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Calculus and Statistics

I'm personally a fan of calculus. I really enjoyed it in high school and college, both in theory (in most math classes) and in application (in physics). I tutored calculus for some time afterwords.

Still, Arthur Benjamin makes a pretty good point in this 3 minute video from TED.

Space Shuttle launch as seen from a plane

This is pretty darn cool. (Note: the audio here does contain some mild profanity, as the person holding the camera is rather blown away by what he sees. If that might bother you, then hit "mute" and watch it anyway.)

(Via 37signals.)

Pheonix Mars Lander

NASA and JPL have a lander en route to Mars. It launched last August and is due to reach Mars in just a few days.

When it approaches Mars, it will be traveling around 12,500 miles per hour. It has to slow down and land pretty quickly. JPL has a cool video describing this process of "Entry Descent Landing". (It's just a few minutes long.)

My favorite part: it will take about 10 minutes for a signal to get from Mars to Earth, while the whole Entry Descent Landing will take about 7 minutes. So there's to be basically no remote control during the process; by the time controllers on Earth get the signal that it's begun, Pheonix will have completed the whole thing. And will be safely on the Martian surface. Everybody hopes.

MathTrek: Spoil-Proofing Elections

The MathTrek blog from Science News has a brief article that provides a good quick overview of problems with election methods. It's called Spoil-Proofing Elections:

Complaints about the obscure Electoral College system are common, but the mathematicians' objection is even more basic. Presidential elections in the United States are decided using a variation of a method known as plurality voting: each person votes for one candidate, and the candidate with the most votes wins.

Seems like the obvious approach—but obvious doesn't always mean effective. "The plurality vote is pretty much the worst voting system there is," says Donald Saari, a mathematician at the University of California, Irvine.

One more interesting excerpt: "69 percent of the time, an election result can be changed by changing the voting rules." The problem is that it's not clear which set of rules produce a "true" result. They all produce results that reflect the voters' wishes as defined in some fashion. The argument is about which definition best serves the purpose of the election in the first place.


Happy New Year!!!

2008 = 251 * 8
2008 = 251 * 2 * 2 * 2

2008 = MMVIII (Many Mortals Valiantly Icing In Igloos)

Interesting moment: 3:04 am and 5 seconds on June 7th (03:04:05 06/07/08)

Duelity: Creation and Evolution animated

Jason Kottke links to a really interesting short animation (approx. 2 minutes).

Duelity is a split-screen movie with one half of the screen showing the six-day creation of the earth & man in scientific terms and the other half showing the Big Bang/evolution origin of the universe as it might have been written in the Bible. (Click on 'watch' then 'duelity' to get the full effect.) Nice use of infographics and illustration. (thx, slava)

It's really interesting to watch. I recommend watching one all the way through, then the other, then both together ("Creation", "Evolution", then "Duelity").


Explain Something Complicated

I was reminded this week of some videos I had seen a while ago by Common Craft. These guys make some really great (and short, usually around 2 minutes) videos in which they explain technological concepts in ways that almost anyone can understand. They use a format they call “Paperworks”, which consists of a mix of live-action and stop-motion done with paper and whiteboard.

They’ve made a few videos on their own, and they also make videos for other companies. I was reminded of them this week when I saw the video they made for Google Docs, coinciding with the addition of presentations to the service. Here’s the video:

Now this video is paid for by Google, so of course it has a marketing message behind it. Here’s another example, one which isn’t sponsored. This one explains the concept/technology/service of social bookmarking:

What I want to say is I really, really like what these guys are doing. (It’s a husband and wife team, as far as I can gather.) Coming up with such an easy to follow explanation of ideas that so many can find confusing or intimidating (including, at times, myself!) is impressive. And I think the “Paperworks” style that they use is fun to watch. I wonder if it’s efficient: does it take a lot of time and effort to shoot the video this way, or is it reasonably straightforward after some careful planning?

Either way, kudos to Common Craft. I can easily imagine making “Paperworks” videos explaining any number of otherwise abstract or intimidating topics: Calculus, Physics, Statistics, etc.

Feynman point

Yesterday I learned of the Feynman point. This is a point 762 digits into pi where there is a sequence of six 9's. It's pretty remarkable that a run of six consecutive repeating digits would appear so soon in what is essentially a string of random digits.

A new proof that the square root of 2 is irrational

This is a very cool, short, geometric proof that the square root of 2 cannot be rational number. The high level summary: If the square root of 2 were rational, it would be possible to construct a 45-45-90 triangle where the sides all have integer lengths. It can be proven that from any such triangle you can construct a smaller triangle with the same properties. This could go on forever, which would be impossible, since there is a lower bound to the positive integers.

A new proof that the square root of 2 is irrational

Found via Daring Fireball.


Happy New Year!!!

2007 = 223 * 9
2007 = 223 * 3 * 3

You can tell right away that 2007 must be evenly divisible by 9 because 2 + 0 + 0 + 7 = 9.

Interesting watch event to look for this year: 2:03 am and 4 seconds on May 6th (02:03:04 05/06/07)

Hope you have a fantastic new year.

Elections and voting systems

Forgive me if I've already chatted with you about this, but I find voting systems pretty interesting. Steve Krause has a nice write up of some of the most common, and some of the important differences. The takeaway is this: given a set of voter preferences, different voting systems can result in different outcomes.

For example, Steve talks about a system used in some local San Francisco elections: Ranked Choice Voting with Instant Runoff Voting:

  • You rank multiple candidates for an office, indicating your first choice, second choice, and so on.
  • If no candidate attains a majority of first-choice votes, the candidate with the fewest first-choice votes is eliminated.
  • Those who voted for the eliminated candidate have their second-choice votes added to the remaining candidates' totals.
  • If that reallocation does not create a majority for one candidate, the process continues until a majority is reached.

There was an article in the March 2004 issue of Scientific American by Partha Dasgupta and Eric Maskin that went into a more detailed analysis. They spoke to the question of "Which voting system is really the most fair?" by asking, in each case, how many of the voters have their preferences reflected in the outcome.

Just some food for thought. The important thing is to make the effort to get out and vote. I'll admit I don't make it to every single ballot date, but I do take it seriously and try not only to go but to show up with at least a basically informed opinion. If you weren't thinking of voting, please do. If you were planning on it, remind someone you know.

It's a bird! It's a plane! It's physics!

This weekend I listened to the podcast of NPR's Talk of the Nation: Science Friday. It included an interview with James Kakalios, a Professor of Physics and Astronomy at the University of Minnesota. Professor Kakalios has a new book coming out called "The Physics of Superheroes".

I can say from experience that he's not the first to use a superhero to try and make the application of introductory physics a little more interesting than most textbook examples. After all, Spiderman is just easier to picture than an "idealized free body". I don't know that I've seen anyone take it as far as it seems Professor Kakalios has.

Here is my favorite line of reasoning from the interview (I'm skipping over the math and ballparking the numbers, so forgive the generalizations).

Superman is able, we're told, to leap tall buildings in a single bound. The original Superman story says that Superman has powers far beyond those of mortal men due to his race coming from Krypton, a planet with greater gravity than earth, and not, as later explained, due to the yellow sun of Earth versus the red sun of Krypton. Early comics specified he could leap 1/8th of a mile into the air. An often-used introductory physics equation asks how fast he needs to leave the surface of the earth in order to leap that high. The answer is something like 140 mph.

An application of Newton's second law (along with a couple of other assumptions) tells us that his legs must be able to apply about 6000 lbs of force on the ground in order to launch him at that speed. Assuming, then, that if his legs are able to supply that force, they are probably genetically coded to support about half of that weight in normal standing weight. In other words, his weight on Krypton was probably around 3000 lbs. Since we know his weight on earth is about 220 lbs, we can determine that the gravitational force on Krypton is about 15 times that of earth.

Knowing the gravitational force of Krypton, it's possible to imagine a model of how the planet of Krypton is constructed. In order to get that much gravity at the surface, you pretty much have to have a planet with a neutron star at its core. And thus (this is my favorite part), it becomes apparent why the planet Krypton exploded. The forces and stresses caused by such a core would make an planet unstable, at best.

Sounds like it might be a fun read.

For more, try the NPR Science Friday audio (download and podcast) and the book on Amazon.