I love xtcd.
I spend a lot of time thinking about chemistry and physics. I have had lots and lots of school and lab time, and I'm lucky to do science for a living.
But there are lots of things that I still find mysterious and weird. Magnets and gyroscope do things that seem completely magical to me. Yes, I've done the math. I barely apprehend the fact that conservation of angular momentum stems from the rotational symmetry of space, and I have worked through the basic relativity to see that magnetism is sort of a consequence of this. I know lanthanides are contracted due to relativistic effects.
Somehow, a magnet rotating downtown makes my lights shine and my computer run. Yes, yes, magnetic induction, Maxwell's equations. Very nice. So why? Why do the electrons in my lamp give a shit what the big magnet downtown is doing? Knowing the math is not the same as knowing the reason. It's deep, and mysterious, and yet so ubiquitous that it is easy to ignore. My lamp ignores the movements of paired electrons. But not those that are unpaired and aligned. I am happy to use electricity, and I feel especially fortunate to have been schooled in physics as an undergraduate. But I am still not satisfied. I don't care if the universe has 3 dimensions or 21. I want to really, really know why my gyroscope doesn't fall over, and why magnets stick to my refrigerator. So I keep poking at physics and mathematics long after my mental prime, hoping I'll get it someday.
Lately I've been playing around with symmetry and Lie (pronounced 'Lee') groups. Symmetry has deep connections with physics, as I alluded to above. Chemists get just a little taste of symmetry and group theory, when they learn how to use point groups to predict the bonding and spectral characteristics of molecules, usually in an inorganic chemistry course. The presentation is usually abysmal, with no foundational theory, and very little motivation. You learn to 'do' group theory without really understanding it. In fairness, it is usually shoehorned into an already filled-to-the-brim survey of all the chemistry not covered in organic, which is, by virtue of the peculiar properties of carbon, pretty unique. If you know only organic chemistry, you still know a lot of what is done in the chemical world.
What I am fiddling with now has little direct connection to chemistry, or at least not that I am able to see. I am looking at it as more of a means of retaining and rebuilding my abstract mathematical skills (since I have forgotten a lot of the analysis and topology I once knew.) What I am interested in doing is tying together a functioning understanding some of the more modern methods of mechanics and field theories (which tend to center a lot on differential geometry). At some level, deep topological symmetry and fields reconnect with statistical mechanics and hence condensed matter physics and chemistry, but I am not sure I'll ever get good enough to see this clearly. I'll be happy to know some of the basic ideas. Every time I've put in serious effort to understand stuff over my head, I get at least something that helps me understand more prosaic stuff, like chemistry...