Ex-News JunkieAncient-meets-modern philosophySun Jul 30, 2017 3:42pm2001:1970:5c22:6100:150f:6e18:46fa:a62a"Pythagoras of Samos (570–495 BC) was an Ionian Greek philosopher, mathematician, and putative founder of the Pythagoreanism movement. He is often revered as a great mathematician and scientist and is best known for the Pythagorean theorem which bears his name.

Legend and obfuscation cloud his work, so it is uncertain whether he truly contributed much to mathematics or natural philosophy. Many of the accomplishments credited to Pythagoras may actually have been accomplishments of his colleagues or successors. Some accounts mention that the philosophy associated with Pythagoras was related to mathematics and that numbers were important. It was said that he was the first man to call himself a philosopher, or lover of wisdom, and Pythagorean ideas exercised a marked influence on Plato, and through him, all of Western philosophy."

"Philolaus, one of "the three most prominent figures in the Pythagorean tradition", was the precursor of Copernicus in "moving the earth from the center of the cosmos and making it a planet".

Aristotle records:

It remains to speak of the earth, of its position, of the question whether it is at rest or in motion, and of its shape. As to its position there is some difference of opinion. Most people–all, in fact, who regard the whole heaven as finite–say it lies at the centre. But the Italian philosophers known as Pythagoreans take the contrary view. At the centre, they say, is fire, and the earth is one of the stars, creating night and day by its circular motion about the centre. "

Wiki - Monad

"The circled dot was used by the Pythagoreans and later Greeks to represent the first metaphysical being, the Monad or The Absolute.

For the Pythagoreans, the generation of number series was related to objects of geometry as well as cosmogony. According to Diogenes Laertius, from the monad evolved the dyad; from it numbers; from numbers, points; then lines, two-dimensional entities, three-dimensional entities, bodies, culminating in the four elements earth, water, fire and air, from which the rest of our world is built up."

"Gottfried Wilhelm (von) Leibniz (1646-1716) was a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy, having developed differential and integral calculus independently of Isaac Newton. Leibniz's notation has been widely used ever since it was published.

Leibniz's best known contribution to metaphysics is his theory of monads, as exposited in Monadologie. According to Leibniz, monads are elementary particles with blurred perceptions of one another. Monads can also be compared to the corpuscles of the Mechanical Philosophy of René Descartes and others. Monads are the ultimate elements of the universe. The monads are "substantial forms of being" with the following properties: they are eternal, indecomposable, individual, subject to their own laws, un-interacting, and each reflecting the entire universe in a pre-established harmony (a historically important example of panpsychism). Monads are centers of force; substance is force, while space, matter, and motion are merely phenomenal.

The ontological essence of a monad is its irreducible simplicity. Unlike atoms, monads possess no material or spatial character. They also differ from atoms by their complete mutual independence, so that interactions among monads are only apparent. Instead, by virtue of the principle of pre-established harmony, each monad follows a preprogrammed set of "instructions" peculiar to itself, so that a monad "knows" what to do at each moment. By virtue of these intrinsic instructions, each monad is like a little mirror of the universe."

Fifty years later, in 1766, hydrogen was discovered.

"Hydrogen is a chemical element with symbol H and atomic number 1. With a standard atomic weight of circa 1.008, hydrogen is the lightest element on the periodic table. Its monatomic form (H) is the most abundant chemical substance in the Universe, constituting roughly 75% of all baryonic mass. Non-remnant stars are mainly composed of hydrogen in the plasma state. The most common isotope of hydrogen, termed protium (name rarely used, symbol 1H), has one proton and no neutrons.

The universal emergence of atomic hydrogen first occurred during the recombination epoch.... Hydrogen gas was first artificially produced in the early 16th century by the reaction of acids on metals. In 1766–81, Henry Cavendish was the first to recognize that hydrogen gas was a discrete substance, and that it produces water when burned, the property for which it was later named: in Greek, hydrogen means "water-former"."

Science Magazine - Famed Number Found Hidden in Hydrogen Atom

A two dimensional symbol representing monatomic hydrogen is common:

In three dimensions the electron orbitals of hydrogen are described by toroidal geometry:

Although modern science has moved beyond ancient philosophy, stripping away erroneous mysticism, it is easily seen that the preoccupation of the Pythagoreans with mathematical relationships had a predictive power, leading thousands of years later to inevitable discoveries about the universe we live in.

Today, one might hypothesize math as an extant abstract, or "lateral", state of the universe, not always directly observable, but manifesting observable effects in all things.

"Commentary from Sir William Smith, Dictionary of Greek and Roman Biography and Mythology (1870, p. 620).

'Pythagoras resembled greatly the philosophers of what is termed the Ionic school, who undertook to solve by means of a single primordial principle the vague problem of the origin and constitution of the universe as a whole. But, like Anaximander, he abandoned the physical hypotheses of Thales and Anaximenes, and passed from the province of physics to that of metaphysics, and his predilection for mathematical studies led him to trace the origin of all things to number, this theory being suggested, or at all events confirmed, by the observation of various numerical relations, or analogies to them, in the phenomena of the universe. "Since of all things numbers are by nature the first, in numbers they (the Pythagoreans) thought they perceived many analogies to things that exist and are produced, more than in fire, and earth, and Avater; as that a certain affection of numbers was justice; a certain other affection, soul and intellect; another, opportunity; and of the rest, so to say, each in like manner; and moreover, seeing the affections and ratios of what pertains to harmony to consist in numbers, since other things seemed in their entire nature to be formed in the likeness of numbers, and in all nature numbers are the first, they supposed the elements of numbers to be the elements of all things". Brandis, who traces in the notices that remain more than one system, developed by different Pythagoreans, according as they recognised in numbers the inherent basis of things, or only the patterns of them, considers that all started from the common conviction that it was in numbers and their relations that they were to find the absolutely certain principles of knowledge, and of the objects of it, and accordingly regarded the principles of numbers as the absolute principles of things; keeping true to the common maxim of the ancient philosophy, that like takes cognisance of like. Aristotle states the fundamental maxim of the Pythagoreans in various forms.'"

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