User:Kasmy/Thomas Bradwardine

Science
In Tractatus de proportionibus (1328), Bradwardine extended the theory of proportions of Eudoxus of Cnidus to anticipate the concept of exponential growth, later developed by the Bernoulli and Euler, with compound interest as a special case. Arguments for the mean speed theorem (above) require the modern mathematical concept of limit, so Bradwardine had to use arguments of his day. Mathematician and mathematical historian Carl Benjamin Boyer writes, "Bradwardine developed the Boethian theory of double or triple or, more generally, what we would call 'n-tuple' proportion". In his Treatise on the Ratios of Speeds in Motions, Bradwardine attempted to reconcile contradictions in physics, where he largely adopted Aristotle's description of the physical universe.

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'''Bradwardine rejected four opinions concerning the link between power, resistance, and speed on the basis that were inconsistent with Aristotle's or because they did not align with what could be easily observed regarding motion. He does this by examining the nature of ratios. The first opinion Bradwardine contemplates before rejecting is one he attributes to Avempace that states " that speeds follow the excesses of motive powers over resistances", following the formula (V ∝ [M−R], where V = speed M = motive power, and R = resistance). The second opinion follows the formula (V ∝ [M−R]/R), which states "that speeds follow the ratio of the excesses of the motive over the resisting powers to the resisting powers". Bradwardine claims this as the work of Averroes. The third opinion concerns the traditional interpretation of the Aristotelian rules of motion and states "that the speeds follow the inverse of the resistances when the moving powers are the same (V ∝ 1/R when M is constant) and follow the moving powers when the resistances are the same (V ∝ M when R is constant)". His last rejection was "that speeds do not follow any ratio because motive and resistive powers are quantities of different species and so cannot form ratios with each other". "Bradwardine’s own rule is that the ratio of speeds follows the ratios of motive to resistive powers." '''

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'''Bradwardine did identify one measurement error in Aristotle's law of motion. Bradwardine's identification of this error was described by Ernest Moody as a “radical shift from Aristotelian dynamics to modern dynamics, initiated in the early fourteenth century.” Aristotle's calculation of average speed was criticized by Bradwardine for not examining “the whole question of how moment-to-moment velocities are related within the whole time of the movement." Bradwardine also believed Aristotle contradicted himself with his explanation of resistance in motion. Aristotle believed "that a force has to be greater than its resistance in order to move, and the “proportion” (Bradwardine’s word; we would say ratio) of force to resistance equaling the proportion of distance to time." Bradwardine did not accept the explanation and instead proposed "that the rate of velocity is the ratio of an exponential increase in force to resistance." Bradwardine's explanation does not align with the modern rules of the rates of motion, yet his goal to reconcile Aristotle's claim was accomplished and he was the first person to be credited for using exponential functions in an attempt to explain the laws of motion. '''

Boyer also writes that "the works of Bradwardine had contained some fundamentals of trigonometry gleane from Muslim sources". et "Bradwardine and his Oxford colleagues did not quite make the breakthrough to modern science". '''Al-Kindi in particular seemed to influence Bradwardine, though it is unclear whether this was directly or indirectly. Nonetheless, Bradwardine's work bares many similarities to the work of Al-Kindi, Quia primos (or De Gradibus). ''' The most essential missing tool was calculus.

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'''Al-Kindi in particular seemed to influence Bradwardine, though it is unclear whether this was directly or indirectly. Gerard of Cremona's Latin translation of Quia primos (or De Gradibus) would have been available to Bradwardine, but Roger Bacon seemed to be the only European philosopher to have had a direct connection to the book, but not to the degree of Arnald of Villanova. Nonetheless, Bradwardine's work bares many similarities to the work of Al-Kindi. '''

Art of memory
Bradwardine was also a practitioner and exponent of the art of memory, a loosely associated group of mnemonic principles and techniques used to organise memory impressions, improve recall, and assist in the combination and 'invention' of ideas. His De Memoria Artificiali (c. 1335) discusses memory training current during his time.

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'Bradwardine's On Acquiring a Trained Memory'', translated by Mary Carruthers, contains, as Carruthers describes it, was similar to Cicero's work on the art of memory. She states, "Bradwardine’s art is notable for its detailed description of several techniques for fixing and recalling specific material through the use of graphically detailed, brilliantly colored, and vigorously animated mental images, grouped together in a succession of ‘‘pictures’’ or organized scenes, whose internal order recalls not just particular content but the relationship among its parts." She acknowledges this being similar to active imaging described by Cicero, along with the memory devices for things and words being changed in rhetoric, but are distinct since the imagery Bradwardine uses is decidedly medieval in nature. '''