Yesterday (June 23), would have been the 100th birthday of Alan Turing, the mathematician who was one of the founders of modern computer science – indeed he is often considered to be the “father of computer science.”
In the 1920s and 1930s, much attention in the mathematics was on the subject of “computable numbers” and finding automatic systems for proving mathematical statements. Based on a series of problems stated by David Hilbert, the mathematician Kurt Gödel ultimately proved that this not possible. Essentially, there is no formal mathematical system that can decide the truth or falsehood of all mathematical statements. This is quite profound and simple to state, but Gödel’s mathematics is cryptic and at some times impenetrable. By contrast, Alan Turing’s formulation of the mathematics as a simple device is quite accessible and laid the groundwork for the positive use of Gödel’s results. Sure, we cannot solve all mathematical problems computationally, but we can do quite a lot with the right tools. The Turing Machine is one of the simpler of such tools.
A Turing Machine consists of a tape, or an infinite sequence of cells, each of which contains a symbol that can be read or written. There is a head, which (much like the head on a tape recorder) moves along the tape and is always positioned at one cell. The state register contains one or more states of the machine. Finally, the transition table contains a series of instructions of the form qiaj→qi1aj1dk where q is a state, a is a symbol, and d is a number of cells to move the head left or right along the tape (including not moving it at all). So, if the machine is at a given state qi and the head is over a symbol aj, switch to state qi1, write the symbol aj1 at the head, and move the head dk positions to the left or right.
The description of the Turing Machine is very mechanical, which makes it a bit easier to understand. But it is nonetheless a formal mathematical model. It was used to demonstrate that the “halting problem”, the ability of such a machine to determine if any set of states and transitions will stop or repeat forever, is not solvable. This remains today, one of the great unsolvable problems in computer science.
About the same time as Turing published his results, American mathematician Alonzo Church published an equivalent result using lambda calculus, a system I personally find more intuitive and elegant because of its basis in functions and algebraic-like expressions (it will be the subject of a future article). But Turing’s work has been more prominent both in mainstream computer science and in the culture at large, with computer designs and languages being described as “Turing complete”. And then there is the “Turing Test” for evaluating artificial intelligence systems. So far, no system has ever passed the test.
During this centennial, especially coming as it does during Pride Weekend in much of the United States, there has been much written about Turing’s homosexuality and his being convicted for homosexual activity that was then illegal in the UK and stripped of his security clearance. This is a very sad statement on the time in which he lived, that someone who was both one of the most influential mathematicians in a growing field of computation and a hero of World War II for is code-breaking exploits was treated in such a mean and undignified way. There was also much written about the mysterious circumstances of his death – long considered a suicide, a recent BBC article on the centennial suggests otherwise. You can read for yourself here. As for us at CatSynth, we prefer to focus on his achievements.
Google honored Turing yesterday with one of their trademark “Google Doodles” in which they implemented a functioning Turing Machine.
But the Golden Gate Bridge is an important practical part of the city. It is a busy transportation carrying US 101 and California Highway 1 north from San Francisco into Marin County and points beyond on the north coast. It is very unusual for a modern roadway in that the opposing lanes are separated only by short poles that are moved to adjust the number of lanes in each direction. It seems a bit quaint, in fact. On the city side, the highway split into a boulevard carrying CA 1 south and Doyle Drive (US 101) until this past month when the latter was demolished. From these points, travelers are dispersed onto the city streets of San Francisco. There is no easy highway or rail connection between my part of the city (near the Bay Bridge) and the Golden Gate Bridge, owing to the city’s hilly geography and quirky political history. As such, I find myself not near the bridge very often except when I need to be. But when I am nearby it is worth stopping to take notice.
Crossing from Virginia into North Carolina on I-95 (which I most recently did in 2009 under cover of darkness), one gets the sense that “now we are really in the South.” It’s perhaps a combination of the vegetation, terrain, but especially the name “Carolina”.
That particular trip involved traveling southward along I-95, and then later returning to the state near the coast on US 17. The contrast between the different corridors was quite apparent. The US 17 corridor, when when it was not exactly on the coast, was surrounded by shorter vegetation in a lighter shade of green. As we got closer to Wilmington and I-140, it was hard to tell whether we were in a quiet coastal region or in an outer suburb with lots of highways but relatively little visible development. From 17/I-140, we turned onto I-40 and headed north. But if I the time for a proper visit, I would have continued up US 17 back towards the Outer Banks.
One can talk a particularly scenic trip through the Outer Banks on North Carolina Highway 12, which stitches together many of the barrier islands via bridges, causeways and ferries with fantastic views. The road goes through the Hatteras National Seashore. It also goes through Kitty Hawk, often credit as the location of the Wright Brothers’ first flight, though it was actually in nearby Kill Devil Hills. One of the most prominent landmarks, in addition to the continuous stretches of beach, is the Hatteras Lighthouse.
If we leave the Outer Banks and head northward and eastward on I-40, we eventually come to the Raleigh, the state capital and one of the main cities of the Research Triangle together with Durham and Chapel Hill. The Research Triangle is home many technology companies (both in the Research Triangle Park and beyond), and is anchored by Duke University, University of North Carolina and North Carolina State University. These schools are also known for their basketball teams. Raleigh is a much larger city and the center of state government, and sports both an inner and outer beltway, I-440 and I-540 respectively, though the latter is only partially built. Durham, to the north and west, looks from images as a grittier city that might attract my interest, especially with the old tobacco-factory buildings that have been converted to mixed use.
It is also home to a large and vibrant African American community with a long history of successful businesses and a neighborhood once dubbed “The Black Wall Street.” It was also a center for early Civil Rights activity including some of the earliest “sit-ins.” Already in decline by the late 1960s, the neighborhood appears to have been torn apart by the construction of the Durham Freeway (NC 147) through the center of the city. It is a familiar sounding story (like the Cross Bronx Expressway in New York).
From Greensboro, we take I-85 south and west towards Charlotte, the state’s largest city. Charlotte has become a major banking center, most notably it is home to “way too big to fail” Bank of America. It has prospered and underwent a major construction boom with a large jumble of post-modern skyscrapers.
We return to Greensboro and head west on I-40. The development becomes sparser and the landscape more hilly and scenic as we approach the Blue Ridge Mountains. And more treacherous as well. We turn onto I-240 to the town of Asheville.
We conclude by turning north onto I-26, a relatively new and quite spectacular highway through the mountainous border region between North Carolina and Tennessee. The highway, which opened in its current Interstate form in 2003, winds it’s way through mountain passes, alongside cliffs, and even through a tunnel. This video gives a sense of what it is like, even though it is traveling in the opposite direction, from Tennessee back to North Carolina.
Another thing that makes talking about New York different from talking about other cities in this series is that there aren’t many highways to talk about, especially in Manhattan. New Yorkers take the subway. But there are still highways even in some of the denser areas of the city. The FDR Drive along the eastern edge of Manhattan is narrow and winding but offers good views of the East River and the changing skyline of the city as it passes underneath the bridges.
On the Brooklyn and Queens side, there is the Brooklyn-Queens Expressway, (I-278, the BQE). It zig-zags through some of the densest areas of Brooklyn on a narrow double-decker path among tall buildings. With the contemporary focus on Brooklyn, the highway has also taken on a significant identity for those who live and work there. There are even multiple art and music pieces dedicated to it, such as this 
The Bronx is bisected by Interstate 87, the Major Deegan Expressway, which travels with length of the borough south to north, passing by Yankee Stadium. As it crosses the city boundary into Westchester County, I-87 becomes the New York State Thruway. The Thruway cuts through the southern part of the county before meeting I-287 and crossing the Hudson River on the Tappan Zee Bridge.
This is the Hudson River Valley, known for its scenery and for inspiring the “Hudson River School”. The paintings may look rather trite and dated now, but the scenery that inspired them is still quite spectacular. One of the more dramatic points along the river is the Bear Mountain Bridge, which carries US 6 and US 202 from Westchester on the east side to Orange County and Bear Mountain State Park on the west side, spanning large hills on either side. It also connects up NY 9D on the east and US 9W and the Palisades Interstate Parkway on the west.
On the west side of the Hudson, one can continue north on the Thruway to Albany, the state capital. However, on the east side, one could take the scenic Taconic Parkway. It begins in suburban Westchester County just north of the city and not far from where I grew up, and then continues north through picturesque rural landscape for the remainder of its route. It is in fact the second-longest continuous road listed in the National Register of Historic Places after Virginia’s Skyline drive.
The Empire State Plaza, conceived and built by then-Governor Nelson Rockefeller, is a huge government-building complex built and arranged in the futuristic international style of the 1960s, a bit like Brasilia. As a result, I am quite fond of it. Nearby along US 20 is the State Capitol building, which is quite different from most others. It is not the Classical style with columns and a large dome or rotunda, but instead looks more like a rich family mansion that one might find in New York in the 19th century. It is a mixture of Roman, Renaissance and Victorian styles all put together.
From Albany, one can continue on I-87 north towards the Canadian border. Along the way, the highway passes through the Adirondack Mountains. In the northern part of the Adirondacks, one can leave the interstate for smaller roads like Highway 86 through the mountains to Lake Placid of Winter-Olympics fame, and nearby Whiteface Mountain.
Meanwhile, the Thruway continues west from Albany with I-90, through many of the other cities that dot western New York, such as Syracuse and Rochester, passing north of the Finger Lakes. The longest is Cayuga Lake. On the south end is the town of Ithaca, home of Cornell University whose campus is on a hillside overlooking the lake, and whose official school song references the lake. Near the northern end of the lake is Seneca Falls, a famous location in the history of women’s rights in the United States. From Seneca Falls, we can also follow the Erie Canal westward. The canal, which was an important transportation route in the nineteenth century, runs largely parallel to the present-day Thruway. It is known for its complex series of locks, such as these at the appropriately named town of Lockport.
The Erie Canal and the Thruway continue westward to the city of Buffalo. We leave the main Thruway and continue on I-190 towards the downtown on the shore of Lake Erie. It is the second largest city in New York State, but I have yet to visit it. It’s location on the edge of the Great Lakes and its industrial past make it seem much closer to the cities of the midwest, such as Cleveland and Detroit, than to the rest of New York. Indeed, one of the city’s landmarks, Buffalo Central Terminal reminds me a bit of Michigan Central Station in Detroit: a once grand art-deco station that has been abandoned and fallen into disrepair.
In the eastern section of the capital, we encounter aptly named “Badger Interchange”, in which no fewer than three major interstates converge, I-90, I-94 and I-39. The interchange also includes state highway 30, a short freeway that connects to downtown Madison.
Highway 30 ends at US 151, which traverses the isthmus that holds downtown Madison and separates lakes Mendota and Monona. I don’t know of too many other cities concentrated on an isthmus like that. Certainly, the location between the two lakes makes for interesting views and architectural opportunities. Consider this view from Lake Monona featuring the State Capitol building book-ended symmetrically by large buildings and standing behind Frank Lloyd Wright’s Monona Terrace.
It of course did not take long for us to encounter a building by Frank Lloyd Wright, a native of Wisconsin. His summer home and studio, Taliesin, is in Spring Green, west of Madison. We take US 14 west from the capital through a green hilly landscape – it’s not hard to see why this might been inspiring for Wright’s prairie style architecture, with its use of horizontal lines and low angles that reflect the expanse of the landscape. 
I-94 continues towards downtown, passing through another large interchange, the Marquette Interchange with I-794, I-43, and US 41. It does look like a complicated tangle.
Wisconsin does not have much shoreline on Lake Superior compared to its neighbors – in particular, Michigan extends quite a bit westward along the south shore of the lake, but it does have the Apostle Islands National Lakeshore. We can get there from Michigan on US 2, passing along the edge of Chequamegon Bay before turning north onto WI 13 along the waters edge to the Apostle Islands. In addition to wildlife and great views of Lake Superior, the islands have unusual “sea caves”, such as these at the edge of Sand Island.
From the western side of the beltway, we begin on Interstate 66 and US 50 heading east from Virginia over the Potomac River. I-66 turns north while US 50 continues eastward as Constitution Avenue, passing alongside the National Mall and all the national memorials and monuments, which are arranged around the mall and the parkland along the Tidal Basin.
The Capitol is surrounded by several blocks of grounds, including the Capitol Reflecting Pool. While wandering around these grounds on foot, one would probably not suspect that there was a major highway passing underneath. I-395 traverses the center of the city in the long Third Street Tunnel, connecting to US 50 (New York Avenue) in the northern sectors. The densely packed residential sections of the Capitol Hill neighborhood can be found to the east, and a lively urban neighborhood to the northwest around Logan Circle.
South of the Third Street Tunnel, I-395 continues towards Virginia and a junction with the Beltway at the Springfield Interchange (aka, the Mixing Bowl). Before crossing the Potomac, it intersects with I-695, a short connector to the Anacosta Freeway in the southeast section of the city. It is signed as I-295 and also as DC 295. It is the only signed DC highway that currently exists, but it is another thing that gives the District of Columbia the trappings of a state, except of course that it isn’t a state and doesn’t have voting representatives in Congress. Hence another state-like item, the district’s license place, continues to bear the Revolutionary War slogan “Taxation without Representation”.
…where it continues as Maryland Route 295, the Baltimore-Washington Parkway. The parkway is partly maintained by the National Park Service. In this segment, it is a wide road through wooded surroundings, although industrial and suburban areas are never far away. Further north, it becomes an expressway through the suburbs south of Baltimore as it heads towards that city. The parkway ends at a I-95. Nearby, a larger and impressive junction over water takes the short I-395 (completely unrelated to the one we just left in Washington, DC.) until downtown Baltimore, passing by Camden Yards and just to the west of the Inner Harbor.
We head south from Baltimore towards the Chesapeake Bay on I-97, where has the distinction of being the shorted two-digit interstate. It passes through hills and suburban towns to US 50 near Annapolis, the state capital. I remember visiting Annapolis in 1999 and 2000. The 1999 visit included walking around the historic district and into the statehouse, one of the oldest in the country with a distinctly colonial look about it, and watching July 4 fireworks on the bay. It was also during an intense heatwave, with some days over 100F. I didn’t mind the heat too much, and it made it great weather for swimming. The towns and cities along the bay, including Annapolis, seemed intimately connected to the water.
Back in Baltimore, we return to the western neighborhoods, not far from the rowhouses we explored earlier, and head west on US 40. Just past Gwynns Falls / Leakin Park, we come to a parking lot that is the eastern terminus of Interstate 70. It was originally planned to go further through the city, but that extension was ultimately cancelled. In this case, we take I-70 westward out of the city.
This part of the state is quite sparse west of the Baltimore metropolitan area is quite rural and sparse, and in some ways would seem to be a separate state, more in common with West Virginia. I-70 and US 40 run together or nearby for much of the region. As I-70 heads northwest into Pennsylvania, I-68 continues with US 40 west through the Appalachian Mountains, including this cut through Sideling Hill.
