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Europe Science Revolution Part 5


The Recovery of the Ancient Learning


Astrology  & Astronomy in the Middle Ages.


The Age of Descartes


By Michael Johnathan McDonald



The Age of Descartes

  • "Plus Ultra:" Francis Bacon's method

  • "Cogito ergo um:" René Descartes' method

  • The Cartesian system (1): A universal physics

  • The Cartesian system (2): A quasi-mathematical physics

  • The spread of Cartesianism

  • The naturalization of comets and the decline of astrology

  • Astronomy in the academics

Francis Bacon, 1st Viscount St Albans, KC (22 January 1561 – 9 April 1626) was an English philosopher, statesman and essayist.

He began his professional life as a lawyer, but he has become best known as a philosophical advocate and defender of the scientific revolution. His works establish and popularize an inductive methodology for scientific inquiry, often called the Baconian method. Induction implies drawing knowledge from the natural world through experimentation, observation, and testing of hypotheses. In the context of his time, such methods were connected with the occult trends of hermeticism and alchemy (wikipedia).

The Masonic term "Plus Ultra" ("more beyond") appears on a banner between two pillars (representing Masonry) in an emblem from Whitney's Choice of Emblems (1586). Bacon is said to have published this book.) (Sir Francis ).

Hercules, on his mythical way west to the Kingdom of Geryon, is supposed to have planted two enormous rocks (named by the Greeks Calpe and Abyla) on each side of the Atlantic entrance to the Mediterranean Sea at the Straits of Gibraltar. Later the Romans pictured these monuments as two classical pillars bearing the inscription, "ne plus ultra"; that phrase was meant as a sailor's warning that there was "no more beyond." These two Pillars of Hercules can be found as frontispieces which adorn several of Bacon's books. In one of them there is shown a three-masted ship with sails rigged in English fashion; it is framed between the Pillars while sailing bravely "beyond." In the same way did Francis Bacon sail, quietly and fancifully in a falsely registered vessel, beyond to a future of applied science where he could truly "serve the welfare of mankind" (Leary).

"Cogito ergo um:" René Descartes' method

It may be said that the physical sciences--with theoretical physics at the forefront--have now been evolving in its search for this top stone during the 383 years elapsed since the renowned mystical experience of Descartes. After having had his famous “cogito ergo sum”, spiritual experience on the 10th of November 1619, Rene Descartes became enthusiastic about what he called the admirable scientific method. A sort of collective general method which would unify all of Man's knowledge into one general wisdom, one general unification theory. This took place at the same time as Galileo was in his prime and men had learned to distil alcoholic spirits to make strong burned alcohol drinks--brandies--to energise their brains. This would bring on the "Second Age of Enlightenment" and send the "Dark Ages" in retreat (PEACE). 

In the beginning of the renaissance around the end of the 15th century, Sir Francis Bacon made the following comment "There are two revelations in reality; The first is given to us in scripture and tradition, and it guided our thinking for centuries. The second revelation is given by the Universe, and that book we are just beginning to read." This prognosis of Bacon turned out to be true and the spirit of the philosophers was reborn in the form of natural-philosophers which later evolved into the different disciplines of the natural sciences. Disciplines which have, for the last 400 years, been progressing away from each other. The motto of the sciences soon became; "Nullius in Verba," or, words alone are not enough. This in turn brought about the doctrines of empiricism and positivism, with the demand that the statement of the investigator be proven through predictions, which later would appear as facts in experiments. This has now been the guiding light of the sciences for the last four hundred years and has justified itself in most fields of investigation into the nature of Nature (PEACE).


Sir Isaac Newton is for many the prime witness in the search for "The Recipe of the Universe". Newton may be described as being enraptured by the beauty and simplicity of his laws of gravity, and hoped that he would stumble on an all encompassing theory, even though he kept this secret, and that this would only be known after his death (PEACE).



Cartesian means relating to the French mathematician and philosopher Descartes, who, among other things, worked to merge algebra and Euclidean geometry. This work was influential in the development of analytic geometry, calculus, and cartography. The idea of this system was developed in 1637 in two writings by Descartes. In Discourse on Method, in part two, he introduces the new idea of specifying the position of a point or object on a surface, using two intersecting axes as measuring guides. In La Géométrie, he further explores the above-mentioned concepts (wikipedia).


Two-dimensional coordinate system

The modern Cartesian coordinate system in two dimensions (also called a rectangular coordinate system) is commonly defined by two axes, at right angles to each other, forming a plane (an xy-plane). The horizontal axis is labeled x, and the vertical axis is labeled y. In a three dimensional coordinate system, another axis, normally labeled z, is added, providing a sense of a third dimension of space measurement. The axes are commonly defined as mutually orthogonal to each other (each at a right angle to the other). (Early systems allowed "oblique" axes, that is, axes that did not meet at right angles.) All the points in a Cartesian coordinate system taken together form a so-called Cartesian plane. Equations that use the Cartesian coordinate system are called Cartesian equations.

The point of intersection, where the axes meet, is called the origin normally labeled O. With the origin labeled O, we can name the x axis Ox and the y axis Oy. The x and y axes define a plane that can be referred to as the xy plane. Given each axis, choose a unit length, and mark off each unit along the axis, forming a grid. To specify a particular point on a two dimensional coordinate system, you indicate the x unit first (abscissa), followed by the y unit (ordinate) in the form (x,y), an ordered pair. In three dimensions, a third z unit (applicate) is added, (x,y,z).

The choices of letters come from the original convention, which is to use the latter part of the alphabet to indicate unknown values. The first part of the alphabet was used to designate known values.

An example of a point P on the system is indicated in the picture below using the coordinate (3,5)(wikipedia).

The arrows on the axes indicate that they extend forever in the same direction (i.e. infinitely). The intersection of the two x-y axes creates four quadrants indicated by the Roman numerals I, II, III, and IV. Conventionally, the quadrants are labeled counter-clockwise starting from the northeast quadrant. In Quadrant I the values are (x,y), and II:(−x,y), III:(−x,−y) and IV:(x,−y). (see table below.)
Quadrant x-values y-values
I > 0 > 0
II < 0 > 0
III < 0 < 0
IV > 0 < 0



The spread of Cartesian philosophy


Cartesianism affirmed the two positive axioms of the supremacy of reason, and the invariability of the laws of nature (Bury).


Dutch-Jewish philosopher Benedict de Spinoza, a rationalist metaphysics promoter is one proof of the spread of the ideas of Descartes. He wrote, Ethics (1677) in mathematico-deductive form, with definitions, axioms, and derived theorems.


Descartes expressed it like Bacon, and it was taken up and repeated by many whom Descartes influenced. Pascal, who till 1654 was a man of science and a convert to Cartesian ideas, put it in a striking way. The whole sequence of men (he says) during so many centuries should be considered as a single man, continually existing and continually learning. At each stage of his life this universal man profited by the knowledge he had acquired in the preceding stages, and he is now in his old age. This is a fuller, and probably an independent, development of the comparison of the race to an individual which we found in Bacon. It occurs in a fragment which remained unpublished for more than a hundred years, and is often quoted as a recognition, not of a general progress of man, but of a progress in human knowledge (Bury).

During the Renaissance period the authority of the Greeks and Romans had been supreme in the realm of thought, and in the interest of further free development it was necessary that this authority should be weakened. Bacon and others had begun the movement to break down this tyranny, but the influence of Descartes was weightier and more decisive, and his attitude was more uncompromising. He had none of Bacon's reverence for classical literature; he was proud of having forgotten the Greek which he had learned as a boy. The inspiration of his work was the idea of breaking sharply and completely with the past, and constructing a system which borrows nothing from the dead. He looked forward to an advancement of knowledge in the future, on the basis of his own method and his own discoveries, [Footnote: Cf. for instance his remarks on medicine, at the end of the Discours de la methode.] and he conceived that this intellectual advance would have far-reaching effects on the condition of mankind. The first title he had proposed to give to his Discourse on Method was "The Project of a Universal Science which can elevate our Nature to its highest degree of Perfection." He regarded moral and material improvement as depending on philosophy and science (Bury).











Wikipedia, Francis Bacon , Free open-source  Encyclopedia. (wikipost Mar 2006)  <> 2006.


Sir Francis Bacon's New Advancement of Learning, An Emblem from Whitney's Choice of Emblems,  [online database]Plus Ultra <> 2006.


Leary, Penn , The Second Cryptographic Shakespeare, [ database online], <> 2006.


PEACE Publication Ltd , The Physics Enigmas And Consciousness Enigmas Files,  The PEACE-Files, [database online] , <> 2006.


Wikipedia, Cartesian System, Free open-source  Encyclopedia. (wikipost Mar 2006)  <> 2006.


Bury, J.B.,  Chapter III: Cartesianism, The Idea of Progress, [database online], Nalanda Digital Library,  <> 2006.




Plus Ultra commentaries.

Part I: The Evolving View of Scientific Knowledge: The Art of Renaissance Science, Galileo and Perspective


Copyright © 1999 - 2006 Michael Johnathan McDonald. . All rights reserved.




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