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.
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22. George Boole. An Investigation of the Laws of Thought: On which are Founded
the Mathematical Theories of Logic and Probabilities (1854). Collected logical
works. Dover, 1958.
23. Émile Borel. Les Nombres Inaccessibles. Collection de monographies sur la théorie
des fonctions. Gauthier-Villars, 1951.
24. Graham Brightwell and Ruth Gregory. Structure of Random Discrete Spacetime.
Physical Review Letters, 66:260–263, January 1991.
25. L. Brillouin. The Negentropy Principle of Information. Journal of Applied Physics,
24(9):1152–1163, 1953.
26. James Robert Brown. Philosophy of Mathematics: A Contemporary Introduction
to the World of Proofs and Pictures. Routledge Contemporary Introductions to
Philosophy. Taylor & Francis, 2010.
27. John P. Burgess. Fixing Frege. Princeton Monographs in Philosophy. Princeton
University Press, 2018.
28. John P. Burgess. Set Theory. Elements in Philosophy and Logic. Cambridge
University Press, 2022.
29. Xavier Calmet, Michael Graesser, and Stephen D. H. Hsu. Minimum Length from
Quantum Mechanics and Classical General Relativity. Physical Review Letters,
93:211101, November 2004.
30. Sean M. Carroll. Is our Universe natural? Nature, 440(7088):1132–1136, April
2006.
31. Sean M. Carroll. The Routledge Companion to Philosophy of Physics, chapter
Why is there Something, Rather Than Nothing?, page 16. Routledge, first edition,
September 2021.
32. Carlton M. Caves and Christopher A. Fuchs. Quantum Information: How Much
Information in a State Vector?, 1996.
33. Gregory J. Chaitin. How Real are Real Numbers? I. J. Bifurcation and Chaos,
16:1841–1848, June 2006.
34. Ming-Cheng Chen, Can Wang, Feng-Ming Liu, Jian-Wen Wang, Chong Ying,
Zhong-Xia Shang, Yulin Wu, M. Gong, H. Deng, F.-T. Liang, Qiang Zhang,
Cheng-Zhi Peng, Xiaobo Zhu, Adán Cabello, Chao-Yang Lu, and Jian-Wei Pan.
Ruling Out Real-Valued Standard Formalism of Quantum Theory. Physical Review
Letters, 128:040403, January 2022.
35. M. C. Chu-Carroll. Good Math: A Geek's Guide to the Beauty of Numbers, Logic,
and Computation. Pragmatic Bookshelf, 2013.
36. Tobias Dantzig. Number, the Language of Science: A Critical Survey Written for
the Cultured Non-mathematician. Macmillan, 1959.
37. G. Dattoli, E. Di Palma, J. Gielis, and S. Licciardi. Parabolic Trigonometry.
International Journal of Applied and Computational Mathematics, 6(2):37, 2020.
38. Paul Davies, Sabine Hossenfelder, and Lee Smolin. The Universe, Fixity and Flux.
In State of Modern Science, Debates and Talks. The Institute of Art and Ideas,
June 2022.
39. René Descartes. Principles of Philosophy. Number 10. Project Gutenberg Literary
Archive Foundation, 1644 (2003). Translated by John Veitch.
40. Keith J. Devlin. Constructibility. Perspectives in Logic. Cambridge University
Press, 2017.
41. Paul Adrien Maurice Dirac. The Principles of Quantum Mechanics. Comparative
Pathobiology - Studies in the Postmodern Theory of Education. Clarendon Press,
1981.
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