#mathematical-singularity #physics #philosophy #uncertainty #humility #open-mindedness #curiosity #black-holes #lightning
Created at 140323
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# [[Epistemic status]]
#shower-thought
Last modified date: 140323
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# Related
- [[Physic/Schwarzschild singularity]]
- [[Physic/Penrose singularity theorem]]
- [[Philosophy/Humans/Singularity]]
- [[Physic/Horizons]]
# TODO
> [!TODO] TODO
# Mathematical singularity
Mathematical singularity is a point or region in a mathematical equation or model where the function becomes infinite, undefined, or ambiguous. This phenomenon occurs when a function or equation reaches a point where it is no longer able to provide a valid solution due to its inherent limitations. Singularities are commonly found in mathematical models of physical systems, such as black holes, where the equations break down at the center of this entity, resulting in a point of infinite density and zero volume. Singularities also occur in financial models, such as in the pricing of certain derivatives, where the model may break down and produce contradictory results. In general, singularities reflect fundamental limits to our understanding of the subject at hand, and are a topic of active research in many areas of mathematics and physics.
Mathematical singularities remind us of the limits of our knowledge and our need to embrace uncertainty. Just as singularities in equations and models signify the point at which our understanding breaks down, there are natural phenomena in the world that defy explanation, such as the origin of the universe or the emergence of consciousness.
In nature, singularities can be seen in the form of black holes, where the laws of physics break down, or in the formation of lightning, where electricity becomes concentrated in a single point. These singularities remind us of the awe-inspiring power and complexity of the natural world, and the need to approach it with humility and respect.
Similarly, the inevitability of singularities in our mathematical models and our understanding of the world should encourage us to embrace uncertainty and be open to new perspectives and possibilities. By recognizing our limitations and the limitations of our knowledge, we can remain humble, curious, and open-minded in the face of the mysteries and wonders of life.