I'm not a fan of how people talk about "first principles" as I think it just leads to lots of confusion. It's a phrase common in computer science that makes many other scientific communities cringe. First principles are things that cannot be reduced and you have to have very good justifications for these axioms. The reason the other scientific communities cringe is because either (most likely case) it's being used improperly and someone is about to demonstrate their nativity, or they know they're about to dive into a pedantic nightmare of nuances and they might never escape the rabbit holes that are about to follow.
In fact, I'd like to argue that you shouldn't learn things from first principles, at least in the beginning. Despite the article not being from first principles, it does illustrate some of the problems of first principles: they are pedantic. Everything stems from first principles so they have to be overly pedantic and precise. Errors compound so a small error in one's first principles becomes enormous by the time you look at what you're actually interested in. Worst of all, it is usually subtle, making it difficult to find and catch. This makes them a terrible place to begin, even when one already has expertise and is discussing with another expert. But it definitely should not be the starting place for an expert to teach a non-expert.
What makes it clear that the author isn't a physicist is that they don't appear to understand the underlying emergent phenomena[0]. It's probably a big part of why this post feels so disordered. All the phenomena they discussed are the same, but you need to keep digging deeper to find that (there's points where even physicists know they are the same but not how or why). It just feels like they are showing off their physics knowledge, but it is well below that which is found in an undergraduate physics degree[1]. This is why you shouldn't start at first principles, its simplicity is too complex. You'd need to start with subjects more complicated than QED. The rest derive out of whatever a grand unified theory is.
But as someone who's done a fair amount of physical based rendering, I'm just uncertain what this post has to do with it. I would highly recommend the book "Physically Based Rendering:
From Theory To Implementation" by Pharr, Jakob, and Humphreys that the author says the post is based on. It does a much better job at introducing the goals and focusing on getting the reader up to speed. In particular, they define how the goal of PBR is to make things indistinguishable from a real photograph, which is a subtle but important distinction from generating a real photograph.
That said, I still think there's nice things about this post and the author shouldn't feel ashamed. It looks like they put a lot of hard work in and there are some really nice animations. It's clear they learned a lot and many of the animations there are not as easy as they might appear. I'm being critical but I want them to know to keep it up, but that I think it needs refinement. Finding the voice of a series of posts can be quite hard and don't let stumbles in the beginning prevent you from continuing.
[0] Well that and a lack of discussion of higher order interference patterns because physicists love to show off {Hermite,Laguerre}-Gaussian mode simulations https://en.wikipedia.org/wiki/Gaussian_beam#Higher-order_mod...
[1] In a degree you end up "learning physics" multiple times. Each time a bit deeper. By the end of an undergraduate degree every physicist should end up feeling like they know nothing about physics.
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