- Hebrew astronomy
Hebrew astronomy refers to any
astronomy written in Hebrew or by Hebrew speakers, or translated into Hebrew. It also includes an unusual type of literature from the Middle Ages: works written in Arabic but transcribed in theHebrew alphabet . It includes a range of genres from the earliest astronomy and mythical cosmology contained in theBible , mainly theTanakh (Hebrew Bible or "Old Testament"), toJewish religious works like theTalmud and very technical works.Astronomy Among the Hebrews in Antiquity
The Tanakh
Not much is said in the
books of the Bible concerning the position of theearth in theuniverse or the designation of thestar s andplanet s. Dependence for the most part must be placed on ambiguous references chiefly in the poetical sections. Although the Bible does use poetry to describe the Universe, there are some details given that would be very improbable for someone to guess during the era of the Bible. Using the stars to predict futures was forbidden (4:19 warns against worshipping the stars andnaked eye planets , but there are descriptions in the Bible which match the constellations such as the four beasts in Ezekiel. According toErnest L. Martin ["The Star that Astonished the World"] four of the symbols of the tribes of Israel as the tribes were positioned match four of the extremities of the zodiac. Some of the constellations are mentioned in the Bible such as Orion in the book of Job.Deuteronomy The sky
During the ages, various Hebrews had different interpretations of the word sky based on the Hebrew word. In Genesis one, the word for sky can mean stretched out as in an expanse, or it can mean beaten out. Actually in a sense, both of these might actually be true. Over a dozen verses in the Bible say God stretches the heavens. Most scientists presently hold that the Universe is being stretched. The earth's atmosphere was formed by violent volcanic eruptions, thus, "beaten out" might not be a bad description. There have been super volcanic eruptions that have been many hundreds of times more powerful than
Mt. Saint Helens . Some early Hebrew translators described the sky as an expanse. Some others described the sky as being solid. The expanse or firmament (depending on ones desired meaning) was set in the midst of the waters, and it divided the waters above from those beneath. It is not clear the meaning of waters above are because God's abode is described as having waters or frost. Since the expanse divides the waters above from the waters below (on the earth), the expanse may mean the Universe separating the seas on earth from God's abode. The raḳia' representing the sky in Ezekiel 1:22 resembled frost which is not a bad description for a lot of the Universe. Recently Scientists have found that there is an unimagined amount of water in the Universe-most is crystal frost, or in water vapor. The word for Heaven is Shamayim. Mayim means waters. The most abundant elements in the Universe are hydrogen, helium, and oxygen. Water is formed of hydrogen and oxygen. It has been speculated that the first sylable in shamayim (sha) comes from esh (anicent Hebrew had no vowels written in the text) in Hebrew which means fire. If this is correct, the Shamayim (heaven) means fire and water.The stars
In Genesis chapter one, God says the stars, the sun and the moon are given for signs. The stars are called the "hosts of heaven" around God and in the heights above. This phrase can also refer to
angels or other creatures (stars symbolize angels in the apocryphal firstBook of Enoch . Thus, the stars may have been living creatures. This conception is accurately paralleled among the Assyrians, who likewise conceive of the stars as soldiers serving the god of heaven,Anu , and probably also the somewhat similar godNinib or Ninurta, who was identified with the planet Saturn. The stars stand in God's presence, to the right and the left of His throne [I Kings 22:19; II Chronicles 18:18.] ; they serve Him [Nehemiah 9:6;Psalms 103:21.] , and praise Him [Psalms 103:21, 148:2.] . Reverence is offered to them as living creatures, even in later times [Jeremiah 8:2.] , and quite naturally upon the housetops [Jeremiah 19:13, 32:29; Zephaniah 1:5.] .At the head of this starry host stands a "captain of the army" [e.g., Joshua 5:14] ; According to Daniel 8:11, he was the star highest in altitude as well. This might have meant Saturn, the farthest removed from earth and therefore the highest in the heavens. It was held by the Assyrians to be the "bellwether" of the flock. This starry army belongs to Yhwh; hence the frequent expression "Yhwh of hosts" or "God of hosts" indicates that He is the actual leader of the heavenly array.
Only a few stars and constellations are named individually in the Old Testament, and their identification is not certain. The clearest references include:
*"Kesîl" [Isaiah 13:10; Amos 5:8; Job 9:9, 38:31.] , usually understood to be Orion, a giant angel.
*"Kimah" [Amos l.c.; Job l.c.] , which may be the Pleiades,Aldebaran ,Arcturus , orSirius .
*"'Ash" or "'Ayish" [Job 9:9, 38:32] , possibly the Hyades orUrsa Major , or even the Evening Star (Venus when seen after sunset).
*"Mezarim" [Job 37:9] , which may be Ursa Major andUrsa Minor , or a synonym for "mazzalot," in which case it would refer to the planets or the constellations of thezodiac .The planets
"Mazzalot" [e.g., II Kings 23:5] as already indicated, can refer to the planets collectively. But only two planets are named in the Old Testament:
*Saturn, called "Chiun" in Amos 5:26, closely related to the Assyrian "Kévan" or "kaiwanu."
*Venus, called "Meleket ha-Shamayim," "the queen of heaven," in Jeremiah 7:18 and elsewhere. That the latter means Venus is shown by the cakes which are said to have been baked for her. Among the Assyrians and Babylonians the cake offerings were called "the bread ofIshtar ."
*"Helel," the "son of the morning," in Isaiah 14:12, is also thought by some to be the morning star (Venus when visible before dawn). This identification is better known to many English speakers asLucifer , the "light-bearer."igns
"Many people considered eclipses as a bad omen...particularly a "blood red moon." Ancient peoples considered comets as bringing something very good, or very evil.
Extra-Biblical Sources
Conceptions of Astronomy in the Talmud
A mistake often made by laymen in their approach to
Aggadah is to assume the Jewish sages write on a literal, superficial level. In actuality, the Aggadah generally is meant toencode fundamental ideas aboutmetaphysics andethics , and is not necessarily relevant tophysical observations. This creates some difficulty in assessing superficially the ancient views ofastronomy .The information preserved in the Talmud contains only a fraction of the astronomical knowledge of the Talmudists; for in their academies they touched upon scientific problems only so far as they related to religious questions, and exercised great reserve regarding their stellar investigations, so as not to betray the secrets of the festival calendar, an important privilege of the house of the Palestinian patriarch and of his tribunal. Furthermore, these fragments do not emanate from one homogeneous system, as they are the accumulations of at least four centuries, and are traceable to various authors in the Jerusalem and Babylonian Talmuds, among whom some were inclined to mysticism.
Astronomy as a religious study
The high value of astronomical knowledge is already demonstrated by the astronomical section of the "
Book of Enoch " (about 72-80), as well as by such sayings as those ofEleazar Ḥisma (about 100), a profound mathematician, who could "count the drops in the ocean" (Hor. 10a), and who declared that "ability to compute the solstice and the calendar is the 'dessert [auxiliaries] of wisdom '" (Ab. iii. 18). Among the sciences thatJohanan ben Zakkai mastered was a knowledge of the solstices and the calendar; i.e., the ability to compute the course of the sun and the moon (Suk. 28a). Later writers declare that "to him who can compute the course of the sun and the revolution of the planets and neglects to do so, may be applied the words of the prophet (Isa. v. 12), 'They regard not the work of the Lord, neither consider the operation of his hands.'" To pay attention to the course of the sun and to the revolution of the planets is a religious injunction; for such is the import of the words (Deut. iv. 6), "This is your wisdom and your understanding in the sight of the nations" (Shab. 75a).Despite the general importance and religious significance attached to Astronomy in the Holy Land, no notable developments in astronomy happened there. The starry heavens of Palestine interested the Jews, indeed, as creations of God, as means to determine the holidays; but for a better knowledge of them the Jews were undoubtedly indebted to the Babylonians and their Hellenic pupils, as evidenced by the foreign term
gematria used to designate the computation of the calendar. Possibly this word represents a transposition of the Greek γραμματεία meaning "arithmetic, mathematics." Most of the observations of a scientific nature were transmitted by Samuel (250), who attended the schools of the Babylonians, and who claimed to possess as exact a knowledge of the heavenly regions as of the streets of his own city Nehardea. Certain rules must nevertheless have existed; for the patriarch RabbanGamaliel (about 100), who applied the above-mentioned lunar tablets and telescope, relied for authority upon such as had been transmitted by his paternal ancestors (Yer. R. H. ii. 58b; Bab. R. H. 25a).Conceptions of Heaven and Earth
As in the Bible, so also in the Talmud, heaven and earth designate the two borders of the universe. The former is a hollow sphere covering the earth. It consists, according to one authority, Who|date=June 2007 of a strong and firm plate two or three fingers in thickness, always lustrous and never tarnishing. Another tannaitic authority estimates the diameter of this plate as one-sixth of the sun's diurnal journey; while another, a Babylonian, estimates it at 1,000
parasang s. According to others, Who|date=June 2007 the diameter of the firmament is equal to the distance covered in 50 or 500 years; and this is true also of the earth and the large sea ("Tehom ") upon which it rests [Yer. Ber. i. 2c; Targ. Yer. Gen. i. 6.] . The distance of the firmament from the earth is a journey of 500 years—a distance equivalent to the diameter of the firmament, through which the sun must saw its way in order to become visible [Yer. Ber. i. 2c, bot.; Pes. 94a.] . The firmament, according to some, consists of fire and water, and, according to others, of water only; while the stars consist of fire [Yer. R. H. ii. 58a.] . East and west are at least as far removed from each other as is the firmament from the earth [Tamid. 32a.] . Heaven and earth "kiss each other" at the horizon; and between the water above and that below there are but two or three fingerbreadths [Gen. R. ii. 4; Tosef., Ḥag. ii. 5.] . The earth rests upon water and is encompassed by it. According to other conceptions the earth is supported by one, seven, or twelve pillars. These rest upon water, the water upon mountains, the mountains upon the wind, and the wind upon the storm [Ḥag. 12b; Yer. Ḥag. ii. 77a.] . The nations of antiquity generally believed that the earth was a disk floating on water. There is also mentioned the terrestrial globe, "kaddur," though it may also be translated as "disk." When Alexander the Great attempted to ascend to heaven he rose even higher and higher, until the earth appeared as a globe and the sea as a tray [Yer. 'Ab. Zarah iii. 42c, bot.] . The earth is divided into three parts, viz., habitable land, desert, and sea.It was assumed that our present earth was preceded by many others which were not good in the eyes of the Creator, who traverses in all 18,000 worlds, and for this reason is frequently styled "Lord of the Worlds" [Gen. R. iii. 7, ix. 2; Midr. Teh. xxxiv.] . The ocean also is mentioned in the Talmud, and the whole world is said to drink of its waters [Ta'an. 9b.] . According to mystic speculation there are seven heavens, the first of which is called "velum" (curtain); the second, "firmament," etc. [Ḥag. 12b.] . Whether these worlds are similar to ours is not stated. The correct impression concerning the infinitude of the starry host is expressed in the following sentence of Rabbi
Simeon ben Laḳish (about 250): "There are twelve mazzalot [signs of the zodiac] , each having thirty armies; each army, thirty camps [= castra] ; each camp, thirty legions [Compare Matt. xxvi. 53.] ; each legion, thirty cohorts; each cohort, thirty corps [Compare Krauss, "Lehnwörter," s.v.] ; and each corps has 365,000 myriads of stars entrusted to it" [Ber. 32b] . If one does the math, the answer is close to the estimated number of stars in the visible universe.Chronology and the zodiac
Chronology was a chief consideration in the study of astronomy among the Jews; sacred time was based upon the cycles of the Sun and the Moon. The Talmud identified the twelve constellations of the zodiac with the twelve months of the
Hebrew calendar . The correspondence of the constellations with their names in Hebrew and the months is as follows:#Aries - Ṭaleh -
Nisan
#Taurus - Shor -Iyar
#Gemini - Teomim -Sivan
#Cancer - Sarṭon - Tammuz
#Leo - Ari - Av
#Virgo - Betulah -Elul
#Libra - Moznayim -Tishrei
#Scorpio - 'Aḳrab -Cheshvan
#Sagittarius - Ḳasshat -Kislev
#Capricorn - Gedi -Tevet
#Aquarius - D'li -Shevat
#Pisces - Dagim -Adar The first three are in the east, the second three in the south, the third three in the west, and the last three in the north; and all are attendant on the sun. According to one account, in the first three months (spring) the Sun travels in the south, in order to melt the snow; in the fourth through sixth months (summer) it travels directly above the earth, in order to ripen the fruit; in the seventh through ninth months (autumn) it travels above the sea, in order to absorb the waters; and in the last three months (winter) it travels over the desert, in order that the grain may not dry up and wither.
According to one conception, Aries, Leo, and Sagittarius face northward; Taurus, Virgo, and Capricornus westward; Gemini, Libra, and Aquarius southward; and Cancer, Scorpio, and Pisces eastward. Some scholars identified the twelve signs of the zodiac with the twelve tribes of Israel.
The four solstices (the Teḳufot of Nisan, Tammuz, Tishrei, and Tevet) are often mentioned as determining the seasons of the year; and there are occasional references to the rising-place of the sun ('Er. 56a). Sometimes six seasons of the year are mentioned (Gen. R. xxxiv. 11), and reference is often made to the receptacle of the sun (ναρθήκιον), by means of which the heat of the orb is mitigated (Gen. R. vi. 6, and elsewhere). The Moon was also a part of the calendar: "The moon begins to shine on the 1st of the month; its light increases until the 15th, when the disk [(δίσκοσ)] is full; from the 15th to the 30th it wanes; and on the 30th it is invisible" (Ex. R. xv. 26).
The heavenly bodies and their motions
Two different cosmologies can be found in the Talmud. One is a
flat Earth mythical cosmology resembling descriptions of the world in the mythology of theAncient Near East . The other, resembling ancientGreek astronomy , is thegeocentric model , according to which the stars move about the earth. According toAristotle ,Ptolemy , and other philosophers among the Greeks, the stars have no motion of their own, being firmly attached to spheres whose center is the earth. A passage in the Talmud, theBaraita Pesahim 94b contrasts the pagan view with that of Jewish sages::"The learned of Israel say, "The sphere stands firm, and the planets revolve"; the learned of the nations say, "The sphere moves, and the planets stand firm." The learned of Israel say, "The sun moves by day beneath the firmament, and by night above the firmament"; the learned of the nations say, "The sun moves by day beneath the firmament, and by night beneath the earth."
The sun has 365 windows through which it emerges; 182 in the east, 182 in the west, and 1 in the middle, the place of its first entrance. The course described by it in a year is traversed by the moon in 30 days. The solar year is longer by 11 days than the lunar year (Yer. R. H. ii. 58a). The sun completes its course in 12 months; Jupiter, in 12 years; Saturn, in 30 years; Venus and Mars, in 480 years (Gen. R. x. 4); however, an objection is raised here (in a gloss) against the last-mentioned number. King Antoninus asked the patriarch why the sun rises in the east and sets in the west. At the time of the Deluge it traveled in the opposite direction (Sanh. 91b, 108b). Every 28 years it returns to its original point of departure, and on Tuesday evening of the spring solstice it is in opposition with Saturn, although Plato maintained that the sun and planets never return to the place whence they started. This is the cycle of 28 years (Ber. 59b); the moon-cycle of 19 years may have been meant in the Targ. Yer. Gen. i. 14.
The names of the seven planets are: (1) "Shabbetai," Saturn; (2) "Ẓedeḳ," Jupiter; (3) "Maadim," Mars; (4) "Ḥammah," the sun; (5) "Kokebet" or "Nogah," "Kokab-Nogah," Venus; (6) "Kokab," Mercury; (7) "Lebanah," the moon. From the names of the seven planets were derived the names of the days of the week; and each day was consecrated to the particular planet that ruled during the early hours of the morning. The Talmudists were familiar with the planets and their characteristics in
astrology ; but only the week-days were counted, while the Sabbath had a name of its own.Fixed stars and comets
The
Milky Way is called "Fire-Stream," a name borrowed from Daniel vii. 10 ("Nehar di-nur"), where it may possibly have had the same signification. The statement is also made that the sting of Scorpio may be seen lying in the Milky Way [Ḥag. 13b; Ex. R. xv. 6, ; Ber. 58b.] . Samuel said: "We have it as a tradition that no comet ever passed across the face ofOrion ["Kesil"] ; for if this should happen the earth would be destroyed." When his hearers objected to this statement, saying, "Yet we see that this occurs," Samuel replied: "It only appears so; for the comet passes either above or below the star. Possibly also its radiance passes, but not its body." Again, Samuel says: "But for the warmth of Orion, the earth could not exist, because of the frigidity of Scorpio; furthermore, Orion lies near Taurus, with which the warm season begins [Yer. Ber. ix. 13c; Bab. Ber. 58b.] . The comet, because of its tail, is called "kokba de-shabbiṭ." (rodstar).Joshua ben Hananiah (about 100), declared that a star appears once every seventy years and leads mariners astray; hence they should at such time lay in a larger store of provisions [Hor. 10a] . Rapoport endeavors to prove that the path ofHalley's comet had been computed by a wise rabbi [Epistle to Slonimski in "Toledot ha-Shamayim," Warsaw, 1838.] . Samuel said: "I know all the paths of heaven, but nothing of the nature of the comet."The following Biblical names of constellations are mentioned and explained:
Pleiades (Biblically know as the Seven Stars) [a cluster of] about a hundred stars, and for the much disputed , its equally obscure Aramaic equivalent (MS. M. ), Syriac , is given [Ber. 58b] . The following two sagas also have reference to natural phenomena. WhenRabbi Jacob died, stars were seen by day; whenRabbi Ḥiyya died, stones of fire fell from heaven [M. Ḳ. 25b.] . The latter may possibly be a reference tometeor s.Post-Talmudic times
With the revival of Greek science which took place in
Islam , Jews were intimately connected, and theAlmagest is said to have been translated by Sahal ibn Tabari as early as 800, while one of the earliest independent students of Astronomy among the Arabs wasMashallah (754-873?). Jews seem to have been particularly concerned with the formation of astronomical tables of practical utility to astronomers. Sind ben Ali (about 830) was one of the principal contributors to the tables drawn up under the patronage of theal-Mamun . No less than twelve Jews were concerned in theTables of Toledo , drawn up about 1080 under the influence ofAhmad ibn Zaid , and the celebratedAlfonsine Tables were executed under the superintendence ofIsaac ibn Sid , while Jews were equally concerned in the less-known tables ofPedro IV of Aragon .Isaac al-Ḥadib compiled astronomical tables from those ofAl-Rakkam ,Al-Battam , andIbn al-Kammad .Joseph ibn Wakkar (1357) drew up tables of the period 720 (Heg.); whileMordecai Comtino andMattathia Delacrut commented upon the Persian and Paris tables respectively; the latter were commented upon also byFarissol Botarel .Abraham ibn Ezra translatedAl-Mattani 's Canons of theKhwarizmi Tables, and in his introduction tells a remarkable story of a Jew in India who helped Jacob ben Tarik to translate the Indian astronomical tables according to the Indian cycle of 432,000 years. Other tables were compiled byJacob ben Makir ,Emanuel ben Jacob ,Jacob ben David ben Yom-Ṭob Poel (1361),Solomon ben Elijah (from the Persian tables), andAbraham Zacuto ofSalamanca (about 1515).The earliest to treatise of Astronomy in Hebrew on a systematic plan was
Abraham bar Ḥiyya , who wrote at Marseilles, about 1134. Discussions on astronomical points, especially with regard to the spheres, and disputed points in calculating the calendar occur frequently in the works ofJudah ha-Levi , Abraham ibn Ezra, andMaimonides , while a new system of Astronomy is contained in the "Wars of the Lord" ("Milḥamot Adonai") ofLevi ben Gershon .Jews were especially involved as translators:
Moses ibn Tibbon translated from the ArabicJabir ben Aflah 's acute criticisms of the Ptolemaic system, an anticipation ofCopernicus , and thus brought them to the notice of Maimonides. Ibn al-Haitham's Arabic compendium of Astronomy was a particular favorite of Jewish astronomers; besides being translated into Spanish by DonAbraham Faquin , it was turned into Hebrew by Jacob ben Makir andSolomon ibn Pater Cohen and into Latin byAbraham de Balmes . Other translations from the Arabic were byJacob Anatoli ,Moses Galeno , andKalonymus ben Kalonymus , bringing the Greco-Arabic astronomers to the notice of western Europe. Jacob Anatoli, for example, translated into Hebrew both the "Almagest" andAverroes ' compendium of it, and this Hebrew version was itself translated into Latin byJacob Christmann . Other translators from the Hebrew into Latin were Abraham de Balmes andKalonymus ben David of Naples , whileDavid Kalonymus ben Jacob ,Ephraim Mizraḥi , andSolomon Abigdor translated from the Latin into Hebrew. The well-known family of translators, the Ibn Tibbons, may be especially mentioned. In practical Astronomy Jewish work was even more effective.Jacob ben Makir (who is known also asProfiat Tibbon ) appears to have been professor of Astronomy atMontpellier , about 1300, and to have invented a quadrant to serve as a substitute for the astrolabe. Levi ben Gershon was also the inventor of an astronomical instrument, and is often quoted with respect under the name ofLeon de Bañolas .Bonet de Lattes also invented an astronomical ring. Abraham Zacuto ben Samuel was professor of Astronomy at Salamanca, and afterward astronomer-royal toEmmanuel of Portugal , who had previously been advised by a Jewish astronomer, RabbiJoseph Vecinho , a pupil of Abraham Zacuto, as to the project put before him byChristopher Columbus , who, in carrying it out, made use of Zacuto's "Almanac" and "Tables."With the Renaissance, Jewish work in Astronomy lost in importance, as Europe could revert to the Greek astronomers without it. The chief name connected with the revival of astronomical studies on the Baltic is that of
David Gans of Prague (d. 1613), who corresponded with Kepler, Tycho Brahe, and Regiomontanus Dubious|date=March 2008; he was acquainted with the Copernican system, but preferred that of Ptolemy, while as late as 1714David Nieto of London still stood out against the Copernican system. .The modern epoch of the science begins with a great Jewish name, that of Sir
William Herschel (1738-1822), whose Jewish origin is acknowledged by his biographer. His systematic survey of the heavens, continued and completed by his son John, his catalogues of nebulæ and clusters, and his discovery of the planet Uranus, may be classed among the greatest exploits in the history of Astronomy. He also started the investigation into the constitution of the universe, determined the path of the sun toward the constellation Vega, and in innumerable ways started this science along the lines on which it developed up to the time of the discovery of spectrum analysis. He was assisted throughout his work by his sister Caroline Herschel (1750-1848). Fourteen of the asteroids were located byH. Goldschmidt (1802-66).Wilhelm Beer (1797-1850), the brother of Meyerbeer, was the first to draw an accurate map of the moon.Moritz Loewy (b. 1833) was director of the Paris Observatory, and the inventor of the coudé or elbow telescope, by which the stars may be observed without bending the neck back and without leaving the comfortable observatory.ee also
*
Jewish views of astrology
*Kabbalistic astrology
**Sefer Raziel HaMalakh
**Sefer Yetzirah
*Islamic astronomy
*Abraham ibn Ezra (1093-1168).
*Abraham bar Hiyya Ha-Nasi (1130).
*Abraham Zacuto ben Samuel (16th cent.).
*David Gans (died 1613).
*Elijah Mizrachi (died 1526).
*Isaac Israeli ben Joseph (1310-30).
*Jacob Anatoli (1232).
*Judah ha-Levi (1140).
*Levi ben Gershon (Gersonides ), (1327-44).
*Mashallah (754-813).
*Moses Isserles (d. 1573).
*Moses ibn Tibbon (fl. 1244-74).
*Creation according to Genesis References
*In the Bible
**Gunkel's "Commentary on Genesis" (Nowack Series) may be consulted for incidental references to Biblical Astronomy;
**for the Babylonian views, see Jensen, "Kosmologie der Babylonier", Strasburg, 1890, passim;
**Jastrow, "Religion of Babylonia and Assyria", xx.-xxii.;
**Joseph Epping andJohann Nepomuk Strassmaier , "Astronomisches aus Babylon", Freiburg, 1889.J. Jr. P. J.
*In the Talmud
**Winer, B. R. ii. 526-529, Leipsic, 1848;
**Hamburger, R. B. T. ii. 77-81, s.v. J. Sr. L. B.
*"Astronomy," "Encyclopaedia Judaica". Jerusalem: Encyclopaedia Judaica & New York: Macmillan, 1971-72. 3:795-807.
*Langermann, Y. Tzvi. "Hebrew Astronomy: Deep Soundings from a Rich Tradition." In "Astronomy Across Cultures: The History of Non-Western Astronomy", ed. Helaine Selin, 555-84. Dordrecht: Kluwer Academic Publishers, 2000.
* [http://jewishencyclopedia.com/view.jsp?artid=2052&letter=A Jewish Astronomy/Astrology]Notes
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