Saturday, December 12, 2015

The Same, The Other, And The Essence │ Theology of Arithmetic

“One, two, three [...] Let me tell you then why the creator made this world of generation. He was good [...] He took the three elements of the same, the other, and the essence, and mingled them into one form, compressing by force the reluctant and unsociable nature of the other into the same. When he had mingled them with the essence and out of three made one, he again divided this whole into as many portions as was fitting, each portion being a compound of the same, the other, and the essence. And he proceeded to divide after this manner: 

First of all, he took away one part of the whole [1], and then he separated a second part which was double the first [2], and then he took away a third part which was half as much again as the second and three times as much as the first [3], and then he took a fourth part which was twice as much as the second [4], and a fifth part which was three times the third [9], and a sixth part which was eight times the first [8], and a seventh part which was twenty-seven times the first [27]. After this he filled up the double intervals [1, 2, 4, 8] and the triple [1, 3, 9, 27] cutting off yet other portions from the mixture and placing them in the intervals, so that in each interval there were two kinds of means, the one exceeding and exceeded by equal parts of its extremes [1, 4/3, 2, in which the mean 4/3 is one-third of 1 more than 1, and 1/3 of 2 less than 2], the other being that kind of mean which exceeds and is exceeded by an equal number. Where there were intervals of 3/2 and of 4/3 and of 9/8, made by the connecting terms in the former intervals, he filled up all the intervals of 4/3 with the interval of 9/8, leaving a fraction over; and the interval which this fraction expressed was in the ratio of 256 to 243. And thus the whole mixture out of which he cut these portions was all exhausted by him.

This entire compound he divided lengthways into two parts, which he joined to one another at the center like the letter X, and bent them into a circular form, connecting them with themselves and each other at the point opposite to their original meeting-point; and, comprehending them in a uniform revolution upon the same axis, he made the one the outer and the other the inner circle. Now the motion of the outer circle he called the motion of the same, and the motion of the inner circle the motion of the other or diverse. The motion of the same he carried round by the side to the right, and the motion of the diverse diagonally to the left. And he gave dominion to the motion of the same and like, for that he left single and undivided; but the inner motion he divided in six places and made seven unequal circles having their intervals in ratios of two-and three, three of each, and bade the orbits proceed in a direction opposite to one another; and three [Sun, Mercury, Venus] he made to move with equal swiftness, and the remaining four [Moon, Saturn, Mars, Jupiter] to move with unequal swiftness to the three and to one another, but in due proportion.” Timaeus - Plato (360 BCE)


Johannes Kepler knew that "ubi materia, ibi geometria" (where there is Matter, there is Geometry), and "that the geometrical things have
provided the Creator with the model for decorating the whole world
". In Harmonices Mundi (The Harmony of the World, 1619) he related musical
consonance and the angular velocities of the planets, for example, the ratio between Jupiter’s maximum and Mars minimum speed is as 5:24. That
is equivalent to the interval of two octaves plus a minor third. The two octaves are eliminated by dividing 24 with 4, which gives the ratio
of 5:6, a minor third. From his studies of planetary harmonics Kepler also arrived at the bold conclusion that between Jupiter and Mars must
exist an unknown planet: "Intra Jovem et Martem posui planetum." (Between Jupiter and Mars I put a planet.") Some 170 years later the so-called
asteroid belt was found in the corresponding place. 

On Harmony And Beauty


The Pythagoreans averred that mathematics demonstrated the exact method by which the good established and maintained its universe. Number
therefore preceded harmony, since it was the immutable law that governs all harmonic proportions. Summarizing the relationship between the
human body and the theory of architecture, Marcus Vitruvius Pollio (80–15 BC) wrote in his De Architectura: "Since nature has designed the
human body so that its members are duly proportioned to the frame as a whole, it appears that the ancients had good reason for their rule,
that in perfect building the different members must be in exact symmetrical relations to the whole general scheme. Hence, while transmitting
to us the proper arrangements for buildings of all kinds, they were particularly careful to do so in the case of temples of the gods, buildings
in which merits and faults usually last forever. Therefore, if it is agreed that number was found out from the human fingers, and that there is
a symmetrical correspondent between the members separately and the entire form of the body, in accordance with a certain part selected as
standard, we can have nothing but respect for those who, in constructing temples of the immortal gods, have so arranged the members of the
works that both the separate parts and the whole design may harmonize in their proportions and symmetry." 

"Harmony is a state recognized by great philosophers as the immediate prerequisite of beauty. A compound is termed beautiful only when its parts are in harmonious combination. The world is called beautiful and its Creator is designated the Good because good perforce must act in conformity with its own nature; and good acting according to its own nature is harmony, because the good which it accomplishes is harmonious with the good which it is. Beauty, therefore, is harmony manifesting its own intrinsic nature in the world of form. The universe is made up of successive gradations of good, these gradations ascending from matter (which is the least degree of good) to spirit (which is the greatest degree of good). In man, his superior nature is the summum bonum. It therefore follows that his highest nature most readily cognizes good because the good external to him in the world is in harmonic ratio with the good present in his soul. What man terms evil is therefore, in common with matter, merely the least degree of its own opposite. The least degree of good presupposes likewise the least degree of harmony and beauty. Thus deformity (evil) is really the least harmonious combination of elements naturally harmonic as individual units. Deformity is unnatural, for, the sum of all things being the Good, it is natural that all things should partake of the Good and be arranged in combinations that are harmonious. Harmony is the manifesting expression of the Will of the eternal Good." Secret Teachings of All Ages - Manly P. Hall (1928)

Credits: Samuel Colman (1912): Nature's Harmonic Unity - A Treatise on Its Relation to Proportional Form

Wednesday, December 9, 2015

Race To The Bottom: Baltic Dry Index Collapsed To New All-Time Low

Freight rates have fallen to levels never seen before, 60% since August, and are currently 25% below the worst days of 2008.
 The Baltic Exchange’s main sea freight index (BDI), which gauges the cost of shipping cargoes including iron ore, cement, grain,
coal and fertilizer, fell to 551 points yesterday. Historically, the Baltic Exchange Dry Index reached an all-time high of
11,612 in August 2008 and a record low of 498 in November of 2015. Unlike stock and bond markets, the BDI is totally devoid
of speculative content and reflects the real economy, since people don't book freighters unless they have cargo to move.