My Guess

I imagine that the calendar based on round numbers will be attractive to Sanhedrin. For one, it keeps the Psak of the gemara in Rosh Hashanah 21, according to which the latest date the Spring Equinox is Nissan 16. Second, it is an eternal calendar, which goes to generation five in the year 6000, 3600+5*480. This is easy to remember.

The Qeviyot of this calendar can be found here, until the year 6500. The complete Java program is here.

Take Us Out

The historical task of the Sanhedrin is to bring back the Judaism of the early prophets, of Yeshayahu, of Hoshea. Currently, the Datiyim imagine a return to the Judaism of the end of Bayit Sheni, and the Chilonim imagine nothing of this kind. Very few imagine a return to the Judaism of Bayit Rishon. But politically, we have already returned to the time of Bayit Rishon. Only religiously, we are still in the Galut. It is the task of Sanhedrin to take us out. If they grab the task, how good. But if not, salvation will come from a different place.

עורי כימי קדם

(Yeshayahu 51:9)

Eternal Calendar Based On Round Numbers

I suggest a fourth possibility for Sanhedrin to consider: an eternal calendar based on round numbers; (year - 3600) / 480. Here is the complete program. Output for the years 5790 + n*19, up till 6200:

5790: 49-03
5809: 48-03
5828: 48-03
5847: 48-03
5866: 51-03
5885: 50-03
5904: 49-03
5923: 50-03
5942: 49-03
5961: 50-03
5980: 49-03
5999: 51-03
6018: 20-03
6037: 20-03
6056: 21-03
6075: 21-03
6094: 22-03
6113: 21-03
6132: 21-03
6151: 21-03
6170: 21-03
6189: 20-03

Here 49-03 is 18-04, et cetera. Note how this does not "allow" the dates 18-03 and 19-03. Here are the first two cycles after 5782:

5782: 47-03
5783: 37-03
5784: 26-03
5785: 44-03
5786: 33-03
5787: 23-03
5788: 42-03
5789: 31-03
5790: 49-03
5791: 39-03
5792: 27-03
5793: 45-03
5794: 35-03
5795: 24-03
5796: 43-03
5797: 31-03
5798: 20-03
5799: 40-03
5800: 29-03
5801: 47-03
5802: 36-03
5803: 26-03
5804: 43-03
5805: 33-03
5806: 22-03
5807: 42-03
5808: 29-03
5809: 48-03
5810: 38-03
5811: 28-03
5812: 45-03
5813: 34-03
5814: 24-03
5815: 44-03
5816: 32-03
5817: 20-03
5818: 40-03
5819: 29-03

Acknowledgements

Thanks are due to Carl Friedrich Gauss for coming up, in 1802, with the extremely brilliant orinigal formula, or algorithm, and to Zvi Har'El for his brilliant elucidation of the algorithm, and for giving programs, in C, and in Java. I propose to have the (generational variant of the) Java code as a part of the Halachic standard (with the required minimal substitutions, specified by the Sanhedrin). The third person to be thanked is James A. Shneer, who wrote the wonderful book The Jewish Calendar and the Torah: Introduction - 2nd Edition. I am sure the book was created with the Gauss algorithm, probably with one of the programs of Zvi Har'El. A change in Halacha would be welcomed by Shneer, I guess, as an opportunity to make a special edition of his book.

Eternal Calendar

We can construct an "eternal" calendar program, which is based on the assumption that the calendar started in 3409, and changes generation every 476 years. The program goes, automatically, to generation 5 in our days. Here is the complete program, which regenerates the output of this post. The "eternal" calendar behaves fine, as you can verify yourself, from year 4000 to year 8000.

Generational Gauss Class

We can define a generational Gauss class by changing three lines of this Java code. We add a generational parameter n to the class constructor. That is we replace the line

public Gauss(int year, boolean g)

by the line

public Gauss(int year, boolean g, int n)

We replace the line

private static final double m0 = T - 10. * K + L + 14.;

by the line

double m0 = T - (10. + n)* K + L + 14.;

and move it down to below the constructor. Lastly, we change the line

a = (12 * year + 17) % 19;

into

a = (12 * year + 17 + n)% 19;

Then generational Gauss objects.with the third parameter 0 are "equal" to the original objects. Generational Gauss objects with third parameter 5 are "equal" to changed Gauss objects specified here. Generational Gauss objects with third parameter 4 are "equal" to the changed Gauss objects hinted to here.

Finally, here is the complete Java program that prints the output of the previous post, with the generational Gauss class.

The Earliest Pesach

The earliest Pesach, according to the proposed new calendar, until the year 6000:

5790: 19-03
5809: 20-03
5828: 18-03
5847: 20-03
5866: 20-03
5885: 20-03
5904: 19-03
5923: 20-03
5942: 19-03
5961: 21-03
5980: 21-03
5999: 21-03

One time, the date is 18-03, too early perhaps. Three times the date is 19-03, acceptable. Five times the date is 20-03, fine.

However, the rule that just two years, 6 and 7, are skipped to arrive at the new calendar, is easily understood. Moreover, the new calendar that we proposed is valid for some 500 years.

If the earliest of the earliest Pesach dates is deemed unacceptable, the solution would be to go from year 5 to year 19 (less intuitive), together with a different, though equally simple prescription to change the Java program. The resulting calendar would be valid maximally until about 5950.

That Is All

Based on this analysis, we change only two lines of code in Java, and the program calculates the Jewish calendar as in this post. We change to the new proposed calendar by replacing the line

private static final double m0 = T - 10. * K + L + 14.;

by the line

private static final double m0 = T - 15. * K + L + 14.;

Moreover, the line

a = (12 * year + 17) % 19;

is changed into

a = (12 * year + 3) % 19;

That is it. That is how I did it.

So, this is what it amounts to, the issuing of the decision that years 6 and 7 of the cycle (one time only) be skipped, and that we proceed with year 8, and the prescription that two lines be changed in the Java code, as above. That is all.

Shneer's Notation for the Qeviyot

I follow Shneer's notation for the Qeviyot. This notation is

(C|L)(D|R|A)(2|3|5|7)

where

C stands for Common year and L stands for a leap year.
D stands for a Deficient (353 or 383 days) year, R stands for Regular (354 or 384 days) year, A stands for Abundant (355 or 385 days) year.
Finally, the number at the end denotes the day in the week Rosh HaShana falls.

For instance, LR3 is a regular leap year (384 days) and it starts on a Tuesday. For instance, CA2 is abundant common year (355 days) and it starts on a Monday.

New Qeviyot and The Dates of Pesach

Below follow the Qeviyot and the dates of Pesach that are going to be be needed if Sanhedrin would decide to go with the proposal here. It is generated by a computer program based on this. Specifics follow in subsequent posts.

Year-Qeviyot--Pesach

5782 LR3(LR3) 16-04
5783 CA2(CA2) 06-04
5784 CA7(LD7) 26-03
5785 LD5(CA5) 13-04
5786 CR3(CR3) 02-04
5787 CA7(LA7) 23-03
5788 LA5(CA7) 11-04
5789 CR5(CR5) 31-03
5790 CD2(LD2) 19-03
5791 LA5(CA7) 08-04
5792 CR5(CR5) 27-03
5793 LD2(LD2) 14-04
5794 CA7(CA7) 04-04
5795 CR5(LA5) 24-03
5796 LA2(CR5) 12-04
5797 CD2(CD2) 31-03
5798 CR5(LA5) 20-03
5799 LA2(CR5) 09-04
5800 CA2(CA2) 29-03

In short, the Qeviyot tell you anything you want know about a year for Halachic reasons. Between brackets are the current Qeviyot. The dates of Pesach are the new dates of Pesach. The earliest Pesach is 19 March, which is just acceptable.

Next Chance

The universal 19-year cycle can be succinctly written in terms of its leap years, 1,3,6,9,11,14,17. In our current calendar, year 17 is mapped to year 1 of the universal cycle. This year, 5776, is year 3 of the universal cycle, a leap year. The Sanhedrin could not change it, not because they are not aware of the fact that 15 Adar Beth 5776, would-be Pesach, is well after the Spring Equinox, but because as a Sanhedrin they are not recognized by the majority of the people of Israel.

The next chance is year 9 of the universal cycle, year 5782. It could be declared, by the Sanhedrin, to be year 11 of the universal cycle. Alternatively, using the standard numbers, year 6 of our current calendar, should become year 8. Going forward then, leap years are as usual, the years 3,6,8,11,14,17,19. May we merit it.

Noach Without A Flood

The Torah Kedumah has Noach without a Mabul, as the inventor of wine. This article argues the same.

The Jewish Calendar

Likewise, these are the "cycle numbers" of the middle path:

8,
10,
29,
35.75,
49,
64,
100,
1000,
35750,
71471.

This is the higher path, the longer path, the more ultimate path. As the middle path, it can help to the right and to the left. To the right, 49 helps the count of Chesed, and because of that, 8*35.75 helps to adjust 16*18, on the left. And, as a compromise between left and right, the age of the Universe is set to be 29^2*2^14 kiloyears.

Together with steps of the Meshichin, the path becomes:

7,8,
10,
12,13,
15,16,
18,19,
27,28,29,
35.75,37
49,
64,
100,
1000,
35750,
71471.

The combined path, until 19, can be completed as:

2,
4,5,
7,8,
10,
12,13,
15,16,
18,19.

This can be read as the 12 normal years of the 19-year cycle. In other words, it represents the Jewish calendar. The current calendar follows if the year 17 of the 19-year cycle in the conventional system, year 5774 is the last instance, is year 1 of the universal cycle.

The Steps Of The Meshichin

To who understands. The cycle lengths of the two Meshichin follow a pattern:

7,
12,13,
15,16,
18,19,
27,28,
37.

This corresponds to "steps" of the Meshichin, as follows:

left,
right, left,
right, left,
left, right,
left, right,
right.

Rightly So

We edited the Torah. It is obvious. Christianity, with its belief in G-d the Father, does not believe that we edited the Torah, as some Jews do not believe that we edited the Torah. But we edited the Torah. The Quran is right. We changed the story of the Akeidah, but we did not substitute Yishmael for Yitzchak, as the Quran has it. We changed the story of the sacrificing, to G-d, of Yitzchak, into the story of his survival, by the grace of Hashem. And by the grace of Hashem, we will survive the onslaught in the name of God.

It is about morality. The western world, and Christianity, has a lesson to learn. The Islam comes to teach that lesson. But we will withstand the onslaught. Because the issue is moral. Yes, the Torah is edited. Rightly so.

(This started as a comment here. As usual, the comment was deemed unacceptable.)

The Square Root Of 2

The square root of 2 is the quintessential irrational number. It can only be approximated, in any numerical system. In the decimal system, it is approximated by 1.41421. Interestingly, it is quite well approximated by 13/19+27/37=1.41394, which is only 0,00027 less than 1.41421. The expression 13/19+27/37 consists of secondary cycle lengths, as explained, 16*18 and 28*15 being the primary cycles, of the two Meshichin.