Weekly Question Archive 21 - 30

Weekly Question Archive 21 - 30

by Remy Landau

Question 21

Assuming the fixed calendar rules, could the Exodus have taken place on a Thursday, in either the years 2448H or 2449H?

NO. According to the fixed calendar, the first day of Pesach would have occurred on
Tuesday 13 Mar -1312g in the year 2448H. Similarly, the first day of Pesach would have taken place on Sunday 31 Mar -1311g in the year 2449H.

By one of these very strange coincidences, the first day of Pesach would have taken place on THURSDAY 24 Mar -1313g in the year 2447H.

A very quick way to derive the day of the week for the first day of Pesach is to subtract two days from the day of the week of the subsequent Rosh Hashannah.

Consequently, it may be entirely possible that the advocates of a Pesach originating on a Thursday in the year 2448H may have overlooked or forgotten to realize that Thursday was the first day of Pesach for the previous year, namely, 2447H.

Another commonly made error in the literature of the Hebrew calendar relates to the number of days in the 19 year period. A manuscript published by Albiruni in the year 1000g implied that every 19 year cycle had exactly 6,940 days. (See page 153, line 18 of the Sachau translation of Albiruni's The Chronology of the Ancient Nations (1879)).

In a more recent book, The Calculated Confusion of Calendars (1976), on page 31, W. A. Shocken noted that the 19 year cycles could have either 6939, 6940, or 6941 days.

The discussion on the Calendar Repetition Cycle in the Hebrew Calendar Science And Myths web page indicates that there are also 19 year cycles of 6,942 days. This is a fact which does not appear to be noted in most of the commonly available references on the Hebrew calendar.

Question 22

In the full Hebrew calendar cycle, how often do 19 year cycles of 6,942 days occur?

The 19 year cycles that are 6,942 days in length occur only 295 times in the full 689,472 year cycle of the Hebrew calendar.

There are exactly 36,288 cycles of 19 years in the full 689,472 year cycle of the Hebrew calendar. Consequently, the 295 cycles of 6,942 days occur only in 0.813% of the 19 year cycles.

Question 23

When will, or did, occur the first 19 year cycle of 6,942 days?

There are only 295 nineteen year cycles of 6,942 days length in the full Hebrew calendar cycle of 689,472 years. Hence, these 6,942 day cycles occur on average, about once in every 2,337 years.

The first such 19 year cycle can be shown to have started in the year
2908H (Saturday 20 Sep -853g).

The second such cycle began in the year 3155H (Saturday 20 Sep -606g).

These 2 cycles were separated by 247 years. At one time, it was believed that
247 years (13*19 years) constituted the full Hebrew calendar cycle. This misconception is discussed in the Additional Notes under the topic of Proving the 689,472 Year Cycle.

The separation between the 2nd and the 3rd of these 6,942 day cycles is equally interesting.

Question 24

When will, or did, occur the third 19 year cycle of 6,942 days?

The first such 19 year cycle started in the year 2908H on Saturday 20 Sep -853g.

The second such cycle began in the year 3155H on Saturday 20 Sep -606g.

The third such cycle will not begin until Rosh Hashannah 6765H corresponding to
Saturday 6 Oct 3004g.

That's about 1005 years from now and its separation from the previous such cycle is 3,610 Hebrew years (3,610 = 10 * 19 * 19).

By the way, did you notice that the first 3 of the longest possible 19 year cycles all begin on Saturday?

Question 25

Will the fourth of the longest possible 19 year cycles also begin on Saturday?

The 19 year cycles have one of 4 possible lengths, which are either 6939, 6940, 6941, or 6942 days.

The rarest of these 19 year cycles is the 6942 day cycle which only occur 295 times in the 36,288 19-year cycles of the full Hebrew calendar cycle of 689,472 years.

These are the start dates for the first 3 of the 6942 day long 19 year cycles:

```2908H Sat 20 Sep -853g
3155H Sat 20 Sep -606g
6765H Sat  6 Oct 3004g
```

The fourth of these rare cycles will begin on Rosh Hashannah 10375H Sat 22 Oct 6614g.

The 3rd and 4th 6942 day cycles are also separated from each other by 3610 years
(19 * 19 * 10 years). However, that does not represent a regular pattern.

The regular pattern appears to come from the fact that the first 4 of the longest 19 year cycles all begin on Saturday.

Question 26

Do all of the 295 longest possible 19 year cycles begin on Saturday?

YES!

The 19 year cycles have one of 4 possible lengths, which are either 6939, 6940, 6941, or 6942 days.

The rarest of these 19 year cycles is the 6942 day cycle which only occur 295 times in the 36,288 19-year cycles of the full Hebrew calendar cycle of 689,472 years.

These are the start dates for the first 4 of the 6942 day long 19 year cycles:

``` 2908H Sat 20 Sep -853g
3155H Sat 20 Sep -606g
6765H Sat  6 Oct 3004g
10375H Sat 22 Oct 6614g
```

The 3rd and 4th 6942 day cycles are also separated from each other by 3610 years
(19 * 19 * 10 years). However, that does not represent a regular pattern.

The regular pattern appears to come from the fact that the first 4 of the longest 19 year cycles all begin on Saturday. Surprisingly, so do all of the remaining 6942 day long 19 year cycles.

It might be interesting, one day, to uncover the mathematical reason behind this phenomenon.

This week's question was asked by Rabbi Steven Saltzman of the Adath Israel Congregation in Downsview, Ontario.

The question involves the frequency of a particular Torah reading on Shabbat Hanukah.

One of the more prevalent practices, among the Jewish people, is that of reading the entire Mosaic text of their scriptures (Torah) over the course of one Hebrew year. At Simchat Torah, the last few verses are read, and then the entire cycle is repeated once again from Bereshit (Genesis).

The scriptural readings are divided into contiguous weekly portions, which are read in their entirety each Shabbat morning. Each division is known as a Parshah or Sedrah. These portions are arranged so as to be completely read over the course of one Hebrew year.

Each portion is given a special name. The two portions whose readings tend to coincide with Shabbat Hanukah are Vayyeshev and Miketz.

These portions are Genesis 37:1 to 40:23 and Genesis 41:1 to 44:17 respectively.

Since one of these two portions will always be read on Shabbat Hanukah, Rabbi Saltzman asked the following question.

Question 27

How often does the reading of Parshah Vayyeshev coincide with Shabbat Hanukah?

Last week's question was asked by Rabbi Steven Saltzman of the Adath Israel Congregation in Downsview, Ontario.

One of the more prevalent practices, among the Jewish people, is that of reading the entire Mosaic text of their scriptures (Torah) over the course of one Hebrew year. At Simchat Torah, the last few verses are read, and then the entire cycle is repeated once again from Bereshit (Genesis).

The scriptural readings are divided into contiguous weekly portions, which are read in their entirety each Shabbat morning. Each division is known as a Parshah or Sedrah. These portions are arranged so as to be completely read over the course of one Hebrew year.

Each portion is given a special name. The two portions whose readings tend to coincide with Shabbat Hanukah are Vayyeshev and Miketz.

These portions are Genesis 37:1 to 40:23 and Genesis 41:1 to 44:17 respectively.

Since there are 14 ways of laying out the Hebrew years (14 keviyyot), there exist only 14 ways of dividing the annual Torah reading cycle. As a result, the 14 different divisions can be easily tabulated in very compact form. One such tabulation may be found at the back of certain editions of the Chumash (Pentateuch) as translated by Alexander Harkavy, and published by the Hebrew Publishing Co. in New York (1928).

Shabbat Hanukah is any Shabbat which occurs anywhere from Kislev 25 through Tevet 2 or 3 (if the year is deficient, ie, 353 or 383 days).

From the Torah reading tables, it can be easily found that Parshah Vayyeshev is read on Shabbat Hanukah only when the preceding Rosh Hashannah began on Shabbat!

Since exactly 2/7 of all of the Hebrew years begin on Shabbat, Parshah Vayyeshev is read on Shabbat Hanukah in two out of every seven years, or on 28.57% of all of the Hanukah's.

Question 28

What is the present difference between the time of the molad and the corresponding mean lunar conjunction?

According to information referenced from the US Naval Observatory web page,

```
the period of the molad = 29.5305 941 358 ... (approx)
the astronomical  mean  = 29.5305 888 531 ... (approx)
```

The difference between the period of the molad and the above given astronomical value of the mean lunar conjunction is 0.0000 052 827 days per mean lunar period.

Hence, the difference between the molad period and the astronomical period is about
0.456 425 seconds per lunar month, equivalent to 0.1369 parts per lunar month.

From that it can be seen that the Hebrew month differs from the current astronomical value by about 1 day in every ((86,400/0.456425)/235)*19 = 15,304.883 years.

Up to Rosh Hashannah 5759H (1998g) 72,127 Hebrew months had elapsed. Consequently, the difference between the elapsed moladot and the astronomical periods had widened to
9.029233 hours, equivalent to 9h 1m 13.57p.

Because of the constantly widening gap between the time of the molad and the time of the astronomical mean conjunction, it is impossible to suggest the geographical location over which the time of any molad does take place.

Question 29

Approximately when will the Gregorian year value be the same as the Hebrew year value?

HAPPY NEW YEAR!

The following discussion assumes no changes whatever to either the Hebrew or the Gregorian calendars.

We are accustomed to determining the Hebrew year at Rosh Hashannah by adding the "constant" 3761. For example, by adding 3761 to Gregorian 1999 we get Hebrew 5760.

The Hebrew calendar moves more slowly in time than does the Gregorian calendar. As a result, the Gregorian year value is rising ever so steadily when viewed against the Hebrew year value.

The average Hebrew year length is 365.246822... days.

The average Gregorian year length is 365.2425 days.

Hence, the Hebrew calendar is slower than than the Gregorian calendar by about 0.004322 ... days per year.

At that rate, it can be seen that the Gregorian calendar year value rises against the Hebrew calendar year value by about 1 year in every 365.2425 / 0.004322 = 84,507.751 years.

To catch up to a difference of 3,761 years would then require 84,507.751 * 3,761 = 317,833,651 years.

Correspondent Derek Bunker wrote a Hebrew to Gregorian calendar program which allowed for a range of several hundreds of millions of years. According to his calculations the probable range of years in which both the Hebrew and the Gregorian year values first become equal would be 317,763,761 to 317,846,899.

Thank you Derek!

Question 30

What was the Hebrew acronym given to this once used leap year distribution
3 5 8 11 14 16 19 ?

The surprising Hebrew acronym given to this leap year distribution was gimel-bet-tet-bet-gimel.

A trace of the answer to this question can be found on page 65 in the 1879 Sachau translation of the 1000g Al-Biruni work The Chronology of Ancient Nations.

The Hebrew numbering system traditionally used a letter of the alphabet to represent a given number. Thus the Hebrew letters alef through yud were used to represent the numbers
1 through 10.

In representing the leap year distributions, the traditional practice was to use only the first nine letters of the alphabet, it being understood that, once the years had passed the 10 mark, 10 would be subtracted and the remainder used to identify the letter to be used.

Hence, the current leap year distribution, 3 6 8 11 14 17 19, has an acronym formed from the Hebrew letters gimel, vov, het, alef, daled, zayen, tet and is usually known as GUChADZaT.

Consequently, it would be expected to see the Hebrew acronym for the leap year distribution
3 5 8 11 14 16 19 written as gimel-heh-het-alef-daled-vov-tet.

What the Al-Biruni work shows is that as early as 1000g calendar scholars gave this leap year distribution a palindromic acronym formed from the Hebrew letters gimel-bet-tet-bet-gimel. The acronym, in Hebrew, actually reads the same backwards as forwards.

Understanding that the difference between the last year of this cycle (19), and the first year of the following cycle (3) is 3 years, it becomes easy to see that the acronym was formed from the differences between successive leap years in that distribution. The tet, representing 9, was an economy derived from the fact that the middle 3 differences were all 3.

The Encyclopedia Judaica, in its article on the Calendar shows the Hebrew acronym for the
3 5 8 11 14 16 19 distribution to be the expected gimel-heh-het-alef-daled-vov-tet with the equivalent, but less economical, notation of gimel-bet-gimel-gimel-gimel-bet-gimel.

``` First  Begun 21 Jun 1998