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Rabban Gamliel and the Antikythera Mechanism

Morris Engelson

The definition of a “month” is not nearly as simple as it seems. After all, April, the month in which Pesach falls out this year, is not the same as Nisan, the month in which Pesach occurs every year. Nisan is a chodesh, a lunar month, while April is an ordinary month and not connected to the phases of the moon. Therein lies the difference between the Torah’s concept of a chodesh and the secular definition of a month: a chodesh is closely (although not exactly) associated with the phases of the moon.

Wednesday, April 04, 2012

camera on landscapeIn a baraisa cited in Maseches Rosh HaShanah 25a, Rabban Gamliel provides the time duration of what would be referred to scientifically as the “mean synodic month”: “Thus have I received a tradition from the house of my father’s father: the rebirth of the moon is not less than 29½ days, two-thirds of an hour, and 73 chalakim.” This is the time that elapses from molad to molad, i.e., the time between lunar conjunctions when the moon, Earth and sun are aligned so that the moon is totally invisible. An hour is comprised of 1,080 chalakim (Rambam, Hilchos Kiddush HaChodesh 6:2).

Thus, Rabban Gamliel’s tradition indicates a period of exactly 29 days, 12 hours, and 793 chalakim. This exact value, written in a different mathematical format known as sexagesimal (meaning mathematics based on 60, as opposed to the decimal, based on ten, with which we are familiar), appears in the Almagest, authored by the Greek astronomer Ptolemy in the year 150 CE. The duration of the mean synodic month according to both Rabban Gamliel and the Almagest, then, is 29.5305941358 days.

Earth-based measurement of the synodic month duration is extremely difficult. It was only with the advent of space-based measurements that a highly precise result was obtained at 29.5305888531 days. The value provided by Rabban Gamliel, as well as, l’havdil, Ptolemy, is only 0.456 seconds more than the value obtained by NASA.

We can understand how Rabban Gamliel possessed a value so strikingly close to the measurement obtained by modern scientists, but how did a Greek astronomer come up with a number anywhere near the one obtained by today’s sophisticated measurements?

Actually, Ptolemy attributes the figure he quotes to Hipparchus, who lived in 150 BCE. Did Hipparchus establish this value, or did he get it from someone else? No one knows for sure. There are numerous learned scientific-historical papers arguing against each other, each advancing theories as to who obtained such a remarkably accurate value and when and how they did so. Some say it was the Greeks, and some say it was the Babylonians. Some argue that one particular scientific-mathematical procedure was used, and some suggest another method. But all agree on one thing: the value was obtained via astronomical measurement combined with sophisticated mathematical analysis.

With this background, consider the following. In my book, The Heavenly Time Machine: Essays on Science and Torah (2001), I noted in passing the remarkable similarity between the scientific value for the synodic month duration and that provided by Rabban Gamliel. Soon thereafter, I received a challenge from a reader on two points:

  1. Everyone knows that the ancient Greeks and/or Babylonians obtained this value through intense scientific effort, as attested to by the information in the Alamagest, and by Babylonian clay tablets that point to this number. So why is it so remarkable if Chazal also knew this information? Any reasonably educated person would know this value.
  2. Moreover, the reader was troubled by my claim that this number comes from Torah. Rabban Gamliel states that the value is “not less than” the figure he gives, but science maintains that it is in fact almost 0.5 seconds less his figure. If the value had been obtained through human effort, then we could only marvel at this amazing accomplishment for someone who did not even possess a telescope, when we today, with all our instruments, had to wait for space-based measurements to get more accurate results. But if the number comes from the Torah itself, the reader contended, then a discrepancy of half a second is just as troubling as a difference of half an hour. “Not less than” means just that, without exceptions. How, he asked, could Rabban Gamliel have arrived at a higher figure than the one indicated by elaborate scientific measurements?

It was clear to me that no amount of scientific evidence could cast any aspersion on a statement of the Torah. As for the reader’s claim that Rabban Gamliel had obtained his information from the scientists of the day, it is clear from his statement in Rosh HaShanah that the information had been received from his grandfather, Rabban Gamliel the Elder, who was the grandson of Hillel. Hence, the phrase “mibeis avi abba refers to a mesorah from Beis Hillel. What’s more, Rambam makes it clear that this information originates from zman matan Toraseinu (see, e.g., Rambam, Hilchos Kiddush HaChodesh 5:2).


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