Spiralling into control - A Program to Unwrap Ulam's Spiral

After a difficult study term, I had the privilege during the holidays to see plans from September come to fruition, thanks to the ingenuinty of one of my colleagues. Fascination with Ulam's Spiral, which launched my interest in exploring the properties of prime-generating polynomials and expansions of the Riemann zeta function, has taken me into the realm of computing.

Vision has become reality, as I now have all the class files correctly compiled in my computer and can, at any time, run the program. What I get is a GUI display of tiles that fill with numbers, as per the winding of Ulam's Spiral, with the added feature of black squares, representing tiles that the number sequence skips.

Playing with the spiral program is a bit like playing Angry Birds, if I can borrow my advisor's analogy. It lots of fun, and at least there's a chance that, by playing with it, you might find something useful. So now I'm playing a game I've dubbed "Prime Chasing", something that is a good way of giving my brain a break from editing.

That is just a game, of course. The real work is much more involved. Presently, my colleague is preoccupied with other work, but we have devised two stages of development of our program to systematically explore ranges of black block permutations and to relate these to the lengths of diagonal lines of primes. The algorithm is simple, but the coding takes a bit of time, a thing which neither of us has a the present.

This project is exciting for me as a student who has a deep interest in prime numbers and their properties. Taking these next two steps will allow me to explore some ideas I have tried to wade through algebraically, to no avail. It is my hypothesis that Ulam's Spiral, as a basis for a larger set of spirals formed by the permutations of skipping blocks, holds some deep answers about the pattern of the primes, and, possibly, to the Riemann Hypothesis. Though the mathematical scope of such analysis is far beyond me, it is my hope that generating such results and refining our project based on the initial set will provide data that will be useful to the community of mathematicians who endeavour to expand our understanding of what numbers are.

At the very least, I hope it is better than a game of Angry Birds.

Building the Foundations

Here I am at the end of an intense study term, and I'm diving under for a big feat: the hardest exam I've ever written, for the hardest course I've ever taken. Writing this post - long overdue - was one of my decided break activities in my planned 12-hour work day. (Day one of 5 :S)

Studying mathematics rigorously has really taught me a lot about myself, mostly about how I think (or fail to). If not for a deep love and fascination for the topic, I would have jumped ship long ago. I'm forever humbled by (and envious of) the prodigies whose natural aptitude lies in mathematical reasoning. Here comes me the writer trying to piece together the story that the beautiful logic makes, and it's quite a mess.

I've realized amidst this, though, that I am a writer at heart. As November passed and I revived my story-telling habits, I realized that, had I to chose one thing to give my life to, it would be writing.

Meanwhile, though, there's so much to learn in mathematics, and by that I don't mean theorems and proofs and calculation techniques. Learning how to organize my thoughts has been an important sort of "mental yoga", an often unpleasant experience of wrestling down faulty logic so that what is true and sound comes out on top. The best part of this: it's transfered to my writing, my daily life, and through it I feel I am growing as a person.

Alright. Break's over. The nice thing is when this is done - December 10th - I will be launching full-swing on the novel I've started. Boy, I can't wait. I aim to finish the manuscript (or at least get to 50,000 words) by January. But I must confess, after I reach my 5000 word goal for each day, I'll be doing some math problems. After all, I might be a writer at heart, but my love for math will never be far away. In fact, on this road I'm coming to know as my life, they make good companions.