The Zero Delusion v0.99x
Zero signifies absence or an amount of no dimension and allegedly exemplifies one of humanity's most splendid insights. Nonetheless, it is a questionable number. Why did algebra embrace zero and dismiss infinity despite representing symmetric and complementary concepts? Why is zero exceptional in arithmetic? Is zero a "real" point? Has it a geometrical meaning? Is zero naturalistic? Is it universal? Digit 0 is unnecessary in positional notation (e.g., bijective numeration). The uniform distribution is unreachable, transmitting nill bits of information is impossible, and communication is never error-free. Zero is elusive in thermodynamics, quantum field theory, and cosmology. A minimal fundamental extent is plausible but hard to accept because of our acquaintance with zero. Mathematical zeroes are semantically void (e.g., empty set, empty sum, zero vector, zero function, unknot). Because "division by zero" and "identically zero" are uncomputable, we advocate for the nonzero algebraic numbers to build new physics that reflects nature's countable character. In a linear scale, we must handle zero as the smallest possible nonzero rational or the limit of an asymptotically vanishing sequence of rationals. Instead, zero is a logarithmic scale's pointer to a being's property via log(1)). The exponential function, which decodes the encoded data back to the linear scale, is crucial to understanding the Lie algebra-group correspondence, the Laplace transform, linear fractional transformations, and the notion of conformality. Ultimately, we define a "coding space" as a doubly conformal transformation realm of zero-fleeing hyperbolic geometry that keeps the structural and scaling relationships of the world.
Zero signifies absence or an amount of no dimension and allegedly exemplifies one of humanity's most splendid insights. Nonetheless, it is a questionable number. Why did algebra embrace zero and dismiss infinity despite representing symmetric and complementary concepts? Why is zero exceptional in arithmetic? Is zero a "real" point? Has it a geometrical meaning? Is zero naturalistic? Is it universal? Digit 0 is unnecessary in positional notation (e.g., bijective numeration). The uniform distribution is unreachable, transmitting nill bits of information is impossible, and communication is never error-free. Zero is elusive in thermodynamics, quantum field theory, and cosmology. A minimal fundamental extent is plausible but hard to accept because of our acquaintance with zero. Mathematical zeroes are semantically void (e.g., empty set, empty sum, zero vector, zero function, unknot). Because "division by zero" and "identically zero" are uncomputable, we advocate for the nonzero algebraic numbers to build new physics that reflects nature's countable character. In a linear scale, we must handle zero as the smallest possible nonzero rational or the limit of an asymptotically vanishing sequence of rationals. Instead, zero is a logarithmic scale's pointer to a being's property via log(1)). The exponential function, which decodes the encoded data back to the linear scale, is crucial to understanding the Lie algebra-group correspondence, the Laplace transform, linear fractional transformations, and the notion of conformality. Ultimately, we define a "coding space" as a doubly conformal transformation realm of zero-fleeing hyperbolic geometry that keeps the structural and scaling relationships of the world.
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
168. Časlav Brukner and Anton Zeilinger. Information and Fundamental Elements of
the Structure of Quantum Theory, chapter 408, pages 323–354. Springer Berlin
Heidelberg, 2003.
169. John von Neumann. Mathematical Foundations of Quantum Mechanics. Princeton
Landmarks in Mathematics and Physics. Princeton University Press, mathematische
grundlagen der quantenmechanik edition, 1932 (1996).
170. John Wallis. The Arithmetic of Infinitesimals. Sources and Studies in the History
of Mathematics and Physical Sciencesources and Studies in the History of Mathematics
and Physical Sciences. Springer New York, 2013. Translated by Stedall,
J. A.
171. Scott Walter. The Non-Euclidean Style of Minkowskian Relativity. In Jeremy
Gray, editor, The Symbolic Universe: Geometry and Physics, 1890-1930, pages
91–127. Oxford University Press, 1999.
172. Paul S. Wang. The Undecidability of the Existence of Zeros of Real Elementary
Functions. Journal of the Association for Computing Machinery, 21(4):586–589,
October 1974.
173. Eric W. Weisstein. Benford's Law. MathWorld — A Wolfram Web Resource,
2020.
174. Eric W. Weisstein. Gauss-Kuzmin Distribution. MathWorld — A Wolfram Web
Resource, November 2022.
175. Eric W. Weisstein. Meromorphic Function. MathWorld — A Wolfram Web Resource,
February 2023.
176. Hermann Weyl and Frank Wilczek. Philosophy of Mathematics and Natural Science.
Princeton University Press, 2009.
177. John Archibald Wheeler. Hermann Weyl and the Unity of Knowledge. American
Scientist, 74(4):366–375, 1986.
178. John Archibald Wheeler. Information, Physics, Quantum: The Search for Links.
In Proceedings III International Symposium on Foundations of Quantum Mechanics,
pages 354–358. Physics Department, Princeton University, 1989.
179. John Archibald Wheeler and Kenneth William Ford. Geons, Black Holes, and
Quantum Foam - A Life in Physics. W. W. Norton, 2010.
180. Wikipedia contributors. Radix Economy — Wikipedia, the Free Encyclopedia,
2019.
181. Wikipedia contributors. 0 — Wikipedia, the Free Encyclopedia, 2022. [Online;
accessed 10-November-2022].
182. Wikipedia contributors. Beltrami-Klein model — Wikipedia, the Free Encyclopedia,
2022. [Online; accessed 22-January-2023].
183. Wikipedia contributors. Positional Notation — Wikipedia, the Free Encyclopedia,
2022. [Online; accessed 11-November-2022].
184. Wikipedia contributors. Prime number theorem — Wikipedia, the Free Encyclopedia,
2022. [Online; accessed 10-December-2022].
185. Wikipedia contributors. Complex projective space — Wikipedia, the Free Encyclopedia,
2023. [Online; accessed 13-February-2023].
186. Wikipedia contributors. Poincaré disk model — Wikipedia, the Free Encyclopedia,
2023. [Online; accessed 20-January-2023].
187. Norman John Wildberger. Real Fish, Real Numbers, Real Jobs. The Mathematical
Intelligencer, 21:4–7, 06 1999.
188. Norman John Wildberger. Divine Proportions: Rational Trigonometry to Universal
Geometry. Wild Egg, 2005.
189. Norman John Wildberger. Set Theory: Should You Believe?, July 2015.