<A>
17th Century: *
“it is pictorially formed and in unison with the great art of oil-painting that died out about 1630;”
Spengler links the great 17th century minds of science with the great age of oil painting- it is the Late period (Summer) of the Culture, when we witness the formation of a group of arts urban and conscious, in the hands of individuals ( the “Great Masters "); it is the Reign of oil-painting from Titian to Rembrandt.
from left to right:
Titian (1488-1576) Venetian school.
Equestrian Portrait of Charles V oil-on-canvas painting 1548 (Titian was at the imperial court of Augsburg); a tribute to Charles V, Holy Roman Emperor, following his victory in the April 1547 Battle of Mühlberg against the Protestant armies.
Caravaggio (1571-1610) Italian Mannerist painter with huge influence on Baroque
The Entombment of Christ, (1603–1604), altarpieces, chapel in Santa Maria in Vallicella (the Chiesa Nuova), built for the Oratory of Saint Philip Neri.
Rembrandt (1606-1669)
Sacrifice of Isaac, (1635) oil on canvas
<B>
18th Century: *
“it acquires the abstract character of the fugue-style and is in unison with Bach”
Spengler links the great physicists & mathematicians of this century with the reign of classical music from Bach to Mozart which takes the Cultural baton from classical oil-painting.
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The Art of Fugue by JS Bach (1685–1750) written in the 1740s, 14 fugues & 4 canons in D minor, each a variation of a single principal subject, each iteration increasingly complex, an experimentation with monothematic instrumental works exploring the contrapuntal possibilities inherent in a single musical subject. The work reflects a mathematical architecture based on bar counts, showing the whole work was conceived on the basis of the Fibonacci series & the golden ratio. In 1746 Bach was preparing to enter the Society of Musical Sciences; the Art of the Fugue was a piece composed for this society. The work also reflects Bach’s belief that counterpoint was a scientific activity as well as cultural.
<C>
Culture at its end (pure analysis): * >
Color wheel graph of the function f(x) [Hue represents the argument, brightness the magnitude.]
LEFT: At the same time, we see the use of atmospheric perspective in the background, employing effective sfumato, showing us a vista in distant space.
RIGHT: Each episode has an autonomous existence. The gesture of the Madonna, as she sits framed by the jutting wing of the building, coincides with the reflection made by the falling light upon the stone, while the close-knit perspective network of the bosom, the controlled movement of the interposed suspended gesture, and the withdrawal of the head, become fleeting signals of emotion.
<D>
theory of functions of several complex variables: *
A differentiable function of a complex variable is equal to its Taylor series. As such, complex analysis is particularly concerned with analytic functions of a complex variable (that is, holomorphic functions).
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BELOW:
a 3-dimensional plot of the absolute value of the complex gamma function
In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is, at every point of its domain, complex differentiable in a neighborhood of the point.
