The signal is the primary feature of a communication. It stands at the very base of understanding. Without a signal there would be no vestige of a communication at all. The signal as a singularity is a rare phenomenon, if not impossible to imagine. Its definition encounters the same problems as the one, which was experienced in the concept of unity. The very moment a definition (limitation) is given, the spell of its existence is broken. The undivided world cannot be caught in definitions without breaking its authenticity. The same characteristic is applicable to the signal, as a voice from the deep unknown. Its initial unity is broken the very moment it is noticed by an onlooker.
The observer deals more often with an array: a multitude of signals of the same nature. Radar and sonar are examples of array signals, which are used to build up a new kind of visibility. Acoustic and vibration signals are illustrations of the practical application of signals, for instance, in seismic prospecting. The present age of computerization is highly indebted to communication signals, which are sent by modem, cable or wireless. The human body itself creates physiological signals, including clinical and speech signals, which can be registered and analyzed. The world is full of noises of a natural or synthetic character. And last, but not least, there are signals from outer space, which possess the challenging prospect of a contact with other creations in the universe.
The Croatian genius Nikola Tesla (1856 – 1943) was one of the first experts to see the potential of the signal as a source of communication. His experiments with electricity and the wireless transmission of energy (including the possible cause of the Tunguska catastrophe in 1908) are a specimen of the incredible forces, which could be unleashed when the potentiality of the unseen is tapped. Tesla followed in the footsteps of Michael Faraday (1791 – 1867), the blacksmith’ son, who pointed the way – some sixty years earlier in 1831 – to the production of electricity by magnetism (if it was accompanied by motion).
Tesla’s inventions included the AC-power (both 2-phase and 3-phase), broadcast power (radio wave propagation), microwaves and radar. The Tesla Coil is a transformer, which generate very high voltages at high frequencies. A most common form of the transformer is used in neon signs. It is interesting to note here that a signal (high voltage) is used to power a sign.
Tesla’s vision included the transmission of electrical energy through the earth to be picked up wherever it was needed. The globe, even with its great size, responded to electrical currents just like a metal ball. He expressed his original idea in 1911 as follows: ‘The entire apparatus for lightning the average country dwelling will contain no moving parts whatever, and could be readily carried about in a small valise.’
The research in signal processing has taken a huge flight since then and continues to do so. The signal is the messenger of the invisible invisibility of the First Quadrant, who brings never-ending opportunities to mankind. The present interest focuses on the domains of influence, which form a direct link to a division-based communication. In particular, the geometric representation of tessellations could be a practical tool in the interpretation of signals used in human relationships. The verb ‘to tessellate’ points to the arrangement of squares in a mosaic pattern. The Greek word ‘tessares’ means ‘four’, because initially square tiles were used.
The so-called Voronoi tessellation (or its name equivalents like the Dirichlet domain, Wigner-Seitz cell, Thiessen polygon or Brillouin zone) is applied for analyzing cell-like structures and the division of space into regions (fig. 13). The Voronoi diagram can be used in a wide field ‘from archeology to zoology’ (DRYSDALE, 1993). The representation of lattices is useful in the identification of clusters (in astronomy), the location of areas of growth (in biology), the modeling of sphere packing in chemistry, the pattern of settlement (in geography), the estimation of mineral reserves (in geology), data analyzing in marketing and much more. A further investigation into its use in quadralectic thinking might be a worthwhile undertaking.
Fig. 13 – The Wigner-Seitz (WS) cell is a volume made up of space which is closer to a given lattice point than to any other point. The construction starts from a lattice point and the drawing of lines to its neighbours. Next is the drawing of perpendicular bisecting planes to these lines, half way along. The smallest volume enclosed within these planes is the WS cell. The example gives a rhombic dodecahedron for a face-centered cubic lattice.
Visions of Four Notions 