Zero signifies absence or an amount of no magnitude 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? 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. Zero, as such, 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 universal relationships of structure and scale.

Zero signifies absence or an amount of no measure. This mathematical object purportedly exemplifies one of humanity’s most splendid insights. Endorsement of the continuum consolidated zero as a cultural latecomer that, at present, everybody uses daily as an indispensable number. Zero and infinity represent symmetric and complementary concepts; why did algebra embrace the former as a number and dismiss the latter? Why is zero an unprecedented number in arithmetic? Is zero a cardinal number? Is it an ordinal number? Is zero a “real” point? Has it a geometrical meaning? To what extent is zero naturalistic? A preliminary analysis indicates that zero is short of numerical competence, contrived, and unsolvable. We find it elusive when we dig into zero’s role in physics, especially in thermodynamics, quantum field theory, cosmology, and metrology. A minimal fundamental extent is plausible but hard to accept due to zero’s long shade. In information theory, the digit 0 is inefficient; we should replace standard positional notation with bijective notation. In communication theory, the transmission of no bits is impossible, and information propagation is never error-free. In statistical mechanics, the uniform distribution is inaccessible. In set theory, the empty set is ontologically paradoxical. Likewise, other mathematical zeroes are semantically vacuous (e.g., the empty sum, zero vector, zero function, unknot). Because division by zero is intractable, we advocate for the nonzero rational numbers, Q-{0}, to build a new physics that reflects nature’s countable character. We provide a zero-free and unique rational-based representation of the algebraic numbers punctured at the origin, A-{0}, the computable version of the complex numbers. In a linear scale, we must handle zero as the limit of an asymptotically vanishing sequence of rationals or substitute it for the smallest possible nonzero rational. Zero, as such, is the predetermined power indicating the beginning of logarithmically encoded data via log(1). The exponential function decodes the logarithmic scale’s beables back to the linear scale. The exponential map is crucial to understand advanced algebraic concepts such as the Lie algebra-group correspondence, the Laplace transform, and univariate rational functions in cross-ratio form. Specifically, linear fractional transformations over a ring lead to the critical notion of conformality, the property of a projection or mapping between spaces that preserves angles between intersecting conics. Ultimately, we define “coding space” as a doubly conformal transformation domain that allows for zero-fleeing hyperbolic (logarithmic) geometry while keeping relationships of structure and scale.

Zero signifies absence or an amount of no magnitude 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? 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 thermodynam-ics, 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 “iden-tically 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. Zero, as such, 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 universal relationships of structure and scale.