Atlantis Online
November 18, 2019, 08:00:24 pm
Welcome, Guest. Please login or register.

Login with username, password and session length
News: Update About Cuba Underwater Megalithic Research
http://www.timstouse.com/EarthHistory/Atlantis/bimini.htm
 
  Home Help Arcade Gallery Links Staff List Calendar Login Register  

"Abraham, Planter of Mathematics"

Pages: [1] 2 3   Go Down
  Print  
Author Topic: "Abraham, Planter of Mathematics"  (Read 226 times)
Bianca
Superhero Member
******
Posts: 41646



« on: October 14, 2008, 10:12:07 pm »










                                              "Abraham, Planter of Mathematics":



                          Histories of Mathematics and Astrology in Early Modern Europe





Nicholas Popper


Princeton University

Francis Bacon's 1605 Advancement of Learning proposed to dedicatee James I a massive reorganization of the institutions, goals, and methods of generating and transmitting knowledge. The numerous defects crippling the contemporary educational regime, Bacon claimed, should be addressed by strengthening emphasis on philosophy and natural knowledge. To that end, university positions were to be created devoted to "Artes and Sciences at large," rather than to the professions. High salaries would render lecturers "able and sufficient," undistracted from their task. Most famously, he argued that teaching of the "operatiue studie of many Scyences" should involve sophisticated technical education. The study of natural philosophy demanded not only books, but globes, astrolabes, and other "instrumentals." Most significantly, yielding reliable and meaningful knowledge from experiential gleanings required a rigorous system of deductive reasoning.

The legacy of this colossal proposal has earned Bacon honored status as devisor of the scientific method.1 But Bacon's educational reform extended [End Page 87] beyond the methods of producing and transmitting knowledge. To facilitate more efficient "vse and administration" of the knowledge produced by his system, he also demanded a searching examination of the history of learning. This history would provide a mirror enabling his contemporaries to deploy the fruits of his method, by considering how learning in the past had been used successfully or ill-advisedly. Producing this history was the ambition of the Advancement, for he explained: "no man hath propounded to himselfe the generall state of learning to bee described and represented from age to age, as many have done the works of Nature, & the State civile and Ecclesiastical."

He continued:
Report Spam   Logged

Your mind understands what you have been taught; your heart what is true.

Bianca
Superhero Member
******
Posts: 41646



« Reply #1 on: October 14, 2008, 10:14:14 pm »










"And yet I am not ignorant that in divers particular sciences, as of the Iurisconsults, the

Mathematicians, the Rhetoricians, the Philosophers, there are set down some smal memorials of the

Schooles, Authors, and Bookes: and so likewise some barren relations touching the Invention of Arts,

or usages. But a iust story of learning, containing the Antiquities and Originalls of Knowledges, & their

Sects; their Inventions, their Traditions; their diverse Administrations and Managings; their Flourishings,

their Oppositions, Decayes, Depressions, Oblivions, Removes, with the causes, and occasions of them,

and all other events concerning learning, throughout the ages of the world; I may truly affirme to be

wanting."2
Report Spam   Logged

Your mind understands what you have been taught; your heart what is true.
Bianca
Superhero Member
******
Posts: 41646



« Reply #2 on: October 14, 2008, 10:15:42 pm »









Bacon thus positioned himself not only as a Father of Modern Science, but also a Father of the History of Science.

Following Bacon's suggestion, I will examine the "small memorials" of the history of mathematics—and particularly the mathematical art of astrology—in the sixteenth and seventeenth centuries. My conclusion, however, will not bear out Bacon's claims. Despite his frustration, Bacon was only one of many early modern scholars appraising the role of mathematics within history. And he devoted less energy than others to mapping its origins and tracing its transmissions between communities. In fact, Bacon's 1605 proposal for a history of mathematics was already out-of-date. Discussions [End Page 88] of the history of mathematics had been rife on the continent and in England throughout the previous century.3

The evidence that Renaissance scholars inherited was sprawling and inconclusive. Several genealogies for mathematics could be found within classical Greek, Latin, and patristic references. One lineage claimed mathematics began in ancient Assyria, where the priestly caste, the Chaldeans, practiced a form of mathematics that seemed a corrupt admixture of philosophy, medicine, and religion, and relied heavily on observation of the heavens. Other scholars traced the origins to Egypt, claiming that the field developed to survey lands frequently flooded by the Nile. The real problem for ancient, late antique, and medieval scholars had not been the origins of mathematics, but what exactly mathematics were. For some, the term strictly referred to the quadrivium: geometry, arithmetic, astronomy, and music. But for others, mathematics' origins amongst the Egyptians or Chaldeans inextricably linked it to forms of astrological divination, augury, and necromancy that were unsavory to both Latin and Christian traditions. Mathematici were included alongside ghastly lists of Magi, Brahmins, Aruspices, Genethliaci, and other diabolic practitioners of idolatrous magic. These might or might not be distinguished from mathematici such as Pythagoras and Euclid, who were considered philosophers, or from useful practitioners such as Archimedes. The term itself was a source of unending confusion. A mathematician in Aristotle's time, as later generations acknowledged, did geometry and arithmetic; but, by late antiquity, Augustine and Jerome could complain that nativity-readers were vulgarly called mathematici. This confusion and distrust spread in turn to later historical understandings of [End Page 89] mathematics, and justifies considering the Renaissance histories of magic, mathematics, astrology, and astronomy, as deeply interwoven.4
Report Spam   Logged

Your mind understands what you have been taught; your heart what is true.
Bianca
Superhero Member
******
Posts: 41646



« Reply #3 on: October 14, 2008, 10:16:53 pm »










Renaissance scholars devoted serious attention to delineating the various kinds of mathematics. To help distinguish the licit from illicit, the question of origins was given a new priority in the years leading up to 1500. The debate originated with Pico della Mirandola's considerations of the orthodoxy of astrology, that most controversial of mathematical arts. Against the backdrop of a late Quattrocentro Italy bursting with astrological prediction, Pico set the grounds for debate in two considerations of the history of magic.5 The first, his Apologia, defended a rigorously narrow range of pious magic. This tract answered the papal condemnation of twelve of his famous 900 theses.6 In defense, he wrote, "I put forward magical theorems, in which I show Magic to be twofold. One side is supported by the work and authority of demons, and consists of things, by my faith, execrable and portentous; the other is nothing other, when it is well explored, than the absolute consummation of natural philosophy."7 Pico went on to claim that natural magic was necessary for faith, since it alone allowed one to distinguish miracles from simple extraordinary events. Pico did not, however, offer much support for modern practitioners of the magical arts. With few caveats, he defended the thesis that, "All the magic, [End Page 90] which is in use amongst the moderns, and which the Church has rightly banished, has no firmness, nor truth, nor support, because it is manipulated by the first enemy of truth."8 In defining contemporary magic as diabolic, Pico suggested that a legitimate natural magic had been corrupted, lost, or, he suggested, enclosed within the ancient Jewish tradition of cabala—orally transmitted and secret wisdom—that Pico firmly supported and to which he claimed unique access. Pico's dismissals of modern astrology enabled him to advertise himself as the lone point of entry to this alternative tradition that would lead to the recovery of an unimaginably potent ancient knowledge.

Pico did not construct a thorough account of the fall of magic in his Apologia, but he did towards the end of his life in his Twelve Books Against Divinatory Astrology. Unpublished in Pico's lifetime, this tract was compiled from his remaining manuscripts and published in 1496 under the close supervision of his nephew, Gianfrancesco. This younger scholar was notoriously unsympathetic to the astrological arts and the publication cemented the family anti-astrological reputation by comprehensively critiquing the philosophical, theological, and rational grounds for astrological divination.9 In the Twelfth Book, the elder Pico dismantled the historical data with which proponents of astrology supported their claims. Two of his points were particularly effective. According to Cicero, the Chaldean astrologers claimed to found their art on 470,000 years of observation. Since this claim set the beginnings of observation roughly 466,000 years before God created the universe, Pico noted, it was extremely unlikely.10 Following Ptolemy, the greatest ancient authority on both astronomy and astrology, he instead allotted relatively modern origins to astrology, an effective means of diminishing its legitimacy. Second, Pico argued that astrology's Chaldean origins did not indicate venerable antiquity. Rather the birth of astrology formed a significant part of Babylon's notorious corruption of true religion.11 Pico's devastating exposé grounded astrological criticism for the next century. [End Page 91]
Report Spam   Logged

Your mind understands what you have been taught; your heart what is true.
Bianca
Superhero Member
******
Posts: 41646



« Reply #4 on: October 14, 2008, 10:18:01 pm »









Pico's critical genealogy of Chaldean magic was not universally accepted. In the last years of the fifteenth century, two substantial works challenged Pico's claims. The first came from Polydore Vergil. An arch-humanist, Vergil argued with Erasmus over which of them had invented the modern genre of collections of sayings, and wrote a hefty history of England that discredited Geoffrey of Monmouth.12 In his 1499 De inventoribus rerum, Vergil devoted the eighteenth chapter of the first book to the origin of mathematics. He began with the proposition, expressed most famously by Proclus, that the Egyptians were the first to practice mathematics. Vergil, however, did not subscribe to this theory. Instead, he turned to the first-century Jewish general and historian, Flavius Josephus.13

According to Josephus, Adam received all knowledge available to man, wisdom he taught his son Seth. Seth's progeny, Josephus wrote,
Report Spam   Logged

Your mind understands what you have been taught; your heart what is true.
Bianca
Superhero Member
******
Posts: 41646



« Reply #5 on: October 14, 2008, 10:20:06 pm »










discovered the science of heavenly bodies and their orderly array. Moreover, to prevent their

discoveries from being lost to mankind and perishing before they became known—Adam having

predicted a destruction of the universe, at one time by a violent fire and at another by a mighty

deluge of water—they erected two pillars, one of brick and the other of stone, and inscribed

these discoveries on both; so that, if the pillar of brick disappeared at the deluge, that of

stone would remain to teach men what was graven thereon and to inform them that they had

also erected one of brick.
Report Spam   Logged

Your mind understands what you have been taught; your heart what is true.
Bianca
Superhero Member
******
Posts: 41646



« Reply #6 on: October 14, 2008, 10:21:04 pm »









"It exists to this day," Josephus claimed, "in the land of Seiris."14 Vergil held Josephus in the utmost respect, and he first referred to this passage to prove that the Hebrews had invented letters, despite Greek and Latin claims to the contrary. He then used it to prove the Hebraic origins of mathematics, and finally to trace the origins of astrology. Vergil also followed Josephus in his postdiluvian histories, claiming that the mathematical arts were [End Page 92] recovered in Assyria, and that the Jewish Patriarch Abraham, an Assyrian, transported them to Egypt 430 years later. Assuming that the "science of heavenly bodies" required mathematics, Vergil yoked the history of star-gazing to the history of mathematics, and installed astrology within a sacred lineage opposed to Pico's diabolic genealogy.15

Pico too had cited Josephus's assertion that Abraham disseminated knowledge in Egypt. But for Pico, this learning amounted only to the mathematical observation of the heavens necessary to formulate a divine calendar; a form of licit, human knowledge similar to the interpretations of nature necessary for sailors, farmers, and physicians. Indeed, Pico claimed, idolatry and astrology had received a nefarious twin birth when the Chaldeans overextended this science, confusing celestial objects with divine entities. Both Pico and Vergil accepted astronomy—and therefore mathematics—as a practice of the ancient Hebrews, but Pico strenuously insisted that all arts that attributed divine agency to natural objects were corruptions of this accepted, Hebraic knowledge. His critique pursued a reformation of natural, non-revealed knowledge.
Report Spam   Logged

Your mind understands what you have been taught; your heart what is true.
Bianca
Superhero Member
******
Posts: 41646



« Reply #7 on: October 14, 2008, 10:21:59 pm »










Vergil launched an extremely cautious challenge: he stated that astrology was extremely venerable, not revealed, and expressed doubts regarding its utility.16 The other response to Pico lacked any moderation. It came from another individual of immaculate humanist pedigree and possessed of a firm respect for and constant attention to Josephus. However, the Dominican Giovanni Nanni, otherwise known as Annius of Viterbo, was not possessed of a scrupulous moral fiber. Rather, he was blessed with a fanatical conviction that the ancient Romans had derived from Etruscan stock, a belief he bulwarked through a series of forgeries and planted archaeological finds.17 [End Page 93]

Annius believed that the ancient Greeks had been inveterate liars, given to taking credit for arts and practices they did not invent, and guilty of corrupting arts as they inherited them. To uncover their lies, he sketched genealogies of all peoples from the Creation onward, focusing on the aftermath of the Flood. Within these he traced the histories of various arts, showing that the sciences that the Greeks claimed to have pioneered had actually been stolen from Chaldeans, Phoenicians, Egyptians, Italians, Franks, and Jews. Annius concocted these claims in the form of commentaries on a set of ancient documents that he allegedly discovered, publishing the entire package in 1498 as Vetustissimi Auctores. . . . Though the texts were denounced as shams within a decade of their publication, for the next century and more scholars treated them as providing legitimate insight into the ancient world.
Report Spam   Logged

Your mind understands what you have been taught; your heart what is true.
Bianca
Superhero Member
******
Posts: 41646



« Reply #8 on: October 14, 2008, 10:22:57 pm »









The prize piece amongst Annius's forgeries was the lost annalistic work of Berosus. The authentic Berosus, a Chaldean priest of the late fourth century BCE, was known largely via fragments quoted in Josephus. The Annian Berosus gave a complete history of the pre-Greek world, rife with proof that the Chaldeans had been notable practitioners of astrology and mathematics well before the flood. Annius made Berosus begin his first book: "Before the famous destruction of the waters in which the entire world perished, many generations went past, which we Chaldeans faithfully preserved."18 The source, as most readers would have immediately grasped, was the Pillars of Seth. Annius granted them expansive significance: "Therefore there were letters in use, and the arts of smelting, and brickwork, and prophesying, one thousand years and more before the inundation of the earth."19 But Annius was not content merely to note that such knowledge had been available at that time. Instead, he showed that the Chaldeans had absorbed this knowledge in its very first stages:
Report Spam   Logged

Your mind understands what you have been taught; your heart what is true.
Bianca
Superhero Member
******
Posts: 41646



« Reply #9 on: October 14, 2008, 10:24:11 pm »










But that letters and disciplines began and were disseminated by their first founder Adam, is proven

not only by faith alone, but also from the history of peoples and the tradition of the Chaldeans, which

asserts that they themselves knew astronomy and letters 3634 years before the monarchy of

Alexander . . . therefore [End Page 94] the conjecture and argument are firm, that Enoch received

letters from Seth the first son of Adam, in whose time, Theologians assert, letters and disciplines were

infused into Adam, and in which same time the Chaldeans affirm themselves to have grasped letters and

astronomy.20
Report Spam   Logged

Your mind understands what you have been taught; your heart what is true.
Bianca
Superhero Member
******
Posts: 41646



« Reply #10 on: October 14, 2008, 10:25:10 pm »










Annius thus dated the origins of Chaldean learning to around 4000 BC; within the first generation of humankind. The Chaldeans and the Patriarchs developed wisdom at the same moment, from the same fount. Indeed, the transparent implication was that Seth and Enoch developed these arts because they were themselves Chaldeans.

Annius's Berosus provided another source, alongside Moses, for the history of early time, but one that overturned the traditional theological status of Chaldeans. But this conflict with scripture did not discredit the text. While for Pico, Chaldean origins had been an incontrovertible demonstration of astrology's illicitness, Annius's forged genealogies made the Chaldeans entirely orthodox, an integral and esteemed part of the scriptural genealogy of knowledge, and Annius's Berosus presented himself as the mouthpiece of what Walter Stephens has called the "pious Chaldean." The Annian Berosus described the Chaldeans as God's first chosen people.21 And the Hebrews inherited and preserved astrology, a pure, original and divine Chaldean practice.

Pico's initial argument had relied on a particular vision of the early Assyrian empire and of Assyrian culture, and debate regarding the propriety of astrological knowledge was framed by discussion of this historical context. Scholars either approved of or denounced astrological arts by locating their origins before or after the Chaldeans abandoned true religion. The very tool that Pico used to criticize and condemn astrology, then, could be recalibrated, given a slightly different history in order to support it. Moreover, the history could also be adjusted to condemn any range of arts: one could further constrict Pico's range of acceptable mathematics by dating [End Page 95] the origins of any mathematical art to after the Chaldean lapse. While Pico had fixed the site of the debate, its terms remained plastic.
Report Spam   Logged

Your mind understands what you have been taught; your heart what is true.
Bianca
Superhero Member
******
Posts: 41646



« Reply #11 on: October 14, 2008, 10:28:37 pm »










Annius provided a powerful genealogical sanction for astrology by evoking a world history that rubbed uncomfortably against the conventional historical narrative derived from scripture. Like those Neoplatonic and Neohermetic scholars who argued for their sources' legitimacy by claiming that all peoples, not just Israel, had received some divine revelation, Annius's vision of history potently suggested that Moses's books were not the only creditable sources for deep ancient history. And Annius's bookish solution, in some ways, hewed more closely to theological orthodoxy then the cabalist tradition glorified by Pico. Pico's vision described a shadowy group of initiates possessing secret, oral knowledge—a vision that displaced the Papacy from the center of the history of learning and described revealed knowledge as fundamentally unwritten. Annius's version, by contrast, rooted the lineage of divine learning in the production and custody of texts and monuments, and granted a continuous, documented history to the Church from the 4000 BC to his present. Perhaps for countering Pico's challenge, Pope Alexander VI appointed Annius Maestro del Sacro Palazzo, or official papal theologian.22

Still, scholars found Annius's claims unsettling, and over the course of the sixteenth century, more cautious commentators—often Protestant and Northern European—reclaimed the infallibility of scripture as a historical source. Rather than turning directly to the Bible, however, they used Josephus to secure the mathematical arts' linkage to the scriptural genealogy.23
Report Spam   Logged

Your mind understands what you have been taught; your heart what is true.
Bianca
Superhero Member
******
Posts: 41646



« Reply #12 on: October 14, 2008, 10:30:09 pm »









Vergil's fragmentary Josephan history met Annius's strident and expansive version in Peter Ramus's 1569 Scholae Mathematicae. From the 1540s until his murder in the St. Bartholomew's Day Massacre, Ramus spearheaded a movement to reform the curriculum of Parisian universities.24 His myriad publications included textbooks on geometry and mathematics, [End Page 96] and in his influential 1569 Scholae Mathematicae, Ramus presented an exhaustive vision of the history of mathematics. As he explained, "Aristotle judged the arts to be eternal, as the world is, but that just as stars rise and set, the arts sometimes are excited and flourish, and at other times are debased and condemned. This was the great verdict of that great philosopher: that the arts deal with eternal and immutable things; but that the knowledge of them among men is not eternal."25 Ramus's history covered more ground than his predecessors, including the entire sweep of history from creation to his present, and he incorporated all mathematical arts, from philosophy to hydraulics.

The revolutions in the fortunes of mathematics, Ramus claimed, could be analyzed by modifying the exegetical theory of the Four Monarchies for periods of mathematics. The first was the Chaldean period, lasting from Adam to Abraham. Ramus needed only the Pillars as evidence. The Abrahamic diffusion inaugurated the second era, but Ramus made clear that Abraham was hardly alone in his divine knowledge of mathematics: Diodorus Siculus, (pseudo-)Berosus, Pliny, and Cicero showed that the ancient world had recognized a general Chaldean mastery in the discipline. For Ramus this did not substantiate a uniform condemnation. Overzealous deployment of these arts was troublesome, but the arts themselves were not.
Report Spam   Logged

Your mind understands what you have been taught; your heart what is true.
Bianca
Superhero Member
******
Posts: 41646



« Reply #13 on: October 14, 2008, 10:31:05 pm »










The Egyptian period that followed, Ramus noted, had witnessed increased sophistication of mathematical knowledge. Ancient Egyptians used mathematics for commercial and mercantile purposes, and for surveying flooded lands. Thales of Miletus transported mathematics from the Egyptians to the Greeks, inaugurating the third age. The final age was emerging in Ramus's time, a rehabilitation of mathematical knowledge similar to the Reformation.

Ramus, Vergil, and other humanists such as Joannes Stadius, Heinrich Rantzau, and Matthew Dresserus agreed on a history of mathematics that traced its origins to the Hebrew Fathers in ancient Assyria.26 This polemic [End Page 97] emerged in England in the last two decades of Elizabeth I's reign, when Bacon was just beginning his career in London. The orthodoxy and utility of mathematics were heavily debated in London at this time, and the issue of the origins of mathematics too faced close scrutiny.

London was a thriving metropolis, flooded with continental texts, and if Bacon did not encounter the history of mathematics from European scholars, local texts too would have offered him cogent histories of mathematics and astrology. The discussion in England surfaced early in 1583, when Richard Harvey's famous apocalyptic prognostication An Astrological Discourse appeared in London. This mathematical and astrological prophecy forecast massive upheaval and turbulence beginning that very spring. The disorder, Harvey claimed, would swell, culminating with a thunderous crescendo in 1588, after which the world would be profoundly and irrevocably altered.27
Report Spam   Logged

Your mind understands what you have been taught; your heart what is true.
Bianca
Superhero Member
******
Posts: 41646



« Reply #14 on: October 14, 2008, 10:32:20 pm »









Henry Howard, Earl of Northampton, and no friend to the Harvey family, adapted Pico's criticism later in 1583 in his weighty and learned rebuttal, A defensative against the poyson of supposed prophecies. Unlike Pico, who wanted to support true magic while condemning its corruptions, Howard brooked no art tinged by a hint of the magical. Still, Howard's criticism drew liberally from the criticism Pico had developed almost a century before. Relying heavily on scriptural condemnations of magical arts, Howard followed Pico in defending the possibility of natural philosophical knowledge that did not encroach on the domain of God. Using examples that astrology's defenders used to support the viability of their discipline, he distinguished forms of licit natural knowledge: "We reade not, that our Saviour Christ condemned those, that deemed of the weather that should follow by the rednes of the skie; nor those that gathered upon the fig trees putting forth her leaves, that Summer was at hand: for that the causes and [End Page 98] effects were tyed together, and combine in so streight a lincke of consequence, as either swerved not at all, or very seldome, from the course which kind had limitted. He rather used them as presidents of lawfull gessing & divining, by the proper causes of al things." Mariners too observed the world in an acceptable fashion. But this neither constituted prophecy, nor relied on mathematics.28

Howard maligned astrology's Chaldean origins with the standard tools of genealogical argument:
Report Spam   Logged

Your mind understands what you have been taught; your heart what is true.
Pages: [1] 2 3   Go Up
  Print  
 
Jump to:  

Powered by EzPortal
Bookmark this site! | Upgrade This Forum
SMF For Free - Create your own Forum
Powered by SMF | SMF © 2016, Simple Machines
Privacy Policy