Notepad
A collection of thoughts, problems, solutions
A Review of Phase Transitions5/7/2018 Just wanted to share this brief review with everyone.
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Intuitionem5/7/2018 With full understanding of a topic comes an intuition. You don't need to understand a whole text to get at least some intuition - some parts are self-contained. What remains true, whatever the amount of information, is that once you understand - truly understand - the material becomes an entity, a friend you have an intimate connection with. You can finish its thoughts, you know what it likes and what it hates - if it were a real-live being, that is. What I mean to say is that you are confident about how that body of knowledge will relate to any other body of knowledge (for the most part), disregarding certain special scenarios which challenge the core of the idea itself. This is what I call intuition.
Sometimes people have an innate intuition that guides them in various tasks; cooking may be one example. However, in all cases it is generally accepted that this intuition can be taught and often requires refining for those who possess at least some measure of it. For myself, I have always relied on my intuition to guide me through my thoughts - sometimes at the expense of ignoring or discounting a more efficient or rigorous means to get to a particular outcome. This is the reason why I decided to study physics - "...to train my wandering wit" (Francis Bacon). Unfortunately, I am still quite the entitled brat. I demand to have an intuitive framework as I am learning formality. To clarify, I first expect that any logical step should be transparent to me given a particular presentation in a book. If I cannot get this intuition immediately, I look at another resource. I don't stop until I can explain the mathematics on an intuitive level, even if this means I must stop at every equation that the text demands `must simply be'. In my opinion, the writing of many technical books follow the bizarre practice of removing the very conceptual scaffolding needed to understand the 'beautifully terse' ideal that is published. Now, this does not mean every step should be worked out, but it means that there should always be a well-established universe in which each mathematical (logical) statement lives that allows one's intuition to coexist, so that past knowledge can be connected with that which is newly acquired. Should I put such a burden on the author? This is a tricky question that is more of a matter of taste than correctness. Suffice it to say that as a person who is guided by intuition, I have always been at odds with academe while often finding a home in it. A sort of love-hate relationship, if you will. So, do you need to actually understand something to get high marks? I think this necessarily must not be true at the graduate level. For many faculty have claimed that they really didn't understand material until they had to teach it. Understanding is not a black-white matter. However, sometimes I suspect that some pedagogical practices slows this process down. it seems to me that there are outdated methods that retard the development of such real understanding. Ye Olde and Wise Mathematician5/4/2018 Leibniz: Free will, Morality, and the Limits of Determinism When people argue about free will, or the need for morality or a "spiritual" mindset i.e., one that reveres something much greater than humanity or self, I am reminded of what Leibniz had to say about these topics. His view seems to have a balance and wisdom that is often lacking in modern discourse. Al DanielsHi. I'm a currently a PhD student at the Vermont Complex Systems Center. I prefer not to use social media platforms, so I occasionally share my thoughts here! Archives
December 2018
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