Positive thoughts to combat the usually-negative tone of the past few years and to set an upbeat plan of action for the next few:

I think my “dark year” may be over. I’m beginning to realize now that there is only one person who can suppress me: me. Perhaps my failure to obtain good training has made my ordeal more difficult, but even at Temple, my ideas are beginning to blossom… and I’m finally being given a chance to pursue them. As for the difficulty of obtaining the training I wanted, I am not responsible for others, and I am not going to be held responsible for the poor decisions others have made. My training is what it is. I am doing what I can. Let society gain returns only to the extent it has invested; I will no longer overwork to compensate for my lack of knowledge. If I live long enough, I have too much talent and too many ideas to be suppressed forever; that is sufficient.

My classwork is finished. I obtained an A- in my last required traditional class, which is sufficient to exempt me from the qualifier altogether. This means all I need to do is pass the preliminary exams (on my research, which I can do now, much less in six months) and defend my dissertation. I’m going to continue on with my dissertation while I wait for feedback, since waiting indefinitely for feedback while doing nothing is a bad idea for making progress.

My idea for extending semidefinite embedding is implemented and working. I haven’t compared the speed or memory requirements, but I imagine it will consume significantly less memory than traditional SDE. After doing the experiments, I’ll put a paper together and it will go off to KDD. It’s completely novel, so if it is rejected, that is their problem; I will no longer assume responsibility for the outcome of others’ decisions. Let it be on their heads; I publish to spread my ideas, not for the fame! Manifold learning is quite an interesting field of research, since, as I mentioned before, it models the cognitive process of abstraction very well. I’m also learning that many things in data mining are guess-and-checks (they like to call it “optimization”, but that’s really what it is – guess, check, move, repeat) on MSE, which is, to put it bluntly, stupid. Gradient descent is probably the optimal stepwise procedure, since the gradient vector points in the direction of maximum ascent by definition, but it’s not optimal in the sense of total convergence: we can converge much faster if we can extrapolate parts of the global MSE curve from local information, which we most certainly can do, especially in the case of polynomials (we know EXACTLY how many roots it will have, we know whether the function is odd or even, and yet we don’t use this information!) We might be wrong, but the error should obey probabilistic bounds, and convergence should still be easy to achieve. I guess I’ll need to figure the error bounds out, even though I hate doing that sort of work.

Anyway, this is a whole class of things to pursue.

The Softee Variations are complete – all seven and a half minutes of them. The theme is something most people would consider trivial, but it really is an excellent theme to write variations to – as evidenced by the fact that I derived a second theme from it, set it at counterpoint with the first (I still have no counterpoint training, but I’ve learned to let my intuition guide me), and still added a third voice in without a problem – and worked with both of these themes for over 7 minutes, making this my longest piece yet. The second theme is simple and translates well into a minor key, after which I overlay a third theme, again loosely based on the first. My musical style is rapidly evolving in the direction I wish it to go – I’m blending the classical theory I’ve learned, the theory I’ve acknowledged I will never learn and thus intuit, and my melodic and fairly modern style. The result is something completely unique. I continue to experiment with orchestration in “Water” and “Painting a Sunrise”, and I am also finding myself establishing my own unique orchestral arrangement, not for the sake of changing things, but because I desire a precise and unique sound from my music. My music will initially be overlooked, because it’s a niche and music is an art, but my scientific work will eventually drive people to examine my artistic work as well if it’s good enough. Since I write music for the sake of the music itself (it compels me to write it down before it is lost forever), I’ll be ready when this happens.

Lower on the list is “Cap”, the capability-oriented programming language. I know how the language syntax will look, but I haven’t figured out how I’m going to compile it yet. I’ve never had the opportunity to take a class in compilers or programming language theory, so I may need to do some reading first. Maybe no one will use it. That’s fine – it models my cognitive processes well and is much more versatile than OO, so these people will simply be left in the dust. I started programming very early and by now I’m very good at it, but I still work in a paradigm that does not model my own cognitive paradigm, which is inhibitory. Once thought and expression are meshed, I’m going to fly.

Following these things (that is, once I have my Ph. D.), I intend to devote myself to my Polymath idea. The job offers continue to stream in, freeing me from the worries of an uncertain financial future and ensuring that I will indeed have the time and resources to devote to such an undertaking. Three students and one faculty member have already praised the idea and given helpful comments where applicable, but I should attempt to organize a larger community around it. It shouldn’t be hard to do so – you’ll be surprised at how many people the current educational system shortchanges simply because they’re capable of handling much, much more than what schools give them. They want to learn in multiple fields – they want to become polymaths. But they can’t. Think of all of the interdisciplinary challenges – we could solve these much more efficiently if we trained individual polymaths instead of devoting teams of specialized experts to them! For example, if I could gain access to laboratory equipment and some better biological training, my knowledge of computational modeling and machine learning would make me excellent at, say, devising cancer treatments (those following the blog have probably noted that I’ve already devised a few, but lack resources to test or refine them). Of course, once given the prerequisite knowledge, insight is universal.

Mathematically, I’m becoming very powerful. Restlessly so, in fact – like having a lot of bottled up energy screaming for release. I need to prove something with all of the new mathematical knowledge I have acquired, so I’m thinking of resuming my divisor function research. Legendre’s conjecture also looks like an interesting question to pursue. The partial failure of my previous approach (what I presented in my divisor function research was actually an intermediate result, not what I set out to prove) was due to a reluctance to use higher, more abstract levels of mathematics. I know better now.

I’ve acknowledged I will never be a particularly excellent pianist. I can perhaps do anything that requires mental effort, but this restriction is physical. I simply cannot compel my hands to move quickly or accurately enough to become an excellent pianist, nor am I sure all of the practice time I would spend attempting would be put to good use. I’ll continue practicing about one hour a day just to steadily increase my proficiency and to maintain my position ahead of everyone else at the recitals.

This is the end of my Dark Year. It’s the beginning of the Second Ascent.