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.
91. Karin Usadi Katz and Mikhail G. Katz. A Burgessian Critique of Nominalistic
Tendencies in Contemporary Mathematics and its Historiography. Foundations
of Science, 17(1):51–89, March 2011.
92. Louis H. Kauffman. Space and Time in Computation and Discrete Physics. International
Journal of General Systems, 27(1-3):249–273, 1998.
93. Achim Kempf. Fields over Unsharp Coordinates. Physical Review Letters,
85:2873–2876, October 2000.
94. Achim Kempf. Covariant Information-Density Cutoff in Curved Space-Time.
Physical Review Letters, 92(22), June 2004.
95. Achim Kempf. Replacing the Notion of Spacetime Distance by the Notion of
Correlation. Frontiers in Physics, 9, May 2021.
96. Maximilian E. Kirschhock, Helen M. Ditz, and Andreas Nieder. Behavioral and
Neuronal Representation of Numerosity Zero in the Crow. Journal of Neuroscience,
41(22):4889–4896, 2021.
97. G. J. Klir and T. A. Folger. Fuzzy Sets, Uncertainty, and Information. Prentice-
Hall International editions. Prentice-Hall International, 1988.
98. Alex Klotz. Planck Length: What It Is and Its Common Misconceptions (in
Physics Forums Insights), September 2015.
99. Donald E. Knuth. Art of Computer Programming, Volume 2: Seminumerical
Algorithms. Pearson Education, 2014.
100. Andrey Nikolaevich Kolmogorov. Logical Basis for Information Theory and Probability
Theory. IEEE Transactions on Information Theory, 14(5):662–664, 1968.
101. Steven G. Krantz. Handbook of Complex Variables. Birkhäuser Boston, 1999.
102. Robert Lawrence Kuhn. Levels of Nothing. Skeptic, 18(2):34–37, August 2013.
103. Kenneth Kunen. Set Theory - An Introduction To Independence Proofs. ISSN.
Elsevier Science, 2014.
104. Prem K. Kythe. Handbook of Conformal Mappings and Applications. CRC Press,
2019.
105. Rolf Landauer. Irreversibility and Heat Generation in the Computing Process.
IBM Journal of Research and Development, 5:183–191, 1961.
106. Rolf Landauer. Information is Physical. In Workshop on Physics and Computation,
pages 1–4, Dallas, TX, USA, USA, 1992. IEEE.
107. Rolf Landauer. The Physical Nature of Information. Physics Letters A,
217(4):188–193, 1996.
108. Philipp Lay. Non Adjacent Form. Math, Computer Science and Cryptography
(phlay), (14), June 2018.
109. Baptiste Le Bihan and Niels Linnemann. Have We Lost Spacetime on the Way?
Narrowing the Gap between General Relativity and Quantum Gravity. Studies
in History and Philosophy of Science Part B: Studies in History and Philosophy
of Modern Physics, 65:112–121, 2019.
110. Theodor Leiber. On the Actual Impact of Deterministic Chaos. Synthese, 113:357–
379, December 1997.
111. Ni Liangkang. Zero and Metaphysics: Thoughts about Being and Nothingness
from Mathematics, Buddhism, Daoism to Phenomenology. Frontiers of Philosophy
in China, 2(4):547–556, October 2007.
112. Ingvar Lindgren. Regularization and Renormalization, pages 237–269. Springer
New York, New York, NY, 2011.
113. Øystein Linnebo. The Individuation of the Natural Numbers, chapter 10, pages
220–238. Palgrave Macmillan UK, London, 2009.
114. E. Jonathan Lowe. Locke. Routledge, 2005.
Change language