September 29, 2005
Networks in our nation's capital
This past week, I attended the Statistics on Networks workshop at the National Academies of Science in Washington DC, where I saw many familiar faces and many new ones. In particular, I was very happy to finally meet Jon Kleinberg, John Doyle, Steve Borgatti and my collaborator Dimitris Achlioptas. And it was nice to see Walter Willinger and Chris Wiggins again, both of whom I met at the MSRI workshop on networks earlier this year. And naturally, it was nice to see my collaborator Mark Newman again, even though we correspond pretty regularly. Now that I've distributed the appropriate linkage for the search engines, let me get on with my thoughts.
This workshop was interesting for a couple of reasons. First, the audience contained statisticians, social scientists, computer science/physics people, and engineers/biologists. Certainly the latter two groups presented very different perspectives on networks, with the former being interested in universality properties and random models of networks, while the latter was much more interested in building or decomposing a particular kind or instance of a network. The social scientists present (and there were many of them) seemed to have a nicely balanced perspective on the usefulness of random models, with perhaps a slight leaning toward the computer science/physics side. Naturally, this all made for interesting dinner and wrap-up discussion. For myself, my bias is naturally in the direction of appreciating models that incorporate randomness. However, it's true that when translated through a particular network model, randomness can itself generate structure (e.g., random graphs with power law degree distributions tend to have a densely connected core of high degree vertices, a structure that is a poor model for the core of the internet, where mixing is disassortative). In the case of real world networks, I think random models yield the most benefit when used to explore the space of viable solutions to a particular constraint or control problem. Eve Marder's work (also at the workshop) on small networks of self-regulating neurons (in this case, those of the lobster gut) is a particularly good example of this approach.
Second, although there were very few graduate students in attendance (I counted three, myself included), the environment was friendly, supportive and generally interesting. The workshop coordinators did a good job of inviting people doing interesting work, and I enjoyed just about all of the talks. Finally, it was interesting to see inside the National Academies a little. This institution is the one that fulfills the scientific inquiries of Congress, although I can't imagine this Congress listens to its scientists very much.
September 24, 2005
Measuring technological progress; a primer
I used to think it was just a silly idea that no one really took seriously, but here I am blogging about it. After reading Bill Tozier's rip on Ray Kurzweil's concept of The Singularity, I'm led to record some of my own thoughts. (Disclaimer: I'm not a regular reader of Bill's, although perhaps I should be, having found his blog via Cosma Shalizi.) I would briefly summarize this Singularity business, but best to let its inventor do the deed:
An analysis of the history of technology shows that technological change is exponential, contrary to the common-sense "intuitive linear" view. So we won't experience 100 years of progress in the 21st century -- it will be more like 20,000 years of progress (at today's rate). ... Within a few decades, machine intelligence will surpass human intelligence, leading to The Singularity -- technological change so rapid and profound it represents a rupture in the fabric of human history.
Bill contends that it's worthless for technological change to happen at an exponential rate if no one is actually using those ideas. But that misses the point of the Singularity a little - Kurzweil is actually claiming that the rate of change in the actual technological state of humanity is advancing at an ever increasing rate, and frequently employs figures showing exponential trends in certain metrics like CPU speed, number of genes sequenced, etc. Were it merely a production of ideas, well, you could argue that it could be exponential by simply claiming it's proportional to the current human population (i.e., if each person has one novel idea to contribute to the world), and be done with it. But the idea of the Singularity implies that the technological power of humanity grows exponentially, so it naturally assumes that ideas will be turned into applications.
Unlike Kurzweil, I'm a bad futurist. That is, I am loath to share my vision of the future because I'm pretty sure I'll be wrong; the future will be more interesting and less predictable than I think anyone gives it credit for. So, let me propose that there is at least one much better metric by which to chart the "growth" of technology's impact on human civilization. To be quantitative, let's measure the average amount of energy that an average human releases (e.g., internal combustion engines, jet engines, electricity, etc.) in a given year. Of course, this ignores, like all of economic theory, the environmental cost of such expenditure in the form of drawing down the bank of natural resources available to us on Earth, and also ignores the fact that energy efficiency is another form of technological advancement. However, my measure at least, is nicely well-defined and has none of the non-falsifiable overtones of Kurzweil's idea; plus, if it is increasing exponentially, then it has lots of nice implications about technology and perhaps even the stability of civilization.
Generally, though, you can't fault Kurzweil for his optimism; he truly believes that the future will be a good place to raise our children, and that the Singularity will ultimately bring about wonderful changes to our lives such as immortality (although, it's not settled if immortality will be a Good Thing(tm), for instance), an end to stupidity and computers that do what you want rather than what you tell them to. In his own words:
The implications include the merger of biological and nonbiological intelligence, immortal software-based humans, and ultra-high levels of intelligence that expand outward in the universe at the speed of light.
Since Kurzweil claims most of us today will be around to witness the Singularity, I suppose I'll just wait to see who's right, him or me (with my own secret and probably way off-base predictions).
September 13, 2005
TravelBlog: Making the summit of Longs Peak
Weekend before last, over the long Labor Day weekend, I trekked north to Rocky Mountain National Park with friend Adriane Irwin, Lauren Meyer and two of their friends Shawn and Cheryl. Our intention was to summit Longs Peak, the tallest non-technical summit in the lower 48 states. Longs Peak's summit stands at 14,259 feet (4321 meters) above sea level. This elevation is significantly higher than my usual elevation of roughly 5,314 feet (1,610 meters; and I'd only been at that elevation for about three weeks since prior to that, I'd been at sea level in New York City), and I was not positive that I would make it to the top.
And yet, I did. Longs Peak was my first 14'er and probably not my last. As I mentioned to my friend Jen from the climbing gym this evening, I've been interested in doing serious outdoors stuff for a long time, but have simply not had a set of friends who were also interested (this makes me wonder if for some other reason I tend not to be selective for crazy adventurous friends). On the other hand, as I mentioned to Keith and Angie this afternoon, I'm much more interested in having good company along for those adventures than I am in crossing them off some abstract list of accomplishments. Still, it will be nice to have both!
Our summit attempt of Longs Peak began after we lucked out and landed a camp site in the small camp ground near the trailhead. We prepped our gear, had a snack and then hit the sack for a few hours. We set the alarm for 1:10am, although I slept restlessly and ended up awake at 12:50am, waiting for go-time to arrive. After assembling our gear, we picked up our two new friends Jake and Luke (brothers who had driven-in the day before from Indiana), and made for the trailhead. Adriane, betraying her excitement, set a quick pace for the first few miles of the hike. As we crossed the tree-line, we could see the lights from Denver in the distance, and the looming darkness of Longs Peak miles away above us.
It wasn't long before I volunteered for lead-duty. This was partially on account of Adriane finally relinquishing the position herself and partially because I wanted to set a slower pace. Above the tree-line, the steps of the trail were tiring, and I was a little concerned that the altitude would wear me out quickly. And so, I led our group of seven along the trail as it snaked its way up the mountain, through the lower tundra. At the break for Chasm Lake, we rested briefly before pushing on to Boulder Field. The cold of the night air and the heat of the hiking kept the girls constantly shifting their layers. I was comfortable in my polypro and nylon layers, content to roll-up or roll-down my sleeves in order to shed a few extra degrees of heat.
Although this hike was filled with spectacular visuals, one of my favorites was, from near Boulder Field, looking back down the trail during the blackness of night. Tracing the twists and turns of the trail were a train of bright points, bobbing with the motion of hikers as they made their way over the foothills. The quietude of the moment combined with the solemnness of the dancing lights made me think of a pilgrimage, in which dutiful worshippers made their way to the mountain sanctuary to offer their prayers to the gods that live within the mountain. Although I doubt any of the hikers on the trail was doing that exactly, among those serious enough to summit Longs Peak (or otherwise revel in the beauty and ruggedness of nature), I can't help but feel that there was a subtle religious subtext to our trek.
At the Boulder Field rest stop, we spotted the sun beginning to peak over the horizon, and our surroundings were visibly more light. We hardly needed our headlamps as we began to pick our way through the large rubble toward to Keyhole. It was near this milestone point that the sun finally broke away from the shadow of the nearby mountain and seared the night sky with orange, red and yellow fire. Given my surroundings, it was one of the most beautiful sunrises I have ever seen, and had I not been with company, I likely would have found a comfortable rock to park myself upon so as to soak it up for a spell.
As we turned through the Keyhole, I laid eyes on the beginning of the difficult part of the hike. James had described this section as being a three-foot wide ledge with a thousand foot drop on one side - it wasn't nearly that bad, but the steep slope off to my right certainly made me more cautious as we began to pick our way through the jagged rocks, hugging the slope while following the painted bulls-eyes that led us forward. From here-on-out, I was careful with my hands, making sure that I always had my balance, and always had one good hand-hold in case I lost my balance. It was also at this point, at 13,000ft, that I began the feel the altitude in earnest. I developed a slight headache and a slight shortness of breath, both of which progressed as we climbed the remaining 1200 feet to the summit.
The bouncing bulls-eyes led us to what's known as the Trough, which is truly the worst part of the hike. With an elevation gain of perhaps close to 700 feet, the Trough is filled with boulders, gravel and dirt, and the footing was significantly less sure than on the jagged but solid rock we had just crossed. It was here that I began to fall behind the rest of the group, and here that Adriane and Lauren began to push ahead. Deciding that being safe was more important to me than keeping up with the group, I let the distance grow until it was only Luke and I at the top of the Trough, while the rest were on to the Narrows. Luke and I hadn't spoken much on the hike up, but as we sat at the top of the Trough, gazing out at the breathtakingly beautiful and immensely expansive landscape, we commiserated about the difficulty of the altitude and the Trough. I could tell he was reluctant to go on, and so I consoled him. Finally, he said that this was the most beautiful spot on Earth he'd ever seen and that he was going to stay right here.
Resolving to push on myself, I bid him farewell and said that perhaps we'd meet up again at the Keyhole on the way down. And then it was into the Narrows. James' description was slightly more accurate here, but still there were plenty of outcroppings and formations to pick your way through - I never felt in danger, but still, I respected the distance between myself and the bottom of the mountain to my right. For this section, I was joined by a young woman who came up behind me in the Trough. We would hike for a period and then rest, then hike and rest, etc. We chatted amicably occasionally, commenting on the altitude. Finally, at the point where the Narrows meets the Homestretch, she pushed forward, and I was again left behind.
The Homestretch is much like the Trough, except without the loose footing. Another 600 foot vertical rise on a steep slope. Slowly, with hikers from behind passing often enough to remind me that my body was suffering, I neared the summit. At about 8:40am, I reached the top and found the rest of the group in high spirits, having been there for a little more than half an hour already. We snapped the requisite group photos, shots of Chasm Lake from above, pictures of the clouds rolling in, and a few more shots of each other. As the weather turned cold and the summit was enveloped in a white fog, we began our descent.
Although going up the mountain was difficult on account of the physicality of raising your body nearly a mile, going down was difficult for the pounding on the knees. It was made no less complicated by the large number of people we met going in the opposite direction - Jen, who has done Longs before, said that starting at 2:00am was excessive, but I'm glad we did because it made the ascent significantly less crowded. With the lightness of day around us, I took many pictures of the descent, chronicling the way-points and landmarks and vistas. It wasn't until about half way down the lower tundra that my knees truly began to ache from the constant pounding on unforgiving stone, and I began to take more frequent breaks.
Again, I fell behind the group as a result. This time, however, it was more intentional. When I'm out in nature like this, I like to take a little bit of time to be completely alone and simply soak it all in. To try to open every pore of my body and absorb the beauty and serenity that surrounds me, to try to store it up for all the days I'll spend away from it, imbedded in a complicated and noisy jungle of concrete and asphalt. Satiated, I wore a big and goofy smile as I bounced down the trail after the group ahead of me. We were briefly reunited at the break to Chasm Lake, where I captured a nice panorama Longs. Finally, at close to 2:15pm, twelve strenuous and exhausting hours later, I made it back to our campsite, tired but happy.