Archive for category science
Math messed with future astronaut’s mind and made him think faster
Last Thursday I enjoyed an inspirational speech by USAF Lieutenant Colonel Duane “Digger” Carey – a Saint Paul guy like me, but one who went far further than possibly any other from our home city. Digger was invited by the University of Minnesota’s Institute of Technology to speak about his experiences as pilot of the Columbia Space Shuttle mission of March 1-12, 2002,* that successfully upgraded the Hubble Space Telescope.**
Although Digger has many stories to tell, not the least of which is his record as a combat fighter pilot, he is most passionate about the benefits of math and science. He feels that his Masters in Aeronautical Engineering, while not directly relevant to flying a jet, enabled him to solve mission-critical problems at afterburner speed.
It was great seeing a hero like Digger Carey talk up math and science to our young people. I recall taking a summer physics camp and working out the equations for rocketry while building a model of the Saturn V. At the end of the course we blasted it off with 5 solid-propellant engines. Unfortunately it went way up and out of sight, so we never recovered the parachuted parts that floated somewhere back to Earth. However, even if we’d found the rocket, there would be no way to recapture the joy of seeing math and science put into action on that first launch. Anyways, that was enough for me. Imagine actually being inside a rocket blasting off! That takes a lot of courage and faith in technology.
“The most important thing we can do is inspire young minds and to advance science, math and technology education.”
— John Glenn, one of NASA’s original astronauts
* The last mission before the disaster of 2003
**See these spectacular new images from Hubble produced by the space telescope after the latest (and likely last) upgrade made by Shuttle Discovery astronauts who just landed Friday.
Coriolis effect continues to make the rounds despite efforts to flush it down the drain
Upon hearing a travel report from an acquaintance spending time this summer in Ecuador, I could not resist asking her to observe which way her sink and toilet drained. I’d heard that, due to the Coriolis effect, when you flush water in the northern hemisphere it swirls one way (clockwise), but below the equator it goes the opposite way.* Here is her enthusiastic report:
“Hi Mark, Yesterday I tested it – it´s true! We went to the Mitad del Mundo (Centre of the World), a big monument where the equator line is supposed to be. Unfortunately, they made a mistake when measuring, so the real equator line is a five minute walk away from the monument. By the real line they built a museum and there you can do funny experiments. For example, they put a sink on one side of the equator and let the water flush down, and then they move it to the other side and the water flushes the other way. On the line itself the water just goes straight down – no kidding! It was very interesting!”
I then had to do some research to see if this phenomenon could be independently verified. I hate to be a party pooper (ha, ha!), but, from what I read, in reality the Coriolis effect is so small that it’s easily overwhelmed the shape of the bowl and the other factors. Thus, most toilets flush in only one direction — clockwise or counterclockwise — regardless of location. This is explained very nicely by Alistair B. Fraser, Emeritus Professor of Meteorology Pennsylvania State University, in his white paper on Bad Coriolis.
In any case, it is fascinating to watch the last gallon of water from a hot bath twirl down the drain, so why not observe whether it exits clockwise or counter? I’ve never been south of the equator myself – the nearest I came was in Singapore. My hope is to do some personal validation on the Coriolis effect, or lack thereof. Why not?
*In a memorable episode (I thought it extremely funny) of the television cartoon The Simpsons (16th one in the 6th season), Bart, purporting to be an official with the “International Drainage Commission,” convinces an Australian boy to do a similar ‘down-under’ experiment. The results proved inconclusive, but very humorous. 🙂
Does good experimental design require changing only one factor at a time (OFAT)?
Posted by mark in design of experiments, science on June 23, 2009
“Good experimental design usually requires that we change only one factor at a time” according to an article I read recently in The Scientist magazine (“Why Don’t We Share Data,” page 33, Issue 4, Volume 23). This guide for science fairs tells students that “you conduct a fair test by making sure that you change only one factor at a time while keeping all other conditions the same.”
Obviously changing two variables together makes no sense, such as the time that as science project one of my kids asked me to do a blind taste test on Coke versus Pepsi, but to keep them straight in their mind, she poured one cola in blue plastic cup and the other in white Styrofoam! Needless to say I was completely confounded.
The OFAT method is so engrained that it’s literally become the law according to scientist who told me that, when as an expert witness he presented statistically significant evidence, it was thrown out of court due to the experiment design having changed multiple factors simultaneously. What a crime!
Multifactor testing is far more effective for statistical power, screening efficiency and detection of interactions. Industrial experimenters are well-advised to forget their indoctrination in OFAT and make use of multifactorial designs. For reasons why, see my two-part series on Trimming the FAT out of Experimental Methods and No-FAT Multifactor Design of Experiments.
Good experimental design does NOT require changing only one factor at a time!
Inverse transformation puts mileage comparisons on track
Tomorrow the IRS adds 8 cents per mile to their allowable rate for deductions on automobile use for business purposes. Precipitated by the rapid rise in fuel prices, this is an unprecedented mid-year boost of over 15 percent from the previous rate of 50.5 cents per mile.
When the price of gas went over 4 dollars a gallon, I started paying attention to which of my three cars went where. For example, my wife and her sister traveled 100 miles the other day to do some work at the home of their elderly parents. They had our old minivan loaded up, but, after thinking about it getting only about 15 miles per gallon (mpg), I moved all the stuff over to my newer Mazda 6 Sport Wagon, which gets 25 mpg. That meant no zoom-zoom for me that day going to work, but it was worth enduring the looks of scorn from the other road warriors.
A few weeks ago, National Public Radio’s All Things Considered led off with this quiz: “Which saves more gas: trading in a 16-mile-a-gallon gas guzzler for a slightly more efficient car that gets 20 mpg? Or going from a gas-sipping sedan of 34-mpg to a hybrid that gets 50 mpg?” Of course the counter-intuitive answer is the one that’s correct – the first choice.
This is a “math illusion” studied by Richard Larrick, a management professor at Duke University. According to a recent article in the journal Science, Larrick found it easy to fool college students into making the wrong choice in puzzlers like that posed by NPR. He suggest that it makes far more sense to report fuel efficiency in terms of gallons per 10,000 miles — an average distance driven per year by the typical USA car owner. Most of you who are likely to read this blog can easily apply this inverse transformation on mpg, but to check your math see this table posted by Duke University’s Fuqua School of Business.
According to this report by Reuter’s Professor Larrick was inspired to promote “gpm” (vs mpg) after realizing in the end that he’d be better off trading in the family minivan and only gaining 10 miles per gallon with a station wagon; rather than swapping his second car, a small sedan, for a highly efficient hybrid. This must be the basis for the NPR’s quiz.
This is definitely an issue where all things should be considered, but most importantly, just how much gas money might be saved one way or the other. Do the math!
PS. News flash: You can rest easy tonight – there will be no leap second, positive or negative, according to this post by the Time & Frequency Division of the National Institute of Standards and Technology (NIST).
Black belt master of multitasking?
Don’t Read This in Traffic says this article by Steve Lohr of New York Times, which many busy residents of that hyperactive city probably viewed on their internet-enabled cell phones while waiting in traffic. The multitask that I assigned this week to executive Six Sigma students at Ohio State University’s Fisher College of Business seemed easy in comparison: While sitting, rotate your right foot clockwise in sigmoidal fashion and then trace the number 6 in the air with your right hand. This stumped the entire class, so none could be declared black belts of Six Sigma, at least so far as being adept at tracing the symbols simultaneously. Do you think you can do it? Go ahead and try!
Seriously though, Lohr’s article did provide some good observations on multitasking:
— Check e-mail once per hour at most
— Listen to soothing background music – preferably not with lyrics
— Figure on 15 minutes being lost for every interruption to a serious mental task, such as composing computer code.
This last point explains why I seem to get so much writing done while home alone, working early in the morning before my staff arrives and filling in dead time at airports and during flights – I need uninterrupted time to compose my thoughts. On the other hand, tasks that do not require much thought, like filing and following up on things, can be knocked off right and left – interruptions and all. Now if only I’d get this Six Sigma thing figured out and get my hand multitasking with my foot.
PS. That reminds me of an amazing multitasking feat (feet?): Seeing my oldest daughter Emily — already an accomplished pianist, learn to play the church organ. This musical instrument requires playing with both hands and both feet! It boggles my mind just thinking of trying to keep track of all these things simultaneously.
Pairing foods and beverages to please the palate
Fish is white. Meat is red. That color pairing helps me decide which type of wine to order. It also sums up my interest and ability as a gourmand! For example, today we had a family brunch to celebrate my oldest daughter’s birthday and I ended up with two pitchers, one with grape juice and the other orange. Each had about a third of the juice remaining and the refrigerator could accommodate only one pitcher. Hmmm, what could I do? Eureka, a thought came to me: Mix the grape into the orange juice to combine it all into one container! Unfortunately, the resulting mixture looked so unappetizing that only my son Hank, an engineer like me (him software, me chemical), would drink it. Also, Hank admitted to having one or two beers –maybe more, while watching the Gopher hockey game last night at the corner pub. The Gophers unexpectedly lost, so I’m thinking my son may’ve drowned his sorrows. Therefore, I think that his positive review of my “orangerape” juice must be considered an outlier. 🙁
So far as beers are concerned, I’ve done equally bad, for example, by seeing what would happen if I mixed cream into it (detailed in my 1/14/07 blog “Mixing beers — synergy of zymurgy?”). One thing I never considered pairing with beer is chocolate, but, according to this article by J.M. Hirsch of Associated Press, Boston’s brahmins attend classes on this! An obvious combo is Belgian chocolate with Belgian abbey ale. However, I prefer to continue studying only beer. Any time our chemical engineering society sponsors a brewery tour and tasting, I am there!
My favorite pairing is apples with cinnamon. For example, this applesauce recipe looks very a pealing (pun intended!), in part because it’s so amazingly simple. I once tested my Stat-Ease colleagues by asking them to rate on a 1 (worse) to 10 (best) scale their taste preference of apple, cinnamon and lemon jelly beans and combinations thereof. The results are detailed in DOE Simplified in the chapter on mixture design, but the ternary diagram *, tells the story: Pairing apple with cinnamon creates a taste sensation (over 7 on the tasting scale) –- they are synergistic. However, putting the two fruits together (apple and lemon) created a sour reaction from our sensory testers (rated less than 3 on average) -– these two ingredients interact in an antagonistic manner. The trick when pairing foods and beverages is to avoid antagonism and seek synergism.
“Look for those opposites that attract. For example, sweet and acidity, sweet and spicy, hot and cold, salty and sweet.” David Kamen, chef instructor at the Culinary Institute of America (CIA).
*(Source of primer on ternary diagram: Lynn S. Fichter, Department of Geology and Environmental Science, James Madison University, Harrisonburg, Virginia.)
Do narrower columns hold up better for body of written work?
Pat Whitcomb came across a very intriguing article in the February ’07 issue of Training & Development magazine that says keeping line lengths shorter makes text easier to read and remember.* (Hmmm – did this asterisk cause you to reflexively glance to the footnote and interrupt your train of thought? Sorry about that!) IBM researchers evaluated paragraphs at 40 percent screen width versus 80 with a device that measures eye-gaze tracking. They found that narrow columns were more comprehensible and required less re-reading. However, this came at the cost of “paragraph abandonment,” a shift by readers to skimming completely over segments of text.
What’s telling to me, is that the IBM web page on this research (linked above) displays text in a single, wide column. I like this wider style for displaying text on my computer because I can then scroll line-by-line and not be forced to go back up again as required with two columns side-by-side. For example, see this latest edition of the Minnesota Section ASQ newsletter. Notice how it shifts format from one column to two. Observe how you read these. Which do you prefer?
My preference is to print pieces written in two-column format and then use my finger as a guide to maintain focus on the line of text. I picked this up from a business colleague years ago after he took a speed-reading course.
* “The Long and the Short of Learning” by Peter Orton, David Beymer and Daniel Russell.
Graupeling for words to describe nature’s emanations
Late Friday I took a call from a client in Hawaii. All day long here in Minnesota the weather forecasters had been harping about the dire prospects for over a foot of snow. The Hawaiian sounded skeptical when I told him of my positive view on these developments. Believe it or not, many of us Minnesotans enjoy the opportunity to ski, snowmobile and just revel in the contrast of winter with our other three seasons.
The first round of snow hit that evening. It was quite unusual – pelletized like Dippin Dots or IttiBitz ice cream, created by flash freezing the sugary dairy mix in liquid nitrogen. Something similar must have occurred naturally over my home town of Stillwater. The American Meteorology Society (AMS) describes this frozen phenomenon as graupel. Evidently it’s a cousin of hail, which we see in the summer-time when thunder storms become severe. This graupel was great for shoveling. I’ve got a low-tech, but amazingly effective, snow scooper, which just pushed it out the way and, with a quick twist, dumped it over. The pellets just poured right out.
That was only the first wave of the storm. Over the next 24 hours, another half-foot of snow fell. The neighbor across the street was really fired up about getting his snow blower running for the first time this year and promised to shovel my driveway after all was done with this winter storm. However, it took so long to start the disused engine, that I scooped him.
Getting back to Hawaii (a very attractive thought at the moment), I once visited their namesake “Big Island” and saw lots of lava from Kilauea. There I learned that Hawaiians differentiate flows as “aa” – rough, versus “pahoehoe” – smooth. (See details by volcanologist J. M. Rhodes.)
Having hand-shoveled snow for half a century, I can readily characterize their types. However, I must hand it to the Hawaiians for putting words to what Mother Nature puts in ones path. More snow is forecast later this week for Minnesota. I predict that this may precipitate many Minnesotans to have an “Aa, ha” and book an impromptu getaway to Hawaii or another warm State!
Overreacting to patterns generated at random – Part 2
Professor Gary Oehlert provided this heads-up as a postscript on this topic:
“You might want to look at Diaconsis, Persi, and Fredrick Moesteller, 1989, “Methods for Studying Coincidences” in the Journal of the American Statistical Association, 84:853-61. If you don’t already know, Persi was a professional magician for years before he went back to school (he ran away from the circus to go to school). He is now at Stanford, but he was at Harvard for several years before that.”
I found an interesting writeup on Percy Diaconis and a bedazzling photo of him at Wikipedia. The article by him and Moesteller notes that “Coincidences abound in everyday life. They delight, confound, and amaze us. They are disturbing and annoying. Coincidences can point to new discoveries. They can alter the course of our lives; where we work and at what, whom we live with, and other basic features of daily existence often seem to rest on coincidence.”
However, they conclude that “Once we set aside coincidences having apparent causes, four principles account for large numbers of remaining coincidences: hidden cause; psychology, including memory and perception; multiplicity of endpoints, including the counting of “close” or nearly alike events as if they were identical; and the law of truly large numbers, which says that when enormous numbers of events and people and their interactions cumulate over time, almost any outrageous event is bound to occur. These sources account for much of the force of synchronicity.”
I agree with this skeptical point of view as evidenced by my writing in the May 2004 edition of the Stat-Ease “DOE FAQ Alert” on Littlewood’s Law of Miracles, which prompted Freeman Dyson to say “The paradoxical feature of the laws of probability is that they make unlikely events happen unexpectedly often.“
Overreacting to patterns generated at random — Part 1
My colleague Pat Whitcomb passed along the book Freakonomics to me earlier this month. I read a story there about how Steven D. Levitt, the U Chicago economist featured by the book, used statistical analysis To Catch a Cheat –teachers who improved their students’ answers on a multiple-choice skills assessment (Iowa Test). The book provides evidence in the form of an obvious repeating of certain segments in otherwise apparently-random answer patterns from presumably clueless students.
Coincidentally, the next morning after I read this, Pat told me he discovered a ‘mistake’ in our DX7 user guide by not displaying subplot factor C (Temp) in random run order. The data are on page 12 of this Design-Expert software tutorial on design and analysis of split plots. They begin with 275, 250, 200, 225 and 275, 250, 200, 225 in the first two groupings. Four out the remaining six grouping start with 275. Therefore, at first glance of this number series, I could not disagree with Pat’s contention, but upon further inspection it became clear that the numbers are not orderly. On the other hand, are they truly random? I thought not. My hunch was that the original experimenter simply ordered numbers arbitrarily rather than using a random number generator.*
I asked Stat-Ease advisor Gary Oehlert. He says “There are 4 levels, so 4!=12 possible orders. You have done the random ordering 9 times. From these 9 you have 7 unique ones; two orders are repeated twice. The probability of no repeats is 12!/(3!*12^12). This equates to a less than .00001 probability value. Seven unique patterns, as seen in your case, is about the median number of unique orders.”
Of course, I accept Professor Oehlert’s advice that I should not concern myself with the patterns exhibited in our suspect data. One wonders how much time would be saved by mankind as a whole by worrying less over what really are chance occurrences.
*The National Institute of Standards and Technology (NIST) provides comprehensive guidelines on random number generation and testing– a vital aspect of cryptographic applications.