unfortunately, in most, if not all seasons of the year, 40 minutes after sunset, is well past the point of chashekha, in the New York area.
5. Chatzot is always at the same time. As with R. Feinstein’s 50 minutes, there is a need for seasonal adjustment. It appears, like a number of Rabbis who oppose this type of complexity in psak, R. Feinstein’s tradition was to use a single time.

On the first three rulings, R. Feinstein’s psak can be easily justified on other grounds. The last two are somewhat less critical and more problematic. However, it is often dangerous for Rabbis to apply or extend elements of R. Feinstein’s logic to other areas where zemanim are critical without his innate sense of psak.

Final Comments:

This monograph was intended to address seminal issues relevant to bein hashemashot without covering in depth many important sub-topics. Hopefully, the approach and observations will make this vast literature easier to study. While I did not want to address explicitly either philosophic issues or practical issues of psak, I suspect that my personal opinions on both are clear. I was strongly motivated to defend minhag Yisroel, a mimetic tradition that for many centuries, even until the Second World War, relied on the opinion of Rabbeinu Tam in many parts of Europe.

As I studied this topic, I was repeatedly revisiting three issues:

 If in ancient times, sunset, a very easily identified occurrence, was considered the precise starting time for Shabbat, how could it have ever been forgotten and / or abandoned? If Shabbat started sometime after sunset, then the position of Rabbeinu Tam and an overwhelming number of rishonim is more plausible. As Jews migrated northward, the required beginning to Shabbat separated even further from sunset, particularly if bein hashemashot was thought to have an unchanging maximum length – the time to walk ¾ of a mil.

 If observation challenged only Rabbeinu Tam’s opinion while leaving the approach of the geonim free of any issues, why did major figures living in southern Europe and even the Middle East, including Ramban and (likely) R. Yosef Caro, adhere to Rabbeinu Tam’s opinion?

 How could generations of practice that relied on the opinion of Rabbeinu Tam or some related variant be so easily discounted? In my mind, the modern bias to treat sunset as a given (and reject even R. Feinstein’s limited reliance on the position of Rabbeinu Tam) is unwarranted.

I hope that what I have written, at least partially, addresses these questions.

The approach developed posits that bein hashemashot begins after sunset, later than many assume, while its end is somewhat earlier than current practice. (R. Y. C. Sonnenfeld’s tshuva 33 (an approbation to a sefer on zemanim) on this topic is remarkably supportive. While speculating that we may have to wait for Elijah to defend the fundamental difficulties with Rabbeinu Tam’s end to bein hashemashot and Shabbat, he raises issues with the approach of the Gaon as to the beginning of bein hashemashot from texts of gemara that imply that the day extends past sunset. While suggesting that we follow both chumrot and stating a personal preference not to attempt to decide on a matter so long in dispute, he expresses hope that this will be clarified one day. I believe that I have taken a step in that direction. In any case, regardless of his suggested practice, like this monograph he raises issues with both the end time of Rabbeinu Tam and the start time of the geonim. While R. Sonnenfeld suggests that one adopt the stringencies of both positions, the approach developed and generations of practice often made use of the leniencies of a hybrid approach.) While some will contend that the criticism, suggested innovations, and conclusions do not exhibit sufficient deference to recent generations of psak, I hope that this monograph demonstrates a commitment to integrity, clarity, simplicity, consistency with basic astronomic observations, faithfulness to basic texts and respect for generations of halakhic insights and in particular, practice.

In summary, a fulsome defense for a later start to Shabbat is anchored on three points:

1. Mishetishkeh hakhamah refers to a point after sunset.

2. The time to walk ¾ of a mil is the maximum length of bein hashemashot not the minimum.

3. When applying the gemara’s interval of bein hashemashot to other locations, its length need not be extended.

The first is the preferred reading of the gemara in Shabbat according to most rishonim. The second is strongly supported by simple logic and arguably by the statement of Shmuel, though certainly at variance with the prevalent contemporary interpretation. The third is clearly debatable, but the viewpoint of some major poskim. All three are needed to defend fully historical practice. However, even the first, or certainly the first two points, should influence contemporary psak in extenuating circumstances.

Those familiar with R. Kapach’s approach to Rambam throughout Mishnah Torah, will recognize that his conclusions as to Rambam’s position on the twilight period and much of this monograph are consistent. While R. Kapach’s approach tacitly assumed stars, as opposed to darkness, as defining both the beginning and the end of bein hashemashot, something I believe that Rambam did not support, R. Kapach’s practical conclusions and insights into Rambam aligns Rambam across Mishnah Torah closely with the ideas that have been developed. (1. R. Kapach also insists on bein hashemashot beginning at 15 minutes after sunset, something we are not convinced that Rambam necessarily maintained. 2. As has been mentioned previously, objections to the approach of the geonim derive from sugyot where sunset does not appear to be a precise delimiter. Similarly, despite Rambam’s clear identification with the position of the geonim, some try to align his position with Rabbeinu Tam based on the fact that he did not consider sunset as critical as many assumed that an approach like that of the geonim had to maintain. As has been argued throughout this monograph, the “either-or” assumption of either Rabbeinu Tam or the geonim, without intermediate positions is an assumption that I find neither conclusive nor correct. 3. Building on R. Kapach’s approach, a future paper will attempt to demonstrate that Rambam maintained a hybrid / intermediate position, similar to the position of the geonim, consistent with the text of the gemara, astronomic observation and supportive of the approach taken in this monograph.)

It should also be clear, that while their rationales were entirely different, many poskim who in practice followed R. Pimential’s approach supported a position akin to what has been suggested throughout the monograph. In practice, they allowed work after sunset proper and awaited only three (small) stars, not a full 72 minutes. As well, they would never allow work on Friday, anywhere near as late as Rabbeinu Tam’s conceptual position would suggest.

Both the practice suggested by these poskim and R. Kapach’s interpretation of Rambam conceptually aligns with the approach developed throughout this monograph.

Clearly, in the study of zemanim, one has to “look up” as well as “look in.” Over the last few hundred years, careful observation of the skies has often been replaced with a fixation on time and timepieces. This contributed a false sense of accuracy as opposed to enhanced clarity to an already complex area.

This is the third of four posts, from a draft of a forthcoming monograph by Dr. William Gewirtz that addresses the period of bein hashemashot, the most fundamental area of dispute in the area of zemanim. What is proposed is an astronomically accurate hybrid position between the diametrically opposed conceptual views of the geonim and Rabbeinu Tam. That position justifies, to varying degrees, the practice of countless generations of European Jewry that started Shabbat well after sunset on Friday evening. Though often ignored in modern times, practical equivalents of this hybrid position have had major adherents throughout the generations. Our goal is to demonstrate that such a position is not just plausible, but in fact the preferred reading of the gemara in Shabbat, the primary text concerning bein hashemashot.
The attached PDF (click here to download) contains the 9 main sections of the monograph. Sections 5, 7 and 8, focused on reading the text of the gemara in Shabbat consistent with observation, detail the core thesis. This post is a commentary on each of the nine sections; unlike the PDF, it takes much wider latitude for conjecture. The next and last post summarizes some major areas of suggested innovation, contrasting the approach taken with an illustrative example of contemporary psak (the various rulings on zemanim of R. Feinstein), before making some closing observations.
Commentary on the 9 sections:

1. How many mil does one walk during the period from sunrise to sunset? What is the time required to walk a mil? – 18, 22.5, 24 minutes, etc.

Except for Rambam and R. Ovadiah Bartenura, few maintain 24 minutes. Both of the other major opinions have significant support. Some geonim and rishonim likely maintained an 18 minute interval. However, many if not almost all later rishonim, particular those following Ramban, adhere to 22.5 minutes. Interestingly, by the time of the Shulchan Aruch most authorities are united around 18 minutes, with a small number of achronim strongly supporting 22.5 minutes.

When I started studying this topic, I was convinced by the overwhelming arguments presented by Prof. Levi based on both the text of the gemara and the opinion of many rishonim, that 22.5 minutes should be strongly preferred. However, 18 minutes also appears well supported. Geography (the distance from Modiin to Jerusalem, for example) seems to support more mil walked per day (even 40 being difficult.) As well, the assumed similarity of the fractions 1/10th and 1/6th used by the gemara in Pesachim would place the twilight period of either the time to walk 4 or 5 mil outside of the daytime period of the time to walk 40 or 30 mil; 5 mil external from 30 mil (1/6th) should imply that 4 mil is external from 40 mil (1/10th.) Arguments in favor of 18 minutes from anyone maintaining 72 minutes, almost all of R. Yosef’s examples, while not conclusive are highly likely. An assumed added vav in the text of the gemara in Pesachim (Our text of the gemara reads “teidah…“u”mealot hashachar” in the second such phrase addressing the interval between dawn and sunrise. The vav does not appear in certain older texts.) when referring to the twilight periods might have been intended to clarify or to lend further support to 18 minutes.

Since it is clear that many if not almost all rishonim supported 22.5 minutes, the change to 18 minutes is puzzling. As we demonstrated, a basic mathematical/logical error allowed many to misread the opinion of all chachmai sforad as not necessarily supporting 22.5 minutes. That error and the limited availability of many of their writings are certainly major contributors for the dominance of 18 minutes as the time to walk a mil. However, I suspect that this might also be an example of the impact on halakhic reasoning from the increasing availability of clocks beginning in the 15th century. Clocks made 90 minutes as the time that three stars appear untenable in central and southern Europe; as a result, perhaps, opinion shifted to a somewhat more reasonable 72 minutes and the associated time to walk a mil of 18 minutes. Prior to the widespread use of clocks, it is likely that observation of the skies, as opposed to either 72 or 90 minutes, was used to determine the end of Shabbat.

2. How long is the period from sunset to tzait (kol) hakochavim (or equivalently alot hashachar to sunrise) in the Middle East around the time of the equinox? – 72 minutes, 90 minutes, 96 minutes, 120 minutes, etc.

96 minutes, four intervals of 24 minutes, referenced in a number of tshuvot, is unsupportable since whoever would maintain a time to walk a mil of 24 minutes must also consider the period from alot hashachar to sunrise as the time to walk 5 and not 4 mil. 120 minutes, while theoretically possible, is rarely encountered in halakha and is inconsistent with the point at which total darkness occurs in the Middle East, approximately 80 minutes after sunset. While both 72 and 90 minutes intervals are good approximations to 80 minutes, I maintain a slight preference for 72 minutes for four reasons: (How adherents of Rabbeinu Tam’s approach reconciled the difference in the length of the interval between dawn and sunrise versus sunset and three stars is unclear. The former would suggest 90 minutes in Europe, the opinion of many later rishonim who lived there. On the other hand, the latter would support 72 minutes. I suspect that given the subjective nature of determining what constitutes the first light and the additional stringencies of three small, adjacent stars, the difference may have become less evident. With the advent of clocks, 72 minutes was perhaps easier to assume if one number had to be chosen for both. This in turn may have made observation yet less authoritative.)

1. The amount of light present at 72 minutes is so minimal that it was likely disregarded in halakha.
2. R. Saadyah Gaon and Rambam, who both lived in the Middle East, support 72 minutes.
3. The simple meaning of 1/10th of the (720 minute) day is 72 minutes; assuming 1/10th to mean 90/900 requires a unique variant of the notion of milebar adding two intervals of 90 minutes to 720.
4. Around the winter solstice in Jerusalem, using an adjusted (or even fixed) 90 minutes in calculating according to the Magen Avraham, results in plag haminkha after sunset. In the winter, when the daytime period is approximately 10 hours and the sun is 20 degrees below the horizon about 96 minutes after sunset, plag haminkha (1.25*66 ~ 83 minutes) occurs approximately 13 minutes after sunset.

3. How is the period from alot hashachar to sunrise or its equivalent from sunset to tzait (kol) hakochavim to be adjusted at different locations and during different seasons (if at all)?

Prior to the widespread use of clocks, latitude and season (and perhaps even altitude) based adjustments were made naturally. The invention of clocks and the subsequent growth of time based expressions of halakha reduced the dependence on observation as have been documented by Prof. Stern.( Time and Process in Ancient Judaism. )

Many calendars exhibit inconsistent behavior, defining misheyakir, for example, based on physical observation, while maintaining an unadjusted period for alot hashachar, a position that creates anomalies at most European latitudes.

In practical terms, the end of a day of the week, when defined either by a measure of darkness or the more common appearance of three stars naturally embed both latitude and seasonal adjustments. However, except for a few isolated exceptions, those who wait 72 minutes after sunset for the end of Shabbat never made upward adjustments. (To my knowledge, no major figure except R. Soloveitchik (and perhaps some family members) applied and practiced precise latitude and seasonal adjustments to lengthen the end of Shabbat when following the opinion of Rabbeinu Tam.) By waiting 72 minutes, they would naturally wait longer than those watching for darkness or the appearance of stars at least until the point that one is approximately 50 degrees latitude or greater from the equator, regardless of the time of year. At latitudes below 50 degrees, even a depression angle of 8.5 degrees, that exceeds the observance of (almost) all communities, would equate to less than 72 minutes. As a result, 72 minutes after sunset remained invariant. Given the location of the vast majority of Jewish communities between 55 degrees north latitude and the equator, those who observed 72 minutes had limited physical motivation to make either latitude or seasonal adjustments; three stars, most often even small ones, are visible by that time. (To the contrary, not just were intervals not adjusted upwards, those who maintained the position of Rabbeinu Tam, either waited exactly 72 minutes or less, not more. As noted previously and first mentioned explicitly by R. Avraham Pimential in the 17th century sefer Minkhat Kohen and practiced in many communities, those following the opinion of Rabbeinu Tam actually reduced 72 minutes (often to around 50 minutes) based on the observation of three stars. I have never read an explanation of how this was reconciled with the calculation for the time of alot hashachar for those following the Rabbeinu Tam. A more traditional view of the Rabbeinu Tam’s position was to wait until 72 minutes after sunset.) (Even for St. Petersburg and certain communities in Scandinavia, given significant variance in how to interpret three small stars, smaller depression angles (but still greater than that which would equate to three medium stars) would allow 72 minutes to remain viable. See Benish chapter 46 on European observance in a number of (very) northern European communities that used the equivalent of a depression angle of approximately 7.5 degrees for the end of Shabbat. In Vilna for example, using a depression angle of 8.5 degrees, the end of Shabbat occurs approximately 95 minutes after sunset in the summer, 40 minutes later than in the spring.)

On the other hand, unlike the end of Shabbat (or any day of the week,) the beginning of the daytime period, alot hashachar, should not have been left invariant, as was often the case. In Prague in June, for example, using a depression angle of 8.5 degrees, the end of Shabbat occurs about 70 minutes after sunset, while alot hashachar, specified by a depression angle of 16 degrees, occurs over three hours before sunrise. However, as it was often axiomatically assumed based on Rabbeinu Tam’s interpretation of the sugya in Pesachim, that the interval between alot hashachar and sunrise must exactly equal the interval between sunset and tzait hakochavim, either both or neither could be adjusted. Particularly in the age of clocks, adjusting one and not the other would visibly violate that assumption. Thus, I suspect that the opinion of Rabbeinu Tam may have contributed to a tradition of not adjusting the time of alot hashachar, in order to maintain similarity with the invariance of the evening zman of a fixed 72 minutes after sunset for tzait hakochavim. The amount of illumination that defines the point of alot hashachar was simply assumed to be greater. (The times for misheyakir may be reflective. The rulings of Middle Eastern poskim tend to equate to depression angles of 11.5 degrees and higher, while European poskim tend to a range between 10 and 11 degrees, as is clear from Benish vol. 1, pages 211 – 215. It is highly likely that a relatively short duration (6 minutes) between alot hashachar and misheyakir that is mentioned by some commentators in OC 58:1 is not the result of an early point of misheyakir but a later point of alot hashachar. As a result, combining such a psak with an accurate (adjusted) time for alot hashachar cannot be justified.)

In summary, three potential impacts of increased reliance on clocks have been suggested in this and preceding sections of the epilogue:

1. Reduced reliance on observation and natural skepticism about of its accuracy, particularly relative to a clock, eventually led to decreased practical knowledge of the meaning of specific physical entities further increasing reliance on clocks. (Arguably alot hashachar, misheyakir, and a medium versus small star have all been impacted .)

2. The clear preference for 72 over 90 minutes as the point at which three (small) stars appear, and the related preference for 18 versus 22.5 minutes as the time to walk a mil.

3. The invariance of the interval from alot hashachar to sunrise resulting from its assumed equivalence to the interval from sunset to tzait hakochavim according to the prevalent opinion of Rabbeinu Tam, created observational challenges. The duration of the interval from sunset to tzait hakochavim rarely exhibits any need for variation by either season or latitudes; the point of alot hashachar clearly does. The use of identical (fixed) intervals for both, weakened reliance on observation and trust in one’s ability to judge levels of darkness.

4. How are we to define the hours of the day – sunrise to sunset or alot hashachar to darkness?

The identification of the opinion of the Magen Avraham only as far back as R. Israel Isserlein as opposed to Ramban (See R. Schechter’s explanation that R. Soloveitchik was completely unconcerned about the opinion of the Magen Avraham because of an implication from Rambam that was a supporting source for the Gaon. It is puzzling that R. Soloveitchik would dismiss an opinion of all chachmai seforad. ) and his school who clearly counted the hours of the day from alot hashachar to darkness remains puzzling. (I assume that this was primarily the result of limited availability of the seforim of chachmai sforad.) Given that the position of the Magen Avraham was held by all chachmai sforad and was the accepted custom of Jerusalem, in spite of the influence of the students of the Gaon, coupled with a lack of any unambiguous reference to the position of the Levushim amongst rishonim, provides additional support to that alternative. The argument of R. Yaffe and the Gaon that time is defined by the angles of the sun, is compelling, but not entirely convincing.

As noted in the past section, current practice, that sets times for the Magen Avraham’s zman based on a fixed 72/90 minutes for both alot hashachar and tzait (kol) hakochavim, is a divergence from zemanim based on observation that was practiced prior to the advent of clocks. For those who wish to maintain the times of the Magen Avraham, their precise approximation / calculation would seem warranted. As hypothesized, the opinion of Rabbeinu Tam and the observance of a fixed 72 (90) minutes at the end of Shabbat might have contributed to a tradition of not adjusting 72 minutes (or 90) minutes in this context as well.

5. Of the three criteria given by the gemara in Shabbat – time, the appearance of stars, darkness (darkening / appearance of the sky / horizon), which if any are the definition of night and which are just approximations or an indication? How can opinions expressed using these three terms be compared?

I maintain a clear bias towards levels of darkness and light defining both the end and the beginning of bein hashemashot, as well as almost all other zemanim. What is not yet fully recognized is that relying on depression angles for defining the level of darkness is akin to relying on clocks to tell time.( I have seen calendars that while using depression angles choose to write three small or medium stars, presumably to make people more comfortable, avoiding marketing challenges and the need to explain.) More importantly, depression angles naturally incorporate adjustments based on season and latitude, something that clocks more than likely obscured. Clocks and even time is just an artifact; depression angles are a mechanism for accurately specifying the halakhic notion of darkness.

While both the appearances of stars and multiple levels of darkness vary naturally with seasons and latitude, clocks likely had impact with their introduction. As time became an easier and preferred method for specifying observance, it is likely that the meaning of darkness levels and the appearance of stars became less observed, relevant or understood.

Motivated by the desire to understand the observations and findings of R. Tukitzinsky more directly, I have carefully observed the appearance of stars and the darkening of the horizon at various latitudes and seasons of the year. As best as I can observe, the point at which the apex of the sky appears as dark as the eastern horizon slightly precedes the appearance of three or more stars. However, it is not yet as dark as the eastern half of the sky will become as one waits longer; the (eastern half of the) sky darkens further until sometime after a point in the evening comparable to the point in the morning of misheyakir. Even at that point, there is still some remaining illumination from the sun visible on the western horizon. Though this level of darkness is in all likelihood what is described in the gemara and has been the psak of generations of poskim for the end of Shabbat, it may well leave one feeling uncertain about the time at which Shabbat ends. Unlike alot hashachar where there is minimal (or no light) light, the end of Shabbat occurs when there is significantly more illumination. Without depression angles that point of chashecha is difficult to specify with precision even relative to three (small, adjacent) stars, perhaps influencing many to view stars as defining.

Assuming that the appearance of three stars and alot hashachar are equidistant from sunrise and sunset also makes it nearly impossible to regard darkness as defining; one would expect it to be equally dark at those two points. Instead, we end Shabbat when there is more illumination than at alot hashachar. This adds yet another reason why some doubted their observation of the degree of darkness, and preferred instead to think both of:

• stars as defining, and
• clocks as more reliable and precise than observation.

6. How is the duration of bein hashemashot to be adjusted at different locations and during different seasons (if at all)? Might this depend on whether bein hashemashot is

1. an interval of uncertainty that is its own unique halakhic category – either

1. a combination of both day and night, or perhaps
2. a category of its own, or

2. an interval with a definitive transition point that we are uncertain how to pinpoint – either

1. practically, or perhaps
2. because of some element of halakhic uncertainty, or

3. an example of the Rabbis establishing a fence?

In this and the following two sections, the approach of the geonim is assumed and options for the length, end, and beginning of bein hashemashot are discussed within their framework. It is easiest to begin with the length of bein hashemashot. This turns out to be a critical method to estimate the beginning of bein hashemashot given the assumption that the end of the bein hashemashot period is not in question. The interval of bein hashemashot can be specified using either of the following constructs:

• the interval between two precisely defined physical events / depression angles, and / or
• an interval of time prior to the end of the day.

Despite the potential dependence of these two constructs on the theoretical alternatives for defining bein hashemashot, I have argued that the issues are independent. The discussion that follows concentrates only on these two alternative constructs; others are either just variations or combinations.

One issue briefly outlined is the difference between safek chashecha and bein hashemashot. I assume that the period of safek chashecha is shorter than bein hashemashot and represents a period of real doubt about whether chashecha and the beginning of Shabbat at a biblical level has occurred. (The remainder of this section could be rewritten independent of this assumed relationship between bein hashemashot and safek chashecha if one were to feel that this assumption is not justified .) Bein hashemashot represents a longer interval, where Shabbat is mandated, but only at a rabbinical level.

The following discussion is not meant to identify a normative position, rather one that presents a preferred, or at least plausible, reading of the gemara and also (partially) justifies the practice of Jewish communities in Europe that started Shabbat well after sunset. Seeking to justify practice even at a rabbinical level requires a relatively short period of bein hashemashot. Using either sunset or even a minimal depression angle would mean that most communities who followed Rabbeinu Tam started Shabbat during bein hashemashot or worse.

Assume, as an illustrative example, that a community ends Shabbat 50 minutes after sunset with the appearance of three small stars. Assume further that while three small stars equate to a depression angle of approximately 8 degrees, three medium stars, the gemara’s end to both bein hashemashot and Shabbat, equates to a depression angle of approximately 6 degrees, and occurs 35 minutes after sunset. Bein hashemashot begins approximately 15 minutes before that, at 20 minutes after sunset. To justify practice, two elements must be considered:

• At the biblical level, the point of chashecha, slightly prior to three medium stars, and
• at a rabbinical level, the interval from the beginning of bein hashemashot until chashecha.

As detailed at the beginning of section 8, three alternative opinions, each to be adjusted by latitude and season advance the beginning of bein hashemashot by 4 to 15 minutes from sunset. At a minimum one would naturally maintain that a level of darkness computed for each of those alternatives must be achieved (to create an element of doubt that is required) to begin bein hashemashot. Additionally, one can maintain that the time to walk 3/4 mil is an absolute upper bound, invariant with respect to latitude and season. Thus, bein hashemashot cannot begin prior to the time to walk ¾ mil before the point of nightfall. If one would want to be as lenient as possible, one would take the later of these two potential times – counting back from chashecha the time to walk ¾ of a mil, while maintaining as well the requirement to reach a particular level of darkness. Thus, bein hashemashot begins at the earliest when a particular level of darkness is reached, (for example, a depression angle of three degrees) but at no time can the interval of bein hashemashot be longer than the time to walk ¾ mil. Using the minimum level of darkness is required slightly north of the latitude of the Middle East and further south approaching the equator. In those locations during certain periods of the year, subtracting the time to walk ¾ of a mil from chashecha might yield time X. However, the time at which a specific level of darkness, which must also occur prior to the start of bein hashemashot, is Y minutes later at time X+Y. For example, assuming that the time to walk ¾ mil is a maximum reached only in the summer, then the bein hashemashot period may begin only within ten minutes of chashekha in the spring and fall when the requisite level of darkness is achieved.

Moving from the Middle East to European latitudes, the focus of this discussion, reaching a particular level of darkness level always occurs at an earlier point than subtracting the time to walk ¾ mil from the point of chashecha. Thus, one obtains the latest (and most lenient) starting point for bein hashemashot by subtracting the time to walk ¾ mil from the point of chashecha, assuming that interval represents an invariant maximum for the period of bein hashemashot. Support for an invariant interval of bein hashemashot came from both R. Lorberbaum and R. Sofer, and in the case of R. Lorberbaum that was coupled with an 18 minute time to walk a mil yielding a period of bein hashemashot of 13.5 minutes. Problematically, in both of those cases the beginning of bein hashemashot was derived subtracting from an end of Shabbat that was determined by the appearance of three small stars. Although their practice was not as stringent as our current practice that equates to a level of darkness associated with a depression angle of 8.5 degrees, it was still one or more degrees greater than the level of darkness associated with a depression angle equating to three medium stars. It appears impossible to justify an overly lenient approach that subtracts from the time that three small stars appear of as opposed to an approach that subtracts from the earlier appearance of three medium stars.

To determine what was the practiced beginning of bein hashemashot requires a detailed historical analysis beyond that begun by Benish. It should be obvious that an early practiced chashecha and a long period of bein hashemashot is likely to avoid both biblical and rabbinic violation on erev Shabbat, while a later practiced chashecha and a short interval of bein hashemashot would create the highest likelihood of even a biblical violation on erev Shabbat. To the extent that the theoretical opinion of the Rabbeinu Tam was used, chillul Shabbat definitely occurred. However, more commonly the opinion of Rabbeinu Tam was equated to three stars with various stringencies, and bein hashemashot began some interval before that. That would make it much more likely that violations that occurred were only at a rabbinic level. Given a large body of evidence including:

• R. Pimentiel’s redefinition of Rabbeinu Tam to the earlier point of three small stars,
• the proposed times of bein hashemashot of both R. Lorberbaum and R. Adler,
• the question concerning the brit of a baby born about 25 minutes after sunset, posed to R. Moshe Sofer,
• the advice from R. Shneur Zalman of Liadi in his Siddur, and
• the natural stringencies that one would expect prior to the existence of clocks.

I doubt any communities (as opposed to individuals) ever started Shabbat as late as the theory of Rabbeinu Tam would have permitted.

While I have scant evidence, one can only assume that any three stars appearing would likely be taken as indicating that the Shabbat had begun. This, together with the halakhic literature only partially referenced above, would all seem to point to a beginning to bein hashemashot, absent tosefet Shabbat, at worse between 30 and 40 minutes after sunset, a point that likely avoided chillul Shabbat at least at the biblical level, particularly in northern European communities. Unfortunately, it is also probable that some individuals started Shabbat even later; the letter of R. Shneur Zalman of Liadi on the beginning of Shabbat, included in all of the Lubavitch movement’s Siddurim, is particularly telling. (R. Shneur Zalman of Liadi suggested that maximal protest be restricted to those who go past approximately a seasonally adjusted 30 minutes, if they refuse to listen initially.)

7. When does the period of bein hashemashot end? How are the criteria specifying the end of the bein hashemashot period interpreted by various authorities?

Of course we assume latitude and season adjustments. We need to specify two points in time – the degree of darkness associated with the approximate appearance of three medium stars (the time given in the gemara) and the degree of darkness associated with three small, adjacent stars (what is now practiced). The former occurs at a depression angle of approximately 6 degrees, and the latter at about 8 degrees. Clearly, practice has many variants around those two points. Currently, a depression angle of 8.5 degrees suggested by R. Tukitzinsky and supported by R. Belsky’s interpretation of R. Feinstein is widely used.

I suspect some will find excessive the intensity with which the opinion of Rabbeinu Tam was found inconsistent with the combination of observation and the gemara’s description of the end of Shabbat. Many might perhaps prefer giving greater credence to difficult and forced efforts at reconciliation. However, current practice, including that of R. Y. Karelitz, which largely disregards Rabbeinu Tam’s opinion on the end of Shabbat, even for absolute biblical restrictions, encourage the conclusions reached. I do not know of another comparable instance where the uncontested opinion of the Shulchan Aruch was so completely overturned.

8. How does the beginning of bein hashemashot relate to what we call sunset? What alternatives might be considered for the beginning of bein hashemashot?

This most controversial topic, moving the beginning of bein hashemashot forward from sunset even according to Rabbah, a variant of the generally assumed opinion of the geonim, successively solves the following issues:

1. at 4 – 5 minutes, the minimal time reported as the custom of Jerusalem (See Minhagei Eretz Yisrael by R. Yaakov Gliss, pages 102 and 282.) as well as the opinion of R. Shneur Zalman of Liadi, the point when the sun disappears from the highest elevations around Jerusalem, Shmuel is consistent at least in a limited sense with R. Yosef but completely inconsistent with Rabbah.

2. at 6 minutes, the opinion of R. Chaim Volozhiner and the appearance of a single star in the spring to an expert observer, Shmuel is more easily consistent with R. Yosef but only consistent in a limited sense with Rabbah.

3. at 7 – 15 minutes depending on a variety of factors, Shmuel becomes entirely consistent with Rabi Yehudah and the time to walk ¾ mil can be considered a practical upper bound. (See Zemanim Kehilkhatam by R. Boorstyn, chapter 2, section 3 where he summarizes different 19th and 20th century poskim in Middle East who supported times beyond 4 – 5 minutes and up to approximately 10 minutes after sunset. The rationale he and some of these poskim used is different from that addressed in this monograph, with heavy reliance on the notion of sea-level in addition to visibility from higher elevations. 15 minutes is the opinion of Rambam according to R. Kapach.)

As stated in the preamble to this monograph, sunset is the established time to start the Shabbat. Where there is a need for greater precision in various circumstances, a posek might consider a construct similar to that provided by R. Nosson Adler. Perhaps a posek can choose to adjust by season and latitude what equates to some point between 4 – 6 and 9 – 12 minutes after sunset in the Middle East around the spring and fall equinox, applying whatever resulting time is the greater chumrah in a d’oraysa and the greater kula in a d’rabbanan. (For a host of reasons, if forced to a single number, I would guess (11 or) 12 minutes. The numbers chosen are purely illustrative.) In cases of (extreme) need, one might also consider limiting the length of the bein hashemashot period to at most 13.5 minutes prior to the appearance of three medium stars, a depression angle of approximately 6 degrees. This area has significant halakhic ramification. (Even if one were to insist on bein hashemashot beginning precisely at sunset, the above zemanim might at least be considered as alternatives for defining the start of safek chashecha.)

Rabbeinu Tam’s late start to Shabbat is yet more troublesome if prior to its formulation, the start of Shabbat was precisely at or even before sunset. I find it highly implausible to imagine Rabbeinu Tam proposing, even as a purely conceptual position, a notion so fundamentally at variance with practice! Even if the practice was to start Shabbat at or before sunset, it would make more sense that the period was only considered a non-mandated interval of tosefet Shabbat. Emergencies that occurred would have clarified the nature of practice. This would lend support to my conclusion: sunset was viewed at most as a non-obligatory start to (tosefet) Shabbat. As Jews migrated to Northern Europe, Shabbat started to separate further from sunset; most likely the start of Shabbat remained at least 15 minutes prior to the appearance of three medium stars. It is for that practice that Rabbeinu Tam provided a conceptual framework. Increased reliance on clocks centuries later, may well have resulted in a (slightly) later start to Shabbat for two reasons. First, the opinion of Rabbeinu Tam could be formulated more precisely. Second, a clock reduced the period of uncertainty that observation of nature naturally introduced.

9. At what time (or within what interval) does one day end and the next day begin with respect to various halakhot? How do the two meanings of day – day as in “day of the week” and day as in “during the daytime” relate? Must the end of the daytime period coincide with the end of a day of the week?

It would be surprising if the different meanings of the term day in both Hebrew and English had no halakhic consequence. On the other hand, one might view this whole category as a modern innovation due to Brisker conceptualization and in opposition to the Gaon finding no halakhic significance to tzait kol hakochavim.