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.
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
8 Concluding Remarks
8.1 Zero impression
We can explain mathematical knowledge in naturalist terms from the perspective
of evolutionary biology, cognitive science, and sociology of science. However,
only the latter can explain why we overlooked the historical and geopolitical factors
that led to the consolidation of the number zero. In Dantzig’s view, the
"guiding motive throughout this long period of groping was a sort of implicit
faith in the absolute nature of the unlimited". Then, Cantor’s approach to conquering
the irrationals consummated the era of modern analysis, delivering the
theory of functions based on infinite processes and the continuum, where zero
fits seamlessly. Our investigation shows that the immeasurable perfection that
zero embodies has as little scientific value as beauty.
Thanks to Cantor’s grandest dreams and his supporters, intellectuals took
real numbers for granted, to the point that mathematicians and philosophers
such as Brentano, Weyl, and Brouwer studied faithful continuum representations
based on discrete elements. As collateral damage, the "real" zero rolled up to
present-day science; today, mathematics and physics use it by habit. This inertial
frenzy combines with professional pressure to put aside the foundational issues
necessary to settle a sturdy QG theory that condemns zero in the name of reality.
The lure of zero is due to its halo of mystique, and none questions the magic
of this mathematical object. Science seems afraid of taking on the uncharted
lands of a vacuous digit, a vanishing quantity, an information gap, a concept
denoting "what remains from the total". One can hardly browse results about
its intrinsic indeterminacy, and essays about the zero’s ontological meaning are
rare, primarily referring to absence or negation. In this metaphysical context,
the threesome {something, everything, nothing} reasonably symbolizes a part
of the universe, the whole of it, and the whole’s complement, represented by
{1, ∞, 0}.
Animal species seem to have a system for approximating numerosity that
includes zero, albeit probably taking emptiness as a simple conception of refuted
presence. Since zero represents "nothing" and has no actual numerical weight,
humans deem it unfamiliar, as the history of humanity proves. We cannot observe
zero in nature; if anything, we encounter many clues that it is a cosmological
ghost. Because it plays a dull role in many mathematical branches and lacks
naturalism, we have posited that zero is often futile and, sometimes, a nuisance.
Zero is nowhere. In statistics and probability theory, every sequence of items
has a first and last but no zeroth element, and no Bayes reasoning assigns null a
priori probabilities. In logic and computer science, nullary (null arity) functions,
i.e., operations with no arguments, always have some hidden input as global
variables or contextual properties of the system in question (e.g., state of memory
or network time). In fractal theory, fractional dimension nil is impossible;
otherwise, we could contract and dilate nothingness. In geometry, the separation
of two points cannot be zero if they represent different entities. The same
applies to the angle between two lines. Physical states, processes, and transfor-
Change language