I remember being so excited when I first found out about Wikipedia by the idea that I could add all of my copious bits of knowledge to it, making it better. That feeling lasted for about an hour, before I realized that there really wasn’t much that I knew that the lazyweb didn’t already know, usually with much more depth that I did.

Today, though I was able to add a little bit of my brain to the mix. I was looking at this guy’s weird contraption for tracing out parabolic volumes (for large solar cookers), but I had a little trouble figuring out why it worked.

Surprisingly, the Wikipedia article on parabolas was no help. Once I figured it out, though, I was able to make a minor adjustment to one of the diagrams there and add it. A good feeling ensued.

Details: The Instructable works on a weird mechanical contraption that relies on the principle illustrated in the diagram that I added:

“Parabolic curve showing arbitrary line (L), focus (F), and vertex (V). L is an arbitrary line perpendicular to the axis of symmetry and opposite the focus of the parabola from the vertex (i.e. farther from V than from F.) The length of any line F – Pn – Qn is the same. This is similar to saying that a parabola is an ellipse, but with one focal point at infinity.”

The wording is a little unwieldy; feel free to tighten it up!

I’ve been consuming TED talks at a fairly rapid pace for a year now, and they keep on coming. As I’ve been going along, I’ve been capturing brief notes on the ones that I’ve found interesting. Going forward, I’m going to post small batches here. This is mostly for my own reference, but maybe the internets will also find them useful.

Here are the first three (you can see all of them here):

Ron Eglash: African fractals, in buildings and braids

I rolled my eyes a couple times as he was introducing his topic, but as the talk went on, most of my skepticism was addressed, and then I was totally absorbed. He seems to have found many instances where fractal math was consciously used in African culture for very practical engineering and cultural purposes. He has also found that this conscious use of fractals is not present in other non-state societies. He finishes his talk by mentioning how these cultural uses can actually be used in the US to show African-American students that their heritage includes a rich mathematical history, as well.

Matthieu Ricard: Habits of happiness

A Quebecois molecular biologist-turned monk relates the basics of Buddhism, from a Westerner’s point of view. This talk is simple and straightforward, they way I like my explanations of Buddhism. There is a good balance here that represents my belief in mindfulness practice: part subjective experience, part science.

Amory Lovins: We must win the oil endgame

Author of the book Winning the Oil Endgame sees the path to an oil-import-free U.S. as a profitable, not a costly one. His ideas are comprehensive, including new materials for making cars lighter, “feebates” to change buying incentives per weight class of car (rather than between them), and an overall focus on efficiency. The latter one is interesting, as he makes those savings clear by pricing efficiency in terms of $/barrel of oil displaced. He is very glib with his free-market cheerleading, however, and explain very well why profit motives haven’t already pushed our industries to make these changes on their own. Some of his comments about the military wanting to defend America rather than oil pipelines in foreign countries are incredibly naive; it’s not our people on the ground who make policy, it’s the politicians who are financially bound to arms manufacturers.

Again, you can see all of the ted talk notes, here.

In December of 2000, Caltech and MIT performed a voting accuracy study, which calculated the “known error” rate for various kinds of voting processes. They didn’t assume any byzantine failures or malicious actors, no externalities such as roadblocks or disasters or suspiciously designed ballots. The study was simply an evaluation of the inherent faults of the vote casting and counting methods. The results showed that each method was accurate to between 1 and 2 percent, with punch cards the best, hand counted paper the worst, and e-voting at about the middle of the pack. Keep in mind that these are “known” errors, cases in which it was discovered to be certain that the vote cast was not correct. These are by definition a strict lower bound, so the real error rates are certainly higher… their exact value cannot be known.

A recent University of Washington study using these minimum criteria to examine the 2004 elections showed that the results of three Senate campaigns, one Gubernatorial election, and the presidential electors of three states were statistically useless. In other words, if you ran time backwards and held these elections again in the same exact circumstances, they would be just as likely to come out the other way.

The important point here is that falling inside the margin of error is not as simple as saying that the results are “possibly wrong.” It’s equivalent to saying that we don’t actually know what the result was. If you have a telescope that can only see objects at a certain distance at 1-meter resolution, should you be relied on to read the newspaper over my shoulder? Better analogy: would you let me (20/600 uncorrected vision) drive your car without my contact lenses?

Now take a look at the (still tabulating) results from some key referenda in tonight’s California special election:

73 N Minor’s Pregnancy 2,563,070 48.9 2,674,283

74 N Teacher Tenure 2,464,243 46.6 2,812,781

75 N Public Union Dues 2,574,991 48.8 2,695,427

These have spreads of 2.2 points, or +/- 1.1 from even, 6.8, or +/- 3.4, and 2.4, or +/- 1.2, respectively. If a scientist published these types of results from an experiment that used methods of the above error rate, they would be lucky to just have their data called inconclusive. What does that say about our voting process? Should we really be ammending our state constitution by these criteria?

Update: The final spreads ended up being a bit wider, but let’s not be fooled into thinking they are authoritative. “My side” won, but does that really mean anything? I maintain that the types of margins we see in these elections are roughly equivalent to a guess as to what the populace thinks at any given moment. The results are especially worthless when you consider the massive volatility in pre-election poll data, indicating the number of voters who voted not out of conviction, but something closer to confusion. This process does not work, and must be changed.

Obligatory-bright-side-comment: Congratulations to new Virginia governor Tim Kaine, whose victory is well beyond any statistical questioning.

In December 2004, two mathematicians from Bristol University constructed a crochet model of the Lorenz attractor, the canonical ‘chaotic’ system. They have offered a bottle of champagne to anyone who can match their achievement by following the pattern they published.

The bottle remains unclaimed.

[via infosthetics]

And, while we’re on the subject, I’d like to mention my favorite mathematical artist, Bathsheba Grossman.

Update 10/16/2005: Looks like there’s at least one professor who does this sort of thing on a regular basis.