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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with our experience, which "seems to controvert at every step the concept of
something unending", as Parkhurst and Kingsland remark.
The thermodynamics of quantum information banishes zero as well. The
connection between thermodynamics and information pivots on the notion of
entropy. Kelvin was the first to recognize the significance of "a universal tendency
in nature to the dissipation of mechanical energy." Roughly, entropy measures
the number of possible configurations the atoms in a system can have.
Hence, a low entropy value means fewer ways to rearrange microscopic things
to create a macroscopic structure. Beings’ activity leads to an enduring growth
of thermodynamical entropy, foretelling that we gradually approach the cosmic
entropic death, characterized by a limiting value of maximum entropy of the
observable universe. Besides, quantum systems tend to decohere mechanically
with decreasing entanglement. Simultaneously, for information is physical, computation
naturally raises global information entropy through free energy consumption,
possibly at an increasingly lower rate. Gisin’s intuitionism suggests
that time passage inevitably drains the environment’s information. Since the
universe seeks to reduce information gaps with every interaction, uncertainty
standardization is unidirectional also from this perspective; physical inaction
would signify no data generation, encoding, transmission, or decoding, i.e., no
time passage. However, we see that computation is pervasive, whence time flows;
can we deduce that the universe in its original state had a null entropy? We can
only confirm that it was minuscule immediately after the Big Bang. If zero is
unreal, as we declare, and if the arrows of entropy and time run in parallel, the
origin of time, i.e., absolute time zero, does not exist.
What a being cannot change is not being’s information. Something unable to
change is not a being. Therefore, a being necessarily possesses nonzero information.
A being is a physical system that can change the statistical or quantummechanical
degrees of freedom that somehow harbor its information. If nature
owns a pragmatic touch, such information must have a positional code. In this
respect, we have posited that standard PN is artificial due to inefficiency; it only
aggregates the nonzero terms, and the leading zeroes introduce ambiguity. We
have shown that signed-digit bijective notation provides zero-free, cost-saving,
specific, and unique representations of rational numbers and their extensions.
Observation of nature led mathematics to introduce and formalize the thought
of grouping beings with the same properties. Unfortunately, ST deviated from
reality, starting to deal with intricate concepts such as the logic of large cardinals.
Surprisingly, this mathematical branch has explored the null class much
less than any infinite set. We have explained why managing collections with no
content makes no sense, concluding that ST should circumscribe to inhabited
and functional sets. The empty set is fictitious; neither the cardinal nor the ordinal
zero exist. If a group of things is possibly void, it is a beable yet not a
set, i.e., a potential collection that precludes the current universe of discourse
by default and temporarily. This "setable" implies abandoning the ideal of completeness
because we cannot anticipate its valuation, renouncing the close-world
assumption.
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