Status Update

I am still struggling with depression, but things are looking up at the moment. I have enrolled in a 6-8 week program in Cleveland, where I attend group therapy three hours a day, every weekday. I am also exercising an hour every day, and I have started meditating again. For the past week and a half, I have been feeling markedly better.

In other news, Betsy and I are watching Buffy the Vampire Slayer. Oh yeah!

Not sure yet when I’ll return to the blog, but it’s definitely coming. I haven’t given up yet. Thanks for your patience. :-)

Blog on hiatus

Not feeling well right now. Hopefully I’ll be back before too long.

Friday Link

Just this :-)

Starting abstract algebra

In school, math progresses more or less in a straight line: arithmetic, algebra, geometry, trigonometry, calculus. In college you may do some more advanced calculus, or a few other things like discrete math or differential equations, but that’s generally it.

But suppose you want to dive deeper. What comes after calculus?

I’m hardly an expert, but from what I can tell, modern mathematics – the stuff that real mathematicians work on – consists of three parts: analysis, topology, and abstract algebra.

I’ve started learning about abstract algebra.

In elementary algebra, you take numbers and add/subtract/multiply/divide them together. In abstract algebra, you take a step back. You say “Instead of numbers, let’s use any elements from a set,” and “Instead of adding/subtracting/multiplying/dividing, let’s do any operation that takes in two and spits out one.”

With those and a few other simple rules, you’re on your way.

The key insight here is that elementary algebra isn’t the only algebra, it’s just an algebra. There are others axiom-based systems that turn out to be just as good.

For instance, in matrix algebra, the things you operate on are matrices instead of just numbers. And multiplication is non-commutative (that is, AB doesn’t necessarily equal BA). How do we handle such a strange situation?

And it isn’t just matrices. Strange new algebras pop up everywhere you look, operating on anything you can think of. Rather than trying to figure out each one individually, abstract algebra asks: what can we say about the structure of mathematics in general?

I got this book from Amazon, and I’m working through it now. Good stuff so far.

What kind of math interests you?

Postmortem: In the Land of Invented Languages


Ever heard of a language called Esperanto? Hundreds of thousands of people speak it worldwide, yet it’s not the official language of any country. That’s because it’s a constructed language, something invented by Ludwig Zamenhof in 1887. He wanted an international auxiliary language, easy to learn, belonging to everybody, owned by nobody, to promote world peace.

Or perhaps you know about Lojban, a more recent language created to be unambiguous and grammatically precise.

Arika Okrent’s In the Land of Invented Languages is a whirlwind tour of these and many others, from Hildegard of Bingen’s Lingua Ignota in the twelfth century, down to Star Trek‘s Klingon in the modern day.

And it’s utterly fascinating.

Part of it is the sheer variety of languages themselves, each trying to fill a different niche in the vast sphere of human activity – like John Wilkins’ philosophical language, where the structure of each word describes the meaning of the word itself.

Part of it is the personalities involved – like Charles Bliss, who was so controlling and erratic that he made it almost impossible for anyone to actually use his “Blissymbols.” He demanded (and received) $160,000 from a center for disabled children as part of a settlement involving his language.

And a big part of it is Okrent herself. Her style is light, quick, and full of vivid detail, which makes her a delight to read. Even better, she leaps into her research, going to Klingon-speaking conventions to see firsthand what it’s all about. You couldn’t ask for a better guide.

If you’ve ever wondered about made-up languages, this is the book for you.

So flying snakes are a real thing

Chrysopelea, better known as the flying snake, is a real thing that actually exists. Technically it glides rather than flies – it can’t gain altitude – but it does in fact move through the air. The video above is legit.

So. How did I not know about these? How does one get through twenty-eight years of life without finding out about flying snakes?

Doesn’t that seem like something they should teach you in schools? First day of biology: Hey kids, there are snakes that can fly. You’d better believe that would’ve gotten my attention.

Perhaps, you argue, it’s irrelevant because they don’t live in the U.S. Even if I grant you that, people need to be warned before they travel to these places. Southern India, southern China, Sri Lanka, the Philippines, Vietnam, Cambodia, Laos, Indonesia. If you buy a ticket to any of these areas, it should come stamped in giant letters HELLO DO YOU KNOW THERE ARE FLYING SNAKES WHERE YOU ARE GOING.

People. I have been to the Philippines. I did not know about this.

It’s not that I’m even especially terrified. They’re only mildly venomous. They’re not going to hurt you. I get that. I’m just saying, that is some necessary, up-front information right there.

Flying. Snakes.

Tell your children!

Sick today