Some national parks have long waiting lists for camping reservations. When you have to wait a year to sleep next to a tree, something is wrong.
- George Carlin

(This post had been decaying in the drafts folder and I felt that I resuscitate it in memory of last May. My feet are itching for a hike.)

The green, rolling hills around San Francisco give way to the desert scrub of the Sonoran Desert. Then suddenly, seemingly out of nowhere, magnificent mountains rise and you are at the edge of Yosemite. Yosemite is the oldest and the most famous of all national parks. Arriving at the edge you climb, and climb to end up at the Big Flat Oak entrance. Your first look at the Yosemite Valley takes you by surprise. The sheer size of monolithic granite walls stuns you. You can stare at all the photographs you want to of the valley, but you get a real sense of scale and appreciation for the grandeur when you are actually there.

The granite of Yosemite is the Mecca for rock climbers. If you are crazy enough, you can scale El Capitan which takes about 2-3 days. A climb during which you not only sleep on a ledge, but also eat and pee suspended thousands of feet above the ground. Climbers from all over the world come and often work for the park during the week so they can indulge in their passion for climbing on the weekend.

Our aims were less lofty, but still intense as we wanted to hike as much as possible and also do Half Dome. We managed to acquire the much-coveted overnight backcountry pass to Little Yosemite Valley. It is almost necessary to escape the Yosemite Valley because it gets overcrowded and resembles a zoo. Going there in the spring was a great idea. This the season when the waterfalls are full from the snow melt. School is still not out, and so the Valley is not yet overrun with visitors. Yet, you can get away if you really wish as most visitors rarely leave the valley and are mostly content looking at the waterfalls and the peaks from afar. John Muir and Ansel Adams would have lived in vain if this was all there was to the park.

Getting a back-country pass gives you a right to camp on the 'secret' backcountry camping ground. This is a rather well-kept secret and even the rangers give you a knowing wink. Set apart from the main Yosemite campgrounds by a footbridge and sheltered under the Three Sisters, it is far enough from the rather annoying trailers and buses. These monstrosities defeat the whole idea of camping and living in the wild. Why come here if you want to watch cable TV?

We settled in, got our rudimentary fire working. For the life of me, to this day, I have not figured out how you can really use two stones to create enough sparks to light a fire. I say this because I tried it in vain before I decided to walk on a paved path (how ironic) to the Yosemite supply store from our campsite. Why? I forgot to get a lighter. Where are the smokers when you need them? We stretched on our sleeping pads, read books, and snoozed.

Later in the evening, wanting to take advantage of the yello light I walked to Mirror Lake and got some wonderful reflections of Mt. Watkins and Half Dome before it started drizzling. Photography is as much about patience as it is about light. You have to wait for the right moment. What would I not give to get a month to live here? Ansel Adams whose photography defines Yosemite spent months on end here. Yet, some of his best photographs were taken when he had only one or two plates left. First you work hard to develop your craft, then you learn patience, so that when the time comes you are ready to seize the correct moment. Digital cameras give people flexibility to correct an exposure or composition instantly and retake the shot, but you still have to wait for the right moment. Some people have the tendency, which I call the 'Monte Carlo method of photography', which is to simply take a whole bunch of pictures without any thought and then hope that you will get a few that will really stick.

Our goal primary goal was to climb Half Dome. After having stared at pictures of the peak for years, now that it was in front of me, I wanted to go and grab it. From a distance the texture of Half Dome resembles elephant skin. Gray, tough to feel with grooves and striations. It's almost like it wasn't a mountain but a giant statue of a large, lumbering mammal that could come to life. A hike to Half Dome is a 17-mile roundtrip, and is done in a day (a long one). Since, we had the backcountry pass, our route was more leisurely (read long). We first went up to Glacier Point by bus and then hiked along the Panorama Trail to reach the Little Yosemite Valley.

The famous vertical face of Half Dome can be seen from most parts of the Valley and is only a few miles away. However, the recommended ascent is from the back which involves a circuitous route ending at the famous Saddle Point. From the Little Valley its only 4-5 miles to Half Dome and we got there early in morning before the crowd from the valley below even made it to the halfway point. To be on Half Dome before it starts resembling a circus and the cables to the ascent becomes a giant human caterpillar is a sheer joy!

Making our way back, we had to pack our tent and sleeping bags and make our way down. This time we would take the most direct route to the valley. If you thought that climbing up was hard with a large backpack, then wait till you have to start climbing down. Unlike people carrying water bottles who can skip their way down the switchbacks, we had to walk like pack animals in a zig-zag fashion, perhaps traversing eventually twice the distance. Nothing gets more attention from a fellow human beings than another fellow human being strapped like an animal. We did get a lot of brownie points for being 'hard-core' when it comes to hiking.

The trails have these rusted metal signpost with the destinations and distances. There is Clouds Rest, other lakes, and also signs for the 211 mile John Muir Trail which begins in the Yosemite Valley and continues to Mt. Whitney. It gets a lot hard-core than our baby steps. Someday, when I have three weeks to spare I will get on it too. But, these are passing thoughts. The more pressing thoughts are of food. At the end of the hike, we were dead tired and ready to eat a horse. There is only so much baked beans and Ramen can do for you.

We had no strength to even get on the bus that took us back to where our car was parked and where the restaurant was located. In the food-court we were probably the dirtiest pair. We had spent the last 3 days in the wild and we looked like it. As we ate we could see the sun setting and the glorious water from the Yosemite Falls gushing down.

Yosemite Photo Album

The math behind galli cricket teams, and other interesting diversions

Group Theory in the Bedroom and Other Mathematical Diversions is Brian Hayes's set of collected essays from the American Scientist.

Full marks for the slightly risque title that will pique anyone's interest, but the book has nothing to with mathematics of partner swapping. The subject of the investigation is to find the golden rule for mattress flipping. Mattresses should be flipped periodically to ensure that all sides of the mattress get equal wear. It's easy enough to see that there are 4 possible configurations: (Side A, Side B) x (Top, Bottom). The goal is to find one rule, or a set or rules, that you can apply each time to perform a set of operations that ensures that you end up cycling through all 4 configurations.

If you only flip (along the long or short axis) you cycle through only two sides - A and B. If you only rotate in a plane then you cycle through - Top and Bottom. Using group theory, Hayes shows why there is no golden rule. You cannot perform the same set of operations again and again because the mattress is a Klein-4 group . A rotate and a flip along the short axis is the same as a flip on the long axis. Any set of two operations are equivalent to one operation. This proves to be the undoing of any rule, as we know that any ONE set of operations is not enough to cycle through all 4 configurations. So, you either need a fixed schedule, or a set of markers to ensure you do an opposite set of operations.

Being a kinda random fellow, I best liked Hayes's analysis of the effects of random flipping. If you randomly performed any one operation on a quarterly-basis then, on average, one side will get 31% of the wear instead of ideal 25%. A rather tolerable discrepancy of 6%. Then he goes on to discuss tire rotation and shows why that is completely different beast since it is a cyclic-4 group and hence there is a golden rule - "quarter turn clockwise (or anti-clockwise)".

What is most interesting about the book is that all these mathematical diversions start as anecdotes and rather innocuously. Consider the problem of partitioning a set of players into two teams: a problem that is encountered and solved on thousands of galli cricket and football 'fields' every day. The usual practice is to select two captains who then toss to decide who picks first. Then they go turn-by-turn to pick the rest of the players. Naturally, the players are chosen in order of ability. In general, this rule results in fairly balanced teams. Hayes calls this the Greedy Algorithm, because at each step the largest number (if you assigned numerical values to the strengths of the players) is chosen in each partition. In reality, of course this partitioning problem is quite a hard one, more technically, it's an NP complete problem and there are number of other algorithms, including the Karmarkar-Karp difference algorithm, but no optimal one. Then Hayes goes on to show why this does not matter on the playing field because on a log scale, abilities don't differ that much between strongest and weakest players and the simple 'greedy' partitions are reasonable without the need for fancy partitioning.

I greatly enjoyed reading the other chapters on namespaces, gear train ratios, and finding the continental divide. If only, mathematics was taught this way in schools.

Murakami on Running

Murakami's memoir on running: On the lit blog. A great rambling, read on running and writing, and living.

A few questions for Indian restaurants in the US

Why no spoon?
Why no finger-bowl?
Why the drinking glass on always on the right-hand side?
and no chai and Indian-style filter coffee?

In seeking nostalgia it can often turn out to be a frustrating and disappointing experience. Food that even my dog won't eat.

And one thing that you should not to do at Indian restaurants: Don't order the cocktails. They are terrible. Given that it hard to screw them up. Better still - ask for the wine menu or help with those selections.