Wednesday, October 26, 2005

Everything and Nothing

Speaking of everything, Wikipedia has been experiencing some sour grapes as a result of rampant trolling and widespread apathy. Of course, their philosophy is still appealing to the anti-corporate vein that runs in several folks.

As a former employee of an ISP, I've always had a soft spot for UserFriendly. So, here's Illiad's jab at the unspoken contractual obligations of dating. Sorry, I'm not crazy enough to try to come up with any personal references to either confirm or deny the cartoon's allegations.

If you're interested in more academic pursuits, here's the Flash gallery of physics animations. Or, you could burn some time in a way that me and the father of BitTorrent have in common -- Sudoku. The nine-by-nine grid of digits is both fun and addictive. Apparently, it's not quite as addictive as EverCrack; I've never played six games at once. If you want to get outside and move, you can still go high-tech with the official Adidas microchip-enabled soccer ball...

Friday, October 21, 2005

Paranoia Express

In case a safe room doesn't give you enough peace of mind, you can also equip your bedroom with the Quantum Sleeper (patent pending). This monster cocoon allows you to encase yourself, and a like-minded paranoiac who is willing to share your bed, in the finest available polycarbonate. The list of features shouldn't be missed...

If you have more dollars than sense, you may also want to put these hide-a-doors on your wishlist. These make me laugh; every installed door that is pictured on their website is 200x more obvious than any secret door in any first-person shooter. Even the secret doors in the original Wolfenstein 3-D (e.g. push the Hitler portrait to get the machine gun) were harder to spot than these are.

Of course, if you're really this paranoid, maybe you should just stay home and watch the movie "Panic Room" -- don't worry, you don't have to leave the house to get it... You could always add a DVD player to the list of essentials for your bomb shelter.

Thursday, October 13, 2005

Great Gallonage

Wired's Gear Factor has a post about Gen-Ryu, one of several prototype 2-wheeled vehicles that Yamaha will be showing at the 39th Tokyo Motor Show later this month. Many of the prototypes are electric vehicles or hybrids, and there's even a fuel cell scooter. Unfortunately, there are no specs available at this time.

Monday, October 10, 2005

DARPA Grand Challenge

The DARPA Grand Challenge has been successfully completed by a few teams, and was won by Stanley, the entry from Stanford University. Carnegie Mellon took 2nd and 3rd place in the 131.6-mile off-road race for autonomous robotic vehicles. Last year, the best entry only managed to travel 7.36 miles. What, you may ask, was the biggest difference between last year and this year? Three words: Corporate cash infusion. The technology didn't improve significantly, it simply became more accessible to the teams.
The prize is $2,000,000.00, but the development cost for these vehicles can easily reach 20x that amount. DARPA (1996) evolved from ARPA (1993), which in turn evolved from DARPA (1972), which evolved from -- you guessed it -- ARPA (1958) [to D or not to D, seems like the DoD doesn't know]. The original (pre-D) ARPA was responsible for the ARPANet, which evolved into today's Internet.

Tuesday, October 04, 2005

Why Was Butthead Angry at Numbers?

Welcome to the inaugural math rant...
Butthead: "I'm, like, angry at numbers."
Beavis: "Yeah, there's like, too many of 'em and stuff. Heh heh."
Tangent (to return to the main rant, simply integrate):
In the UK, mathematics is abbreviated as maths; in the US, the preferred term is math. Of course, those stateside who are concerned with "The Three R's" should be made aware of the following:
  • Neither writing nor arithmetic begin with the letter "R"
  • Although arithmetic is an important foundation, the discipline does not even adequately encompass the level of mathematics education that is required for high school graduation.
The Problem:
I have a theory regarding why so many people profess a dislike of math. This theory is based in part on the educational methods employed, and in part on a great deal of social/societal baggage that tends to travel with the subject. You see, in my opinion we've been teaching math incorrectly for several generations, which has created a self-perpetuating cultural and societal bias.
Take, for example an arbitrary parent of a junior high / middle school aged child. In America, the vast majority of such parents will have found math to be "a difficult subject." The parent's recollections of their unpleasant math-related experiences then inadvertently socialize their child to believe that math must be difficult. Said socialization is then reinforced when the parent ceases to have the necessary skills to answer the child's questions regarding the subject. Test scores decline, and the media takes up arms proclaiming that math must be too hard, otherwise our children wouldn't perform so poorly. And the cycle goes on...
Aside, Mark 1:
Do I have any data to support this? No, it is simply a hair-brained theory that I'm posting on a practically unread blog that I write for the fun of it. Did I happen to mention that my robots.txt file doesn't allow any search engines to index anything on my site. Do the math...
The Root Cause?:
We teach math in a manner that places the emphasis on arriving at a solution and then provides a rote, mechanical, formulaic method for transmogrifying the problem into an answer. The vocabulary that we use to describe the process -- working a math problem -- reinforces this fundamentally flawed methodology. The focus on mechanics and procedures removes intuition from the equation. However, intuition is the key to shifting the focus toward understanding the problem. Only by focusing on the actual problem itself and devising a means of approching a solution can we instill understanding, therefore removing the fear and baggage that are often the only remainder of the current system.
Aside, Mark 2:
It's really easy to insert bad math-related puns into a math rant. I'm sure there will be more. Stay tuned. Oh, and no, I don't know exactly how to "grade" a rational thought process that doesn't necessarily converge onto the expected solution. Perhaps that whole concept needs to be explored more carefully...
That's Nice, but So What?, Mark 1:
I haven't quite figured out the answer yet, so I will try to distract you with an example. For this example, you will require the skills expected at the culmination of somewhere in the 3rd-to-5th grade range of arithmetic. However, you will also require an understanding of what numbers, and particularly digits, represent. This example focuses on adding a set of four four-digit numbers. Please play along by putting away your calculator (even the one on your computer), putting down your pencil (or other writing implement), and solving the following in your head: 1234 + 5678 + 9012 + 3456
The Way You Were Taught:
Consider the problem, and apply the method that has been demonstrated to arrive at an answer to the problem. Be sure to mentally visualize everything in nice little columns, so that you'll be able to "carry" any digits as required. Then, start turning the "add like this because it works" crank. The process works something like this (starting from the right-hand side):

  1. Four plus eight is twelve, plus two is fourteen, plus six is twenty. Write down zero and "carry" the two.
  2. The carried two plus three is five, plus seven is twelve, plus one is thirteen, plus five is eighteen. Write the eight to the left of the zero, and "carry" the one.
  3. The carried one plus two is three, plus six is nine, plus zero is still nine, plus four is thirteen. Write the three to the left of the eight and zero, and "carry" the one.
  4. The carried one plus one is two, plus five is seven, plus nine is sixteen, plus three is nineteen. Since we've run out of places to "carry," simply write nineteen to the left of the three, eight, and zero.
  5. Congratulations, you have magically arrived at an answer of 19380. Based soley on this mechanical solution, I defy you to explain why you arrived at that answer or to justify whether it makes sense.
The Way That Makes More Sense:
What are you being asked to do? You are computing a sum of four four-digit numbers. What does a four-digit number represent? Well, any arbitrary sequence of four decimal digits WXYZ represents W thousand, X hundred, etc... So, let's solve the problem intuitively, applying something akin to "iteratively refined estimation, until exhaustion of data." With regard to acquiring the sum of numbers, I call this solving the problem "forwards instead of backwards," and it works something like this (starting from the thousands, and working "bitwise" down to the ones):
  1. One thousand plus five thousand is six thousand, plus nine thousand is fifteen thousand, plus three thousand is eighteen thousand. [Estimate one]
  2. Two hundred plus six hundred is eight hundred, plus nil plus four hundred is twelve hundred. Eighteen thousand plus twelve hundred is actually nineteen thousand two hundred. [Estimate two]
  3. Thirty plus seventy is one hundred, plus ten is one hundred ten, plus fifty is one hundred sixty. Nineteen thousand two hundred plus one hundred sixty is nineteen thousand three hundred sixty. [Estimate three]
  4. Four plus eight is twelve, plus two is fourteen, plus six is twenty. Nineteen thousand three hundred sixty plus twenty is nineteen thousand three hundred eighty, or 19380. [Yes, that is my final answer]
That's Nice, but So What?, Mark 2:
That little exercise is meant to demonstrate that often, the best methodology for solving math problems is exactly the same methodology employed for solving arbitrary problems. First, start with the data that has the highest significance and formulate a first-order estimated solution. Then, apply the additional data, in order of significance, to refine the estimate. Finally, when all of the data have been exhausted, the solution becomes apparent. Does this sound like troubleshooting to you? It should.
Consider another problem, such as "My car won't start." Applying my as-yet-really-poorly-named (I'm open to ideas) "iteratively refined estimation, until exhaustion of data" principle, a mechanic would be faced with a vast plethora of possible solutions to the stated problem. By performing investigations and asking questions, the mechanic gains data that provides additional granularity to the problem. This data presents other avenues for investigation or raises other questions, which in turn provide further granularity. Eventually, when the available data have been exhausted, our competent mechanic will have arrived at a solution to the problem (or at least a small discrete set of potential solutions that can be tested and verified).
Ah, but how does our mechanic become a better troubleshooter? Although the question sounds rhetorical, it is actually easy to answer. The key to successful troubleshooting is rooted in repeated observation and experience. The same is true for any subject of study...
Aside, Mark 3:
Granted, the vocabulary that I have used is heinously raw, the one type of example I provided is the most trivial, and even the concept of working a summation bitwise in order of decreasing significance isn't something that we can immediately go shoving down the throats of our children today. However, what if the whole system was grabbed by its ear and yanked down to the principal's office? What if we built a foundation based on number theory as well as arithmetic? If we're willing to trust that little Johnny and sweet Sally are capable of understanding what numbers signify, perhaps Butthead can learn to forgive them...

Sunday, October 02, 2005

Big 12 football results

My horrible spreadsheet-turned-crappy-web-page o' Big 12 conference football results will live here for the rest of the season. So far, so good for the 'Horns.