Accountability

I’m back in California now, which has been pretty fun. I did miss posting yesterday, mostly because it got late without me noticing and I got too tired to complete my habits. Right now, I went to a nearby place to work on some stuff, particularly because I still need to prepare for my interview.

Also, something that my mom pointed out to me is that a lot of my posts are beginning to revolve around the same ideas. This is probably true, but I think talking through my ideas every day, even if they do not change very much day to day, should help accelerate and deepen my line of thinking over time. I believe that investing the 45 minutes each day to write these posts is a worthy investment–compared to the time I waste on irrelevant things, 45 minutes to help keep me accountable and enhance my critical thinking is a good use of my life. Technically, this time could be spent on improving my technical STEM abilities, but I should first look to cut the time I waste rather than the time I spend writing these blogs.

Productive Thinking

when I was in the sixth grade, having just started learning about physics, my dad posited a simple yet intriguing question: “How do we know that the fundamental laws of physics have such nice exponents? As in, how do we know that F_gravity = GMm/R^2 and not GMm/R^1.999999?” This was a question that, at the time, stumped me, and recently resurfaced when I read the book “Seven Brief Lessons on Physics” by Carlos Rovelli.

In the book, Rovelli explains the genius of Einstein’s theory of relativity–the reason why it’s considered a masterpiece on the level of the Sistine Chapel is not simply due to its widespread revolutionary effect in the scientific realm, but mostly due to its shocking simplicity. Einstein’s genius lay not in discovering complex and abstracts ideas in physics, but rather in his historically unparalleled ability to draw out the fundamental laws and ideas behind these effects.

The answer to my father’s question regarding formulas such as “F=ma” is rather straightforward. Humans have defined it in such a way–Newton decided that Force, the product of mass and acceleration, was a useful concept for investigating how the world worked. This is true for many basic physics concepts/formulas.

The second part of the answer lies in the effect of superposition–when we have two physical tangibles at once, they obey the mathematical laws of superposition. That’s just a fancy way of saying that if the effect of having A and B is the same as the addition of effect A and effect B (don’t take this literally, but that’s the general idea). Through this and taking derivatives and the like, we get our nice round exponents in the vast majority of our formulas. To summarize, the reason why we have nice formulas is because we define very straightforward equations for fundamental physical ideas and let math do the rest.

Where the line begins to blur is for fundamental laws–these concepts are not ideas that we humans have explicitly defined. How did the fundamental law of gravity just so cleverly line up, or, for that matter, Maxwell’s equations or Einstein’s theory of relativity?

One of my good friends at Columbia, Leo, studied physics like I did throughout high school. He is planning to pursue a PhD in physics while staying educated in Computer Science. In contrast, I’ve switched to planning to pursue a PhD in Computer Science while staying educated in Physics. The ways we think, even after just a year, have already fundamentally shifted away from each other (more on this topic possibly in the future).

Specifically relevant to the topic at hand, Leo talked to me about how he realized that elegant code design and the laws of physics are not unlike each other at all. In programming, the greatest coders spend a lot of time thinking out about how their code will ultimately pan out–it has to be designed in a way that’s easily scalable, very legible, and leads to as few bug conflicts as possible.

In physics, the legends such as Maxwell, Planck, Einstein, Newton have done the exact same over a much greater time. The “API” of physics has been built in such a way that when we find new fundamental laws like Maxwell’s equations or Einstein’s relativity, it is easily and elegantly added to the spectrum of physics knowledge. These additions are more than hard–if you look at the years in between these major physics breakthroughs, one would be lucky if less than 100 years pass in between each one.

In the world of physics today, physicists are attempting to solve something called the “Standard Model.” It is a theory that’s been painstakingly pieced together by the likes of Richard Feynman, and, as it stands today, checks out for nearly every experiment that people throw at it. New theories are proposed here and there, but they are debunked relatively quickly–in contrast, the Standard Model still stands.

Now, you might be thinking, what’s the issue? The Standard Model is actually an ugly mess of a theory–its programming analogy would be a hackathon project that you’ve added random, hacked-together lines of code to every time you found a bug. Many physicists are unsatisfied with how it is as it lacks an elegance that’s been true for every single physics law that’s come up to this point. This dissatisfaction is really cool to me–it exemplifies the human tendency to be unhappy with imperfection, and this drives societal progress.

The Standard Model problem is unlikely to be solved anytime soon–maybe I’d see it in my lifetime, but again, there’s no guarantee. It takes luck and time as researchers across the world rack their brains for every possible solution until some lucky genius chances upon the correct idea. This is, despite the fact that I love physics, the reason why I’m choosing to pursue CS over physics. I feel uneasy about dedicating my life to a wild goose chase, but at the same time, I have the utmost respect for those in academia who are choosing to do so. If everyone in history was as selfish as I was, we’d have no Einstein, Feynman, or Maxwell.

What I do take away from this is that there are a lot of parallels between my goals in CS and my knowledge of other fields. I shouldn’t limit myself to the pursuit of a singular goal when I have genuine passions that I can pursue elsewhere–as long as I keep an open mind, I can develop a truly unique way of thinking that combines elements from all of my favorite fields. This is true for anyone–your mind is your own, your experiences are different from others, and you may be surprised by how your thinking can add to those of others.