The Rambam Knew Math!!!

There has been a question that I have had regarding an opinion stated by the Rambam for which I think I may have finally found the answer. Before I delve into it, let me provide some background. As many are familiar with, Chazal understood that the constellation that serves as the backdrop to the sun is considered to be the mazal of the month (since we see the sun from a different part of our orbit every day, the sun appears to slowly move across the constellations behind it. The path it "takes" is known as the ecliptic). In Sivan, for example, the stars that are behind the sun are those that form the constellation Teomim, Gemini; therefore, Teomim is the mazal of Sivan.

The issue that one can have with this is that, currently, this is no longer true. Over hundreds of years the stars shift, relative to us, and currently things are one constellation off. The stars that currently reside behind the sun during the month of Sivan are actually those that form the constellation Shor, Taurus.

The reason for this shift is usually described by comparing the earth to a spinning top (dreidel). As a top spins it also wobbles. The earth's wobble is relatively slow; it completes one "wobble" every twenty-five thousand plus years. During the in between time, the constellations slowly "shift" and that results in the system that Chazal put forth not being recognizable to us.

The Rambam notes this phenomenon in his Mishnah Torah (Yesodei HaTorah 3:7) and provides a relatively accurate rate of wobble (1 degree per approximately seventy years; interestingly enough this number is also given by the Ibn Ezra in his Sefer HaTa'amim. The Greeks felt it was more like 1/100; the Arabs refined it more in line with the number chosen by the Ibn Ezra and Rambam. It was only after Newton provided his theory of gravity that the currently accepted number of 1/72 was chosen). The Rambam mentions that the mazalos have shifted and states that the mazal of a month is not connected to the physical arrangement of stars, rather, it is connected to the time of year and, therefore, the mazal of the month of Sivan (from our example) is still Teomim. The Rambam then informs us that the time the names of the constellations were chosen was during the time of the Mabul, Great Flood.

Since Chazal and the Greeks seem to agree on the names, positions and forms of the constellations, it stands to reason that they would agree upon where the exact borders between constellations can be found. The problem I had with the Rambam was the if one does the math of when the Mabul was and "moves" the stars back to their relative positions, he will find that the vernal equinox was located in the constellation of Shor (both using the 1/72 ratio agreed upon by contemporary science, and the 1/70 provided by the Rambam himself). The vernal equinox is the place where the sun is on the first day of spring. Since Nisan is the month that this should be happening in, the vernal equinox should be in T'leh, the mazal of Nisan. The Rambam was certainly capable of doing the simple math of calculating how many degrees one needs to move the constellations based on how many years had passed since the Mabul. How could the Rambam state that the constellations shift at a rate of 1/70 and in the same halacha mention that the origination of the names of the mazalos was in the time of the Mabul!?!

The answer seems to be that the assumption that Chazal necessarily agreed with the Greeks as to the place of the borders is incorrect. There is a discrepancy in Rashi as to where the stars of Kimah are located, either in T'leh (Rashi R"H 11b) or in Shor (Rashi in a note at the end of R"H). The Rashash on Midrash Rabbah in last week's parsha (that's why I decided to post this now) writes that these "Rashis" are in disagreement and that this reflects a disagreement between Shas and the Midrash Rabbah. (Rashash Bamidbar Rabbah 10:8:29; also see 30 in which the Rashash refers to an alligator as an Akrav) I believe many would assume (and perhaps the Rashash himself believes) that the disagreement is that we do not know what Kimah is and there are different star patterns that are being suggested (perhaps the Hyades would be the other opinion). I, however, believe that it is possible that all agree that Kimah is the Pleiades (the conventional translation), and the disagreement is where the borders of Shor and T'leh are (and, perhaps, other borders could be disputed).

If correct, Kimah was in T'leh at the time of the Mabul. It would, therefore, be logical to assume that the Rambam would be of this second opinion and then his statement makes sense perfectly (based on his calculations).

I have included a recreation of these constellations and borders as they were in the time of the Mabul. The recreation reflects the currently accepted numbers and, therefore, if one were to draw a vertical line just to the right of Kimah, the equinox would still be in Shor. One must keep in mind that the Rambam had a ratio of 1/70 and not 1/72. According to his calculations, the equinox would be a few degrees more to the left and Kimah would barely be in T'leh. The Rashi that is of this opinion calls Kimah "the tail of T'leh" making this position seem accurate.

Yeshaya HaNavi's New World Order?

The astronomical reference in this week’s Haftarah is pretty fantastic. Although many of these posts are theories, I have found that there is a disproportionate amount of wording in Sefer Yeshaya that often has a dual meaning in the astronomical sense (Yechezkel is a close second). Because of that, it seems that when one encounters some of these underlying themes in this sefer that it is hard to discount them. Also, has to realize that the average person was as in tune with the stars, their movements and representations (they were perceived to be the ideas of nature and necessary for their agricultural society) and would certainly see these references as being obvious (like allusions in poetry or literature that are referencing contemporary issues).

The pasuk states (Yeshaya 66:3),

"שוחט השור מכה איש זובח השה ערף כלב מעלה מנחה דם חזיר מזכיר לבנה מברך און וגו'"

One who slaughters an ox [is as if he] has struck a man, the offering of a sheep [is like] the killing [by means through the back of the neck] of a dog, the giving of a flour offering [likened to] pig’s blood, the burning (see Metzudos) of frankincense is a forced blessing, etc."

The prophet is discussing the order of the world as man develops. At first the prophet focuses on the destructive path of man (as seen above) but the end of the chapter details the end of times when order will be restored and the wicked punished. It is interesting to see that the aforementioned verse seems to contain a very astronomical idea.

As we all know, there are four season and they start on the dates of the two equinoxes and two solstices. These dates are not just points in time, but the placement of the sun in the sky on these dates is integral. The location against the backdrop of stars is also referred to by the names of equinox and solstice. These areas were given significant weight by all ancient civilizations (see Ibn Ezra’s Sefer HaTa’amim).

At the time of Creation these four points were located in Shor/Taurus, Aryeh/Leo, Akrav/Scorpius, D’li/Aquarius. Over long periods of time, the stars appear to drift from their original place and, by the time of Chazal, these points shifted to being in the location of T’leh/Aries, Sartan/Cancer, Moznayim/Libra and G’di/Capricorn. Currently they have shifted even more and are in: Dagim/Pisces, Teomim/Gemini, Besulah/Virgo and Keshes/Sagittarius. The next shift will be similar to the first one mentioned, but with the order having D’li first and Akrav last. The shifts will continue in that fashion causing one to state that there are three basic makeups of these four points over the course of this world’s lifespan.

When analyzing the pasuk above, one sees that every grouping of three has two objects that seem to refer to two points of four from each set. All show the destruction of that item and could be showing that that item’s importance was being destroyed as the sun will no longer be placed in it during these important times.

The slaughter of an ox is compared to the striking of a man. The ox is the first point mentioned, Shor, and D’li, the last point, is considered to be a human pouring water and described, astrologically as human (see Ibn Ezra’s Reishis Chachma and Sefer HaTa’amim). The next grouping has a sheep and a dog. The sheep is T’leh, the first of the second set, and the dog, perhaps, is referencing Sartan. The dog is described as being killed from the back of its neck. If one looks to the constellations representing dogs in the sky, Canis Major and Canis Minor, he will see Cancer/Sartan, riding on the back of their necks. The next reference is the offering of flour and the blood of a pig. This seems to be showing the in between stage of the second and third set. (The first switching of sets had primarily happened in the time of Yeshaya , so perhaps, from the first to second set the prophet saw no need to discuss the in between motion.) In the hand of the Besulah is the star Spica and it is considered to be represented as stalks of wheat (see Ibn Ezra’s Reishis Chachma) and it is on the edge of Besulah. On the edge of Cancer is a star pattern that the Ibn Ezra tells us is represented as an iron pig (Reishis Chachma). Finally, the frankincense and the forced blessing can be shown as Dagim and Besulah. Dagim is considered to rule over many species plant life, including frankincense, and the way to describe the destruction of a Besulah would be to discuss the idea of her being forcibly taken (this is how Chazal reference the act of forcibly taking a woman as Ones, force). Therefore, perhaps, the "forced" blessing is showing the destruction of the Besulah.

Throughout the exile these changes of stellar position have all happened. Perhaps, the future will bring us something new. This can be seen in the phrase used by Yeshaya later in the Haftarah (Yeshaya 66:22),

"כי כאשר השמים החדשים והארץ החדשה אשר אני עשה וגו'"

"Because like the new heavens and the new world that I make, etc."

May we all merit to seeing this realization soon.