The origin of this site can be attributed to the widespread social phenomenon of people who are stuck at home engaging in personal projects during the COVID-19 pandemic. Luckily I had the privilege of being one of those people trapped in [their own personal spaceship orbiting earth](https://www.youtube.com/watch?v=snAhsXyO3Ck) during the global pandemic. This site was built to benefit _me_ by helping me create order in the midst of chaos. The best I can hope for is that my time does not go to waste and that it helps at least one other person. This is structured in a way some may refer to as a [digital garden,](https://www.technologyreview.com/2020/09/03/1007716/digital-gardens-let-you-cultivate-your-own-little-bit-of-the-internet/) but all that means is that this is a public notebook. # So what is this website becoming? This is in exercise in taking notes, but also an exercise in presenting information. As such, even if no one else reads these notes, I hope I will continually use this site as a reference for years to come. This is a personal wiki where I apply organizational and writing techniques that I find useful in aiding my own memory for things I've encountered in the past and it is also a place where I develop my own voice for explaining highly technical topics. A day doesn't go by where I'm not expanding this site or tweaking it. I believe that by optimizing how each part of this site is written and how each part is linked to other parts, that this could become what I'd consider a problem solving [engine.](Thoughts%20on%20What%20this%20Site%20is.md#The%20importance%20of%20seeing%20underlying%20mechanisms) Such an engine would allow someone or something to quickly mine for helpful bits of information in one place while also minimizing the barrier of entry for someone who might be less experienced with the type of content on here. In practice, what this also means is that such an engine is able to also generate new problems and questions I may not have anticipated, which is a feature of any properly implemented [_Zettelkasten_.](Knowledge%20Management.md#A%20basic%20overview%20of%20_Zettel_%20and%20_Zettelkasten_) In addition, I want to slowly begin building a bibliography of academic sources and summaries - both past seminal papers and current research. However, for now my focus is on ideas as they've already been distilled in textbooks and monographs. This will never be finished and it will never even appear finished no matter how huge I can make it. This is simply because each new note will create some number of branching notes, and, as I've come to realize, the topics I'm covering are massive. Some vague sense of the scope of topics in physics I want to cover, excluding original research, can be gained from obtaining a copy of [Landau and Lifschitz's 10 volume course on theoretical physics](https://en.wikipedia.org/wiki/Course_of_Theoretical_Physics). It's important also to remember that the material that gets distilled into textbooks is only a tiny fraction of what gets published! Naturally, I'm not the only individual looking into different ways to curate knowledge online. Links and my commentary on similar websites can be found [here.](Similar%20Websites.md) ## Motivation In the following sections I elaborate on my motivation in a series of short essays. ### Solving problems more efficiently The main problem I've identified in my learning is an inefficiency in the collection and retention of _insights._ That is, bits of information needed to solve problems. One way this becomes apparent is in finding that the harder a problem gets, the more time I have to spend sometimes looking through multiple textbooks for bits of information that might be helpful. Occasionally I would have an obscene number of tabs open to different lecture notes, papers and Wikipedia pages. In addition, flipping between multiple notebooks from courses I may have taken years ago was becoming difficult to manage. I would also find myself having to constantly review the same topics periodically over and over again, just in different ways and with sprinkles of more advanced insights added. Having indexed and searchable notes seemed like an obvious step to remove this friction in my study and review process. By following a [networked approach](Knowledge%20Management.md), I can better keep track of the insights I've found (rather than deal with multiple sets of notes that cover the same damn topic but in slightly different ways) as well as hopefully generate new insights through connections that may not have been obvious if laid out in a long treatise on a particular topic or in sets of bullet points I have to flip through in a notebook. ### The importance of seeing underlying mechanisms An analogy to describe the experience of studying and doing physics is to think of yourself as a pilot in an absurdly complicated cockpit that interfaces with an engine (and I guess integrated with this engine are its on-board computers, breaking systems, gyroscopes, reaction control systems... ). The equations and tools in physics are the controls of the cockpit, proofs and pure mathematical definitions are the engine (and all the other systems that are 'under the hood'), and as a physicist you are the pilot driving through the space of all possibility. In going through school or building some experiments one could very well learn to pilot this vehicle pretty well without needing to understand how the engine works. In doing so you learn how a bunch of mathematical relations relate to each other and gain a fluency based on intuition. However human intuition is limited - it can be a bit squishy. Relying on hunches and heuristics that reflect how the vehicle "feels" when you pilot it may be enough in many situations, but fails when pushing new limits. In building a system in which I can click through from a physics topic down to an abstract mathematical topic, I hope to build that engine below the cockpit. I have the sense that being able to see how the engine connects to different parts of the cockpit, I can maybe solve problems more quickly and grasp why certain relations are so in systematic ways that don't rely on the squishy nature of human intuition. In doing so, I may be able to work more effectively at the cutting edge of physical science. ### The utility of public facing notes Countless times I've come to a realization where I come to some new insight and I just end up wondering why no one explained this or that in a particular way in the first place. Of course, hindsight is 20-20, and certain insights are unique to the individual and possibly not useful to anyone but myself. However, the frustration I feel when I wonder why I had to figure out something I could've had explained to me right from the beginning is what motivates me to share what I know in order to maybe help someone else in the same situation. By learning, taking notes, and presenting what I know publicly I also open myself up to feedback and the corrections and the potential to learn something new by simply having the right person stumble upon what I have. ### "And thus by combining equations 3.5.4 with 3.5.6, we obtain expression 4.1.5" This sort of thing doesn't need to happen when you have hyperlinks. You can also add hyperlinks to pdfs, but many people don't do that either, and you still have to scroll back to where you were reading before anyway. I have a lot of hyperlinks here though, and every page you open stays open. --- _This is one of several blog-post style pages that's not part of the [indexed notes](Welcome%20to%20The%20Quantum%20Well!.md#Indices) that constitute what I consider to be the core content to this site._