Physical Method

Ontophainetic Platform

The unveiling of the invariants, literally making them appear in light, called "epiphaneia'', in its philosophical and technical meaning as a spectrum of distinguishable appearances following the analysis of distinctions incident to the architectonics of adjoining and modular substitution, requires for its articulation a canon of transcription to the visual domain of colour, called "chroma'', pre-conditioning the process of resolution.

The "functorial canonics" of unfolding requires tempering within uniformly-partitioned chromatic intervals, underlying in turn the notion of an objective uniform probability distribution in relation to a directly inaccessible domain. In this way, a spectrum is subordinate to a specific partition, although the invariants are independent of the partition employed.

In general, the role of a partition spectrum is the instantiation of distinct blocks or cells consisting of equivalent elements with respect to some relation. The notion of an element is not that of a constituent part, but it refers to the observable distinction that is capable of imprinting on the concomitant spectrum. Each block of a partition consists of all those elements imprinting the same distinction, being thus equivalent to each other, and therefore indistinguishable from the perspective of the imprinted distinctions.

The artefact of a partition spectrum is that it provides the means to reduce the complexity of an obstacle-laden domain through an analysis pertaining only to a finite, or countably infinite, number of blocks. Each block, since it contains indistinguishable elements, requires a single representative to be grasped. Every other element equivalent to this representative will be surely located within the same block of the partition.

Modularity of an Abstract Partition Spectrum

An economy principle is at work here, which is operationally reductive, but not reductionistic, since it gives rise to a manageable quotient, preserving all the distinctions afforded by the spectrum. This is the conceptual core of the modularity characteristic of a partition spectrum. Of course, the actual utility of a spectrum rests on its resolution capacity in relation to the invariants.

Recall that the invariants of the obstacle-laden domain are independent of the partition spectrum devised for its articulation, but simultaneously, a partition spectrum offers indirectly and metaphorically the only possible way to gain access and grasp these invariants.

This makes the notion of a uniform partition, equipartition, and uniform distribution, especially important in the unveiling of the invariants. A uniform distribution amounts to a well-defined condition of neutrality at this level, pertaining essentially to averaging. The idea is that in the absence of an obstacle of any particular type everything would behave uniformly, setting in this manner the standards of comparison and congruence that are not existent ab initio.

Spectral Metronomy

The specification of the appropriate means suitable to a directly inaccessible domain amounts to the metronomy applied to this domain. It is the metronomy that underlies the architectonic techne of adjunction and functorial conjugation giving rise to the modularity of a tempered distribution over a spectrum. Concisely put, the technics of weaving a grid in relation to a partition spectrum is the explication of the underlying metronomy in the presence of obstacles.

For example, the deviation of the spectrum of black-body radiation from the average expected according to the standard of equipartition - known as the ultraviolet catastrophe - led Max Planck to the hypothesis that energy should be quantized, a hypothesis that pertains to the metronomy of energy in terms of integer quanta, which marks the beginning of quantum mechanics.

Therefore, we should follow the thread that qualifies an obstacle as a source of invariance. Invariance can be operationally recognized only through action directed initially away from the level or context of a pertinent obstacle.

The purpose of action is to initiate a stream flow that is capable of retracting the inaccessibility or obstruction imposed by the obstacle to some generic situation at another level through which a passage becomes viable, and then re-direct the flow back toward the initial level, so that the obstacle can be successfully evaded.

The anholonomy of a spectral flow due to the obstacle amounts to a residue, to be thought of in terms of "countable quanta'' of a spectrum emerging through the corresponding metronomy of ontophainetics. These quanta are spectral quantities, which encode the invariance of the obstacle they refer to with respect to all possible flows along cycles initiated by temporal actions.