Category: mathematics

Bridging the Great Stagnation: Why Taking an Extra Decade to Master the Fundamentals Matters

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In the 1800s, educated elites were expected to be proficient in Latin, Greek, classical literature, religious knowledge, moral philosophy, public speaking, writing, basic arithmetic, geometry, natural philosophy (covering fundamental physics, astronomy, and biology), music, art, poetry, classical and national history, geography, French, and social graces. Physical activities like horseback riding, rowing, and fencing were also Read More …

The Game of Life-simple rules, complex behavior

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Here’s a video introduction to the Game of Life Historically, one of the pioneers of computer science John von Neumann was interested in finding machines which could reproduce themselves. He developed an abstraction allowing him to mathematically model his work on a computational grid. A mathematician John Conway took up and simplified his work publishing Read More …

Road To Reality–Part I

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This past year I read Roger Penrose’s The Road to Reality: A Complete Guide to the Laws of the Universe

The tome is definitely the read for anyone interested in our current understanding of reality from the ground up. It doesn’t shy away from mathematics like most popular science accounts. Rather, as mathematics is the gasoline to travel the Road, it fuels the reader up along the journey. Yet the mathematics quickly progresses from exploring what a number exactly is to a graduate level textbook equivalent and this whirlwind journey is not to be taken lightly. Rather than a Road, I actually consider The Road to Reality to be more of a Roadmap indicating a path to reality without fully providing the reader with the tools to travel it. It worked for me–a Physics PhD student–as most of the book was putting familiar things in a grander context. However, for those not on the Road as a career, supplemental work is probably needed to get the most out of the book. In the that spirit I am presenting a condensed Roadmap in chunks of 6 chapters (there are a whopping 34 chapters covering 1123 pages) with additional links to online courses (primarily sourced from the wonderful Khan academy, Coursera, and MIT OCW).

Without further ado, I present the Roadmap I of VI of Chapters 1-6 of The Road to Reality: Read More …

Dynamic Bayesian Combination of Multiple Imperfect Classifiers

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Using the new Voxcharta.org system, I was the only physicist at my institute to upvote this paper, Dynamic Bayesian Combination of Multiple Imperfect Classifiers (pdf), more in the realm of machine learning or computer science than traditional astrophysics or astronomy. As such I was nominated to discuss it at our weekly journal club. Here I give a brief review of concepts needed to follow the paper, and then go in depth into how we can use the opinions of multiple lay people as to whether an object is a supernova or not to achieve a highly accurate classification at the expert level. Read More …