miniature forms:

Plato’s theory of Forms posits that there are 2 worlds: the apparent world of concrete, particular objects, grasped by the senses, which constantly changes, and an unchanging & unseen world of Forms or abstract objects, grasped by pure reason; specific & particular objects have a universal & perfect Form in this 2nd world; abstract values like justice, truth & beauty, refer to objects in this abstract realm; Plato cites geometry as just such a notion

 

minimal quanta:

more commonly quantum (the plural of quanta) as in Quantum Physics;  the minimum amount of any physical entity (meaning a measurable physical property) involved in a gravitational or electromagnetic interaction.  The idea that a physical property can be "quantized" is referred to as "the hypothesis of quantization" & means that the magnitude of the physical property can take on only discrete values consisting of integer multiples of one quantum.  An example of this: a photon is 1 quantum of light.  Similarly, at the atomic level, the energy of an electron orbiting around an atom is quantized and can exist only in certain discrete values or orbits

 

Dalton (his chemical atoms):

(1766 -1844) English chemist, physicist & meteorologist, pioneer researcher in colour blindness, most famous for introducing atomic theory into chemistry.  The idea of atomic weight arose in his mind as a purely physical concept during his study of the physical properties of the atmosphere & other gases.  In his paper "On the Absorption of Gases by Water and other Liquids" (1805) he proposes relative weights for the atoms of a few elements but gives no detail.  His atomic theory posited that elements are made of extremely small particles (atoms); atoms of the same element are identical; atoms of different elements differ in size, mass & other properties; they cannot be subdivided, created or destroyed; in chemical reactions they are combined, separated or rearranged, atoms of different elements combine in simple whole-number ratios forming chemical compounds; much though not all of his atomic theory proved prescient.  In 1808 he published his first table of relative atomic weights containing 6 elements (hydrogen, oxygen, nitrogen, carbon, sulphur & phosphorus).  The extension of this idea to substances in general necessarily led him to the law of multiple proportions; his deductions were confirmed by experiment. 

 

electrons: * see Endnote<A>

stable subatomic particle with a charge of negative electricity, found in all atoms, acting as the primary carrier of electricity in solids.  Together, all of the electrons of an atom create a negative charge that balances the positive charge of the protons in the atomic nucleus.

 

thermodynamics (quanta): * see EndNote<B>

branch of physics dealing with heat, work & temperature, and their relation to energy, radiation & physical properties of matter; the behaviour of these quantities is governed by the 4 laws of thermodynamics which provide a quantitative description using measurable macroscopic physical quantities .

 

Non-Euclidean geometries:

the 2 traditional non-Euclidean geometries are hyperbolic geometry & elliptic geometry; there are however many other non-Euclidean geometries discovered by Faustian mathematicians (e.g.  Kinematic geometries).

and see Chapter II, page 83, Chapter V page 170

 

Theory of Groups:

see Chapter I, page 47

 

Leibniz (Monads):

most famous contribution to metaphysics (in Monadologie, 1714); he proposes the universe is made of an infinite number of simple substances or monads, which are the "ultimate units of existence in nature"; they have no parts but exist by the qualities that they have, which continuously change over time; each monad is unique, unaffected by time, subject only to creation & annihilation.  They are centres of force; substance is force, while space, matter & motion are merely phenomenal. 

 

superlatively:

of the highest kind, quality, or order; surpassing all else or others; supreme; extreme

 

Rutherford (his atom): * see Endnote<C>

(1871-1937) English/New Zealand physicist,  father of nuclear physics; at McGill University, Montreal he discovered  radioactive half-life.  Atoms were assumed to be the indestructible basis of all matter; in 1903 Rutherford published his findings: radioactivity involved the spontaneous disintegration of atoms into other unidentified matter.  Here he also discovered the radioactive element radon & differentiated & named alpha & beta radiation.  In 1908 he received the Nobel Prize in Chemistry.  In 1907 he moved to Victoria University Manchester; he & T. Royds proved alpha radiation is helium nuclei.  Famously, at Manchester he & colleagues experimented with alpha particles; from this he developed his model of the atom.  In 1917 he performed the first artificially induced nuclear reaction (nitrogen nuclei were bombarded with alpha particles); from this he discovered the emission of a subatomic particle he named the proton.  Appointed Director of the Cavendish Laboratory (Cambridge University); under his direction the neutron was discovered by Chadwick in 1932; also in 1932 he led the first successful experiment to split the nucleus in a fully controlled manner.

 

Niels Bohr (& the quanta of Planck): * see Endnote<D>

(1885-1962) Danish physicist, advanced understanding of atomic structures & quantum theory, for which he received the Nobel Prize in Physics (1922).  He was also a philosopher & promoted scientific research.  He developed the Bohr model of the atom, where he proposed that energy levels of electrons are discrete, the electrons revolve in stable orbits around the atomic nucleus but can jump from one energy level (or orbit) to another.  Although supplanted by other models its underlying principles remain valid.  He conceived the principle of complementarity: that items could be separately analysed in terms of contradictory properties, such as behaving as a wave or a stream of particles.  Complementarity dominated his thinking in science & philosophy.  He founded the Institute of Theoretical Physics (University of Copenhagen) in 1920; he mentored & worked with Hans Kramers, Oskar Klein, George de Hevesy, and Werner Heisenberg. 

 

Planck (quanta): * see EndNote<E>

(1858-1947) German theoretical physicist whose discovery of energy quanta won him the Nobel Prize in Physics (1918).  He made many contributions to physics but his fame rests on his role as the originator of quantum theory which would change the understanding of atomic & subatomic processes.  Planck investigated the black body problem & solved it with his theoretical formula.  This revolutionized physics thru its use of “quanta” or discrete packets, particles.  These represent the minimum amount of any physical property that can be measured, which is involved in an interaction (such as electromagnetic interactions, electrical currents). 

 

Leucippus and Democritus (atoms): * see EndNote<F>

Leucippus, a 5th century Greek philosopher & purportedly originator of atomism; we know little of him other than this.  His pupil Democritus (460-370 BC) also a philosopher & touted as the originator of the atomic theory.  He did not believe in a first causes but looked to mechanical explanations.  He held that everything is composed of "atoms" which are physically, but not geometrically, indivisible; between them lies empty space (the void); atoms are indestructible, have always been & always will be in motion; there is an infinite number of atoms & of kinds of atoms, differing in shape and size.

 

atomic indivisibility:

Apollonian: In the 5th century BC, Leucippus & Democritus proposed that all matter was composed of small indivisible particles, atoms.  Since it was impossible to keep dividing matter infinitely, it must be made of extremely tiny particles, which are indivisible & cannot be broken down any further.

Faustian: In 1903, Rutherford & colleagues at Victoria University Manchester published their "Law of Radioactive Change" based on experiments between 1900-03.  They challenged the idea of the indestructible atom.  Rutherford and Soddy demonstrated that radioactivity involved the spontaneous disintegration of atoms into other, as yet, unidentified matter.  Their idea, that radioactive substances breaking up was radically new .

 

the static-plastic:

unchanging 3D form; a clear reference to Greek sculpture (Apollonian prime symbol)

 

the dynamic-contrapuntal:

active 2 or more independent melodies sounded together, a clear reference to German Baroque music (the Faustian prime symbol)

 

Democritus (confused atoms):

reference to  the mechanistic materialism of Democritus; this echoes Plato , who described Democritus’ atoms as randomly crashing into other atoms; Plato argued this could never produce the beauty & form of the world.