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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
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).
Notes
Wikipedia, Francis
Bacon , Free open-source Encyclopedia. (wikipost Mar 2006)
<http://en.wikipedia.org/wiki/Francis_Bacon>
2006.
Sir Francis Bacon's New
Advancement of Learning, An Emblem from Whitney's Choice of Emblems,
[online database]Plus Ultra <http://www.sirbacon.org/links/whitneyemblem.html>
2006.
Leary, Penn , The Second
Cryptographic Shakespeare, [ database online],
<http://home.att.net/~mleary/pennl12.htm> 2006.
PEACE Publication Ltd , The
Physics Enigmas And Consciousness Enigmas Files, The
PEACE-Files, [database online] ,
<http://www.peace-files.com/PHISICS_FILES/00_B-Part_One_A.html>
2006.
Wikipedia, Cartesian
System, Free open-source Encyclopedia. (wikipost Mar 2006)
<http://en.wikipedia.org/wiki/Cartesian_coordinate_system>
2006.
Bury, J.B., Chapter
III: Cartesianism, The Idea of Progress, [database online],
Nalanda Digital Library, <http://www.nalanda.nitc.ac.in/resources/english/etext-project/history/progress/chapter5.html>
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. Bookoflife.org . All rights
reserved.
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