Oxford Calculators
Encyclopedia
The Oxford Calculators were a group of 14th-century thinkers, almost all associated with Merton College
, Oxford
, who took a strikingly logico-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
.
These men built on the slightly earlier work of Walter Burley
and Gerard of Brussels
.
from dynamics
, emphasizing kinematics, and investigating instantaneous velocity. 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. They also demonstrated this theorem—the foundation of "The Law of Falling Bodies" — long before Galileo
, who is generally credited with it.
The mathematical physicist and historian of science Clifford Truesdell
, wrote:
In Tractatus de proportionibus (1328), Thomas 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 O. Boyer writes, "Bradwardine developed the Boethian theory of double or triple or, more generally, what we would call 'n-tple' proportion".
Boyer also writes that "the works of Bradwardine had contained some fundamentals of trigonometry
gleaned from Muslim
sources". Yet "Bradwardine and his Oxford colleagues did not quite make the breakthrough to modern science" (Cantor 2001, p 122). The most essential missing tool was algebra
.
Merton College, Oxford
Merton College is one of the constituent colleges of the University of Oxford in England. Its foundation can be traced back to the 1260s when Walter de Merton, chancellor to Henry III and later to Edward I, first drew up statutes for an independent academic community and established endowments to...
, Oxford
University of Oxford
The University of Oxford is a university located in Oxford, United Kingdom. It is the second-oldest surviving university in the world and the oldest in the English-speaking world. Although its exact date of foundation is unclear, there is evidence of teaching as far back as 1096...
, who took a strikingly logico-mathematical approach to philosophical problems.
The key "calculators", writing in the second quarter of the 14th century, were Thomas Bradwardine
Thomas Bradwardine
Thomas Bradwardine was an English scholar, scientist, courtier and, very briefly, Archbishop of Canterbury. As a celebrated scholastic philosopher and doctor of theology, he is often called Doctor Profundus, .-Life:He was born either at Hartfield in Sussex or at Chichester, where his family were...
, William Heytesbury
William Heytesbury
William Heytesbury , philosopher and logician, is best known as one of the Oxford Calculators of Merton College, where he was a fellow by 1330....
, Richard Swineshead
Richard Swineshead
Richard Swineshead was an English mathematician, logician, and natural philosopher. He was perhaps the greatest of the Oxford Calculators of Merton College, where he was a fellow certainly by 1344 and possibly by 1340.His magnum opus was a series of treatises known as the Liber calculationum ,...
and John Dumbleton
John Dumbleton
John Dumbleton , one of the Oxford Calculators, was a Scholastic logician and natural philosopher at Merton College, Oxford, where he was a fellow by 1338...
.
These men built on the slightly earlier work of Walter Burley
Walter Burley
Walter Burley was a medieval English Scholastic philosopher and logician. He was a Master of Arts at Oxford in 1301, and a fellow of Merton College, Oxford until about 1310. He spent sixteen years at Paris until 1326, becoming a fellow of the Sorbonne by 1324. After that, he spent seventeen...
and Gerard of Brussels
Gerard of Brussels
Gerard of Brussels was an early thirteenth-century geometer and philosopher known primarily for his Latin book Liber de motu , which was a pioneering study in kinematics, probably written between 1187 and 1260...
.
Science
The Oxford Calculators distinguished kinematicsKinematics
Kinematics is the branch of classical mechanics that describes the motion of bodies and systems without consideration of the forces that cause the motion....
from dynamics
Dynamics (mechanics)
In the field of physics, the study of the causes of motion and changes in motion is dynamics. In other words the study of forces and why objects are in motion. Dynamics includes the study of the effect of torques on motion...
, emphasizing kinematics, and investigating instantaneous velocity. They first formulated the mean speed theorem
Mean speed theorem
In the 14th-century, the Oxford Calculators of Merton College and French collaborators such as Nicole Oresme proved the mean speed theorem, also known as the Merton 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. They also demonstrated this theorem—the foundation of "The Law of Falling Bodies" — long before Galileo
Galileo Galilei
Galileo Galilei , was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations and support for Copernicanism...
, who is generally credited with it.
The mathematical physicist and historian of science Clifford Truesdell
Clifford Truesdell
Clifford Ambrose Truesdell III was an American mathematician, natural philosopher, historian of science, and polemicist.-Life:...
, wrote:
In Tractatus de proportionibus (1328), Thomas Bradwardine extended the theory of proportions of Eudoxus
Eudoxus of Cnidus
Eudoxus of Cnidus was a Greek astronomer, mathematician, scholar and student of Plato. Since all his own works are lost, our knowledge of him is obtained from secondary sources, such as Aratus's poem on astronomy...
to anticipate the concept of exponential growth
Exponential growth
Exponential growth occurs when the growth rate of a mathematical function is proportional to the function's current value...
, later developed by the Bernoulli and Euler, with compound interest
Interest
Interest is a fee paid by a borrower of assets to the owner as a form of compensation for the use of the assets. It is most commonly the price paid for the use of borrowed money, or money earned by deposited funds....
as a special case. Arguments for the mean speed theorem (above) require the modern concept of limit
Limit (mathematics)
In mathematics, the concept of a "limit" is used to describe the value that a function or sequence "approaches" as the input or index approaches some value. The concept of limit allows mathematicians to define a new point from a Cauchy sequence of previously defined points within a complete metric...
, so Bradwardine had to use arguments of his day. Mathematician and mathematical historian Carl O. Boyer writes, "Bradwardine developed the Boethian theory of double or triple or, more generally, what we would call 'n-tple' proportion".
Boyer also writes that "the works of Bradwardine had contained some fundamentals of trigonometry
Trigonometry
Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...
gleaned from Muslim
Islam
Islam . The most common are and . : Arabic pronunciation varies regionally. The first vowel ranges from ~~. The second vowel ranges from ~~~...
sources". Yet "Bradwardine and his Oxford colleagues did not quite make the breakthrough to modern science" (Cantor 2001, p 122). The most essential missing tool was algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
.
Further reading
- Sylla, Edith (1982) "The Oxford Calculators", in Kretzmann, Kenny & Pinborg (edd.), The Cambridge History of Later Medieval Philosophy.
- Longeway, John (2003) "William Heytesbury", in The Stanford Encyclopedia of Philosophy.