Wednesday, July 6, 2011

Twist and shout

I twisted Rubik's World to an inclusive standstill, but I had the last laugh. 

Sort of.

For those unfamiliar with things Rubik, the "world" is a sphere composed of 8 pieces. It's like a 2 by 2 cube, but spherical.

I insouciantly tore the wrapper off and started to fiddle around. It didn't look that complicated.

What followed was hour upon hour of spinning the pieces, matching South America to North America, trying to get Australia in the right place, and so on. With Africa and South America in the correct spots, half of Asia was somewhere in the Pacific.

Then I managed to get most of it right, realizing that either the eastern or western hemisphere was upside down.  If I keep moving things around, I reasoned, sooner or latter I will blunder into a solution. Then I realized that that strategy is useless. 

Yes, there is an algorithm that sorts everything out, but  the knowledgeable people on You Tube either covered the puzzle with their hands, or were vague. Among the more confusing aspects of the explanations is that regardless of how the puzzle is held, the top is called the top, the left called the left, and so on.

Consequently, one second you're looking at the top, and the next you're looking at the top, which is now a side. Some day the Khan Academy will post understandable instructions on Rubik puzzles.  Meanwhile, more clockwise, up, clockwise down, left, left. etc. 

Eventually I'd had enough and proceeded to take the thing apart so I could reconfigure it in the correct position and put it away.  This is the real puzzle, I thought, as a bunch of black plastic pieces fell out. I must admit shamefully that after I got all but two of the pieces back inside, I glued the whole thing together. 

Now it is forever (relatively speaking) solved.

Are there people who enjoy puzzles? Who actually like the bewilderment and repeated false steps? Doesn't seem likely. Trying to fit the World back together was far more enjoyable than the puzzle itself. 

Part of the problem with Rubik puzzles is that they are abstract. The sole purpose is to figure out how to manipulate the thing. Everyday puzzles are more rewarding. You may think about how to fabricate a bird house, or a shelf, or some other minor wooden project. 

Consider doing this, or that. Maybe Plexiglas is the best bet.  Perhaps cut this piece at an angle, or put the frame on the outside, or build the thing out of cardboard boxes. 

At the end, you have something to show for your trouble.  If it's junk you can rip it apart and do over.

Rubik-wise, the reward seems to be the knowledge of how to solve the puzzle. People compete to see who can rearrange the cubes fastest. No one in his right mind fiddles with a Rubik's cube or world for 20 minutes a day, before taking a walk, or after breakfast. 

Having an unsolved Rubik sitting around is practically intolerable. Chess puzzles are similar. They are made to solve, not ponder. 

One conclusion has become clear: I am not a Rubik's kind of person: too many screwdrivers and types of glue.

Friday, July 1, 2011

The measure of a bridge

Measure twice, cut once, woodworkers say.

Accurate and precise measurement are the keys to 90-degree square corners, even legs, and generally, pieces fitting together properly. On a small project it's usually possible to correct errors  by cutting, planing, sanding, gluing, or using wood putty.

Now imagine you are building an enormous bridge, highways, and on and off ramps over New Haven Harbor to replace the old bridge.

The materials are way too big to measure with a tape. Can a steel fabricator guarantee that a 50-foot girder will be within 0.001 inch of the blueprint girder?  When construction workers pour concrete into stories-high wooden molds,  how are they able to make the finished product exactly the right size? Also, all of the angles have to be correct, because the bridge and associated sky ways are curved.

Who is out there with a yard stick making sure the project is built according to specifications? A cursory inspection does not reveal anyone with prospecting tools, and you do not see the workers looking at plans. Maybe this all takes place in a trailer somewhere.

Still, who determines the correct height of the mold and how is this applied in practice? How do they make the towers plumb?

Sure, there are project engineers, bridge engineers, and all of those people. You ever see them measuring anything?
Maybe they are doing the equivalent of drawing out a tape measure and marking a spot, but using unrecognizable equipment. Infrared or laser beams? Global positioning systems? 
But even if an engineer can determine that a particular support needs to be 35 feet, six and half inches tall, how do the workers possibly fabricate something that big and with such precision?

It's not easy to make six two-by-fours all exactly eight feet long, for example. However, in theory, the job is straight forward. What theory do builders use when six pieces of concrete have to be exactly 50 feet long?

Maybe all highway support columns and other construction elements are a standard size, and so all of the fabrication equipment is automatically gauged properly.  That does not seem plausible. 
Or maybe the crews just eyeball the whole thing and modify as they go. That doesn't seem plausible  either.

Same holds true for skyscrapers, dams, stadiums,  oil tankers, and all enormous man-made things.

Suppose 100 men and women are working at a site, and each one is accurate down to a hundredth of an inch. At the end, won't whatever they're building be off by at least an inch?