February 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
Chapters 3 & 4
February 1, 2008
“Perhaps we should go to your office, as this is a rather delicate matter.” The tone of the gentlemen noticeably changed from one of congratulatory accomplishment to one of enforcement. The change did not go unnoticed by Principal Ragnar.
The ACT men followed Principal Ragnar into the small, non-descript office. A worn desk, a round meeting table with four chairs, a filing cabinet, and three full bookshelves completed the office, with the exception of a large wall with two boards: one chalk and one marker. The principal cleared the meeting table of what looked like large drafting paper, and invited the men to have a seat.
“Thank you for taking the time to see us unannounced, Principal Ragnar. Regulations require these visits to be unannounced. I am Charles Jones, and this is my colleague, Michael Anderson. We work for the ACT testing service out of Des Moines, Iowa. As you’re probably aware, hundreds of thousands of students take our exam each year, and nearly all colleges and universities use the results of this test, in some form or another, in the college entrance process. Because of the importance of these exams, the integrity of the results must be maintained at all times. We are here because of “abnormalities” in the test results by the 146 students who took the test in September. We’d like to start by asking you about the security measures and test-prep procedures to see how our test may have been compromised.”
“I see”, Principal Ragnar said, once upright in his chair, now reclining in his worn chair. “You saw ‘abnormalities’ and now want to see how this could have happened. Please tell me what specific steps took place for you to be here unannounced.”
“We’re here only on a fact-finding mission, that’s all. After the first round of tests was completed and scored, our system not only tabulates the scores, but aggregates the scores on a school-by-school basis. We then compare these scores with the scores from prior years. We search for instances where the performance from year-to-year changes dramatically, what our statisticians call “statistically significant”. We then review the tests for that school to ensure the data is correct, and there have been no miscalculations on our part. Once we are certain all numbers are correct, we visit the school.”
“I see”, said Principal Ragnar in the manner of a polished lawyer. So the presumption is, “If you see statistically significant change, then it’s likely due to cheating. Is this true?”
“As I said,” repeated Mr. Anderson confidently, but now finding himself in the unfamiliar position of being questioned, “we’re here on a fact-finding mission only. However, the majority of our investigations do turn up significant cheating, and those where the scores legitimately improved, the improvement was in the range of 3-5 points. Your school improved over 8 points this last session. From what I’ve read of your school and the troubles it faces now with the loss of your chartering agency, coupled with the fact our statisticians tell us this type of improvement is not just statistically significant, but impossible, off the record, 'yes', we have come here because we believe there has been cheating.”
The response was unexpected: “Fair enough”, said Principal Ragnar in a tone suggesting triumph. “I’ll agree to answer any questions you have, but on one condition: when you’re done here, I’ve got some questions for you. Fair enough?”
The ACT-representatives were not sure what to make of this request. Normally, the mere appearance of impropriety has people anxious to get rid of them, and they all-too-often are shown the door rapidly and rudely. Yet here was a principal demanding they stay after their investigation to answer his questions? What possible questions could he have of them?
“Fair enough”, said Mr. Anderson.
Mr. Jones began: “First off, could you show us the ACT-test prep materials your kids used in preparing for the exam?”
Principal Ragner replied coolly: “We didn’t use any. The only materials we used were the sample exams your firm hands out to schools. Since they were free, that’s all we used. As you can see, money is not a luxury around here.”
“You didn’t use any other materials? No outside consultants? No materials from the internet? No store-bought materials? Nothing else?”
“Was there anything abnormal about your training?”
“We did ask the ACT if we could bring scratch paper to the test – blank pieces of paper – to do our work. Imagine that! Blank paper, and your firm declined! We then asked if we could show up at the testing center and be given blank paper. Again – that simple request was declined! Apparently, your company calls such a request abnormal because they declined it! Other than that, our kids worked problems from your practice test, showed up at your testing facility, and took your test.
“So you’re telling us you don’t know how the scores improved dramatically – it was just luck?”
“Oh no – I assure you it’s not luck!”
MASSIVE IMPROVEMENT IMMEDIATELY
The First Chautauqua
The Principal retreated to his deck for a lonely evening. His wife was working late, and suggested fast food or pizza as “supper”.
His thoughts drifted to the events of the day. The gentlemen from the ACT had left, perhaps convinced the school had indeed “performed miracles”, whatever that meant. Likely they’d report back to the home-office there was no overt cheating – nothing was apparent, at least – meaning the school and students likely were on some watch list.
Is massive improvement possible?
He paced about the yard. He enjoyed times like this – times to think. Aristotle had called such practice “peripatic”, but he liked the phrase “Chautauqua”, named after the popular educational movement in the nineteenth century. His “chautauquas”, however, were personal investigations – trains of thought.
The gentlemen from the ACT were not questioning whether massive improvement was possible. That was not it. The sheer speed with which it had occurred was what brought them to the school today. Is massive improvement immediately possible?
That was the question.
Of course, if you looked at the building industry, the question itself provides the answer merely by looking at the buildings of today. Prior to steel, tall buildings were unheard of because buildings were made of concrete – they were heavy – and the higher you went, the bigger the base had to be. Introduce steel and the nature of the building changes immediately. Skyward they went. Massive improvement immediately? Whether it’s improvement or not, it’s certainly a change – taking place immediately.
Of course, nobody would question this because there was a reason behind it. Concrete – steel – revolution.
But this required a material change in the environment. In the school, they had no such change. Even with evidence, who would believe it? Are there other such examples of “revolutions” where no material change in the environment took place?
He thought of baseball and Babe Ruth. Prior to Babe Ruth, the idea of hitting double-digit home runs was outrageous. Babe Ruth comes along and suddenly he’s hitting 40, 50, and even 60 home runs. Same game. What happened? What did he do? Did he change the nature of the swing, the mindset of the game, or something similar to this? Probably.
The gentlemen from the ACT, if put back into the 1920s, likely would be at the residence of George Herman Ruth, demanding an explanation for how he accomplished what he did!
But it seemed a good example of revolutionary changes – improvements – taking place without the need for revamping the environment.
He continued to walk around the yard, now at the big tree in the back corner. This was his third time around the yard, and he marked the occasion with another small rock.
But what about education? Is massive improvement immediately possible in education? It’s reasonable for educators to be skeptical about the assertion. After all, if it were possible, why hadn’t it been achieved?
Can people look at what they’re doing – at themselves – and question what and why they’re doing what they’re doing? Not impossible, he thought, but probably hard. That is, if one had the time to do such thinking.
But if not them, what of non-educators making such a claim to educators? He had heard that specific claim so often when he was both teaching and previously a principal he laughed. If you stacked up all the marketing claims of such firms, we’d all be geniuses! Of course, it’s likely some did generate improvement – to some degree, but skepticism was the earned evaluation of the educational establishment.
He also knew the majority of claims came as improbable solutions to actually implement. How many math programs had he seen where “real-world-applications” was pushed? Too many to count. Of course, he too was for such materials! Who wasn’t? He also knew his staff had to teach to certain standards within a certain timeframe. These people claiming to have all these solutions – walk a mile in our footsteps, he thought, and you will quit a quarter-mile down the road.
He liked the analogy, and laughed slightly – out loud.
Where did this leave him? He modified a set of rules he had thought up years ago.
Rule #1: “If we can’t do it, why should we believe you can.”
Rule #2: “If you say you can, see Rule #1.”
Again he laughed out loud. How true.
But something was missing. He knew because his school was doing it!
February 2, 2008
The soldier is asked to charge an enemy encampment, himself knowing civilians are present. What to do? The officer is mandated to arrest pot-smoking citizens in the privacy of their own home, despite his belief in individual rights. What to do? The judge is forced to sentence a non-violent offender to 30 years for the third offense, though he believes this wrong. What to do?
Socrates provided the historic - and wrong - answer. One must obey the law. The law sentenced him to death? Then death it is!
What did Victor Hugo, writing of the officer Javert, say on the issue? What did Javert himself think? Jean Valjean was a criminal. Yet at a moment in the barricades, this criminal had spared Javert's life! What to do?
The Fate of Javert Rests in His Own Hands - and His Own Mind
"His supreme anguish was the loss of certainty. He felt that he had been uprooted. The code was no longer anything more than a stump in his hand. He had to deal with scruples of an unknown species. There had taken place within him a sentimental revelation entirely distinct from legal affirmation, his only standard of measurement hitherto. To remain in his former uprightness did not suffice. A whole order of unexpected facts had cropped up and subjugated him. A whole new world was dawning on his soul: kindness accepted and repaid, devotion, mercy, indulgence, violences committed by pity on austerity, respect for persons, no more definitive condemnation, no more conviction, the possibility of a tear in the eye of the law, no one knows what justice according to God, running in inverse sense to justice according to men. He perceived amid the shadows the terrible rising of an unknown moral sun; it horrified and dazzled him. An owl forced to the gaze of an eagle.
He said to himself that it was true that there were exceptional cases, that authority might be put out of countenance, that the rule might be inadequate in the presence of a fact, that everything could not be framed within the text of the code, that the unforeseen compelled obedience, that the virtue of a convict might set a snare for the virtue of the functionary, that destiny did indulge in such ambushes, and he reflected with despair that he himself had not even been fortified against a surprise.
He was forced to acknowledge that goodness did exist. This convict had been good. And he himself, unprecedented circumstance, had just been good also. So he was becoming depraved.
He found that he was a coward. He conceived a horror of himself.
Javert's ideal, was not to be human, to be grand, to be sublime; it was to be irreproachable."
February 3, 2008
Super Bowl 42 kickoff is hours away, with the Patriots closing in on a 19-0 season. We say it as "42", but it's never written as "42". It's "XLII". Why?
Of course, we're all familiar with the basic Roman Numerals:
Let's back up a moment: why not write "42" as "IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII"? After all, that's "42"!
We see the folly in this, as did the Romans - as did the ancient cavemen, who achieved the remarkable conceptual advancement of spacing the tallies.
But why does "42" not equal "XXXXII"?
It did, at one time.
But the Romans saw the folly in this, just as the cave-men did above.
"How can we 'save-space' in writing our numerals?", the Romans asked, and they answered it with an brilliant - yet simple - solution: anywhere we see "4" of anything, that's a problem. They solved the problem by making numbers not simply accumulative, but also subtractive.
Does 4 only equal 1+1+1+1? Of course not. It also equals 5 - 1.
Does 9 only equal 5 + 1 + 1 + 1 + 1? Of course not. It also equals 10 - 1.
But how to make this operational when writing numbers?
And numbers 1-50 look as follows:
A couple things stand out in this brief table: the amount of substitution grows as the numbers increase. Good! That was a goal. Secondly, as the numbers become larger, the substitution leads to an immense decrease in the size of the representation of the numeral. Again, good! That was a goal as well! Unit economy! 49, once represented with 9 characters (XXXXVIIII), is rewritten in only 2 (IL).
Well, now I'm curious: how much space is saved with this new method of number representation? Let's graph the length of the numbers from 1-2,000 and see. I'd expect to see no difference in numbers like 2,000, since there is no difference in the representations. However, looking at "49" above, there is a tremendous difference. Let's see:
What does this look like if I plot only the differences?
Amazing - but not unexpected. In fact, exactly what we wanted to achieve. 1,999 goes from MDCCCCLXXXXVIIII (16 characters) to MIM (3 characters).
Of course, our system takes this to a whole new conceptual level: place value!
February 4, 2008
|Full-swing into the season
of political platitudes, Iraq is no longer on the front-burner as a
political issue, but it's interesting to listen to candidates talk about
the situation. No promise to withdrawal - a promise to withdrawal
with time-tables - secret time-tables - no time-tables.
Herein lies the discussion.
I'd prefer to talk about the origins of the Iraqi-invasion. The CIA told us things in the midst of the chaos of 9/11. These were not new things. Then-President Clinton himself had ordered the bombing of Iraq, and Iraq itself had used chemical weapons on its own citizens.
So its natural to believe, if Iraq was previously considered a threat, if they still possessed capabilities, and 9/11 has just put us in a state of prevention versus retaliation, then Iraq likely must be dealt with now - and severely.
I do not excuse the CIA for it's poor intelligence gathering. I neither excuse President Bush nor any member of congress who took the word of the CIA and did not have verification of the weapons Iraq supposedly had.
That being said, I do not excuse the public for the following intellectual inconsistency. Many people believe we should not invade an independent country. Fine.
Many of these same people, however, see the genocide in Sudan and immediately demand we do something! How can it be, on the one hand, they demand we stay out of the affairs of other countries, and on the other, demand we involve ourselves?
A SIMILAR ISSUE
What is the relationship between the Supreme Court and the Presidency? Many believe the Supreme Court is "the law of the land". Is it? After all, at one time, the Supreme Count affirmed slavery in this country in the Dred Scott case. But if the Supreme Court is the law of the land, should (could) Lincoln issue the Emancipation Proclamation?
IN SEARCH OF CLARITY
Looking at anomalies like this helps clarify our thinking. But it's one thing to acknowledge a contradiction in one's thinking. It's another to either ignore it or allow it to continue.
Consider most any issue now-a-days, and you'll see the inconsistencies running rampant: the government should not involve itself in the economy, but tax incentives are good.
The government should not involve itself in our personal lives, but the requirement of seat-belts and the abolition of smoking in the home is reasonable.
The government should not involve itself in the price of food commodities, but it's good they reimburse us for "a fair price".
Do I blame our politicians for perpetuating the platitudes and inconsistencies they spout on the campaign circuit? You bet. But I blame even more the public for allowing it to happen.
February 5, 2008
|It was the summer / fall
of 1978 when Hurricane Ella bore down on Manhattan. As winds ripped
through the maze of skyscrapers, a vulnerable 59-story colossus sagged and
gave way. A catastrophic collapse with thousands dead.
You don't remember it?
It never happened.
Why it did not happen is an epic story of heroism!
The structural engineer of the marvelous 59-story Citicorp Center, William LeMessurier, received a call in June of 1978 from a student regarding stresses on the unique skeleton of the 1-year-old structure. The skeleton was unique. Supporting columns were centered on each side of the building, rather than on the corners, giving the cantilevered building the appearance of a man on stilts.
The student claimed his professor had told him the structure was not safe, due to stress loads on the odd-shaped building from the Manhattan winds.
LeMessurier assured the student the calculations were right.
The calculations had assumed wind striking the structure perpendicularly. But a thought came to him, given the positions of the support columns. What happens if the wind struck the building at a 45 degree angle instead? Surprisingly, he found the building much weaker than he believed.
But something else nagged at him. At a recent and unrelated meeting, the issue of welding joints versus bolting joints had come up. Bolted joints was the preferred method of construction, as it was cheaper than welding while affording similar strength. If bolting does not jeopardize the structural integrity of the building, there is no need to over-build a building - or to over-price it.
His initial skeleton structure had called for welded joints, but he had allowed for bolting to be substituted. This was not seen as a compromise, but instead recognition bolting provided sufficient structural strength cheaply. All was well.
But these two issues together - the wind-direction assumption and the bolted joints - made the building much much weaker than believed. The dire predictions suggested the building would suffer catastrophic failure once every 16 years. 16 years!
Now, at this point, only he knew this. Nobody else in the world had access to all of this information. Only him. What should he do? What would you do?
Before you boldly say you'd announce the findings, consider the professional humiliation you'd incur. Think of the additional costs you and your firm would incur fixing the problem.
For the whole story on what he actually did do, see here:
An Extension to the Story
There is a related entry here regarding the extension of principles into domains outside the "experience area". The Tacoma-Narrows Bridge collapsed, we know now, because of the use of plate girders to support the road bed, versus traditional open lattice beam trusses. A small change leads to a tremendously different outcome. So too with the Citicorp building, in the extension of principles outside the "experience area".
Fortunately, the issue was caught in time.
More fortunately, LeMessurier was the man to catch it, because of what he did with the information. Lesser men would have done less.
February 6, 2008
The Broken Window
by Henry Hazlitt in Economics in One Lesson
"Let us begin with the simplest illustration possible: let us, emulating Bastiat, choose a broken pane of glass.
A young hoodlum, say, heaves a brick through the window of a baker’s shop. The shopkeeper runs out furious, but the boy is gone. A crowd gathers, and begins to stare with quiet satisfaction at the gaping hole in the window and the shattered glass over the bread and pies. After a while the crowd feels the need for philosophic reflection. And several of its members are almost certain to remind each other or the baker that, after all, the misfortune has its bright side. It will make business for some glazier. As they begin to think of this they elaborate upon it. How much does a new plate glass window cost? Two hundred and fifty dollars? That will be quite a sum. After all, if windows were never broken, what would happen to the glass business? Then, of course, the thing is endless. The glazier will have $250 more to spend with other merchants, and these in turn will have $250 more to spend with still other merchants, and so ad infinitum. The smashed window will go on providing money and employment in ever-widening circles. The logical conclusion from all this would be, if the crowd drew it, that the little hoodlum who threw the brick, far from being a public menace, was a public benefactor.
Now let us take another look. The crowd is at least right in its first conclusion. This little act of vandalism will in the first instance mean more business for some glazier. The glazier will be no more unhappy to learn of the incident than an undertaker to learn of a death. But the shopkeeper will be out $250 that he was planning to spend for a new suit. Because he has had to replace a window, he will have to go without the suit (or some equivalent need or luxury). Instead of having a window and $250 he now has merely a window. Or, as he was planning to buy the suit that very afternoon, instead of having both a window and a suit he must be content with the window and no suit. If we think of him as a part of the community, the community has lost a new suit that might otherwise have come into being, and is just that much poorer.
The glazier’s gain of business, in short, is merely the tailor’s loss of business. No new “employment” has been added. The people in the crowd were thinking only of two parties to the transaction, the baker and the glazier. They had forgotten the potential third party involved, the tailor. They forgot him precisely because he will not now enter the scene. They will see the new window in the next day or two. They will never see the extra suit, precisely because it will never be made. They see only what is immediately visible to the eye."
Watch for the fallacy in practice - it's everywhere. And watch how our politicians attempt to repeal the law of identity - that a thing is a thing. If money intended to buy a suit must now be used to buy a new window, how do we make it so both the tailor and the glazier can benefit? We give the baker more money - in fact, we give everybody more money!
When inflation creeps, there's no sense complaining. The hypocrite who wants to have his cake and eat it too deserves only a cake in the face.
And the Sweet Taste of the (modified) Greek Trivium
February 7, 2008
Teachers and administrators are constantly inundated
with "the flavor of the month" educational philosophy to improve
education. Who is not aware of the research regarding "Right Brain /
Left Brain"? What of the Theory of Multiple Intelligences, where an
explicit philosophy expounding the differences in learning is discussed.
An additional popular educational theory revolves about the theory of Benjamin Bloom, called "Bloom's Taxomony", which takes the common-sense approach there are levels of learning a subject. One can know, for example, Topeka is the capital of Kansas, but why? Why is a different question. There are many such levels.
It's instructive to ask where Bloom came up with his taxonomy: in grading. How do we determine the quality of a paper we're grading?, and the taxonomy evolved.
Now, what of the teacher in the classroom? Right brain - left brain. Multiple intelligences. Bloom's taxonomy. A 1,000 more. All vying for precious time from the teacher's day. How do they do it?
They don't, of course. They do their best, but let's be honest. Presented like this - in a system where teacher time is the valuable commodity not to be wasted - there's no hope for implementation, either for these ideas or others.
Wouldn't it be nice if a theory came along, recognizing the constraint in the system, and instead of providing solutions in the way of week-long training sessions that, regardless of their goodness, still failed to reflect that teacher in the classroom needing to get from Point A to Point B by day's end, instead did something with that constraint? Wouldn't it be nice to actually see some free time, to afford the teacher the ability and opportunity to actually do something with these great ideas?
It would be nice!
What still nags me about this is the insistence upon all of these metrics being met. Do I get a "6" for "knowledge", a "5" for "information", etc. That, to me, has nothing to do with "education and learning", particularly at early ages.
The Greeks also had a powerful educational metric system, condensing all of these categories into three general branches:
and it was called "The Trivium". They reasoned, before one can make sense of things, one must have knowledge of things, and hence "Grammar" preceded "Logic", "Grammar" defined as the accumulation of "things", be it rocks, streams, clouds, or math facts. Logic answered the questions of "why" and "how are these related". The apex of the learning structure was "rhetoric", where one could talk coherently about such things - comfortably.
I don't like it.
Why the linear structure? Why not have logic raise a question for which there is not yet an answer? Go find the answer. Why reserve rhetoric to the end of the structure? Why not embed it within the structure?
Of course, the structure above is our understanding of their educational process 2,000 years after the fact. I think we've got it wrong. What I think they did, and what, to me, constitutes an authentic system of "joy in learning" is:
Chapters 5 & 6
February 8, 2008
Coach Thompson slumped over his lunch in the teacher’s lounge when Principal Ragnar approached, and, seeing the open spot across the table, down.
“Rough game last night?” said the Principal, sympathetically.
“I knew this year was going to be a tough one. We lost two seniors from last year’s 13–8 team. Then Michael Smith – who was going to be our star player this year – left because his father was transferred to North Carolina. Our losing accreditation didn’t help either, because no new players transferred in to our school. But even with all this, I did not expect to be 1–3 at this point in the season.”
The principal looked on, awaiting more.
“That’s not the worst of it – conference play starts next week, and all I see is things getting worse! In a month, we could very easily be 1–8.”
“But that’s not even the worst of it. The things we’ve been working on in my PE classroom have been unbelievably fun – for both the students and I. My teaching has really improved, and the students? Unbelievable. Did you get my e-mail about the latest results from the course on CPR? They not only aced the test and became CPR-certified, but you should have heard the classroom discussions on the new training standards. Oxygen in the blood, chest compressions, breathing, in what instances is breathing important and why – it went on and on. I wasn’t sure if I was in a PE class or a biology class! I talked with the CPR instructor afterwards, and she said this is the first class she’s ever taught where students stayed after class to ask her questions!
That’s why I feel so down right now. It’s not just the lack of progress in basketball; it’s that compared to the amazing success I’m seeing in the classroom. I wish some of the latter could help me with some of the former.”
“Are you sure it can’t?”, said the principal, seriously.
Coach looked up, interested. “What do you mean?”
The Principal rubbed his chin. “Don’t you remember our summer meetings, looking at what we were doing here, teaching, education, etc.? So much of it ending up focusing on assumptions. We had come to so take things for granted we rarely had questioned why things were the way they were.”
“Of course I remember, but what has that to do with basketball?”
Sensing this tract was not going anywhere, the Principal moved in an unexpected direction. “Let me ask you a question: if we raced from the front of the school, just you and I, down the exit to Main Street, who would win?”
“Are you serious?”, said the coach? “No offense, but I think I’m in a lot better shape than you. The race wouldn’t even be close.”
Principal Ragnar stood up, the smile gone from his face, and challenged the coach to the race.
“What’s this all about, Ragnar? Sit down, and let’s finish our lunch.”
“This won’t take long. Come on. I want to show you something.”
The two men, their lunches left unattended, marched through the front door and down the corridor at the front of the school. The Coach stopped at the designated starting spot, but looked in confusion as the Principal continued on into the parking lot towards his car. Believing the principal was simply retrieving his running shoes, the coach knelt to tighten his own shoes.
The sound ripped through his unexpecting ears. HONK! HONK! The principal sat behind the steering wheel, smiling, and approached the arranged starting line. The coach, not knowing what to do, burst into laughter, explaining, “What is this? I thought we were going to run! I’m not racing any car?”
“I accept your forfeit,” said the Principal, driving back to his assigned parking spot.
The two met up in front of the school, and returned to their uneaten lunches. “What was that all about?” the coach inquired?
“Look at what we’ve done in our classrooms. Do you not recall how many of our summer meetings ended up focusing on assumptions? Take reading, for example. We’re taught strategies like skimming, browsing, highlighting, etc. There’s a laundry list of others. We’ve been taught these for so long we rarely question if they work – are they good – do they help, yet look at the degree to which they impact our behavior! Here, I said “Let’s race” and you immediately assumed we were going to “run”.
“OK – this makes sense, but what has it to do with my basketball team?”
“We’ll see. Tomorrow at the close of practice, I’m going to play one-on-one against your best player. I guarantee you he will not be able to guard me.”
“Certainly not if you pull a stunt like that in the parking lot! What are you going to do – drive your car onto the basketball floor?”
“Nope – but you’re on the right track.”
PRINCIPAL VERSUS PLAYER
Principal Ragnar sauntered onto the court, a slight clumsiness to his dribble, but a happy confidence in his grin. Approaching center court where the team was stretching, he addressed the team amiably.
“Good afternoon, gentlemen. I hope Coach has told you what I’m doing here. Now, who here thinks he can stop me from scoring?”
Nate Johnson arose from the group. Nate was a 2–year starter, a 6’3” senior, and a reasonably good athlete. Principal Ragnar knew him well, and liked this choice particularly because he was well aware of Nate’s outward personality. Nate did not suffer from a lack of confidence. One might confuse it with arrogance.
The Principal joked: “I guess you young men need to stretch a bit so you don’t hurt yourself against this old man.” The joke drew a meager laughter, but accomplished its mission of putting the players at ease. “Before we start, Nate,” said the Principal addressing both Nate and the Coach, “let’s set the rules. We’re going to play one–on–one to five points, make–it–take–it, as you youngsters say”, referring to the custom of maintaining control of the ball if you score, rather than trading turns.
“Also, I hope you don’t mind if I start with the ball, or are you afraid you won’t get a chance to score?”
Nate grinned and bounced the ball back to the Principal, standing on the free-throw line.
The principal chided: “You’re sure you’re ready, Nate?” Nodding yes, the principal went to shoot, and Nate, anticipating the move, leapt into the air. No ball was there to block. There was only the slow-footed principal, driving to the basket for a simple layup!
The team broke into banter against Nate. “What was that?” shouted one, followed by “Come-on, Nate! You can’t let him do that to you!”
The principal jogged back to the free–throw line, confidently handing the ball to Nate with an arrogant “1–0” statement.
“That seemed pretty easy, Nate. But that was probably beginner’s luck, right?”
The ball bounced back to the principal, aggressively. Waiting for a similar ball fake, Nate retreated on his feet. The principal waited, and calmly swished the ball from the free throw line, without jumping at all.”
“You’ll remember, coach, I at one time could play. Many years ago, of course. What’s that, Nate: 2–0?”
The team crowed at the now–angry Nate. The principal seized on the opportunity by calling on the boisterous teammates. “Billy, why don’t you come take Nate’s spot.”
As Nate retreated to the group of boys, he met Billy’s confident stride and comment: “Let me show you how to stop a principal in his tracks.”
Billy strode to the free–throw line and set himself in a good defensive position, and handed the ball to the Principal.
“You’re sure you know the rules, here, Billy. I wouldn’t want you making the same mistakes Nate just made.”
“Whatever mistakes Nate made, I’m not going to make. Your ball.”
The principal gave a half–hearted attempt to fake Billy, a fake Billy did not accept. The principal then went to shoot and Billy leapt to block the shot. “Ahhh” came the cry as this time the Principal had dribbled by him to the left, and slowly jogged in for another layup! Grabbing the successful shot, the Principal returned to the free throw line, passed the ball to Billy, and calmly said “3–0”.
The coach stepped in. “Hold it right there. OK, you boys get started with practice. You know the routine. Get started, and we’ll start the formal practice in 15 minutes.”
“Would you mind telling me how you just did that? And let’s not forget you were going to show me how all the work we’ve been doing in the classroom relates to this.”
“No problem at all, and this relates directly with everything we’ve been doing in the classroom. Do you think I’m fast enough to go around these boys? Of course not. But that’s assuming I need to be fast to go around them. What happens if we challenge that assumption? If not speed, what then? So I went home and watched ESPN classic basketball of Michael Jordan and Larry Bird. I mean really watched them. How did they get around their defenders? It’s rarely speed. It’s almost always preceded by the slightest of movements to get their defenders out of position. Always! After watching that, I went to our big bathroom mirror with a basketball and watched myself trying these same fakes. It’s funny at first because what you think is a good fake in your mind would really fake nobody out. So I practiced and practiced and got really good. Then I asked my wife to “guard me”. She was only to jump when she thought I was going to shoot. We did about 50, and I got her moving on all but 6.”
“So I came here knowing I was going to shoot mostly layups because I could go around every one of these kids."
“Are you telling me if we just work on ball fakes, we’ll turn our season around?”
“No, because that’s just a part of it. That’s all I worked on, and I don’t know much basketball anymore. That’s your job. But what I am saying is if you’re telling me basketball is 5 players playing against 5 other players, the team with the best players will probably win, which means if your team does not have these players, you’ll probably lose. But this assumes you’re playing the game the same way the other teams are. What if you don’t? Think about that. What assumptions are in the game you play right now that can be challenged?”
February 9, 2008
The room abuzz, the people talking,
Down the aisle the shapes came walking.
Variable here and formula there;
The rhombus seemed to have no care.
The shapes had gathered to strut their stuff.
and badger those whose data was fluff!
The Quadrilateral Jam-Bor-Ee!
Was in full swing for all to see.
Rectangle first, down the aisle.
Parallel sides and a great big smile.
b times h is my area.
While I spin around with a tra-la-la
2 of me makes one of him!
Triangle boasts with a great big grin.
one-half b times h is me
a fraction for my fans to see!
I don't mean to boast - I don't mean to slam,
But here I come: Mr. Parallelogram.
I may be dull with my b-h rule;
But my slantiness makes me very cool.
Square is next, looking confident;
With a fine felt hat, he was a snappy gent.
With a grin that showed his happiness!
My area is s times s!
The crowd cheered and then subdued
The last thing the crowd wanted to be was rude.
What came next was the star of the show.
Red carpet out, the lights turned low.
Trapezoid was on his way
Three variables had caused his delay.
b sub 1 + b sub 2
In parenthesis times h over two.
The crowd cheered and then they roared!
bs and hs and ss! Good lord!
Shapes and formulas galore!
"WE WANT MORE! WE WANT MORE!"
A meek small figure then appeared.
The silence was such a pin-drop you could hear.
The crowd gaped in astonishment.
For this fellow lacked embellishment!
It's true I lack your flare and style
You wonder why I have this smile.
You've played this game for oh-so-long,
Stop and ask why kids get you wrong.
The essential "area" element;
Is hidden from development.
Note my interior's light gray-grid.
Unfortunately, this is what you've hid.
The implications have a consequent.
"Units betrayed" is what this has meant.
Memorization of formuli ...
I shake my head "Why oh Why!"
Tonight I come here not to preach
Not to blame but only to reach
To start anew with geometry.
To bring back students we've forced to flee!
Mathematical spirits I aim to lift,
But to do so requires a paradigm shift.
We'll reach for that what our soul is yearning!
Joy in living! Joy in learning!
A FURTHER THOUGHT
We can easily derive, algebraically, the formula for the area of the trapezoid, done here. But this misses the point.
It's all about the manipulation and movement of squares and triangles. That's the mindset. The algebra is along for the ride, but the "geometric mind" is what needs to take over here - to take precedence over the numbers.
It's quick to realize, when you actually perform these geometric manipulations, it's not a matter of remembering one formula or two. You don't have to remember any!
This is part of the paradigm shift: from the algebraic to the geometric mindset.
A Closing Word
A final word on this issue, because I don't want to leave the impression the goal of the above derivation was to arrive at the general formula for the trapezoid via geometric methods. Clearly, we can. But should we? Do we have to? Below is a worked example of finding the area of a trapezoid. Clearly, there is a place for both methods. Obviously, both methods arrive at the same answer. Wonderfully, the mental processes in doing so is radically different.
February 10, 2008
There is an airport just south of us, and many planes
fly overhead. It's amazing to watch these gigantic pieces of steel
fly through the sky when the smallest pebble, when lightly tossed into the
air, returns - without exception. How do these planes stay aloft?
The common explanation deals with the curvature of the wing. As air approaches the wing, it encounters the curved portion of the wing. Because the wind must travel a greater distance atop the curved surface than the accompanying flat surface on the underside of the wing, lift is created.
I'm tempted to say this is wrong, because it makes no sense to me, but I also know, given my 1/3/2008 plea, to resist such a temptation, and instead state simply, "I don't understand".
Likely, the proponents of this theory know of Bernoulli's principle of fluid flow. Likely, the proponents realize the crucial role atmospheric pressure plays in forcing the airflow acceleration. Likely, the proponents realize there is an optimal speed the plane must be moving for lift to be created.
We can explore these a bit in a moment. For the time being, my weekly logical haiku explores the marvel of flight.
Let's back up, now, and systematically deal with this issue. Consider a large aircraft, soaring high, coupled with our introductory explanation of how this happens: The curvature of the wing and airflow forces is the typical explanation for this behavior. That is:
This is likely reasonable for the seasoned aircraft professional. This cause-effect diagram and the issues above are perhaps second-nature to them - so ingrained in their understanding of the topic there's no sense verbalizing them to me. That's why I've said above their explanation above "is not wrong". So I have to view it from the only perspective I have: mine, and from the viewpoint of neither "rightness or wrongness", but do I understand? No. I'm troubled. Several reasons are provided above. Another is the shape of the curvature. We've simply said the wing is curved. How much? Does it matter? According to my theory, I could increase the curvature of the wing until it nearly approaches a flat surface. I'm fairly certain the plane would not fly, encountering massive wind resistance! In other words, my initial airfoil theory leads me to an anomaly.
What does this mean? Does this anomaly invalidate the theory? In a word: yes! I've said my theory accounts for flight, yet I found an example where the theory was proven wrong. But rather than discard the theory and start afresh, let's search for the conditions in which the theory is true. There likely is a context in which this is the case. What is the context? Right now, I don't know, so I'm comfortable merely asserting there is a context.
Where does the searching stop? The context is continually updated to account for additional features in the environment, be it altitude and atmospheric pressure, plane weight, etc., that are relevant.
Note too how this structure was abandoned in the Tacoma Narrows bridge failure, in that the assumption of an open-lattice beam trusses was not verbalized. Even this requires further thought, for the requirement is not essential when there is no wind! The lesson: the learning - the investigation of how reality works - never stops!
(untying the knot)
February 11, 2008
The logical methods of Mr. Sherlock Holmes are well
documented - or are they? How is it cases are solved seemingly "out
of nowhere"? How is it the good doctor Watson is often left at a
loss of words due to the conclusion that strikes without warning?
Let's break down the analysis of Mr. Holmes with a well-known story:
The Red Headed League.
A well-endowed red-headed gentleman obtains membership in "The Red-Headed League", paying him money weekly for staying in a room and copying from a book. All at once, the payment stops and the gentleman finds there is no such thing as the League. He goes to Mr.. Holmes in search of answers.
What answers are there?
Holmes focuses on "the anomaly": this odd thing called the Red-Headed League, requiring diligent and daily work from Mr. Wilson. Why was this created? Is it a coincidence it's a red-headed league, and not a dark-headed league? Let's assume not. Then why the charade? If Mr. Wilson has a full head of hair, which can be exploited, then we'll created the Red-Headed League, requiring diligent and daily work ... WHY? Because someone obviously wants Mr. Wilson out of his shop for a while each day.
Why? Why? Why? The initial thought is the exploitation of a woman at the shop, but Holmes finds no woman in the employment of Mr. Wilson. What then?
Theft? Mr. Wilson assures Holmes the shop has little in the way of cash, so theft is likely not the reason.
The motive must be something other than women or theft.
Holmes finds the new worker has been spending a great deal of time in the cellar with photography.
Why would he be doing that?
But if it is tunneling, I ought to be able to rap about the shop on the street and hear a slight echo. Hence, Holmes raps on the neighborhood street surrounding the shop until he indeed finds such a spot. A tunnel - heading from the shop to ... where?
The bank - behind the building!
The tunnel is headed towards the bank, but for what purpose? Remember, Mr. Wilson came to Holmes because the Red-Headed League had been disbanded. This likely means the tunneling is done, and something is bound to happen at the bank - quickly.
Would the robbers tunnel into the bank during the day? Likely not, even if the bank was closed, because people are still milling about. Would they wait until Sunday night? If so, they would have a short get-a-way time, as the bank opens Monday morning. Saturday night provides both optimal cover of darkness and get-a-way time.
Holmes has reasoned this all out, and announces to Watson to show up at the bank Saturday night, carrying a revolver! The astonishment is evidenced with the words of Watson:
"I trust that I am not more dense than my neighbours, but I was always oppressed with a sense of my own stupidity in my dealings with Sherlock Holmes. Here I had heard what he had heard, I had seen what he had seen, and yet from his words it was evident that he saw clearly not only what had happened but what was about to happen, while to me the whole business was still confused and grotesque.
Dénouement and "The Moral of the Story"
And so our good friend, Dr. Watson, properly assesses the undeniable logic as follows: "You reasoned it out beautifully ...It is so long a chain, and yet every link rings true."
Means - Motive - Opportunity - and The Critical Chain. Detection and problem-solving involves an infinite number of possibilities. What constitutes an "essential clue - something screaming, "Look at me! I'm more important than all others?" Often times it's the anomaly - that something "odd" that points the way!
February 12, 2008
“living with awareness”
from Chautauqua to Today
In the mid-19th century, as the American frontier became for many easterners a landscape for a new type of life, the population-packed Atlantic coast moved westward onto the sparse Midwest plains. Isolated yet in search of education and culture, an adult education movement – Chautauqua – arose. From this came the famous “Chautauqua Literary & Scientific Circle”, a reading program predating “The Great Books Program”, spanning the country and affecting millions of people starved for learning.
What happened to Chautauqua? With competing means of entertainment, Chautauqua moved to a “Tent Chautauqua” format in the early 20th century, focusing on entertainment and lectures. The advent of movies and radios delivered the death blow to what was once the greatest educational movement the United States had ever seen.
My new weekly column “about town” seeks to revitalize the spirit of Chautauqua – of educational excellence for all!
But if mere movies and the radio were the final blows to the Chautauqua movement, what need is there today – in this era of instant global digital communication, where practically everything is viewable instantly, where all data is seemingly at our fingertips now, where we hurriedly rush to and fro - for such a publication?
Because of all of these things.
How can it be, for example, with all of these things, educational improvement is stagnant? How can it be, not just kids but adults as well, can remain mathematically “illiterate”? How can it be, with the war in Iraq waging for years, a large part of the adult population cannot even find Iraq on the map?
Ray Bradbury, in Fahrenheit 451, provides a context with ominous parallels to our society of today. Regarding the role of future firemen burning books instead of putting out fires, Captain Beatty says to Montag:
“When did it all start, you ask, this job of ours, how did it come about, where, when? Well, I'd say it really got started around about a thing called the Civil War. Even though our rule book claims it was founded earlier. The fact is we didn't get along well until photography came into its own. Then - motion pictures in the early Twentieth Century. Radio. Television. Things began to have mass.
"And because they had mass, they became simpler," said Beatty. "Once, books appealed to a few people, here, there, everywhere. They could afford to be different. The world was roomy. But then the world got full of eyes and elbows and mouths. Double, triple, quadruple population. Films and radios, magazines, books leveled down to a sort of paste pudding norm, do you follow me?"
Beatty peered at the smoke pattern he had put out on the air. "Picture it. Nineteenth century man with his horses, dogs, carts, slow motion. Then, in the Twentieth Century, speed up your camera. Books cut shorter. Condensations. Digests. Tabloids. Everything boils down to the gag, the snap ending." "Classics cut to fifteen-minute radio shows, then cut again to fill a two-minute book column, winding up at last as a ten- or twelve-line dictionary resume. I exaggerate, of course. The dictionaries were for reference. But many were those whose sole knowledge of Hamlet (you know the title certainly, Montag; it is probably only a faint rumor of a title to you, Mrs. Montag) whose sole knowledge, as I say, of Hamlet was a one-page digest in a book that claimed: now at last you can read all the classics; keep up with your neighbors. Do you see? Out of the nursery into the college and back to the nursery; there's your intellectual pattern for the past five centuries or more."
Ominous parallels indeed! What are the implications for a democracy? What are the implications for simply being the best we can be?
But is the answer a rigid course of study? I think not.
“about town” simply seeks to look at our surroundings - sometimes carefully, sometimes from a dynamic distance - but always with the intent of seeking a story. Leaves have a story – as does coal, the rainbow, and a streetlight. Everything has a story. A logical story, perhaps. An entertaining one. A sad one. Whatever the case, everything has a story to tell – a good one.
In addition to brief stories seeking to understand “our town” will be the inclusion of a visual means of checking our logic. Do I really understand what I'm talking about? How can I check?
Where are more stories? A friend owns a jewelry store. What’s his story? Another runs a pharmacy. One has a dental office. A beautiful church opens down the street. What are their stories? Garmin, Hallmark, Ford, and Russell-Stover all have headquarters here. What are their stories? The Jazz Museum, the WWI Memorial, and the Plaza are amazing sites. What are their stories? Kansas and Missouri was at the center of the Civil War. What is our story?
This is a column about brief stories. But where do they come from? Louis L’Amour gives a wonderful explanation in “Education of a Wandering Man”:
They are out there by the thousands, wonderful stories. Many have never gotten into the histories, although occasionally told by local newspapers or in privately printed booklets. Stories of wagon-train massacres, buried treasures, gun battles, cattle roundup, border bandit raids – no matter where you go, east, west north, and south, there are stories. People are forever asking me where I get my ideas, but one has only to listen, to look, and to live with awareness. As I have said in several of my stories, all men look, but so few can see. It is all there, waiting for any passerby.
But in the process of trying to understand something, do I run the risk of being wrong? Of course! Why is it the case everything in print must be entirely right? Forget the fact this would seemingly promote very active reading – it would. If I say “leaves change color in the fall”, you might think, “most do – but there are leaves that don’t”. Therefore, my statement was wrong – how do I fix it? Active learning. I like that.
"Not dry research, but affection that puts life-blood into the material. It is merely hoped that this column will give the reader an idea of what a great and wonderful place" Kansas City is. (paraphrasing Jacob Marmor, i.e., William James Sidis, from "Meet Boston".
Do I need to travel around the country to find these stories? I think not. As L’Amour said, one need only look … about town!
Closing the Gap between The Map and the Territory
February 13, 2008
While at a concert in Parkville, Missouri, over the
weekend, I stepped outside the chapel on the hillside and looked down upon
the town. "How bucolic", I thought.
Then I rethought.
"Bucolic" means "rural", but why didn't I just say "rural"? Why decorate the perception with an unnecessary ornament?
"OK - How rural", I thought.
Well, I wasn't fine with that either. "Rural", to me, is merely a geographic term, distinguishing one area from another. That's not what I was doing. I was trying to describe a "sense" and not an "area". Maybe "bucolic" was right. What has the dictionary to say on the issue?
The word derives initially from a combination of two phrases:
1. "boukolos", meaning "herdsman", which came from "bous", meaning "cow";
2. "kolos" and "colere", meaning "tending to till"
This suggests to me a reference to "geography". But why not simply say "rural", then? But words and meanings change over time. So do the perceptions of words and meanings. How is "bucolic" actually used in discourse?
As I said in my 1/15 note, the British National Corpus is wonderful for addressing the question, "How are words actually used?" The BNC can be found here: http://www.natcorp.ox.ac.uk/
Let's see. Here are several actual uses of the word.
ED6 1394 The bucolic finale also goes rapidly, but I cannot complain, since Mozart invites that by labelling it both Vivace and a minuet.
EFN 541 A bucolic English gentleman `;by election';, in G. M. Young's phrase, he was always very highly strung.
FA2 107 Or the little portable sundials which shepherds used to carry up into the mountains to tell the time by; or, a last reassuringly bucolic reminder that Bayonne's fighting days are over, an English bayonet from the Napoleonic wars converted for stripping corn-cobs.
FA2 324 The church is lovely, both in itself and for its bucolic setting.
FA2 555 I shall come into Béarn from the Soule by way of Tardets and through a small, thoroughly bucolic bit of country known as the Barétous.
FRC 127 London!'; cried Victoria every time the train, a slow, halting, bucolic train, drew to a standstill, either at a drowsy country station where cow parsley foamed along the line or simply nowhere, among the fields, to have a little rest.
I'm not sure this sample settles anything, as there seems to be a mixture of both "sense" and "geography" sprinkled about the sample. So what do I mean by "sense" when I use the word "bucolic". Do I mean "rural"? No. Do I mean "simple"? The picture I get from "simple" is "unsophisticated", which is the opposite of "urbane". I don't mean that either. How about a "simple elegance"? I like that.
And since it's me doing the talking, I prefer the following distinction - having now thought things over:
How woefully inadequate is the quick dictionary definition of "rural". It may allow me to get an answer right on a vocabulary test, but does it help me in describing reality? Hardly. It really does take a "picture" to "see" the difference between words. One can't help but visualize a scene when saying a word. And yet, even when I try to put a description to the word, as in "Bucolic means a sense of elegant simplicity", to me, it doesn't capture the "essence" of what I'm trying to describe. Can any word do this? Is this one of the implications of "the map is not the territory"?
February 14, 2008
George Johnson was a happy man. He was an
energetic man. This was going to be a new year, and he greeted it
with the enthusiasm of a 3-year old facing three burning candles atop a
For Christmas, George had received a copy of The Goal, a wonderful business novel by Eli Goldratt. Christmas Day - night - George found himself reading the book - nonstop.
This was describing his company, he thought, and he could not wait to get to work to start the new year! Why was he off until then? The company had mandated he take his vacation time or lose it. Fine. It gave him all the more time to think.
George's company, Widgets Inc., made widgets (of course), the manufacturing of which was a simple two-step process: assembly (4-parts) and packing (which he was in charge of). Of course, there was a small administrative office in charge of miscellaneous items and the purchasing of materials, in addition to a small sales force (of 1), who took orders.
Having a few days to think about Widgets, Inc., before the new year started, he thought about the ramifications of The Goal. What was the goal of his company? They certainly make a lot of widgets, and he, in charge of packing, had always assumed his goal was good packing. Now he knew this was ridiculous - what was the goal - of the company? To make money?
He thought about how he had been ordered to work overtime Christmas Eve to pack the extra widgets assembled earlier in the day so the morning shift on December 26th could start with a clear floor. He had praised himself for his good work, but now he was certain the work wasn't so good. Nobody was going to buy these widgets - at least not for a couple weeks. Why waste the money on overtime?
He couldn't wait to get into the office January 1st.
George eagerly approached Henry Marshall, in charge of manufacturing, to tell Henry about The Goal. Henry wasn't in the mood for New Year's resolutions. "Happy New Year, George - did you see what our quota is for the month? They've made our bonus contingent on a 10% increase! 10%! Do you remember how many hours of overtime we clocked just to hit last year's goal? By the way: Happy New Year!"
George thought twice about talking with Henry, and instead went to Janice in administration, to talk about purchasing. After all, thought Henry, they made far more pieces the last year than they sold - why are they buying so many? Janice welcomed George with a tepid smile, and explained her job was to get the best discounts. Buying lower quantities meant lower discounts, which meant she would show a negative change (from the prior year) to start the new year.
Hurt only slightly, George decided he could at least improve his work station. He'd been giving the packing process much thought over the last week, and had come up with a number of ways of improving the speed in which packing took place.
Packing, of course, simply meant placing the plastic wrapping the mold, inserting the assembled widget, placing the cardboard backing on top, and lowering the machine, creating a solid seal. Sounds easy. It is easy! But sometimes things go wrong.
Many times, for example, the assembled piece would come with the widget top at an angle. George had always fixed this before the seal. How much time was wasted he didn't know. He experimented with accumulating these pieces in a box to the side, and by fixing them all at the same time, he found he could increase his speed 10%!
Also, as silly as it sounds, the monotony of the job often led to the compression seal machine being depressed with no cardboard backing in place. It usually took about 10 minutes to clean the machine, and he cursed himself every time this happened. It would keep happening, he thought, unless he did something different.
The solution was simplistically brilliant! Rather than place the mold, the piece, and the backing separately into the mold, he completed the assembly first, and then placed the total unit into the mold. It was now impossible to damage the machine! Speed again increased, this time 20%!
As other measures were implemented, George's unit became an efficiency machine. Everyone marveled at the speed at which packing now progressed.
They also noticed the amount of free time George's unit seemed to have.
You see, last year both processes took approximately 2:00 minutes to process a unit (4 complete widgets). George could now pack a unit in slightly under 1:30 minutes, but assembly still took 2:00 per widget. This meant, though George was moving faster and faster, he could not do more, because assembly was stuck on 2:00.
The call came unexpectedly the evening of January 28th. It was Jack, the division manager. George wasn't expecting this call for four days. The company usually announced the monthly bonus the first of the next month.
Jack had different ideas.
George was being let go. The storage costs of widgets had doubled, sales were stagnant, and it was determined George's department was overstaffed.
George hung up.
He thought back to the excitement of his Christmas present. He thought of making things better! He thought of having fun at his job again! Sure, nobody else had shared his enthusiasm, but he thought, in time, they'd see what was going on - ask him how it was happening! He'd be his own "pilot program".
But where had it led him? To getting fired? How had it come to this? He retraced the steps of the new year. He had tried getting others to buy in to the new overall improvement strategy. Not surprisingly, they had demurred. Did it have to end there? Of course not. He could still work to improve his department, couldn't he? But what had happened? The more he improved, the more "free time" his department had! Why was that?
He thought about Henry and his department. They weren't doing anything new this year, and their assembly times had not changed at all. And George could only pack widgets that were assembled. George, therefore, was dependent on the work of Henry. But it was more than a dependency - his unit was simply faster than Henry's department.
Assembly was the limiting factor - the constraint - in the system. Regardless of how fast George went - regardless of how much George improved, he was dependent on assembly. The implications hit him squarely between the eyes: if packing is not the constraint, then packing will have more (and more) excess capacity - in a never-ending loop.
That wasn't correct, of course. No loop is "never-ending", and the exit strategy in this system was his firing. But why? "I will work alone" was the clear cause.
What could he have done differently? He had tried to get the others to listen to him! Do nothing? Maintain the status quo? Is that what the company was rewarding? But why would he have done this? In retrospect, the answer was obvious: job security.
Why had the company put him in this dilemma? What did they want of him? What did they want of themselves?
He felt like Jonathan Livingston Seagull - he had been soaring high, and yet, here he was, "Being Called to Center - for shame - in the sight of his fellow gulls!"
The Occupational Dilemma
Between a Rock and a Hard Place!
What should George have done? He wanted both "Job Happiness" and "Job Security" at the same time. Was that asking too much? The company apparently thought so! What should the Company have done?
The Logic of the Shot Clock
February 15, 2008
Watching Chicago play Miami last night in the NBA, another “24-second violation” was called, indicating the team had failed to shoot within 24 seconds. Why is there a clock, and why is it set to 24 seconds?
What if there was no shot clock? Is that bad? My only thought, at first, is if there is no shot clock, then teams could hold the ball as long as they wanted.
Is that bad? Who would do that? Surely not good teams, because good teams want to shoot, don’t they? They want to score points. What about bad teams? Would it help them to hold the ball as long as they wanted? It seems like it, because it would at least stop the better team from scoring.
Well, if teams could hold the ball as long as they wanted, the games could really be boring, right? After all, what fun is it watching a game where nothing is happening? Not much fun at all. I wouldn’t go to games like that, and crowds wouldn’t either. But if the games would be boring, and if crowds won’t come to boring games, then the NBA will not draw many paying fans to the games. Is that the reason for the shot clock?
But why is the NBA shot-clock set to 24 seconds? Why not some regular number like 20 seconds or 30 seconds?
I wonder if I watched a game where both teams were reasonably good (and therefore, nobody held the ball), what would happen? How long would it take them to shoot? Sometimes, like in a fast break, it would only take a couple seconds. Other times, it might take a minute. What would happen if I watched for an entire game? That’s what was done when the shot was created for the 1955 season. It was determined a good team would shoot about 60 times each game, meaning, with both teams, there were about 120 shots taken in a game. How long is a game? As is the case now, games were 4 quarters, each 12 minutes long, meaning each game was 48 minutes long. This is 2,880 seconds. Therefore, in 2,880 seconds, it’s expected there will be 120 shots taken, or a shot taken every 24 seconds.
There's a second item I'll take up shortly regarding this sphere. It got down to about 5 degrees over night, and when I went to my trunk to get my basketball, it would hardly bounce. What has cold weather to do with this?
My initial thought is there is an "equilibrium" in place between the internal pressure of the ball pushing out, and the external pressure pushing in. When it gets colder, somehow and for some reason, the external pressure decreases, the equilibrium is disturbed, and air is forced out of the ball until the new equilibrium is reached.
I also notice when I bring the cold and flat basketball in the house where it is warm and let the ball sit, it becomes bouncy again!
How can this be if my initial theory was correct? Is air "getting back in"? I don't think so.
What's actually going on within an air molecule? Lots of movement. What happens when it gets cold. The movement lessens, and the molecule becomes both smaller and, with the same weight, more dense. This is the reason "hot air rises".
But the ball didn't shrink. Is this right? Thinking about other types of balls, however, I know they do lose their structural shape. Perhaps the difference lies in the rigidity of their outside. Basketballs have a pretty rough and solid exterior. That makes sense, too, because it's the bounciness I'm calling in to question, here.
A test to see if this is right, it would seem, would be to weigh the ball. My claim is the same number of molecules are still in the ball; nothing escaped If nothing escaped, then the weight should the same.
That's one experiment I could pursue.
Another thought comes to mind, regarding the compression of air molecules. Let's suppose, in the internal combustion engine, the air-intake stroke brings in air. By this, I now know "air molecules" are brought in. They are compressed. Next comes the fuel, a spark, an explosion, and we have the power stroke.
What if we brought in more air molecules? Would this change the power of the stroke, and the operation of the engine? Perhaps!
But how would we bring in more air? We just said it above - by cooling the air before it is forced in the cylinder! Right now, I suspect "intake stroke" simply means "surrounding air", and therefore, assumes environmental temperature. What if a cooling mechanism was put in place just prior to the intake stroke. More air molecules. Compress. Ignite. Expand! More power?
Likely someone has already thought of this - which is not the point, of course. The point is I just thought of it, and it was only possible because of the acquired knowledge from my flat basketball.
The verbalization of the analogy might go as follows: The flat basketball is like engine efficiency: both are due to cooling of the air.
More to come on general principles, and the (tragic) differentiation of the comparison terms of analogy, metaphor, simile, and similarity / difference.
Chapters 7 & 8
February 16, 2008
REVISITING THE ASSUMPTIONS
Following practice that afternoon, Coach Thompson drove around town, thinking about what Principal Ragnar had said, also thinking about what Principal Ragnar had done – to his players. He “ball–faked”, got the player to commit, and then calmly drove around the player. Fine. We practice ball–fakes, too. How does any of this apply?
Something was not quite right. Of course we practice ball fakes. But I’ve never seen our players do what the Principal had done today. Sure we practice them, but do we really practice them? What does it mean to “practice”?
The Coach stopped at the local Community College. There was a game tonight between two local junior college teams. Not expecting a large crowd turnout, the coach thought about the opportunity of eating a hotdog, spreading out in sparsely populated stands, and thinking about his team.
“Are my practices any different than other teams’ practices?” He thought to himself while chewing a $2.50 hotdog. “We warm–up, we practice shooting, we practice another drill, we go through offensive drills, defensive drills, scrimmage, and then run. What ‘assumptions’ are there to challenge?”
“Let’s back up a second. Why are we doing all this? Sure, other teams practice like this, but does this make it good? Is there a better way to win than this?”
“To win. Yes. That’s the goal, but the practices are geared to do this. Or are they?”
“How do I know if the practice – or game situations – my team is in a position to win?”
The coached watched the two opposing teams jog onto the court and assume their respective lay–up lines.
“Is the goal to win?” Of course, he thought, finishing the hotdog, and now wishing he had also bought a pop. But how do you win? You must outscore the opponent. Nothing was helping.”
He decided to watch part of the game.
The two teams raced up and down the court, the play of good jump–shots sprinkled with the types of violations that drive a coach wild. Obvious violations and lazy violations. And the shot selection! He was getting angry just watching!
“But is my team any different? What would it take to not commit such stupid violations. How do I get my players to take only good shots?” He focused in on the game, finding himself thinking more intensely about the fundamentals of the game than he could ever remember.
“How do I get value from every possession of the ball? If the goal is to win, the way to win is to value each possession – and not waste them.”
“Is it enough to tell the players not to take bad shots? I’ve been saying that for years. Sometimes it seems effective; other times I’m howling at the wind. Are these players stupid?”
“Or might it be the case they take the bad shot because they can’t get to a good shot?”
“Wait a minute! That’s exactly what Principal Ragnar had done!” The coach laughed thinking to himself about yelling to the principal to ‘take a good shot’. “What meaningless chatter that would have been. Take a good shot? I’ve got to show him how!”
And that’s exactly what the principal had done. He had gone home that night after our lunch discussion, watched what types of ball fakes really work – not some artificial movement we go through in practice, and then he showed up for practice ready to beat my players!
Not wasting possessions. Yes! Getting value from each possession! Yes!
But the thing that excited Coach Thompson most was the Principal had gone to his home and within a couple hours, had done this. That means the coach can get to practice the next day and immediately try this!
But more than this, as he thought about the idea of challenging the assumptions of the game, of considering every possession valuable, and the Principal’s “ball–faking” example, he thought of other ways practice “cheats” the players. “We have ball–faking drills, but do they teach ball–faking? No. What other drills do we do that are ineffective?”
Something to think about.
IDENTIFYING THE VALUABLE RESOURCE NOT TO BE WASTED: THE CONSTRAINT
The Second Chautauqua
The Principal looked at the clock reading 3:30 and heard the school bell announcing the end of the day. He watched the students load the buses, the parents pick up kids, and other kids walk and ride their bikes home. Another day. He retreated to his office to finish up some administrative activities.
The recent visit by the ACT representatives had left him uneasy, because they had left with a promise they’d probably be back after reporting their findings to the home office. Findings? They had found nothing! There was nothing to find! Another day, another battle.
The basketball event had left him with a feeling of exhilaration, not because he beat younger kids, but rather because it was another instance of challenging the status quo – and assumptions. It had been a busy couple of days, and he had not been able to follow-up to see what the coach had done with the event.
Looking up at the wall calendar, the earlier words stuck in his head. Another day. “Another day has come and gone,” he thought silently. “Here at 7:30 and gone at 3:30 – that’s 8 hours these students are here with us.” Another day? Put three of these together and you literally have a day! Is it too much to ask of a parent, if their kids are here 1/3 of a day, their kids learn to read and write and do arithmetic?
The thought mirrored discussions he’d heard his entire life. With the internet and cable TV, the discussion only intensified, with severe blame interjected into the conversation.
The consequence, of course, was to be expected. If you were facing a budget crisis, art and music go, and work intensifies in the “core areas”.
Who could blame them? To be measured based on reading and math performance, of course you’re going to focus efforts on: reading and math! There’s no surprise here.
But increasing the focus on reading and math ultimately means taking resources from other subjects (art, music, and PE, to name a few). The complaint seems justified, yet at the same time, why blame us!
Though sitting in his chair alone in his office, he felt pulled in opposite directions by the competing requirements of his teachers and the community.
He checked his e-mail. He browsed his educational websites for items of interest. Interdisciplinary Education shouted the headline, and Principal Ragnar read on. “Who could possibly be against interdisciplinary education?”, he thought. But as a solution? Right now? How would he organize his teachers to teach this way when their lesson plans are already made, and standards for many of the classes are set at the state level? These same people who demand we improve reading and math simultaneously ask us to revamp our teaching to integrate social studies, history, and current events! Who do they think we are? God?
But if it seems reasonable, he thought, why is it not practical? He walked about his office, occasionally out into the hall to see who was moving about. Why is it not practical? It is, he thought, just not right now. With demands to improve core subject material, does one have the time to integrate “interdisciplinary” materials, look at new teaching methods, and start a foreign-language program? Of course not. What a tremendous waste of time. All such programs do right now is make our teachers – our hard-working teachers – envious of what is possible in the future!
The dilemma we’re facing, he thought, was showing massive improvement immediately versus integrating all this great stuff everybody – including he and his teachers – knew was out there.
There was no dilemma to him, of course. Without the former, he could never implement the latter.
“Another day?” His mind raced back to his prior thoughts. “Every three days of school equals a 24-hour day. A full day.” But do kids get 24-hours of teaching or instruction? Of learning? He chucked, not solely because he knew kids were not, but also because many of these “new fads”
It all comes back to time, he thought. How to use it wisely – that’s the key. Of course, when you’ve got to do so much in the classroom, teach certain curriculum, move kids around, lunch, recess, plan “real–world” field trips, it all adds up. Don’t waste time? What a cliché!
But if time is a precious resource, how might it be wasted now? His memories as a teacher came back to him, and he remembered grading papers after school, at home, on weekends, goodness! It seemed all the time! Surely this was a waste of time, wasn’t it – or at least valuable time being – well, wasted. There was no other way to put it. He could have been working on lesson plans, playing with his kids, or fishing.
And he thought of all the problems students repeatedly got wrong. Nothing is more frustrating to a teacher than having to repeat a lesson to a student who did not learn it the first time. Surely, this is waste, isn’t it? But what’s the alternative? Is there an alternative?
“Effective learning time,” he thought to himself. Let’s not waste this precious resource.
February 17, 2008
As the price of a barrel of oil hovers around $100, the political climate is addressing the question, "What are we going to do? We're using too much foreign oil!"
Part of me says if we were really concerned about the issue (as consumers), we'd want the price of a gallon of gas to soar to $5 / galloon - only then will we change out habits, and reduce consumption.
I see no problem.
For the sake of this argument, however, I will assume there is a problem.
Why is this a problem? I've included "foreign" in the description of the problem above - is the issue one of importing? Likely not. We import many things, and although we talk of trade deficits, it's neither a serious nor sustained discussion. Perhaps oil is deemed "critical", and that's why we call this a problem.
What would we like to see? "Self-sufficiency regarding critical resources"? Fine.
There are many ways to achieve this - more plants, nuclear, solar, wind, etc. Let's focus on one specific debate: the Arctic National Wildlife Refuge. We want to become self-sufficient regarding oil? Drill in ANWR.
Of course, this is a huge issue - drill or not to drill. If there are significant reserves in the ANWR, why not drill? The answer usually centers about maintaining the environment, the habitat, etc. Wonderful.
So we have an interesting dilemma: in order to have a good country, now and in the future, we need to be self-sufficient regarding critical national resources. To do this, we should drill in the ANWR.
On the other hand, in order to have a good country, now and in the future, we need to maintain the beauty of the environment. Consequently, we should not drill in the ANWR.
An interesting dilemma.
What has been the result of this interesting dilemma? Politicians have jumped aboard the ethanol bandwagon, affording tax incentives for the construction of ethanol plants for the production of alternative fuels.
That's their solution.
This seems reasonable, doesn't it? After all, the technology exists, and at least one country, Brazil, has shown ethanol-based fuel is possible on a large scale.
But if we're to use corn from the field to create ethanol, where is it coming from? Surely, "we can't have our corn and eat it, too!" Corn once headed for the food-market is now headed for the ethanol plant. What happens to the price of food where corn is an element in the process? It will rise! Did the politicians anticipate this?
Moreover, let's not forget we're a net-exporter regarding corn. We were. What farmer would agree to export his corn at one price when it can be sent to the plant at a subsidized higher price?
But if this happens, what happens to those net - importers? They must now grow their own corn! How will then go about doing this? They will, likely, destroy forests to create fertile crop-land.
And the unintended - yet predictable - effect is the releasing of more greenhouse gases to the atmosphere!
So the "logical haiku" of the week is in honor of charging ahead, acting without thinking of the consequences of the action!
Charging Blindly to the Predicted Future
problem / solution?
think before you act!
The Quadrant Solution
In considering above consequences that are both predictable yet unintended, the "quadrant solution" is a handy device for examining the range of possibilities. For example, how would we describe the thinking of a person who undertakes an action with predictable consequences - yet they are unintended? This is what we see above, isn't it? How about "ignorance"! Is there a description for consequences that are intended - but not predictable?
Let's see ...
A SHAKESPEAREAN TRAGEDY
A tragic irony of the situation lies in our initial assumption: we must become more self-sufficient regarding a critical resource. To do so, we took away a critical resource (food) from other countries who were content importing this critical resource!
Circular Logic - Literally and Figuratively!
February 18, 2008
“Although most of the economic news was good, investors saw signs that the Federal Reserve is unlikely to cut interest rates anytime soon and took stocks down Tuesday.” The article continued, quoting an equity trader: “The market is hoping for slow growth and moderate inflation, and now there’s concern they might have to bump up rates in the second half of the year.”
What kind of nonsense is this? It shows some validity, perhaps, to the old adage "the only economic news is bad news". How can it be when economic news is good, the stock market tumbles?
What is the relationship between interest rates, the stock market, the economy, and the Federal Reserve?
A possible explanation:
A note about the use of logical arrows here: they are intended to depict the chronological timeline of my thinking, and not the logical. For example, consider this sentence: “If the Federal Reserve likely will seek to slow growth, then the Federal Reserve will increase interest rates, because interest rates are a means of regulating the flow of money in the economy”. This is a much different sentence than “If the Federal Reserve likely will seek to slow growth, and if interest rates are a means of regulating the flow of money in the economy, then the Federal Reserve will increase interest rates.”
But look what we've got: we start with an admission the economy is doing well. Through a series of causal explanations, we arrive at the economy NOT doing well! Can you imagine what will happen now?
Of course you can imagine it:
The scenarios above suggest circularity – if something is going too fast, slow it down. If it’s slow, speed it up. A system with feedback. Systems Dynamics has been modeling such behavior for decades, of course, but the logical processes, I believe, bring a great deal of clarity to the issue by verbalizing the entities in reality.
There seems to be one entry point sending the system into a circular spiral: "The job of the Federal Reserve is to regulate economic 'wellness'." Let's check that premise.
Let’s take all of this one step further. Let’s unify the logic to enable us to concretely see the circularity and feedback. In this regard, with scissors and tape at the ready, cut the following structure, and align the top of the cutout with the bottom (as though you were wrapping the paper around a soup can).
From Rock to Light: A Brief Journey
February 19, 2008
Coal and Electricity
From Rock to Light: A Brief Journey
Going west on College Boulevard, I passed over I-35 and saw below a coal train heading south. Looking both right and left, I saw neither beginning nor end to the massive mechanical caterpillar.
Where was it going? Where was it coming from? Of what use is coal anyways? How frequent are these trains? What is coal?
These massive coal trains, 80 to 100 per day, rumble through town, originating in the Northwest coal mines, winding their way through the Midwest, ending in electrical plants in Texas and Louisiana.
From Coal Mines to Electricity
But why? Electricity? What is the relationship of coal to electricity? To the light that brightens when I flip my switch?
Electrical plants produce electricity by way of a spinning turbine. The mechanics of this I’m not sure, but there is an interaction between the speed of this rotation and the resulting electro-magnetic field. The result is electricity.
What’s of interest to me is the relationship of coal to this process. The turbine must spin rapidly. But how? An old waterwheel spun because streaming water continued to strike the paddles, spinning the paddle wheel. What is the analogy to the power plant and the spinning turbine?
Rather than water punishing the turbine, electrical plants use steam – heated water – to accelerate the turbine. But where does the heat come from to transform water into steam?
But coal is a rock, and the rocks outside my house are also rocks. Why does coal burn, but my rocks don’t?
Coal as an Engine for the Creation of Steam
Coal is a unique form of sedimentary rock because of what it is that is being condensed. Many forms of sedimentary rocks are just that – rocks formed by the pressure from other sedimentary rocks atop them.
Millions of years ago, when plant life started to form on earth, plants would die and decay. This is the fate of most plants today.
But in swampy areas, dying plants would sink into the swamp and, not harassed by moving water or oxygen, simply accumulate. When the swamps dried up and were covered by rocks, this “dying plant life” would become compressed, with carbon the main element trapped in these. Upon the geologic timeline, this era is known as the “Carboniferous Period”, and it lasted approximately 70 million years, from 360 million BC to 290 million BC.
But is all coal “equal” in terms of heating value? That is, if coal is compressed carbon, and if compressed carbon set ablaze provides the heat necessary to create the steam, then it seems some coal would provide more “flame”, as not all coal would be subjected to the same pressure.
This map gives a distribution of coal, and the various types of coal, as defined by their “compactness”, or “heating value”.
The Appalachian Mountains in western Pennsylvania contain a high degree of compact coal. Why is this? During the Carboniferous Era, this area must have been a tremendously swampy area. Dying plants remained on the swampy floor, eventually compacted by rocks and surrounding erosion. But if this was all, this type of coal would be similar to other types of coal. Why is it more compact? The area tells us.
The Appalachian Mountains, formed by Continental Drift, pushed one plate under the other. The Appalachian Mountains were formed, and in the process, provided an immensely powerful “crushing force” for the layer of bio-degrading material underneath it.
Let’s see if this fits into logic branches, confirming I know (or don’t know) what I’m talking about:
Carbon is apparently the reason coal burns at a high heat, but why? The smoke from coal plants is subject to great debate in this era of environmental discussions. Where does this smoke come from, and is there a way to contain it? What is the average person’s “coal consumption”? For example, how much coal is required as a fuel to create electricity to run the computer I’m typing on now?
Of what use are the various types of coals? Lots of questions – lots of research to follow, once I return from my trip to the coal mines in Eastern Ohio.
Qualifications for the Presidency of the United States of America
February 20, 2008
Try to imagine, if you can, life in the eastern United
States before it was the United States. We were colonies, operating
under English rule and English law. Things weren't working out.
We went to battle. We won.
But what does this mean? How do we achieve it? How does it work?
Through a lot of discussion, there came the realization there must be a head of all this - a President. What type of person should fill this role? The richest? The wisest? The best-known?
How do we decide? Remember, you've just shed the authoritarian blanket of King George - we don't want another one of him. What's our ambitious target?
It's one thing to have an ambitious target; it's quite another to reach it. What action plan - what set of necessary conditions - what set of requirements - should we put in place to make sure we get to the target?
You must be an American. This seems obvious, but it isn't a requirement of either the Senate or the House, so maybe it's not so obvious. Maybe the Presidency is different. It is different. We don't want a King George, after all, coming over here, and somehow becoming President.
A citizen of the USA is a must.
But how do we define it? After all, we just created this beast through war! You can't require the president to be born in the USA when there was no such thing when all the eligible candidates were born! How about a requirement candidates must have been born on this soil - a "natural born citizen". This is our criteria.
But is it a good one? Many people, at the time, were born here, and moved back to England? Do we want such a person coming back to be president, even if they were born here? Surely, some form of residency requirement is necessary. What constitutes "reasonable"? 14 years.
Let's see where we're at?
Is this good enough? What about experience? It's tough to mandate intelligence, but often a proxy for experience is age. Older suggests more "life experiences". Should there be an age limit - or an experience limit? Likely.
What might this look like if it were written formally?
To be eligible for Presidency of the United States, an individual must be a natural born citizen, a resident on these soils for at least 14 years, and be at least 35 years old.
Most people would say this is what the Constitution says. Here is what the Constitution actually says:
No person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty-five Years, and been fourteen Years a Resident within the United States.
I think this is one of the most poorly written paragraphs I've ever read (perhaps surpassing my 1/10 post!). For example, is Austrian-born Arnold Schwarzenegger eligible to become president? Most people say "no". I think maybe.
After all, the constitution only seems to address the situation "at the time of the Adoption of this Constitution". What about AFTER the adoption?
OK - perhaps a mere technicality - perhaps not. Let's drop this argument and move on to issue #2.
Is Arnold a Citizen of the United States? I think so. The language seems to say if you are either a natural born Citizen OR a Citizen of the US, then you are eligible to be president. He is. Why did the founders make this distinction?
Likely the issue of how to state things addressing the "now" and the "future" hampered our founders' thoughts. For us now, it's easy to consider the phrase "natural born citizen". As I said, back then there was no country. Legitimate issues. What I'm concerned with right now is whether the founders stated things correctly.
In this spirit of investigation, I think the first three three sentence fragments were intended to address "the now and the future". What was intended, I believe, was you're eligible to be president . . .
if you were born on this soil
if you were NOT born on this soil, but you were a Citizen at the time of the adoption of the Constitution.
THIS is summarized as:
No person except a natural born Citizen, or a Citizen of the United States at the time of the Adoption of this Constitution,
What THEY said was:
No person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution,
Notice the slight difference - the comma after the United States. It changes the entire meaning of the sentence!
What's going on here? Why was the paragraph written like this? Why, in fact, were the two designations (Citizen and 'Natural Born Citizen') used? Why was 35 chosen as the necessary age? Why was 14 years chosen as the residency requirement? More research, as always, to follow!
Now, the interesting aspect of this research is what else turned up. What I didn't know was the likely Republican nominee, John McCain, was not born in the United States of America. He was born in the Panama-Canal-Zone, a US territory, in 1936! What is the status of his "eligibility"?
The Washington Post reported on this issue when McCain was running for presidency a decade ago!
Some might define the term "natural-born citizen" as one who was born on United States soil. But the First Congress, on March 26, 1790, approved an act that declared, "The children of citizens of the United States that may be born beyond sea, or outside the limits of the United States, shall be considered as natural-born citizens of the United States." That would seem to include McCain, whose parents were both citizens and whose father was a Navy officer stationed at the U.S. naval base in Panama at the time of John's birth in 1936.
Citizen McCain's Panama Problem?
By Ken Rudin
Special to washingtonpost.com
Thursday, July 9, 1998
February 21, 2008
It's hard to believe it's been nearly three years since
the tragic school bus accident in Liberty that killed two citizens and
injured many kids aboard the bus.
The KC Star reported yesterday the grand jury declined to indict the school bus driver - as I predicted last year in a brief letter to the National Transportation Safety Board.
a school bus like the one involved in the Liberty crash
Why did I write the NTSB? First, a bit about the case.
The bus, heading south on 291, approached the intersection of 291 & 152. Approaching stopped traffic and unable to stop, the driver veered to the right, plowing through stopped cars and killing two motorists. The veteran bus driver claimed the brakes did not work, giving rise to the actions of the bus at the intersection.
Initial investigations focused on the possibility of "pedal misapplication", applying the accelerator instead of the brake. A reasonable place to start: I myself have been guilty of this, plowing into the rock supports of my garage!
But the driver had filed numerous complaints regarding this bus and the braking system in the past, casting doubt on the theory of "pedal misapplication". What did maintenance find regarding the many complaints? Nothing.
A time-out here for a thought: what should be done when a driver complains of a braking problem - in any vehicle - and maintenance can find nothing? Put the vehicle back on the road? I hope not. Time-in.
So we've got two statements that seem contradictory:
1. the brakes were working fine;
2. the bus would not stop when the brakes were applied.
Is it possible both are valid - at the same time?
HOW CAN THIS BE? LEADING TO A POSSIBLE EXPLANATION
I speak from experience here, because the following incident actually happened to me. Driving around 635 coming from South Dakota, my Nissan Altima suddenly accelerated. I mean really, really accelerated. The more I applied the brake, the louder you could hear the engine roar, seeking to resume to it's "previous speed". I had no idea what I had touched, and my only thought was getting home. But then I realized I had to fix the problem there, because I would not be able to park the car! I have no idea what buttons I hit to solve the problem, nor have I been able to recreate the event since.
I'm certain it was some combination of setting the cruise control, braking to exit right onto 635 from 35, hitting the "resume" button . . .
But this is a school bus - not a car. Would there be any need for "cruise control" in a city school bus? There wouldn't. But this specific route was not a city route; it was a rural one.
So a theory: the driver on a rural route sets the cruise control while on a prolonged stretch of highway 291. The bus approaches a busy intersection and the driver applies the brakes. The bus fails to slow down, not because the brakes are faulty but rather because the faulty cruise control is commanding the bus to resume its speed.
Likely? I don't know. There may not be cruise-controls in buses, which would obviously invalidate the theory. But I know it's reasonable in a car, because it happened to me. Note: I talked with a school-bus driver yesterday (25th), who said all new buses do have cruise control. This does not prove my theory, but it keeps it alive. A "no" invalidates the theory immediately.
Where is the NTSB left to go? The grand jury said the driver was not at fault, so there must be reasonable evidence the cause is not "pedal misapplication" nor other types of driver error. The brakes, said the garage, were working fine.
THE DIAGNOSIS, THE PROGNOSIS, THE MAP AND THE TERRITORY
I know in anything there is the danger of jumping to conclusions. As our good friend, Sherlock Holmes, reminded us in "A Scandal in Bohemia": "It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts."
Of course, this begs the question, "What constitutes a fact worthy of investigating?" This itself requires some form of theory! As Dr. Deming reminds us in The New Economics: "Without theory, experience has no meaning. Without theory one has no questions to ask." Maybe what we're looking for here is not a linear path, but a spiraling back-and-forth between theory and data, constantly checking to see if data matches the theory, looking for any points invalidating the theory.
A GOOD STARTING POINT
Is there a way to integrate both theory and data for a reasonable starting point? "The brakes do not work" is a theory - a diagnosis from the patient - if you will. It restricts investigation. However, saying "the bus did not slow down, even when the brakes were applied" leaves open many possibilities, and incorporates both theory and facts.
February 22, 2008
"IS THIS THE FABRIC OF THE UNIVERSE?"
"Roger Highfield describes a heroic mathematical enterprise that could lay bare the fundamentals of the cosmos. Mathematicians have successfully scaled their equivalent of Mount Everest. Today they unveil the answer to a problem that, if written out in tiny print, would cover an area the size of Manhattan. A two dimensional representation of E8, courtesy of Peter McMullen and John Stembridge. At the most basic level, the calculation is an arcane investigation of symmetry – in this case of an object that is 57 dimensional, rather than the usual three dimensional ones that we are familiar with. Although this object was first discovered in the 19th century. there is evidence that it could contain the structure of the cosmos."
The UK Telegraph
March 19, 2007
I don't know about "the fabric of the universe", and I know I don't know a lot about what is being talked about at the E8 website, 57-dimensions, etc. However, I do know the similarities between this structure and some of my line designs are strikingly similar
In fact, if I modify the line coloring, change and overlap the radius' of the structure on the far left, the result is very, very interesting ...
What's going on, here? Is there anything going on here? Is there any relationship between the two figures above? Do I even care? I've always enjoyed making these designs for the mere joy in making them. Does there have to be "relevancy" involved?
Some Thoughts on Line Designs and Pedagogy
In the quest to make math "relevant and engaging", there has been a recent surge in "Line Designs" and "Curve Stitching". The re-creation of many pictures and the use of computers has made for many design projects, but has it led to educational improvement? How would we know if it had? What is the nature of these designs that so fascinates both children and adults? What is the goal of these designs? Towards what end? This workshop will explore the historical (including the George Boole connection), philosophical, and pedagogical nature of line designs, with a focus on good designs and what constitutes the proper context / good environment ensuring "joy in work" is realized, now and in the future.
Math curriculum frequently includes line design lesson plans, a careful structure on how to achieve a desired result, and a method to grade the results. To ensure relevance to a topic, many line designs are crafted to mimic some picture, such as a face or a valentine. Further “enhancements” include many java-enabled web sites affording ease of creation of these designs. As this integration of line designs increases in math curriculum, it’s instructive to consider what it is about these designs we consider “good”.
Mary Everest Boole, wife of famed mathematician George Boole and known by many as the origin of this type of activity, said the following regarding this process:
“The beauty of some of the designs is unquestionable; and there can be no second opinion about the value of the method, as training, from the point of view of geometry as well as from that of art. What is not quite so obvious at first sight is its bearing on the training of the unconscious mind for science. Without the slightest intellectual strain it puts the children through that normal sequence of orderly attention to classification and detail, interspersed with nodal points of synthesis, which may be called the very breathing-rhythm of the scientific discoverer.
But to make this exercise of any use there must be no copying from diagrams; the value of it depends on the child evoking a curve, watching it growing, under his fingers, from mere obedience to a law … and beauty has resulted, not from understanding but from obedience … the act of evoking a curve ‘out of the everywhere into here’, by simple obedience to a rhythmic law, lodges an impression on the unconscious mind which will be ready to surge up in ten years’ time.” 
Clearly, what we as adults consider “good” qualities are necessary conditions for a good activity, but are they sufficient? Ms. Boole addresses ‘orderly attention’ and ‘classification of detail’, leading to ‘beauty’ as the result, with a particular benefit the training of the mind for future excellence. How is this process captured in a rubric concentrating on product? To emphasize this point, Edith Somervell said the following about the “process versus product” dilemma:
“Beautiful curves are produced by a process so simple and automatic that the most inartistic child can succeed in generating beauty by mere conscientious accuracy; and the habit of doing this tends to produce a keen feeling for line. It has also been noticed in some cases, where clean, pure, and strong colour has been used, that a remarkable sensitiveness to colour relation has grown.” “The results obtained by a child, of exquisite curved and flower forms on the ‘back’ of his card, by faithful obedience to a dull little rule in making straight stitches on the ‘front’, is of the nature a miracle. It should, therefore, be hardly necessary to insist that the less said the better, when the little worker produces anything especially beautiful or unexpected.” 
What as adults can we do regarding the working environment to ensure a good process with beautiful results? What types of designs are appropriate for children? How do we translate “dull little rule” into practice? And finally, if the method is so powerful we can see the impression years down the road, how can we ensure the children continue creating such designs outside the classroom?
Chapters 9 & 10
February 23, 2008
The next day’s practice started with no balls. The coach brought the team aside before stretching, placed the team in a circle, and called Nate out. “What’d you think about the old man yesterday,” said the coach, joking? “He got lucky. Play a whole game and we’ll see who would win.”
“Of course you’d win – any of you playing him. But what did he do? He was able to get around you – all of you – easily. Here’s what we’re going to do before stretching. I want you to pair up, one person pretending they have the ball, and try to get the other person to flinch. It does not matter how much they move. Get them to flinch.”
They broke off into pairs around the midcourt area, and immediately broke into seemingly random movements, jutting and jerking and bobbing and stabbing – all with the intention of getting the other player to move. After a few minutes, the coach called the team over. “Pretty easy, isn’t it – and you all look pretty funny. Now, I want each pair to go get a ball, and try to do the same thing, only this time, you cannot dribble, you can only pretend to shoot. Same results: I want to see if you can get the other player to flinch.”
The results were astonishing. He couldn’t believe what he was seeing. The ‘ball–fakes’ faked nobody. There was no flinching, because there was no faking. “It’s as I thought,” he said quietly to himself. “That which is totally natural in one instance is foreign to most of these kids – and I’ve not helped any of them by saying, ‘ball–fake’. They don’t know how.”
But far from being excited about this revelation, which in itself just demonstrated he and most coaches don’t do a very good job, he was more excited about what he had seen with the Principal yesterday. This was a real chance to show dramatic improvement in helping his team win – right now! He didn’t have to wait a month for some conditioning program, or simply play out the season. This was a real chance to do something about his season – right now!
He called the players over.
“I want you all to think about what just happened. Before, it was easy to make your teammate jump. With a ball, however, nothing happened. Why?”
William jumped in. “That’s easy – did you see Steve try to fake me? Who’d believe he was going to do anything with the ball? All he did was pump the ball in the air a couple of times and bat his eyes. Was that supposed to fake me out?”
“I didn’t exactly see Steve jumping into the bleachers when you had the ball,” the coach said, jokingly. “In fact, I didn’t see anybody jumping into the bleachers! But what about the Principal yesterday? How about what he did?”
“How did he do that?” said one player.
“He told me he stood in front of the mirror and tried to fake himself out. He said right away he saw what was a bad fake – and then what was a good fake. He got really good really fast, and then came out here yesterday and beat your butts.”
“Is that what we’re going to do – stand in front of a mirror and try to fake ourselves out?”
“Why not? We’ve got huge mirrors in the locker room. The Principal only had a bathroom mirror. We should be able to do much better than him!”
As they marched towards the locker room, Principal Ragnar stepped into the gym, puzzled as to why players were heading for the locker room. Hadn’t practice just started? He was expecting something to come from the prior events, but this?
“Hey coach,” he yelled across the vacant gymnasium to the exiting Coach Thompson. “Is practice all over?”
“Hardly, my friend. We’re going into the locker room to continue. Why don’t you come back in half-an hour to see how we’re doing.”
Caught up in brief conversations with faculty staying late, Principal Ragnar returned 45 minutes later and took a seat in the bleachers. He had been thinking what the coach would do, if anything, with what had gone on during the last couple days. After all, it had not been a recommendation as to how to coach, but rather a simple example of focusing on “the stuff that matters”. There were likely many more such things – or were there? How can there be “many things that matter”? Or do they all matter equally? Nonsense.
But what he saw did please him immensely. The team was aligned into two lines, and each player was taking a turn driving to the basket against the opposing player. The only hitch was they had to continue this until they had driven past every player in their line!
Coach Thompson joined the Principal in the stands, handing off coaching duties to the two assistant coaches.
“You’ve really got something here,” said the Coach excitedly. “Look at these kids. I’ve never seen them fake so well. Of course, it took a bit of practice in front of the locker room mirrors to realize what they’d been doing in the past was of little help.”
“So that’s where you went! Here I thought you were stopping practice early. So it works well, huh? Will it work in a game, however?”
“Stop stealing my thunder, would you?”, the coach retorted. “That’s all I’ve been thinking about. We’ve got two days until our next game, so this is all we’re working on today and tomorrow. What will be most difficult is actually getting them to do this in a game situation, they’re so conditioned to do things other ways. What I’m hoping will help is here we’re focusing on the mindset of ‘getting by the defensive player by deception’ Previously, we just said, ‘fake’. How helpful is that? We shall see, but I’m very excited. Are you coming to the game? You know it’s across town.”
“I would not miss it for the world”, said the Principal, joyfully. “I’ll bring my wife also. After all, she was my ‘defender’ in getting the fakes to work!”
A BRAND NEW GAME
The Jackson Central High coach strode across the floor to shake Coach Thompson’s hand. 'Coach – that was one of the most unbelievable exhibitions of ‘old-school’ basketball I’ve seen in a long time. Congratulations.”
Graciously accepting the compliment, Coach Thompson proudly looked up at the scoreboard:
Washington High: 75 Jackson Central: 58
Last season, Jackson Central had defeated Washington by 7 points, and this year, returning all starters, they were a 15–point favorite. Washington entered the game 1–3, and then this!
The surprising thing was this was not surprising to Coach Thompson. He had seen remarkable changes in his team in the last three days of practice. Remarkable? That doesn’t even do his team’s performance justice. His players had become, in a short period of time, as good of ball–fakers he had ever seen – every last one of them.
It didn’t take the Coach long to realize, in practice, the impact of this powerful tool. To get around a player, of course, was how this all started. And his players now – and quickly – were as good as any in doing this. “This”, of course, assumed the player guarding the ball assumed you were going to shoot, and it didn’t take the coach long to realize if there were no real threat to making a basket, there was no use in providing a quality ball fake.
However, this simple tool executed properly paid off in many other areas which were practiced over the past two days. When a shorter player found himself under the basket guarded by a taller player, the coach had always taught the player to ball–fake. And they did – ineffectively. Now, with the same advice but the skill on how to do this effectively, the Coach found his players not just more effective under the basket, but drawing more fouls, converting more free throws, and making an occasional three-point basket.
The statistics from the Jackson Central game proved this out. Washington High shot 38 free throws to Jackson Central’s 22, despite Washington being the much shorter team.
The coach greeted his team in the locker room – an exuberant locker room – filled with yelling high school basketball players excited about an unexpected victory.
“Well done, boys – that was as fine a basketball game as I’ve ever seen. And do you know what? We’ve got a lot more where that came from. RIGHT?” His yell was echoed with a similar cry.
“This is why I wanted to be a basketball coach,” he thought. “Sure, the winning is great. Who doesn’t like to win. But seeing his kids happy – that’s what it’s all about. But that’s not even right. Hadn’t he seen kids happy before, though they hadn’t played very well? That’s it: his kids were happy because they had played well.
Principal Ragnar met the coach exiting the locker room. “That was unbelievable, my friend. And you should have heard our parents up there. There were as astounded as I!”
“Unbelievable” doesn’t even describe what I’m feeling right now, and I know how you must have felt when you first started that ACT experiment. By focusing on a simple thing, extraordinary things happened. But simply thinking like this has really got me thinking about other aspects of the game. What happens when other teams catch on to what we’re doing? They simply won’t go for the fakes. If that’s the case, we’d better be in a position to do something. One thing is for sure, however; we’ll never have another practice again like we used to practice!”
The coach walked to join his team boarding the bus. He looked back to a happy Principal Ragnar: “See what you’ve done to me! We win a great game, and you’ve got me thinking about many other ways to improve the team!”
“You’re welcome”, said the Principal, again joyfully.
February 24, 2008
Last Wednesday, a news high-light was the coming lunar
eclipse. I had my telescope at the ready, though I unfortunately
could not get it to work. Additionally, cloud cover seemed to
obscure the event as the evening passed. Part
of what I did see was similar to the following:
What exactly was going on here? By "lunar eclipse", I've read the earth passes between the sun and the moon, giving rise to the lunar eclipse. That is:
What strikes me as odd about this explanation is the following: I thought the moon orbited the earth - just as the earth orbits the sun. And if this is the case, and the earth moves between the sun and the moon during the earth's orbit, I'd expect to see lunar eclipses all the time - so often, in fact, this would be a non-event.
So I know, if my theory about the relationship between the sun, moon, and earth is correct, there must be some solar context giving rise to lunar eclipses being rare. Why? I was being told this was somewhat of a rare event. Yet if my theory about the event were true, I'd expect to see lunar eclipses all the time! Therefore, something's wrong somewhere. Either my theory is entirely wrong, of there is some context I'm missing.
Observe this is a slight variation to the Iterative Effect-Cause-Effect pattern above - the only modification being I made explicit the context giving rise to the anomaly.
What might this "solar context" consist? I assumed the orbit of the moon about the earth was in the same plane as the earth's orbit about the sun. Apparently, the moon's orbit is tilted 5˚, which means there are only two points / nodes of intersection. This fact, couple with the necessity of a full moon, apparently gives rise to the "lunar eclipse" event - the intersection of these two events. Apparently, these two events do not happen together often. I'm still working through the logic of this. As of yet, I have no information - just data. The data, as I understand them, are as follows:
A DIFFERENT CHAIN OF THOUGHT
There's another aspect to this event, however, I'd like to focus on. I always assumed, in the event of an eclipse, things simply go dark. Where does the "redness" come from?
Light from the sun, in hitting the earth's atmosphere as the earth passes between the sun and the moon, is deflected. If we had no atmosphere, the light would continue unabated, and we would see no moon at all. We do (thankfully) have an atmosphere. The light strikes it, and is bent. Light with short wavelengths is scattered. Light from the spectrum with longer wavelengths survives the atmospheric change of direction, and is redirected towards the moon. What light in the spectrum has long wavelengths? Red and Orange.
Therefore, during a lunar eclipse, some light emanating from the sun strikes our atmosphere and arrives at the moon. This week's logical haiku is dedicated to this phenomenon.
February 25, 2008
The issue is a common one,
the commonality of the debate itself a clue a problem exists. A
chronic one. If not, surely the problem would be solved. The
issue (complaint / demand), from the community's perspective, goes
something like this:
"Why are our elementary kids not taught a foreign language? It's a global economy, after all. And kid's learn foreign languages much better than adults. What are 'you people' doing?"
Let's not stop at foreign languages, however. There are similar issues: computers and the internet. New and relevant math. Probably a dozen more. The Junior Great Books program and the Socratic Method. A ton of great stuff out there!
This is the clarion call from the community - there's a ton of great stuff out there! Do something! Do it all!
What would it take to "do it all"? At a minimum, we'd have to modify and expand the curriculum. We'd have to train teachers. We'd have to hire teachers! Infrastructures changed! A lot of things. Does the "community" ever verbalize such things? Of course not. We just pay the bills - we're the customer, and "we're always right", right?
The educational community, on the other hand, is surely receptive to such things. They're not ignorant. They know as well as us "all this good stuff". Why don't they share our excitement? They live "in the real world", where NCLB and AYP are breathing down their necks. In some communities, merely maintaining accredidation is a chore. More stuff? You must be kidding!
What to do?
What is typically done in any such conflict? Compromise? Pacification of one group with a some action - any action - to be seen as "doing something"? Pilot programs? Special courses for "gifted" kids, pulling them from classes to show the community "we teach to the needs of all"? What about foreign language programs? One popular method is to implement a foreign language via DVD.
I don't blame the educational establishment for this "solution". They're caught in a tremendous bind and must do something. I don't blame the community either. Their request is a sincere one. I do believe in honesty at all times, however. An honest response to the community would be "we're in a tremendous bind". A less-than-honest response is implementing a program you know will not and cannot possibly deliver "the goods".
When I spoke on this issue in 2006, it was to two issues: one was addressed to the community: don't force more things on the educational system (because of the dilemma above); the other was addressed to the educational system: don't respond with something that will not work to pacify the crowd.
What has changed? Why am I writing this article?
A FOREIGN LANGUAGE WISH LIST
I claim a DVD-based program will not work. But what will? Let's see if we can flush out some "necessary conditions" to meet our goal of "a good foreign language program".
I know English - and want to learn French. I want to know how to say "hello" in French. A translation book will show me the letters, but will not provide the audio pronunciation. This is out. But what of a DVD-based program - or a CD? They say the words. Why won't they suffice? Because I need to hear the word over - and over - and over. Many times. Does such media provide such repetition - at my request - at my speed? No.
Therefore, foreign-language wish list Item #1: the program must allow me to have repeated at my request the specific word or phrase. I must be able to listen - say - listen - say - etc.
But is this enough? I often hear phrases on the internet, but they're said so fast I can't understand them. I can't hear the minor accents or the pronunciations of syllables. I must be able to slow down the translated pronunciation - at my discretion. This is wish-list Item #2: I control the speed the word or phrase is being spoken.
But what phrases? Sure it's nice to know phrases like "How are you?" and "Where is the bathroom?", particularly if you're visiting the country. But let's remember right now we're not visiting a foreign country. We're simply trying to learn the language! Well, how do we learn our own language? This simple question is rarely asked. Shinichi Suzuki, the master violinist, was one person who did ask it. Isn't it a miracle a Japanese child can speak Japanese? We don't teach kids phrases. We don't start with grammar rules. We start by talking to the kids. Single words. Repeated words. Long before any grammar is taught, children are fluent speakers! How might this work in our wish-list?
Foreign-language wish list Item #3: I must be able to type in my own phrase. Then another. And another. Often modifying slightly the phrase. "This is a ball". "This is a chair". Repeated. I get fluent at saying "This is a" in French. I learn the specific nouns, verbs, etc., along the way.
Is this it? I must be able to request anything I want spoken at any speed I want as many times as I want.
There's one more thing - at least - I'd like to see. Who is doing the speaking above? There is a tremendous difference when one simply hears something spoken, and when you see someone speaking - with their lips moving. Why? I don't know. But the result is astonishing.
So my foreign-language wish list now sounds like a professional tutor! A person repeating what I'm saying, fast or slow, as many times as I want. This tutor will also be able to explain how my words translate into foreign words - not every word or phrase, after all, uniquely migrates from language to language.
Have I described a professional and personal foreign-language tutor?
What I've also described are the features of one of the most remarkable sites I've found on the Internet.
Does this marvelous site have everything? No - at least not yet. However, I wouldn't put anything past them. What about an "understanding" component? Instead of asking the site to translate English to French, the site instead gives you random words/phrases/sentences in French, and you must translate. It can be either written or spoken, with a spectrum of ability - ranging from "easy" to "really hard". Likely they're already thinking of it. What can be done for schools with this program? Likely they've thought of it. What of specific lessons to assist the student in moving forward? Likely they've thought of it. A frequent comment regarding foreign languages is "why offer just Spanish?" They have thought of this - offering 19 different languages! What of the price? Remarkable.
However, don't take my word for it. In the words (paraphrasing) of Arthur Jones, inventor of the Nautilus exercise equipment, "Strap it on your back - run down the runway - see if it will fly!"
With www.virtuallanguagetutor.com , we all can be Jonathan Livingston Seagulls!
February 26, 2008
Likely if you're a practicing physician, you belong to
a number of health insurance networks. You agree to be in these
networks in order to be a "preferred" provider in a health-insurer system.
The "preferred" status, from the health insuree's perspective, affords a
higher level of benefits than the "non-preferred" set of benefits.
They'll likely search for benefits from a preferred provider - you.
As you also know, this comes at a price. You accept lower payments for your services, in exchange for being "preferred". You may charge one individual $100 for a service. For a member in the network, you only get $80.
You finally know the difficulties of the negotiations from year to year regarding your fee schedule. Does this conflict look familiar?
A Different Train of Thought
Let's put your anger in check for a moment - I'd like to pursue what may seem something "off the track": Medicare, Medicaid, and LBJ. When Medicare and Medicaid originated in the 60s, the clarion call was one of achievement: finally, all citizens will be covered - old and poor. But where would the funding come from? A combination of member premiums and government taxes. But surely, regardless of cost, no legislator will approve a double-digit increase in premiums to their constituents. Additionally, the annual "budget-balancing" show suggests there is only so much that will go into the coffers. Consequently, regardless of the cost of the plan, we're pretty sure funding can only grow so fast.
And what of costs? What of the nature of technological advances? They're everywhere - and they're not cheap. Couple this with the issue of "defensive medical practice" so necessary in our litigious society, and costs are likely to rise rapidly.
But where does this leave us? Funding creeping up - costs racing up. What are the consequences of this tremendous gap?
The Consequence of this Financial Gap
What will the government do, with an increasing gap between cost and funding? What can they do? Decrease benefits? They can try - and the backlash will be quick and brutal. Increase premiums? We already addressed that. Payments to physicians? This is the only avenue available. If you're a physician, you know all too well how they have done this.
The Inevitable Results - and Conflict
You know how they give you cents on the dollar for your services. You know you can't run your practice on what they reimburse you. What outlet have you to retain your practice and your living standards? The commercial market. It's no wonder you want increased fees from that market - it's all that's left open to you!
The Fight Worth Fighting
You have many reasonable complaints. Your profession is constantly under attack, and your services are taken for granted. Not by me. I respect your concerns the commercial market wants to hold down your reimbursement levels. I don't believe there is an inevitable tension between those who pay and those who provide services. This is a manufactured conflict - an artificial one - created four decades ago. This conflict was inevitable. Your fight is with the government. Fight on! But fight the right fight. Advocate a "national health care plan" and imagine how the scenario above plays itself out.
The Circumference of the Earth
February 27, 2008
The brilliant mathematician, scientist, geographist,
librarian, tutor, and about everything else - Eratosthenes, is known to
most for his "Sieve", whereby a simple algorithm denotes prime numbers by
eliminating non-prime numbers.
I'm concerned today with a different question: how big is this planet we live on?
Since Eratosthenes is not around to defend himself, I'm going to take his place, trying to retrace his intellectual footsteps, seeing what assumptions he made, what mistakes (if any), and what he really would have to have known in order to answer the question above. I am Iatosthenes - mathematical detective.
Where do I even start? Even drawing the sphere on a piece of paper - allowing me to see things in two dimensions, I'm stumped. Let's start playing around. What I'm looking for is the circumference. I know the general formula for this is C=2πr. I know neither C nor r, so this seems no help, though it does, at least, get something on the table. What else do I know of circles?
Suppose I carve out a slice of the circle. Does this do anything for me? Suppose I create two radii emanating from the circle, forming angle x. Let's say they carve out some distance along the circle. What happens as x grows? The "some distance" grows. There is a direct relationship between the two. If I knew both of these things, and knowing there are 360˚ in a circle, then I could then derive the circumference.
But how can I get either of these? I certainly can't drill to the center of the earth, and even if I could, what good would it do?
Being the librarian at Alexandria, I have access to a great many texts. I know Thales of Miletus, centuries earlier, had measured the height of the Great Pyramid at Cheops - not by measuring it's height, but by measuring the length of the shadow cast by it. Can the sun help me, too?
Let's suppose I stick a large rod straight up, and assume the light rays are coming straight down. A shadow is cast. But so what - a shadow is always cast when the sun is out! Well, I know something about proportions, and I know if I knew both the length of the rod and of the shadow cast, I could determine the angle where sunlight struck the rod. Again, so what!
Well, I know something about Euclid, parallel lines, and a line bisecting them. The angle I'm talking about here is equal to the angle I'm actually looking for - the angle at the center of the earth
Knowing angle x is one part of the puzzle - a huge part.
(No doubt you'll recognize the Euclidean theorem used above was also used in the January 7th post regarding the sum of the angles in a triangle).
Other Necessary Steps
I think I'm on the right track here, but let's not get ahead of ourselves. I know of at least three huge assumptions in the logic above needing more work / investigation:
1. I'm able to determine the distance between the two points on the circle / earth. Let's remember we're talking thousands of years ago. There were no maps. There were no GPS systems. There were only people. How would I go about this?
2. I've assumed the sunlight is coming straight down. Does it always? Does it ever? How can I find this out?
3. I've said if I had the length of the rod and the length of the shadow, I could determine the ratio of the two, and determine the angle x. Is this so? Where does this "fact" come from? Remember, there were no calculators back then? Is there some relationship between this ratio and angles?
The search continues ...
February 28, 2008
IT’S NOT LUCK
Principal Ragnar welcomed back the gentlemen from the ACT. Having reported back to headquarters nothing was evident thus far regarding cheating, the school had been placed on a “watch list”. The gentlemen were back of their own choice, however, interested in learning more about the improvement by Washington High.
“I’m glad you came back, gentlemen,” said Principal Ragnar, happily. “We’ve been doing some wonderful things, not just with the ACT but with our course materials in general.”
It was Michael Anderson who spoke first. “You know we’re here unofficially. But your school really has us curious. We’re still skeptical, but if what you say is true, then tests like ours have been doing quite a bit of harm to kids.”
The Principal appreciated the candor. He himself, over the past few weeks, had thought a great deal of harm the educational system has done to a lot of kids over the years. Thinking now about the skepticism these gentlemen had towards the improvement, the Principal thought back to how they had won over the students using simple–yet–powerful thinking processes to improve test scores. They started with an actual test and simply had the kids go at it. Would such a strategy work with these gentlemen? Probably not. They would certainly score well. This would prove nothing. But what if some Washington High seniors took the exam in front of them? It was a risk, for sure. It would come as a surprise to the students. How would they do? How would they score? Who would test?
But he also knew, regardless of how they scored, the process would be on display, and the results surely would be higher than the national average.
He liked that course of action.
Principal Ragnar stepped outside the office and said to the receptionist, “Ms. Taggert? Could you provide me a list of our seniors?”
Moments later, Ms. Taggert appeared with a 4–page list of Washington seniors. The principal presented the gentlemen the list. “What I would like you to do is pick from this list at random six students. Some of these may have taken the ACT in September; if they’ve not, they will soon, so we’ll call this a ‘representative sample’ of the Washington High senior class.”
Once done, the Principal continued: “Again, at random, you pick which three will take the science part, and which will take the reading part.” Once picked, the Principal asked Ms. Taggert to come in.
“Ms. Taggert: these gentlemen are here to see what we’ve done to achieve such dramatic results in our recent test. Would you track done these nine students and ask their 11:00 teachers if it’s OK if they can miss that class and instead participate in a study with myself and these two gentlemen in the library?”
“As it’s now only 10:30, I’d like to tell you a little story. Then we’ll have the kids come down and take a practice exam in front of you – and as you can see, they’ve not prepared for this at all, so it will be random. After that, I want to tell you why, after this whole process, it’s not us who should be accused of cheating, but you!”
“Us?”, said Mr. Anderson, quizzically. “What is that supposed to mean?”
“Take it easy – I, of course, don’t mean you personally, but your organization, and others like it.”
“Do you know what most seniors do as part of their senior year? They spend a great deal of time applying to get into the best possible college they can. There are two metrics used by colleges and universities to judge the ‘intellectual ability’ of the student. The first, of course, is the cumulative grade point average. This GPA is the result of 3+ years of effort. Do you know if the student slacks off for even one class – for one test, it could ultimately make the difference between going to Harvard and going to a different school? So this metric is the result of a great deal of time and study.”
“The second metric is the ACT and the SAT. Colleges and Universities look at this as well, don’t they? Well, what are these tests everybody puts such great emphasis on? One test? That’s it? One test – and this is the judge of one’s ‘potential’ in higher education? You hold substantial power, don’t you?”
“Well, if this did judge accurately the intellectual predictability of a student, I might not object so much. However, I’m not sure that’s the case.”
“Consider this: you all write the test, right? And do you also know who writes the best–selling materials on how to pass the test? You do, of course! Imagine that! One would think, in such a situation, scores would be sky–rocketing! However, look at this graph showing student performance on the ACT over the past decade.”
Principal Ragnar reached into his desk and pulled out a graph on ACT-performance:
“Now, this is what you show everybody about your test - right."
The gentlemen glanced at the figure, recognizing the slope of improvement so highly discussed by the organization, and nodded in the affirmative.
"Well ... I had my assistant redo this graph, but rather than the scale displaying "tenths", I had her reformat the y-axis so it went from 0 - 36, the possible scores of the ACT. Here's what this graph looks like." He pulled a second piece of paper from the drawer and placed it atop the first:
"The first thing that stands out, to me, is the lack of progress over the years. Does this not strike you as odd as well, given the materials on how to pass the exam are written by you?”
Mr. Anderson responded defiantly: “Now wait a minute. You can’t compare years like this. More kids than ever are taking the exams, including those who haven’t done that well in school. In the past, only the best would take the exam – now everybody does. You can’t compare apples and oranges.”
“Fair enough,” said Principal Ragnar matter-of-factly. “But it’s also fair to say more and more students are taking more and more test–prep exams, and using your material as well.”
A knock came at the door, and the receptionist stuck her head in the door: “Pardon me, sir. The students you asked to come down are here. Would you like them to come in?”
Principal Ragnar thought for a moment: “No, please take them down to the library, and have them sit around three tables in a corner of the library, would you?” He thought for a moment about the uncertainty that may be racing through the students’ minds, and added, “No, wait just a minute. Have them come in here first, would you?”
The students entered the principal’s office, unsure why they were called to the office.
“Good morning”, said Principal Ragnar happily. “I’m sure you’re wondering why you’re here. These gentlemen are from the ACT, and they’re here to see how it’s possible our school did so well on the recent ACT. To show them, I thought we could go to the library and take part of a sample exam, some of you doing the reading section, and the others the science section.”
The ACT–gentlemen, knowing the focus was on them, smiled apprehensively. “How was it possible” was a polite way of saying they thought the students cheated. Did the students realize this? Probably.
“No warm up? No practice? Just like that?”
“Well, these gentlemen have come a great distance to see how we’ve done so well.”
“I’d be happy to take a section again,” said Michael Storm, an athletic-looking boy, tall and lanky, always looking for a challenge. “Because these gentlemen are from the ACT, they probably wouldn’t mind taking the exams with us, would they? But we’re each only taking a part of the exam, right, so why don’t they take the reading test?”
Principal Ragnar, liking the sounds of that challenge, looked at the ACT representatives, and seconded the proposal. “That does sound like a great idea. Don’t you gentlemen agree? What better way to demonstrate our success than to compare it with a well-educated adult’s performance?”
The students left the room and headed towards the library. Principal Ragnar continued: “I assure you gentlemen this is no trick, no plot, nothing of that sort. We talked for a while about how we achieved the success we did, and now I’ve pulled students out of their classrooms to demonstrate this to you. The least you can do is give us 45 minutes of your time to play along. I said ‘It’s Not Luck’. Let me show you what I mean. This will probably make the student less apprehensive as well.”
The ACT–representatives agreed, and off to the library they went.
February 29, 2008
2008 is a Leap Year, and today is "Leap Day", February 29. Why do we go through the process of adjusting the calendar "every four years"? What is it we're "putting back in alignment"?
The earth orbits the sun "once every year". That's our definition of "year" - one complete orbit. If we left our calendrical units here, there is no issue. However, the further use of "days" gives rise to a slight discrepancy. You see, one year doesn't equal 365 days, but instead 365.242199 days.
But let's round this to 365.25 days to get a better idea of what's going on here. After one "of our years", our calendar has moved 365 days. However, for the earth to get to it's initial starting position, it needs an extra 1/4 of a day. It's just short of the starting point. After the second year, it's short 1/2 day. A third year moves the distance another 1/4 day, and finally, a fourth year leaves the earth one complete day from it's orbital "starting point". Leap Year intends to correct for this "drift".
What happens if we do this? What does this look like - graphically?
But let's return to reality, now. One year does not equal 365.25 days. More precisely, it equals 365.242199 days. What happens if we add a day every four years? We over-compensate slightly! That is:
So, we've got to somehow correct for this "over-compensation". But how? Right now, the rule is "every 4 years, add a leap year unless the year is divisible by 100". Let's see what this looks like:
Correcting for this 100-year glitch seems to put us on track - or does it? It certainly resets the bar, but does it do so accordingly? By the graph below, we seem to be losing ground now! Let's take a guess at how the rule was modified: at 400 years, it's clear we're at a point where, if we ignore the "100 rule", we're back on track.
The New Rule
every four years is a leap year - we add a day to get us back in line. But this day over-shoots the target. Therefore, every 100 years, skip the rule. Doing this, however, erodes the "over-shooting", so every 400 years, we need to add back the leap day!
Well - let's implement our algorithm here and see what happens. Graphing the results for the next 10,000 years yields some amazing results. The process does not stabilize! We get out of whack around the 4,000 year! Now, likely, calendar-adjusters know this, but see no reason to make this an issue, but it is interesting to see what happens if we ourselves make it part of the rule.
What makes this most interesting to me is the official rule, regarding every 4/100/400, was made by Pope Gregory XIII in 1582 (hence the name 'Gregorian Calendar') long before there were calculators, satellites, and GPS systems.
The Logical Haiku of the Week
This weeks "logical haiku" is in recognition of this cosmic / calendrical calibration process!