Sunday, May 23, 2010

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.


Anonymous said...

Not explained clearly enough. I got lost at the conclusion.

Ari S. said...

Firstly, thanks for reading and telling me. I apologize for the lack of clarity. What I am trying to suggest is that the currently recognized border between Shor and T'leh is actually disputed. From the variant Rashis it seems that there is a debate as to the location of this border. One opinion would maintain that Kimah is in Shor and this is consistent with the currently accepted border. The opinion that states Kimah is in T'leh would have to draw the border somewhere to the left of Kimah in the picture I included.

If the Rambam was of the second opinion everything works out beautifully. The vernal equinox wold be located in his T'leh during the time of the Mabul (based on his calculations) and it would seem to conform to Rashi's description of Kimah being the tail of the T'leh (it is at the edge of the constellation). Since the Rambam's statement is based on simple mathematics, this seems to be the most logical explanation.

Was that better or should I explain some more (or other aspects)?