I really enjoyed this, thanks! Do you think he uses theory in his songwriting, or is it a "bang things together until I get the sound I want" approach? I can't find any evidence that he was classically trained, but that doesn't mean he wasn't. I just write pop music, where interesting chord progressions are almost by definition not allowed, and any dissonance whatsoever is a no-no. I can cover some of the older Mars Volta songs on drums, though :).
Probably a mixture of both. I hadn't heard of him before this post but he sells a Theory Primer video on his website. Includes: Building Chords - Modes - Playing in Key - Intervals - Harmony You could always ask him through his website. This release features a comprehensive run-down of what I believe to be the 'need to know' of music theory. This primer comes with detailed Guitar Pro and PDF files of all material.
I composed without theory knowledge for a long time. I think there are two types of "banging things together". The first is when you don't have any expectations. You're playing random things and seeing what catches your attention. The second is when you have half an idea already or you want to add a layer. You can hear where you want it to go in your mind's ear, but you're not sure how that translates to actual music. So you end up mindlessly testing things and it can get really frustrating the longer the search for the sound you want goes on. You feel lost. In my experience, learning theory has helped the former by allowing me to add a catalyst to my noodling when absolute freedom isn't fruitful. And it's decreased the latter as I now know how my intuition translates into the craft. From being on /r/musictheory, this seems to be the case for most other composers too. So I reckon bhrgunatha is correct, it's a mixture. That's why it's best to look at music theory as just a collection of frameworks and techniques gleaned from analysing music. In that way, it becomes a toolbox to draw from when needed. If you see it as an actual system for composing, it can become a prison.
I think there's less incentive than ever to learn more than a dash of music theory. You can outsource it to software, grab any bits you like, and then learn to play them live, if you're into that. Arpeggiators have been around forever, of course. cue Baroque music There's an analogy to be made with designing timbre from scratch. Knowing what happens with you modulate the modulating modulator with phase-shifted LFO that varies in time... MMMMmmmm dubsteppppppmusic theory ... can become a prison
For sure, there are some impressive tools popping up nowadays. One I saw recently that I thought looked great was Scaler 2. I think it comes down to whether you value having that understanding for yourself. I feel it deepened my practice and also my connection with the music I love. But ultimately it doesn't matter if you know theory or not. A cool piece of music is a cool piece of music.