“The safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato.”
Alfred North Whitehead (1929), Process and Reality, Part II, Chap. I, Sect. I
“Le principal dans un tableau est de trouver la juste distance. La couleur avait à exprimer toutes les ruptures dans la profondeur. C’est la qu’on reconnaît le talent d’un peintre.” – Cézanne
Paul Cézanne [ 1839–1906 ] | Montagne Sainte Victoire [ 1905–06 ]
Watercolour on paper 362mm x 549 mm | Tate Gallery [ Bequeathed by Sir Hugh Walpole 1941 ]
One of the oldest [ca. 75-125 A.D] and most complete diagrams from Euclid’s Elements of Geometry is a fragment of papyrus found among the remarkable rubbish piles of Oxyrhynchus in 1896-97 by the renowned expedition of B. P. Grenfell and A. S. Hunt. It is now located at the University of Pennsylvania. The diagram accompanies Proposition 5 of Book II of the Elements, and along with other results in Book II it can be interpreted in modern terms as a geometric formulation of an algebraic identity – in this case, that ab + (a-b)2/4 = (a+b)2/4
“If a straight line be cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole together with the square on the straight line between the points of section is equal to the square on the half.” (from the classic translation of T. L. Heath)
Claude Lorrain 1650
192 mm x 267 mm
Sea coast with the landing of Aeneas in Latium, preliminary drawing for the painting; figures alighting from boats in the foreground, a shepherd with flock at right, trees on the rocky cliffs at right, ships at left. c.1650 Pen and brown ink and brown wash, touched with white; on pink-tinted paper; squared with diagonals.
“Quantum field theory is a very rich subject for mathematics as well as physics. But its development in the last seventy years has been mainly by physicists, and it is still largely out of reach as a rigorous mathematical theory despite important efforts in constructive field theory. So most of its impact on mathematics has not yet been felt. Yet in many active areas of mathematics, problems are studied that actually have their most natural setting in quantum field theory. Examples include Donaldson theory of four-manifolds, the Jones polynomial of knots and its generalizations, mirror symmetry of complex manifolds, elliptic cohomology, and many aspects of the study of affine Lie algebras.
To a certain extent these problems are studied piecemeal, with difficulty in understanding the relations among them, because their natural home in quantum field theory is not now part of the mathematical theory. To make a rough analogy (Figure1), one has here a vast mountain range, most of which is still covered with fog. Only the loftiest peaks, which reach above the clouds, are seen in the mathematical theories of today, and these splendid peaks are studied in isolation, because above the clouds they are isolated from one another. Still lost in the mist is the body of the range, with its quantum field theory bedrock and the great bulk of the mathematical treasures.”
this is most lovely….
see the entire film here
|Panopeia (Πανόπεια)||Kymodoke (Κυμοδόκη)|
|Thaleia (Θάλειά)||Nesaie (Νησαίη)|
Virgil, Aeneid 5. 825 ff (trans. Day-Lewis) :
“Lightly skims the dark-blue chariot [of Poseidon] over the sea’s face: . . . then come his retainers . . . on the left are Thetis and Melite and maiden Panopea, Nesaea, too, and Spio, Thalia and Cymodoce.”
· Panopeia (Πανόπεια) The Nereid of the sea’s “panorama.” (Hesiod, Homer, Apollodorus, Hyginus, Virgil)
· Kymodoke (Κυμοδόκη) The Nereid of “steadying the waves” who, with her sisters Amphitrite and Kymatolege, possessed the power to still the winds and calm the sea. (Hesiod, Homer, Hyginus, Virgil)
· Thaleia (Θάλειά) The Nereid of the “blooming” sea. (Homer, Hyginus, Virgil)
· Nesaie (Νησαίη) The Nereid of “islands.” (Hesiod, Homer, Apollodorus, Hyginus, Virgil)
· Speio (Σπειώ) The Nereid of the sea “caves.” (Hesiod, Homer, Apollodorus, Hyginus, Virgil)