You know what?

It doesn't seem like there's any good way to handle armchair "philosophers" who think they have something deep to say about the idea of certainty. "See, the thing is, you can't actually know anything for sure! I mean, like, what if we're all just brains in vats?" The only compelling argument I see for this point proceeds by example: The claim is that nobody can truly know anything whatsoever. Anybody who can in all sincerity make this claim must know very little -- perhaps little enough to serve as supporting evidence.

Joking aside, this is one of the silliest ideas out there. Those who contract it generally do so within a year of their first serious exposure to the great philosophers, in that honeymoon phase where everything makes sense and the ideas of "discarding all assumptions" and "questioning everything" still seem novel. Socrates and Descartes are particularly severe offenders, as brief or unconsidered treatments of their works can easily give the impression that they advocated this total uncertainty. What, more precisely, is this misconstrued idea, though?

It's the idea that we just can't know anything for real, man. You know? Like, think about it -- everything we know comes from observing the world, via our senses, right, and how can we trust our senses? What if we all see, like, different colors? What if two plus two doesn't always equal four? What if it could equal five, but we don't believe that because we've never seen it? Or because we can't see it? Would we even know how to count if we were all blind? I, like... I dunno, dude. I dunno. Whoa. We don't even know that. We don't know anything. Not really.

Symbolic Computational Geometry in Python: Heron's Formula

Floating point numbers suck. Sometimes they're the best we've got, but they still suck. Floating point numbers are to math as Physics 101 lab measurements are to the laws of physics: you get basically what you expect, but with a margin of error tacked on. Sometimes that's okay. Sometimes it's not. But what choice do we have? I'm so glad you asked, because it turns out we have plenty.

But before we get into that, let's convince ourselves that we have a problem to solve. Luckily, this is really easy. Suppose we want to find out, for some terribly important reason, the area of the triangle with vertices at (3,4), (7,10), and (11, 161). We don't get pen and paper -- in fact, the only tool at our disposal is a Python shell. If we know some geometry, then our naive approach might go something like this:

Cheat Sheet: Windowing in Screen & Vim

As a lazy computer science student, I find myself working on programs over SSH a lot. This tends to pose some challenges. Unless you want to mess around with -X and -Y flags, all you get is one terminal to do all your work in. Having to work in this environment has taught me one lesson: When all you have is a terminal, everything looks like a window manager. Or something. Anyway. There are lots of ways to split up a terminal session, and this post covers some common commands involved.

Cracking General Substitution Ciphers

As some of you have requested, today we'll be talking about paper-and-pencil cryptography and how we can use computers to poke it full of holes!

We're going to start with some background on basic (pre-digital) cryptography. Then, we're going to describe the specific cipher we're attacking here, along with some standard paper-and-pencil approaches to cracking it. Thirdly, we'll discuss one algorithmic approach powered by a dictionary file. Then, we'll look at some Python scripts implementing the discussed ideas. Two different scripts will be provided: A bare-bones one written to be simple to understand, and a batteries-included fancy one which elegantly implements the main logic using coroutines.

By the end of this post, we'll know what this script is doing and why it works.