New math sums digits from left to right: Does this add up as an improvement?
Posted by mark in Basic stats & math on November 22, 2009
A recent article in my local newspaper, the Stillwater Gazette, provided enlightenment on our school district’s new way of adding numbers – from left to right, rather than right to left. I might have to try this – maybe it will help me improve my accuracy when tallying checks on deposit slips. (I always hand-calculate these as a way to maintain my math muscles.)
Supposedly this left-to-right approach makes it easier for children to learn, because it goes in the same direction for processing numbers as for reading words. Here’s how it works. Let’s say that you and your spouse both collect up pennies and the first jar nets 237 cents versus 159 for the second. How much in total can be taken to the bank? The way I learned to add one first adds 7 and 9, recording 6 as the right-most digit (the ones column), and then carrying a 1 to the second column (the tens). This carrying part is where I sometimes get off, mainly due to my poor handwriting, which even I cannot always read. The new left-to-right approach eliminates a lot of carrying, but not all, I figure, as shown in the following case. Start by adding the left-most (hundreds in this case) column of numbers:
247
+159
=300
Do not forget to put in the zeroes to hold the place of what you just added. Now go to the next column to the right and add it:
= 90 (4 + 5)
And so forth until there’s no more columns:
= 16 (7 + 9)
Finally, tally up all the numbers you calculated:
300
+90
+16
406
I have a feeling that the old saying about not trying to teach an old dog new tricks might be operative for me in regard to this new math. I think I will just keep adding the old way, or admit that using a calculator or, better yet, a computerized spreadsheet for doing my deposits would be smarter. Am I shortchanging myself (pun intended)?
PS. This innovation in learning math struck a chord with my son Hank, who programs for Stat-Ease. He made me aware that “endianness” is a major issue in coding. Evidently programmers continually feud over the order in which bytes in multi-byte numbers should be stored – most-significant first (Big-Endian) or least-significant first (Little-Endian).* The “endian” terms come from Jonathan Swift who mocked the pettiness of social customs, such as which end one ought to first attack when shelling an egg.
“…the primitive way of breaking Eggs, before we eat them, was upon the larger End: But his present Majesty’s Grand-father, while he was a Boy, going to eat an Egg, and breaking it according to the ancient Practice, happened to cut one of his Fingers. Whereupon the Emperor his Father published an Edict, commanding all his Subjects, upon great Penaltys, to break the smaller End of their Eggs.”
— Jonathan Swift, Gulliver’s Travels, A Voyage to Lilliput, Chapter IV.
*For more details, see Basic concepts on Endianness.
Gambling with the devil
Posted by mark in Basic stats & math, design of experiments on November 15, 2009
In today’s “AskMarilyn” column by Marilyn vos Savant for Parade magazine she addresses a question about the game of Scrabble: Is it fair at the outset for one player to pick all seven letter-tiles rather than awaiting his turn to take one at a time? The fellow’s mother doesn’t like this. She claims that he might grab the valuable “X” before others have the chance. Follow the link for Marilyn’s answer to this issue of random (or not) sampling.
This week I did my day on DOE (design of experiments) for a biannual workshop on Lean Six Sigma sponsored by Ohio State University’s Fisher College of Business (blended with training by www.MoreSteam.com.) Early on I present a case study* on a training experiment done by a software publisher. The goal is to increase the productivity of programmers by sending them to workshop. The manager asks for volunteers from his staff of 30. Half agree to go. Upon their return from the class his annual performance rating, done subjectively on a ten-point scale, reveals a statistically significant increase due to the training. I ask you (the same as I ask my lean six sigma students): Is this fair?
“Designing an experiment is like gambling with the devil: only a random strategy can defeat all his betting systems.”
— RA Fisher
PS. I put my class to the test of whether they really “get” how to design and analyze a two-level factorial experiment by asking them to develop a long-flying and accurate paper helicopter. They use Design-Ease software, which lays out a randomized plan. However, the student tasked with dropping the ‘copters of one of the teams just grabbed all eight of their designs and jumped up the chair. I asked her if she planned to drop them all at once, or what. She told me that only one at a time would be flown – selected by intuition as the trials progressed. What an interesting sampling strategy!
PPS. Check out this paper “hella copter” developed for another statistics class (not mine).
*(Source: “Design of Experiments, A Powerful Analytical Tool” by Christopher Nachtsheim and Bradley Jones, Six Sigma Forum Magazine, August 2003.)
Statisticians do not see global cooling trend
This story by Seth Borenstein, AP Science Writer, is sure to create a lot of heat from those who dispute global warming. Without revealing what the numbers represented, his news organization gave temperature data to four independent statisticians and asked them to look for trends. They found no evidence of any decline – only a long-term increase over the last 130 years, thus taking away fuel for the fire that the world is now cooling.
I like the idea of this being a blind analysis, although I wonder if these four statisticians might’ve seen through this. Also, what is a good sample size for statisticians? Four seems meager. Do you pick statisticians at random, or what?
Anyways, I am more concerned about my Minnesota Gophers going to a new outdoor stadium in what will turn out to be one of the coldest Octobers ever in this region. They play Saturday night, which is Halloween – scary enough on a college campus –but it might be wickedly cold as well. Fortunately I have a good collection of Gopher shirts, sweats and jackets to put on layer-by-layer. I noticed something funny about being outdoors after so many years of under the Metrodome: People clapping with mittens on just doesn’t work as well for cheering purposes.
Experiments for school now safer, but less educational
Posted by mark in Uncategorized on October 18, 2009
A colleague in our field of experimental design told me today that he will be making a big career change by moving out of industrial research to teaching high-school science. He may think twice about this after seeing this thread from TheScientist Community that educators’ caution is killing science fun. Actually, being a bit squeamish about blood and guts, I like the idea of dissecting a jellybean rather than a frog. That’s sweet!
The blog stemmed from this TimesOnline article detailing how School lab health and safety rules ‘could stop future scientists’ . I like their picture of students in a high school chemistry lab who are clearly thrilled by their production of a huge flame-ball. That seems very educational! Unfortunately, this sort of thing, such as making volcanoes, can no longer be tolerated. That’s a pity, I think.
On a brighter note, the Royal Institution of Great Britain, an independent charity dedicated to connecting people with the world of science, report that kids are keen to do more experiments, according to this SchoolGate blog.
“When things are taught without true experimentation, students don’t understand it. And that needs to change. Children can do science at school, but they don’t necessarily learn what a real scientist is – planning an experiment, needing to repeat things, having a clear hypothesis and testing it.”
— Baroness Susan Greenfield. Director of the Royal Institution
I enjoyed many fun and educational experiments in my school career, back when the teacher ruled supreme. All of them impressed on us the importance of being safe and we learned first-hand how to handle hazardous chemicals and biological materials. My favorite in-class experiment, which I doubt would be allowed nowadays, was a fermentation reaction that my team of high-school honors students ran as our final project for senior biology class. The alcoholic product, albeit not of vintage quality, served very well, we judged. I do not exactly recall the consequences, but they must not have been too bad, because the teacher gave us a pass.
NASA shoots the Moon
I got up a bit earlier than usual to set up my 8-inch reflector telescope for a view of the 6:31 AM CDT collision of NASA’s Lunar Crater Observation and Sensing Satellite (LCROSS). The weather was ideal – clear skies with no wind. Never mind that we had our first frost – Minnesotans like me don’t mind temperatures at the freezing point (knowing full well that soon this will be considered balmy!). However, despite a spectacular view of the Moon’s South Pole, I saw no evidence of the “man in the moon” getting ‘goosed.’ To placate the alarmists who thought the Moon might be destroyed, NASA likened their crash to an eyelash hitting a jetliner. From what I could see myself and the video by NASA, that is an apt analogy, assuming the eyelash came off a gnat.
So LCROSS proved to be a lot less dramatic than us skywatchers hoped for. However, if the follow-up satellite sensed water blown up by its self-destructive predecessor, the mission will be a big success. This will take a while to decipher as noted by Wired magazine’s GeekDad blogger Brian McLaughlin. If you are geeky like me, you will keep an eye out for the final outcome of this shoot-for-the-moon experiment.
PS. All this is mindful of the book by Jules Verne From the Earth to Moon posted with illustrations from an 1886 edition by NASA in their Space Educators Handbook
(“One small click for all mankind.”). It’s fantastic!
Digging into numbers to the last vigintillionth of a yoctometer
Posted by mark in Basic stats & math on September 25, 2009
I love esoteric measures, for example when working early in my career for an oil company where barrels ruled, I made it my business to know the number of firkins in a hogshead.* Therefore I was piqued by “Coding the Wheel” blogger James Devlin making a point about precision to level of “the last vigintillionth of a yoctometer” (yes, evidently those are real units of measure!).
Fyi, math whiz Landon Curt Noll made a “heroic attempt to put names on hippopotomonstrosesquipedalian numbers” (quoted from this web page on Naming Large Numbers). He provides this utility for getting the English name of any number you enter. I entered 1,000,000,000 and got “one billion” as the result. But then I changed from the American to the European system and Noll’s number-namer spit out “one milliard”! So then I tried 1,000,000,000,000,000 and came up with “one billiard”!! That sent me back for a draft of brew from my firkin (depicted in this video).
Thus fortified, I kept after these mind-muddling measures and verified that this pool-player’s favorite number (billiard) is considered acceptable under the “long scale” (European) branch of the SI (Système International) of units – the modern metric system.
Who knew? (Please forgive my ignorance of European styles, being that I’m a mid-continent dweller of North America. I am learning!)
*See this picture of a 19th century hogshead barrel and learn how it varies in gallons depending on whether it contains beer, wine or tobacco.
An ideal world: Ballpark beer cost correlated completely with quality of baseball
Indian's lefty Laffer delivers a pitch to Twin's slugger Cuddyer
When offered a free $149 seat behind home plate, I abandoned my desk last Wednesday for a matinee game between Minnesota and Cleveland. It was dollar-a-dog day so I enjoyed a $2 lunch washed down by what the Wall Street Journal (9/11/09) considers to be one of the Major League’s best-valued beer. They figure that the cost per ounce of brew – 27 cents at the Metrodome — should be based solely on the quality of the team.
The Twins have been consistent winners for some years and remain in the hunt for the Central Division of the American League after winning 2 out of 3 from the Detroit Tigers this weekend. Nevertheless, they chronically play second-fiddle to East Coast teams like the Boston Red Sox. WSJ reports that the crimson-hoser’s home field, Fenway Park, charges more than twice as much for beer for the Twins – far more than they merit by their winning percentage – a 46% overcharge, to be precise. Boston fares poorly on price-to-value across the board according to this in-depth analysis by a blogger writing as “JinAZ” for Beyond the Box Score – a Saber*-Slanted Baseball Community.
However, being a lifelong fan of baseball, and having been to many ballparks around the League, but never Fenway, I’d gladly pay a premium to see the Red Sox some day. (That explains why they can charge so much!)
*Referring to sabermetrics — a statistician specializing on baseball
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.