New post at Not About Apples.

What do you mean when you say two things are the same? One thing’s for sure, you don’t always mean the same thing. The mathematical idea in the background is called an “equivalence relation”.

Still digressing after all these years…

New post at Not About Apples.

What do you mean when you say two things are the same? One thing’s for sure, you don’t always mean the same thing. The mathematical idea in the background is called an “equivalence relation”.

New post at Not About Apples.

Some more examples of how “well-defined” is used and why that concept can be useful, both mathematical and not.

Permalink: “Well-Defined”: More Examples

Now, there are a lot of bumper stickers out there, funny, political, all kinds, and I enjoy looking at them when I’m driving. Every once in a while, I see once that makes me think, or gives me a good laugh, but a few years ago, I saw one that has taken up more of my personal processing time than any other. Because I have absolutely no idea what it could possibly mean. Actually, I had come to the conclusion that I must have read it wrong or made the whole thing up, at least until I saw the same bumper sticker just last week.

The bumper sticker: “Just because I’m an atheist doesn’t mean I don’t believe in God.”

So I’m thinking, “But it does, doesn’t it?”

New post at Not About Apples.

Why is it that mathematicians see themselves as cousin to poets? And vice versa?!

Permalink: Math and Poetry

New post at Not About Apples.

Another one of my attempts to explain a piece of mathematical jargon that really shouldn’t be specific to mathematicians. The word of the day: *well-defined*.

Permalink: Mathematician-speak: Well-defined

I delight in the full moon every month. And while, despite the large number of objects I own in a wolf motif, I have never literally howled at the moon, I do feel a surge of something when I notice a full moon in the sky. It’s primal.

I don’t consider myself a superstitious man (a whimsical one, surely, but that’s different), but it often seems that I am more better at what I do when the moon is bright. It could be a coincidence, it could be my imagination, it could be placebo effect. Or maybe some part of my mind is on a 28-day cycle of highs and lows, just as I know I am a faster reader in the evening and a faster typist in the morning. It doesn’t seem so hard to believe that there is a cycle at play. And if I know anything about how my mind works and where my creativity comes from, it is that I know very little about how my mind works or where my creativity comes from. So who am I to say?

As I see it, my duty is to to be as open as possible to inspiration and new ideas, and to make my mind a welcome place for sparks of ideas to start a fire, not to try to predict or understand the whimsy of the Muse.

Do I actually believe that there is a Muse for my mathematical ideas? Sometimes I do. The inimitable Ramanujan said that his astonishing (and astonishing really is an understatement) insights and formulas were revealed to him by a goddess in visions. If you know anything about Ramanujan, it’s as plausible a story as any.

In any case, the last three days have been good for my work; I’ve figured out how to confirm some of my hunches, and taken a chunk out of the next batch of questions I want to answer about number theory. It’s becoming clearer in my mind how the transition from my current whiteboard and Mathematica explorations into a handful of publishable papers is going to happen.

What I haven’t done much lately is update this blog. As the full moon winds down, it’s a good time to play a little bit of catch-up and vignette my way to a new blog post.