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December 30, 2011 12:22 PM Subscribe
Why are most buildings rectangular?
It's not that I can't use Google, it's that I am too ignorant to assess the relative importance/reliability of the answers it gives me. Also, I'm not sure how much of what I see is suspect as causal oversimplification or sloppy thinking. I can't even choose a category for this post, because I'm not sure if this question falls under "science and nature" (some overriding physical law?) or "society and culture" (cultural preferences?). Why don't we all have hobbit doors?
So hivemind, what say you?
It's not that I can't use Google, it's that I am too ignorant to assess the relative importance/reliability of the answers it gives me. Also, I'm not sure how much of what I see is suspect as causal oversimplification or sloppy thinking. I can't even choose a category for this post, because I'm not sure if this question falls under "science and nature" (some overriding physical law?) or "society and culture" (cultural preferences?). Why don't we all have hobbit doors?
So hivemind, what say you?
Certainly the switch from using plaster/lath to using pre-made (planar) wallboard/sheetrock contributed to the decline in the incidence of curved interior walls.
posted by janell at 12:27 PM on December 30, 2011 [2 favorites]
posted by janell at 12:27 PM on December 30, 2011 [2 favorites]
If you build a wall that's straight, then straight timber can be used anywhere along it. When the shape is more complex than that, you have to prefit the timber to the shape, which means the timber has to be specially made. That's slow and expensive.
Also, making curved timber out of straight trees is inherently wasteful. It also goes across the grain, so it isn't as strong.
posted by Chocolate Pickle at 12:30 PM on December 30, 2011
Also, making curved timber out of straight trees is inherently wasteful. It also goes across the grain, so it isn't as strong.
posted by Chocolate Pickle at 12:30 PM on December 30, 2011
At least in Europe, rectangular buildings predated the industrial revolution by a fair bit.
Did you look at the Steadman article (third result down in the Google results you linked)? His answer makes a lot of sense -- in a multi-room building, you need to efficiently put in interior walls without creating a lot of wasted space or using extra materials, and rectangles work well for this. Have you ever been in a hexagonal or octagonal house? They are beautiful, but you end up with odd corners and difficult to use spaces, making what are theoretically more efficient building forms less so.
Why not hobbit doors? Because it takes a bunch of extra materials, but you can still only walk through the center (unless, of course, you are hobbit sized); there's not much demand for deliberately inefficient doorways.
posted by Forktine at 12:34 PM on December 30, 2011 [1 favorite]
Did you look at the Steadman article (third result down in the Google results you linked)? His answer makes a lot of sense -- in a multi-room building, you need to efficiently put in interior walls without creating a lot of wasted space or using extra materials, and rectangles work well for this. Have you ever been in a hexagonal or octagonal house? They are beautiful, but you end up with odd corners and difficult to use spaces, making what are theoretically more efficient building forms less so.
Why not hobbit doors? Because it takes a bunch of extra materials, but you can still only walk through the center (unless, of course, you are hobbit sized); there's not much demand for deliberately inefficient doorways.
posted by Forktine at 12:34 PM on December 30, 2011 [1 favorite]
I'm a set designer. I recently did a production of The Hobbit, for which I built a circular door and doorframe. In the past, I've built normal doors, slanted doors, rectangular walls, weird shaped walls, curved walls, all kinds of crazy theater stuff.
Flat, rectangular things are fast and easy to build. Look, every time you design something and then figure out how to build it, there is math. The math is just simpler with rectangles. The build process is faster. I don't have to carefully gauge the angles on the saw, I don't have to figure out how to build a curve that can take weight, I can just do some very simple math and then build it. Much faster. In terms of construction, time is money. It is super expensive to build custom things that take a lot of time.
This is all theater building experience, but I'm betting it applies to home/building construction also.
Also, I once lived in a building that was circular, with sort of pie-slice shaped apartments. Let me tell you, it is much more difficult to satisfyingly place furniture in a non-rectangular room.
posted by Adridne at 12:34 PM on December 30, 2011 [18 favorites]
Flat, rectangular things are fast and easy to build. Look, every time you design something and then figure out how to build it, there is math. The math is just simpler with rectangles. The build process is faster. I don't have to carefully gauge the angles on the saw, I don't have to figure out how to build a curve that can take weight, I can just do some very simple math and then build it. Much faster. In terms of construction, time is money. It is super expensive to build custom things that take a lot of time.
This is all theater building experience, but I'm betting it applies to home/building construction also.
Also, I once lived in a building that was circular, with sort of pie-slice shaped apartments. Let me tell you, it is much more difficult to satisfyingly place furniture in a non-rectangular room.
posted by Adridne at 12:34 PM on December 30, 2011 [18 favorites]
A round door is easier to trip over when going through it.
You also can't wheel things in and out through it (e.g. a hand cart).
posted by Chocolate Pickle at 12:35 PM on December 30, 2011
You also can't wheel things in and out through it (e.g. a hand cart).
posted by Chocolate Pickle at 12:35 PM on December 30, 2011
Oh and- the circular door was was less resource efficient than a rectangular one- it created much more wasted material. And, if it's in a building you are heating, a circular door will have an enormously larger hole in the wall, creating a bigger heat leak.
posted by Adridne at 12:36 PM on December 30, 2011
posted by Adridne at 12:36 PM on December 30, 2011
People are roughly rectangular, when you think about it. We fit best in rectangular doorways, beds, and furniture. Our buildings are shaped to efficiently house our furniture and ourselves, so they end up being rectangles too.
More concretely, to build a regular rectangle you only need two measurements: perfectly vertical and perfectly horizontal. Both are easy to measure with simple instruments: a plumb bob and a bubble level. Building a regular sphere or dodecahedron or triangular prism requires more measuring and checking for each part.
posted by echo target at 12:46 PM on December 30, 2011 [2 favorites]
More concretely, to build a regular rectangle you only need two measurements: perfectly vertical and perfectly horizontal. Both are easy to measure with simple instruments: a plumb bob and a bubble level. Building a regular sphere or dodecahedron or triangular prism requires more measuring and checking for each part.
posted by echo target at 12:46 PM on December 30, 2011 [2 favorites]
Some people tried round barns.
"The work needed to build round barns was phenomenal. All the boards and planks had to be cut different and much of the wood had to be soaked in order for it to be bent into circles. But the reason round barns were built was because they were more economical. All the live stock could be arranged in a circle in the middle of the barn, and all the waste pushed toward the center of the barn, this could not be done in the conventional square barn. But because of the extensive labor needed to build these round barn structures, the idea was soon abandoned and people went back to the conventional less labor demanding square barns."
posted by iviken at 12:48 PM on December 30, 2011 [1 favorite]
"The work needed to build round barns was phenomenal. All the boards and planks had to be cut different and much of the wood had to be soaked in order for it to be bent into circles. But the reason round barns were built was because they were more economical. All the live stock could be arranged in a circle in the middle of the barn, and all the waste pushed toward the center of the barn, this could not be done in the conventional square barn. But because of the extensive labor needed to build these round barn structures, the idea was soon abandoned and people went back to the conventional less labor demanding square barns."
posted by iviken at 12:48 PM on December 30, 2011 [1 favorite]
Rectangular buildings make it easier to subdivide the interior into rooms without any wasted space. It is also easier to make additions to a rectangular building.
As discussed a few moths ago on the blue, there was a fad for octagonal houses in the 19th Century. It was short-lived, for the reasons I stated.
posted by 1970s Antihero at 1:01 PM on December 30, 2011
As discussed a few moths ago on the blue, there was a fad for octagonal houses in the 19th Century. It was short-lived, for the reasons I stated.
posted by 1970s Antihero at 1:01 PM on December 30, 2011
It seems to also strike a balance of area enclosed to amount of material needed to enclose it. Triangular buildings would use more wood for walls, with less efficient interior space (surely some of that corner space would be wasted). Pentagons (and shapes with greater numbers of sides) would be more efficient, but would run into the construction problems outlined above. Rectangles meet that happy middle of not only being easy to construct (which really may be most important), but also efficiently using available resources to do so.
posted by BevosAngryGhost at 1:04 PM on December 30, 2011 [1 favorite]
posted by BevosAngryGhost at 1:04 PM on December 30, 2011 [1 favorite]
Rectangular buildings are much more economical to construct because most materials are built with them in mind. Designing is simpler because the physics is based on simpler principles and deals directly with known forces. Gravity works normal to the level surface. Post and lintel construction isn't complicated and you don't need fancy computers to calculate how loading will work after the house is built. Now that we have fancy computers and people with lots of money, Gehry can let his mind wander and build damned near anything.
posted by JJ86 at 1:05 PM on December 30, 2011
posted by JJ86 at 1:05 PM on December 30, 2011
Best answer: From an historical perspective, it's a really good question. I can only say that round houses used to be prevalent in some areas of the world, with the switchover to rectangular occurring long before the need for standardization. There is likely to be a reasonable answer, but it's one that takes account of stone and clay building technology thousands of years ago, and not recent developments or problems with wood. The internal space efficiency argument is also weak, as many ancient buildings were very simple internal division, with little or no large furniture. Oh, and ancient roundhouses had rectangular not circular doors, so that too played no part.
My own hunch would be that round stone built houses were often constructed with rubble masonry but without mortar or adequate bonding, and so used their shape to provide strength. Once better masonry or the regular use of mortar appears, rectangular buildings become clearly more efficient.
posted by Jehan at 1:08 PM on December 30, 2011 [3 favorites]
My own hunch would be that round stone built houses were often constructed with rubble masonry but without mortar or adequate bonding, and so used their shape to provide strength. Once better masonry or the regular use of mortar appears, rectangular buildings become clearly more efficient.
posted by Jehan at 1:08 PM on December 30, 2011 [3 favorites]
Best answer: There are a lot of overlapping reasons for this. Here are a few:
In non-industrial, non-European cultures, there's plenty of situations where rectangular, or at least, "rectangular prism" is not the norm. One of the big determinants here is building technology. If your building technology involves making rotated A-frame of sticks and covering it with animal skins, it's much easier to build non-rectangular buildings than rectangular ones. If your building technology involves hollowing out cylindrical tree trunks, it's easy to be non-rectangular. There are examples of this in the world. But if you're building technology is post-and-lintel, you're definitely going to have straight lines, at the very least, because that is how the physics of post-and-lintel works.
In the old world, many, many cultures settled on the idea of either cutting down trees and forming them into posts and lintels, or doing the same thing with dressed stone. It was extremely popular:
Next, in Europe, people started building furniture that wasn't intended to be portable around the Medieval period. Before that, most people figured they'd move around a lot (even rich people, they'd be in this castle during that campaign and this castle during another). I don't really know very much about this, but I was stuck in traffic with my mom on a really long drive where she was listening to At Home: A Short History of Private Life and so I heard a lot of the sections on the development of furniture as being intended to stay in one place. You can still see this distinction remembered in language: a lot of the other Euro languages use words like "muebles" or "mobilario" as the word for furniture, distinguishing it from fixed "real property". Rectangular building furniture is a lot more interchangeable and flexible than furniture for non-rectangular buildings. Talk to anyone who has spent any time in a non-rectangular dwelling. Furnishing it with normal stuff, even stoves, ovens, refrigerators, etc. is a huge pain. My current apartment has a crazy turret area in it and it's very difficult to use. Nothing pre-manufactured fits there.
This is why you see things like classic 19th century loft buildings being repurposed over and over again: it's a print shop, it's a factory, it's an art studio, it's an apartment, it's an office, it's a retail store. The spaces are very general and flexible. Meanwhile, near where I grew up, there's this property with these enormous, tagine-shaped kiln buildings on it that was a ceramics factory before it went out of business. They look really neat, but no one can figure out what to do with them, so it's sitting there, empty. Been on the market for years. This is addressed at length in How Buildings Learn by Stewart Brand, which I've linked up on Ask several times before but it's been a while so what the hell. I really like it.
Finally, the construction industry forms a culture or industry in the archaeological sense. All the processing of raw materials into building materials assumes you are building a rectangle, or series of rectangles. This makes deviating from that assumption very expensive. My parents built a wall in their house that curves through 90 degrees. Building that one wall took a grossly disproportionate portion of the construction time, because everything had to be done custom, one-off, by hand. I think they had to actually build some sort of custom jig to bend some of the materials but I don't remember for sure.
Going back to Stewart Brand, he addresses this with less hand-waving somewhere in his writings. Brand was a huge advocate of geodesic domes as shelter, along with the rest of the Whole Earth Catalog crew. One of the advantages of geodesic domes in theory is that by more closely approximating spheres, their usage of material per unit of enclosed volume is a lot lower than a box. However, after years of working on dome building and advocating for domes, Brand found that dome construction actually consumed more material per unit enclosed, because things like sheets of plywood didn't perfectly suit the dome construction and so more waste was generated. Further, he found that issues with using the domed space effectively led to people actually having to build larger domes, so while their per-unit material use was lower, for the same application, they frequently had to be build larger volume structures, negating the per-unit material use advantage. I don't have a reference handy for where Brand has written about this, but I'm sure you can turn something up with some searching. I know he mentions it in passing in How Buildings Learn.
In summary, I think it's a bit of the old Space Shuttle / Roman Horse's Ass situation.
posted by jeb at 1:17 PM on December 30, 2011 [155 favorites]
In non-industrial, non-European cultures, there's plenty of situations where rectangular, or at least, "rectangular prism" is not the norm. One of the big determinants here is building technology. If your building technology involves making rotated A-frame of sticks and covering it with animal skins, it's much easier to build non-rectangular buildings than rectangular ones. If your building technology involves hollowing out cylindrical tree trunks, it's easy to be non-rectangular. There are examples of this in the world. But if you're building technology is post-and-lintel, you're definitely going to have straight lines, at the very least, because that is how the physics of post-and-lintel works.
In the old world, many, many cultures settled on the idea of either cutting down trees and forming them into posts and lintels, or doing the same thing with dressed stone. It was extremely popular:
In architecture, a post and lintel or trabeated system or order refers to the use of horizontal beams or lintels which are borne up by columns or posts. The name is from the Latin trabs, beam; influenced by trabeatus, clothed in the trabea, a ritual garment.Pretty much, when settled, agrarian societies move towards urbanization, they go through a phase where they build at least some of their buildings by balancing one strong straight thing across two sticking-up things, which results in straight wall segments. There are non-rectangular post-and-lintel buildings, they are just more complicated to build and use.
The trabeated system is a fundamental principle of Neolithic architecture, Ancient Greek architecture and Ancient Egyptian architecture. Other trabeated styles are the Persian, Lycian, nearly all the Indian styles, the Chinese, Japanese styles. The traditions are represented in North and Central America by Mayan architecture, and in South America by Inca architecture.
Next, in Europe, people started building furniture that wasn't intended to be portable around the Medieval period. Before that, most people figured they'd move around a lot (even rich people, they'd be in this castle during that campaign and this castle during another). I don't really know very much about this, but I was stuck in traffic with my mom on a really long drive where she was listening to At Home: A Short History of Private Life and so I heard a lot of the sections on the development of furniture as being intended to stay in one place. You can still see this distinction remembered in language: a lot of the other Euro languages use words like "muebles" or "mobilario" as the word for furniture, distinguishing it from fixed "real property". Rectangular building furniture is a lot more interchangeable and flexible than furniture for non-rectangular buildings. Talk to anyone who has spent any time in a non-rectangular dwelling. Furnishing it with normal stuff, even stoves, ovens, refrigerators, etc. is a huge pain. My current apartment has a crazy turret area in it and it's very difficult to use. Nothing pre-manufactured fits there.
This is why you see things like classic 19th century loft buildings being repurposed over and over again: it's a print shop, it's a factory, it's an art studio, it's an apartment, it's an office, it's a retail store. The spaces are very general and flexible. Meanwhile, near where I grew up, there's this property with these enormous, tagine-shaped kiln buildings on it that was a ceramics factory before it went out of business. They look really neat, but no one can figure out what to do with them, so it's sitting there, empty. Been on the market for years. This is addressed at length in How Buildings Learn by Stewart Brand, which I've linked up on Ask several times before but it's been a while so what the hell. I really like it.
Finally, the construction industry forms a culture or industry in the archaeological sense. All the processing of raw materials into building materials assumes you are building a rectangle, or series of rectangles. This makes deviating from that assumption very expensive. My parents built a wall in their house that curves through 90 degrees. Building that one wall took a grossly disproportionate portion of the construction time, because everything had to be done custom, one-off, by hand. I think they had to actually build some sort of custom jig to bend some of the materials but I don't remember for sure.
Going back to Stewart Brand, he addresses this with less hand-waving somewhere in his writings. Brand was a huge advocate of geodesic domes as shelter, along with the rest of the Whole Earth Catalog crew. One of the advantages of geodesic domes in theory is that by more closely approximating spheres, their usage of material per unit of enclosed volume is a lot lower than a box. However, after years of working on dome building and advocating for domes, Brand found that dome construction actually consumed more material per unit enclosed, because things like sheets of plywood didn't perfectly suit the dome construction and so more waste was generated. Further, he found that issues with using the domed space effectively led to people actually having to build larger domes, so while their per-unit material use was lower, for the same application, they frequently had to be build larger volume structures, negating the per-unit material use advantage. I don't have a reference handy for where Brand has written about this, but I'm sure you can turn something up with some searching. I know he mentions it in passing in How Buildings Learn.
In summary, I think it's a bit of the old Space Shuttle / Roman Horse's Ass situation.
posted by jeb at 1:17 PM on December 30, 2011 [155 favorites]
Another thing to consider is the land, most building plots will have straight edges, perhaps with a straight road on one side and the straight edge of a field on the other. You could build a round house with oddly shaped bits of land left on each corner of the plot, or a square house leaving a useful strip of green in front and back.
posted by Lanark at 1:32 PM on December 30, 2011
posted by Lanark at 1:32 PM on December 30, 2011
Best answer: Because rectangles are easy to subdivide. Whether it is the property the house is on, or the rooms inside the house, the most efficient way to divide things up is 90 degree corners. Big buildings aren't so bad, since big wedges are as good as rectangles. But not in house sized buildings.
In other words, any other shape is less efficient. If you have room for a circular building, you can fit a square building in the same usable space and get more area.
posted by gjc at 2:23 PM on December 30, 2011 [1 favorite]
In other words, any other shape is less efficient. If you have room for a circular building, you can fit a square building in the same usable space and get more area.
posted by gjc at 2:23 PM on December 30, 2011 [1 favorite]
Going along with jeb here. A huge factor is the roof system. While trial and error made many different folk-cultural roof approaches work, any sort of urbanization requires a more industrialized approach and you want to have an easily replicable system. Whether wood, stone, or whatever, the rectangular structure with a parallel ridgeline and two gables is simple and works very well even for very amateur builders. Combine these factors and the advantages of rectangles are pretty clear.
posted by dhartung at 5:27 PM on December 30, 2011
posted by dhartung at 5:27 PM on December 30, 2011
Interestingly, squares are more material-efficient than rectangles. Consider two rooms: one that is 20 x 5 and one that is 10 x 10. Both are 100 square feet, but the rectangle requires 50 linear feet of walls while the square only requires 40. That's a big difference in the long run.
posted by Benny Andajetz at 6:38 PM on December 30, 2011
posted by Benny Andajetz at 6:38 PM on December 30, 2011
Perhaps, with the advance of building technology, the day of arbitrarily shaped building isn't too far off:
http://www.youtube.com/watch?v=xvN9Ri1GmuY
posted by curiousZ at 8:45 PM on December 30, 2011
http://www.youtube.com/watch?v=xvN9Ri1GmuY
posted by curiousZ at 8:45 PM on December 30, 2011
I've lived in a round building. Decorating was an absolute bitch. No walls were parallel so if you put a TV on one wall the couch either had to be against the wall and everyone would watch TV at an angle, or the couch would be parallel to the TV, but at a weird angle to the wall that wasted the space behind it. The bedroom was a nightmare because no matter where you put the bed it divided part of the room into a nearly unusable pie slice. In fact every room had an unusable pie slice. The bathroom was hilarious.
And having done carpentry I can't even guess how much harder it woud be to build. Building at right angles is simple. Pythagorus had everything you need to know figured out 2500 years ago. Building on the round is not.
Also: Roads like to be straight. Best use of space is to make the buildings have straight sides.
posted by Ookseer at 10:53 PM on December 30, 2011
And having done carpentry I can't even guess how much harder it woud be to build. Building at right angles is simple. Pythagorus had everything you need to know figured out 2500 years ago. Building on the round is not.
Also: Roads like to be straight. Best use of space is to make the buildings have straight sides.
posted by Ookseer at 10:53 PM on December 30, 2011
Best answer: Rectangular is more efficient use of the land, as well. Sure, if you've got a large enough acreage, you can build any shape you'd like; but consider urban areas, where the land is at a premium: say you want to build the highest possible number of building units on your ground space. Rectangular works because if you just drew a line from one front doorway to the next, you'd have a relatively flat-fronted row of buildings; plus the easiest way to divide them is a straight line from the building's front to rear --- and that saves even more on the building materials, because then you're only putting up one joint wall to divide two units (instead of two walls), so adding another unit to the end of a row only costs you *three* additional walls, as opposed to four (or more) walls' worth of material for a free-standing building.
posted by easily confused at 8:47 AM on December 31, 2011
posted by easily confused at 8:47 AM on December 31, 2011
In summary, I think it's a bit of the old Space Shuttle / Roman Horse's Ass situation.
Which is an urban myth, although the rest of your post was very informative.
posted by Halloween Jack at 9:04 AM on December 31, 2011
If you actually read that entry, HJ, it's not actually debunked at all. The chain of causation maybe doesn't go back as far, but it's quite literally true that the Space Shuttle's tanks are the size they are because of the load size that horses could easily carry. The Roman chariot was the first really common wheeled device pulled by horses. Roman roads were made to suit Roman chariots, later wagons were made to suit Roman roads, and then railroads used existing wagon designs when they first started. And the Shuttle's tanks had to fit in rail tunnels. Yes, the limits in what horses could pull put some limits on how wagons could be shaped, but the transition to rail had no such limitation.
I mean, consider this paragraph from Snopes:
Although we humans can be remarkably inventive, we are also often resistant to change and can be persistently stubborn (or perhaps practical) in trying to apply old solutions to new conditions. When confronted with a new idea such as a "rail," why go to the expense and effort of designing a new vehicle for it rather than simply adapting ones already in abundant use on roadways? If someone comes along with an invention known as an "iron horse," wouldn't it make sense to put the same type of conveyance pulled by "regular" horses behind it? That is indeed exactly what was tried in the early days of American railroads, as captured in the following illustration:
So they say it's debunked, when their entire article basically supports the original contention.
posted by Malor at 6:39 PM on December 31, 2011
I mean, consider this paragraph from Snopes:
Although we humans can be remarkably inventive, we are also often resistant to change and can be persistently stubborn (or perhaps practical) in trying to apply old solutions to new conditions. When confronted with a new idea such as a "rail," why go to the expense and effort of designing a new vehicle for it rather than simply adapting ones already in abundant use on roadways? If someone comes along with an invention known as an "iron horse," wouldn't it make sense to put the same type of conveyance pulled by "regular" horses behind it? That is indeed exactly what was tried in the early days of American railroads, as captured in the following illustration:
So they say it's debunked, when their entire article basically supports the original contention.
posted by Malor at 6:39 PM on December 31, 2011
Malor, did you actually read the Snopes article? There were three different railroad gauges used in the early days of American railroad; the one that's standard now enjoys that status because the side that used it was the one that won. (Standardization of rail still isn't universal; there are two separate divisions of the NYC subway because they were originally three different systems, and the former IRT (the numbered lines) uses narrower cars than the other lines.) And I've yet to see any outside verification that the design of the solid rocket boosters (not the "tanks) for the space shuttle took the width of train tunnels into consideration; the actual external liquid fuel tank was certainly much larger.
posted by Halloween Jack at 7:30 PM on January 1, 2012
posted by Halloween Jack at 7:30 PM on January 1, 2012
I don't know if jeb was referring to this article about geodesic domes as surprisingly inefficient shelter, but it's the one I thought of: Domebuilder's Blues, by George Oakes. It's a good read.
posted by dreamyshade at 7:56 AM on January 2, 2012 [5 favorites]
posted by dreamyshade at 7:56 AM on January 2, 2012 [5 favorites]
That's a great article, and there are some other good ones on that site. I can remember as a kid visiting friends of my parents who had built funky 1970s hippie houses. They were beautiful, and I still have a nagging itch to build one, but there were all kinds of livability issues, like the amplification of peeing sounds mentioned in the dome article. Simply changing to a rectangular plan form fixes many of these issues; I'd guess that livability concerns are as large a factor as construction efficiency in terms of keeping most buildings and rooms mostly rectangular.
posted by Forktine at 10:00 AM on January 2, 2012
posted by Forktine at 10:00 AM on January 2, 2012
This thread is closed to new comments.
posted by dfriedman at 12:24 PM on December 30, 2011 [1 favorite]