ANAXAGORAS (c.500 – c.428 BC)

‘The notion of the indivisible particle’

Anaxagoras came from Ionia but settled in Athens, where he remained for thirty years and taught both Pericles and Euripides. Charged with impiety because of his theory that the Sun is a red-hot stone (such an explanation, denying the role of Helios the sun-god, was enough to warrant prosecution) he fled Athens before the trial and settled in Asia Minor.
What we know about Anaxagoras is based on references to him by later writers.

In the cosmology of Anaxagoras, the Universe began as a homogenous sea of identical basic particles. Nous gave this sea a stir, in the knowledge that in time the particles would so combine to arrange themselves such that everything would be as it is today.

Picture of a document showing a seal with a likeness of Anaxagoras ©

Nous was a vital principle akin to the life force of vitalism – the nearest English words being ‘mind’ or ‘intellect’.
The range of the word ‘Nous’ is vastly greater, however, as it refers to the combination of insight and intuition which permits the apprehension of the fundamental principles of the cosmos – the concept is closer to the oriental idea of ‘seeing’ than the occidental notion of intelligence founded upon EUCLIDEAN LOGIC.

At the same time, Nous could be the creative, motive intelligence behind the cosmos, almost indistinguishable from the Christian concept of the will of God.

Bust said to be of ANAXAGORAS ©

ANAXAGORAS

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PAUL DIRAC (1902- 84)

1928 – UK

‘Every fundamental particle has an antiparticle – a mirror twin with the same mass but opposite charge’

English Physicist Paul Dirac, who developed a wave equation for the electron. --- Image ©

PAUL DIRAC

‘It appears that the simplest Hamiltonian for a point-charge electron satisfying the requirements of both relativity and the general transformation theory leads to an explanation of all duplexity phenomena without further assumption’

1931 – UK

‘A magnetic monopole is analogous to electric charge’

A magnetic monopole is a hypothetical particle that carries a basic magnetic charge – in effect, a single north or south magnetic pole acting as a free particle.

Until recently no one has observed a monopole.

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ERWIN SCHRODINGER (1887-1961)

1926 – Austria

‘The complex mathematical equation describing the changing wave pattern of a particle such as an electron in an atom. The solution of the equation gives the probability of finding the particle at a particular place’

the Schrodinger equation

This equation provides a mathematical description of the wave-like properties of particles.

Schrödinger developed what became known as ‘wave mechanics’, although like others, including EINSTEIN, he later became uncomfortable with the direction quantum theory took. His own proposal was built upon that of LOUIS DE BROGLIE – that particles could, in quantum theory, behave like waves. Schrödinger felt that de Broglie’s equations were too simplistic and did not offer a detailed enough analysis of the behaviour of matter, particularly at the sub-atomic level. He removed the idea of the particle completely and argued that everything is a form of wave.

PLANCK’s work had shown that light came in different colours because the photons had different amounts of energy. If you divided that energy by the frequency at which that colour of light was known to oscillate, you always arrived at the same value, the so-called Planck’s constant.

Between 1925 and 1926 Schrödinger calculated a ‘wave equation’ that mathematically underpinned his argument. When the theory was applied against known values for the hydrogen atom, for example in calculating the level of energy in an electron, it overcame some of the elements of earlier quantum theory developed by NIELS BOHR and addressed the weaknesses of de Broglie’s thesis.
Schrödinger stated that the quantum energies of electrons did not correspond to fixed orbits, as Bohr had stated, but to the vibration frequency of the ‘electron-wave’ around the nucleus. Just as a piano string has a fixed tone, so an electron wave has a fixed quantum of energy.

Having done away with particles, it was required that a physical explanation for the properties and nature of matter be found. The Austrian came up with the concept of ‘wave packets’ which would give the impression of the particle as seen in classical physics, but would actually be a wave.

The probabilistic interpretation of quantum theory based on the ideas of HEISENBERG and BORN proposed that matter did not exist in any particular place at all, being everywhere at the same time until one attempted to measure it. At that point, the equations offered the best ‘probability’ of finding the matter in a given location. Wave mechanics used much simpler mathematics than Heisenberg’s matrix mechanics, and was easier to visualise.
Schrödinger showed that in mathematical terms, both theories were the same and the rival theories together formed the basis for quantum mechanics.

Photograph of Schrödinger ©

ERWIN SCHRODINGER

Schrödinger joined Einstein and others in condemning the probabilistic view of physics where nothing was explainable for certain and cause and effect did not exist.

Ironically, PAUL ADRIAN MAURICE DIRAC went on to prove that Schrödinger’s wave thesis and the probabilistic interpretation were, mathematically at least, the equivalent of each other. Schrödinger shared a Nobel Prize for Physics with Dirac in 1933.

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GEORGE BOOLE (1815- 64)

1854 – England

‘Logical operations can be expressed in mathematical symbols rather than words and can be solved in a manner similar to ordinary algebra’

Boole’s reasoning founded a new branch of mathematics. Boolean logic allows two or more results to be combined into a single outcome. This lies at the centre of microelectronics.

picture of mathematician George Boole

GEORGE BOOLE

Boolean algebra has three main logical operations: NOT, AND, OR.
In NOT, for example, output is always the reverse of input. Thus NOT changes 1 to 0 and 0 to 1.

Boole’s first book ‘Mathematical Analysis of Logic’ was published in 1847 and presented the idea that logic was better handled by mathematics than metaphysics. His masterpiece ‘An Investigation into the Laws of Thought’ which laid the foundations of Boolean algebra was published in 1854.

Unhindered by previously determined systems of logic, Boole argued there was a close analogy between algebraic symbols and symbols that represent logical interactions. He also showed that you could separate symbols of quality from those of operation.

His system of analysis allowed processes to be broken up into a series of individual small steps, each involving some proposition that is either true or false.
At its simplest, take two proposals at a time and link them with an operator. By adding many steps, Boolean algebra can form complex decision trees that produce logical outcomes from a series of previously unrelated inputs.

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PRELUDE

IMHOTEP (c.2650 BCE)

Photograph of King Huni pyramid at Maydoum the 3rd dynasty Old Kingdom at Elfayom (427 x 500) ©

‘Architect of civilisation’

Medical sage, astronomer, mathematician, architect

Architect of the first pyramid built during the reign of the second pharaoh of the Third Dynasty, with the unification of Upper and Lower Egypt.
Came to be revered as a god of healing and identified by the Greeks with their own Aesculapius.

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