Monday, October 26, 2015

Chicago Shapes #1: The parabola


Plunging into all things parabolic for today's column proved too much fun to let the matter drop, so I'm using it to kick off an occasional series I'm calling "Chicago Shapes" that will continue, now and then, until I run out of shapes to write about. Tomorrow: The Circle.

    "Cool parabola," I thought, when I first noticed this arch traced across the front of River Point, the new 52-story tower going up at 444 W. Lake.
     A very 1950s, Jet Age shape, the parabola, defining the curve of a rocket in flight, "Gravity's Rainbow," to use Thomas Pynchon's wonderful phrase, the title of his dense, 1973 masterpiece that uses the parabola as a metaphor for fate, for the arc of life's, the upward spring of youth, the downward pull of age:
     "But it is a curve each of them feels, unmistakably. It is the parabola," Pynchon writes. "They must have guessed, once or twice — guessed and refused to believe — that everything, always, collectively, had been moving toward that purified shape latent in the sky, that shape of no surprise, no second chances, no return. Yet they do move forever under it, reserved for its own black-and-white bad news certainly as if it were the Rainbow, and they its children...."
     "No surprise, no second chance" — that sounds about right, to a guy in his mid-50s, about 2/3 the way across his own life's parabola, in the descending part of the curve, hurtling toward the Big Splat.
Parabola formed on an x/y axis.
     Not that you need gravity to make a parabola. There are other ways. Math will do. A parabola also represents an algebraic equation, plotted out on an x/y axis.
     For instance, here is a graph of the equation y=6x²+4x-8, a curve very much like the arch at 444 W. Lake, only flipped upside down:
     You can also slice a curved 3-dimensional geometric figure, such as a cylinder or a cone, like this:

     That's how they came up with the parabola at 444 W. Lake, as I discovered after I phoned the building's designer, Connecticut architectural firm Pickard Chitlon and spoke with Anthony Markese, one of the firm's principals, who was happy to hear from his home town.
     "I'm actually a suburban Chicago boy," said Markese, who grew up in Schaumburg "pre-mall."
     How did you decide to stick that parabola there?
     "The parabola form at the base of the tower and the top of the tower come from the building's response to the site," he said. "If you look at the building through Google Earth, one of the really interesting things about the site is a major portion of the Metra tracks run right through the site. The piece left to build on is a funny wedge shape left between Lake, Canal and the tracks."
      Not only did the site pose a significant engineering challenge -- the building had to be constructed over operating train tracks— but it also suggested the shape of the building.
     "What fit well in there in terms of the tower plan was the kind of curved cut football shape, the elliptical shape the body of the tower is," Markese said. "We started looking at how to make it more elegant, how to make it meet the ground plane. One way we came up with is to cut it, If you take an extended ellipse, and make a cut, you are left with that parabolic form."
That seemed right, aesthetically.
     "The idea of this grand arch that looked out to the river seemed really compelling to us," he said. "Sort of a ceremonial archway one could look through the lobby plaza out onto the river."
     You can't see it yet, but the shape will be echoed at the summit.
     "The top of the building has a series of cuts as well, lower parabola, dips downward to create another ellipse shape at the top of the building." he said. "The whole language of the building comes form cutting the building's surface for a variety of parabolic forms."
     Markese said parabolic shapes will also run through the pathways in the green space, and elsewhere.
Illustration of River Point when finished.
     "Once you start with an idea you try to run that idea through the building, to knit it all together," Markese said. "It seemed to fit the flowing nature of the river as well, a confluence of the three branches, curves against cures, a nice open sunlit area of the city."
     In that sense, it sort of mirrors the iconic green curved 333 W. Wacker building cross the river.

     "That building does a beautiful job bending around from one branch to another," he said. "We were very conscious of that, to have two curved building create this sort of flowing gateway to the south, quite beautiful and elegant. We very much had 333 on our minds when looking at this building."
     Making a large steel parabolic span like that and having it mesh seamlessly into the building took some computing power."Most of the parabolic shapes are framed with large curved bent steel beams, and we were pushing the envelope of a steel a bit," Markese said. "Marrying the steel, concrete and glass in a smooth way took a lot of computer time."
     That, he said, represented the most advanced aspect of the building.
     "The real change in technology was in computer software," he said. "We and the rest of the design team used to plot out those complex curves. All the surfaces come together in smooth, uninterrupted curves. All those surfaces have to have gutters to drain water, heat tracing to melt ice, and we had the ability to think about all that with advanced computer technology...10 years ago that would have been much more difficult."
     Do you worry, I wondered, that all these design nuances will fly past Chicagoans who will just see the parabola and think, "O00, 1950s retro."
     "I never thought of it as retro," Markese said. "Some people will look at the arch and not know any better. But it still looks fresh and modern. It's really more a geometric exercise."
     As is life. Geometry and math and physics. Writing about the design of the building as it goes up, I couldn't help but imagine some journalist in 22nd century Chicago digging the column up to celebrate the building as it goes down.
     "Because the given must be taken," the poet Philip Levine writes. "Because each small spark/must turn to darkness."
     Or, like the old saying relates, less poetically: What goes up must come down.


  1. I see in the paper there was no room for the geometric figures or other mathematical explanations that we see here. We can all use a few more geometry lessons.

    1. I didn't include them in the newspaper version, which I made considerably shorter, just hoping to get the photo in, for those readers who would have no idea what a "parabola" may be.

  2. Splendid! Some fresh ideas for my river boat architecture tour (always welcome)! I, too, think the arch look is 50s retro; I like it. I often compare Marina/River Cities to the Jetsons, get recognition from the elderly in the crowd (including myself). I missed the resemblance to 333 W. Wacker, will begin to note that. Realizing how barren Wolf Point was before all the new work...

  3. Great info. We have a prime view of all 3 new buildings going up (plus the newer Wolf Point additions moving forward). Amazing what it takes to get them built - but really neat to hear the design side of it. I wonder the same thing about the one south of it - another huge design feat I'd imagine. And I guess taking them all down will be even more so - can't really do an implosion over the tracks (unless we're all on hover trains by then, won't really matter).

  4. Very interesting column today. I never noticed the connection between the bend in the river and the curvature of 333 W. Wacker before. Cool! One small nit to pick - the 2 in the expression 6x2 should be a superscript to denote "x squared".

    1. Strange, when I read the article this morning it was: y=6x²+4x-8.

    2. The type was odd -- I wrote it in Blogger, then transferred it over to the paper's system, then moved it back. In recasting the font, I must have lostthe superscript. I'll fix.

  5. I realize that all the construction in the city is a good thing, and that building seems nice enough, and a well-thought-out addition, I suppose. One could do a lot worse than to attempt to complement 333 Wacker, after all. But, personally, I miss the much more wide-open view to the western sky that used to be available when looking down the river. "a nice open sunlit area of the city" -- not that 52-story towers don't tend to close things up a bit...

    Very interesting column, regardless, and the additional graphics for the blog are swell.

    1. I remember when the condo to the North of 444 W. Lake went up, it really was the first building to block off the view to the West. But every new building blocks somebody's view, and that really isn't an argument against it.

  6. Agree, this is quite interesting and fun. Looking forward to the "circle" post.
    Math Is Fun
    When you kick a soccer ball (or shoot an arrow, fire a missile or throw a stone) it arcs up into the air and comes down again ... ... following the path of a parabola!

  7. Basically, they ripped off the arch in St. Louis!

    1. I thought of the St. Louis arch, then decided, since this is about Chicago shapes, in essence: "Fuck 'em."

    2. Mr. S, you must have taken advanced math courses in hs and college.

    3. Nope, haven't taken a math course since high school. Of course, that was honors calculus. Not that I remember any of it.

    4. no thanks, liberal arts for me please and practical math

    5. I took the basic calculus class in college and was in danger of flunking it, because I had a hard time doing the arithmetic, keeping decimal points in the right place and distinguishing between + and -. However, the TA offered an A for whoever aced the final, which was a standardized test, and I got my A, because I was excellent in"filling in the bubbles."


    6. Some students are taking advanced math, some of which they may never use and they barely know how to give change or do simple multiplication or division. That should be stressed first and moreso than it is.

      What your TA did, isn't right, John.

    7. There was a time when I really enjoyed math, but my love for words was greater. My kids are an architect and an actuary, so I guess I at least passed it on. Computers have made a huge impact on both fields, as Markese mentions.

      Having never read Gravity's Rainbow, I never knew that the title referenced the parabola. Too many books, too little time!

  8. "Chicago shapes." A worthy subject for exploration. Chicago is no Venice, but Goethe, visiting that fabled city, famously dubbed its most renowned architecture "frozen music."

    Tom Evans