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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length cubed). This rationale leads many physicists to conceive spacetime as a
network of fixed quantum states of areas and volumes that evolves sequentially
to rearrange its connectivity [158]. Such a network would fluctuate as a foam if
arrayed in multiple tiny ever-changing regions [179]. This model can explain how
spacetime grows but not, for example, how time dilates or a process develops.
The time dimension should preexist mated to the spatial regions, furnishing the
network instances with a nonzero temporality to enable the relational cohabitation
of its elements. All in all, our universe must host beings with nonzero
hypervolume.
Moreover, the patch of spacetime occupied by a being should be large enough
to interact with the environment; otherwise, the being would be incapable of
yielding the "least" action, staying unconnected from the presence of other bodies.
This view points to the Planck length as the minimum distance (or equivalently,
the Planck time as the minimum duration) needed to carry out a move,
deformation, or modification to reality in general. A photon’s energy is the multiplication
of its frequency by a physical constant, the quantum of electromagnetic
action. This Planck constant is the minimum force integrable over a spacetime
interval. Thus, we can formulate the Uncertainty Principle as σ st σ F ≥ /2, where
σ st and σ F are the standard deviations from the spacetime interval and force
means. The more precisely the force applied to a body is determined, the less
predictable its four-dimensional position is from initial conditions. The shorter
the spacetime interval available for action, the stronger the push must be, i.e.,
our endeavor will be in vain if we exert strength during a too-short period or
shift. In summary, a change needs nonzero (and finite) force and spacetime; the
precondition for a transformation is the capability of a "natural" quantity of
work and impulse.
3 Zero Information
On why zero has no information content and needs no representation.
3.1 Gap
Adopting a minimal length scale is also an old idea of quantum IT to provide
a minimal discrete model of QG [200]. A minimal length as a fundamental level
of resolution implies a finite bandwidth and density of degrees of freedom for
IT-reconstructable physical fields [93], agreeing with the fact that "theories formulated
on a differentiable spacetime manifold can be completely equivalent to
lattice theories" even when the radius of curvature is minuscule [94]. At the
opposite end, spacetime tends to flatten on large scales. Since the strength of
the correlations is inversely proportional to the distance [95], quantum entanglement
phenomenology progressively evaporates as the universe expands, albeit
not entirely. Quantum IT tells us that we gain detail in the observed object by
descending enough up to the appropriate layer of reality. The other way around,
we embrace a sense of continuity by ascending sufficiently, i.e., scaling up to a