The last few months have been devastating to our societies, our economies, and our ability to get out of bed before attending meetings. In anticipation of the tumultuous days that inevitably lie immediately ahead, I wanted to get out some thoughts about the pandemic. COVID-19 is, among many other things, a collection of “big” numbers—more than 40 million cases worldwide, almost 1.2 million deaths, and so on. At least for me, when the numbers get this big, I have trouble visualizing them, and need a kind of visual aid. This post is going to be mostly USA-centric, simply because (1) I live here and (2) our collective response to COVID-19 has been comically egregious. I hope the interested reader can proportionately scale their anguish to the global scale.Continue reading
After recently having graduated with a physics and astrophysics degree at the University of California, Berkeley, I can finally fulfill a long-awaited desire to write down a reflection of my college experiences with some sort of satisfying completeness. In writing this reflection, I hope to achieve two broad goals: (1) to view my experiences with respect to some overarching lessons in summary of how I have developed as both a researcher and a person, and (2) to provide some anecdotal advice and expectations for students hoping to follow a similar path through undergraduate.
As for the former point, when looking back over a significant chapter of one’s life, a question begs to be asked: “what was it all for?” I find that it can be incredibly rewarding to try to understand what exactly there was to be gleaned out of a personal experience, mistake, or struggle. Under a composition of such meditations, I can hope to learn precisely how my overall college experience has shaped me from the shy, anxious freshman to the graduating senior today.
As for the latter point, when making big decisions in one’s life, one often hopes to optimize over the space of all possible futures. In practice, I have learned that the closest thing one can do to this is to learn from the experiences of mentoring figures. I would characterize my experiences at Berkeley as overwhelmingly positive, but I also must emphasize that this is only one of many perspectives, with a unique combination of privileges and struggles which surely differs from person to person.
Over the years, after every semester/summer, I have attempted to succinctly capture the overarching “lesson” within a single word. This is, of course, extremely reductive, perhaps overly so at times, but I think that such a summarizing “term” can provide some useful context for further insights. For the purposes of actually writing down my experiences, it also yields a very convenient partition of this essay in some vaguely coherent fashion. Sometimes the summarizing term is academic, reflecting some scientific theme, and other times it is a more general lesson about how I interact with others and view the world that I live in.
I started my journey at Berkeley in the fall of 2016, unsure of what to expect.Continue reading
Over my two-week vacation before I returned to Berkeley for the summer, I read Leonard Susskind and George Hrabovsky’s The Theoretical Minimum: What You Need to Know to Start Doing Physics. This book was based on the first course in a series of courses called the Theoretical Minimum, taught by Leonard Susskind at Stanford targeted at curious older students who had, in their lives, fallen through the cracks of physics education but wanted to learn.
This book was focused on mechanics, but dived pretty rapidly into more advanced formulations of mechanics that I had never really learned in a class. Coincidentally, I’m scheduled to take that class next semester, so I wanted to dive in to get a brief taste of Lagrangian and Hamiltonian mechanics.
So, to start, I set out to simulate the squishy pendulum.
When I was younger, I would occasionally hear about higher math classes that one was able to take. To me, then a naïve high schooler, AP Calculus represented an attainable pinnacle of mathematical knowledge beyond which lie a plethora of weird maths to explore. I had heard of multivariable calculus, which sounded like more of the same with more letters, differential equations, which was just calculus with more tricky problems, and so on and so forth.
However one, linear algebra, seemed like a mystery. It’s name evoked, to me, the kinds of problems done in middle school where I was painstakingly asked to grind through systems of three equations to find , , and . Sure, I thought, maybe there’s a use for solving ever bigger systems of equations of ever increasing complexity with bigger and better techniques. But, if multivariable and diff-E.Q. were “more of the same,” jumping back to middle school lines and planes was definitely going be a bore.
Spoiler alert: It wasn’t, and, while related, linear algebra really isn’t about that stuff. It’s actually about a lot of other, cooler stuff, including really cool stuff like quantum mechanics.
Note: This is just a primer on linear algebra. I introduce the axioms, and then paint over the subject with a broad brush that isn’t meant to be comprehensive. Quantum mechanics is inseparable from linear algebra, so I try to get to the meat of linear algebra while not glossing over too much. At the same time, this obviously shouldn’t be taken as a substitute for a more rigorous treatment of linear algebra.