(Note: The two spherical illustrations from this weblog post are taken from a post which I wrote last year. Anyone who knows wheel theory should be able to at least vaguely see the concepts I'm playing with here. These two are a small corner, although perhaps the prettiest corner, of the pile of artifacts I've collected on this subject.)
It's true that the original discovery goes back to the late 1990s, and the first serious paper on this new branch of mathematics was in 2001, over two decades ago, and numerous others have written papers and discussed it since, but it's also true that it's a very obscure branch of mathematics with what seems to be only about a dozen people seriously working on it. Due to this obscurity, thus I only just now discovered these facts, just within the past few hours.
It's also true that I apparently went zooming right past a detailed description of the theory a couple years ago when I was reading a website on a related topic, otherwise the moment I'm experiencing now would have happened then. I see now that if I had clicked on a certain link on that page, I would have been jumping for joy then, as I am now. I'm jumping for joy.
I've been working out a number of details, and have blog posts and social media posts and math journal entries going back more than a decade on this subject, as I discovered new angles of it, slowly piecing it together to the point where I have been sincerely researching (as a non-mathematician) "how to write a legitimate paper for a real math journal" and preparing to write papers on this for the past year.
True, all true.
But also true, that I sincerely, as a complete amateur knowing literally nothing about mathematics when I started, have been developing all the central insights -- and some curious corollaries -- of what is properly called Wheel Theory. Having worked on this for years, it is my understanding that this new theory is deeper and broader than people realize, as it reaches out and touches the very foundations of math, if my insights continue to hold.
It is exhilirating to discover that other mathematicians have already worked out the core details, and figured out how it relates to group theory, and how it can be mapped onto the Riemann Sphere, and how it all fits together elegantly and so on. The labor of laying a foundation is already done, and all the insights I've been gathering for years, which have not yet been observed within Wheel Theory now have a home.
Granted, my approach has been that of an amateur, and I've made some wild conjectures, I've come at this from some crazy and crackpot angles at times, but I've definitely worked out enough of these elements to jump up and down like a happy Rumpelstiltskin and shout Wahoo! right now.
I have learned so much in the world of mathematics in order to work on this, and yet I feel like I only know a tiny corner. Mathematics, and the related field of logic, is so huge it goes on and on and on.
I have been baffled for years as to how I could be discovering these things that seemed to just make sense to me, being intuitively obvious, yet I could find no sign of them, or see only bits and pieces usually in the midst of other mathematical insights, often ones that seem quite remote from each other.
Just last week I found an important key while reading the appendix to a book by Roger Penrose, where he's talking about the circle of convergence, a region in complex space where divergent infinity and convergent infinity are right beside each other, solving a riddle I had been working on intuitively for several months, which I thought was pure nonsense because it made no sense... until there it was, in a book by someone who knows what he's talking about.
I'm writing this here to mark the moment. I have a lot of work to do, re-orienting my insights to the nomenclature of group theory and learning yet more math in order to be able to write about some of the things I see, but the hardest part is now already done, and, after more than a decade of being "homeless," realizing that I now have an intellectual "home" in a legit branch of math which is new enough that I actually have room to stretch wings, is awesome and humbling and very relieving, to say the least.
As I write, it's dawning on me that this present experience is extremely rare. If this were a normal-sized discovery, within a field that was well-established, that would be one thing. If this were what I thought it was for years: a unique discovery, that would be another. This is something in between those two extremes. The delightful combination of emotions that accompany this moment are like a bouquet of wildflowers, some beautiful, some scraggly, some awkward, some elegant, all together making something like a bottle of wine that has been sitting quietly in the darkness for a long time, awaiting a special day, and today's the day and we're now enjoying the wine, and soon the moment will pass, but for now... the wine.
Look at it this way: Imagine being a conspiracy theorist who discovers the ever-elusive but now irrefutable proof -- not only that his wild-haired theories are true, but that there's a whole group of people who believe the same thing, who are all accredited scientists in their fields.
I'm not a crackpot, after all. I've annoyed all my friends who know anything about mathematics. I've been incoherent and illogical too many times to count. I've learned how to mostly keep my math to myself as a consequence. Me and my weblog that nobody visits. I've learned to be content with this. What I'm experiencing now is what all crackpots dream will someday happen, but even better, more reasonably framed, because crackpots usually have far-out egos at the center of their World Domination Plans which drive everyone away, thus preventing them from laying a proper foundation for their far-out ideas, but look: that part's already done, so I get to skip to the next part, where all I need to do is politely add my contribution to what already exists... no that's not capturing the aspect of deep gratification, a sense of having accomplished something remarkable, like climbing a mountain that took a decade to climb, and now looking out over the other side of the mountain... seeing that the dream is achieved... yes, that's part of the experience, too... bringing me back to the wine metaphor.
I have felt similar exhiliration before, and will again: the joy of math discoveries is one of the finer feelings there is, as mathematicians know. But never have I experienced this with such comprehensive external confirmation.
I feel a little like Inigo Montoya at the end of the movie: "Is very strange. I have been in the revenge business so long, now that it's over, I don't know what to do with the rest of my life."
I'm sure I'll find something.