Halakhah su Esodo 12:2

We find that the light of the sun and of all the stars is eternal, of itself it does not increase nor decrease. However, the light appears to increase or decrease depending on whether the object being viewed is far or near. Also, the light varies due to changes in the atmosphere at the beginning or the middle of the day. Only the moon has a renewal of its light.¹ Ibn Ezra believes that the sun, all planets and all stars, generate their own light, and only the moon reflects light of another body (the sun). Therefore, the Hebrew term for month, “hodesh,” can truly apply only to a lunar month.² In Hebrew, a month is called “hodesh,” which is derived from the root “hidesh” meaning “renew.” Since only the moon has a renewal of its light, “hodesh” can only refer to a lunar month. We examine when such a month begins.

One revolution, which includes all the spheres, is from east to west. The twelve zodiacal constellations¹³ The order of the zodiacal constellations and zodiacal signs is: Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, and Pisces. complete a revolution in twenty-four hours,¹⁴ This is known as a “sidereal day,” which is the interval between two successive passes of the vernal equinox point over the meridian. A sidereal day is slightly less (by about four minutes) than a “solar day,” the interval of time between two successive passes of the sun across the meridian. Apparently Ibn Ezra used sidereal time rather than solar time. and the seven planets¹⁵ The seven planets known at that time are: Moon, Mercury, Venus, Sun, Mars, Jupiter, and Saturn. also finish their revolutions in approximately the same amount of time. The second revolution is from west to east. It also includes all of the spheres, for the poles of the spheres of the planets are similar to the poles of the zodiacal sphere.¹⁶ All of the lower eight spheres that contain the planets and the fixed stars rotate at various rates around the earth from west to east. Only the sun maintains the path of the ecliptic, not deviating south nor north. It traverses the complete zodiac in 365 days, five hours, and fractions of an hour. This is a solar year and the true year, for the days return a second time to what they were in the preceding year. For this reason a year is called “shana” (repetition).

All astronomers agree that the lunar month begins at the moment when the moon and the sun are in conjunction in the same longitude. This is what our Rabbis called the “molad ” (birth, i.e., new moon). Our scholars calculated it for the mean orbit,³ This figure is given in the Talmud: 29 days, 12 hours, and 793 halaqim (Rosh haShana 25a), or 29 days, 12 hours, 44 minutes, and 3 and ⅓ seconds, approximately 29.5306 days. Such a month is known as a “synodic month” and is defined as the mean time between new moons. The current approximation for a synodic month is 29 days, 12 hours, 44 minutes, and 2.7 seconds, or 29.5306 days. and all astronomers did the same. Then they adjusted it.⁴ “Mean conjunction” is conjunction of the sun and the moon relative to their individual spheres. However, since the moon’s sphere, the sun’s sphere, and the earth are not concentric, conjunction relative to the zodiacal sphere may differ from conjunction relative to the individual spheres. Conjunction relative to the zodiacal sphere is called “true conjunction.” Thus our Rabbis, their memory should be a blessing, said: “Sometimes it comes by a long path and sometimes it comes by a short path” (Rosh haShanah 25a). Since conjunction involves two bodies, we must know with regard to each one when it is a long path or a short path. Sometimes both are long, or both short, or the sun long and the moon short, or vice versa. Also, sometimes the length or shortness is small, sometimes large, to the extent that the length or the shortness may be as much as thirteen hours. Thus at times there is a difference between our calculation of conjunction and true conjunction of these many hours, either earlier or later.

The commandment of sanctifying the new month To sanctify months and intercalate [months into] years in the court [whose members are the] great in wisdom and ordained in the Land of Israel, and to establish the year's holidays according to that sanctification; as it is stated (Exodus 12:2), "This month shall be to you the first of months." This means, when you see the renewal of the moon, establish for yourselves the new month - or even if you do not see it, since it is appropriate for [the moon] to appear according to the accepted calculation. Likewise, this commandment includes the commandment of intercalation, since the basis of the commandment to sanctify the month is for Israel to observe God's holidays at their appointed times. And the commandment of intercalation has the same basis. However, beyond this verse are more Torah passages concerning the commandment of intercalation, and that is what is written (Exodus 13:10), "You shall observe this commandment in its proper time"; and likewise, "Observe the month of Spring" (Deuteronomy 16:1).

The laws of the commandment - for example, interrogating [those who offer] testimony concerning the new month; instilling fear in the witnesses on occasion; the law concerning circumstances under which the Shabbat may be desecrated for this testimony; for what [considerations] we do or do not intercalate; which month they would intercalate, i.e. Adar, as they, may their memory be blessed, expounded, "'You shall observe this commandment in its proper time' (Exodus 13:10), this teaches that we only intercalate at the time near the holiday"; and they, may their memory be blessed, further expounded on this verse, "From where do we know that we only intercalate the month during daytime? [We learn this from the] verse, [which] states, 'from year to year' (yamim yemima, literally from day to day) (Sanhedrin 10b); and they, may their memory be blessed, further expounded, "'For the months of the year' (Exodus 12:2) - it is months you calculate towards the year, not days" (Megillah 5a); furthermore did they say on this matter, "'A month of days' (Numbers 11:20), it is days you calculate towards the month, not hours" (Megillah 5a); and the rest of its details - are [all] elucidated in Tractate Rosh Hashanah, and in the first chapter of Sanhedrin, and similarly in Berakhot (see Mishneh Torah, Laws of Sanctification of the New Month 1).

Judah the Persian¹⁹ Mentioned by Ibn Ezra in his Commentary to the Pentateuch and elsewhere. Nothing is known of this scholar. (See Encyclopedia Judaica, second edition, vol. 11, p. 505.) said that the years used by Israel were solar years, because he found the festivals were on fixed dates: Passover when the barley ripens (Exodus 34:18), Pentacost at reaping time (ibid. 34:22), and Tabernacles at harvest time (Deuteronomy 16:13). However, what can be done since Moses did not specify the length of a year?²⁰ Since the Bible does not specify the exact length of a solar year, the Karites are left with the matter being undecided. This will also affect determination of the festivals. Also, how will he explain the use of the Hebrew term “hodesh” (new) for “month,” for what is renewed relative to the sun? The uncircumcised (Christians), because their years are solar years and they found that a full year contains twelve lunations, divided the days of the year into twelve parts, for this number is closest to the number of lunar months. The result is that some months are 30 days and some months are 31 days.²¹ Here Ibn Ezra accounts for the division of a year into twelve parts, even if one uses a solar calendar. However, the term “hodesh” would not be appropriate for such solar months.

There are those of our generation who calculate the Hebrew calendar. Because they know the calculation based on 1:12:793,⁸ A mean lunar month is 29 days, 12 hours and 793 halaqim. If we discard the four complete weeks from this figure, we have the “character” of 1 day, 12 hours, and 793 halaqim (1d, 12h, 793p). This is the amount of time that the molad proceeds through the week from month to month. Thus the molad advances monthly by 1d, 12h, 793p of a week. they think that they have discovered the principle of the calendar. They then examine the duration between the molad and the beginning of the night, and they tell the uncircumcised (Christians) when the moon will be visible.⁹ I do not know why the Christians, who use a solar calendar, need to know when the moon will be visible. Perhaps there is an error here in our texts and it should read “Arabs.” When they see that in their place the duration [between molad and sighting] is sometimes less that six hours,¹⁰ It sometimes happens that the molad is less than six hours before sunset yet the moon is visible that evening. they think that the time given for the molad applies to the location of each individual calculator. However, there are times when the moon is seen at the beginning of the night and sometimes there are seven or eight hours between the molad and dusk, and the moon is still not visible. Therefore, they think that the calculation of our calendar is incorrect. Heaven forbid! Rather they err, for they think they are wise. For a scholar cannot know when the moon will be visible until he does as I shall explain: He must know the moment of the molad. He should not assign to the night twelve hours. Rather he should begin to count from the beginning of the night until the moment of conjunction so many and so many hours.¹¹ He should count night followed by day on a 24-hour clock and not begin a new count with dawn. He should know where conjunction will take place as to the minute of the degree of the zodiacal sign. He should see if the sun’s path is long or short, and how long the path of the moon is. He should then add or subtract until he knows the moment of true conjunction for Jerusalem. He should then calculate how far this conjunction is from the beginning of the night by hours and minutes. If he is west of Jerusalem he should add to those hours the hours of his distance in longitude, or subtract hours if he is east of Jerusalem. He should know the daily distance that the sun travels in hours and add it to the place of the sun at the moment of true conjunction. He should do similarly for the position of the new moon based on its orbit. Then he should record in a chart the degrees of the zodiacal signs in his land, and take those degrees that he will find relative to the position of the sun. He should similarly do this in degrees relative to the moon, and subtract the smaller from the larger. Then he will find the arc of the chord (between the sun and the moon). He should find the positions of the nodes,¹² The nodes are the two points at which the moon crosses the ecliptic. They are called the “head” and the “tail” of the “dragon.” Berry (p. 48) explains: “The moon’s path on the celestial sphere is slightly inclined to the ecliptic, and may be regarded as a great circle cutting the ecliptic in two nodes, at an angle which Hipparchus was probably the first to fix definitely at about 5÷. Moreover, the moon’s path is always changing in such a way that, the inclination to the ecliptic remaining nearly constant, the nodes move slowly backwards from east to west along the ecliptic, performing a complete revolution in about 19 years.” so that he will know the latitude of the moon,¹³ There is a difference in the time of visibility of the moon if it is north of the ecliptic or if it is south of the ecliptic. in order to correct this arc. Then he should adjust the arc based on the correction of the sighting, both in longitude and in latitude. Then we will know the true arc of vision.¹⁴ This is the arc between the longitude of the sun and that of the moon. In order for the moon to be visible, an arc of vision of at least 12÷ is necessary. Then he will know when the moon will appear in each place for any desired month. One who knows these matters can understand the principle “If it is born before noon” (Rosh haShana 20b).¹⁵ The Talmud states: “If it [the moon] is born before noon, it will be seen before sunset; if it is not born after noon, it will not be seen before sunset.” In Sefer ha‘ibbur (p. 10b) Ibn Ezra explains this statement.

We find the solar cycle of Shmuel³² A scholar of the Talmud (’amora) who lived around 300 C.E. in Neharde‘a, Babylonia. Shmuel was well acquainted with astronomy and declared “The paths of the heavens are as clear to me as the paths of Neharde‘a” (Berachot 58b). to be exactly 365¼ days, not more nor less.³³ Shmuel said that each of the four seasons is 91 days and 7.5 hours (‘eruvin 56a). Thus a solar year consists of 365 days and 6 hours. In his days that was close to the truth,³⁴ Although Shmuel’s solar cycle is excessive, relative to the currently accepted value of a solar year, by about one day every 128 years (see Appendix A), however, Shmuel also set the first (virtual) vernal equinox at the time of Creation about seven days before the accepted date. Hence, at the time of Shmuel the discrepancy in his approximation of the vernal equinox (and hence of the solar calendar) and the actual vernal equinox was not great. To see this we calculate (see Appendix A): Shmuel lived around the year 4010 Anno Mundo (A.M.) (250 C.E.), the first year of the 212th mahzor. Multiplying the character of a mahzor by 211 (the number of past mahzorim), we obtain 211 ׳ (1 hour, 485 halaqim) = 12 days, 17 hours, and 815 halaqim. Subtracting the starting interval of 7 days, 9 hours, and 642 halaqim, we have the span between molad Nisan and the vernal equinox for the year 4010 of approximately 5 days. So according to Shmuel, the vernal equinox took place about the fifth of Nisan, which corresponds with March 25, 250 in the Gregorian calendar. This is quite close to the true vernal equinox (March 21). and he cited a figure appropriate for his students. He did a similar thing in a Bereita,³⁵ See Bereita of Shmuel, ch. 5 (p. 29). Apparently Ibn Ezra is of the opinion that the author of Bereita of Shmuel was the ’amora Shmuel, the same scholar quoted in the Talmud regarding the seasons. where, in calculating the mean lunar month, he did not include the 73 halaqim³⁶ One heleq (part) is 1⁄1080 of an hour. We have the following conversions: 1 hour (h) = 1080 halaqim (p), 1 minute (m) = 18p, 1 second (s) = 0.3p. Also 1 heleq is 3 and ⅓ seconds. which are in addition to ⅔ of an hour.³⁷ According to the Talmud, a mean lunar month consists of 29 days, 12 hours, 40 minutes, and 73 halaqim (Rosh haShana 25a). In the Bereita of Shmuel the 73 halaqim are omitted. It is also written that there are two cycles, the cycle of Rav Adda³⁸ Rav Adda bar Ahava, a third-century Babylonian ’amora. He composed a treatise on the calendar titled Bereita deRav Adda. in private and the cycle of Shmuel in public. The reason that Rav Adda’s figure was in private was because of prognostications, lest their scholars know the true cycle.³⁹ If unscrupulous astrologers would know the true solar cycle, they might use the information for nefarious purposes. (See Sefer ha‘ibbur, p. 6b.)

Today Shmuel’s cycle is not correct.⁴⁰ In the year 4919, the year that Ibn Ezra wrote The Sabbath Epistle, the vernal equinox according to Shmuel should have been April 1, about ten days later than the true vernal equinox (see Appendix A, Table 7). Thus, referring to the vernal equinox for the year 4918, Ibn Ezra writes: “Even the simplest of simpletons can see that the day and night were equal close to eleven days ago” (Ha‘ibbur, p. 8b). The daily shadow in each place is positive proof for the scholar.⁴¹ Thus for example, at the time of the winter solstice it is easily observed that the true solstice does not coincide with Shmuel’s calculation. A sundial would be useful for these observations. Also it is written “If you see that the winter season extends until the sixteenth of Nisan, do not hesitate to intercalate that year” (Rosh haShana 21a). Now, according to Shmuel’s calculation, last year (4918) spring began on the 25th of Nisan.⁴² See Appendix A, Table 7. So we transgressed the words of our Sages. Heaven forbid! We certainly observed the holiday in its correct time. Thus the cycle of Rav Adda is more exact than that of Shmuel, for the beginning of spring will not go beyond the given date (16 days in Nisan).⁴³ See Appendix B, Table 5. In Sefer ha‘ibbur (p. 3b), Ibn Ezra sets Rav Adda’s figure for a tropical year as 365 days, 5 hours, 997 halaqim, and 48 rega‘im (secondary parts, s), where 76 rega‘im constitute one heleq. This is equivalent to 365 days, 5 hours, 55 minutes, and 25 + 25⁄57 seconds, approximately 365.2468 days. This value is obtained by equating 19 tropical years to 235 mean lunar months. 235 months calculates to 6939d, 16h, 595p. Dividing by 19, we arrive at Rav Adda’s figure. (See Appendix B.) This same figure is given by Maimonides in Mishne Torah, Laws of Sanctification of the New Moon 10:1. Note that earlier Ibn Ezra set a tropical year at approximately 365.2423 days (see note 13). Summarizing, we have the following opinions for the length of a tropical year: Shmuel: 365.25 days (exact), Rav Adda: 365.2468 days (rounded off), Ibn Ezra: 365.2423 days (rounded off), Current value: 365.2422 days (rounded off). Thus Shmuel’s cycle differs from the currently accepted approximate value by 0.78 day per century, or about ¾ of a day per century. Rav Adda’s figure differs from the currently accepted approximate value by about 0.46 day per century, or about ½ day per century. So it is difficult to understand why Ibn Ezra is so critical of Shmuel’s cycle and not that of Rav Adda. At the time of Ibn Ezra (4919), Rav Adda’s cycle had fallen behind by over 22 days; Shmuel’s cycle had fallen behind by over 38 days. Note that Ibn Ezra’s figure differs from the currently accepted figure by less that ½ day over the 49 centuries since Creation. Also, looking at Table 6 of Appendix B, we see that Rav Adda’s date for the vernal equinox differs from the true current vernal equinox by about seven days.

I also found explicit with regard to the first of the holidays (Passover), which God gave to Israel prior to instructing them about the Sabbath, “on the fourteenth day of the month at evening you should eat unleavened bread, until the twenty first day of the month at evening” (Exodus 12:18), a total of “seven days” (ibid. 12:19). Thus the evening of the fifteenth is the first day. It is also written “[neither shall any of the flesh] from which you offered in the evening of the first day [be left over] until the morning” (Deuteronomy 16:4). Also, it is known that the firstborn were smitten at midnight (Exodus 12:29), yet it is written “on the day that I smote all firstborn” (Numbers 3:13, 8:17).⁴ The verse informs us that God sanctified all Jewish first born on the day that the Egyptian first born were slain. It seems likely that this took place on the first day of Passover. Also in Scripture “this day is a day of tidings…if we wait until the morning light” (2 Kings 7:9).

Also, Shmuel’s figure contradicts the fixed calendar. For according to his calculation there remains in each mahzor (nineteen year cycle) one hour and 485 halaqim.⁴⁵ In 19 solar year, Shmuel’s figure gives us 19 ׳ (365d, 6h) = 6939d, 18h. Also, in one mahzor, the Hebrew calendar (‘ibbur) contains 12 “ordinary” years of 12 lunations and 7 “embolismic” years of 13 lunations, a total of 235 lunations. Each lunation is 29d, 12h, 793p. Thus 235 lunations is 6939d, 16h, 595p. So the difference between Shmuel’s cycle and the calendar is 1 hour and 485 halaqim per mahzor, approximately 0.0604 day per mahzor. This comes to about 0.0032 day per year, or 0.32 day per century. This is the difference between Shmuel’s cycle and that of Rav Adda. However, by right not even one heleq should remain, for then you will not have a complete mahzor. In addition, all scientists agree that 19 solar years is equal to 235 lunar months.⁴⁶ Based on current approximations, 19 tropical years do not equal exactly 235 lunar months. 19 tropical years totals 19 ׳ 365.2422 = 6939.6018 days. 235 lunar months is 235 ׳ (29d, 12h, 793p) = 6939.6896 days, a difference of 0.0878 day per mahzor. Over a century this would amount to a difference of almost one half day. That is the reason for having seven embolismic years. But today, as a result of the excess, there has accumulated approximately one-half month.⁴⁷ In the year 4919, 258 mahzorim and an additional 16 years had passed since Creation. Each mahzor has an excess of 1h, 485p. Thus 258 mahzorim would give an excess of 258 ׳ (1h, 485p) = 15d, 13h, 930p, or approximately ½ month. Perhaps those who love Shmuel’s cycle will tell us what we should do with them.

When we investigate the Torah’s year, we find written “This month shall be for you the beginning of months” (Exodus 12:2), so it is first of the months of the year. It is also written “This day you depart, in the month of ripening” (ibid. 13:4), and “Observe the month of ripening” (Deuteronomy 16:1). The explanation is that Israel counts by lunar months, and the month in which the barley ripens in the Land of Israel is the first of the year’s months. The beginning of that month is the beginning of the year, whether the equinox has passed or not. However, in order to perform the waving of the Omer ⁷⁸ The Omer waving took place on the second day of Passover, the sixteenth of Nisan (Leviticus 23:10–11). the court should ensure that Passover will occur when the barley has ripened.⁷⁹ There are exceptions to this requirement. See Ibn Ezra’s commentary to Exodus 12:2 and to Deuteronomy 15:1. Most years the ripening coincides with the equinox, but sometimes they are separated slightly because of an abundance of rain or because of drought.

The beginning of Israel’s year is determined by the court, as it is written regarding Hezekiah “And the king consulted” (2 Chronicles 30:2). He intercalated the year on advice of the court, and the Passover that he conducted was in the first month (Nisan). There are clear proofs that the revered God accepted his decision. However, he made one small error, namely, he did not intercalate the year on the day before the first month. This is the meaning of “He intercalated Nisan in Nisan, to which the Rabbis did not concur” (Mishna, Pesahim 4:9).

When the new moon comes again at the time of ripening in the Land of Israel, then one year is complete, whether the year is twelve months or thirteen. For this reason, in Hebrew they did not refer to the month of ripening as Nisan, rather “first.”⁸⁰ The first month in the Hebrew calendar might not always coincide with the Babylonian month of Nisan. The same is true for all the months. Therefore, other than in books of the exilic period, you will not find in the twenty-four books (the Hebrew Bible)⁸¹ The canon for the Hebrew Bible contains 24 books: Pentateuch (5), Early Prophets (4), Later Prophets (4), Psalms, Proverbs, Job, Daniel, Ezra-Nehemia, Megilot (5), and Chronicles. names for the months as they are known today, of which the first is Nisan.⁸² The names used for the months of the Hebrew calendar – Nisan, Iyar, etc. – for approximately the last two and a half millennia are Babylonian in origin. These names were adopted by the Jews after the destruction of the first Temple. Until that time the months were not given names and were referred to numerically – first month, second month, etc. So the year for Israel does not begin with the equinox, rather with the day of the new moon. Once we know that this month is the first, we observe the holidays in the seventh month from it. Thus, if Passover was in the days when the barley ripens, then Pentacost will be at the time of cutting and Tabernacles at the time of gathering.

We also find written⁸³ Ibn Ezra now proceeds to show that for some matters the year begins with the month of Tishre. Here he seems to be countering the Karites, who did not accept the first of Tishre as Rosh haShana. The Karites argued that there is no Scriptural basis for the first of Tishre being anything other than a day when work is forbidden (Leviticus 23:23–25) and special sacrifices are offered (Numbers 29: 1–5). The Karites began the year for all religious matters with the first of Nisan. with regard to Tabernacles “at the turn of the year” (Exodus 34:22), and also “at the departure of the year” (ibid. 23:16). Now the same day when one year ends a new year begins. We also find that God instructed us in a law of Haqhel, when the entire Torah is read during the holiday of Tabernacles of a Sabbatical year (Deuteronomy 31:10–13). There it is written “in order that they may learn” (ibid. 31:12). It is not likely that this took place after half a year.⁸⁴ Thus, Haqhel certainly took place at the beginning of a Sabbatical year, indicating that a Sabbatical year began around the time of Tabernacles. Do not be perplexed by the word “At an end (miqqez) of seven years” (ibid. 31:10),⁸⁵ The verse concerning Haqhel reads: “At the end of seven years, in the time of the Sabbatical year, on the holiday of Tabernacles,” which seems to indicate that the celebration of Haqhel took place at the conclusion of the Sabbatical year and the beginning of the eighth year. for we similarly find “At an end (miqqez) of seven years you shall send forth, each man his brother” (Jeremiah 34:14).⁸⁶ We know that servants were set free after six years (Exodus 21:2). Thus “miqqez” must here refer to the beginning of the seventh year. Similarly for Haqhel, the word “miqqez” means “beginning” rather than “end.” For each thing has two edges, a front edge and a back edge. The Sabbatical year began with Tishre,⁸⁷ Here Ibn Ezra refutes the Karites who began the Sabbatical year with Nisan. (See Ibn Ezra’s commentary to Leviticus 25:20.) which is the seventh month, since then the half year of planting began. Thus it states regarding the Sabbatical year “do not plant” (Leviticus 25:4), and “You shall plant on the eighth year” (ibid. 25:22).

Be aware that the moon does not generate a year, for it traverses the zodiac in twenty seven and one-third days.¹⁰⁴ This is called a “tropical month,” and is defined as the mean time it takes for the moon to travel from one equinoctial point, all the way around the zodiac, and return to the same point. In his Sefer haLuhot (quoted by Rabbi Yosef Tov ‘elem, Tzafnot Pa‘neah, vol. 1, p. 13), Ibn Ezra records a more exact figure for a tropical month: 27 days, 7 hours, and 775 halaqim; or 27 days, 7 hours, 43 minutes, and 3 and ⅓ seconds, approximately 27.3216 days. The current approximation for a tropical month is 27 days, 7 hours, 43 minutes, and 5 seconds, also approximately 27.3216 days. This is less than the mean time between new moons or full moons (called a “synodic month”), since the sun advances easterly along the ecliptic in the course of a month, and it takes time for the moon to catch up with the sun. See Ibn Ezra’s commentary to Exodus 12:2. However, since twelve lunar months are approximately a full solar year, we call a twelve month period a “lunar year.”¹⁰⁵ An ordinary lunar year consists of twelve synodic months, totaling 12 ׳ (29d, 12h, 793p) = 354d, 8h, 876p, approximately 354.3671 days. According to Shmuel, a solar year is 365d, 6h, thus a solar year has an excess of 10d, 21h, 204p, approximately 10.8829 days, over an ordinary lunar year. According to Rav Adda, a solar year is 365d, 5h, 997p, 48s (see note 43), hence a solar year has an excess over a lunar year of 10d, 21h, 121p, 48s, approximately 10.8797 days. The Arabs count by such lunar years, therefore their holidays occur sometimes in the summer and sometimes in the autumn. However, Israel’s years will equal exactly the true solar years every nineteen years.¹⁰⁶ The Hebrew calendar is a “lunisolar calendar,” being basically lunar but incorporating adjustments (leap years and adjustable months) to accommodate the solar year. Only Israel’s calculation is correct.¹⁰⁷ “Of all methods of intercalation which exist today, the Jewish calculation is the oldest, the most skillful, and the most elegant” (Joseph Justus Scaliger, De Emendatione Temporum, 1593; quoted by Reingold and Dershowitz, p. 96).

At issue is the nature of the principle that subclinical phenomena are to be disregarded. The concept can be understood in two distinct ways: 1) The Torah simply ignores any and all subclinical entities and phenomena and regards them as non-existent. That notion mirrors the reasoning of Resh Lakish, Yoma 73b, who maintains that a quantity of forbidden food less than the minimum for which statutory punishment is prescribed, is entirely permissible according to biblical law because, in effect, the Torah completely disregards its existence.⁵⁸Rabbi Halberstam, Ayin Lo Ra’atah, pp. 27f., cites the comments of the Brisker Rav, R. Yitzchak Ze’ev Soloveitchik, Ḥiddushei Rabbeinu ha-Griz al ha-Torah (n.d.) and idem, Ḥiddushei Maran Riz ha-Levi al ha-Torah (Jerusalem, 5723), Exodus 12:2, in support of his position regarding recognition of the sub-visual state. Mekhilta 1:6, cited by Rashi, Exodus 12:2, reports that Moses was perplexed with regard to the precise time at which the new moon might be sanctified. God responded by showing him the nascent moon and declaring, “This is what you shall see and sanctify.” The Brisker Rav explains that, in replying to Moses, God announced a shi’ur, i.e., he specified the minimum arc that must be visible as a requirement for announcing the new month. That exchange, argues Rabbi Halberstam, presumes that Moses knew that the Torah generally does take cognizance of subvisual phenomena but that he was in doubt only with regard to the shi’ur for sanctification of the new moon.
That deduction is not at all warranted. As the Brisker Rav himself remarks, it would have been impossible to sanctify the new moon on the basis of sighting the moon before it becomes visible. Moses’ doubt was with regard to whether sanctification is contingent solely upon the astronomical phenomenon of the emergence of the new moon, in which case “sighting” is merely confirmatory evidence of the moon’s return to a particular point in its orbit, or whether the new month does not commence until a visible portion of the moon has emerged. When the new moon is sanctified on the basis of actual sighting, resolution of that question is of no consequence. However, when the new moon is sanctified on the basis of astronomical calculations—as was the method utilized by Hillel II in establishing a perpetual calendar—the question assumes profound significance: Is it the exposure of even a minuscule sliver of the nascent moon that should be calculated or is it the appearance, some six hours later, of a portion of the moon of sufficient size to be perceived on earth that must be calculated? God’s reply affirmed the latter to be the case. The Peirush (anonymous marginal commentary published in standard editions of the Mishneh Torah), Rambam, Hilkhot Kiddush ha-Ḥodesh 7:1, cites a commentary on Rosh ha-Shanah attributed to Rambam indicating that it is the time of possible visual appearance of the moon that must be calculated. That issue is in no way related to the general question of the halakhic status of subclinical phenomena or entities.
Nor can Mekhilta be cited as proof that events taking place in a subclinical state are not given cognizance even when their results later become perceivable. The fact that the non-perceived emergence of the nascent moon is of no import even though the moon subsequently becomes visible does not constitute evidence for that thesis. The response, “This is what you shall see and sanctify” establishes a shi’ur, namely, that the new month does not begin with the earliest emergence of the moon but commences only when a portion of the moon sufficient for it to be visible to the human eye actually emerges. 2) The phenomena are indeed recognized as real but, since the Torah was given to human beings rather than to angels, no mandate or stricture can be attendant upon such entities or phenomena⁵⁹Cf., R. Ephraim Fishel Siegal, Or Yisra’el, no. 61, p. 69. There is actually a third possibility, viz., that “the Torah was not given to angels” means only that humans cannot be held accountable for what they cannot know, just as man cannot be held culpable in instances of force majeure, but, objectively speaking, such phenomena are regarded as existent. That formulation of the principle is quite correctly dismissed by R. Zevi Fried, Or Yisra’el, no. 61, p. 49 and by Rabbi Siegal, ibid., p. 68. unless and until there is perceivable evidence of such entity or occurrence.⁶⁰It has been argued that genetic engineering involving the introduction of one or more genes from another citrus fruit into the seed of an etrog does not result in a halakhic murkav or hybrid because the foreign gene is microscopic at the time that genetic manipulation is undertaken. Kereti’s thesis raises the possibility that the etrog may indeed be pasul, or disqualified, if characteristics of the alien fruit become recognizable in the mature etrog. See this writer’s Bioethical Dilemmas (Southfield, Michigan, 2006), II, 213f. If all subvisual events are to be entirely ignored, the "creeping" of minuscule Anisakis is of no moment. If, however, subclinical phenomena are ignored only until there is clinical evidence of their occurrence, the "creeping" of the Anisakis, while yet microscopic, renders it a "swarming creature" at least at such time as it becomes visually perceivable.⁶¹A difficulty arises from the fact that fermentation of wine as detected by taste buds is evidence of the presence of yeast in the wine. There is no source indicating that wine is permitted only because it is explicitly sanctioned by Scripture. Cf., Ḥokhmat Adam, Binat Adam, no. 35. Yeast, however, are incapable of independent locomotion and hence are presumably not members of the prohibited class of “swarming creatures.” See Claudio Delfini and Joseph V. Formica, Wine Microbiology: Science and Technology (New York, 2001), p. 49.

It's taught in Sanhedrin 42a: "And Rabbi Aḥa bar Ḥanina says that Rabbi Asi says that Rabbi Yoḥanan says: With regard to anyone who blesses the new month in its proper time, it is as if he greets the Face of the Divine Presence. Alluding to this, it is written here concerning the sanctification of the new month: “This month shall be for you the beginning of months” (Exodus 12:2), and it is written there, where the Jewish people encountered the Divine Presence at the splitting of the sea: “This is my God and I will glorify Him” (Exodus 15:2). The term “this” is employed in both verses. The school of Rabbi Yishmael taught: If the Jewish people merited to greet the Face of their Father in Heaven only one time each and every month, it would suffice for them, since in the blessing of the moon there is an aspect of greeting the Divine Presence. Abaye said: Therefore, we will say the blessing while standing, in honor of the Divine Presence." Behond it's clear that sanctification of the moon is a great and terrible matter like greeting the Shechina. And certainly there are great and terrible secrets regarding it, as the wise receivers of tradition have elaborated: the matter of the moon's diminishing and the matter of the First Man's sin, they touch one another. In the future, when the First Man's sin is rectified - then the diminishing of the moon will also be rectified. And regarding that moment it is said "And the light of the moon will be like the light of the sun" (Isaiah 30:26).