User:Chancewilber1/Oxford Calculators

Reference


 * Wrote by David C. Lindberg and Michael H. Shank
 * 8 pages 426-432, 434 about Oxford Calculators
 * 3 pages 418,428,480 about John Dumbleton
 * Lots about the Oxford Calculators work on the Mean-Speed Theorem
 * "The concept of instantaneous speed set the stage for the most significant contribution of the Oxford calculators to the kinematics of local motion- the mean speed theorem." pg 429
 * Pg. 431 has great information breaking down the mean-speed theorem in one paragraph
 * Side note: 415 also speaks about Bradwardines Rule which can be added to his list of accomplishments on this page


 * Wrote by Lawrence M. Principe
 * Has one excerpt about Galileo referring to the Oxford Calculators

Lead

The lead starts the article off very well and I do not see much that can be changed.

The Oxford Calculators were a group of 14th-century thinkers, almost all associated with Merton College, Oxford; for this reason they were dubbed "The Merton School". These men took a strikingly logical and mathematical approach to philosophical problems. The key "calculators", writing in the second quarter of the 14th century, were Thomas Bradwardine, William Heytesbury, Richard Swineshead and John Dumbleton. Using the slightly earlier works of Walter Burley, Gerard of Brussels, and Nicole Oresme, these individuals expanded upon the concepts of 'latitudes' and what real world applications they could apply them to.

Article Body

The advances these men made were initially purely mathematical but later became relevant to mechanics. Using Aristotelian logic and physics, they studied and attempted to quantify physical and observable characteristics such as: heat, force, color, density, and light. Aristotle believed that only length and motion were able to be quantified. But they used his philosophy and proved it untrue by being able to calculate things such as temperature and power. They developed Al-Battani's work on trigonometry and their most famous work was the development of the mean speed theorem, (though it was later credited to Galileo) which is known as "The Law of Falling Bodies". Although they attempted to quantify these observable characteristics, their interests lay more in the philosophical and logical aspects than in natural world. They used numbers to disagree philosophically and prove the reasoning of "why" something worked the way it did and not only "how" something functioned the way that it did.

The Oxford Calculators distinguished kinematics from dynamics, emphasizing kinematics, and investigating instantaneous velocity. It is through their understanding of geometry and how different shapes could be used to represent a body in motion. The Calculators related these bodies in relative motion to geometrical shapes and also understood that a right triangle's area would be equivalent to a rectangle's if the rectangle's height was half of the triangle's. This is what led to the formulating of what is known as the mean speed theorem. A basic definition of the mean speed theorem is; a body moving with constant speed will travel the same distance as an accelerated body in the same period of time as long as the body with constant speed travels at half of the sum of initial and final velocities for the accelerated body. Relative motion, also referred to as local motion, can be defined as motion relative to another object where the values for acceleration, velocity, and position are dependent upon a predetermined reference point.

The reason these two subjects are here below the body is because these are two topics that are covered a lot about the Oxford Calculators that can be separated from "The Body" rather than having one big section.

Mean Speed Theorem

'''"From this the mean-speed theorem and the distance rule immediately follow, for it is evident that the area of a right triangle, representing the total intensity of a quality distributed uniformly difformly from zero to some intensity, is equal to that of the rectangle on the same base with half the altitude, representing a uniform quality at the mean degree." '''

'"Its earliest known statement is found in Heytesbury's Rules for Solving Sophisms:'' a body uniformly accelerated or decelerated for a given time covers the same distance as it would if it were to travel for the same time uniformly with the speed of the middle instant of its motion, which is defined as its mean speed." '''

Kinematics and Dynamics

Bradwardine's Rule

The initial goal of Bradwardine's Rule was to come up with a single rule in a general form that would show the relationship between moving and resisting powers and speed while at the same time precluded motion when the moving power is less than or equal to the resisting power. Before Bradwardine decided to use his own theory of compounded ratios in his own rule he considered and rejected four other opinions on the relationship between powers, resistances, and speeds. He then went on to use his own rule of compounded ratios which says that the ratio of speeds follows the ratios of motive to resistive powers. By applying medieval ratio theory to a controversial topic is Aristotle's Physics, Brawardine was able to make a simple, definite, and sophisticated mathematical rule for the relationship between speeds, powers, and resistances. Bradwardine's Rule was quickly accepted in the fourteenth century, first among his contemporaries at Oxford, where Richard Swineshead and John Dumbleton used it for solving sophisms, the logical and physical puzzles that were just beginning to assume and important place in the undergraduate arts curriculum.

Response to Peer Review


 * My references do appear at the bottom of the page in my sandbox, so I believe that I am good to go there. ￼
 * It is now time to go back through the bullet points that I made above and start implementing those notes throughout my sandbox. ￼
 * We did just receive the book that we have been waiting on a majority of the semester, so we will be able to add a pretty large source to our list of references. ￼
 * Elexis made a suggestion to maybe go back through and see if we can find any information on how the group formed and if they knew each other before Oxford.
 * Something that I really liked about this peer review is that Elexis looked that this article with fresh eyes and thought of something way out of the box that wasn't even brought up between my partner and I.

References