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.
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
146. H. P. Robertson. The Uncertainty Principle. Physical Review, 34:163–164, July
1929.
147. Takahiro Sagawa and Masahito Ueda. Second Law of Thermodynamics with
Discrete Quantum Feedback Control. AIP Conference Proceedings, 1110(1):21–
24, 2009.
148. Flavio Del Santo and Nicolas Gisin. Physics Without Determinism: Alternative
Interpretations of Classical Physics. Phyisical Review A, 100(6):062107, December
2019.
149. P. Saulson. Mach's - From Newton's Bucket to Quantum Gravity. Classical and
Quantum Gravity, 13(7), jul 1996.
150. Erwin Schrödinger. What is Life? (1944). Cambridge paperbacks. Cambridge
University Press, with mind and matter and autobiographical sketches edition,
2012.
151. Antonio Sciarretta. A Local-Realistic Model of Quantum Mechanics Based on a
Discrete Spacetime. Foundations of Physics, 48(1):60–91, 2018.
152. Charles Seife. Zero: The Biography of a Dangerous Idea. Profile, 2019.
153. Lynden K. Shalm, Evan Meyer-Scott, Bradley G. Christensen, Peter Bierhorst,
Michael A. Wayne, Martin J. Stevens, Thomas Gerrits, Scott Glancy, Deny R.
Hamel, Michael S. Allman, Kevin J. Coakley, Shellee D. Dyer, Carson Hodge,
Adriana E. Lita, Varun B. Verma, Camilla Lambrocco, Edward Tortorici, Alan L.
Migdall, Yanbao Zhang, Daniel R. Kumor, William H. Farr, Francesco Marsili,
Matthew D. Shaw, Jeffrey A. Stern, Carlos Abellán, Waldimar Amaya, Valerio
Pruneri, Thomas Jennewein, Morgan W. Mitchell, Paul G. Kwiat, Joshua C.
Bienfang, Richard P. Mirin, Emanuel Knill, and Sae Woo Nam. Strong Loophole-
Free Test of Local Realism. Physical Review Letters, 115:250402, December 2015.
154. Claude Elwood Shannon. The Mathematical Theory of Communication. The Bell
System Technical Journal, 27(4):623–656, 1948.
155. Claude Elwood Shannon. The Mathematical Theory of Communication. The
Mathematical Theory of Communication: By Claude E. Shannon and Warren
Weaver. University of Illinois Press, 1962.
156. A. B. Shidlovskii. Algebraic Number. Encyclopedia of Mathematics, February
2020.
157. Rob Siliciano. Constructing Möbius Transformations with Spheres. Rose-Hulman
Undergraduate Mathematics Journal, 13(2 (8)), 2012.
158. Lee Smolin. Atoms of Space and Time. Scientific American, 290(1):66–75, 2004.
159. Lee Smolin. Three Roads to Quantum Gravity. Basic Books, 2017.
160. Ray Solomonoff. A Formal Theory of Inductive Inference I. Information and
Control, 7(1):1–22, March 1964.
161. Ian Nicholas Stewart. Galois Theory. CRC Press, 2015.
162. John Stillwell. Modular Miracles. The American Mathematical Monthly,
108(1):70–76, 2001.
163. Patrick Suppes. Introduction to Logic. Dover books on mathematics. Dover Publications,
1999.
164. Leó Szilárd. Über die Ausdehnung der phänomenologischen Thermodynamik auf
die Schwankungserscheinungen. Zeitschrift für Physik, 32(1):753–788, 1925.
165. Alfred Tarski and Steven R. Givant. A Formalization of Set Theory Without Variables.
Number 41 in Colloquium publications. American Mathematical Society,
1988.
166. Michael Tooley. Time, Tense, and Causation. Clarendon Press, 1997.
167. Peter van Inwagen. Nothing Is Impossible. In Miroslaw Szatkowski, editor, God,
Truth, and Other Enigmas, pages 33–58. De Gruyter, 2015.
Change language