Thursday morning seemed surreal on my dawn commute to the shaken city of Minneapolis the morning after their downtown’s entryway collapsed catastrophically. Drivers darted this this way and that, seeking alternate routes. As I walked in from the parking lot, a helicopter hovered directly overhead our building taking pictures of the I35W bridge remains. Cartoonist Marshall Ramsey captured all of our anxieties nowadays by picturing a span held up by question marks. I just hold my breath and speed up until crossing over and then breathe a sigh of relief!

The really important question is the cause of this precipitous breakdown in this vital structure. CNN’s widely seen video seemingly pinned the south end as the point of failure, but the northern end of I-35W bridge is now focus of probe. I heard one expert on the engineering of bridges say we should not be overly concerned about another bridge failure anytime soon because this one is an “anomaly”!

When the consequences are trivial, it is easy to dismiss events of such extremely low probability. However, in an extremely high-impact case like this, we want to know the risks of it happening again – assuming no intervention will be accomplished any time soon. This weekend I saw the August issue of The American Statistician magazine, which features reviews of a book titled The Black Swan: Impact of the Highly Improbable by Nassim Nicholas Taleb. According to Taleb’s home page named after his first book Fooled by Randomness /, Taleb’s goal in life is “…teasing people who take themselves & the quality of their knowledge too seriously & those who don’t have the guts to sometimes say: ‘I don’t know’….”

Taleb borrowed the black swan concept from philosopher Karl Popper. Before these birds were found prevalent in Australia (beautifully detailed by Black Swan wines ), they were thought to be extremely rare by the Western world. Taleb says that it may be emotionally satisfying, but we accomplish little by trying to explain catastrophes such as the 9/11 attack, and fool ourselves by quantifying their risk of re-occurrence. (I wonder if this serves as an example — the five threat levels predicted by the US department of Homeland Security, Low = Green; Guarded = Blue; Elevated = Yellow (current level); High = Orange; Severe = Red.)

Taleb obviously gets a kick out of tweaking the noses of pontificators purporting predictive powers on the next improbable high-impact event. However, I am studying with great interest all ongoing reports from the investigation of the I35 bridge collapse just down the road from my Stat-Ease office, not only for it being so proximate, but also for my peace of mind in having to constantly cross other spans over our region’s rivers and highways. I look forward to the day when our bridge gets rebuilt and perhaps we can again enjoy swans of any sort swimming along the banks of the Mississippi in downtown Minneapolis.

I just completed a wonderful book by Ross King about Brunelleschi’s Dome — an engineering marvel that dominates the skyline of Florence, Italy. The dome crowns the cathedral of Santa Maria del Fiore, the foundation of which began in 1296. It took 140 years for the church to be considered complete enough to be consecrated. The 140 foot diameter of the dome exceeds that of Saint Paul’s in London and Saint Peter’s in Rome. It was masterminded by Filippo Brunelleschi who dared to span it without a centering arch for support. He also came up with ingenious devices to lift some seventy million pounds of rock hundreds of feet up to their final resting places. For pictures and detail on Brunelleschi’s feat, see this site by Maria Patricia Farfan of McGill University.

Aside from the lasting fame he earned from the marvelous dome of Santa Maria del Fiore, Filippo should be venerated for something much more important for all inventive engineers and scientists – being the holder of the world’s first patent issued in 1421. Ironically it was for an invention that did not work out – an ungainly vessel dubbed Il Badalone – “The Monster.” It failed miserably at carrying the marble from Carrara needed for the final stages of construction to provide a beautiful façade. However, the advent of patent law provided protection against the rampant plagiarism of engineering innovations. It should be considered one of the milestones that separate the Middle Ages* from Renaissance times.

“Many are ready, when listening to the inventor, to belittle and deny his achievements…but after some months…they use the inventor’s…design…[and]…boldly call themselves the inventors of the things they first condemned…”
— Filippo Brunelleschi

*(I went to the Monty Python play Spamalot today. One of the characters, King Arthur perhaps, ponders how anyone would have known it to be the Middle Ages. The play poses many imponderables of this sort as well as non-stop implausible and improbable happenings – all in great fun. I give it two thumbs up, but as a native son of Hormel’s hometown of Austin, Minnesota, I must confess to liking anything concocted of Spam (excepting email).)

The results of my mixture design on Alka Seltzer rockets are shown in the graph, which reveals that the flight time in centiseconds (hundredths) lengthened as the proportion of air-to-water increased (p<0.01 for linear mixture model with no significant lack of fit). The predictive equation in terms of real components (fraction of actual space within the film canister) is: Flight time (seconds) = 1.24Water+1.95Air

For example, a container filled half way with water before dropping in the Alka Seltzer can be expected to propel the lid for 1.59 seconds (159 centiseconds) of flight time (= 1.24×0.5 + 1.95×0.5).

Give this a try and tell me how close you come to this outcome. I guarantee that you will flip your lid. However, be careful — you’d best wear goggles. I can imagine my mother catching wind of me doing something like this and yelling “that thing will poke your eye out!”

To illustrate design of experiments on mixtures at its simplest level, I blew up a plastic film canister Tuesday evening – not just once, but at least a dozen times. It was really nerve-wracking, but I was prepared to have a headache because the explosive power came from Alka Seltzer® — an amalgam of citric acid, sodium bicarbonate (baking soda) and aspirin.

You can see the apparatus for my experiment pictured: launching tube, container with water, the tablets, plastic film canister (Fuji’s works best), a scale and stop-watch. Research via the Internet produced many write-ups on making Alka Seltzer “rockets.” They generally recommend using only a quarter of one tablet and advocate experimentation on the amount of water, starting by filling the canister half way. I quickly discovered that the tablets break apart very easily, so it was most convenient and least variable to simply put in a whole tablet. Unfortunately, my assistant Katie is a troublesome teenager who discovered that the canister would blow up a second time when I went over to record the first shot’s results in Design-Expert. That’s what frazzled my nerves.

However, I must say that Katie was incredibly cool under the pressure of the plop, plop, fizz, fizz. It took a steady hand to quickly snap on the top of the canister, over which I then placed the launching tube and prepared to press my stop watch. After some seconds the explosion occurred – propelling the lid nearly to the roof of our two-story house. See (and hear!) a launch video from Mad Physics Dot Com (“…where knowledge becomes dangerous”). They flipped the film canister over, whereas I left it upright, thus shooting off the lighter lid.

Before designing my experiment, I did some range finding to discover that only 4 cc of water in the 34 cc canister would produce a very satisfactory explosion. However, it would not do to fill the container because the Alka Seltzer effervesced too quickly and prevented placement of the lid. After some further fiddling, I found that a reasonable maximum of water would be 20 cc’s – more than half full. I then set up a user-defined mixture design with Design-Expert that provided the extreme vertices (4 to 20 cc of water), the centroid (12 cc) and axial check blends at 8 and 16 cc’s. I replicated the vertices and centroid to provide measures of pure error for testing lack of fit.

I am the oldest of seven siblings, so naturally I agree with new evidence reported by Benedict Carey of the New York Times that eldest children develop higher IQs. Aside from getting a big head over this news, what I find intriguing is the assertion by Robert Zajonc, a psychologist at Stanford University, that the main source for intellectual stimulation comes from tutoring — a natural role for the oldest.

“Explaining something … solidifies your knowledge and allows you to grow more extensively.” — Professor Robert Zajonc

That’s why when I teach workshops for Stat-Ease on-site I suggest that students work in teams of two, with the more advanced ones paired up with those that may be just beginning. Both partners learn more as a result of this tactic to encourage tutoring. Also, this purposeful pairing reduces the odds of two slow learners dragging back the class relative to a more dynamic duo. If students are allowed to select their own partners, it seems inevitable that the range between teams of two will be maximized, making it very difficult to achieve just the right pace for presentation.

An editorial cartoon by Steve Sack of the Minneapolis Star and Tribune (pointed out to me by Pat Whitcomb) provides an alternative explanation for why younger siblings end up a bit slower mentally: They get regularly rapped on the head by their elders! If you are the oldest, like me, you will get a kick out of emailing Sack’s cartoon to your family.

Baseball aficionados in Minnesota cringed last month when their home-state baseball star Joe Mauer laid down a bunt with runners at first and second and no outs. However, a self-styled ‘Twin’s Geek’ supported this decision with an interesting statistics grid called the “expected runs matrix” published by Pete Palmer and John Thorn in The Hidden Game of Baseball. I came across this today in the Gameday program for the contest between the Minnesota club and the Toronto Blue Jays (Twins win! :)). If you are a baseball nut like me and enjoy digging into all the stats, check out this case made for making the sacrifice. In a nutshell, statistics compiled over 75 years of major league baseball indicate that Mauer’s success in advancing two runners made the out moot – the expected runs did not change. The Twins’s Geek (TG) thinks that Mauer, the reigning American League batting champ, thought he might get a surprise bunt hit, which would have increased the expected runs by a big margin. However, TG notes that the sacrifice may have gone in vain by not advancing runners (force at third, for example) or created a disastrous double play (pop to the pitcher and double up at first). What made this really interesting for me was the juxtaposition of situational stats provided by Gameday in this same issue. It shows that Joe Mauer is the premier clutch hitter on the Minnesota Twins and possibly all of baseball. For example, he bats nearly .400 with runners in scoring position! Therefore I must say: Joe, give it a go – swing away and make our day!