Lysippus (after…no great sculptor):

Lysippus died in 305 BC; by then his great peers (Skopas -active 395-350 BC, Praxiteles-active 375-335 BC, Leochares-active 340-320 BC) were gone.  Although not the last sculptor, he was the last of the Great Masters.  This century transitioned from Classical towards the more emotional & dramatic Hellenistic art.  Demand for art shifted from the polis & sanctuaries towards wealthy private patrons who purchased statues & reliefs for their homes.  Monumental sculpture was no longer created solely for an austere religion; it was also a promotional tool for the autocratic regimes of the Diadochi (e.g. Pergamum).  Demand for sculpture increased as Greek culture spread throughout the Middle East; increased demand & the expansion of function meant sculpture becoming (like Greek pottery) less art, more industry.  Designs became standardized.  Demand from Rome led to unabashed copying.  The copyists fixed points by measurement but the points were often far between, the intervening spaces & details were carved freehand, often without care.  Copies give a likeness to pose, but were harsh & insensitive in their treatment of surface.  Overall the Hellenistic age saw the quality of sculpture decline.

 

the Impressionists (after…no painter): * see Endnote<A>

[ this discussion of Spengler’s projection is restricted to contemporary art he might have seen & with which he would have been familiar, i.e. European art produced between 1880 & 1936 and in particular the Ecole de Paris (Paris School) ]

​

despite initial rejection by the Paris Salon the Impressionist won recognition following their Paris exhibitions (1874-86).  Their artistic premise was the objective recording of nature in terms of the fleeting effects of colour & light; the leading artists were: Monet (1840-1926), Boudin (1824-98), Pissarro (1830-1903), Sisley (1839-1899), Manet (1832-83) & Degas (1834-1917).  With success in the 1880S the group fragmented.  At the turn of the century they were superseded first by the Post-Impressionists (1880-1905), then the Expressionists (1905- current).  Art as a whole fragmented into a series of movements across the Western world (USA, USSR, Europe).  Tradition was abandoned; experimentation was embraced with new ways of seeing & new ideas on the material & function.  Art was moving from narrative (characteristic of the traditional arts) towards ever greater abstraction.  Painting took on overtly political messages (Dada, Social Realism) & totalitarian regimes used it as a propaganda tool (Soviet Realism).  While oil painting continued in Modernism, new mediums & forms emerged such as collages, assemblages, lithography & posters. 

 

Wagner (after…no musician): * see EndNote<B>

[this discussion of Spengler’s projection is limited to music he would likely have heard & with which he would have been familiar, i.e. European music produced between 1880 and 1936; I have further reduced the scope to the Austro-German school of music]

​

Wagner’s (1813-83) influence lived long after his passing, in the symphonies of Bruckner (1824–96) & Mahler (1860–1911), the tone poems of R. Strauss (1864–1949) & operas of Verdi (1813–1901) & Puccini (1858–1924).  Not the least of his influence was his exploration of the limits of the traditional tonal system (which give keys & chords their identity), pointing to atonality, most notably with his Tristan chord.  In the early 20th century Modernism was born, compositions became more & more outlandish and inventive; musical rules themselves were rewritten.  Atonality, serialism & the 12 tone composition are key to this wave of experimentation which abandoned their musical legacy in reaction against established historical musical trends.  One of the main figures in this movement was Arnold Schoenberg (1874–1951).

 

Eratosthenes:

(276-195 BC) Greek from Cyrene Libya, founder of geography, using terminology still used today; first to accurately calculate the circumference of the Earth & tilt of its axis; first global projection of the world (with parallels & meridians); founder of scientific chronology

 

Archimedes:

(287-212 BC) greatest of Classical mathematicians, calculated the areas of circles, ellipses & spirals, area under a parabola; surface area & volume of a sphere; volumes of segments of a paraboloid of revolution & hyperboloid of revolutions; other mathematical achievements include an accurate approximation of pi, defining & investigating the Archimedes spiral, creating an exponent system to express large numbers; as a scientist he was first to apply mathematics to physical phenomena, founding hydrostatics & statics & an explanation of the lever; designed innovative machines (eg screw pump, compound pulleys & defensive war machines)

 

Posidonius:

(135-51 BC) Greek politician from Syria; general polymath, celebrated for his mastery of the knowledge of his time; he attempted to create a unified system for understanding the human intellect & the universe which would provide an explanation of and a guide for human behaviour; he wrote about physics, meteorology, geography, astronomy, astrology & divination, seismology, geology, mineralogy, hydrology, botany, ethics, logic, mathematics, history, natural history, anthropology, and tactics.

 

Pliny:

(23-79 AD) aka , Pliny the Elder, Roman author, naturalist & natural philosopher & military commander, famous for the encyclopaedic Naturalis Historia (Natural History), a collection of all known knowledge, 37 books, based on his personal experience & prior works as well as extracts from other works & was

 

Ptolemy:

(100-170 AD) of Alexandria, last of the Hellenistic astronomers, made few original discoveries, he systematized the work of others; his main work the Almagest (based upon the geocentric theory) survived as the classic summary of ancient astronomy.

 

Galen:

(129-200 BC) born in Pergamum, prominent medical practitioners in Rome, the great encyclopaedist of medicine, he summarised & synthesised the work of his predecessors; promoted Hippocrates' bodily humours  theory; thru his works Greek medicine was handed down to subsequent generations

​

dynamics (from 1600):

branch of physics developed in classical mechanics concerned with the study of forces & their effects on motion; Newton was the first to formulate the fundamental physical laws governing dynamics in classical non-relativistic physics, especially his 2nd law of motion

 

morphology:

branch of biology dealing with the study of the form, structure of organisms & specific structural features which includes aspects of the outward appearance (shape, structure, colour, pattern, size) as well as the form and structure of the internal parts (bones & organs); contrast with physiology which deals primarily with function

 

physiognomic:

the outward appearance of anything, taken as offering some insight into its character; from the noun Physiognomy, the practice of assessing a person's character or personality from their outer appearance, especially the face, or the general appearance of a person, object, or terrain without reference to its implied characteristics

 

systematic:

having, showing, or involving a system, method, or plan; given to or using a system or method; arranged in or comprising an ordered system:

 

chemical affinity:

the electronic property by which dissimilar chemical species are capable of forming chemical compounds; it may also refer to the tendency of an atom or compound to combine by chemical reaction with atoms or compounds of unlike composition; the term is sometimes synonymous with the term "magnetic attraction"; many writings, up until about 1925 refer to a "law of chemical affinity".  T. Donder (1872-1957), Belgian mathematician & physicist was famous for his work of 1923 in developing correlations between the Newtonian concept of chemical affinity & the Gibbsian concept of free energy.

 

diamagnetism:

refers to materials that are repelled by a magnetic field; an applied magnetic field creates an induced magnetic field in them in the opposite direction, causing a repulsive force. In contrast, paramagnetic and ferromagnetic materials are attracted by a magnetic field; caused by the orbital motion of electrons in the atoms of the material and is unaffected by temperature

​

separate sciences…converging:

Spengler’s perception reflects early 20th century debate in Germany.  The unity of science has a long history going back to the 16th century & Galileo who proposed unity based on theological axioms; in the17th century the mechanical philosophy of Descartes & Newton provided a promising framework.  Leibniz had a unifying vision based on symbolic language & physics,embracing science, religion & politics.  The Enlightenment saw a peak in the unity of science, notably with the Encyclopédie (1751–1772), a unity based on classification rather than logic.  Kant perceived underlying unity, a reflection of the universal a priori character of concepts & Reason itself.  However English Empiricism seemed to work against unity this trend.  Some philosophers (JS Mill) arguing for diversity based on methodologies; this worked towards spliting science into the social sciences & natural sciences.  In the early 20th century unity took another step backward with the perceived conflict between the mechanistic paradigm (Newton) & the electromagnetic worldviews (Einstein).  Nonetheless in Germany the Mach-Planck debates assumed a unified scientific world-picture though they differed in their details.  Early in the century Germany was inundated with work on energy physics & books on the unity of science.  Prominent German thinkers promoted Monism.  In 1912, Mach, Felix Klein, David Hilbert, Einstein & others signed a manifesto aiming at the development of a comprehensive world-view. .

 

denominators to those numerators:

a phrase which means all the collected data, formulae & laws, a massive corpus, will receive meaning from a small number of unifying theories which simplify or explain the data

 

physiognomically:

adverb, from physiognomy; see above

 

physics & chemistry (affinity):

both physics & chemistry are concerned with matter & its interaction with energy, both study matter; the fundamental laws that govern the behaviour of matter apply to both; they overlap when the system under study involves matter composed of electrons and nuclei made of protons and neutrons

 

spectrum analysis:

aka spectral analysis, analysis in terms of a spectrum of frequencies or related quantities (e.g. energies or eigenvalues); it may also refer to spectroscopy (in chemistry & physics), a method of analysing the properties of matter from their electromagnetic interactions.  Spectroscopy began with Newton's optics experiments (1666–1672); in 1802, Wollaston built an improved spectrometer that included a lens to focus the Sun's spectrum on a screen; in 1815, German physicist Fraunhofer produced dispersive spectrometers enabling spectroscopy to become a more precise & quantitative technique.  Since then spectroscopy has played a significant role in chemistry, physics & astronomy.