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Guitar improvisation from May 23, 2025



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OPINION - On the axiom of choice

I find it distasteful that non-mathematicians think that Gödel's work introduces a level of subjectivity to mathematics. I agree that one can construct an arbitrary number of mathematical universes via selecting an arbitrary set of axioms. But I disagree that they are somehow all equivalent in value or structural consistency. I personally believe that there is one mathematical universe (or category of universes that are structurally equivalent via something like an isomorphism) that has the most structural consistency and can give the human mind the most insight. I personally believe that there are axioms that are representations of structural properties of physical reality. And I believe that there is a set of axioms that aligns perfectly with the physical universe, and subsequently allows the human mind to comprehend its logic to the fullest extent. I believe this because the way that the human mind understands logic is already a consequence of physical reality. Our ability to un...
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Time, partitioning, and synchronization

Any time measuring method inevitably runs into the issues of partitioning and synchronization. Partitioning deals with the issue of dividing a larger measure into smaller measures, and combining smaller measures into a larger measure. Synchronization deals with the problem of how a set of devices can self-correct if some of them are corrupted. The two are fundamentally related because often a choice in one determines a choice in the other. A measure is often defined by a set of synchronization points, such as the radioactive decay of an element or the frequency of a crystal oscillator. Synchronization points can often be defined as a measure of a change in space, such as the revolution of a planet around a star, or the change in energy state of an oscillating structure. Fundamental to both is the notion of change. A synchronization event can only be defined if there is a unit of space in which a change is observed. And either the magnitude of the space is large (such as the movement of...
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