Take [the nerd] out to the ball game

My mother-in-law, my wife, my five-year-old twins, and I went to our first St. Paul Saints game last night. Cue the reminiscing and the tenuous connection to geocaching...

I made the varsity baseball team at my high school as a sophomore. That was a big deal at the time, but anyone who has played baseball knows that the young folks on the team get hazed -- carrying all the equipment, stupid nicknames, emotional and physical abuse, all that fun team-building stuff.

I hit a grand-slam home run in my first varsity at-bat, but it was a humiliating experience, because the seniors had nicknamed me "E=MC^2" and were chanting it on my trip around the bases -- I sprinted around to get it over with as quickly as possible. They were yelling "Look at that TRAJECTORY!" and "Calculate the INITIAL VELOCITY!"

Between then and my second at-bat, I wondered if it was really possible for me to hit a home run every time to the plate for my entire career. So the next time to the plate, I uppercut the first two pitches... 0-2. On the third pitch I hit a weak pop-up to the pitcher, and my coach at third base yelled, so that everyone could hear, "Jesus Christ, Bryan, you're not going to hit a home run every time!" The chanting resumed. MC^2! MC^2!

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When I was in college, our dream road trip was to visit all 26 (at that time) major league ball parks, and the list expanded to include all minor league ball parks. Now if that kind of road trip could be combined with geocaching...

GPS, linear algebra, and fractals in computer graphics

Fellow math guy Bunganator called to my attention this article about the linear algebra that is used by the Global Positioning System to determine location.

My puzzle cache Where's Yoda? is a simplified version of this -- think of the data from each guess in the Yoda game as the input from one satellite. Finding Yoda's location amounts to solving the system of equations that results from the information given by each guess.

The article Bunganator sent includes a reference to a book called Linear Algebra, Geodesy, and GPS by Gilbert Strang and Kai Borre. I'll have to check this book out -- I've wondered how to incorporate GPS topics into my courses (rather than the other way 'round... Gah!) -- but I note that the first 274 pages appear to be straight linear algebra that can be found in other books, including other Gilbert Strang books that I've taught out of before. I wonder why the publisher or the author felt the need to pad out this title with a introductory linear algebra treatment that is readily available elsewhere.

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I have a question for the computer people out there. I have a programmer friend who, in the context of 3D virtual environments, came across the term "2 1/2 dimensional space". This has a specific meaning in mathematics: the Hausdorff dimension of a set can be a non-integer when it has fractal properties. For example, a set resembling a shoreline could have a Hausdorff dimension between 1 and 2, or a set resembling the face of a mountain could have a Hausdorff dimension between 2 and 3.

I remember vaguely that there are algorithms involving fractals or randomization for realistically rendering natural features like these, but don't know much about them. Does anyone else? And, when people in 3D graphics use the term "2 1/2 dimensional", are they using it in an informal sense, or does Hausdorff dimension actually arise in the description of these rendering algorithms?

He won't rest in peace if he hears this composition!

You may be able to tell from my most recent post that I derive great pleasure when a cache log is more than a simple "TFTC". This morning, incrediblemagpie was not the only creative cache finder. sparkyfry found my cache Rest in peace, Jaco Pastorius, a puzzle cache for which the hint is embedded in a piece of music that I "wrote". sparkyfry made a video of himself playing that piece of music on the piano, and I have been laughing about it all day. Take seven seconds out of your day to experience cache coordinates set to music, and be on the lookout for a version on bass guitar: