[RascalPuff]

You see logarithmic spirals every day. They are the natural growth curves of plants and seashells, the celebrated golden curve of ancient Greek mathematics and architecture, the optimal curve for highway turns. Peer into a flower or look down at a cactus and you will see a pattern of logarithmic spirals criss-crossing each other like so:



Other places you will find logarithmic spirals:

1. Many buildings, from Greek temples to modern skyscrapers, are proportioned in accordance with the golden mean, a constant which is the ratio of the sides of a rectangle circumscribed about a logarithmic spiral.
2. The silhouette of the base of a Greek column has a number of log-spiral sections.
3. Leaf edges in some plants (e.g., begonias) roughly follow logarithmic spirals.
4. Euler proposed that tracks curved in a logarithmic spiral were optimal for slowing and turning trains in railyards.
5. Many artists have consciously and unconscously incorporated it into their work.
6. The horns of many bovids such as gazelles have growth programs are similar to that of seashells.

Matthew Brand / MIT Media Lab / brand@media.mit.edu
______________________

A more comprehensive, simplified, less mathematical approach to this logarthmically spiraling dissertation, follows.
Continuous Field theory inherently begets Discontinuous Particles:
Note the accelerating transition of the four dimensional mass, consisting of four ninety degree quadrants. Any more energy generated by that system, has no more room to occur inside that spheroidal electromagnetic charge (of 360o 4-D mass/matter system); the 5th component of ninety degrees - generated by and a result of the four dimensions constituting the material energy that generates it, moves - is emitted - at right angles out of 4-D matter, in a fifth ninety degree unit of electricity, the 5th dimension. 'Quantum Leaping' out of the four ninety degree quadrants of physical matter. For this reason - of a 5th 90o unit, all quanta/photons have the same 'Quantum' value (plural - 'quanta'), though they may occur - always having the same value - in more extended units of or toward infra red, or more compact units of or toward ultra violet.

The following information is extracted from The Dictionary of SCIENCE, by E.B. Uvarov and D. R. Chapman, Penguin Publishers, copyright 1943 to 1975.
"Quantum - According to the quantum theory, energy exists in discrete units, only whole numbers of which can exist: each unit is called a 'quantum' <plural 'quanta'>. The quantum of electromagetic radiation is the photon; in certain contexts, the quantum of energy associated with nuclear forces may be taken as the meson.

Quantum Mechanics. The system of mechanics which, during the present century, has replaced Newtonian Mechanics as a method of measuring physical phenomena occurring on a very small scale (e.g., the motion of electronsandnuclei within atoms; see atom, structure of).

Quantum Theory originated with the discovery by Max Planck that the heat radiation from a black body (see black body radiation) is quantized, i.e., emitted in discrete quanta of energy, the magnitudes of which are given by the products of the frequency of the radiation and a universal constant, now known as Planck's constant. It was soon realized that all electromagnetic radiations are quantized (see photon) and the theory was developed by Niels Bohr, so that the spectrum of hydrogen could be accounted for quantitatively (see Bohr theory). This early version of quantum mechanics was refined by Sommerfield to take into account the elliptical orbits of electrons. More recently quantum mechanics has been developed in a speciaized form, known as wave mechanics, which is more versatile and involves fewer arbitrary assumptions than the original theory."

'Photo-electric effect'. In general, any effect arising from the result of a transfer of energy from light incident on a substance to electrons in the substance. The term is normally restricted to one type of the effect, namely the emission of electrons by substances when irradiated with light of a certain frequency greater than a minimum threshold frequency. Electrons emitted in this way are called photo-electrons and constitute a photo-electric current when the system is included in a suitable circuit."

(*Quanta may sometimes be collectively measured and/or otherwise improvisationally considered, in erg seconds <one erg = 10-7 joules> or Angstrom units <One AU=10-10 metre. A measurement of wavelengths of light & intra-molecular distances.> - KBR)
- The Dictionary of SCIENCE, by E.B. Uvarov and D.R. Chapman, Penguin Publishers.

Beware the lurking Jabberwock, paraphrased.
This record will not venture to define such terms as 'quarks', 'strangeness', or 'charms', let alone 'tacheyons', 'gravitons', 'glueons', leprechauns, put-ons or take-offs; until any of these exotically spun, spin-doctored r.p.m.'s and an entire genre of similarly angularly momentized fantasys are proved to exist at all. Until further notice, none of these stick-on, would be elemental genus specimens, are so predisposed beyond a tangle of woofs, warps and waffling warbles, invented (without any sober dignity or restraint known to this record) to displace what would otherwise be innocent and viable ignorance of the behavior and dynamics of microcosmic entitys.... (For which the above innovated 'vocabulary', in the reserved perspective of this observer, departs the realm of study, while indulging in flapping flippancy.) Yes. The considered dynamics and/or entities likely do require a vocabulary, but this record cares not to seriously embrace such similarly levititious expressions of *'cleaving unto the spousal' arousal of the exemplary excercise in bad taste, namely the improvised dissolution to the 3-Body Problem, so aptly represented by *Misner, Thorne & Wheeler (*'Forego talk of acceleration. Fall is <'Your fault'>', for example. If this is *GRAVITATION, Barbara Lovett Cline is *MACHO, and Newton was a *WIMP.)
And now, this:
May the Reader mark the above issued definition of 'Quantum Theory', and especially its closure quote, alluding to the evolved adaptation of 'wave mechanics':
"More recently quantum mechanics has been developed in a speciaized form, known as wave mechanics, which is more versatile and involves fewer arbitrary assumptions than the original theory."

The above information with its closing note is simply a reminder that the popular perception of quantum mechanics is that it contradicts 'field-wave' considerations, whereas, the enigma of quantum mechanics is addressed here more comprehensively (and non mathematically), in context of 'wave mechanics'.

Excerpt: http://forums.delphiforums.com/EinsteinGroupie