| _version_ | 1866901538034679808 |
|---|---|
| author | Faliari, Tiago |
| author_facet | Faliari, Tiago |
| contents | <p>his paper proposes a cohesive framework that unifies indeterminacy across<br>mathematics, quantum phenomena, and astrophysical observations through a single<br>constant, denoted by I. First, we extend the real number system to R ∪ {I} and<br>specify algebraic rules for handling previously undefined expressions—such as 0<br>0 ,<br>∞ − ∞, and ∞<br>∞ —which now yield I rather than causing analytical breakdowns.<br>This approach not only streamlines the resolution of indeterminate operations in<br>calculus, infinite series, and set theory, but also motivates the introduction of a<br>specialized ExtendedReal data type that allows numerical algorithms to gracefully<br>handle divergences without halting.<br>Building upon this reinterpretation of indeterminacy, we propose that certain<br>astrophysical singularities and quantum uncertainties may, in fact, encode high-<br>density “information states” rather than representing mere breakdowns in theory.<br>Drawing parallels from the quantum condensation of ultra-cold lithium atoms to the<br>extreme densities in sunspots and supermassive black holes (e.g., Sagittarius A*),<br>we argue for a universal mechanism in which matter transitions between particle-like<br>and wave-like behaviors. High-resolution black hole imaging—analyzed via contrast<br>enhancement, edge detection, Fourier transforms, and thermal mapping—reveals<br>ring-like structures and internal radiation patterns, further suggesting a link be-<br>tween gravitational singularities, indeterminate mathematical forms, and creative<br>potential at the heart of cosmic processes.<br>Lastly, we introduce the hypothetical element J, an exotic constituent poten-<br>tially associated with dark matter, dark energy, and emergent cognitive phenom-<br>ena. By placing I and J at the center of both micro-scale (quantum mechanics)<br>and macro-scale (cosmology) discourses, this paper offers a holistic viewpoint in<br>which undefined operations, cosmic singularities, and consciousness converge. Fu-<br>ture research aims to validate these concepts through multi-wavelength astrophysi-<br>cal observations, advanced numerical simulations, and interdisciplinary studies that<br>span mathematics, physics, and artificial intelligence. Through this unified lens,<br>longstanding problems involving infinite expressions, gravitational extremes, and<br>quantum indeterminacies may be recast as manifestations of a deeper, universal<br>structure woven into the fabric of reality.<br>1=0</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_14967363 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Black Holes, Quantum Atoms, and Cognitive Structures Faliari, Tiago <p>his paper proposes a cohesive framework that unifies indeterminacy across<br>mathematics, quantum phenomena, and astrophysical observations through a single<br>constant, denoted by I. First, we extend the real number system to R ∪ {I} and<br>specify algebraic rules for handling previously undefined expressions—such as 0<br>0 ,<br>∞ − ∞, and ∞<br>∞ —which now yield I rather than causing analytical breakdowns.<br>This approach not only streamlines the resolution of indeterminate operations in<br>calculus, infinite series, and set theory, but also motivates the introduction of a<br>specialized ExtendedReal data type that allows numerical algorithms to gracefully<br>handle divergences without halting.<br>Building upon this reinterpretation of indeterminacy, we propose that certain<br>astrophysical singularities and quantum uncertainties may, in fact, encode high-<br>density “information states” rather than representing mere breakdowns in theory.<br>Drawing parallels from the quantum condensation of ultra-cold lithium atoms to the<br>extreme densities in sunspots and supermassive black holes (e.g., Sagittarius A*),<br>we argue for a universal mechanism in which matter transitions between particle-like<br>and wave-like behaviors. High-resolution black hole imaging—analyzed via contrast<br>enhancement, edge detection, Fourier transforms, and thermal mapping—reveals<br>ring-like structures and internal radiation patterns, further suggesting a link be-<br>tween gravitational singularities, indeterminate mathematical forms, and creative<br>potential at the heart of cosmic processes.<br>Lastly, we introduce the hypothetical element J, an exotic constituent poten-<br>tially associated with dark matter, dark energy, and emergent cognitive phenom-<br>ena. By placing I and J at the center of both micro-scale (quantum mechanics)<br>and macro-scale (cosmology) discourses, this paper offers a holistic viewpoint in<br>which undefined operations, cosmic singularities, and consciousness converge. Fu-<br>ture research aims to validate these concepts through multi-wavelength astrophysi-<br>cal observations, advanced numerical simulations, and interdisciplinary studies that<br>span mathematics, physics, and artificial intelligence. Through this unified lens,<br>longstanding problems involving infinite expressions, gravitational extremes, and<br>quantum indeterminacies may be recast as manifestations of a deeper, universal<br>structure woven into the fabric of reality.<br>1=0</p> |
| title | Black Holes, Quantum Atoms, and Cognitive Structures |
| url | https://doi.org/10.5281/zenodo.14967363 |