FarmerMaggot

Happy (belated) birthday.

He'll regret this when his son grows a forehead ridge.

From the page: "The primary role of math teachers, constructivists say in turn, shouldn't be to explain or otherwise try to transfer� their mathematical knowledge to students; that would be ineffective. Instead, they must help the students construct their own understanding of mathematics and find their own math solutions."

I agree, and here's a supporting anecdote:

Throughout most of my primary and secondary education, I hated math. That changed in a high school geometry class when I was the only student to solve an advanced problem on parallelograms, one that had stumped even our teacher. The answer (a general solution) came to me intuitively, and my teacher challenged me to prove it. At that time, proofs were cerebral torture devices, but I eventually came up with three of them for this identity, and I was amazed. I began to see the straightforward way that proofs followed from definitions and postulates. That dawn of clarity transformed mathematics from a confusing collection of arcane rules and procedures into almost a game, a way of discovery by valid restatement. For the first time in my life, I enjoyed math.

I began reading ahead in my textbook, and a brilliant Slovak friend recommended The Book of Numbers by Conway and Guy, which became my Bible. By the time I was 18, I had independently generalized the binomial theorem to what I later learned is called the multinomial theorem, and had even generalized the combination (or "choose") function to generate its coefficients, discovered that these coefficients take the shape of higher-dimensional simplices (tetrahedron, pentatope, etc.), and come up with a general way to produce the n-bonacci sequence from the coefficients of the nth instance of the multinomial theorem. I didn't realize at the time that most of this had already been done by others, and I never attempted to publish the few genuine discoveries of my own. It was all for my personal enjoyment and enlightenment.

Later, my interests broadened to include linguistics, history, archaeology, anthropology, religious studies, and (as I grew familiar with the theoretical debates and competing methodologies within and between these fields) philosophy. These were subjects I probably never would have pursued if that high school math teacher had not set me on a course of autodidactic curiosity and confidence.

Therefore, I strongly believe that the best way to teach a subject is to encourage students to develop their own understandings of it and to make their own discoveries within it. However, I recognize that my motivation was also fueled by that intuitive discovery about parallelograms, which prompted my teacher to push me harder. Not all students will have that kind of experience, so perhaps constructivism isn't the most productive method for everyone all the time. Still, instructors should use that technique if and when a student shows signs of readiness.

As Plutarch said, "The mind is not a vessel to be filled but a fire to be kindled."

From the page: "Culture isn't knowing when Napoleon died. Culture means knowing how I can find out in two minutes. Of course, nowadays I can find this kind of information on the Internet in no time. But, as I said, you never know with the Internet."

This interview called to mind a line from The Name of the Rose, which only yesterday caught my eye: "There is nothing more wonderful than a list, instrument of wondrous hypotyposis."

This song always reminds me of a monologue in one of my favorite episodes of Northern Exposure. Chris, the town's philosopher-DJ, delivered it to explain his soul-searching decision not to tone-down his playlist, even after a politically incorrect selection drove his friend to suicide and motivated others to call for musical censorship:

"I want you to think of the words of Tom Paine, who said, 'Man did not enter this society to be worse off than he was before, nor to have fewer rights than he had before, but to have those rights better secured. When it comes to the right of the mind, he never surrenders it.' The mind, that wonderful breeding ground of contradictory impulses like love and hate, rage and empathy. They've all been invited to the party, so you might as well make room for them. I want to play this next song for my friend Edgar Hankins, who has gone to a place where he's never going to be upset or agitated or offended ever again. Sensitive and PC souls, cover your ears."

"Heaven" was not included in the episode (the two songs were "Pencil-Neck Geek" and "Hey Joe"), but its lyrics and Chris's speech seem to convey the same message. The ups and downs, the surprises, all give life meaning, then vanish forever. Make the best of life's variety while you can.

R.I.P.

From the page: "Augmented reality is a catchall term for overlaying what we see with computer-generated contextual data or visual substitutions. The point of the technology is to enhance our ability to interact with things around us by providing us with information immediately relevant to those things."

This list gets a thumbs-up for furthering awareness of AR, but we need to think bigger about its applications. Notice words and phrases in the above quotation such as "contextual data," "enhance our ability," and "information." No doubt, the first few generations of AR will probably focus on these kinds of geographical conveniences, just as the first PC software focused on word processors and spreadsheets. But that's nowhere close to full potential.

I mean, putting Google Maps in a mobile device is unimaginative even by purely utilitarian standards. How about apps that keep track of not only where you parked your car, but also where you left your keys? How about automatically scanning barcodes as you shop and displaying your running total, budget and account balances, unit-price comparisons, and whether you can find a better deal in another store or online? How about tagging acquaintances and coworkers with their names, contact information, how you met, and upcoming events, so you never again forget a face? (Or, by networking the AR devices, create the most convenient matchmaking service of all time. "Just walk this way to find someone who shares 87% of your interests.") How about taking pictures in the blink of an eye to catch that criminal or capture that license plate without wasting time and attracting attention by fumbling with your camera phone? These apps aren't terribly sophisticated, but they would be extremely useful, and in theory they could be chosen like Firefox add-ons.

Take it a step further. Making AR platforms not only mobile but wearable (with EyeTaps, say) would open up countless possibilities. Write a biofeedback app that monitors your response to music. (This could be music from your own playlist, or music in your environment, since computerized song-recognition is now available.) Then let your AR play soothing music when you're stressed, energetic music when you're sluggish, etc. Also, by adding cell-phone-scale video cameras and microphones to these devices and networking them with others, you could move a small step closer to omnipresence. For example, specify an out-of-earshot sound source that you want amplified, or download live images, video, or even 3D photo collages of remote locations via other users' AR platforms. You could virtually navigate from location to location, live, as if controlling a wandering webcam.

Now dream really big. Tag real-world locations with audio, video, text, and pictures, and never ask again, "If these walls could talk..." Create virtual objects, even virtual characters, to populate your space. If the AR devices are networked, you could have the choice of making this content public or restricting it to certain "channels" within the network. Customize the atmosphere of your home or workplace without spending a dime, redecorate your entire city, or write your beloved's name in the sky. Give yourself a virtual mask or costume for others on your channel to see. Create and share real-time "DOOM mods" for the AR world. Simpsonize everyone, instantly and automatically. Play Second Life in this life. (To say nothing of the educational potential.)

Share this vision, foster this kind of imagination, and it will shape the future.