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Rabbi Levi

Baruch Sterman

On a clear night when the full moon shines, one can look up and make out the dark patches called mare

or seas by the first observers who thought that the dim smooth areas were water. With binoculars or asmall telescope, the craters can be seen. They are named for great scientists and mathematicians whose

work helped our knowledge of astronomy progress. Bright Tycho and the impact rays emanating from itis the most pronounced, and nearby is Copernicus, whose light rays stand out against the mare which

surround it. Down in the shadowy crater field towards the bottom of the moon, at latitude 34.7S,

longitude 23.6E, one can find a crater approximately 81 km in diameter named Rabbi Levi. How did a

nice Jewish boy end up in a place like that?

The namesake of that crater is Rabbi Levi Ben Gerson (12881344), known by his acronym RaLBaG, by

his full name, Meister Leo de Bagnols, or by the Latin, Gersonides. He is best remembered today for his

commentary on the Bible, which is printed in the margin of the popularMikraot Gedolotseries on the

books of the Prophets. His magnum opus was the philosophical work called Wars of the Lord, in which he

boldly put forth his theories on fundamental theological issues such as the doctrine of choice (free will)

and providence, Gods knowledge, and creation. Whereas his predecessor, Maimonides, had been

particularly ambiguous about such matters, Ralbag makes his (often controversial) opinion clear andunequivocal, to the point where many later Jewish philosophers were harshly critical of his views. (Ibn

Shem Tov pejoratively terms Ralbags bookWars against the Lord!)

In addition to his accomplishments in the Jewish arena, as a philosopher, Talmudist, and Biblical exegete,Rabbi Levi was also an expert logician, mathematician, physician, and astronomer. He wrote

commentaries on many of the philosophical works of Aristotle and Averroes. He composed three major

books on mathematics (in addition to his commentary on some of Euclids books, and sine tables accurate

to the fifth decimal); the first on general mathematics both theoretical and practical, the second on

harmonics, and the third book (which he dedicated to Pope Clement VI) on trigonometry. Some claim

that he was the first to use the important method of mathematical induction (e.g., if some property is true

for 1 and the truth of that property forn implies its truth forn+1, then that property will be true for every

natural number), which he called hadragah or rising step by step.

In terms of astronomy, he presented a novel planetary model and compiled precise astronomical tables.

Ralbag demonstrated that Ptolmeys geocentric model predicted results which did not accord with

observation, thus setting the foundations for the revolution that would eventually lead to Copernicus

heliocentric model. While the regnant opinion was to put the stars at a distance of a few tens of thousands

of kilometers, Levi put them ten billion times farther about 10-100 light years in modern parlance close to our current notions, but remarkably unique in terms of medieval thinking. In an age where dogma

ruled, Ralbag was the consummate empiricist; he mistrusted all previous data and relied only on his own

observations. Levi writes:

No argument can nullify the reality that is perceived by the senses, for true opinion must

follow reality, but reality need not conform to opinion.

But Levis greatest contribution to the field of astronomy was his invention of an instrument for precise

determination of the angular separation between two stars. He called it theMegalleh Amuqot, (Revealer ofProfundities), but the popular name was baculus Jacobi, Jacobs Staff.

The design put forth in the fifth section of Levis Wars describes a rod which slides along a length of

track which is positioned directly in front of the observers eye. By adjusting the distance of the cross rodfrom the eye, one can line up the rod precisely such that edges of the rod just block the two stars being

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measured. It is then a matter of simple trigonometry to determine

the angular separation of the two stars (or a star and the horizon, or

even two terrestrial objects) from the width of the cross rod and its

distance from the eye.

In addition to its elegant simplicity, I find three aspects of the

instrument to be particularly noteworthy. First, Levi invented aunique method ofmarking the distance along the track, known as atransversal scale, which dramatically improved the precision of his

measurements. In addition to the equidistant lines across the width

of the track, Levi drew lines lengthwise as well. He then etched

diagonals from the side of one unit measuring line to the oppositeside of a subsequent line so that the intersection of the diagonal

with the transverse rows designated a finer scale for more accurate

measurement. This is shown in the accompanying diagram (based

on Bernard Goldsteins translation ofWars).

Furthermore, Levi realized that the plane of vision was not actually

the front of the eye, but somewhere behind that. The differencewould have to be taken into account if the measured distance of the

cross rod to the center of vision was to be accurate, and he devised

a precise method of determining what was later called the

eccentricity of the eye.

These features are of a scientific and engineering nature, but there is another dimension to Levis

invention that sheds light on his fundamental worldview. It is of supreme significance that Ralbag chose

to present his most important astronomical treatise as a section in his most important religious work. At a

recent lecture on Torah and Science, Rabbi Adin Steinsaltz compared the relationship between the two to

a rocky marriage, where the particular argument shifts from time to time against a backdrop of constant

bickering. If this is a more or less accurate impression of the current situation, for Ralbag the relationship

was closer to a newlywed couple dreaming of building a harmonious and loving life together. Levibelieved that the ultimate function of astronomy was to understand God, and at the same time he was sure

that God given reason could never be in conflict with God given Torah.

Ralbags invention enjoyed a long and illustrious

history and its use was ubiquitous for the next 300

years. The German cartographer and navigator,

Martinus de Bohemia brought the Jacobs staff to

Portugal and it was used both by Columbus and

Magellan as a navigational tool. Copernicus, Tycho,

and Kepler used the instrument extensively. Indeed,

the frontispiece of Keplers Ruldophine Tables has a

drawing of the temple of Urania, the muse ofAstronomy which depicts the progress of astronomy

through history. Towards the top of the pillar

representing Copernicus, a Jacobs staff hangs

prominently.

The picture on the right shows the German

astronomer Peter Apian (in 1531) using a Jacobs

Staff to determine that the tail of a comet (his

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particular comet was later found to be Halleys) always points away from the sun. (Coincidentally, the

Hebrew word for staff or scepter (shevet) is related to the term for comet (shavit).)

A star shall come out of Jacob, and a staff shall rise out of Israel, (Numbers 24;17) proclaims Balaam

the prophet. Ralbags staff of Jacob rose from Israel and shined brightly for hundreds of years,illuminating the paths of the stars in heaven and guiding the course of men as they sailed across the earth.

For further reading:

1. http://plato.stanford.edu/entries/gersonides/

2. A completeBibliographia Gersonideana can be found at:http://hcc.haifa.ac.il/Chairs/Wolfson/bibliographia.htm

3. Bernard R. Goldstein, The Astronomy of Levi Ben Gerson 1288-1344: A Critical Edition of

Chapters 1-20. New York: Springer Verlag, 1985

http://plato.stanford.edu/entries/gersonides/http://hcc.haifa.ac.il/Chairs/Wolfson/bibliographia.htmhttp://plato.stanford.edu/entries/gersonides/http://hcc.haifa.ac.il/Chairs/Wolfson/bibliographia.htm

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Rabbi Levi (crater)

General characteristics

Latitude 34.7 S

Longitude 23.6 E

Diameter 81 km

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Depth 3.5 km

Colongitude 336 at sunrise

Eponym Levi Ben Gershon

References See listing

Rabbi Levi is a lunarimpact craterthat is located among the rugged highlands in the southeastern part of theMoon's near side. Several notable craters are located nearby, includingZagut crater just to the north-northwest, the

heavily impactedRiccius crater to the southeast, andLindenau craterto the northeast next to Zagut.

This is a heavily worn and eroded crater formation, with several smaller craters lying along the incised rim and acrossthe interior floor. A group of these craters form a cluster in the western part of the floor, consisting of the satellitecraters A, L, M, and D, as well as lesser craterlets trailing away to the south-southeast. The largest of these craters is'Rabbi Levi L', a bowl-shaped formation just to the northwest of the mid-point. The remainder of the floor is relativelylevel and nearly featureless. Clusters of craters also lay across the eastern and southwestern sections of the rim.

Attached to the northeast is the remnant of an old formation that intrudes into the Rabbi Levi crater, producing astraightened section of rim along that face. This unnamed formation has been almost completely obliterated, and is

overlaid in the northwest by Lindenau, and along the outer northeast side by Rothmann crater.

Satellite craters

By convention these features are identified on Lunar maps by placing the letter on the side of the crater mid-pointthat is closest to Rabbi Levi crater.

RabbiLevi

Latitude Longitude Diameter

A 34.3 S 22.7 E 12 km

B 34.5 S 24.8 E 13 km

C 34.3 S 27.0 E 20 km

D 35.4 S 22.8 E 10 km

E 36.7 S 22.1 E 35 km

F 36.0 S 20.5 E 12 km

G 36.9 S 22.0 E 12 km

H 36.4 S 20.2 E 8 km

J 37.6 S 22.7 E 7 km

L 34.7 S 23.0 E 13 km

M 35.2 S 23.2 E 11 km

N 36.4 S 23.7 E 8 km

O 35.7 S 25.1 E 7 km

P 34.5 S 25.8 E 15 km

Q 33.7 S 25.8 E 6 km

R 33.6 S 28.2 E 12 km

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S 34.2 S 27.5 E 14 km

T 36.2 S 22.4 E 10 km

U 35.6 S 21.9 E 14 km

Categories: Craters on the Moon

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The picture is of the temple of Urania, the muse of astronomy, and it depicts the progress of thediscipline of astronomy through history. Mindful of the fact that the Tables were originally Brahe's

project, and in order to appease his heirs, Kepler makes the figure of Tycho Brahe take centre

stage. Tycho, in his ermine robe, wearing the medal of an elephant (the highest award from theDanish crown), proudly points out his cosmological model (the earth in the centre of the universe

with the sun orbiting around earth, but all the other planets orbiting around the sun) to the seated

Copernicus. The title of the book, Rudolphine Tables, hangs down proudly from that cosmologicalmodel, possibly an allusion to Tycho's wish that the tables be based on his system. At Tycho's

elbow is his book on planetary theories, the Progymnasmata. Tycho is leaning on an elegant

Corinthian column, complete with an achanthus-leaf capital, which proudly displays hisinstruments, the quadrant and the sextant that perfected observations. The columns that support the

temple symbolize by their form and condition the state of astronomical observation through

history. The starry heaven is depicted on the floor of the base because it is the foundation on which

the observations (columns) are built. Copernicus' column is of a much simpler form, carrying aJacob's staff and the parallalactic ruler which induced some careless errors in Copernicus'

observations. On the column rest also the observations of Regiomontanus and Walther which aided

Copernicus' work.

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The firm, but less elegant columns made of bricks with plenty of cracks flank Brahe and

Copernicus and signify the achievements (from left to right) of Aratus, Hipparchus, Ptolemy andMeton. Aratus (4th c. BC) wrote a poem entitled the Phaenomena which explained the

configuration of the heavens and their movements; his column sports an armillary sphere.

Hipparchus improved on Aratus with a sphere of fixed stars and a catalogue of them. Ptolemy isdepicted with an astrolabe, drawing a diagram. Part of the Greek title of his book, the Almagest, is

visible. At the foot of the column is the diagram of a deferent whose centre was removed from the

earth. Meton's column shows a dial, showing the Metonic cycle indispensable for calculating thedate of Easter. It shows the nineteen-year cycle after which the lunar phases will recur on the same

date. At the back, there are two columns made of tree trunks, with stumps, implying the absence of

instruments to render them into more elegant shapes. They do not quite reach the heavenly roof, so

Kepler has inserted some wedges. In front of these columns stands a Chaldaean astronomer, tryingto gauge the angular distance of planets using his fingers.

On top of roof of the Temple are six goddesses, signifying the important elements of Kepler's

astronomy. From left to right, they are optics (the shining head of the goddess is creating a shadowof a globe), the telescope, logarithms (holding in her hands rods of the ratio of one to two, and the

number around her head showing the natural logarithm of 2: 0.6931472), geometry (with acompass, square-ruler and a diagram of an ellipse), 'stathmica' namely the laws of the lever and

balance (the sun at the fulcrum of the balance shows that this is describes Kepler's area law), and

magnetics (holding a lodestone and compass). At the summit of the temple is the imperial eaglewith his sceptre, showering a few gold coins down to the astronomers. Tycho's island of Hven is

depicted in the centre panel of the base. To its left is a portrait of Kepler, with a miniature of the

temple and a list of his books. To the right is a portrait of the printer

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