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Probability of immortality and Godâs existence. A mathematical perspective
What are the probabilities that this universe is repeated exactly the same with you in it again? Is God invented by human imagination or is the result of human intuition? The intuition that the same laws/mechanisms (evolution, stability winning probability) that have created something like the human being capable of self-awareness and controlling its surroundings, could create a being capable of controlling all what it exists? Will be the characteristics of the next universes random or tend to something? All these ques-tions that with different shapes (but the same essence) have been asked by human be-ings from the beginning of times will be developed in this paper
Probability of local bifurcation type from a fixed point: A random matrix perspective
Results regarding probable bifurcations from fixed points are presented in
the context of general dynamical systems (real, random matrices), time-delay
dynamical systems (companion matrices), and a set of mappings known for their
properties as universal approximators (neural networks). The eigenvalue spectra
is considered both numerically and analytically using previous work of Edelman
et. al. Based upon the numerical evidence, various conjectures are presented.
The conclusion is that in many circumstances, most bifurcations from fixed
points of large dynamical systems will be due to complex eigenvalues.
Nevertheless, surprising situations are presented for which the aforementioned
conclusion is not general, e.g. real random matrices with Gaussian elements
with a large positive mean and finite variance.Comment: 21 pages, 19 figure
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A Quantum Probability Perspective on Borderline Vagueness
The term âvaguenessâ describes a property of natural concepts, which normally have fuzzy boundaries, admit borderline cases, and are susceptible to Zeno's sorites paradox. We will discuss the psychology of vagueness, especially experiments investigating the judgment of borderline cases and contradictions. In the theoretical part, we will propose a probabilistic model that describes the quantitative characteristics of the experimental finding and extends Alxatib's and Pelletier's () theoretical analysis. The model is based on a Hopfield network for predicting truth values. Powerful as this classical perspective is, we show that it falls short of providing an adequate coverage of the relevant empirical results. In the final part, we will argue that a substantial modification of the analysis put forward by Alxatib and Pelletier and its probabilistic pendant is needed. The proposed modification replaces the standard notion of probabilities by quantum probabilities. The crucial phenomenon of borderline contradictions can be explained then as a quantum interference phenomenon
When can statistical theories be causally closed?
The notion of common cause closedness of a classical, Kolmogorovian probability space with respect to a causal independence relation between the random events is defined, and propositions are presented that characterize common cause closedness for specific probability spaces. It is proved in particular that no probability space with a finite number of random events can contain common causes of all the correlations it predicts; however, it is demonstrated that probability spaces even with a finite number of random events can be common cause closed with respect to a causal independence relation that is stronger than logical independence. Furthermore it is shown that infinite, atomless probability spaces are always common cause closed in the strongest possible sense. Open problems concerning common cause closedness are formulated and the results are interpreted from the perspective of Reichenbach's Common Cause Principle (RCCP)
Perspective Reasoning and the Solution to the Sleeping Beauty Problem
This paper proposes a new explanation for the paradoxes related to anthropic reasoning. Solutions to the Sleeping Beauty Problem and the Doomsday argument are discussed in detail. The main argument can be summarized as follows:
Our thoughts, reasonings and narratives inherently comes from a certain perspective. With each perspective there is a center, or using the term broadly, a self.
The natural first-person perspective is most primitive. However we can also think and express from othersâ perspectives with a theory of mind.
A perspectiveâs center could be unrelated to the topic of discussion so its de se thoughts need not to be considered, e.g. the perspective of an outside observer. Letâs call these the third-person perspective.
First-person reasoning allows primitive self identification as I am inherently unique as the center of the perspective. Whereas from third-person perspective I am not fundamentally special comparing to others so a reference class of observers including me can be defined.
It is my contention that reasonings from different perspectives should not mix. Otherwise it could lead to paradoxes even independent of anthropic reasoning.
The paradoxes surrounding anthropic reasoning are caused by the aforementioned perspective mix. Regarding the sleeping beauty problem the correct answer should be double halving. Lewisian halving and thirding uses unique reasonings from both first and third-person perspectives.
Indexical probabilities such as âthe probability that this is the first awakeningâ or âthe probability of me being one of the first 100 billion human beingsâ also mixes first- and third-person reasonings. Therefore invalid.
Readers against perspectivism may disagree with point 1 and suggest we could reason in objective terms without the limit of perspectives. My argument is compatible with this belief. Objective reasoning would be analytically identical to the third-person perspective. My argument would become that objective reasoning and perspective reasonings should not mix. In the following I would continue to use âthird-person perspectiveâ but readers can switch that to âobjective reasoningâ if they wish so
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