Tuesday, July 27, 2010

Friday, July 16, 2010

Galileo's Giant: Nicole Oresme

Nicole Oresme (c. 1320 - 1382) argued, a couple hundred years before Galileo, that a rotating earth is a simpler explanation than that of Ptolemy. He invented the coordinate system long before Descartes (1596-1650). He also investigated fractional powers and determined that the distance a freely falling body travels (x) is proportional to the square of the time (t) it has been traveling, viz., x = ½ g t², where g is the acceleration due to gravity. He used a slightly different notation, however, beginning in his first page of Algorismus proportionum:

From the first page of Oresme's Algorismus proportionum (fourteenth century)

The original Latin
The original Latin

An English translation of the Latin
An English translation of the Latin

—Cajori's A History of Mathematical Notation, Vol. 1 pgs. 91-93

From the excellent introductory physics textbook Physics for Realists (available here) by the M.I.T. and Princeton physicist Dr. Anthony Rizzi, founder of the Institute for Advanced Physics:

Nicole Oresme (o'rem) was born c. 1320 AD in Normandy, France, and died in 1382. He was, among other things, a mathematician, a physicist and a priest (made bishop of liseaux, France, in 1377). His major mathematical work is "Tractatus de Difformitatum." Among his accomplishments are the use of rectangular coordinates and graphing of the intensity of a quality then called latitudo (say, temperature of a rod), against a length then called longitudo (e.g., distance along the same rod), on such a rectangular coordinate system. He also discovered that speed versus time graphs can be constructed. Further, he investigated, in his own notation, fractional powers, saying 43/2 = 8.

In dynamics, he shows, following Jean Buridan [...], that the movement of the Earth is consistent with immediate experience, though it does not seem so at first. And, he points out that the movement of the Earth, not the geocentric hyothesis, is, indeed, the simpler one. These arguments we be employed by his successors, including Copernicus and Galileo.

He also made an argument for an international dateline. His argument fundamentally rests on noticing that only the relative motion of the earth and sun defines a conventional day (i.e., based on the rising and setting of the sun for a given observer). The principle can be understood by noting that if one moved fast enough to say "under" the sun, one would never experience a single conventional day. The roundness of the earth, which is also needed in the argument, was commonly assumed in the Middle Ages.

He proved, using graphical methods, the mean speed theorem [...] which Galileo imported into his work without reference. He determined the distance = ½ acceleration time² law for uniformly accelerated motion that was later applied by Fr. Dominic De Soto (1494-1560 [...]) to free falling objects.

PFR pg. 48

A page from Tractatus de latitudinibus formarum (1505)

—"Nicole Oresme" in the MacTutor History of Mathematics archive: A page from Oresme's Tractatus de latitudinibus formarum (1505 reprint)

Could not have Oresme, being a theologian, progressed science and mathematics more had he not seemingly wasted his time becoming a Master of Theology at the University of Paris? The answer is no. Fr. Benedict Ashley, O.P.—a key contributer and reviewer of Physics for Realists—explains that philosophy, which includes mathematics and science, is a handmaiden of theology:

Benedict Ashley, O.P.

True philosophy, the perennial philosophy of St. Thomas Aquinas, supports true theology, both of which demand a pursuit of truth. Mentioning the horrible state of the philosophy that Pope Pius XII condemned in Humani Generis, "Nouvelle Théologie" (New Theology)—which is opposed to true, scientific theology and definitely merits the stereotypes of theology being an irrational, unscientific discipline, proceeding haphazardly from from shaky first-principles and jumping to non sequitur conclusions, ignoring that parvus error in principio magnus est in fine ("a small error in principle is a big error in conclusion"), and ultimately upholding the relativism of truth, that it is based on the changing state of man—the great 20th century Thomistic philosopher Fr. Reginald Garrigou-Lagrange, O.P., wrote that
no new definition of truth is offered in the new definition of theology: “Theology is no more than a spirituality or religious experience which found its intellectual expression.” And so follow assertions such as: “If theology can help us to understand spirituality, spirituality will, in the best of cases, cause our theological categories to burst, and we shall be obliged to formulate different types of theology…For each great spirituality corresponded to a great theology.” Does this mean that two theologies can be true, even if their main theses are contradictory and opposite? The answer will be no if one keeps to the traditional definition of truth. The answer will be yes if one adopts the new definition of truth, conceived not in relation to being and to immutable laws, but relative to different religious experiences. These definitions seek only to reconcile us to modernism.

It should be remembered that on December 1, 1924, the Holy Office condemned 12 propositions taken from the philosophy of action, among which was number 5, or the new definition of truth: “Truth is not found in any particular act of the intellect wherein conformity with the object would be had, as the Scholastics say, but rather truth is always in a state of becoming, and consists in a progressive alignment of the understanding with life, indeed a certain perpetual process, by which the intellect strives to develop and explain that which experience presents or action requires: by which principle, moreover, as in all progression, nothing is ever determined or fixed.” The last of these condemned propositions is: “Even after Faith has been received, man ought not to rest in the dogmas of religion, and hold fast to them fixedly and immovably, but always solicitous to remain moving ahead toward a deeper truth and even evolving into new notions, and even correcting that which he believes.

Many, who did not heed these warnings, have now reverted to these errors.

—“Where is the New Theology Leading Us?” by Fr. Reginald Garrigou-Lagrange, O.P.

Oresme did not fall into these errors. He studied true theology because he did true science.