I had never heard of The Burzynski Clinic until today, when I read this blog post by Rhys Morgan.

You probably haven’t heard of a man named Stanislaw Burzynski. He offers a treatment called antineoplaston therapy, which he claims can treat cancer, in a centre called the Burzynski Clinic in Houston, Texas. That’s quite a claim, but the Nobel Prize Committee does not need to convene quite yet, because this treatment has been in non-randomised clinical trials since its discovery by Burzynski some 34 years ago. Moreover, no randomised controlled trials showing the effectiveness of antineoplaston therapy have been published in peer reviewed scientific literature.

It goes on to say that the clinic’s lawyer has been threatening Rhys with a libel lawsuit over some claims made in an earlier post about the ineffectiveness of the antineoplaston therapy.

Now, I don’t know any of the facts about the therapy, other than what I’ve read in those two posts. But assuming that the posts are accurate, I really want to see Rhys stick it to the man (in this case Burzynski and his lawyer, Marc Stephens) because it shows that being right beats being tough. When it …

Problem 12.9 in the infamous Jackson Classical Electrodynamics asks you to find (or prove) that magnetic field lines of the Earth are described by the equation

Your starting point is the equation for the magnetic field of a dipole,

Sure, you can look at a vector plot of the field, and join the arrows to make lines. This is the kind of thing they have us do in introductory E&M classes. But how do you do it mathematically? There are two ways that I know of:

1. Define some scalar function \(f(\vec{r})\) whose gradient is everywhere perpendicular to the magnetic field, by the condition \(\vec{B}\cdot\grad f = 0\), and use that condition to solve for \(\grad f\). This is useful because the level curves of a function (lines of constant \(f\)) are perpendicular to the gradient. So once you find what the gradient is, you can integrate it to find \(f(\vec{r})\), and get the level curves from that.
2. Or, just use the traditional “rise over run” definition of slope. Imagine a spherical polar coordinate grid …

A while ago, somebody posed an interesting problem on Physics Forums: how to evaluate the infinite sum

It’s not hard to start: convert it to

The first term is obviously equal to 1, and in the second term, the series \(\sum_{k=1}^{n}\frac{1}{k}\) is well-known under the name “harmonic numbers.” It’s easy to look up the behavior of this sum as \(n\to\infty\) and thereby determine the answer, but I’m not interested in the answer. I’m interested in the method that you could use if you didn’t have the world’s mathematical references at your fingertips.

A common way to evaluate a sum with large numbers of terms like this is to approximate it by an integral. You may know that the Riemann integral, which is the first definition of an integral that students in intro calculus classes usually learn, is nothing more than the infinite limit of …

One of the must-have necessities for any blogging or other web publishing software is the RSS (Really Simple Syndication) feed. RSS, or its younger and sexier sibling Atom, is the file format used by news aggregators, which give you a frequent listing of posts and stories published by your favorite blogs, newspapers, journals, whatever you want, without you having to actually go to their website. Usually the RSS feed is generated by some library of code where you construct your feed as an array of objects or data structures. Here's how you put together an RSS feed with PyRSS2Gen, for instance:

rss = PyRSS2Gen.RSS2(
    title = "Andrew's PyRSS2Gen feed",
    link = "http://www.dalkescientific.com/Python/PyRSS2Gen.html",
    description = "The latest news about PyRSS2Gen, a Python library for generating RSS2 feeds",

    lastBuildDate = datetime.datetime.now(),

    items = [
       PyRSS2Gen.RSSItem(
         title = "PyRSS2Gen-0.0 released",
         link = "http://www.dalkescientific.com/news/030906-PyRSS2Gen.html",
         description = "Dalke Scientific today announced PyRSS2Gen-0.0, a library for generating RSS feeds for Python.  ",
         guid = PyRSS2Gen.Guid("http://www.dalkescientific.com/news/030906-PyRSS2Gen.html"),
         pubDate = datetime.datetime(2003, 9, 6, 21, 31)),
       PyRSS2Gen.RSSItem(
         title = "Thoughts on RSS feeds for bioinformatics",
         link = "http://www.dalkescientific.com/writings/diary/archive/2003/09 …

Thanks to campaigns like last week’s American Censorship day, computer users around the United States (and beyond) have been sitting up and paying attention to two bills regarding online copyright infringement that are now working their way through Congress: SOPA and PROTECT-IP. There is a lot of hype about how the law represented by these bills would be a terrible affront to free speech, and it may or may not be right, but as usual when it comes to legal matters, many people don’t have the knowledge to judge for themselves. With this blog post and possibly others like it, I’m trying to get relevant information out there so we can all make more informed decisions.

(Full disclosure: I am personally opposed to the passage of SOPA/PROTECT-IP, but I’ve tried not to let that bias come through too strongly.)

A brief history of information exchange

Back in the days before internet use was so widespread, media redistribution was not a major problem. If you wanted to share a song or a video with someone, you had to physically lend them a tape, CD, or DVD. Yes, it was possible to make copies of media, but …

Some time ago I posted about the theoretical justification for exponential decay. In that post, I showed that you can quantify exponential decay with this equation:

where \(N(t)\) is the number of undecayed atoms at time \(t\) and \(\lambda\) is a constant representing the decay rate. If you plug in \(N(t) = \frac{1}{2}N(0)\), the condition for the half-life, you can find that

But physicists usually write the formula like this,

where \(\tau\) is called the time constant. We prefer this to using the decay rate because, as I wrote in Calculating Terminal Speed, it’s often best to write a physics question in terms of dimensionless ratios like \(\frac{t}{T}\), where \(T\) is some time characteristic of the physical system you’re studying. We could use the half-life for \(T\), but the time constant \(\tau\) is more appealing for a couple of reasons: it keeps that ugly factor of \(\ln 2\) out of the formula, and more importantly, \(\tau\) is physically meaningful because it’s the average lifetime of an individual atom …