Architects of Their Own Future

Chapters 3 & 4

February 1, 2008

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Chapter 3

THE MEETING

“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?”

“That’s right.”

“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!”

Chapter 4

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.

But why?

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!

Caught in a Timeless Dilemma

February 2, 2008

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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."

Victor Hugo

Les Miserables

The Super Bowl, Roman Numerals, and Cognitive Development

February 3, 2008

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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).

Unit economy.

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!

A Preference to Apathy over Ignorance

February 4, 2008

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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.

Reality, to be Conquered, Must be Obeyed!

February 5, 2008

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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:

http://www.duke.edu/~hpgavin/ce131/citicorp1.htm

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.

Economic Fallacies and Uneaten Cakes

February 6, 2008

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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.

Flavors of the Month all Taste the Same (when they're still in their wrappers)

And the Sweet Taste of the (modified) Greek Trivium

February 7, 2008

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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:

Architects of Their Own Future

Chapters 5 & 6

February 8, 2008

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Chapter 5

THE TEAM

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.”

Chapter 6

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?”

The Quadrilateral Jamboree

February 9, 2008

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round@rationalsys.com

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.

Iterative Effect-Cause-Effect Logic and the Context Syllogism

February 10, 2008

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round@rationalsys.com

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.

Second Thoughts

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!

The Dénouement-Detective

(untying the knot)

February 11, 2008

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round@rationalsys.com

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.

But why?

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?

TUNNELING!

TUNNELING!

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!

First-Hand-Accounting

February 12, 2008

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round@rationalsys.com

“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!

Visual Vocabulary

Closing the Gap between The Map and the Territory

February 13, 2008

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round@rationalsys.com

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:

Closing Thoughts

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"?

The Ultimate Occupational Dilemma

February 14, 2008

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round@rationalsys.com

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?

Chronologic Basketball

The Logic of the Shot Clock

February 15, 2008

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round@rationalsys.com

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?