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.
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
stone, an obstacle for the number sets N, Z, Q, R, C, et cetera. Next, we explain
the paramount significance of a "natural" ratio, an irreducible fraction between
nonzero magnitudes. The irregularities and inconsistencies that the number zero
provokes to the rationals resound through the R-based number sets, so we bet
for ˇQ to build nonzero algebraic numbers and Ǎ instead of C as the number
system upon which computability must grow. Then, we point out where and
how to apply the nonzero algebraic numbers to obtain versatile mathematical
structures with a high impact on physics; e.g., LFT of the Möbius, Laguerre,
and Minkowski planes. Finally, we review the cross-ratio, a prominent rational
construct that gives rise to generalized conformal transformations and the idea
of coding space. In the concluding remarks, we underline that zero’s involvement
in science is not innocuous and that we have already devoted too much effort to
it.
Thanks to this work, we have learned that zero is a foreign construct whose
utilization separated from infinity is deceptive. We have also discovered that
zero and infinity are dual beables, so we can throw light on how to respond
to the following existential question; [102] "Lump together literally everything
contained in ultimate reality. Now call it all by the simple name ’Something’.
Why is there ’Something’ rather than ’Nothing’?" In picturesque language, the
sum of (an infinite amount of) "nothing" (absolute nonexistence, 0) and (a finite
amount of) "everything" (complete existence, ∞) constitutes the primeval
duality principle (valid for the universe, multiverse, or metaverse) [31] pivoting
on the identity (relative nonexistence or existence, 1) as a brute fact [46]. In
turn, multiples of this unit ("something") appear in two versions, the encoded
or intensive arrangement, which nature keeps on a logarithmic scale, and the
decoded or extensive one, which the cosmos exhibits on a linear scale. The infinite
nothingness, i.e., zero, "lives" on the boundary of the encoded world as a
potential unit, namely log (1), lingering where spacetime begins (see Figure 1).
1.2 The troubles with zero
Zero is a recent creation [36] "destined to become the turning point in a development
without which the progress of modern science, industry, or commerce is
inconceivable." Theoretically, "the integer immediately preceding 1" [181] plays
a chief part as the additive identity of the mightiest algebraic structures. "Zero’s
absence would stunt the growth of mathematics" [152]. Nowadays, most people
think zero is a number like others [115]. Many mathematicians will contend
that saying the contrary is a sad mistake, and some will even discredit those
who impugn the verisimilitude of zero. Not so fast! Zero is peculiar and causes
complications immediately. For instance, in Frege’s view [51], "0 is the number
which applies to the concept unequal-to-itself". Mathematics deals with it ad
hoc; zero is an even number (the evenest number! [63]), but the only function is
odd and even. It produces disturbing dichotomies, too; zero is both a positive
and negative value, neither a prime number nor a composite number.
Change language