lyric:

poetry having the form & musical quality of a song, especially the character of a songlike outpouring of the poet's own thoughts & feelings, as distinguished from epic or dramatic poetry.

 

Differential Calculus: * see Endnote <A>

In mathematics,  a sub field of calculus concerned with the study of the rates at which quantities change; one of the 2 traditional divisions of calculus, the other being integral calculus.

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Dynastic principles…of age of Louis XIV:   * see Endnote <B>

a sequence of rulers from the same family, usually in the context of a feudal or monarchical system; the dynastic family is often known as a "house" which may be styled "royal", "princely" or "comital" depending upon the chief title borne by its members; "dynastic legitimacy meant  that a family ruled by virtue of an inherited right; this principle justified most regimes up until the late18th century & the emergence of "popular sovereignty".    Louis XIV, of the House of Bourbon, ruled France from 1643 until 1715 and was the epitome of the strong dynastic crown

 

city states:

a sovereign state, a type of small independent country, usually a single city with dependent territories; historically included cities such as Rome, Athens, Carthage and the Italian city-states during the Renaissance.

 

Euclidean geometry: * see Endnote <C>

a mathematical system attributed to Euclid, an Alexandrian Greek mathematician living around 300 BC.  He described his theory in The Elements begining with plane geometry, it being the first axiomatic system & first examples of formal proof.  It progresses onto solid geometry (3 dimensions).  Euclid assumes a small set of intuitively appealing axioms & deduces other propositions (theorems) from these.  Although much of the work had been stated by earlier mathematicians, Euclid was the first to create a comprehensive deductive & logical system.

 

space-perspective:

approximate representation, generally on a flat surface (such as paper), of an image as seen by the eye.  Objects are smaller as the distance from the observer increases; they are also subject to foreshortening ( the object's dimensions along the line of sight are shorter than its dimensions across the line of sight).  This technique was developed in the Italian Renaissance by painters & architects (e.g. Brunelleschi, Masaccio, Paolo Uccello, Piero della Francesca, Luca Pacioli) who studied linear perspective, wrote treatises on it & incorporated it into their artworks.  It was used extensively in Western oil painting from the 15th century until the 19th.

 

contrapuntal music:

(aka counterpoint) musical term from the Latin punctus contra punctum meaning "point against point", defining the relationship between voices that are harmonically interdependent (polyphony) yet independent in rhythm and contour; part of the European classical tradition, commonly used 1600-1900, developed during the Renaissance & particularly the Baroque.

 

credit economics:

economic concept  based on trust, allowing one party to provide money or resources to another party where the second party does not reimburse the first immediately (thereby generating a debt) but instead promises either to repay or return those resources at a later date.  It is a  method of making reciprocity formal, legally enforceable and extensible to a large group of unrelated people.

 

Egyptian administrative system: * see Endnote <D>

institutions used to govern Egypt, from to the 5th dynasty (early 25th to mid-24th century BC) onwards; Egypt, ruled by a pharaoh, absolute & superhuman, also utilized a centralized bureaucracy & associated departments, active until the end of the Late Period (664 to 332 BC).  This administration was divided into 2 separate geographic regions: Upper and Lower Egypt, each governed by a Vizier.  Supporting this was a complex array of departments with different functions:  the court (palace & harem), the treasury and granaries, governors of foreign territories, the military commander and regional administration.

 

Classical coinage: * see Endnote <E>

form of currency, originated in Lydia 600 BC; the first coins were made from electrum (a gold & silver alloy) & had a standardised purity, size & shape for general circulation; in theory they had the value of their metal content; the technique of minting coins arrived in mainland Greece around 550 BC, first in coastal trading cities like Aegina & Athens.  It soon spread to other Greek city-states, who quickly secured local monopolies. 

 

analytical geometry:

aka coordinate or Cartesian geometry; mathematical term for geometry using a coordinate system, in contrast to Euclidean geometry; it is the foundation for most modern fields of geometry, including algebraic, differential, discrete & computational geometry; widely used in physics, aviation, engineering, rocketry, space science & spaceflight.

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the cheque:

a document that orders a bank to pay a specific amount of money from a person's account (a checking account) to the person in whose name the cheque has been issued; in use since the 9th century AD; widely employed in the 20th century as an alternative to cash payments.

 

Chinese book printing: 

printing, first developed by China in the Han dynasty; the earliest form (220 AD) was woodblock: a relief pattern was carved into a wooden block by knife, chisel or sandpaper; white areas were cut away, black areas designating the characters, were left are at the original surface; the block is inked & brought into contact with paper leaving a mirror image.  A 2nd printing technology, the movable type, was invented by the Chinese printer Bi Sheng (circa 1040 AD) using porcelain.  In 1298 AD Weng Zhen introduced wooden movable type replacing the fragile porcelain.  In the early 12th century Chinese printers began using movable copper type for the large-scale printing of paper money issued by the Northern Song dynasty.

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Roman road engineering:

physical infrastructure vital to the maintenance & development of the Roman state, built from 300 BC during the expansion of the Republic and then the Empire; efficient for the overland movement of armies, officials, civilians, official communications & trade.  Many are still used today.  Immune to flooding, when the engineers encountered obstacles they overcome them with bridges, raised causeways or tunnels rather than redirect the road, hence Roman roads were very straight.

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Kant & formal rules of cognition:

(1724-1804) German philosopher central to modern philosophy; his rules of cognition posit that the mind creates the structure of human reason. This structure is a priori.  This argues against Locke’s tabula rasa- a mind without built-in mental content, all knowledge being derived from experience or perception.

 

Critique of Pure Reason:

seminal text in Western philosophy, by Kant (1781), investigating the foundations & limits of human knowledge; expounds new ideas on the nature of space & time, provides solutions to Hume's skepticism regarding human knowledge, the relation of cause and effect, and Descartes' skepticism regarding knowledge of the external world.  Kant claimed to have established a ‘Copernican revolution' in philosophy: knowledge does not "conform to objects", but rather objects "conform to our knowledge".   The a priori Mind shapes and structures the world of experience, making knowledge possible.

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Intuition forms:

term used by Kant; the basic sensory information provided by perception; mind casts all external intuitions in the form of space, and all internal intuitions (memory, thought) in the form of time.  Mathamatics is the knowledge of the pure form of intuition (non-empirical).

 

Categories of the reason: * see Endnote <F>

In The Critique of Pure Reason Kant argued we understand objects through the application of the categories of understanding to perception, the latter shaped through our senses- eyes or ears.  “Things in themselves” (the noumenal world) are inaccessible.  We only experience them thru our senses & to understand them we apply the categories to them.

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innate:

existing in one from birth; inborn; native: inherent in the essential character of something; a priori

 

Schopenhauer:

(1788-1860) German philosopher famous for his "The World as Will and Representation" (1818) where he characterizes the phenomenal world as the product of a blind & insatiable metaphysical will.  Based on Kant’s transcendental idealism, he developed an atheistic metaphysical & ethical system often described as philosophical pessimism.  This rejected the contemporaneous post-Kantian philosophies of German idealism.  He was one of the first Western thinkers to share & affirm aspects of Eastern philosophy (e.g., asceticism, the world-as-appearance), having initially arrived at similar conclusions.

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viz.:

an abbreviation of the Latin word videlicet, meaning that is to say or namely (used especially to introduce examples, details)

 

logic of space:

Spengler’s reference to causality (or cause and effect) which he sees as the methodology of natural science (in contrast to the logic of time).  He refers to it as “a necessity of cause and effect-…” and copies Schopenhauer’s retention of this single category of the 12 original Kantian categories of reason.

 

organic:

characteristic of  living organisms; of or relating to an organ or the organs of an animal, plant, or fungus; of or relating to, or affecting living tissue; an important idea in Spengler's  philosophy of history.

 

the logic of time:

Spengler’s reference to Destiny.  It is in contrast to the logic of space.  He refers to it as “another necessity, an organic necessity in life, that of Destiny“.  These necessities are his categories, analogous to Kant's categories.

 

suffuses:

to overspread with or as with a liquid, colour; to cover, pervade, diffuse, bathe or flood.

 

Galileo:

(1564-1642) Italian polymath, astronomer, physicist, engineer, philosopher & mathematician, regarded as the father of science & scientific method, he played a major role in the 17th century scientific revolution. His contributions to observational astronomy included the telescopic confirmation of the phases of Venus, the discovery of the 4 moons of Jupiter and the observation & analysis of sunspots. He championed Copernicus’s heliocentric theory which was controversial during his lifetime; most astronomers subscribed to either a geocentric theory (the earth is the centre of the universe) or the Tychonic system (the planets orbit the sun, the sun orbits the earth).  

 

Saggiatore:

(aka The Assayer) book by Galileo, published in Rome, 1623; one of first works to promote scientific method, suggesting nature is to be understood with mathematical tools rather than scholastic philosophy.