Resonances Part One (original) (raw)
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To understand the phenomena present in the "Intimate Nature of the Universe", in its various evolutionary processes, it is necessary to look beyond the boundaries of our current knowledge, where the evolutionary processes are guided not by statistical science, but by an elementary form of Intelligence inherent in Universe system capable of guiding the “Spark of life”, regardless of where we collapse the Schrödinger Wave Function. The study of "Universal Reality" has been led onto false tracks, as the two foundations on which current science is based (Relativity and Quantum), in addition to not being reconcilable with each other, are incomplete and/or false compared to the " Intimate Nature of the Universe". This parameter needs to be represented by a new "Algebra of Nature", connected to the role of Geometry in the Universe, which lately is losing its historical identity. Instead of being in tune with the Multiplicity Universal, more and more elements are added to the Geometry in the Universe that cages it into "static syntheses", which constitute the pretext for eliminating the role of Intuition in geometry. From which it can be deduced that, as for the Causal Law, to represent our experience in "condensed matter", geometric axioms are little necessary, so we can think of spaces, and therefore geometries, in which completely different axioms are valid than our ones, as non-Euclidean geometry showed after Kant. We can therefore deduce that the foundation of mathematics lies in a "super-intuition" inherent in the illusion of the passage of Time, while recognizing that mathematics has its own content which comes directly from Intuition, and as such is independent as much as from sensorial experience, as well as from logical structuring. In this sense, logic is nothing but a guise that for communication purposes is imposed on contents that are completely independent of it, since mathematics is like a magician's hat, from which anything put inside first can come out. We can deduce here that the Algebra of the "Intimate Nature of the Universe", through the phenomenon of Resonance, represents the existing relationship between Form and Frequency, where Nature, visible and invisible to us, behaves like an enormous transceiver antenna, as it is DNA with its characteristics of electronic conduction and self-symmetry. The DNA evolves through a modality that transcends the second principle of thermodynamics, as for example Life is born and evolves by gathering around itself everything that it serves him, transforming it into "order" and not into "disorder" as entropy would like. This "intelligent evolutionary path" inherent in the "intimate nature of the Universe", in order to function, requires the function of Intuition and Error, which between the Past, Present and Future perform the function of driving the "Universal Evolutionary Arrow". The meaning of "Error" is seen as the need to interrupt a state of "Perfection" in order to exist, creating the pulsation present in every corner of this Universe. This vision of Universal Reality leads us to understand that Nature is pure Art, powered by a form of intrinsic Universal Intelligence, which has nothing to do with Artificial Intelligence, which cannot be "Intelligent" as it lacks Intuition . Finally, we note that due to the current stalemate of contemporary Science, many questions still remain open in our coexistence with the Harmony of Universal Nature, which should be addressed with courage and imagination, through the support of a new, more scientific vision close to the Intimate Nature of the Universe, investigated in this article.
TIMELESS IMAGINATION - A Critical Review/Essay of "Infinite Ascent: a short History of Mathematics"
This review/essay allows me to review the history of mathematics over the last 2500 years by building on an extensive survey from a qualified author, who has shown how to successfully describe simple and complex mathematical topics to the general public. The book's title is a reflection of the admiration that the author shows to his professional discipline, as it climbs forever (in his view) to the peak of human understanding. My own essay's title is a sceptical hint of digging deeper than this shrewd author has failed to go. This is surprising, as Berlinski has been ready to criticize Darwinian Evolution (he is a member of the controversial Discovery Institute in Seattle) but he is not prepared to attack his professional colleagues and their unquestioning faith in the Pythagorean/Platonic Religion that he shares from his own education in philosophy. Berlinski tells this tale (well-known only to mathematicians) in historical order that is truly appropriate for a subject that has grown cumulatively over time and is probably still the best sequence to learn to understand the coherence of the Rules and Definitions that are the heart of mathematics that need to be memorized by anyone wishing to master it. This historical approach is also a suitable framework to introduce the few (a dozen or so) geniuses that invented this topic (Platonists would deny this and count them as the Discoverers of the Eternal Truths). None-the-less, this focus on individuals makes the story more human and approachable, while the 10 key topics are lightly reviewed. This is NOT a text to learn mathematics from but an amusing journey through a central part of European culture. The author obviously loves mathematics but perhaps found it too hard to appreciate its difficulties by the many who have been categorized as "unintelligent" by the mathematics cognoscenti, who place themselves at the peak of the European academic world. He does acknowledge that mathematics is best grasped intuitively by those whose can imaginatively see the connections. From his written and spoken style, one would have to place Berlinski in an English literary or poetics class. This essay was written with two objectives: firstly, to provide an even shorter introduction to these major ideas than Berlinski did in his 180 pages but secondly, expose more of the hidden assumptions that even few mathematicians admit to, so that those who gave up on mathematics early do not feel too badly or "third-rate". This essay continues my campaign against the arrogance of abstract intellectuals-both ancient theologians and two millennia of mathematicians-who have promoted one aspect of human brains [see my Split Minds essay] over every other part and activity of human beings. I shall emphasize here the commonalities of these two rivals (deeper than Science and Religion) as both invent concepts that have no existence in reality. This book reaches its logical conclusion by focusing on the Foundations of Mathematics. This is an area I have invested much time investigating, as my own interests zero in on Deep Topics; so, I conclude with a few suggestions for those mathematicians, logicians and philosophers, who share this interest. As one who has spent over 60 years studying physics (experimental and theoretical) and researching Natural Philosophy (and also paid for several years as a successful systems analyst), I now feel obligated to act as a 'Whistle-Blower' exposing the exaggerated claims of mathematical physics that are still used to extract billions of dollars annually across the world and in fact might only produce a Bigger Bomb !
On the Emergence of Mathematical Objects : The Case of
2013
In this report we propose an alternate account of mathematical reification as compared to Sfard’s (1991) description, which is characterized as an “instantaneous quantum leap”, a mental process, and a static structure. Our perspective is based on two in-service teachers’ exploration of the function f (z) = e , using Geometer’s Sketchpad. Using microethnographic analysis techniques we found that the long road to beginning to reify the function entailed interplay between body-generated motion and object self-motion, kinesthetic continuity between different sides of the “same” thing, cultural and emotional background of life with things-to-be, and categorical intuitions. Our results suggest that perceptuomotor activities involving technology may serve as an instrument in facilitating reification of abstract mathematical objects such as complex-valued functions.
How the World Became Mathematical
My title, of course, is an exaggeration. The world no more became mathematical in the seventeenth century than it became ironic in the nineteenth. Either it was mathematical all along, and seventeenth-century philosophers discovered it was, or, if it wasn't, it could not have been made so by a few books. What became mathematical was physics, and whether that has any bearing on the furniture of the universe is one topic of this paper. Garber says, and I tend to agree, that for Descartes bodies are the things of geometry made real ( Ref). That is a claim about the world: what God created, and what we know in physics, is nothing other than res extensa and its modes. Others, including Marion after Heidegger, hold that in modern science, here represented at its origins by Descartes, representation displaces beings: the knower no longer confronts Being or beings but rather a system of signs, a "code" as Marion calls it, to which the knower stands in the relation of subject to object. The Meditations, or perhaps even the Regulae, are the first step toward the transcendental idealism of Kant.
How Mathematical Concepts Get Their Bodies
Topoi-an International Review of Philosophy, 2010
When the traditional distinction between a mathematical concept and a mathematical intuition is tested against examples taken from the real history of mathematics one can observe the following interesting phenomena. First, there are multiple examples where concepts and intuitions do not well fit together; some of these examples can be described as “poorly conceptualised intuitions” while some others can be described as “poorly intuited concepts”. Second, the historical development of mathematics involves two kinds of corresponding processes: poorly conceptualised intuitions are further conceptualised while poorly intuited concepts are further intuited. In this paper I study this latter process in mathematics during the twentieth century and, more specifically, show the role of set theory and category theory in this process. I use this material for defending the following claims: (1) mathematical intuitions are subject to historical development just like mathematical concepts; (2) mathematical intuitions continue to play their traditional role in today's mathematics and will plausibly do so in the foreseeable future. This second claim implies that the popular view, according to which modern mathematical concepts, unlike their more traditional predecessors, cannot be directly intuited, is not justified.
The Evolution of Number in Mathematics
2016
Mathematics is the science of number, time, motion, and space (FAQ1). Over the past five millenia our understanding of these four concepts and their inter-relations has changed significantly, due largely to mathematical researches which over the same period have transformed mathematics and its applications. Where the four were once viewed as distinct concepts, they are now unified in a generalized concept of number that has been enlarged through algebraic and analytic extension, in a process that characterizes modern mathematics (FAQ2). In this paper we trace the evolution of number from the whole numbers known since the dawn of counting, to the discovery of the octonions in the 19th century and their connection with string theory and the grand unified ‘theory of everything’ in the 20th century.(FAQ13) The main paper is a very brief three pages, followed by remarks, historical notes, FAQs, and appendices covering theorems with proofs and an annotated bibliography. A project guide is...
Sociological Focus, vol.6, no. 2, pp. 107-116, 1983
How is the historical development of mathematics to be understood sociologically? The writings of Mannheim and Wittgenstein suggest two contrasting approaches which may be evaluated through a detailed analysis of the development of the number concept. Five main number systems can be distinguished of which the most basic is the system of whole numbers and, given that importance attaches to generalizing power, there can be shown to be a tendency for the number concept to be progressively augmented. This process may be understood by reference to the basic pre-Darwinian evolutionary idea of "unfolding." Complementing this intrinsic element, in actual historical instances a variety of extrinsic factors may be seen to be operative, facilitating or retarding development. To explain historical change fully an elaborate normative structure must be analyzed incorporating a macro-institutional level, the "rules of the mathematical game", notational considerations, and relations internal to mathematics itself (e.g., between number and geometry).
The emergence of mathematical structures
Educational Studies in Mathematics, 2011
We present epistemological ruptures that have occurred in mathematical history and in the transformation of using technology in mathematics education in the twenty-first century. We describe how such changes establish a new form of digital semiotics that challenges learning paradigms and mathematical inquiry for learners today. We focus on drawing analogies between the emergence of non-Euclidean geometry with recent advances in technological environments that are dynamic and interactive both visually and haptically. This analysis yields a new digital semiotic theory.