If you needed a reason ...

If you needed a reason to feel good today, this could be it.

Ok, it’s just getting to senior exams, and getting anything out of a senior right now is like squeezing Ketchup out of a Heinz bottle, you're not sure what you get out is worth the effort you put in. You are starting to think the next generation just isn’t going to make it…. Then you hear about someone like Neil Sauter of Blissfield, Michigan. ...Ok, I never would have known.. I keep my head well buried in my math books and never see the news, but my wife calls from the staes and says, “Hey, you’ll never believe the kid I just met” And tells me the story.

Neil is 25, and when he graduated from Grand Valley State University in 2006, he was looking for adventure. The Peace Corps sounded good, being the kind of kid who wanted to make a difference in the world AND have some adventure; but they turned him down. (all the kids go “ahhhhhh”). Neil has cerebral palsy, and it has effected his legs, so he has trouble walking… pay attention folks, he has trouble walking, tightness in the thighs, ankles turning in… walking is HARD…pay attention.. it matters in the story.

So Neil decides that he wants to pick his own challenge, something where no one else can tell him “No!”. He decides, in his words, “I would take a stand for people with disabilities right here in Michigan." How??? Well, for starters he decides to walk across Michigan to promote Cerebral Palsy…. No… you still don’t get it…

First, when Neil says across michigan, he doesn’t mean, like, go from Detroit over to Muskegon or something… no ticky tacky cake walk across the bottom of the state for this boy… he is going to walk all the way up the lower Peninsula to the Big Mac Bridge, then across the Upper Penisula to the Wisconsin Border…. NOOOOO wait.. you still don’t get it.. The kid with CP in his legs is going to walk the LONG way across Michigan, 830 miles, ____ ON STILTS____




Ok, so now enter my wife and her group of friends. You see, while I take care of all the hard stuff, like teaching kids math, Jeannie has the easy job of bringing peace into the world and feeding the hungry… Every week she and her friends get together and talk about how to make the world a better place… what THEY can do..Thinking globally, acting locally; trying to get people to realize how powerful they can be, and one of them decides that Neil is a guy with a story to tell and they invite him to attend. Neil gets an evening of entertainment with some beautiful ladies(mostly,except for Joey and Cleve), and I get to hear a story that pulls me out of my bout of self-pity.

Neil is off to Norwood today, another 24 miles to notch off, but the last bit along Eagle Highway is beautiful, and then next week he is off to the Bridge. Along the way he is raising money for a fund he created that buys the tools and technology to allow CP sufferers to live a fuller life. He even has a grant from the government to match what he raises when he reaches a specific leve. He could use a hand.. so if you are camped out somewhere across the Upper Peninsula of Michigan and you were just thinking,now what could we do for excitement this week, then think… “Hey, we could do a fundraiser for CP and pass it on to Neil when he comes by”..Or maybe just buy him a burger, the boy looks a little thin in the picture. Maybe you would want to walk a few miles with him for company.. not much between all those pine trees up there, and I understand the boy is an amusing and interesting story teller, and a really talented juggler.

And if you don’t live along the way in the UP, and not many of you do, you can make a donation on his web site, or mail a check to:
Fresh Earth Peace Project
Box 402
Elk Rapids, Michigan
49629

and we will get it to him. Either way it is totally tax deductable..and maybe matched by the government.

Ahh, Kids today… don’t they make you proud? Good luck Neil.. Left, right, left, right..

Taking things to a New (and some old) Length

While reading "Zero to Lazy Eight" by Alex and Nicholas Humez and Joseph Maguire, I came across the unusual measure of length called a smoot. I looked it up on Wikipedia and found this:

"The smoot is a nonstandard unit of length created as part of a Massachusetts Institute of Technology (MIT) fraternity prank. It is named after Oliver R. Smoot,(class of 1962), an MIT fraternity pledge to Lambda Chi Alpha, who in October 1958 was used by his fraternity brothers to measure the length of the Harvard Bridge between Boston and Cambridge, Massachusetts.
One smoot is equal to his height (five feet and seven inches ~1.70 m), and the bridge's length was measured to be 364.4 smoots (620.1 m) plus or minus one ear, with the "plus or minus" intended to express uncertainty of measurement. Over the years the "or minus" portion has gone astray in many citations, including the

Oliver Smoot ’62 is used to measure the bridge in 1958.

commemorative plaque at the site itself. Smoot repeatedly lay down on the bridge, let his companions mark his new position in chalk or paint, and then got up again. Eventually, he tired from all this exercise and was thereafter carried by the fraternity brothers to each new position. Everyone walking across the bridge today sees painted markings indicating how many smoots there are from where the sidewalk begins on the Boston river bank. The marks are repainted each year by the incoming associate member class (similar to pledge class) of Lambda Chi Alpha.
(Image from *slice.mit.edu)

Markings typically appear every 10 smoots, but additional marks appear at other numbers in between. For example, the 70-smoot mark is omitted in favor of a mark for 69 (boys will be boys!) The 182.2-smoot mark is accompanied by the words "Halfway to Hell" and an arrow pointing towards MIT. Each class also paints a special mark for their graduating year.
The markings have become well-accepted by the public, to the point that during the bridge renovations that occurred in the 1980s, the Cambridge Police department requested that the markings be maintained, since they had become useful for identifying the location of accidents on the bridge.The renovations went one better, by scoring the concrete surface of the sidewalk on the bridge at 5 feet and 7 inch intervals, instead of the conventional six feet.

Google Calculator also incorporates smoots, which it reckons at exactly 67 inches (1.7018 meters). Google also uses the smoot as an optional unit of measurement in their Google Earth software.

Oliver Smoot later became Chairman of the American National Standards Institute (ANSI) and President of the International Organization for Standardization (ISO)."  

He returned to MIT on October 4, 2008 for a 50th anniversary celebration,including the installation of a plaque on the bridge. Smoot was also presented with an official unit of measurement: a smoot stick.

Speaking of stange measurements and their origins... two ancient measurements that really have a common origin are the cubit, and the ell. Both, in some form, measure the distance from the elbow to the finger tips. At one time almost every country had an Ell, and almost none of them were the same. During the monarchy of Edward I, he made a law that every town have an ellwand, a rod of length one ell, that was used as an official measure. The cubit is the same measure but the word is from the Latin cubitum (elbow), and is related to the Latin word that means to lie down. By whichever name it is a very old unit of measure and frequently known by a word relating to "forearm" or the elbow, such as, Greek pekhys and Hebrew ammah.

The NEW Friendly Numbers

Friendly Numbers

Up until the spring of 2008, if you asked me what "friendly" numbers were, I would refer you to my listing for amicable or aliquot numbers. Two numbers were amicable (friendly) if the sum of the factors of each equaled the other. 220 and 284 are the oldest pair known, and they date back to Pythagoras. The numbers were inscribed on "magic charms" in the middle ages which were sold to insure the fidelity of ones lover. Other stories suggest that the gift of 220 Goats from Jacob to Esau in the Biblical story was an expression of love made significant by the use of one of the pair. The proper divisors of 220, 1, 2, 4, 5, 10, 11, 20, 22, 44,55, and 110, add up to 284 and the same is true the other way around. Until very recently, at least to the best of my knowledge, this was what people meant when they referred to "friendly" numbers. This is how Simon Singh describes them in his book Fermat's Enigma; Western mathematics knew only the one pair until 1636 when Fermat discovered a second pair; 17,296 and 18,416 . This was also how Hoffman described them in his book about Paul Erdos, The Man Who Loved Only Numbers, and how Alfed Posamentier had used the term in Math Charmers: Tantalizing Tidbits of the Mind. These were world class mathematician/authors. I assumed I was in line with the current usage.

Then recently, I came across a reference on Mathworld that described them as the ratio of the sum of all the divisors (including the number itself) divided by the number. For example, 8 can be divided by 1, 2, 4, and itself, 8. The sum of its divisors is 15, so its ratio, is 15/8; this is sometimes called the "abundance" of the number. Do not confuse this with the much older term "abundant" for a number for which the sum of the proper divisors (factors, or divisors not including the number itself) is greater than the number itself.. For example the proper divisors of 8 are 1, 2, and 4, which total 7, so 8 is NOT abundant, but deficient.

The classification of numbers as being deficient (the sum of the proper divisors is LESS than the number), abundant (the sum is greater than the number) and perfect (the sum is equal to the number, as in 6 and 28) goes back at least to Nicomachus (about 100 CE) who separated the even numbers into abundant (it was the mistaken belief for a long time that all odd numbers were deficient) or perfect.

When the ratio of the sum of the numbers divided by the number equals two, the number is perfect, so all perfect numbers are friendly under this new usage. Other numbers that are mutually friendly besides 6, 28 and the rest of the perfect numbers include 30 and 140, with a ratio of 12/5, as well as 80 and 200, whose ratio should be 2.325, if I calculated right. There are many numbers, such as all the primes, that are known to be solitary, that is, they have no friends. All the primes have a ratios of (p+1)/p, so their ratio would get smaller towards a limit of 1 as the size of the prime grew larger. There are other numbers, some relatively small like 10 and 14, that we do not know if they are friendly or solitary. I wondered as I computed these if there is a number or a pair with the greatest ratio? (write if you know, please)

I am not sure, and am presently searching to find the first use of the newer use of friendly numbers, but it seems to exist at least since the 1970's (surprised me!) from a citation on Sloans integer sequence site for ...Anderson, C. W. and Hickerson, D. Problem 6020. "Friendly Integers." Amer. Math. Monthly 84, 65-66, 1977. Ok, if you know about this stuff, drop me a line and set me straight.

Over Protected and Under Educated?

I’ve been thinking a lot about how kids grow up today, and how it impacts on their education, which should not be surprising since teaching is what I do. I’m sure there has never been a generation that didn’t ask that same old question, “What’s the matter with kids today?” Several articles and a couple of TED broadcasts seemed to resonate with what I’ve been thinking lately.

Robert Siegler, a psychology professor at Carnegie Mellon University in Pittsburgh, has done some research that suggests that children’s early concept of a number line is more logarithmic than linear, and that’s bad for math achievement. As they grow older, they usually develop a linear conceptualization of the number line but it happens in bits, and how long it takes to happens seems to be closely related to how well they do later in mathematics. The ones who seem to develop later spend more time with video entertainment while the ones who develop earlier, and therefore have a better chance of being successful in math, are the ones who play card games and board games. There are exceptions to every rule, but most mathematicians tend to have a game aspect to their mathematical learning.

Sir Ken Robinson, is an internationally recognized leader in the development of creativity and innovation. In one of his TED talks, he suggests that creativity is as important in literacy, and we should treat it so. I think he is right, but I think the problem, or at least a part of the problem, is the lifestyle of young children today. Don’t take my word for it, watch the TED video below by Gever Tulley creator of the "Tinkering Schools".
Tulley thinks that our children are over protected, and suggest five dangerous things we should give our children (he admits he has none of his own). I’m going to give my two cents worth about some of these, so if you want to, just skip down and run the video first…

Tulley suggests that you let your children play with fire. He makes some suggestions about what they might pickup, but relapses back to a faith based mantra… You don’t know what they are going to learn, but they are going to learn.
His second dangerous recommendation for children is a pocket knife … OF course they will cut themselves... and while you are wondering if you were a terrible parent to give them something so dangerous, they are proudly peeling back the bandages to show their cut to their friends on top of the garage as they take turns jumping off the roof and onto the limb of the tree a few feet away...(you won't find out until they fall, and incredibly, many of us never do).

I still remember the wisdom of my father-in-law telling me the story of his experience as a child at a carnival near Perry, Michigan… after paying a dime at the tent that said “Life Saving Advice Inside”... they entered a string of other curious visitors. The line passed by an old guy with a pocket knife and a stick that was quickly turning into wood chips...as he repeated... "Whittle from you, never cut you”| and through the next tent flap which led... outside... I’m not sure how many times he told me that story in the forty years I’ve known him, but it was more than once for each of those years. Ten cents when you are a child for a story you could still be telling at in your 90's... a bargain...

The third dangerous thing he recommends is a spear. I’m not sure I see the benefit of a spear, but our brains do seem to be wired for throwing things, and when you let one part of the brain go soft, other parts seem to follow. So throw a spear or a baseball, girls and boys NEED to play baseball, even if they don’t compete in organized sports, a game of catch can build both body and mind....Throwing and catching are incredible analytic teaching methods visual acuity, 3 d analysis, and attention and concentration skills.

Number four was to give them your broken appliances to take apart. The land fill can wait a couple of days. Seeing what things look like and trying to figure out what they do is BIG.. and the curiosity is BIGGER..I suspect it develops a belief that they can KNOW difficult things.. and an awareness that it may not come all at once. I worry that kids today don’t seem to persevere at difficult tasks. I suspect that a kid who takes apart a toaster or spin dryer (with parental supervision even) will look at all the “black boxes” he encounters differently. They will always be wondering what might be “in there” and how it could work…. Did I mention that curiosity is GOOD!

And finally, about ten or twelve, let them drive the car. Find a good safe place out in a vacant lot, sit them in your lap if you have to, and let them control the steering wheel and any other parts they can reach while you roar across the lot at 15 mph. Being in charge of this huge piece of moving steel can give them a sense of control… Kids need to feel they have some control over their world… If you really believe that children are the future, you better help them feel they can be in control.

Here are a couple of extras that I think are important for life and math skills… Teach them to play games... NOT video games,, they'll do that on their own.. Teach them to play card games, board games... Monopoly, Parcheesi, Snakes and Ladders are GREAT childhood games, even for kids UNDER 8 years old.. Teach them to juggle, to ride a unicycle, to do card tricks, to play a musical instrument, to speak a foreign language. All those things take discipline and focus, both of which are essential for success in education and life. When my youngest son was learning to play soccer in elementary school, we would go out in the front yard in the evening and take turns seeing who could juggle the ball with our feet for more touches. It only took a month or so and he had gone past the best I would ever do. When a parent watches their kid go past them in anything, it’s a great feeling.. that’s the natural order of the universe, each generation gets a little better and smarter.. I worry if we are doing that lately.