Category: Math

Ballistic Monte Carlo Methods

This is a paragraph I never thought I’d see in the academic literature:

“[W]e advocate the use of ballistic-assisted (i.e. projectile-based) random sampling methods because they are both easily accessible and parallelizable. In particular, shotgun-assisted random sampling seems very suitable becaues of the presumed abundance of shotguns in cataclysmic times and the speed at which they can generate samples.”

– Vincent Dumoulin, F?lix Thouin – “A Ballistic Monte Carlo Approximation of ?“

Awesome. That’d make for an amazing grant application.
See here for a summary article that explains things for non-mathematicians.
Edit: Somehow I borked the initial post by forgetting the title and screwing up a link. I’ve now corrected these errors. If you’re still seeing those errors in your feed reader, please refresh the feed.

Useful Math Site

It’s been a while since I’ve written about science here.
Recently, I’ve had need to exchange rather complicated math formulas with someone via email.
Sending formulas like
[hat{x}hat{p},frac{hat{p}^2}{2m}]=[hat{x},hat{p}]frac{hat{p}^2}{2m}+ frac{hat{p}^2}{2m}[hat{x},hat{p}]
is difficult to do clearly via email, as there’s no real means of formatting one’s text with math markup.
Fortunately, there’s LaTeX, an excellent typesetting system that is the de facto standard for marking up documents containing math. I hear it’s also common in the publishing industry, but have no personal knowledge of that industry.
For a long message, it’s probably easier to create a LaTeX document and attach it to the email, but my messages are often less than a page, and that is a bit of a hassle. Sending the raw LaTeX markup via email would also be unsuitable. That assumes the other person (a) has the software installed to read it, and (b) the time to copy-paste the code into their program and render it.
Similar problems exist for computer programmers, and the pastebin service exists as a highly effective way of exchanging programming code with other users. Surely there’s a similar thing for math and science folks, right?
Turns out there is: the Mathbin site allows one to enter text marked up with LaTeX and display it to others without any installed software. Very handy.

Pet Peeve of the Day: Exponents

How often do you see people using the words “exponentially greater” to me “very much greater”?
Pretty often.
Of course, it’s almost always used incorrectly by the mainstream press and general public, and this irritates me greatly.
Just like how there’s a clear meaning for words like “clip” and “magazine” (and they don’t mean the same thing), there’s a very clear meaning in math and science for “exponent” and “exponential growth“, and they don’t mean “very fast”, “very large”, or anything of that nature.
Don’t get me wrong, for large exponents, exponential functions increase extremely rapidly. But one can also have negative exponents (resulting in “exponential decay”, which is used to model things like radioactive decay), or very small positive exponents which result in extremely slow growth and long e-folding times.
In short: unless one intends to describe the actual expoential growth or decay of a certain function, please refrain from describing very large things as being “exponentially greater” than some other reference point. It makes you look almost as tardful as using “decimated” (to reduce by one out of every ten) to mean “utterly destroyed.”

I Was Told There’d Be No Math

I bet you’d never hear this on a gunny blog, but it has to be said:
The Fundamental Theorem of Calculus is amazing.
It may seem incomprehensible to those who haven’t seen it, but those who have will appreciate the Theorem’s simplicity, its power, and its mind-blowing elegance. As much as a math formula can be, the Fundamental Theorem of Calculus is sexy*.
Back when I took integral calculus, these properties were not evident to me. It was simply a formula to be memorized and employed to solve equations. Tonight, after about six hours of solving problem after problem with it, I had an epiphany and sat in stunned amazement for several minutes.
Probably 99% of the world’s population will never need to use calculus, and most of those who do use it won’t really appreciate its beauty. Those of us who do lead very interesting (and often very weird) lives.
* Thank goodness I’m dating a geeky math teacher who understands me and my quirks. Fortunately, she doesn’t get jealous when I think that formulas are sexy. She also thinks I look cute whilst wearing a lab coat. Go figure.