It’s been a while since we’ve done one of these:
This is the interchange of I-85, I-75 and I-20 in Atlanta, GA. No personal significance, though I do like how the incredibly complex curved shapes are bounded by the very rectangular city streets.
Of course, the combination of curved forms and rectangular geometry is not too uncommon here at CatSynth.
Well, it has been a while since I have done a “fun with highways” post here at CatSynth, so why not visit some of the highways I traveled while in China?
Shanghai has a series of highways, most of which are designated with the letter “A” followed by a number:
[photo by ramonyu]
During my trip, I became quite acquainted with the A11 (Huning Expressway) that connects Shanghai to Suzhou and beyond. However, one cannot really view either city from the A11. Nor can one really see the details of the delta region. It’s just a big highway traversing sprawling suburban development like one can see in many parts of the U.S.
By contrast, the A9 extends into the center of Shanghai as the Yan’an Elevated Road. Shanghai makes a distinction between “expressways” and “elevated roads”, though I don’t really see much difference.
The elevated roads are multi-lane freeways, and the Yan’an cuts right through the downtown of the city, closely paralleling the pedestrian thoroughfare Nanjing Road and People’s Square, before ending at The Bund along the river.
[photo by ramonyu]
Essentially, it parallels a major part of my walking tour only a few blocks away.
Photographer Liao Yusheng has a fantastic series of architectural and landscape photos along the Yun’an Elevated Road, along with this description:
Yan’an is part of a sprawling elevated highway system in the heart of Shanghai that epitomizes the gung-ho mega public-works projects that are going on all over China at the moment. This is a six-lane highway that is literally jammed into the middle of a densely packed modern city. Hundreds of thousands of families were displaced and hundreds of millions of dollars were spent to make this happen. In forcing this monstrosity onto an already fully-developed (yet still evolving) megalopolis, Shanghai has created a conduit with which to examine the multilayered texture that makes up this city.
I only discovered his work in preparing this article, but it was a great find and reminds me of my own urban and architectural photography. I encourage readers to check it out!
The story does remind me of the highway development in New York City in the 1950s and 1960s, where entire neighborhoods were demolished to build, among others, the Cross Bronx and Bruckner Expressways. Somehow, we often end up back there.
I did also find that China has it’s own highway enthusiasts, including the blogger Wang Jian Shuo.
This weekend included a 30-hour but still too brief visit to Shanghai. Shanghai is of course a massive city, and an increasingly vertical one, and probably reminds me more of New York than most cities I visit.
This photo captures both the old and new of the city. In the background is the iconic Oriental Pearl Tower. In the front, we see a high-rise building on side, and one of the tenement buildings that line many streets, with five or more stories of clothes (and the occasional cooked duck) hanging to dry.
It was taken while walking east from a downtown neighborhood towards The Bund, the riverfront in an older part of the city One can look across the river and see the new Pudong district that is most visually associated with Shanghai and features it’s tallest, newest buildings.
Visibility was relatively poor on both days, and I did not cross to the other side of the river to see the view of the Bund.
Food was a major part of day (as it has been throughout my stay in China), and Saturday featured both a snack of “soup buns” at small hole-in-the-wall shop where the upper level was barely tall enough to stand in, and an extraordinary Japanese-fusion meal at which my friends and I over-indulged for a couple of hours. After that, we headed to a local jazz club called the Cotton Club (I wonder where they got that name from?), where we heard what I would describe as a “typical jazz-club combo” that wouldn’t be very memorable except of course that it was at a jazz club in China.
The night concluded with brief stops at a few of the dance clubs. One featured two sections, an upstairs with a mixed-crowd of foreigners and locals, and a downstairs that was almost exclusively local. The latter definitely had better music (deep synth trance and beats). Of course, one of the main attractions of the nightlife (which continues well beyond the hour when almost every city in the U.S. closes down) is the people watching. Without dwelling upon it too much in this article, Shanghai did afford great opportunities for people watching, starting with our walk along the extremely crowded Nanjing Road and concluding as we departed the last club well into the morning.
I did have an opportunity to explore more on my own Sunday. I began in some of the quieter neighborhoods near where I was staying, and experienced a more local view of the city.
A walk through Zhongshan Park was in some was a more aural experience than visual. The park was already relatively crowded, with numerous groups practicing traditional Chinese exercises, dance lessons, and band practicing for the upcoming New Years celebrations:
The “music” of the park would change every few meter, as one moved from the metallic percussion of the band to a group dancing to disco from the 1970s. A few feet later, the disco and 1950s pop is overtaken by slower more meditative traditional Chinese music that serves as the background for exercises. Finally, a small portable player of low quality provides something akin to circuit bending.
Regular readers of this site know that I am fond of urban side streets and alleys, so I spent a few minutes in the narrower side streets of the neigbhorhood:
This alley reminded me of a photo I took not far from home in San Francisco last summer.
Along Ding Xi Road, I met the proprietor of a small boutique clothing store and her cat. Look for them to be featured in the next “Weekend Cat Blogging.”
After lunch together with friends again (one really cannot dine alone here), I headed back downtown via the Metro. I pride myself on being able to get around a city when I have a good subway system, a map and a general sense of direction. I was able make my way back to the Bund and Nanjing Road to see them during the daytime. I think the one word description of this area would be “crowded.” And I mean crowded on a level one rarely would see even in New York, and with far more dangerous street crossings. Plus, unlike my earlier walks, people expect foreigners in this district and are constantly on the look for sales opportunities. It is relatively easy to simply ignore them, but the crowds and constant interaction did become a little draining at times. It’s something to consider, I am a “city person” and I don’t mind crowds, but I do need breaks.
At Peoples Square, I did brave one last round of crowds to arrive at the Shanghai Art Museum. Even though it was only a block from one of the busiest open spaces and transit hubs in the city, the courtyard was a remarkable oasis of calm. After taking a moment to relax, I went inside to see the current exhibition, a retrospective of Wu Guanzhong. His work, which includes both oil painting and ink painting, and often focuses on Chinese scenes and themes. Many of paintings are of clearly of landscapes, animals and architecture of China, with an impressionist quality but also more minimal. However, many of later works were more abstract, although with Chinese themes. This was especially true of his ink paintings, some of which were quite large in size and reminded me of the “Autumn Rhythm” series of Jackson Pollock. One of the abstract in paintings called Entanglement relates back to the Humble Administrator’s Garden in Suzhou, which I had the opportunity to visit before heading into Shanghai and will be the subject of the next article…
Yesterday while was in the F train in New York, a young blond man came through the crowded car soliciting donations. I would not have given him much notice, except that as he was carrying a small black cat, and supposedly collecting for an organization called “Homeless Pets NYC” with a website hpnyc.org. The URL will take you to a site that describes the person I saw and his black cat, and suggests that like most subway solicitations it’s a scam. Very sad.
We return to a favorite topic here at CatSynth with a highway interchange that we know quite well.
The Alemany Maze is the large interchange in southern San Francisco between US 101 and Interstate 280. It derives it’s name from Alemany Boulevard, which runs parallel to 280.
In the upper-left corner of the interchange is a large lot that is home to the Alemany Farmers Market, which has been operating at this location since 1947. I wish it wasn’t only on Saturdays (indeed, it would be great if it operated on a weekday evening to pick up fresh ingredients for dinner on the way home from work). Beyond the lot is 5lowershop (pronounced “flower shop”), where I performed two years ago at the headphone festival. I will be performing there again in October.
The section of the I-280 north of the interchange is the last double-decker freeway in the Bay Area.
[photo by /\/\ichael Patric|{] on flickr]
In the years since the infamous collapse of the I-880 Cypress Freeway in the 1989 earthquake, the other double-decker freeways have been torn down, leaving only this far less controversial section of I-280. You can read more in this article.
Whenever I drive to work (sometimes I take BART), I pass through this interchange on I-280. Besides it’s largeness and the annoyance of having to change lanes just to up against the freeways and the ramps.
Indeed, the houses along Boutwell St lie in between 101 and the ramp to 280, which seems like a somewhat surreal place to live. Similarly, I see these and other houses on the top of the hill on Charter Oak Avenue (north of 280) when driving south:
The houses on Charter Oak are actually on a steep hillside, so are somewhat sheltered from the freeway, though they also have a rather direct view of the double-decker section.
All these houses are part of the Bayview District of San Francisco (also known as the Bayview-Hunters Point District), which extends east from 101 to the bay. I can only imagine that these house all pre-dated the construction of I-280, which was built in the late 1960s. More information on the history of I-280 can be found at California Highways.
Today we explore the topic of Knot Theory. Most of us have a conventional idea of what a “knot” is; and those who were once Boy Scouts may have a more formal idea. But in mathematics, a knot has a very formal defintion: an embedding of a circle in 3-dimensional Euclidean space, R3, considered up to continuous deformations (isotopies). An example of a mathematical knot, the “figure eight knot”, is illustrated below:
Basically, it is a continuous curve in three-dimensional space that loops back on itself, crossing an arbitrary number of times but never cut or spliced. It relates to the conventional notion of knot as a piece of string connected at the ends.
Knots relate to other topics that have been explored here at CatSynth, such as Lissajous curves.
Many knots, when projected onto a two-dimensional plane form Lissajous curves.
It also relates to our interest here at CatSynth in highway interchanges, such as this the intersection of I-105 and I-110 in Los Angeles:
Indeed, our friend whaleshaman of Jelly Pizza suggested the link between highway interchanges and knots, although mathematically such interchanges are really tangles.
Knots (and tangles) can be arbitrarily complex with twists and crossings. But there is order in this twisty world, and indeed knots have properties analogous to numbers, such as equivalency and prime decomposition.
Two knots are considered equivalent if one can be converted to another by simple scaling (stretching or rotating), or performing one of several Reidemeister moves, twisting or untwisting in either direction, moving one loop (or segment) completely over another, or move a string completely over or under another crossing. Basically, this is any operation you can do on a closed string without cutting or splicing it.
Here at CatSynth, we are quite familiar with Reidemeister moves, as they seem to occur spontaneously on our audio cables:
Even more interesting is how knots can be decomposed into prime knots. Just as any integer can be expressed as the product of prime numbers, any knot can be expressed as the “sum” of prime knots.
Here is a chart of the first 15 prime knots:
[Click image for original and more info]
Here, the prime knots are grouped by the number of crossings. For example, the trifoil knot (second from the left on the top) has three crossings. The circle is a degenerate case, known as the “unknot”, with zero crossings. As the number of crossings increases, the number of possible prime knots also increases. For example, there are seven unique prime knots with seven crossings.
For any positive integer n, there are a finite number of prime knots with n crossings. The first few values are given in the following table.
| n | number of prime knots | |
| 1 | 0 | |
| 2 | 0 | |
| 3 | 1 | |
| 4 | 1 | |
| 5 | 2 | |
| 6 | 3 | |
| 7 | 7 | |
| 8 | 21 | |
| 9 | 49 | |
| 10 | 165 | |
| 11 | 552 | |
| 12 | 2176 | |
| 13 | 9988 | |
| 14 | 46972 | |
| 15 | 253293 | |
| 16 | 1388705 |
This sequence (formally listed as A002863), appears to grow exponentially. Indeed, results by Welsh show a lower bound of 2.68 for the exponential base, and an upper bound of 10.40 due to Stoimenow. However, as far as I can tell, there is know known analytical formula for this sequence, and the values for n=17 and above are not known.
I find such sequences of numbers fascinating. Where to they come from, and how does one figure out the next value? In the case of prime knots, these appear to be open problems.
For more information, Giovanni de Santi has an excellent introduction to the theory of knots. Another paper by [url=http://algo.inria.fr/bsolve/constant/constant.html]Steven R. Finch is a resource for advanced analysis of knots and tangles, including more on counting prime knots.
When nothing else is happening on a quiet weekend afternoon, I will often go for a walk through our neighborhood, South of Market (SOMA) and South Beach. Our neighborhood is in many ways more like New York than the rest of San Francisco, with its old industrial buildings, dilapidated piers on the waterfront, and new condo developments. But perhaps that adds to the sense of familiarity, and of “home”, amidst the concrete.
Our walk usually begins on Townsend Street, heading east towards the waterfront. This area is dominated by AT&T Park, home of the San Francisco Giants. But while crowds head towards the stadium in the summer, we often head in the opposite direction. There is a little park at the end of Townsend along the Embarcadero, where I often see older Eastern European folks. Across the park is the cul-de-sac that marks the end of Delancy Street, a name reminiscent of the Lower East Side of Manhattan. Here I often stop at a small cafe – it has a large garden that can be enjoyed on its own or for the glimpses of the bay it affords.
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There are some books I only seem to read when I’m out at places like this, rather than at home. One such book is The Cat: A Tale of Feminine Redemption. I will stop and read a chapter while enjoying a coffee and the views. Though sometimes I opt for one of our free weekly papers instead. I like the idea of being contrary, reading esoteric books while a major sporting event is going on nearby. But in a large, cosmopolitan city, there are always people doing their own thing. One is never really alone. |
Beyond the cafe is the southern portion of the Embarcadero, which contains glimpses of a seedy and crumbling past while being revitalized with the stadium and frenzied development.
Heading south along the Embarcadero, one approaches the Bay Bridge. Commercial buildings, as well as residential complexes, have sprung up in its shadow. I enjoy seeing these buildings fit comfortably beneath the bridge:
Some of them have appear older, more reminiscent of the 1970s or even earlier, while huge new high rises are going up all around them.
I then often turn back inward from the waterfront on Bryant Street. This is generally a wide street that crosses SOMA and the Mission District, but here it is a narrow alley between the steep approaches to the Bay Bridge and a residential block.
Again, the feeling is more of a residential section of New York, perhaps Riverdale in the Bronx, or the Upper West Side. Of course, the fact that this block interests Delancy Street adds to this impression.
Longtime residents and admirers of San Francisco often look down upon this area, but I find it a comforting place to walk and explore. Certainly, there is familiarity coming from New York, which has always defined “city” for me. And perhaps the sense that I am finally living the city life that I should have done long ago – I am finally home.
The narrow streets and tall buildings abut the hill and the approach to the bridge, with a complex array of staircases and ramps. I often find an excuse to climb at least one, such as this that connects the lower alley section of Bryant Street to the main section that begins on top of the hill.
At the top, one is amazingly close to the freeway and byzantine ramps that feed onto the bridge:
Heading back down the hill towards the west, one can take a detour through South Park, which has nothing to do with the popular cartoon. Instead, it is a small park surrounded by two-story residences that feels more like a neighborhood in Brooklyn. Although it is not far from the this section of freeway we featured a few weeks ago, such things seem invisible and far away. But step outside this oasis, and one is back in the “concrete jungle” and the streets that lead home.
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