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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no set, no categorical sum, no knot, no link, and no uncomputability. We will
only examine the empty set among these zero objects because of its impact on
R (see section 4.1).
Furthermore, some facts sustain that zero is beyond our sensory and processing
faculty, an imaginary and often false friend. According to Richardson’s
undecidability results [172], determining whether a simple expression that involves
polynomials and the sine function vanishes is theoretically unsolvable,
not to mention in practice. If "the coordinate system remains as the necessary
residue of the ego-extinction" [176], the geometry of the origin (zero) is mute,
nay, impregnable subjectivity. The probability of encountering nothing in the
cosmos is so infinitesimally small that it is de facto nil; "it is impossible for
there to be nothing" [167], nothing is physically outside our universe [159], and
even debatable that nada existed with exclusiveness before the Big Bang [121].
In the next section, we will further reason that zero is unobservable and unbelievable.
We have already introduced the contention that zero is neither naturalistic
nor motivated by dependable scientific criteria. Despite living in a quantum
universe where information is physical [106,136], possesses a discrete character
[32], and serves computational purposes [127], our central mathematical tools
give off the continuum’s aroma. The immaculate real numbers, "true monsters"
[57], govern the n-dimensional Euclidean space, a mythical realm of maximum
density having no room for holes. However illogical as it can be, we need the
continuum because its perfection provides us with protection, which is again
not a scientific reason but a psychological one. Zero satisfies our longing for
(mathematical) "connected compactness".
Nothing points to nothingness in IT. A system’s information (lack of entropy)
correlates with its internal thermodynamical activity, which depends on the system’s
quantum mechanical degrees of freedom. In turn, these reify the system’s
properties to sign the mantra "quantum physics is an elementary theory of information"
[168]. The system balances when its entropy reaches a maximum.
However, given that a generic quantum system is "contextual", excepting possibly
the universe, and never definitely hermetic [117], the environment causes
decoherence interacting with the system’s degrees of freedom that bear its intensional
information [107]. The fluctuation of the corresponding microstates
permanently unchains processes that take the system out of equilibrium, permeating
the universe with a renewed distribution of information. This emergent
thermodynamics indicates that nature associates "transformation" with "information
exchange". The present constantly varies through interactions, so we
always perceive a series of material effects and a notable phenomenology linked
with information currents. Since propagating null information is nonsensical, inaction
is equivalent to a lack of information flow. Because inactivity is never
absolute (e.g., like a time crystal reveals [144]), information flow is incessant.
The notion of infinity as the limit of a diverging sequence sounds logical,
despite considering its twin, zero, not a limit value but a number. This inconsonance
has negative consequences in thought, algebra, and calculus. Perhaps,
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