Serious Security Flaw in Internet Explorer

Not that I have terribly many readers, but if anyone using IE happens to stumble across this post, you should immediately and without hesitation obtain another browser. It's probably a good idea under any circumstances, but a really terrible security flaw was recently discovered that could compromise your passwords and possibly allow other parties to "take control of your computer."

Good browsers include:

• Firefox (Windows, Mac, Linux; vast number of languages available, excellent adblocking add-on, high compatibility with sites designed for IE; open source)
  
• Safari (Windows, Mac; simple, lightweight, fast, made by Apple)
  
• Opera (Windows, Mac OSX, multiple Linux versions, Solaris, QNX, OS/2, FreeBSD, BeOS; highly customizable; proprietary)
  
• Chrome (Windows XP SP2 and Vista only; extremely minimalist, lightweight, made by Google; based on open source Chromium project)

You can also check out the Comparison of web browsers entry on Wikipedia. Most any browser other than IE and AOL will do fine.

If you use IE on a work computer and do not have software installation privileges, you can use OffByOne, which has a horrible GUI but can run from a floppy, CD, or thumb drive without installation. However, you'll want to alert your network administrator to the problem with IE; perhaps you could gently encourage him or her to install a less vulnerable browser for your workplace.

If you believe your information may already have been compromised, now would probably be a good time to change your passwords. I'm afraid I can't give any advice on the vague threat of a remote user taking control of your computer; personally, I would back up everything and re-format my hard drive.

This would also probably be a good place to recommend some safe browsing habits. Don't use IE, don't click on ads, and avoid all sites that offer illegal downloads, hacks, cracks, pirated software, nudity, gambling, or other activities that attract shady people in real life. If you must use torrents or peer-to-peer software, do it in Linux. I recommend Ubuntu.

Above all else, do not under any circumstances trust virus scanners or spyware detection programs to keep you safe. They will not. They will merely lull you into a false sense of security while evil little digital critters infest your system. The dirtiest systems I have ever come in contact with all had Norton or McAfee installed, updated, and running their "active protection" memory-hogging placebo programs. While I'm sure the big-name virus protection programs do something and I have occasionally known them to detect actual viruses and malware, they cannot and will not protect against irresponsible and dangerous Internet behavior. Again, if you must indulge in risky activities, install Linux.

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Fun with Math Software

One of the things I occasionally enjoy doing in my spare time, odd though it may sound, is playing with math software to make it create cool visuals. I've had a couple of results I've been particularly happy with, so I thought I'd share them with the world.

The first is an animated graphic of a particular concept in vector calculus. The idea is that you have a curve in space, and at any given point you can define three orthogonal vectors with respect to the curve. The first is tangent to the curve (it points along the curve); the second is the normal vector which points in the direction of greatest curvature; and the third is the binormal which is perpendicular to the first two. In terms of physics concepts, if you think of the space curve as the path along which an object is travelling, the tangent vector is in the direction of its velocity (and tangential acceleration), the normal vector is in the direction of its centripetal acceleration, and the binormal vector is, I suppose, just a convenient normal vector to identify the plane in which the object is travelling at a given instant. In this picture, the green vector is the tangent, blue is the normal, and red is the binormal.



The second animation I have for you is an illustration of what's called a parametric surface. The equation for this surface is rather ugly and complex, but the surface itself is quite beautiful. I have it rotating to give you a complete visual of it. This is an example of math-as-art.


Both of these were done in Maple, which is my personal preferred software for math-art. However, you can do similarly cool things in not only other proprietary software like Mathematica, but also with free (in all senses of the term) software like Maxima, although I don't know the extent to which any free software does animations.

The thing I like most about Maple is that you can talk to it almost entirely in standard math notation, with a few (relatively intuitive) text commands for things like plotting and animating. What I like least about it is that it's a horrendous memory hog and a bit unstable on your standard PC. However, my laptop runs it quite nicely on 64-bit Linux, despite having been entirely incapable of running it under Windows, so it's possible that it may simply have Windows issues.

I rather dislike Mathematica's interface, but there are people who swear by it. As far as Maxima, if you're the sort of person who finds Matlab and command-line Linux easy to deal with, then Maxima is the package for you.

Regardless, however, I do recommend playing with some 3-d graphing-capable software if you're currently a math student (or if you last took math back when slide rules were in vogue); the coolness factor of today's software is really high in the graphics department, and these programs can do some really amazing symbolic math work too.

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