R. A. Schwaller de Lubicz
"If, on the other hand, we see an image that represents a man walking (or simply lines depicting a man) we no longer imagine him, we no longer situate him; he is there, it is the function that interests us, and the quality of that function. We can then paint this man green: it will no longer be solely the function of walking with one's legs that is evoked - this movement could also signify vegetation or growth. But to our reason, walking and growing are two different functions, while in reality there is an abstract connection between them: it is movement outside consideration of Time, or pathway, or specific direction." [R. A. Schwaller de Lubicz, The Temple in Man, page 18]
"Proportion belongs to geometry and harmony, measurement to the object and to arithmetic; and one necessitates the other. Proportion is the comparison of sizes; harmony is the relationship to measures; geometry is the function of numbers." [R. A. Schwaller de Lubicz, The Temple in Man, page 61]
A function, in mathematics, associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can also be elements from any given set. An example of a function is f(x) = 2x, a function which associates with every number the number twice as large. Thus 5 is associated with 10, and this is written f(5) = 10.
The input to a function need not be a number, it can be any well defined object. For example, a function might associate the letter A with the number 1, the letter B with the number 2, and so on. There are many ways to describe or represent a function, such as a formula or algorithm that computes the output for a given input, a graph that gives a picture of the function, or a table of values that gives the output for certain specified inputs. Tables of values are especially common in statistics, science, and engineering.
The set of all inputs to a particular function is called the domain. In modern mathematics functions are normally defined to have a codomain associated with them which is some fixed set which includes all possible outputs, for instance real valued functions have a codomain which includes all the real numbers even though each particular real valued function may not include every real number as an output. The set of all the ordered pairs or inputs and outputs (x, f(x)) of a function is called its graph. A common way to define a function is as the triple (domain, codomain, graph), that is as the input set, the possible outputs and the mapping for each input to its output.
The set of all outputs of a particular function is called its image. The word range is used in some texts to refer to the image and in others to the codomain, in particular in computing it often refers to the codomain. The domain and codomain are often "understood". Thus for the example given above, f(x) = 2x, the domain and codomain were not stated explicitly. They might both be the set of all real numbers, but they might also be the set of integers. If the domain is the set of integers, then image consists of just the even integers.
There are many ways to describe or represent functions: for instance by a formula, by an algorithm that computes it, or simply by enumerating its values for every possible argument. A function may also be described through its relationship to other functions, for example, as the inverse function of a given function, or as a solution of a differential equation. Functions can be added, multiplied, or combined in other ways to produce new functions. An important operation on functions, which distinguishes them from numbers, is the composition of functions. There are uncountably many different functions, most of which cannot be expressed with a formula or an algorithm.
Collections of functions with certain properties, such as continuous functions and differentiable functions, are called function spaces and are studied as objects in their own right, in such mathematical disciplines as real analysis and complex analysis. [Source unknown]
Christ Returns - Speaks His Truth
"After the Big Bang, the Father-Mother Creative Process was divided into two different energies, continually working apart and together, independent yet mutually constrained to work together having individual characteristics or 'natures' - and different functions. Therefore, their work load was/is different yet indivisible." [Christ Returns - Speaks His Truth, Letter 5, page 23]
 Dynagen: This is one of three forms of Ethericity, a term that refers to those supra-normal, near non-dimensional, energetic, bio-electric, bio-magnetic, catalytic, high-frequency, vibratory, super-potent entities of quasi-material, quasi-etheric nature belonging to the 4th and 5th dimensions of being. As such these ethericities can be further categorised as 'fructigens', 'qualigens' and 'dynagens', which respectively represent those subtle energies, whose function is the enhancement of fructification (fructigens), the generation of quality (qualigens) and the amplification of immaterial energy (dynagens). According to their function or location these may be male or female in nature. — Ed. [From Special Edition Mensch und Technik, Vol. 2, 1993, section 3.1]
Modern intuitionless science has regulated the eternal flow of evolution (panta Rhei) in the wrong way and thus failed to notice the possibility of generating ur-forces. Instead of additional products of emulsion possessing development-enhancing functions, it had to make do with development-disturbing reactive forces and resistances to motion that increase by the square of the reversed form of acceleration. According to an age-old maxim, "she half-pulled him down, he half-sank on her". In this play on words there lies a far deeper meaning. It would take too long here to enumerate all the catalysts with various functions, which as Goethe already recognised, form the 'connecting' emulsifying bond. They are ray-forms, upon whose function the development-disturbing rising temperature gradient and the development-fostering falling temperature gradient depend. Paramagnetic catalysts act decentratingly diamagnetic catalysts concentratingly. This fact alone pin-points the incorrect form of development, which ultimately results in the destruction of atoms. Wise Nature, on the other hand, proceeds by way of atomic transformation, which from, a biological viewpoint is the exact opposite. Pressure and fire technology therefore produce retrogressive atomic energies, whereas implosion technology generates super-powerful, forward-thrusting atomic energies, i.e. an almost 100% formative and levitative force. And so the question arises, what actually is a catalyst? The answer is simple. It is a condenser that has been galvanically alloyed with oppositely-charged substances, which radiates predominantly negatively potentiated ray-forms into the naturalesquely inwindingly moved medium. This then activates a flowing diamagnetism, the formative and levitative force that soars upwards and sucks the generating device up in its wake, and which can be regulated by the rate of rotation. With this, the force was rediscovered that enables air-craft to overcome gravity effortlessly and stationary machines to be powered for virtually nothing. According to accounts from earlier times, the high priests of ancient cultures had a commanding knowledge of this power, which they cherished and guarded like life itself so as to be venerated as Gods for their skill. [The Energy Evolution - Harnessing Free Energy from Nature, The Catalysts]
In both cases we are therefore concerned with supplementary ur-forces having opposite functions, which inaugurate either a progressive economic decline or the opposite. This explains why even the ancient Greeks rejected technology. Derived from the ancient Greek word 'technao', its literal translation means 'self-deceit' or 'self-cheating'. The Greeks preferred the natural labour of slaves in order to spare their evolutionally older descendants from later perils. [The Energy Evolution - Harnessing Free Energy from Nature, Cadaverine Poison in Ray-Form - Ptomaine Radiation]
All forms of heat that give rise to falling and concentrating effects and all forms of cold that exhibit rising and expanding functions belong to group A and are thus development-promoting. [The Energy Evolution - Harnessing Free Energy from Nature, Bio-Technology: Active and Reactive Temperatures]
The fact of the matter is that all forms of heat applied and exploited by science today, however and wherever they occur, engender rising and expanding effects. Similarly, all the forms of cold it utilises have falling and concentrating (mortally solidifying) functions, which lead to degrading, life-destroying expressions of temperament. These wise Nature employs to eliminate everything unfit for further development as well as for purposes of [The Energy Evolution - Harnessing Free Energy from Nature, Bio-Technology: Active and Reactive Temperatures]
Entirely unknown to contemporary science, however, is that apart from this familiar form of temperature, there are also 'higher' forms of heat and cold, which are equally attributable to molecular motion. These 'higher' temperature-forms are to be differentiated from those referred to at the beginning in that the 'usual' forms of heat have a rising and expanding function and their associated cold-forms have a falling and concentrating function. [The Energy Evolution - Harnessing Free Energy from Nature, The Life-Current in Air and Water]
The 'higher' heat-forms are characterised by the fact that they possess falling and concentrating functions, and their associated cold, or refreshing forms have rising and expanding properties. So much for the general appreciation of this bio-technical finding, which is essentially founded on 'higher' physics, or biophysics. [The Energy Evolution - Harnessing Free Energy from Nature, The Life-Current in Air and Water]
In every respect, experiments with this formative and levitative (synthesising) current produced surprising results. Thus, for example, 2,000,000 volts per drop of water, which were measurable, visible and palpable, and therefore incontrovertible, could be freed with appropriate charge-releasing devices. With 50 pairs of needle-jets about 200 million volts can be produced for virtually nothing, for which today's science requires giant machines. Even then it can only produce an exceptionally disintegrative (analysing) current, which has life-negating properties. This is to be differentiated from the formative and levitative, therefore life-affirming, functions of the synthesizing current mentioned elsewhere. [The Energy Evolution - Harnessing Free Energy from Nature, The Life-Current in Air and Water]
In opposition to this dualistic formative, levitative and life-affirming force, however, there is a counterforce, which comes into being in a similar manner. It is also a biotechnically producable current, but functions in a life-negating way and can thus be described as the 'death-current', since, with the exception of developmentally harmful bacterial life-forms, it slowly but surely destroys all life. It breaks down and decomposes every organism so that under very specific pre-conditions and with the aid of a very peculiar movement it can ur-generate new life or death forces of increased and intensified power from the product.
 In regard to fig. 22, while the diagrams depict a submarine, theoretically the same process should also apply to a similarly shaped aircraft. — Ed.
[6.1] Editor's Note: The original Keely Motor has two descending pistons. [The Energy Evolution - Harnessing Free Energy from Nature, The Life-Current in Air and Water]
Fundamentally, therefore, we are dealing with two metabolic processes entirely different in nature and function, both of which are necessary, for without any purging and purifying process no more highly evolved forms could be built up.
which, while known to today's chemist, are initiated unnaturally, therefore in the wrong way, and carried out with the use of ordinary temperature-forms. [The Energy Evolution - Harnessing Free Energy from Nature, The Life-Current in Air and Water]
This involves two temperature groups:
(A) the formative, life-affirming (incremental), and
(B) the disintegrative, life-negating (decremental).
[See T1 and T2.] [The Energy Evolution - Harnessing Free Energy from Nature, The Life-Current in Air and Water]
This two-fold interplay of perpetual motion can be directly observed and studied in deep, cool cellars, for through differences in temperature, what has grown large in the Sun and then reduced in size by squashing, will be moved 'cycloidally' in the cellar. First refined, then made 'cloudy', it slowly becomes clear after termination of this adolescent period. This is how wise Nature operates, who is known to have unlimited developmental periods at her disposition for all things. We, poor souls, to whom only a single, unique life is available in which we will also be forced to make use of cycloid-space-curve-motion in order to alleviate almost intolerable reactive energies through their abreaction, will have to behave more sensibly in order to become somewhat more blissful while still on this Earth than has been the case due to the efforts of 'active' technicians. In other words, we must reverse the way things are done. Cycloid-space-curve-motion must therefore be given pride of place, which logically leads to the almost cost-free mechanical generation of reactive differences in potential, which in turn give rise to increased and intensified active differences in motion. Harnessed once more, these trigger further high-grade differences in potential of a reactive nature, and so on and so forth until temperatures and reactive forces of such a kind are triggered that it is a veritable art to devise an operating load heavy enough to brake and control these elemental suctional and pressural forces. At the right time, therefore, we must keep our eyes open for the specialists and experts, who function as super-brakes on development!! Most certainly, however, we must replace those, who today brake the normal course of development with the reversed interplay of forces, which they do in such a way as to increase and intensify precisely those kinds of energy that promote decomposition and the expulsion of what is unsuitable for further development. In so doing they trigger a form of perpetual motion, because here too the self-intensifying decomposive and repulsive forces also increase by the square owing to the cycloid-space-curve-motion of the Earth. Sadly they do not see what they have themselves created, namely boundless decline and disintegration instead of an equally [The Energy Evolution - Harnessing Free Energy from Nature, New Forms of Motion and Energy]