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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Despite everything, this research on zero has helped us recognize that the
primordial master duality is nothing-everything (zero-infinity) and that nature
yields geometric and arithmetic series managed by linear and logarithmic scales
onto which "something" is respectively decoded and encoded. Zero is mathematically
a power rather than a number, philosophically a beable instead of a
being. However, a beable introduces indefiniteness to a degree; otherwise would
be nothing. Therefore, zero is budding information implemented as a limiting
value that indicates the commencement of spacetime, much as infinity suggests
the end of it. We must treat zero and infinity on par with one another and
interpret them as permanent nascent possibilities.
9 Postcript
This apopemptic chapter includes additional information about our activity’s
circumstances during the essay’s development.
9.1 Acknowledgements
We herein express our tribute to some personalities or entities influencing this
work.
José Mira and our UNED colleagues were the starting point for directing our
scientific vocation.
Working for Indra, we acquired a pragmatic character for managing a scientific
endeavor like this and realizing that nature must be productive in the first
place.
Recently, a variety of scientific media has nurtured our minds. We found
largely instruction and motivation in the channels of Norman J. Wildberger and
Sabine Hossenfelder. Their continual lessons and tireless effort to disseminate the
essence of mathematics and physics are inspiring and deserve a commendation.
We especially thank Joan Baez, Lee Smolin, and Sean Carroll for their ken,
profoundness, and explanatory capacity. We owe them an enormous debt of
gratitude.
We include an extensive literature list of relevant works related to this research.
However, the scope of the work is so broad that we deem it incomplete
and always have the feeling of ignoring something or someone crucial. Browsing
the Web is exhausting, and the information available is overwhelming; we apologize
to all those working on related matters that were ignored or not studied
as they deserved.
We thank those who are offering comments and critical insight on this version.
We cannot help but mention the Spanish government’s invaluable support
during these past years.
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