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Add to an Article: Oxford Calculators

John Dumbleton became a member of the calculators in 1338–39. After becoming a member, he left the calculators for a brief period of time to study theology in Paris in 1345–47. After his study there he returned to his work with the calculators in 1347–48. One of his main pieces of work, Summa logicae et philosophiae naturalis, focused on explaining the natural world in a coherent and realistic manner, unlike some of his colleagues, claiming that they were making light of serious endeavors. Dumbleton attempted many solutions to the latitude of things, most were refuted by Richard Swineshead in his Liber Calculationum.

Article Sources: Oxford Calculators

• Sylla, Edith Dudley. “The Oxford Calculators' Middle Degree Theorem in Context.” Early Science and Medicine, vol. 15, no. 4/5, 2010, pp. 338–370. JSTOR, www.jstor.org/stable/20787421. Accessed 26 Feb. 2021.
• Sylla, Edith D. “MEDIEVAL CONCEPTS OF THE LATITUDE OF FORMS: THE OXFORD CALCULATORS.” Archives D'histoire Doctrinale Et Littéraire Du Moyen Âge, vol. 40, 1973, pp. 223–283. JSTOR, www.jstor.org/stable/44403231. Accessed 26 Feb. 2021.
• Podkoński, Robert. “RICHARD SWINESHEAD'S ‘DE LUMINOSIS’: NATURAL PHILOSOPHY FROM AN OXFORD CALCULATOR.” Recherches De Théologie Et Philosophie Médiévales, vol. 82, no. 2, 2015, pp. 363–403. JSTOR, www.jstor.org/stable/26486060. Accessed 26 Feb. 2021.
• Weisheipl, James A. “The Place of John Dumbleton in the Merton School.” Isis, vol. 50, no. 4, 1959, pp. 439–454. JSTOR, www.jstor.org/stable/226428. Accessed 26 Feb. 2021.
• SPADE, PAUL VINCENT. “William Heytesbury's ‘Position on ‘Insolubles’ : One Possible Source.’” Vivarium, vol. 14, no. 2, 1976, pp. 114–120. JSTOR, www.jstor.org/stable/42569691. Accessed 26 Feb. 2021.

Draft Additions: Oxford Calculators

• They used Aristotelian logic and physics. They also studied and attempted to quantify every physical and observable characteristic, like heat, force, color, density, and light.
  • Replacement > Using Aristotelian logic and physics, they studied and attempted to quantify every physical and observable characteristic: heat, force, color, density, and light. ~~~~
• They first formulated the mean speed theorem: a body moving with constant velocity travels the same distance as an accelerated body in the same time if its velocity is half the final speed of the accelerated body.
  • Replacement > They first formulated the mean speed theorem: 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. ~~~~
• Talk about the importance of topics like: latitude of forms, mean speed theorem, proofs from both sides (arithmetical vs geometrical)

Science (Straight from Oxford Calculators article for editing purposes)

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 every physical and observable characteristic: 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 right triangles area would be equivalent to a rectangles if the rectangles height was half of the triangles. 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 mathematical physicist and historian of science Clifford Truesdell, wrote:

The now published sources prove to us, beyond contention, that the main kinematical properties of uniformly accelerated motions, still attributed to Galileo by the physics texts, were discovered and proved by scholars of Merton college.... In principle, the qualities of Greek physics were replaced, at least for motions, by the numerical quantities that have ruled Western science ever since. The work was quickly diffused into France, Italy, and other parts of Europe. Almost immediately, Giovanni di Casale and Nicole Oresme found how to represent the results by geometrical graphs, introducing the connection between geometry and the physical world that became a second characteristic habit of Western thought ...

In Tractatus de proportionibus (1328), Bradwardine extended the theory of proportions of Eudoxus 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 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".

Boyer also writes that "the works of Bradwardine had contained some fundamentals of trigonometry". Yet "Bradwardine and his Oxford colleagues did not quite make the breakthrough to modern science." The most essential missing tool was algebra.

Peer Review Response to cmatcv: Oxford Calculators

For clarification, the mean speed theorem in the article is incorrect. The article mentions that a body moving a constant velocity will travel the same distance as an object under constant acceleration in the same time as long as the constant velocity is HALF of the FINAL velocity. This is only true if the object starts from rest, but for all other cases where the object starts at an initial velocity this is untrue. The replacement is a just a better worded mathematical correction. Latitudes are not gone into at all and after reading into the Oxford Calculators we've realized that they were actually very important to them. We shall continue to expand upon them and make sure the reader has at least a rough idea of what these latitudes are. As for the John Dumbleton part, the text we found said that he became a member in 1338-1339, but we can look into that again to see if we can clarify if it was a two year process or not. The quote about Galen is a direct quote from an article, but we can try and ease into it better to make it not as awkward. On the subject of the new philosophy section, we are currently trying to collect more information that will go in that section so we just hadn't marked certain things down for that yet. That section is where we will talk about the latitude of forms as well as other philosophical approaches the calculators took. When it comes to the information about other calculators, it is difficult to add a lot of information about them because they have their own Wikipedia articles and it wouldn't be right to add words from their articles to ours whenever we should be talking about the calculators as a whole, and not specific individuals as much. We will also add where we cited our sources and how they were used. Thank you for your review it helped clarify some things and I appreciate the help you've done. Dplf2b (talk) 16:46, 2 April 2021 (UTC)