Geometric Sequence Quotes

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Buckminster Fuller explained to me once that because our world is constructed from geometric relations like the Golden Ratio or the Fibonacci Series, by thinking about geometry all the time, you could organize and harmonize your life with the structure of the world.
Einar Thorsteinn
lovelight' and 'lightlove' are geometric codes. The phrase 'love and light' creates a geometric code that fires directly into the matrix field creating an instant clearing or upgrade. Lovelight and lightlove are very high geometric frequencies linking into the golden frequency, that which is known as the 'golden mean' or 'golden equation', also known as 'the Fibonacci sequence'. It is the mathematical equation of creation itself.
Magenta Pixie (Masters of the Matrix: Becoming the Architect of Your Reality and Activating the Original Human Template)
The tragedy of the Western mind, beautifully described by Koyré, is a direct consequence of the stark Cartesian division between mind and world. We discover the “certain principles of physical reality,” said Descartes, “not by the prejudices of the senses, but by the light of reason, and which thus possess so great evidence that we cannot doubt of their truth.”7 Since the real, or that which actually exists external to ourselves, was in his view only that which could be represented in the quantitative terms of mathematics, Descartes concluded that all qualitative aspects of reality could be traced to the deceitfulness of the senses. It was this logical sequence that led Descartes to posit the existence of two categorically different domains of existence for immaterial ideas—the res extensa and the res cognitans, or the “extended substance” and the “thinking substance.” Descartes defined the extended substance as the realm of physical reality within which primary mathematical and geometrical forms reside and the thinking substance as the realm of human subjective reality. Given that Descartes distrusted the information from the senses to the point of doubting the perceived results of repeatable scientific experiments, how did he conclude that our knowledge of the mathematical ideas residing only in mind or in human subjectivity was accurate, much less the absolute truth? He did so by making a leap of faith—God constructed the world, said Descartes, in accordance with the mathematical ideas that our minds are capable of uncovering in their pristine essence. The truths of classical physics as Descartes viewed them were quite literally “revealed” truths, and it was this seventeenth-century metaphysical presupposition that became in the history of science what we term the “hidden ontology of classical epistemology.
Robert L. Nadeau (The Non-Local Universe: The New Physics and Matters of the Mind)
Weirdly, the more standard classroom math you’ve had, the harder it’s going to be to avoid answering in an impoverished way. Such as, e.g., validating a/(1-r) by observing, in the best Calc II tradition, that the relevant geometric series here is a particular subtype of convergent infinite series, and that the sum of such a series is defined as the limit of the sequence of its partial sums (that is, if the sequence s1, s2, s3, …, sn , … of a series’ partial sums tends to a limit S, then S is the sum of the series), and that sure enough, w/r/t the above series, Lim (sn) = 1 so a/(1-r) works just fine … in which case you will once again have answered Zeno’s Dichotomy in a way that is complex, formally sexy, technically correct, and deeply trivial. Along the lines of ‘Because it’s illegal’ as an answer to ‘Why is it wrong to kill?
David Foster Wallace (Everything and More: A Compact History of Infinity)
We recall that the term inflation stands for the explosive growth of the universe by a factor of 10^50 in the time span between t = 10 ^-36 and t = 10 ^ -33 seconds. This is the time sequence suggested by the original Big Bang model but does not necessarily depend on it. In our present context, it is important to see what triggered the inflationary expansion. The models we mentioned have a vacuum state of our world pass from a symmetric phase into one with reduced symmetries. At the onset of inflation, some 10^-36 or 10^-35 seconds after the Big Bang, the initial era of the universe, when all the forces had the same strength, has long since passed; that ur-state had held only until t = 10^-44 seconds. Tryon's model includes the possibility that no matter at all existed before the onset of inflation; there was only empty space, but all the laws of nature did exist. In the model of Hartle and Hawking, inflation simply follows what they call the Planck time, the time at which quantum mechanical uncertainty also included space and time. It is at that time that the symmetry of the TOE, the theory of everything, collapsed. Now back to the start of inflation at t = 10^-36 seconds: Up to it, and ever since the Planck time, there have been two forces-gravity and the unified forces of the elementary particles. All particles shared mass zero at the onset of inflation; all forces shared range infinity. The universe was, at a temperature of 10^28 degrees- sufficiently cold to permit the crystallization of a preferential direction in the abstract space of particle properties. This is analogous to the emergence of a direction of magnetization, as we discussed above-with the one difference that we have generalized geometric space to an abstract space.
Henning Genz (Nothingness: The Science Of Empty Space)