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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Nothing
Everything
Something
Exp
Indeterminate
Element
⌾
1
Linear scale
(Geometric series)
Object
Being
p 1 /2
Lie group
Laplace transform
Conformal space
Logarithmic scale
(Arithmetic series)
Subject
Beable
Log 1
Lie algebra
Inverse Laplace
Compactified space
Log
Fig. 1. Nothing, Everything, Unit, Something, the two natural scales, and the "natural
projective line" in yellow with the indeterminate element ⊚.
Detractors of zero affirm that it is not cardinal or ordinal and cannot even
be an object’s property. For example, the class "apple" disappears if we have
no apples and the attribute "age" is not in a birth certificate. Zero is even an
unneeded number. Arithmetical operations with the number zero are spurious.
For instance, consider the arithmetic mean calculation of the number of things
in a group of bags; should we regard the empty ones? If affirmative, the answer
is the total number of pieces in bags with content divided by the sum of empty
bags and bags with content; zero is not involved in the calculation. We can write
the equation x − y − z = 0 as x = y + z. Mathematical definitions and theorems
largely allude to nonzero numbers, entities, or solutions because the scope of
applicability of zero is usually bland or negligible.
Zero uselessness appears not only in algebra (zero number, vector, matrix,
tensor, ring, et cetera). Functional analysis, ST, and Category Theory consider
the zero function, the empty set, and the empty categorical sum as additive
constants, despite being trivial elements. In knot theory, a zero knot
(unknot) is topologically equivalent to a circle, and any two closed curves in
three-dimensional space with a linking number zero are unlinked. In computer
science, the zero Turing degree is the equivalence class that contains all the algorithmically
solvable sets. All these zeroes are mathematical sugar, flimsy stuff
denoting the same idea of "nothing" addressed to a specific branch in mathematics,
namely no number, no vector, no matrix, no tensor, no ring, no function,
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