||Abraham bar Hiyya (d. c. 1136), Spanish philosopher, mathematician, astronomer, and translator. Little is known about Abraham's life apart from the fact that he lived in Barcelona. Two titles by which he was known provide clues to his public activity. One was Savasorda, a corruption of the Arabic ṣāḥib-al-shurṭa, originally meaning "captain of the bodyguard," but by Abraham's time denoting a functionary whose duties were both judiciary and civil, the exact scope of which can only be surmised. A court position was not unique for a Jew in Christian Spain at that time, and Abraham would have been useful for his mathematical and astronomical knowledge, his skill in surveying, and his linguistic abilities (he states in his writings that from his early youth he "gained honor before princes and royalty"). The other title, nasi, was not uncommon in Spanish Jewry and although in this instance also the exact significance is undetermined, it appears to denote an office within the Jewish community exercising a judiciary function with the power of imposing punishments and regulating communal taxation.
The only incident known from his life is a clash with his distinguished contemporary in Barcelona, Judah b. Barzillai al-Bargeloni. This occurred at a wedding which Abraham insisted on postponing because the stars were not propitious, whereas Judah wished to proceed with the ceremony as he held astrological beliefs to be "a custom of the Chaldeans." At some period of his life Abraham visited France – perhaps Provence – which at that time was ruled by the count of Barcelona. It appears that this visit was connected with the problems of land surveying. The dates and places of his birth and death are unknown. A manuscript dated 1136 refers to him as "of blessed memory" but this could be a later interpolation. However, Plato of Tivoli, who cites him as a collaborator in his translations up to 1136, does not mention Abraham in connection with a translation in 1138. As there is no evidence of his having lived subsequently, it has been assumed that he died c. 1136.
Philosophy - Concentrating on cosmogony, Abraham held that all things were first created in potentiality where they could be divided into matter, form, and not-being. In order to actualize them, God removed the not-being and joined form to matter. Matter is divided into pure matter and the dregs of matter, while form is divided into closed form and open form. The first stage in the process of creation is the emanation of a light from the closed form. This closed form is too pure to combine with matter and is identified with the form of angels, souls, etc. The light shines on the open form, qualifying it to combine with matter; one part of the open form combines with the pure matter and from this juncture the firmaments are created; the other part joins the dregs, thereby creating the four elements and the beings of the corporeal world. A further emanation of light over the firmament causes that form already attached to matter to change its place – and this brings about the creation of the moving stars; while a further emanation of light touches that matter which can change its form, and from this are formed all that fly, swim, and go. Man is the summit of creation, distinguished by his rational faculty. He has free will and can choose between the right way and sinning; if he sins, he still has the possibility of repentance. The way to repentance is always open, but the reward of eternal life is only for the God-fearing and God-acknowledging. All aspects of this world are transient and the important consideration is the world to come. The saintly individual lives an ascetic life in this world in order to be rewarded in the next. By observing the Torah, Israel obtains the reward of the world to come. Just as time had a beginning, so it must have an end and this will usher in the era of salvation when the wicked will be destroyed and only Israel and any others who accept the Torah will survive. Only Israel will be resurrected – the righteous to eternal life, the wicked to eternal justice.
Although points of similarity with other medieval thinkers are frequently discernible in Abraham's philosophical work, his writings contain an original admixture of Neoplatonic, Aristotelian, and rabbinic ideas, with original interpretations. He was sufficiently independent to reject philosophical for rabbinical theories when he deemed necessary, and his philosophy falls into no ready-made categories. He was one of the very first to write on scientific and philosophic subjects in Hebrew and many of the terms coined by him have passed into accepted Hebrew usage. His Hebrew is simple and lucid, similar in style to the later Midrashim.
Mathematical Works - Abraham was the author of the first encyclopedic work in Hebrew, Yesodei ha-Tevunah u-Migdal ha-Emunah ("Foundations of Understanding and Tower of Faith"). This was probably based on translations from the Arabic (it was published by Steinschneider in Hebraetsche Bibliographie, vol. 7, Sp. tr. by J.M. Millás Vallicrosa, 1952). Only sections have been preserved and these deal with geometry, arithmetic, optics, and music. He also wrote about mathematics in his Ḥibbur ha-Meshiḥah ve-ha-Tishboret ("Treatise on Mensuration and Calculation"; Sp. tr. by J.M. Millás Vallicrosa, 1931), the original object of which was to help French Jews in the measurement of their fields. This is the first Hebrew work to show that the area of a circle is πr2 and is the first known work – after an Egyptian papyrus of the 18th century B.C.E. – to give the formula of a truncated pyramid. It was published by M. Guttmann (2 pts., 1912–13). Plato of Tivoli translated the work into Latin in 1145 as Liber Embadorum ("The Book of Areas") and this introduced Arabic trigonometry to the West. It was the chief source for the writings of the celebrated mathematician, Leonardo Fibonacci of Pisa.
Astronomical Works - Abraham's main astronomical work, known as Ḥokhmat ha-Ḥizzayon, consisted of two parts. The first part, Ẓurat ha-Areẓ ve-Tavnit Kaddurei ha-Raki'a ("Form of the Earth and Figure of the Celestial Spheres"), is a geography – "a short review of lands according to the seven climates" – which long remained the chief source of geographical knowledge among Jews (it was published by M. Jaffe and Jonathan b. Joseph in Offenbach, 1720; Sp. tr. by J.M. Millás Vallicrosa, 1956). The second part, Ḥeshbon Mahalekhot ha-Kokhavim ("Calculation of the Courses of the Stars"; with Sp. tr. by J.M. Millás Vallicrosa, 1959), was often quoted; it incorporates a complete section on intercalation. The whole work is probably the first exposition of the Ptolemaic system in Hebrew and was the first complete textbook on astronomy in that language.
Abraham further considered problems of intercalation in his Sefer (or Sod) ha-Ibbur ("Book of Intercalation"), which was written in 1122 "to enable the Jews to observe the festivals on the correct dates." This work explains the principles of intercalation and shows how to calculate the Hebrew and Arabic years (publ. by H. Filipowski, London, 1851). It was often quoted by later authorities and was accepted as authoritative. Mention should also be made of the astronomical and astrological tables compiled by Abraham which were also often quoted, although never published. They include reckonings for year-cycles, the New Moon, the Egyptian, Arabic, Roman, and Alexandrian years, etc.
Astrology and Eschatology - Another of Abraham's smaller compositions was his letter to Judah b. Barzillai al-Bargeloni, defending astrology in connection with the above-mentioned incident at the Barcelona wedding (publ. by Z. Schwarz, 1917). However, the main source of knowledge of Abraham's astrological views is to be found in Megillat ha-Megalleh ("Scroll of the Revealer"; publ. by A. Posnanski, 1924; Sp. tr. by J.M. Millás Vallicrosa, 1929). This is an eschatological book, the first by a European rabbi, written with the object of determining the end of time. After working out a correspondence between the seven days of Creation with seven eras of world history, Abraham came to the conclusion that redemption would come to the world in the year 1383 C.E. and resurrection in 1448. He adduces proofs from both the Bible and astrology. This work was of considerable influence, for example, on *Judah Halevi , whose theory of the transmission of the prophetic spirit derives from it, and on the kabbalists, particularly those of the German school. Most of *Abrabanel 's astrological knowledge was derived from this work, parts of which were translated into Latin and French.
Knowledge of Abraham's philosophy is partly derived from this work but even more from his Hegyon ha-Nefesh ha-Aẓuvah (publ. by E. Freimann, Leipzig, 1860; Eng. tr. by G. Wigoder, "Meditation of the Sad Soul," 1969). This deals with creation, repentance, good and evil, and the saintly life. The emphasis is ethical, the approach is generally homiletical – based on the exposition of biblical passages – and it may have been designed for reading during the Ten Days of Penitence. It is less frequently quoted than Abraham's other works. A so-called "lost work" called Geder Adam is probably identical with Hegyon ha-Nefesh. Apart from his original compositions, Abraham collaborated in several of the translations made by Plato of Tivoli from Arabic to Latin. These played an important role in the transmission of Arabic scientific knowledge to Europe. There is also a translation of De Horarum Electionibus, a work on algebra by Ali ibn Aḥmad al-Imrānī made by Abraham; it is not known whether he did this on his own or in collaboration with Plato of Tivoli.