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instead of using opaquely complex phraseology. Finally, let me say that mathematics is effective as there is a large variety of constants relative to various transformations.” Dirac said that the presence of a large number of constants is often an indication of the profundity of a theory. This polytechnic professor defined the matter well: “the presence of constants associated with some transfor- 1 oat oat eat . c oa of reality,’ of something that possesses a relative independence, just as we succeed in acknowledging the ‘reality’ of an object in normal per- ception, by seeing how it behaves when we change our relative posi- tion to it.” However, what is an element of reality, he asked. “Being able to speak of a reality requires that something subsists or persists in tempo- ral flux or in changed points of view or observation instruments. A first criterion of reality is therefore the existence of constants under specific transformations.” To conclusively prove the existence of something we must look at an object from every angle. “However, reality,” he added, “is also what appears to be endowed with a certain unity, a certain inter- nal coherence.” We are very far from pure and solid materialism. We can say, for instance, that astrology possesses a certain internal coherence. We become aware of a specific reality when we perceive a relation between the parts and the whole,. Therefore, persistence and coherence constitute the foundations of reality, mathematical or otherwise, but unstable particles do not necessarily prove the accuracy of these crite- ria. In technical terms, this is called general covariance, i.e., the invari- ance of physical laws that take the same mathematical form regardless of their expression in a reference frame: the Galilean transformation in classical mechanics and the transformations of the Poincaré group in special relativity. This covariance describes a physical reality instead of an effect caused by a specifically chosen point of view. To identify this element of reality, it must still be linked to a more general concept, while guaranteeing its singularity. This is where science fails in its the- oretical foundations. Conceptual links and singular identification are two indispensable requirements in establishing an element of reality. The indisputable, astonishing and quite real effectiveness of evolved mathematics in particle physics and cosmology is connected to this intuitive property of a language rich in constants, the scientist suggested. These rich and constant structures are nothing other than generalized symmetries. It is the code of conduct I propose in the next 108 The Science of Extraterrestrials: UFOs Explained at Last * Eric Julien boundaries of science.” I take this demonstrative stance on the matter mations is always seen as an indication of the existence of an ‘element rere wae tia 4 wo