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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9.2 Statements and Declarations
The author asserts that only scientific rigor, significance, and clarity drive the
high-level goals of this work. It contains no known minor or significant incongruencies,
errors, or inaccuracies.
The author claims to have committed no ethical wrongdoing related to this
paper on purpose, including plagiarism, far-fetched self-citations, conflict of interest,
inaccurate authorship declarations, and unacceptable biases concerning
the references. This work generally respects third parties rights such as copyright
and moral rights.
The author declares that they have no competing financial or non-financial
interests directly or indirectly related to the work submitted for publication. No
personal relationships have influenced the content of this work.
This work is an original one-piece that must be kept unsplit into several
parts. It has not been published elsewhere in any form or language, partially or
in full (no self-plagiarism). We have excluded from it no sensitive information in
the form of confidential or proprietary information or data.
The author deems disclosing our background appropriate to realize the milieu
of research. We have comprehensive experience in artificial intelligence, fuzzy
logic, computational science, and general physics. For a decade, we have had to
learn algebra and fundamental physics in depth, at least to a point where we can
fathom the troubles with zero. Many study fields have been hard to apprehend,
including general relativity and topology, to give some significant examples.
To minimize our cognitive bias, we have bet on the long-term, on our own,
and out of the programs ruled by budgets and subventions. We have been relatively
separated from the scientific world during the development of this work to
avert group thinking; it is a radical strategy to prevent the excessive enthusiasm
produced by social reinforcement. This way, the criticism will lead to a better
refinement process and unveil many mistakes we indeed have made.
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