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.
Fair food follies – sticking on calories at a prodigious rate
The weather here in Minnesota has been incredibly clement this summer – encouraging more State Fair goers than ever before. The total for the dozen days will likely break the record, now approaching nearly 2 million visits!
My wife and I went for a second time yesterday. Thanks to a tip from my son, I found healthier food fare this time around – a pot-roast sundae (savory roast beef atop a scoop of mashed potatoes mixed with corn – yum!). On our first visit I succumbed to the siren call of a vendor selling deep-fat fried Hostess Twinkies on a stick, to which I compounded the calories by agreeing to it being dipped in chocolate and powdered with sugar. You can see this terrifically calorific confection pictured alongside a free yardstick — a mandatory pickup for any serious fairgoer.
I avoided the bacon on a stick dipped in chocolate at the advice of my daughter, who tried it last year. She worked the Haunted House at the last two Minnesota State Fairs and ate just about everything on a stick. My wife ate a piece of corn on a stick and part of a foot-long corn-dog on a stick. That looked good to me, but I was already satiated by my second sundae — the pot roast: I’d already eaten an ice-cream sundae with rhubarb and strawberries (highly recommended by my colleague Pat).
Several years ago I ate a deep-fat fried Snicker’s candy bar on a stick. Based on a sample size of two, I advice not eating any dessert confection that’s been deep-fat fried. I really think this can be hazardous to one’s health, especially on an empty stomach. However, if you like to live dangerously culinary-wise, see the recipes at the end of this report from the Seattle-Post Intelligencer on the Puyallap Fair. (“Puyallup” does not sound too appetizing, though, does it?)
Making random decisions on the basis of a coin flip
Posted by mark in Basic stats & math on August 28, 2009
I watched the movie Leatherheads last night – a comedic tribute to the early days of professional football. It re-created the first coin flip used to determine which team would kick off. The referee allowed the coin to fall to the ground – introducing a bit more randomness into the outcome (as opposed him catching it). That’s one of the findings presented in the Dynamical Bias in the Coin Toss by a trio of mathematics and statistics professors from Stanford and UC Santa Cruz. Surprisingly, they report that for “natural flips” the chance of a coin coming up as started is 51 percent. In other words, this procedure for creating an even probability is biased by the physics.
My “heads up” (ha ha) on this came from a former colleague of mine. He sent me a link that led me to this flippant (pun-intended) summary by blogger James Devlin . Devlin warns against spinning a coin to create a 50/50 outcome – a heavy-headed coin can fall tails-up as much as 80 percent of the time! It seems to me that this approach would also increase the odds of a flipistic singularity – normally very rare (1 in 6000 chance).
Another colleague, who once collected comics about Donald Duck, told me the tale of flipism – a random way to live life. However, I think I will not go down this road, but rather quit this blog while I am still ahead.
“Life is but a gamble! Let Flipism chart your ramble.”
– Slogan in Flip Decision by Carl Barks
PS. A fellow trainer starts off statistics workshops with a fun icebreaker that gets students involved with flipping a coin. He asks the class what they expect for an outcome and then challenges this assumption experimentally. The first student gets heads, which the trainer tallies on a flipchart. Each student in turn gets the same outcome until someone finally gets suspicious and discovers that it’s a two-headed quarter.
Are you happy? If so, be careful not to laugh: It may trigger gelotophobia!
Posted by mark in Uncategorized, Wellness on August 20, 2009
Check out this freely posted study by math & stats profs Dodds & Danforth (“D&D”) on Measuring the Happiness of Large-Scale Written Expression: Songs, Blogs, and Presidents. Or for a simpler synopsis, see this spin by PHYSorg.com, which harkens back to a utopian dream of “hedonometers” measuring happiness. Not surprising, the D&D hedonometer dropped way down on the day of Michael Jackson’s death this summer. 🙁
>”Our method is only reasonable for large-scale texts, like what’s available on the Web,” Dodds says. “Any one sentence might not show much. There’s too much variability in individual expression.” But that’s the beauty of big data sets* and statistics.< — Source: PHYSorg.com
Here’s an observation by D&D really tickles my ribs: Happiness of blogs increased steadily from 2005 to 2009, exhibiting a striking rise and fall with blogger age and distance from the Earth’s equator. Figure 9 of their publication reveals a maximum happiness valence near my age (56 years), latitude (45 degrees North) and the day I normally blog (Sunday). Thus I think that StatsMadeEasy must be near the top of the blog pile for cheerfulness, particularly given my guiding principal to keep it simple and make it fun (KISMIF).**
Nevertheless, I am throwing in a wet blanket over this whole write-up by alerting you to a recent (8/1/09) Science News report about “When Humor Humiliates.” I now fear that being overtly happy, to the extent of laughing out loud (LOL), might provoke hard feelings from those who suffer from gelotophobia – fear of being laughed at. According to a survey of more than 20,000 people in 73 countries this phobia is widespread, but particularly active in certain cultures. The USA seems to fare well in specific aspects of gelotophobia – particularly the city of Cincinnati. So if you just cannot contain your belly laugh, let it all out there in the midsection of America. 😉
* These two enterprising professors report they examined nearly 10 million blog sentences!
** Search on “happiness” for my prior musings on statistics related to this subject.
Regions with aging populations are experiencing higher death rates!
Posted by mark in politics, Uncategorized on August 10, 2009
If the USA moves to government-sponsored health care on the scale of Europe, death rates here (now 8.3 per thousand) are sure to increase to the trans-Atlantic level of 10.3 — that’s a fear which Economist Edward Lotterman rebuts in his newspaper column today. As you educated readers might guess, the discrepancy in death rates can be easily explained by differing demographics: Due differing post-WWII dynamics, Europe’s population is older than ours, which can be seen in these animated population pyramids on Europe versus the United States developed by Professor Gerhard K. Heilig.
Specific statistics like this, when used indiscriminately by strongly-biased people, give statistics as a whole a bad name. However, those who are not duly diligent in vetting inflammatory stats are just as much to blame as the originators misleading them.
“It is proven that the celebration of birthdays is healthy. Statistics show that those people who celebrate the most birthdays become the oldest.” — Widely quoted as stemming from a PhD thesis by S. den Hartog (perhaps too good to be true!)
Walk fast to stay ahead of the grim reaper
Mark (in blue) blocked by slow-paced tourists
I added another 10 miles to my Minnesota State Park trail tally this weekend, leaving me only a few more treks short of the century mark and another patch from the Hiking Club.
My idea of a good walk is moving at the briskest pace possible that can be sustained indefinitely. That really gets my blood pumping and thus it is most invigorating. Besides, then I get to more places faster. The tricky part is getting around those who prefer a more leisurely stroll, such as the tourists who impeded my “push hike” to the Mendenhall Glacier outside Juneau, Alaska last year.
Some people I know have questioned my lust for long striding, but a recent report by gerontologists provides support for fast walking – it adds as many as 15 years to one’s life. Specifically, a 74-year old who walks at a gait of 1.4 meters per second (3.1 miles per hour) is more than twice as likely to be alive in 10 years than those oldsters who dawdle at 0.4 m/s (0.9 mph). Now that’s a stat for getting to where you’re going “pdq” (pretty darn quick).*
“Walk steadily and with a purpose. The wandering man knows of certain ancients, far gone in years, who have staved off infirmities and dissolution by earnest walking, hale fellows close upon eighty and ninety, but brisk as boys.”
– Charles Dickens
*Disclaimer: A more logical conclusion is that anyone who can walk this fast at age 74 must be very healthy – possibly just by luck and good genes. Thus, high gait speed is correlated with long life, not the cause of it.
USA health care system “Pareto-inefficient”?
Being a Certified Quality Engineer (CQE) I am well-versed in the Pareto Principle – a term coined by quality guru Joseph Juran for what’s commonly known as the 80-20 rule. When I was the team leader for manufacturing improvement projects, I’d start by categorizing causes for failure and graphing them on an ordered bar chart — most to least, while keeping a running tally on the accumulation in terms of percent. (See this primer on Pareto by the American Society of Quality.) Typically the first 20 percent of causes created 80 percent of the failures – that’s where I first focused the firepower of my quality team.
Today I learned of another concept attributed to the great Italian economist*: Pareto inefficiency. The Concise Encyclopedia of Economics explains that a “Pareto-optimal allocation of resources is achieved when it is not possible to make anyone better off without making someone else worse off.” I found this detailing by The New School which is too much for me to completely digest, but my attention was caught by this heads up:
“An economy can be Pareto-optimal, yet still ‘perfectly disgusting’ by any ethical standards.”
– Harvard Economics Professor Amartya Sen (1970)
So, while I am enticed by the idea that we can make most everyone (80 percent?) better off without making the others (20 percent?) worse off, I remain skeptical. However, having seen what a focused quality improvement team can do with the aid of Pareto charts at a micro level, I remain hopeful that some big strides can be made at the macro level for health care nationwide.
Small sample sizes produce yawning results from sleep studies
Posted by mark in Basic stats & math, design of experiments on July 15, 2009
“Too little attention has been paid to the statistical challenges in estimating small effects.”
— Andrew Gelman and David Weakliem, “Of Beauty, Sex and Power,” American Scientist, Volume 97, July-August 2009 .
In last week’s “In the Lab” column of the Wall Street Journal (WSJ)*, Sarah Rubinstein reported an intriguing study by the “light and health” program of the Rensselaer Polytechnic Institute (RPI). The director, Mariana Figueiro, is trying to establish a lighting scheme for older people that will facilitate their natural rhythms of wakefulness and sleep. In one 2002 experiment (according to WSJ), Dr. Figueiro subjected four Alzheimer patients to two hours of blue, red or no light-emitting diodes (LEDs). After then putting the individuals to bed, their nurses made observations every two hours and found that the “blue-light special” out-did the red by 66% versus 54% on how often they caught patients napping.
Over the years we’ve accumulated many electrical devices in our bedroom – television, cable box, clocks, smoke and carbon monoxide monitors, etc., which all feature red lights. They don’t bother me, but they keep my wife awake. So it would be interesting, I think, if blues would promote snooze. Unfortunately the WSJ report does not provide confidence intervals on the two percentages – nor do they detail the sample size so one could determine statistical significance on the difference of 0.12 (0.66 minus 0.54). (I assume that each of the 4 subjects were repeatedly tested some number of times.) According to this simple calculator posted by the Southwest Oncology Group (a national clinical research group), it would take a sample size of 554 to provide 80% power for achieving statistical significance at 0.05 for this difference!
So, although whether blue light really does facilitate sleep remains questionable, I am comforted by the testimonial of one of the study participants (a 100 years old!) – “It’s a beautiful light,” she says.
PS. Fyi, for more sophisticated multifactor experimentation (such as for screening studies), Stat-Ease posted a power calculator for binomial responses and provided explanation in its June 2009 Stat-Teaser newsletter .
* “Seeking a Light Approach to Elderly Sleep Troubles,” p. D2, 7/7/09
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. 🙂
Cartoon guides to math & stats
Posted by mark in Basic stats & math on July 5, 2009
In the latest issue of Scientific Computing, Statistician John Wass reviews The Manga Guide to Statistics. He suggests that this simplistic guide may be better suited for middle school than the adult learners it’s aimed at. See for yourself by viewing this excerpt from Chapter 4 of The Manga Guide to Statistics: “Standard Score and Deviation Score” .
I am partial to the Cartoon Guide to Statistics myself. See these sample pages on comparing small sample means . I think this hits the target for those looking for a light refresher on basic stats.
Wass confesses to a “lifelong infatuation” with Walt Disney’s Duck clan, which led me to a movie featurette on Donald in Mathmagic Land, which one can find posted on YouTube and the like. June 25 was the 50th anniversary of its release. Unfortunately, as noted in Wikipedia, a cartoon character states that “Pi is equal to 3.141592653589747, et cetera, et cetera, et cetera.” The last two digits should be 93 – not 47. So the scientist who wrote the script had to eat some humble pi. 😉