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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between two quantum objects or states. Moreover, a path’s probability can be
a mean of the intermediate quantum objects or processes it transits through
and depend on the curvature of a manifold of these transition quantum states;
negative curvature (regarding the mean) would decrease occurrence probability,
while positive curvature would be attractive. Specifically, when a body computes
a Sum over Histories [118], the different nonzero wave-like amplitudes integrated
over a curved space will reinforce or cancel each other to produce the quantummechanical
course that the particle depicts. This least-changing action represents
an asymptotic stability limit, not a concrete static path; absolute steadiness is
unphysical.
Irrespective of a body’s action, many observable quantities of interest in
QFT can only take values in discrete sets of integers or half-integers. Discrete
physics, especially discrete spacetime [24,92,151], wonders if the premises of R-
based laws and principles are mistaken. The question is pertinent because the
reification of zero and infinity is a longstanding controversy, pending no matter
how much physicists think these are well-settled mathematical concepts. R is
infertile [187] and "unphysical" [148], thwarting the most elementary change
no matter how long the universe could spend processing it (see subsection 6.1).
Besides, a minimal size integrated into fundamental discreteness understandably
exists, as we will analyze in the following subsection.
This latter issue links to a crucial question; how long is "now"? We do not
know what "now" is [123] and can only offer partial responses. Classically, a
"Timing on the scale of tens of milliseconds to a few seconds" [133] protracts
the subjective stint between past and future if we admit that our consciousness
emerges from the activity of neuronal nodes. Concerning Special Relativity (SR),
how can a spacetime event have different non-null properties or bear a change?
There must be fundamental tensed facts or relations; [166] "if the direction of
time is given by the direction of causation, and spacetime points themselves
stand in causal relations, then time is, as one naturally thinks of it as being, an
all-pervasive feature of the world." Likewise, some events are in our past cone
by the time we watch them, and we are in the past cone of those observers with
whom we can communicate. Thus, part of the past and future exist, extending
behind and in front of us. This thickness, compatible with an extinct past
and an unborn future, guarantees a minimum flow of information and sidesteps
many paradoxical situations of the block universe. At a fundamental level, the
Margolus-Levitin theorem [119] states that a quantum system of average energy
E needs at least a time π /2E to transit between orthogonal states. In general,
neither a computational process can be instantaneous nor a time interval can
have zero duration. Therefore, the present is feasibly pure "becoming" conformed
by tics separated by Planck time multiples.
Zero is also strange when we focus on an interaction’s inherent uncertainty.
Empirical results come with two essential sources of error. On the one hand, the
observer effect tells us that measurement modifies the examined system, limiting
"the fineness of our powers of observation and the smallness of the accompanying
disturbance" [41]. We notice this prod’s disruption as a measuring apparatus’s
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