Classical:

reference to Greco-Roman Culture/Civilization which Spengler often refers to as Apollonian

 

Magian:

reference to a Culture/Civilization, born in the Middle East, from 1 AD to roughly 1000 AD

 

a fortiori:

Latin, meaning with greater reason or more convincing force, used in drawing a conclusion that is inferred to be more certain than another

 

Archimedes:

see Chapter II, page 59 Chapter III, page 111, 112 Chapter VII page 236

 

polarized light-rays: * see EndNote<A>

light (electromagnetic waves) consist of a coupled oscillating electric field & a magnetic field perpendicular to each other; "polarization" refers to the direction of the electric field.  Un-polarized light consists of short wave trains with an equal mixture of polarizations; with linear polarization, the fields oscillate in a single direction, with circular polarization, the fields rotate at a constant rate in a plane as the wave travels, either right or left circular.  Polarized light is produced by passing un-polarized light through a polarizer, which allows waves of only one polarization to pass through.  Only optical materials that exhibit birefringence, dichroism or optical activity are used to make polarizing filters.  Light is also partially polarized when it reflects from a surface.

 

ions: * see EndNote<B>

a charged atom or molecule in which the number of its electrons does not equal the number of protons; an atom can acquire a positive charge or a negative charge depending on whether the number of electrons being greater or less then the number of protons.

 

gas-particles (flying & colliding): * see EndNote<C>

a gas state has no fixed shape or volume & lower density than solids or liquids.  There is empty space between gas particles which have a lot of kinetic energy.  They move quickly in random directions.  Speed varies but on average is quicker than in liquids or solids.  The fast moving particles frequently collide; these collisions may be between 2 particles, between a particle & the wall of the container, or between a particle & something else in the container.  If more gas particles enter a container, there is less space for the particles to spread out & they become compressed. The particles exert force on the interior volume of the container; this force is called pressure.

 

magnetic fields: * see EndNote<D>

a vector field that describes the magnetic influence on moving electric charges, electric currents & magnetized materials. A charge that is moving in a magnetic field experiences a force perpendicular to its own velocity & to the magnetic field.  Magnetic fields that move will exert a force on a range of non-magnetic materials by affecting the motion of their outer atomic electrons.  Magnetic fields surround magnetized materials & are created by electric currents (e.g. electromagnets) & by electric fields varying in time

 

electric currents & waves: * see Endnote<E>

electric currents are streams of charged particles (electrons or ions) moving through an electrical conductor or space; the moving particles are called charge carriers, which (depending on the conductor) are electrons when moving through a wire, in semiconductors they are electrons or holes, in an electrolyte they are ions, and in plasma (ionized gas), they are both electrons & ions.  Electromagnetic waves (or their quanta, photons) is energy radiating through space, carrying electromagnetic radiant energy; it includes radio waves, microwaves, infrared, visible light, ultraviolet, X-rays & gamma rays.

 

Romanesque ornamentation: * see EndNote<F>

art of Europe 1000 AD to the 12th century, first international style of Christendom; its architecture reflected Roman roots but its ornament was typified by the production of small, decorative religious works stimulated by the construction of new & larger churches & monastic establishments.  These new churches used relief carvings on windows, capitals, pedestals, friezes, corbels, tables of arches & elsewhere, from which eventually human figures emerge.  These distinctive reliefs are free of the classical figure tradition, enjoyed a heritage of angular Germanic design & religious inspiration,  The expansion of monasticism in the 10th & 11th centuries led to the art of the reliquary, metal work & illuminated manuscripts (religious books, Bibles) copied by the monks.  In these smaller decorative arts, the old Viking legacy was alive, with its interlacing straps or ribbons, knots, loops & unconvincing attempts are made to relate these to the technique of weaving.  They reflect disdain for symmetry, the avoidance of geometrical forms & restless, undisciplined energy.  

 

Gothic architecture up thrust: * see EndNote<G>

A fundamental characteristic of Gothic architecture is verticality.  New building techniques, the flying buttress, the pointed arch, vaulted ceilings, enabled architects to spread the weight of taller walls & loftier towers.  Gothic buildings scaled new heights reaching into space.  It became popular in France from the 1150s & quickly spread across the whole of Europe; by the 1450s, Renaissance architects began to deride the Gothic & it went out of fashion.

 

Viking's voyages (into unknown seas):

see Chapter II page 88, Chapter IX page 330

 

Columbus (longings): * see Endnote<H>

Columbus’ longing are rooted in his own experience as a sailor & as commercial agent working for Genoese firms.  He had been a sailor since age 10 and had worked with commercial Italian interests almost as long.  There were of course huge commercial advantages in circumventing Venetian & Ottoman middlemen in the East to West trade.  Columbus was self-educated & well read in Greco-Roman works; he was directly influenced by Toscanelli, a visionary geographer.  He was also a millennialist which may have influenced his thinking.  In any case, to the end of his life he remained fixated on the belief he had discovered Asia, not the New World.

 

Copernicus (longings): * see EndNote<I>

famous for his model of the universe placing the Sun rather than Earth at the centre; the publication of Copernicus' model in On the Revolutions of the Celestial Spheres (1543), triggered the Copernican Revolution.

 

perspective oil-painting (contemporary with science): * see EndNote<J>

The birth of a true, geometrically-based perspective is unique to the Italian Renaissance, from around 1415 with Brunelleschi.  It was then developed further by Italian artists & later by Dutch painters. 

 

The scientific revolution is usually dated from 1543 on the publishing of Copernicus' On the Revolutions of the Heavenly Spheres.  It continued through the late 18th century influencing the Enlightenment; it marked the emergence of modern science, with developments in mathematics, physics, astronomy, biology & chemistry, transforming Western views about nature.  

 

instrumental music (contemporary with science): * see EndNote<K>

The move to instrumental music & away from vocal began about 1600 when composers began to specify in writing explicit parts for particular instruments (idiomatic writing)- parts became specific to instruments.  Orchestration meant specific phrases were reserved for solos or definite groups of instruments- no longer did the entire ensemble play thru the entire composition.  Composers discriminated against Medieval & Renaissance instruments unable to perform in solo or to hold a melodic line, in favour of a new family of solo type instruments, especially the violin.

 

The Scientific Revolution began in 1543 with the publication of Copernicus (his On the Revolutions of the Celestial Spheres); this first phase, the 'Scientific Renaissance' focused on the recovery of the knowledge of the ancients, ended with Galileo's Dialogue Concerning the Two Chief World Systems (1632).  The Scientific Revolution was finalized with Newton's Principia (1687) which formulated the laws of motion & universal gravitation, completing the synthesis of a new cosmology.

 

Gothic centuries:

the Spring time of Faustian Culture, Spengler defines this period 900-1500 AD

 

Catholic versus Materialistic views of the world:

Christian cosmology assumes a transcendent & sovereign God who created the universe & Nature and continually maintains its existence. The world only exists because of an ultimate and supernatural cause skilled in Mechanics and Geometry.

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Materialism is a form of philosophical monism holding that matter is the fundamental substance in nature, that all things (including mental states) are results of material interactions.  Mind & consciousness are by-products of material processes (the biochemistry of the human brain & nervous system), without which they cannot exist.  Materialists deny the existence of God and the soul.