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The Incomparable Chuck Jones

 

The "YES" Session

 

 

April 1, 2008

 

 

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Adult or child, who isn't aware of these classic cartoons? 

 

 

Watch many great cartoons and you may notice a common characteristic:  "Directed by Charles M. Jones" is proudly displayed among each.  Chuck Jones.

 

 

It's easy to watch cartoons like this and take for granted the question, "What makes a good cartoon?  How does the person come up with such ideas?"  Indeed, is creativity like this innate, or accessible to all of us?

 

At Warner Brothers, after agreeing on a basic story line, Chuck Jones said a meeting - a story session - would be called, attended by three directors, three writers, the production chief, and the producer.  This was "The Jam Session".

 

 

The "Yes" Session

The "Jam" session was, I believe, an event unique to Warner Bros.  Unique at that time, perhaps anytime.  Because this was not a brainstorming session in the usual sense, it was a "yes" session, not an "anything goes" session.  Anything went, but only if it was positive, supportive, and affirmative to the premise.  No negatives were allowed.  If you could not contribute, you kept quiet.  For want of a better term, I have always called it ... THE "YES" SESSION.  Again, the "yes" session is not a brainstorming session; repeat, it is not a session in which anything goes.  The purpose is to advance an idea or ideas, not an emotional outburst for the emotional benefit of the participants or as a story man's confession of a buried affair with a girl's track shoe.  The "yes" session only has one objective: to write a story.

The "yes" session imposes only one discipline: the abolition of the word "no."  Anyone can say "no."  It is the first word a child learns and often the first word he speaks.  It is a cheap word because it requires no explanation, and many men and women have acquired a reputation for intelligence who know only this word and have used it in place of thought on every person who can only say "no" finds it an eternity.  Negative-minded people have been known to finally inflate and burst with accumulated negatives and say something positive, because it is also true that a person who heretofore can only say "no" is also a person who must say something.

A "no" is defined as any negative: "I don't like it."  "There must be a better way."  "I don't like to criticize, but ..."  "I've heard that one before."  "I don't know."  Or: ""Oh, for Christ's sake, Chuck."  All are roadblocks impeding the advancement and exploration of the value of an idea and are forbidden.

Of course, all story ideas are not good or useful, and if you find you cannot contribute, then silence is proper, but it is surprising how meaty and muscular a little old stringy "yes" (which is another name for a premise) can become in as little as fifteen or twenty minutes, when everyone present unreservedly commits his immediate impulsive and positive response to it.  And, of course, the enlightened self-interest of pouring your contributions unreservedly out in another director's story session is sufficient motivation; your turn will inevitably come to present an idea to the group in another session, and at such a time you, too, will want, need, and expect full cooperation.  A good premise always generates the most astonishing results.

 

Chuck Amuck

by Chuck Jones

 

 

 

 

HELLO MY BABY

 

Hello, my baby,

Hello, my honey,

Hello, my ragtime gal!

Send me a kiss by wire;

Baby my heart's on fire!

 

If you refuse me,

Honey, you'll lose me,

Then you'll be left alone;

Oh, baby, telephone,

And tell me I'm your own.

 

 

The Interests of the One - The Interests of the Many

 

The Wonder of the Electoral College

 

 

April 2, 2008

 

 

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A New Nation - the United States of America

But what's "United" about them?  Sure, independence from England had been declared, and victory over England had been achieved.  But what now?  There are many individual states, differing in size, population, and culture.

 

If there's to be a "united" government, argue the people of Virginia, surely we should have more 'say' than Delaware.  On the other hand, why would Delaware agree to be part of the union where there was not 'equal' say in how things are run?  That doesn't seem "fair".  They might as well remain a colony under British rule.  Why should Pennsylvania agree to be part of the union when a small state like Georgia has as much say as them, despite being a fraction of the size?  That doesn't seem "fair".

 

An interesting dilemma - what should the drafters of the Constitution do?  If the government is to be one "of the people", "the people" should be represented where the people are - proportionately.  Is that fair, however, to a state with a smaller population?  Not to them, of course!  What to do?

 

 

What is "fair"?  How does one reconcile the interests of the majority and the interests of the minority?

 

 

Having Our Cake and Eating It Too!

Where once a dilemma existed, a solution emerged, achieving both the need to protect "the will of the people", while simultaneously protecting "the minority".  Of course, the real protection affording the littlest guy - the individual - was the recognition of individual rights - the right to life, liberty, and the pursuit of happiness, with the proper acknowledgement government is not established to create these rights, but to secure them. 

 

A Timeless Conflict

Of course, this same dilemma plays itself out even today.  There are fights over the issue of state versus federal control, local versus state control, and even between the levels of the judicial system.

 

In all of these conflicts, it's easy to lose sight of what was the crowning achievement in the founding of this country:  a government established to secure the rights of the individual. 

 

The ACT:  A Conversation with Myself

 

 

April 3, 2008

 

 

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Another chance at the ACT … I took this at the end of my junior year and did horribly.  Here I was a B student, carrying a 3.2 GPA, and did reasonably well in math.  Some say they have test anxiety and that’s the reason for their poor showing.  Me?  I don’t recall feeling any more anxious than the next person. 

In two weeks, it’s time for that same test.  I’ve purchased all the same study materials I used last time.  The massive “The Real ACT Prep Guide” is 621 pages long now!  Who can read such a thing?  And why does it take 621 pages for the people who created the test to tell me how to study for the test?  And the sample tests?  They never seem to resemble the actual tests!  What good are these things?

Well, I’ve done some research and it’s very interesting.  Scores are pretty constant over the years, yet at the same time schools promote their study programs as being so successful they raise scores 3-5 points.  Imagine that!  If scores have remained constant, and if study programs have raised scores 3-5 points, does that mean actual learning has gone DOWN 3-5 points?  Who can make sense of all of this?

My concern now has to do with this test; here it comes again, and I’m not sure I’m any more ready for it now than I was then.  I’ve just finished another study session, answered some questions correctly, cheated myself a bit by looking at the answer key (artificially inflating my score and my ego), and in reality I am worried.  Last year was simply a “trial run”; this year is the real thing, and my scholarship and choice of college are riding on me doing well.

Well, time to open my big book and “cram”, whatever that means.

Opening the book with scorn, I look at the first reading section and their recommendations:  here I’m told to read thoroughly … here skim … here highlight key words, blah, blah, blah.  What kind of recommendations are these?  They themselves are all over the board!  And what good has it done me?  I still end up guessing at these random reading topics.  I consider myself a pretty good reader, yet with some of these topics I really have no clue what the story is about.  It’s no wonder I jump to the answers quickly in cases like that … what choice do I have?  Continue reading?  Towards what end?

This does seem odd, the more I think about it.  Where do these “reading strategies” come from?  Why do I need a strategy when there is only one page of material – and it’s right in front of me?

It seems self-evident no such strategy is necessary, given what I’ve just said, until I remind myself I’m only getting a bit more than half correct, about the same as everyone else.  Isn’t that odd … a single page of reading, with all the material right in front of us, and the majority of students score as poorly as me.

I go for a walk, clutching my study manual, more than ever believing it’s to blame for my lack of success, rather than a crutch helping me along.  Why is this?

I stop at the subway shop and order a large BLT.  “Look at this material!”, I yell to myself silently:  “I start to read and immediately have no idea what the passage is talking about.  Why should I continue to read in such a case?  And the strategies … ‘Read thoroughly’ versus ‘skim and get to the questions’ …  They’re all over the board!”. 

Why should I read thoroughly?  Isn’t it obvious?  How can you learn something unless you “read thoroughly”?  On the other hand, why should I skim?  That answer, too, is obvious: I’ve got 40 minutes to work through 4 sections of reading and 35 questions.   

In order to perform well on the reading section, I must be aware of the time problem.  Obviously.  In order to recognize the time problem, I immediately jump to the questions.

On the other hand…

In order to perform well on the reading section, I must have full awareness of the content of the reading passage.  In order to have full awareness of the content, I must read the passage through entirely.

What a dilemma! 

And what do I do – in fact?  Do I stick with a specific strategy?  Of course not.  I, and probably everybody, panic, and immediately switch back-and-forth from “strategy” to “strategy”.

The more I think about this, the more troubling something else becomes: is this dilemma or conflict new?  Of course not.  Every student who has ever taken this test has faced this dilemma.  Why do I think I will do any better than they?  That’s a troubling thought!

Is there no hope?

Let’s look at the passages for a clue to the score-stagnation problem.  Why can’t I and other college-bound students read a simple passage and answer a few questions?

One clue may lie in the nature of the passages.  I am thrust into an extract from the middle of a larger passage, and expected, with time pressures, to do well.  I don’t know a thing about the story, with the exception of a brief statement about the nature of the passage.  Is it any wonder, paraphrasing one Florida high-school student, I end up “reading the words but not remembering anything about the passage?”

But surely “test-taking” strategies account for this problem, right?  Or do they?  The story lacks meaning to the reader, and what do the strategies afford us?  Methods of REMEMBERING the story.  Is there a difference between REMEMBERING the story and UNDERSTANDING the story?  Is there an inherent conflict, or is this the compromise “test-taking” strategies have arrived at?

Is there any way I can “have my cake and eat it to?  That is, have full awareness of the content WITHOUT reading the passage through entirely?”

Wait a second … that’s not even necessary.  I don’t need “full awareness”!  When I read these passages, they are immediately just words to me.  What I need is “any awareness” … a “foothold” if you will!  Something that allows me to have a good picture of what the story is about.

But wait a minute:  “form a mental picture” is one of the strategies I’ve read about.  I’ve not invented anything new here – or have I?  “Form a mental picture”?  HOW?  They do not tell me!  If I had a process to create the mental picture, then I’d really be in business!

How would I do this?

Can I do this?

Well, I’ve taken the test, and the results are indeed in!  In practice exams, I averaged 20 out of 40 right answers on the reading test.  When I applied diligently my simple algorithm, my score jumped to 38! 

Of course, these were practice exams.  But if I could score similarly on the actual exam, my ACT score would jump by nearly 4 points – by simply doing this!

Imagine what that ACT score will do when I apply this to the science, grammar, math, and writing sections of the ACT!

But I should close with a restatement of what this simple process actually was …

If you've read this and are curious, write ...

 

The Quadratic Stream

 

 

April 4, 2008

 

 

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Swimming in the Algebraic Stream of Numbers

 

The Question

The current of a river is 3 miles per hour. It takes a boat a total of 3 hours to travel 12 miles upstream and return 12 miles downstream. What is the speed of the boat in still water?

 

In Search of an Answer

What do I know about rate, time, and distance?  Rate = distance / time.  I’ll start with that, and see where it leads me.

 

OK … now I’ve got to translate the information I was given into this equation.  How fast is my actual speed going upstream?  The current provides resistance, so I’m going slower than I will be swimming downstream, where the current instead provides assistance.

 

Ah – the dreaded quadratic formula.  I know the general solution for this formula, so simply applying this general formula to my specific problem should lead to the solution.

 

Is this right?  Let’s check with an example where the answer is obvious – that is, let’s suppose the stream is not flowing at all.  Therefore, I’m just swimming back and forth (a total of 24 miles) in 3 hours in still water, an average speed of 8 mph.  Let’s see if this formula confirms this.

 

My General Solution:

This leads to a pretty simple solution, but is it good to always simplify?  To bring “common terms” out of the radical, for example?  What happens if I leave these terms together?  Let’s go back and see:

 

I wonder what the geometric meaning of this is – what the intuitive understanding of this is – because its elegance suggests some simple explanation.  Of course, we still need to understand the “+ or -”   in the solution – how is that relevant?  Why do we exclude situations after the fact?  Why do we say the quadratic formula yields solutions, and then we reject one of them?  Is it really true if I swim at 9 mph against a 3 mph current, my effective rate is only 6 mph?

 

The Question and Answer

The current of a river is 3 miles per hour. It takes a boat a total of 3 hours to travel 12 miles upstream and return 12 miles downstream. What is the speed of the boat in still water?

 

 

Logical Haiku

This last thought gives rise to this week's logical haiku.  Going through an entire mathematical process led me to two possible solutions, and one was thrown out as irrelevant.  Why?  Does one ever know before the analysis the number of "viable" solutions?

 

The Aluminum Bat

 

More from the Law of Unintended Consequences

 

 

April 5, 2008

 

 

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The great Bill James, in his "Historical Baseball Abstract" manifesto, discusses the hitting conditions giving rise to the boom in hitting in the 1990s.  I want to focus on two:

aluminum bats and fighting.

What have either to do with great hitting, particularly when the former is not relevant in professional baseball, the latter nothing to do with hitting?

Let's see.

The use of aluminum bats in amateur baseball, it was thought, is not only dangerous (to the pitcher), but may lead to bad habits by hitters.  Hitters swinging late or hitting an outside pitch, for example, were told if they attempted to drive the ball to the opposite field, they would instead find themselves grounding out to that side of the infield.  The wooden bat validates this theory; the aluminum bat encourages the behavior, because it allows the ball to be driven to the opposite field.

 

Why allow a player to develop a skill at one level, only to be hamstrung at the next level when the circumstances change?

Such was the thinking.

What was found, however, was much different.  What the use of aluminum bats showed regarding driving the ball to the opposite field was not that it could not be done, but that it could!  And in showing it could be done with aluminum, it encouraged batters to try it with wood bats.  And what did they find?  It was possible!

But the aluminum bat did more than this: it allowed batters to fight off inside pitches.  With wood bats, an inside pitch yields a meager ground ball or pop-up.  With an aluminum bat, on the other hand, those same hits have the chance to become singles.  Therefore, these bats afforded the hitter the ability to crowd the plate to reach the outside corner with immunity, because an inside pitch could be fought off.

But what of pitcher controlling the plate with "brush-back" pitches to batters who do crowd the plate?  Tired of players rushing the mound, the major leagues made both charging the mound - and the intentional throwing at players - offenses warranting suspensions. 

The aluminum bat, coupled with a change in enforcement, led to the following dilemma for the pitcher facing a batter crowding the plate: 

if I brush him back, I risk suspension for intentionally throwing at a batter;

if I try to throw to the outside of the plate, he (crowding the plate) has both a good swing at the ball with the knowledge he can drive it to the opposite field!

It required a new way to pitch - a new mindset.

 

Deal or No Deal

 

Some Thoughts on Randomness

 

 

April 6, 2008

 

 

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A recent edition of "Deal or No Deal" ended with a contestant facing an odd choice:  the two remaining dollar amounts were $1,000 and $1,000,000, and the banker's offer was $400,000 (I forget the exact amounts here, but I'm fairly close).

If the Banker was using simple averages, the offer would have been $500,500.  The offer was clearly less than the average, but how much?  Is it this amount all the time - and for each round?

 

Modeling the Game

The game consists of 26 suitcases containing the following amounts of money:

The contestant selects a number of cases, and after each selection is offered a dollar amount from the banker to leave - or continue.  The choice of the contestant: Deal or No Deal?

To start, the contestant selects six cases at random.  The best case scenario has all six cases being the lowest six amounts, as this leaves all the high-dollar cases in play.  Consequently, the banker must offer you more money to make your choice "reasonable". 

The worst case scenario has you selecting $1,000,000 in the first round, as this amount pulls the average way up.

The rounds continue, selecting 6 cases, then 5, 4, 3, 2, and finally proceeding one case at a time.

Let's play a couple of games, and see how things work?  A sample game is as follows:  To start, the total amount in all the cases is $3,418,416.  With 26 cases, this gives an average per case of $131, 478. 

 

 

A Modeled Game 1

Game 1 provided me a lucky first round - I selected six low cases!  My average went up!  Unfortunately, my luck was short-lived, because, as you can see, in Round 2, I picked cases containing the two highest amounts!  My average plummeted!

 

The game continues ...

 

A Modeled Game 2

 

 

A Modeled Game 3

 

 

Numerous Models

As you can see, the average-offer jumps all over the place, and there are two types of fluctuations:

 

1. from game-to-game, the offer amount for the respective rounds varies radically.  In the three games above, for example, Round 1 provided averages of $169,063, $57,168, and $132,856;

 

2. within each game, the average from round-to-round jumps all over the place, depending on the amount of money left in the remaining cases.

 

Now that we've got the gist of the game with a couple of examples under our belts, let's capture only the relevant data (offer after each round), and model lots of games.  Here's the results of 50 such games:

 

 

The results are in, but what do they tell us?  One person went all the way, winning $1,000,000, but several others left with little money.  "How many others?"  Is there a better way to display the data?

 

Let's start by merely ordering the data so, for each round for our games, we have a better idea of the "low-to-high" ranges.

 

 

 

A Visual Feel to the Game

Rather than either the actual results or the ranked results - in tabular form - what does the data look like visually?

 

 

 

With so many lines (10) in my line graph, it's hard to tell what is going on.  Let's break the graph into individual rounds to see more closely what's going on:

As expected!  Round 1, graphed from low-to-high, returned a relatively stable graph.  What does this mean?  There are 26 cases to choose from, and the average after choosing six is relatively stable.  In other words, the banker's offer after Round 1 should not vary much from player to player.

However, as the rounds progress, this changes.  Why?  Many cases have already been opened, and the fluctuation increases accordingly, until we reach Round 10, the other end of the spectrum.  This is the offer when all cases are exhausted; therefore, it's not even an offer - it's what the player will leave with.  Few people leave with $1,000,000, while many people leave with little or nothing.

 

A Final Thought (for now)

The graph above, combining all 10 rounds, had many of the lines converging at one point - about $130,000, and this number is pretty close to the average amount in the original 26 cases ($131,478).  This can't be a coincidence, can it?  Let's smooth out all the rough spots by, instead of having the above 50 simulated games, we have 30,000:

 

Fortunately, in this day and age, this type of question is easily addressed by writing a simple program.  Such computing power was not available to the average person even 20 years ago.  Now, the power of the desktop computer allows anyone to do most anything - if they try!

 

What were the results of our experiment?  Above, 30,000 simulations were run with the belief the expected value for each round was equal to the average dollar amount in the cases to start with.  What have our experiments shown?

 

Not only were Rounds 1-8 equal to the average amount per case - ALL ROUNDS ARE EQUAL!

 

LOGICIONARY-1

 

A Submission to the Upcoming AI / Wikipedia Conference in Chicago

 

 

April 7, 2008

 

 

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LOGICIONARY-1

Wikipedia and Artificial Intelligence:  An Evolving Synergy

WikiAI08

 

Michael Round

The Center for autoSocratic Excellence

www.rationalsys.com

(913) 515-3911

The growth of Wikipedia as an online repository of structured knowledge gives rise to a broad range of educational and research opportunities.  The issue of “legitimacy” has been a frequent criticism of Wikipedia, opponents claiming inaccuracies and biases in the creation of articles.

The taxonomic structure of a Wikipedia-article provides an exciting opportunity to gauge the validity of the description of a concept in a number of ways. 

One exciting method of validation is the game LOGICIONARY-1, which I would like to provide either a short-paper on, or alternatively demo the game.

 

THE GAME

LOGICIONARY-1 is a combination of ESP (the Google-Image Labeling Program), Password, and “The $20k Pyramid”, in that a description is given by one player, with the hopes the other player will guess that being described.

For example, suppose Player 1 is describing “Topeka”.  The first clue likely would be “Kansas”.  Many answers come to mind:  wheat, Dorothy, Jayhawks.  All wrong (in the context of this round), but relevant in the data-capturing aspect of the game.  Player 1 has the option to “direct” Player 2, with a “hot or cold” response.  Clue 2 might be “capital”, to which Player 2 would most likely respond “Topeka”. 

This hardly revealing entry can be confirmed with the Topeka, Kansas Wikipedia entry:

Topeka is the capital city of the U.S. state of Kansas and the county seat and most populous city of Shawnee County.  

 

Completed in two steps affords both players more points than had the back-and-forth taken more steps.

Observe what happens, however, if instead of “Topeka”, the object to be guessed is “capital”.  In this instance, the majority of the work is being done by the “clue-giver”, because it’s hard to capture and convey the essential meaning of this concept!

How does our generated definition (the place in the state with a governor) compare with the Wikipedia lead entry?

A capital is the area of a country regarded as enjoying primary status; it is almost always the city which physically encompasses the offices and meeting places of the seat of government and fixed by law, but there are a number of exceptions. Alternate terms include capital city and political capital; the latter phrase has a second meaning based on an alternative sense of "capital".

The word capital is derived from the Latin caput meaning "head," and the related term Capitol refers to the building where government business is chiefly conducted.

 

The back-and-forth between the two players becomes an education tour de force, one working hard to communicate the meaning of the concept, the other trying to focus in on that being communicated.

A last example deals not with a concept but a concrete – how might the communication work with something like “Fort Sumter”?

How does our definition (The Battle marking the start of the Civil War) compare with the Wikipedia entry?

Fort Sumter, a Third System masonry coastal fortification located in Charleston harbor, South Carolina, was named after General Thomas Sumter. The fort is best known as the site where the shots initiating the American Civil War were fired, at the Battle of Fort Sumter.

 

THE INTEGRATION OF WIKIPEDIA

Where do the ideas originate from above?  They are randomly chosen from Wikipedia, according to a point-system based on difficulty.  A new player may want to start with easy concepts to get the hang of the game, and will be presented with items like “chair, United States, flag, coin”.  More difficult ideas generate more points, but also take more time and one runs the risk of not getting the word correctly. 

The “clue-giver”, additionally, not only has the word but the Wikipedia description in front of them, so if they have little idea what to say, the Wikipedia description is in front of them for assistance. 

This leads to another step in the validation process of the opening description of the Wikipedia entry: not only is it right, but is it useful?

The epistemological goal of the game is the communication of the essential characteristics of either a concept or definition into its constituent genus and differentia components, using interchangeably the processes of integration and differentiation.

 

LEARNING STYLES

Clearly, there are many ways people understand a subject.  Many people operate by way of the genus/differentia structure noted above:  general class differentiated by a unique characteristic leads to the concept under consideration.  There are other ways, of course.  Many examples lead to a general thought.  A characteristic not “technically” the taxonomic-defining thought may be the one most known to people proves effective.  Successive clues as “animal” and “ruffff” leads one to automatically say “dog”, for example, though one would be hard-pressed to find such a description in a dictionary!

A secondary goal of LOGICIONARY-1 is the creation of a database of learning styles with examples.

 

FURTHER THOUGHTS

Logicionary-1 is only “part 1” of an online system of learning, integrating the traditional Greek Trivium of Grammar, Logic, and Rhetoric into a game-like structure, using description, logic, metaphor, and haiku!

 

Architects of Their Own Future

 

Chapter 14

 

 

April 8, 2008

 

 

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Chapter 14

AN INTERESTING DILEMMA

The Third Chautauqua

Principal Ragnar walked the halls.  Classes were long over, but extra-curricular activities were going on, and the ambient sound of activity was evident.  He poked his head in the gym to watch a bit of practice.  He smiled.  Coach Thompson had the team working on some type of drill with books stacked on a chair.  He'd need to ask the coach about that one!

It had been several days since the men from the ACT had taken "The Challenge".  Principal Ragnar wondered what they were doing now.  Had they gone back to the ACT and told of the remarkable things going on?  Unlikely.  One's bound to lose their job, rocking the boat like that!

He walked to his office, sat at his desk, and opened his mailbox.  "42 unread messages", it read.  Despite diligent attempts to rid himself of unwanted e-mails, they nonetheless somehow found their way to his computer.

He looked in his "in-basket" of regular-mail.  It too was over-flowing.

While the e-mail messages were being received, he picked up the mail and flipped through it casually.  Item after item announced some new finding, some new product, some new innovative device for improving educational performance.  He frowned.  He knew most of this was nonsense, though sprinkled in the stack was likely a golden nugget.

The e-mails retrieved, he glanced at the subject headings and noted the remarkable similarity of these headings with what he was looking at.

He frowned again.

Reclining, he looked to the wall containing the large school calendar.  He noted the field trip to the museum in a couple of weeks.  A special exhibit of French Impressionism was to be displayed, and the school had scheduled a trip to the museum.  He thought of the works of these painters - of Degas, Monet, Van Gogh.  Impressionism - a different way to look at the world.  A revolution in painting!

His smile disappeared when he thought about this.  He, of course, had truly gained a deep respect and understanding of these paintings and era in his 30s.  He vaguely remembered a trip to the museum when he was in school, but nothing stood out.

Would anything stand out for his students?

He imagined the response from parents in canceling the trip.  "A once in a lifetime chance - gone!"  He imagined his e-mail basket and voice-mail, both over-flowing.

He also knew he was right.

"It's just a half-day," he thought, knowing a half day was still a half-day.  He also knew there could be a great deal of good coming from such a trip, but under different circumstances.

He continued to flip through his regular mail, and came upon a demo DVD for foreign language instruction.  He again frowned.  This was a hot topic in education, and it was the one topic he heard more about from parents than any other.

Of course, with no foreign language teacher nor an adult speaking a foreign language, and without money to buy anything, it was hard to justify starting such a program.  But it was not just that: they were working hard to improve scores to merely exist in the coming years!  Science, reading, math ... isn't that where the focus had to be?

Why can't these people understand the spot I'm in?

What spot am I in?

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?

We - the educational community - on the other hand, is receptive to such things.  We're not ignorant.  We know all about "all this good stuff".  We, however, live "in the real world", where NCLB and AYP are breathing down our necks.  We're fighting for survival and you want more stuff?  You must be kidding!

What to do?

What do we typically do 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.  Does this help?  Maybe.  OK - let's be honest.  No.

Then why do we do it?

Is the alternative to listen to the public about these issues, and ignore them?  Whether that's right or not, it's most of the time what's done.  But our intentions are good - we're just dealing with reality.

He thought back to his earlier question to himself: "Why can't these people understand the spot I'm in?"  Has the school ever shown the public "the spot we're in"? 

He paced the office:  rather than fight a battle that cannot be won, why not explain to the public the nature of the battle - the conflict - they're facing!  Rather than the doomed attempts at compromising solutions that please no one, instead show the situation as it really is!

He looked at the books on his bookshelf, and came upon Covey's "Seven Habits of Highly Effective People".  Paging through the well-read book, he came upon a habit resonating with his current train of thought:  Seek first to understand - then be understood.  Is this what was going on here?

Maybe - but something was missing.  He did understand - it was others that did not!  However arrogant that sounded, it knew it to be true.  How does one communicate to others their need to understand his position? 

Is it his position needing communicating - or the dilemma that's the issue?

He made a note to his secretary to dictate a letter to parents the following day to talk about education in general.  He scratched that - too general - too misleading.  He didn't want to talk about education in general - he wanted to talk about the goal: good schools, now and in the future. 

How to title this?  "You're Invited"?  "Come to a Meeting"?  "Learn about Education"?  "A Discussion on our School"?  None conveyed the enthusiasm he felt earlier, nor the sentiment he was feeling.  Sure, he wanted this to be a discussion, but he wanted the discussion to focus on the dilemma - the conflict - above.  He wanted people understand the situation the school was in - the conflict all educators face!

"Have a Seat!"  he penned at the top of the paper.   Rather than crude compromises leading to wasted effort with little educational gain, or simply ignoring the requests of the tax-paying public, let's invite the public to "have a seat" and show them the dilemma we face.  Don't attempt to solve the problem - let's get them to understand the problem!

 

Questions I Get

 

 

April 9, 2008

 

 

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Rather than start up a new thread today, I'd like to address several of the questions I've received regarding various posts.

 

Question 1:  George Sisler

One careful reader noted my change to the added axis in the George Sisler article "No Season Better", and wondered the reason for the change.

My goal was to establish the best possible season (combining at-bats and batting average), and determining who fell first within an expanding circle centered at the intersection of these two axis.

Initially, my axis represented a 425 batting average and 700 at-bats.  One player had exceeded the former, and only a couple the latter, so I thought having these points outside the control range would be OK.

But then I thought about my distance algorithm, graphically considered as a simple square, and realized I would rate two players, each with 600 at-bats, but one hitting 420 and the other 430, as having equally good years.

Why?  As you can see below, the distance for these points, symmetric about the vertical axis, are the same!

 

Hence, my new control limits / axis lie just outside all relevant data points, thus ensuring no such error repeats itself.

 

Question 2:  George Sisler

A second question from the same article suggests we are a baseball loving country!  The reader wanted to know why the years 1892 and 1894 produced such different results.

 

A bit of research reveals the special cause: we're accustomed to the pitching mound being where it's always been.  That's because it's been there for a long time:  60'6".  It wasn't always so.  You can infer when the change took place, and whether the previous distance was closer or more distant to the plate.  The 1893 change moved the pitching mound from 50' to the modern distance of 60'6".

 

Question 3:  The Electoral College

The recent discussion on the establishment of the electoral college as a means of representative government brought forth the following question:  is this the best form of governing?

 

My claim above was, given the dilemma faced by the new nation, their solution of a House and Senate was a good solution - but not necessarily the good solution.  Likely, there are other means of establishing representation.

 

There is an important point here to be considered: the context of the solution.  Consider, for example, the governing of a business.  The business-CEO runs the company, and reports to the Board of Directors.  Other decisions are voted on by share-holders.

 

If I have no share in the company, I have no vote.  Moreover, the more shares I have, the greater my vote counts.

 

This suggests our representative governing system above is a good solution in a particular context; in other contexts, the solution fails.

 

Question 4:  Deal or No Deal

I was asked by a curious reader about the close of the article on Deal or No Deal.  Specifically, I started the article by noting the odd nature of the banker's method of providing a "deal" to the contestant - offering $400,000 when the "right" answer seemed to be $500,500.

 

Yes, there is an issue here.  A fun part of an issue like this is having all the numbers and then playing around with the numbers, seeing what the system is saying - and is not saying.  Who would have thought - certainly not I - the expected value of all rounds, regardless of what suitcases are picked previously, is - in the long run - the same as the average amount in each case to start the game?

 

I guess there seems some intuitiveness to that statement, but to do the calculations, to see the calculations visually - why not make this part of the analysis?

 

My guess as to what the banker is doing relies on what I've seen watching the game.  I rarely see an offer above $40,000 in the first game, despite the expected average being about $131,000.  What's he doing?  Apparently offering about 30% of the expected value of the amount left in the case. 

 

What about as the game progresses?  In the one example where I've seen the game go to the end (above), the offer was 40% of the expected value.  Let's assume these start-and-end points are reasonable.  Possibly, for rounds 2-9, there is simply an increasing proportion to move from 30% to 40%, as:

 

 

 

 

Question 5:  Logical Haiku

My article on "The Origins of Logical Haiku" generated, as expected, discussion to the effect this process "spoils the intent of the haiku", and this style of writing is not for everybody.

 

Indeed!

 

It was for ME - and like-minded people who have trouble "getting started" in the creation of poetry like this!

 

A funny - and related - story comes to mind.  Regard the Scripps Spelling Contest discussion, I asked Scripps why a contestant couldn't write down their word, and then spell it out loud.  I'm a horrible speller - long or short words - unless I can sound out the word, and while doing this, write it down so I can "keep track" of where I'm at.

 

Nothing doing, they replied.

 

Fine, I thought.  An alternative, though not as good, is to write the word down on my hand.  This helps immensely.

 

When I told others of this obvious but helpful idea, the idea was criticized because not every student learns this way.

 

Indeed!

 

BUT THEY DISREGARD THE OBVIOUS FACT THEY'RE ASKING ME AND EVERY STUDENT TO LEARN THEIR WAY!

 

So too is the lesson valid regarding haiku.  No, logical haiku is not for everybody - AND NEITHER IS THE TRADITIONAL WAY OF LEARNING HAIKU!

 

 

 

 

In Closing ...

Thanks for all the questions - this feature will become a weekly entry, and I hope to get to between 5 and 10 questions each article.

 

Turkey Dinners and Steering Wheels

 

From One Context to Another

 

April 10, 2008

 

 

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Last Thanksgiving, Martha was preparing the turkey for Thanksgiving dinner when her daughter, Margaret, asked if she could watch.

"That'd be fine," said Martha,  "Just make sure you're careful of the big knives around the kitchen."

Martha put the large turkey on the cutting board, and with concentrated effort, lopped off both ends of the turkey.  Placing the turkey in the massive pan, she asked Margaret to open the oven door.  Margaret pranced to the oven, grateful to help in the preparation of dinner.

As Martha moved to dispose of the unwanted turkey sections, Margaret innocently asked, "Why'd you cut all that off before putting the turkey in the oven, Mom?"

"That's the way my mom showed me."

Being a Thanksgiving reunion, Margaret's Grandma was in the next room.  Margaret darted across the kitchen floor into the family room, where Grandma was reading the paper.  "Grandma?  Mom said you use to cut off both ends of the turkey for Thanksgiving dinner.  How come?"

"Our oven was so small, child, that's the only way I could get the turkey in our small pan."

This didn't make sense to Margaret, slowly marching back to the kitchen.  Our pan was huge!  She peered through the small oven window at the massive pan dominating the shortened turkey, confirming what she already knew.

"Mom ...?"

She was cut off.  "Stay away from that oven, child - you don't know what you're doing!"

Margaret, pouting, walked into the family room to talk with Grandma when Martha yelled into the room:  "Dad - can you run to the store to get some dinner rolls?"

"Sure thing, honey."  Patting his granddaughter on the head, he said, "Come-on, squirt. Let's go for a ride."

They got in the car, backed from the driveway, and headed down the street.  Margaret, now 12, was watching Grandma steer with interest.  It did not go unnoticed by him.

"In no time at all, you'll be driving your own car!"

"But it looks hard, Grandpa", watching him make a right turn and head towards the grocery store down the street.  His hands moved in a rapid motion, one over the other.

"There's nothing to it.  Just think of a clock, and keep your hands at the 10:00 and 2:00 positions, and the rest is easy."

 

 

Poor Margaret

We chuckle at the turkey story.  We even use it as a metaphor for blindly sticking to traditions despite changing circumstances.

 

We chuckle because we know we would never be so guilty of this crime of ignorance.

 

Really?

 

Do you remember what it once was like to steer a car?  It was not an easy task to make a turn - it took effort.  It was virtually impossible to move the wheels while the car was at rest or moving slowly.  To best navigate the steering wheel, we were taught to do what was natural - pull with one hand, and, as it's pulling, reach over, get good leverage, and pull with the other, repeating the process until the turn was completed.  "Hand over hand."

 

Similarly, driving down the street, it was best to put one's hands in the best position to control the car.  That was the only way!  If one needed to move these massive beasts, best to let gravity help you, which means hands at the top of the steering wheel.

 

"10 and 2" and "hand over hand".  The tried and true.  The best way to drive a car. 

 

Really?

 

If I drive a car today, there is no sense it's "hard to steer".  Change lanes.  Make turns.  I can do it with one finger.  Why?  Power steering and lighter cars.

 

But what happens if we apply an old strategy to new circumstances?  If you hold your hands at the "10 and 2" position on the steering wheel of a car with power steering, you likely will over-correct if you veer to one side or the other.  Gravity suddenly is not your friend, but your enemy!

 

For best control in a car with power steering, your hands should be at the bottom of the wheel, or, heaven-forbid, one hand at 9:00, gripping the wheel between the thumb and forefinger, with the arm resting on one's leg.  Why?  It's nearly impossible to over-compensate for an error, while simultaneously allowing yourself the ability to easily steer with comfort.

 

For similar reasons, the "hand-over-hand" turning philosophy no longer applies.  The wheel turns easily.  Shuffling hands - without crossing over - makes most sense.

 

 

In Search of an Appropriate Metaphor

What should we call a person who laughs at the turkey story, yet commits the same error in another context?

 

 

 

 

Catching a Baseball?

From turkeys to driving to catching a baseball?  How did this latter item get in there?  We teach kids to catch a high ball by putting their glove - where?  Above their head?  Why do we do that?  Talk about something unnatural!  The ball is coming at your head and you're suppose to put your glove between the ball and your face? 

 

This is all wrong!  I smell ----- TURKEY DINNER!

 

The basket catch!

 

But if the "over-the-head-catch" was once appropriate, what circumstances existed giving rise to it?  Why would one put their glove slightly in front of their face to catch the ball?  My guess is it was to shield one's eyes from the sun.  Of course, the sun is still here, but my guess is when the catch became part of the game, likely the sun was bright and high in the sky, and the method of catching the ball was taught right there - and the rule has stuck ever since.  Forget clouds, sunglasses, and eye black - all which negate the effect of the sun.  Put your glove in front of your face to catch the ball coming at your face!  TURKEY DINNER!

 

The basket catch!  It's natural and it's safe!

 

And it's more effective.  What happens when the ball pops from your glove with the glove facing out, as it does when it's stretched above your head? The ball bounces to the ground.  How about the basket catch?  If the ball pops out, it pops up!  Likely against your body, mostly around your body, but almost always up - giving you an opportunity to "second-catch" it!

 

But what about the outfielder catching a ball and having to throw to a base to catch an advancing runner?  Go through the motions yourself when you doubt what I'm about to say: the basket catch puts you in a better position to throw!  When you catch the ball over your head, the first thing you do when you prepare to throw is ----- try it yourself before reading on below ...

 

 

 

 

 

you bring the ball to your waist.  What wasted motion when juxtaposed with the basket catch, where the ball is already at your waste!

 

Of course, this is nothing new .. the great Willie Mays knew this 1/2 a century ago!

.

 

 

 

In Search of The Missing Yard

 

April 11, 2008

 

 

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In our question-and-answer session earlier this week, the issue of statistical change (1892 to 1894) in baseball was brought up.  The causal explanation was the moving of the pitcher's mound back to 60'6".

 

What we didn't ask - or answer - was why the distance became 60'6"?  That's an odd number, particularly in light of the otherwise normal distances of 90' between bases.

What's going on here?

Baseball historians tell us the agreed-to distance was 60'0", but the hand-writing or the work-order containing this distance was sloppy, consequently misread, and the mound placed at 60'6".

Likely they're right.  Of course, it doesn't answer the question of where 60' came from.

 

Another Proposition

Let's be reckless and romantic, and see if we could come up with an alternative hypothesis - just for fun.

 

One thing I've always wondered but never answered until now, for example, is where the pitcher's mound lies in relation to the imaginary line between first and third.  Is it directly in the line of sight between the two bases?

 

Let's see:

 

It's tough to tell from this diamond, so let's ourselves draw a diamond, and determine the distance from home plate to the mound , and see if it is directly half-way between first and third.  Here's our field:

 

Fine.  What now?  I need to find x.  Fortunately x lies in the middle of a square, so the distance from home to the mound is equal to the distance from 1st to the mound.  I also know a bit about geometry and the Pythagorean Theorem.  Putting this all together, I get:

 

A Coincidence - or a Logical Explanation?

Looks like my explanation and calculations were for naught.  I hoped to see 60'6" come from all this work.

 

But let's play out the scenario.  In 1893, let's suspect they did initially build the pitcher's mound at the intersection of the two interior lines above - at 63'6".  All you really need is two long pieces of rope, outstretch them, and mark the intersection.

 

Fine.

 

Let's further imagine the first time this is tried, a ball is hit down the third base line.  Tinkers, playing third, effortlessly scoops up the ball, starts to throw to Chance, and ...the pitcher is right in the way!

 

Therefore, placing the pitcher's mound in this place leads to the undesirable effect of the pitcher being in the way of the action.

 

But what should he do?  "Take a big step forward" is the call, one such step approximately one yard, or three feet!  But if the derived distance was 63'6", and we close the distance by three feet to get the pitcher out of harm's way, we're left with .... drum roll ... 60'6"!

 

Of course, the likely explanation is a guy misread 60'0".  It's fun to imagine, however!

Logical Thinking

 

The Real Lever to Move the World

 

April 12, 2008

 

 

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Archimedes Reconsidered

In the next installment regarding Archimedes, we'll consider a specific example to refute the claim above.  The "Eureka" moment was indeed valuable in the development of science, and it may have been a necessary condition in the analysis of the crown, but it was it sufficient?

 

We'll see!

 

 

To Have a Neighbor, You've Got to be a Neighbor

 

 

April 13, 2008

 

 

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Is there life elsewhere in the universe?  A great line from Contact puts the question in context:  "If there's not, it'd be an awful waste of space!"

 

 

 

We send probes to Mars in search of traces of ancient water, as if this is an indicator of life.  It's OUR definition of life, which gives rise to the biased nature of definitions.  Who says, in other parts of the universe devoid of water, life didn't find a different way to evolve?

 

In this regard, I'm reminded of this excerpt from Michael Crichton's "The Andromeda Strain":

It was a long-standing problem. Early in planning Wildfire, the question had been posed. How do you study a form of life totally unlike any you know? How would you even know it was alive? This was not an academic matter. Biology, as George Wald had said, was a unique science because it could not define its subject matter. Nobody had a definition for life. Nobody knew what it was, really. The old definitions--an organism that showed ingestion, excretion, metabolism, reproduction, and so on--were worthless. One could always find exceptions. The group had finally concluded that energy conversion was the hallmark of life. All living organisms in some way took in energy--as food, or sunlight--and converted it to another form of energy, and put it to use. (Viruses were the exception to this rule, but the group was prepared to define viruses as nonliving.) For the next meeting, Leavitt was asked to prepare a rebuttal to the definition. He pondered it for a week, and returned with three objects: a swatch of black cloth, a watch, and a piece of granite. He set them down before the group and said, “Gentlemen, I give you three living things.” He then challenged the team to prove that they were not living. He placed the black cloth in the sunlight; it became warm. This, he announced was an example of energy conversion--radiant energy to heat. It was objected that this was merely passive energy absorption, not conversion. It was also objected that the conversion, if it could be called that, was not purposeful. It served no function. “How do you know it is not purposeful?” Leavitt had demanded. They then turned to the watch. Leavitt pointed to the radium dial, which glowed in the dark. Decay was taking place, and light was being produced. The men argued that this was merely release of potential energy held in unstable electron levels. But there was growing confusion: Leavitt was making his point. Finally, they came to the granite. “This is alive,” Leavitt said. “It is living, breathing, walking, and talking. Only we cannot see it, because it is happening too slowly. Rock has a lifespan of three billion years. We have a life span of sixty or seventy years. We cannot make out the tune on a record being played at the rate of one revolution every century. And the rock, for its part, is not even aware of our existence because we are alive for only a brief instant of its lifespan. To it, we are like flashes in the dark.” He held up his watch. His point was clear enough, and they revised their thinking in one important respect. They conceded that it was possible that they might not be able to analyze certain life forms. It was possible that they might not be able to make the slightest headway, the least beginning, in such an analysis.

Michael Crichton

The Andromeda Strain

 

 

Let's suppose, then, rather than looking for life out there by going out there, we instead search "out there" while staying here?  Massive telescope arrays do this, searching the universe for signals indicating "something".

 

Isn't this the same (analogically) as searching for "water" as a sign of life?  Our search for signals we detect is another tremendous introduction of our bias into the system.

 

For example, earth-based communications, once solely analog, and now mostly digital.  Two means of communication, related, but at the same time not.  If you're operating in a digital world, the analog means nothing.  It's like working in a spreadsheet and attempting to open a Word document.  Nonsense.

 

Of course, that metaphor fails in this respect: you're clicking on the Word document, and therefore have evidence "something" is out there.

 

Perhaps there's value to that.

 

But let's suppose we're searching not just for evidence something is out there, but also to communicate with that "something".

 

How would we do this?

 

A first requirement, noting the problems above, is the "something" needs to be able to communicate with us.  That means they need to be able to understand us.  We'd consider it folly to try to talk with a duck - or, vice versa, for the duck to try to communicate with us.

 

Is that it?

 

Not quite.

 

Where do we send our message?  Here, it seems we have lots of choices, and a good decision might be to send it lots of places - the bigger variety the better.

 

But this is not a new idea - the first person to do the following might have had the right idea!

 

                        

 

 

 

The Message Revised

You've got the general idea, which is, "If you can understand this message, do the following ..."  That's my understanding of "intelligence".  And it works both ways - if a duck picks up the bottle, no sense calling.  On the other hand, if a super-advanced entity found the bottle and was unable to read it, again, no sense calling - in both cases, I won't be able to understand what's being said!

 

OK - we send our "bottle" (let's call it a beacon) out into space.  If we really wanted the entity to contact us, what would we put in place of a piece of paper with a phone number?  A homing device?  A signal pointing back to earth? 

 

Why not?  And the same criteria apply exists, only at a different level: if you can't figure out the device is pointing back to earth, we're probably operating at much different intellectual levels.  One of us hasn't "grown up" yet.

 

Is this a description of the theme of Arthur C. Clarke's great short story, The Sentinel?

 

 

 

Visualizing Prime Numbers

 

 

April 14, 2008

 

 

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Earlier, I talked about Prime Numbers from a geometric perspective.  In doing this, another thought came to mind: Euclid (poorly, I believe) showed there are an infinite number of primes.  We'll investigate next week my claim about Euclid's proof.  In the meantime, how could I see what "a lot" of primes look like?  Is there a pattern to them?  Is there a pattern in here, somewhere?

I could never tell looking at a table of numbers like this.  How could I present them so I could see "a pattern", if it existed?  The only way I've ever plotted points is with the traditional "Cartesian" coordinate system.  Can anything come of it?  The first prime is "2", the next "3", etc.  I've somehow got to "move about" the grid, and I'm just supplying numbers.

 

Movement About the Grid

What if I "moved about" by creating evenly-spaced angles, and then moving up an imaginary line on that angle by the distance of the prime number?  For example, if I evenly spaced out the angles by 45 degrees and started plotting the prime numbers, what would happen?  Here's a start:

 

What happens if I let this run for the duration of my "1,000" primes above?  Let's see:

 

Certainly, there's a pattern here, but it's not very interesting.  What's going on?  Because I've chosen 45 degrees as my shift, I plot on the 0, 45, 90, 135, 180, 225, 270, 315, 360, etc.  Since 360 degrees = 0 degrees, I merely plot on the same lines, the points moving outwards as the points themselves grow bigger.

So what happens if I choose a degree shift that does not go evenly into 360?  Let's choose 14:

 

Simulation Continued

Now we're talking - this is a type of pattern I'm interested in - something interesting.  Now I see there are two variables of interest to the creation of a "good" graph:  the number of primes I'm graphing, and the degree shift.

 

 

Extending the algorithm to a larger set of prime numbers, and reversing the colors, yields some very interesting results!

 

Pretty Pictures - Pretty Math

The pictures are neat, but what's more neat is the math necessary to create them.  It's all accessible to any high-school student.  A portion follows:

 

I've got a circle, and I clearly need to do something with it.  We obviously need a circle, and given this circle, we're trying to find - and plot- points on it.  Let’s label the point on the circle as (x,y).

 

After all, this is what I’m trying to find.  What else do I need to know?  Well, what is the center of the circle?  For simplicity sake, let’s label it (0,0), and correct for this later.  Finally, how big is our circle?  We haven’t specified that, so let’s assume our circle has radius r, and let's put in 45˚ as something to start with.

 

But how do I find (x,y)?  A bit of trigonometry helps in this regard, as I know the following relationships:

It seems simple enough:  substitute x, y, r, and 45° and I can arrive at sine and cosine relationships, enabling me to solve for x and y:

But plugging these into my spreadsheet, I do not get points looking reasonable.  The formulas, I’m certain, are correct, yet the results are not.  Why not?

A bit of research reveals Microsoft Excel does not perform trigonometric calculations using angles, but rather by radians!  Therefore, to properly use my formulas, I must convert all degree measurements into radians. 

What are radians – and how do I convert degrees to radians?  Let’s find out.

 

Degrees to Radians

I know something about the circumference of a circle, and I know this formula includes the circle radius r.

But does this lead me anywhere?  I’m still talking about “distance”, while I’m looking for something regarding “angle” or “degree”.

Radian, then, must refer to the angle carved out by the radius along the perimeter of the circle.  And if one radian carves out one radius, and there are 2π radii on the circumference, then there are 2π radians in a circle.

 

I’m closing in on the answer to my question: how do I translate degrees into radians?  Above, I gave an expression for one degree, but I don’t have one degree.  I have lots of different degrees.  Fortunately, the translation is now easy.

 

 

Pretty Pictures - Pretty Universe

Browsing the internet-image database, I came upon the following NASA graphic which look eerily similar to some of our images above:

 

 

 

The Main Way in Education

 

 

April 15, 2008

 

 

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Making TOC the Main Way in Education

A New Year’s Resolution

Oh Really? – Not Again!

Let's forecast out to late 2008 / early 2009, and pretend the New Year of 2009 is coming, and we'd like to make some New Year's Resolutions.  I’d like to talk about the state of the Theory of Constraints for Education – let me clarify that – Theory of Constraints IN Education: TOCIE.  This way, I’m assured of not being in conflict with TOCFE as an organization, which is not my purpose.  My purpose is educational excellence.  Period.

 

What is the State of TOC in Education?

What is the state of TOCIE?  “What are we going to do in 2009?”  An appropriate resolution might be “Making TOCIE the Main Way in Education”.  In achieving this goal, we might start with barriers not allowing us to achieve this goal right now.  Obstacles.  Having detailed these obstacles, we might then list accompanying intermediate objectives.  With obstacles and intermediate objectives listed, we’ve got what’s called an “ambitious target”.  Splendid.  This is one tool in the TOCIE arsenal.  In the case of education, one obstacle might be the lack of teacher training.  This is reasonable, isn’t it?  After all, if teachers train kids, a necessary condition to reach kids, it would seem, is to train teachers.  If this is a legitimate obstacle, an appropriate intermediate objective – and powerful one – is the training of teachers.  It’s no wonder this has been high on the tactic list of TOCFE.  Very good.

But wait a minute.  Is it appropriate in this context?  Santanya has informed us those failing to remember the past are condemned to repeat it.  Does the Ambitious Target, in this context, deal at all with the past?  With a system in place for over a decade, it would be nice, wouldn’t it, to ask why many teacher trainings have not resulted in demonstrable results – evidence of learning by kids.  This suggests a logical insufficiency, does it not, because what we’re saying is “we provided teacher training” and “we did not see results”.  Something has happened?  What?  Why? 

In this context, then, the use of the Ambitious Target seems simultaneously ambitious yet misplaced.  Why has the system faltered?  Does TOC offer reasoning methods to address this issue?  Of course!  The use of the Current Reality Tree and Chronic Cloud, Prerequisite Tree, Future Reality Tree, and Transition Tree provide additional powerful reasoning tools to move from a current state to a desirable future state by recognizing not simply the core problem in the system, but more powerfully, the chronic core conflict allowing the core problem and myriad UDEs to maintain themselves.

But here, I’ve brought into the discussion another method to use TOC.  We’re told many tools in the toolbox is a good thing, but is it?  I’ve got one method of using TOC above: the ambitious target, and now another: the trees.  What is the relationship between these two powerful tools?  When is each appropriate?

But I don’t want to stop here, because the name of the organization is the Theory of Constraints.  Where above has the concept of “Constraint” been used at all?  It’s not – and this is important.  The ambitious target tree, for example, targeted teacher training as an important tactic to achieving the goal.  Do teachers have time for training?  Are they able to implement such training in a rigid schedule?  If their time is the constraint – that valuable resource not to be wasted – are we managing the constraint, or wasting its resources?  Are we putting more on Herbie’s back, to use the trailwalk example from The Goal?

But are we sure “teacher time” is the constraint, and if so, how do we manage it?  Sure, we know constraint management philosophy includes constraint identification, exploitation, subordination, elevation, and the important reminder to avoid inertia, but is this relevant here – in our story?  Why was it not included in the Ambitious Target philosophy above?  What is the relationship between the “system-improvement via trees” and “constraint management?”

Another tool?  Good?  Maybe.  Let’s continue.

Surely we’re not done here, are we?  The powerful new analytic tool in the TOC arsenal is the Strategy and Tactics Tree, a method of sequencing actions and incorporating the causal logic both why a tactic exists and why other tactics don’t, to achieve a desired end.  Powerful indeed, because it integrates all of these elements succinctly and logically. 

But again, the question arises to me: does the S&T tree supplement the other analysis above?  Replace them?  How is the constraint explicitly relevant to the tree – if at all?  What role does the powerful chronic conflict cloud play in this analysis – if any?

Suddenly, we’ve got quite a populated toolbox of analytical materials, and it is this point the question comes to mind: is this good? 

 

What is this thing called “The Theory of Constraints”

Have you been asked “What is this thing called the Theory of Constraints?”  How do you answer such a question?  If you’re at all like me, many thoughts (squared) come to mind:

  1. Philosophy of system improvement by focusing on the constraint of the system;
  1. Philosophy of system improvement by focusing on the core problem / core conflict of the system;
  1. Philosophy of system improvement by way of logically overcoming obstacles to achieve a desired result;
  1. Philosophy of system improvement by recognizing and addressing legitimate layers of resistance;
  1. Philosophy of recognizing the interrelationships between entities in a system, and exploiting inherent simplicity.

How do we often present this last description visually?  By way of a “System A vs. System B” diagram:

 

And here we end up: to me a promising yet ominous junction: we’ve described our system (by way of several powerful methods & tools in #1-#4) by means of one of the methods we’re against  (#5: system A)!  We’ve said we’re a philosophy recognizing the interdependence of entities (SYSTEM B), but have presented ourselves as a philosophy of Independence (SYSTEM A)!

This explanation, of course, assumes there is no relationship between the multiple explanations above, and we know this not to be the case.  What are the relationships?  How do these philosophy descriptions tie together?  More importantly, how do these tie together in moving a stagnant system forward?

In considering these important issues, another comes to mind, equally important.  TOCFE has been described as the teaching of three tools: the cloud, the logic branch, and the ambitious target.  Is this all TOC is?  If so, and with these three simple yet powerful tools in the public domain, is there any need to establish or continue an educational movement under the TOC umbrella?

Or is TOC much more than this, and aligning oneself with a powerful system improvement philosophy will lead to dramatic change?  I think the latter.

But why?

 

The Future of “The Theory of Constraints” in Education

TOC is immensely powerful and popular in the business world.  Has any of this popularity enhanced the use of TOC/Education in any aspect of the educational community?  Have we leveraged the popularity to expand our base?  Have we used the business community, for example, to sponsor conferences?  Is that a good idea?  Have we used them to sponsor anything?  Do they have a stake at all in what we do? 

Of course.

I’d like to address one more issue regarding TOC/E and education.  We talk of “layers of resistance”, agreement on the problem, agreement on the direction of the solution, etc.  Yes?  The educational establishment, much more so than the business community, has been inundated with “flavor of the month” solutions – quick fixes promising massive change.  You need only check any educational magazine or website to see this is true.  Along comes another such movement: TOC/E, promising massive change immediately.  Oh really?  Yes, and not only this, we ensure: the tools can be used immediately in the classrooms by all teachers, they’re so simple!  Oh really?  Of course the “reservation of skepticism” is immense!  “If we can’t achieve such dramatic change in the classroom immediately, why should we believe you can?”  And herein lies the challenge to us as educators.  Indeed – what a challenge!

Teacher trainings?  At this point in time, at least in the USA: nonsense.  They’ve been tried with little success, and it’s no wonder.  We violate the very principles that defined us as an organization.  We fail to recognize the constraint!  We absolutely fail to define the core conflict giving rise to many system UDEs.  We fail to recognize the extreme and legitimate skepticism of the educational community. 

So where are we in “Making TOC the Main Way in Education” as “A New Year’s Resolution”?  I see there are at least three items of exploration necessary to achieving this goal:

A. a more thorough understanding of what TOC is, how it applies in systems improvement, and how it applies in curriculum;

 

B. a viable plan to make TOC the main way in education;

 

C. a reason to maintain “TOC in name” in the movement. 

 

Wait a minute - where did this third item come from?  Well, there already is an educational organization with 'TOC' in the title.  Can one create an organization based on TOC-principles without TOC in the title?  Clearly.  Should one?  That's another question - actually, two questions: should one form an alternative organization, and, if so, should one include "TOC" in the title?

"YES" to both questions!

Why? 

Let's address this issue in the next entry on TOC ...

 

Making TOC the Main Way in Education

A New Year’s Resolution

 

  

Hypocrisy in Action

 

 

April 16, 2008

 

 

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George Johnson sat uneasily in his office chair.  Since being fired from his position at Widgets, Inc., he had run and  been elected to the state legislature, and been a popular figure in office for five years.  His campaigns had been run on the message of "a voice for the people", and he regularly held town meetings to get "the pulse of his people".

April 15th - tax day - had come and gone, and the restlessness he felt this day after was due to the issue of taxes.

The local paper - the Kansas City Star - had run a scathing article on the complexity of the tax code, and the amount of annual waste (resources, money, time, etc.) used to complete personal and business taxes.  Who would disagree with that? 

It's not simple.

"But why not?", he thought?  "Why is it so complex?"

George looked at the business section of that same day's paper, page 1, and there was a lengthy article on the tax rebates given to citizens as a "stimulus package".  The article talked about how, though the majority of press coverage related to the personal rebates, there was a great deal of money to be had by businesses.

The article noted several companies benefiting from the package.

But what happens when these companies have to account for this money?  For the huge machines they've purchased?  For depreciation expenses?

He thought of home mortgages, of charitable contributions, and suddenly, the idea-faucet was running wild.  All sorts of things "tax-related" came to mind. 

And all requested - by people and businesses like those he represented.

The KC Star itself had been the beneficiary of such a large tax break!  Of course, to be on the receiving end of "something out of the ordinary" means you've got to somehow keep track of the finances.

Put all of this together - and you get:  a complex tax code!

"They ask for tax simplification, and yet advocate policies mandating tax complexity!"

He read the editorial and came upon this gem  "The core problem is that politicians like to hand out special favors — tax breaks — to certain industries, individuals and pressure groups."

WE hand them out?  How can we hand them out?  PEOPLE DEMAND THEM!  And when we grant them to something related to themselves, they cheer us!

"Who is the hypocrite?", he thought.  "The core problem is US?  How can that be the case?"

He thought more about how things had gotten to where they were ...

 

This makes sense, but is it right?  People and businesses demand tax breaks and get them, and even if they didn't, isn't this part of the role of government?  To govern "social behavior"?  But in order to do all of this, a tax code must take into account everything being done.

 

The logic was sound, he thought, yet something was missing.  He thought back to his school-days about the founding of the country, the Constitution, and what it was that set the United States apart from other countries in the world.  We were founded on the principal of individual rights, and governments are instituted to protect those rights.

But how can the role of government simultaneously be to protect the rights of the individual and govern "social behavior"?

 

"This is the fence legislators straddle all the time - this is the fence we're asked to straddle," George thought.  "How dare the Star state we're the problem!  The problem is people demanding they have their cake and eat it, too!"

"But what are individual rights?  What is the relationship between individual rights and the government?" 

George poured himself a cup of coffee and paced the office.  His journey towards being a good legislator had just begun.

 

The Olathe School System - Visually

 

 

April 17, 2008

 

 

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No school district in the state has experienced the growth seen in the Olathe School District over the past two decades.  Nearly double the elementary schools have been built over this period, and recent growth hovers around 1,000 new students a year.

How can this growth be viewed?

One way is to graph elementary schools over time:

 

This is fine - it shows the growth, but it doesn't say anything about where?  Does viewing the map of schools from the OSD website help?  Let's see:

 

Well - this shows where, and it's a graph also where there's so much going on it's hard to tell where the elementary schools actually are.  Something else is also missing.  After all, not all schools are equal.  Some are larger than others, some older than others.  There are lots of ways to sort the data:

And when data is presented this way, I lose the location of the school.

How about this try at showing the location and age of the school ...

 

This shows growth + age, but not size.  Also, it spreads schools out over different grids, though I think a format like this is very useful - in certain contexts.

Is there any way to put all of this together?

 

The Olathe School System - Visually

Below is the start of a graphic combining size, age, and location.  The size of the circle shows 2007-2008 enrollment, and the color of the circle represents the decade the school was built (lighter colors older, darker colors more recently).

 

The oldest schools, also the smallest, were built in downtown Olathe where the population center was.  As one can see, growth has generally been to the east and south, with these also representing the largest schools. 

There's a lot more coming from the data available from the state, as well as integrating the geographical component from the map above (though scaled back and in a light-gray scale).

 

 

The Olathe School System - Visually

Above was a snapshot of the school district, though also showing location, size, and age-of-school.  What it doesn't show is how schools have grown over time?  Let's add in the last 16 years ...

 

 

The Case of the Submerged Theory

 

April 18, 2008

 

 

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The scene:  a courtroom in Syracuse, Sicily.  Three participants:  The Judge, Mike Mason, and the great Archimedes:

 

 

 

 

Mike Mason, Plaintiff, acting on his own behalf (to the judge): 

Your Honor - I want to again extend sincere appreciation for your granting what seems to be a most unusual request.

 

Judge:

Unusual indeed, Mr. Mason! You've requested only three parties in the courtroom: yourself, myself, and the famous scientist, Archimedes!  You've neither told me the nature of the charge, nor why it involves Archimedes.  What it is you're up to this time.

 

Mason:

My request was unique, Your Honor, because I'm not charging Archimedes with any crime.  I am charging him with something, however, the nature of which will come out in the course of my brief questioning.

 

Archimedes:

May I say something, Your Honor?

 

Judge:

Of course, Archimedes.

 

Archimedes

Your Honor - I have no idea why I'm here, and I have no idea who this gentleman is.  Before I take the stand to be questioned, I'd like to know exactly who I'm talking with.

 

Judge

A reasonable request.  Mr. Mason?  What is your standing in this case?

 

Mason:

Your Honor, I was good friends with a goldsmith of Syracuse.  You may be aware of his story.  Though a good man, he had fallen on hard times, and, given a bar of gold to transform into a crown for the king, instead took some of the gold for himself, substituting cheap but similarly-colored metal in its place.

 

Judge:

I don't understand.  What has this to do with Archimedes?

 

Archimedes:

If I may, Your Honor.  The king, wanting assurances the crown was indeed solid gold, employed me to answer this question.  After fumbling and stewing over the issue, I arrived at the answer, and proved what Mr. Mason has already said.

 

Judge:

Does this have anything to do with you running naked through the streets?

 

Archimedes:

In the course of scientific investigation, Your Honor, things don't happen smoothly and naturally, as most people believe.  In this instance, I was sitting in the bathtub watching the water rise as I lowered myself in the tub.  It was this idea of "displacement" I realized was the key to the question!  I forgot myself, and dashed about the streets shouting "Eureka", because, indeed, I had found it!

 

Judge

But naked, sir?

 

Archimedes:

I explained everything to the local officers, and all charges were dropped.

 

Judge:

Very good - very strange - but  ... OK, I understand everything.  But I still don't understand why we're here?

 

Archimedes:

It's very clear, Your Honor.  Mr. Mason, being a friend of the goldsmith, has chosen the courtroom to extract revenge of some sort.

 

Mason:

Your Honor.  I wish no such revenge.  As I said, he was my good friend, but had fallen on hard times, and made a bad decision.  I merely wish to question Archimedes on a couple of relevant issues regarding this "Eureka" moment you two have been joyously chatting about.

 

Judge:

Very well.  Please proceed, Mr. Mason.

 

Mason:

Archimedes, there's no reason for you to take the stand or recite an oath.  I know of your background, and I know you to be a man of honor.  I'd like to ask a few questions.

 

Archimedes:

Very well.

 

Mason:

It's my understanding the goldsmith was given a large chunk of gold to make a crown.

 

Archimedes:

That's right.  It was about 4 pounds of gold.

 

Mason:

And the crown made for the king also weighed 4 pounds.  Is that right?

 

Archimedes:

That's right.

 

Mason:

Both amounts being equal, does that not confirm the crown was made from the initial gold the goldsmith received?

 

Archimedes:

Not necessarily.  If the gold were substituted for a combination of other metals - some more dense and some less, for example - the combination could equal 4 pounds, but not be the gold.

 

Mason:

I see.  So another test was necessary.

 

Archimedes:

Indeed, and this is what I fumbled about with for days.  How to answer that very question.  And then I arrived at it!

 

Mason:

Your "Eureka" moment?

 

Archimedes:

Exactly.

 

Mason:

Could you explain what rising water had to do with the crown, gold, and substituted metals?

 

Archimedes

Certainly.  What I found was water is displaced by the volume of a substance, not it's mass.  You could submerge a box filled with bricks and that same box filled with balloons, and the amount of water displaced is the same.  Water does not care about the matter, only the volume.

 

Mason:

Which meant what in our case?

 

Archimedes:

I borrowed four pounds of gold from the king's palace, and submerged it in water, and measured this distance.  I then took the crown, also weighing four pounds, and submerged it in water.

 

Mason:

And what did you find?

 

Archimedes:

Not so fast.  Let me tell you what I expected to find.  If the crown was pure gold, then it should have displaced the same amount of water as the gold I submerged. 

 

Mason:

And what did you find?

 

Archimedes

It displaced more water, meaning the goldsmith had substituted some less dense materials into the crown.

 

Mason:

And you reported this to the king.

 

Archimedes:

Indeed.

 

Mason:

And the goldsmith was killed as a result.

 

Archimedes:

I'm very sorry for that.

 

Mason:

As I said, he was a good man fallen on hard times.  I too wish he had made a better decision, or had thinking tools available to him to help work himself out of his sad state of affairs.

 

Judge:

Mr. Mason: where are you going with all of this?

 

Mason:

I said at the outset of these discussions this was an unusual request, Your Honor.  If I may have just a bit more latitude, I have just a few more things to ask of Archimedes.

 

Judge:

I'll grant your request, Mr. Mason, seeing as this is not technically a hearing.  But given your tendence towards court-room shenanigans, I'm granting you very little latitude!

 

Mason:

Rebuke accepted in the manner it was delivered, Your Honor!  Archimedes, could you say your theory then is as follows:

 

 

Archimedes:

I've never been asked to consider my logic visually like this.

 

Mason:

I'm asking it.

 

Archimedes:

This seems to be what I said in the Case of the Gold Crown.  If I have the weight and the water displacement, then I can identify an object.  Yes, that's what I did.  I had the weight of the gold, and knew how much water that amount of gold displaces.  When I checked the crown, it displaced more water.  Yes, Mr. Mason: I'm OK with your description of my theory.

 

Judge:

I'm putting an end to this right now!

 

Mason (ignoring the Judge's rant):

Archimedes:  could you tell me the weight of these Perry Mason books?

 

 

 

Archimedes:

The scale reads 1.96 pounds.

 

Mason

I've also taken those same books and submerged them in a large kitchen bowl.  As you said, the books now occupy a place in the bowl, and the water has been displaced according to the volume of the books.

 

  

 

 

Archimedes

I've noted the amount of water displacement.  Too bad for the books, however!

 

Mason:

Indeed - but they are books by Erle Stanley Gardner, and he likely would appreciate the use of the books in these circumstances.

 

Archimedes:

We'll see.

 

Mason:

Now, if you will, Archimedes, tell me the scale reading of this empty jar of peanuts?

 

 

 

Archimedes:

The scale reads 1.96 pounds.

 

Mason:

The same amount as our earlier books.

 

Archimedes

Indeed.  I suspect the readings are not coincidental, and I further suspect the jar is not empty.  It must have taken some time to get the jar to equal the weight of the books.

 

Mason:

A bit - a few small rocks got me close, and slowly adding sugar sealed the deal.

 

Archimedes:

You'd make a great scientist.

 

Mason:

Anybody employing logic is a scientist in my book.

 

Archimedes:

I agree.  I suspect you've also submerged the bottle in water?

 

Mason:

Indeed.  Can you tell me what I found when I did this?

 

Archimedes:

Some amount of water was displaced.

 

Mason:

Of course some water was displaced.  We know both objects (the books and the bottle) weigh the same amount (1.96 pounds).  The books displaced a certain amount of water - let's call it 1 inch.  Can we agree the displaced water cannot be 1 inch?

 

Archimedes:

That is what my "Eureka" moment showed. 

 

Mason:

Here is the bottle underwater:

 

 

 

Archimedes:

That can't be!

 

Judge:

What happened?

 

Mason:

Your Honor, Archimedes has just testified an empty bottle of peanuts is a stack of books!

 

Judge:

You mean "resembles".

 

Mason:

No, Your Honor.  I literally mean Archimedes claims these two items are the same!

 

Judge:

This is nonsense.  What's going on here, Archimedes?

 

Archimedes

Your Honor, let me explain.  In the case of the goldsmith, what I said in my theory was:  If I know the weight and water displacement of an object, then I can uniquely describe that object.  That's what I found with the fake crown.  It was fake because the weights were the same, but the water displacement was not.

 

What Mr. Mason has shown is here are two different objects, but each with the same weight and water displacement!

 

 

 

Judge

Mr. Mason.  I understand your point, but the circumstances are different, aren't they?  In the case of the goldsmith - your friend - you and Archimedes have both testified the water displacement was different, and you've both agreed the crown was a fake.  What charge are you making, Mr. Mason?

 

Mason

Your Honor, I've already told you I'm not charging Archimedes with anything.  It's true his theory worked - for that one example.  But it, as you can see, is an incomplete theory.  It reveals when things are out of whack, but it could inadvertently give a false confirmation things are OK when they may not be!

 

Archimedes:

If I may, Your Honor.  I'll pick up the fees for Mr. Mason's time, as well as associated court costs.  He's possibly saved me from the same fate as the goldsmith!

 

Judge:

How's that?

 

Archimedes

Luckily, the readings in "The Case of the Golden Crown" were different.  Suppose they had been the same - but the crown not pure gold.  I would have attested to it's validity!  Can you imagine my fate if the king, accidentally dropping and breaking the crown, saw crude materials and not gold?  My fate would be sealed!

 

Mason:

Your Honor: I'm all for payment of fees while advancing the discipline of logic!

 

Judge:

Case dismissed - if this was a case.  But I will caution both of you not to run the naked through the streets when you do improve on Archimedes' theory!

 

 

 

Fall, Water:  Just Don't Fall on Me

 

 

April 19, 2008

 

 

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The King and I

have Some Questions about Water:

I S    A    P U Z Z L E M E N T  !
 
 
 
 
THE KING
There are times I almost think 
I am not sure of what I absolutely know. 
Very often find confusion 
In conclusion I concluded long ago 
In my head are many facts 
That, as a student, I have studied to procure, 
In my head are many facts.. 
Of which I wish I was more certain I was sure! 
 
 
enter MIKE ROUND
Take, for instance, the issue of flowing rivers.
North or south, which direction are them from?
Neither, you will tell me, they flow downhill!
But I know this can't go on - ad infinitum!
 
 
 
Can it be there is a water cycle process?
Whatever state the water takes, there is a total.
But the news I read suggests the total's dropping,
And the crisis isn't local, but rather global.
 
 
 
The Antarctic region falls prey to global warming;
Worldwide calamity as sea levels rise!
But when I conduct a simple ice experiment;
The results come to me as no surprise!
 
 
 
While I think some more about the water issue;
Underground aquifers - less water to give.
I look upon the globe covered with blue,
The salt - why can't we find a simple sieve.
 
 
 
 
(THE KING RETURNS)
There are times I almost think 
Nobody sure of what he absolutely know. 
Everybody find confusion 
In conclusion he concluded long ago 
And it puzzle me to learn 
That tho' a man may be in doubt of what he know, 
Very quickly he will fight... 
He'll fight to prove that what he does not know is so! 

 

The Time for Proper Action

 

The Dangers of Tampering with a System

 

 

April 20, 2008

 

 

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W. Edwards Deming is known as the founder of the quality movement in America. One of the experiments used to demonstrate the operation of a system is the funnel experiment.  Consider dropping a marble through a funnel towards a target.  Will it hit the target?  There are lots of variables in place.  How does the marble exit the funnel?  Does the initial placement of the marble mean anything?  What of the marble's behavior when it hits the ground?  Will it roll?  The same always?

So you drop a marble and mark the spot.  What do you do now?  Should you adjust the funnel?  If so, how?

Below are four possible rules to how one might operate and position the funnel.  The graphic at the end of each display shows the final placement of 100 marbles in accordance with the rule in place.

If you're the manager of the plant, and consistency of product is a goal, which rule provides products you'd be proud of?

 

 

 

 

 

 

 

 

The Final Map Only

Removing the targets above, let's now extend our process from 100 marbles to 2500 marbles.  What do the results look like?  Some sample runs:

 

The System

The above scenarios suggest the optimal strategy ensuring consistency of product is not tampering with the system.  But is this right?  It can't be completely right, because we know the product can be consistent, but also defective.  What are the conditions under which a system ought not be "tampered" with?  What are the conditions under which a system ought to be under the control of Rule 1?  What is the relationship between variability within one aspect of the system and global variability - considering all processes in the system?

 

 

I Declare April

"System A" Month!

 

 

 

April 21, 2008

 

 

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April is simultaneously "National Poetry Month" and "Math Awareness Month".  Rather than focusing on the coincidence of this, I'd prefer instead to ask why they are needed in the first place.

 

     

 

Math and Poetry

The mere mention of the words "MATH" and "POETRY" give us a hint to the nature of the action taken by sponsoring organizations of creating "special months".  Both words incite fear, hatred, dislike, and hostility in many - young and old, alike.

 

What should governing organizations do to reverse the trend of "fear, hatred, dislike, and hostility"?

 

"We need to get the word out there we're not so bad."  "We need to show everyone our stuff is 'fun'."  etc., etc., etc.  But how is this done?  If many people already are turned off by the subject matter, they're likely not to be reached. 

 

Maybe the goal is not to reach them, but those who have not been exposed to the joys of the two subjects.  Might this be our target audience?  Perhaps.

 

This seems to ignore a common element in the process - "what's being taught"!

 

 

 

Why, for example, do many people exposed to math and poetry dislike the subjects?  It seems an important question, if we're suggesting a National Month will help spread the word about our subjects?  Sure, people are different, but that, I believe, misplaces the primary blame.  The curriculum, the teaching methods, or a combination of the two likely are the culprits. 

 

But how are we going to reach those individuals not yet exposed to our subjects?  Is there anything "new under the sun"?  Not really.  And if we take which has already been tried and repeat it to a new class of students, what's likely the result? 

 

 

 

 

The Nature of the Problem - a Direction of the Solution

The inference seems to be "do nothing".  Hardly.  There is plenty to do.  But the "Rule of Holes" is relevant here; when you find yourself in one, stop digging!

 

Why, for example, don't kids respond to these subjects?  What is it about the teaching of the subjects that leaves students "disconnected from reality"?  There is work to be done, but "national months", to me, only perpetuates the status quo.

 

More maddening to me is the justification often seen in promoting a subject:  it's fun!  it's relevant!  The implications are bells, whistles, and colors run amuck in the classroom materials.  Fun?  I think so, but it's a different kind of 'fun' than I describe above.  It's a joy in effort in striving to solve a problem, to find the word appropriate to my thought, to understand the poet.  It's simultaneously joy and work!

 

I'm reminded of the great Richard Rodgers of "Rodgers & Hammerstein fame" in this regard.  He was asked "where does your music come from - does it just come to you?"  He responded:  "Never - I've got to go get it - I've got to reach for it."

 

Indeed! 

 

You teachers know this is the case.  Likely you're thinking I'm only saying the obvious.  But if it is so obvious, what are you doing about it?  To change things, there is a tremendous bridge between "is" and "ought" to be addressed.  Will "national months" do this?  I think not.

 

In the meantime ...

 

 

 

Math and Poetry:  An Integration

Here are three math/haikus from articles earlier in the year, ranging from the quadratic formula to prime numbers to the derivation of pi.  These are all math-related.  Look back for others to see a true interdisciplinary consideration of poetry in the curriculum!

 

 

 

 

 

 

 

Communication Breakdown

 

Having Another Breakdown - Drives Me Insane!

 

 

April 22, 2008

 

 

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Why do bad things happen?

When bad things (undesirable effects) happen, are they immutable laws of nature … inevitable consequences of doing business?  Or are many undesirable effects avoidable? If so, what steps need be taken to avoid them?

What is the common theme - a link - uniting many situations where undesirable effects occurred? At the Critical Moment, where ACTION takes place, the wrong message was communicated.

But the messengers are neither ignorant nor fools - they don’t knowingly communicate the wrong message causing these undesirable effectsThey communicate the wrong message because they were given the wrong message!

How did they get the wrong message?  And, more importantly, how can we make sure they get the right answer in the future?

 

The Flow of Information

What is the flow of information in an organization to see how a person ends up with the eventual message? A typical “request for information” flow:

 

But this is just a request - surely, the end-worker must communicate the results of the request back to their supervisor who, in turn, must communicate it to their supervisor - the person who first made the request.  In other words:

 

 

 

The Flow of Information

What can we conclude from this Flow of Information Design:

1. At each interaction between two people, someone is making a request of someone else;

2. At each interaction between two people, someone is interpreting the message they are being given.

 

 

The Flow of the Message

This describes the flow of INFORMATION - the interaction between two people, but does it adequately describe the flow of the MESSAGE?  What I say above sounds like "there's a person talking and a person listening.  Big deal."  What are the implications of "listening"?  Of "receiving"?  Is it "a big deal"?

 

Let’s consider a simple example: I want to know what to expect when I flip 500 coins.  I ask the question of a person working for me.  What will I get back as the Message - THE ANSWER TO MY QUESTION?

A Tabular Probability Message?

 

A Graphical Probability Message?

 

A Graphical Simulation Message?

 

A Statistical Summary Message?

 

A Narrative Summary Message?

 

As there are many ways to catch a fish, there are many versions of the same message - and these are all good messages.  Are they equally good?  Are some appropriate, but only in certain contexts? 

 

 

The Flow of Information: III

What can we conclude from this Flow of Information Design - in addition to this aspect of “The transfer of the Message” above:

1. At each interaction between two people, someone is making a request of someone else;

2. At each interaction between two people, someone is interpreting the message they are being given;

3. At each interaction between two people, there is a number of ways the message can be transmitted.

 

 

What are the implications for communication?  For "communication breakdown"?  Stay tuned for Part II of "Communication Breakdown" ...

 

The Politics of "Interest"

 

 

April 23, 2008

 

 

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Is My Home My Castle?

Tax Policy and Mortgage Payments

 

 

I’ve learned, via the bank in my loan process, there’s more than my simply paying them a monthly check in 360 installments.  Each payment must be broken down into “principal repaid” and “interest” components, because the interest on a mortgage payment is tax deductible.

I wonder why interest only is tax deductible.  Why not the whole payment?  Why even the interest?  What kind of "social engineering" is going on here?  But that's a question reserved for another column.

How do I make these calculations,

Let’s suppose the bank loans me $70,000 to buy a house, at 5% interest, over 360 months.  What else could they have done with the money?  Well, they could themselves have invested it, seeking a return of 5%.  In this first month, how much would they have earned?

 

In other materials, I showed how to calculate house payments.  If my payment was $375.78, and the bank could have earned $291.67, then the amount of “principal repaid” was only about $84.11.  Amazing!  This large payment – and only a fraction actually went to “home ownership”; the larger portion went to interest.

Well, the tax policy now seems to make sense.  Should tax policy allow a deduction for the portion of the payment that actually went to the outstanding principal?  Or should tax policy allow a deduction for the portion of the payment NOT going to reduce the outstanding principal?  It is a tax policy question, but I now see why the system is what it is.

The second part of my question was the actual calculation of the “interest” and “principal repaid” amounts.  Fortunately, I’ve done a good part of the calculations above.  Assuming I’ve calculated the actual payment amount, I need only know the outstanding balance at any point in time.  Applying the interest rate to that outstanding balance, I get an amount I’m assuming the bank could have earned had they had this money instead of me.  This is my interest charge.  The difference between the payment and this interest charge, then, is the amount of my payment going to pay down my outstanding balance.

This seems to be a lot of work!  How do I keep track of such a monster table?

 

THE AMORTIZATION SCHEDULE

The Payment Broken Down:  Interest versus Principal

The Amortization Schedule provides a method of keeping track of all values:  payment, interest, principal repaid, and remaining principal.  Continuing with the example above, this amortization schedule would look as follows:

 

The Payment Broken Down:  Interest versus Principal 

Well, at least at the end of my 360th payment, I see I own my entire house!  That’s good news.  I also notice a good portion of my early payments go directly to interest, and I’m not paying down much of the outstanding principal.  Finally, as I reach my final payments, I see the majority of the payment goes to reducing the outstanding principal. I wonder what all this data looks like graphically?

 

And the corresponding plot of my “outstanding balance” as it goes from the initial loan of $70,000 to zero …

 

Amazing.  But this was with a 5% interest rate.  Does this change with other interest rates?  Let’s see …

 

A Comparison of the Outstanding Balance and Interest Rates

These graphs show a tremendous difference in the “interest versus principal” parts of each payment.  When rates are low, payments are low, and a lot of my money goes straight to the outstanding principal – I’m owning more of my house quicker.  Conversely, when rates are high, not only are payments high, but the majority of the payment goes to pay off the interest!

What does this look like graphically?

The tragedy of the interest rate phenomenon strikes me.  Not only does a higher rate mean higher monthly mortgage payments, but these higher rates also rob me of the house I could actually be owning!

Is my home my castle?  Apparently, it depends on the interest rate.  Given a high interest rate - nope!  It's the bank's castle, and I'm just a tenant defending it!

 

 

If I Were a Blossom

 

An Introduction to Anthropomorphological Haiku

 

 

April 24, 2008

 

 

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Basho:

Your haiku certainly seems to differ in method and substance from my haiku.

 

Me:

No disrespect intended, Master.  But despite many attempts, I found I could not simply "look at nature" and arrive at a haiku.

 

Basho

What makes you think my statement implied disrespect?  I merely said it was different.  I've read your previous articles on why you write the way you do and I would like to ask you one thing:

I wonder what is it you're seeing when you say you find it difficult to write haiku.

 

Me:

What do you mean?

 

Basho:

You say you're looking at nature, right?

 

Me:

Indeed.

 

Basho:

But you can't describe this in terms of haiku.

 

Me:

That's right.

 

Basho:

Can you describe what you're seeing - at all?

 

Me:

I don't understand.

 

Basho:

Look at that tree over there (pointing at a tree).  What do you see?

 

Me:

A tree.

 

Basho:

That's where you're wrong.

 

Me:

But it is a tree, right?

 

Basho:

That's just a word.  What's behind the word?

 

Me:

OK - I think I understand.  There's branches, bark, leaves.  Many things.

 

Basho

That's it?

 

Me

What else?

 

Basho:

Do you see the tree bending to the breeze?  Do you hear the soothing sound of the leaves in the wind?  Do you see the long shadow cast by the sun against the tree?  Do you see the manner in which the limbs branch out from larger limbs?  Do you see the woodpecker hole?  Do you see the colored leaves? 

 

Me

I do!

 

Basho

But when I asked you what you saw, you mentioned none of these.

 

Me

Indeed.  I'm beginning to see what it means "to see".  But I have a question for you.

 

Basho:

Yes?

 

Me:

Do you see the oak tree over yonder?

 

Basho:

I do.

 

Me

It grew from a fallen acorn over many years, right?

 

Basho:

Many years indeed.

 

Me:

And it could not grow to be any other type of tree, right?

 

Basho:

Agreed.

 

Me:

But this is something we don't "see".  It happens over such a long period of time we really infer it.

 

Basho:

I'll grant this, for now.

 

Me:

I might describe this occurrence as follows:

 

O Fallen Acorn

Chronologically Conceived?

Climb Mighty Oak Tree!

 

Basho:

I love it!

 

Me:

But I thought haiku was "directly experiencing nature"?

 

Basho:

Isn't that what you've done?

 

Me:

I had to think quite a lot about the logic and my words to arrive at it.

 

Basho:

You think I don't with mine?  Don't believe everything you've read about me.  In fact, don't believe anything about what you've read about me!  Do your own thinking!

 

Me:

Let me ask you a question regarding a method I've been toying with to help me "see nature".

 

Basho:

Please!  I'm all ears!

 

Me:

I was watching a robin carry a piece of straw the other day, and started writing my "logical haiku" about the creation of a nest.  But then I thought a bit about it and tried to find a way to "see the robin" more clearly - to observe nature as you described above.

 

Basho:

And ...

 

Me:

I pictured myself as the bird, and suddenly I had a clear picture - a first-hand perspective!

 

Basho:

The result?

 

Me:

 

Caring for my young;

Blue Egg Feathery Soft Home

Whistle While I Work!

 

 

Basho:

Wonderful!

 

Me:

Finally, Sweet Spring!

I Just Want to Celebrate!

Sunshine!  Breath!  Rain!  Life!

 

 

Basho:

And who who were you in that one?

 

Me:

I was the blossom on a branch of a tree!

 

Basho:

Marvelous!  What do you call this unique approach to "seeing nature"?

 

Me:

Since I'm ascribing human characteristics to non-human elements, I call it ANTHROPOMORPHOLOGICAL HAIKU!

 

 

 

Center Pivot Irrigation

 

 

April 25, 2008

 

 

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If you use Google Earth and spend some time just looking at the earth, zooming in and out, here and there, you're likely to come upon this picture which must be a satellite imaging error. 

 

It's not.  It's an image of fields irrigated via center pivots in southeast Nebraska.  Marvelous.  But why here?  Why is center-field irrigation so popular here?

My first thought was of the Ogallalah Aquifer, the massive underwater storage unit under this part of Nebraska and seven other states. Such circumstances seem perfect to explain the presence of center-pivot irrigation here - drop a well, pump water, and rotate an arm to irrigate the land.  But I know this cannot be completely valid, because if this was the case, I'd expect to see the agricultural landscape throughout this 8-state region peppered with this design, and I don't.  There must be some other circumstance present in Nebraska giving rise to this phenomena.

 

Lost Land

As I look closely at the square grids and round irrigated fields, a thought comes to mind: if only the round portion of the field is irrigated, how much of the land is not?  That is, what is the relation of the white circle below to the black outer region not irrigated?

 

 

 

Let's suppose I set the length of my pivot arm equal to one unit.  I don't know how big these machines typically are, so rather than guess at a quarter-mile, 100 yards, etc., let's just use one unit.  This arm sweeps out a circle, and I know the area of a circle, so I can calculate the irrigated area (as the length of the pivot arm then is the radius of my enclosed circle).

 

Additionally, if I know the length of the pivot arm, I know the length of the side of my square.  Knowing this, I can find the total area (irrigated and non-irrigated).

 

The ratio of the two gives me the percentage of land irrigated.  Let's see:

Nearly 4/5ths irrigated - meaning approximately 1/5th is left non-irrigated.  Is this waste?  Is this the best to be done?

Maybe.

 

Lost Water

One significant manner agriculture has eliminated waste with center-pivot irrigation is the manner in which sprinklers operate.  First, consider most yard sprinkler systems, spraying the water from a spout inches from the ground.  In doing so, the water has no choice but to go up and out.  How much of this water makes it to the intended spot on the lawn?  How much is lost to evaporation?  Is there anything to be done to reduce the loss?

Like lawn sprinkler systems, center pivot irrigation had sprinklers spraying water in a similar fashion.  How much was lost to evaporation?  A lot.  Unlike lawn sprinkler systems, center pivot irrigation sprinklers are already up in the air.  Directing the water flow downwards, in the form of drip-irrigation, results in massive water savings.  A great example of "doing more with less"!

 

 

"These are a Few of My Favorite Things"

 

 

April 26, 2008

 

 

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Digital Turkish Rugs

 

 

April 27, 2008

 

 

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THE TIMELESS WAY

A building or a town will only be alive to the extent that it is governed by the timeless way.

 

 

THE QUALITY

To seek the timeless way we must first know the quality without a name.

 

 

THE GATE

To reach the quality without a name we must then build a living pattern language as a gate.

 

 

THE WAY

Once we have built the gate, we can pass through it to the practice of the timeless way.

 

 

THE KERNEL OF THE WAY

And yet the timeless way is not complete, and will not fully generate the quality without a name, until we leave the gate behind.

 

 

Christopher Alexander

The Timeless Way of Building

 

 

 

 

 

 

 

 

 

 

 

 

 

Aunt Polly and the Get-Back Plan

 

 

April 28, 2008

 

 

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When we last left our good friend, Tom Sawyer, you'll recall Aunt Polly had set aside Saturday as the day of reckoning for Tom's skipping school Friday.  The task?  Whitewashing the fence.

You may also recall what happened that sunny Saturday.  Tom, in his haste to abandon the work assigned by his good aunt, had tricked Ben Rogers and other neighborhood boys into painting the fence for him!  Not only that, but his trickery was so well conceived the neighborhood boys paid Tom for the privilege of doing the "work"!.

What you may not know is "the rest of the story".

Having corralled an apple, a kite (in good repair), a dead rat and a string to swing it with, twelve marbles, part of a jews-harp, a piece of blue bottle-glass to look through, a spool cannon, a key that wouldn’t unlock anything, a fragment of chalk, a glass stopper of a decanter, a tin soldier, a couple of tadpoles, six fire-crackers, a kitten with only one eye, a brass door-knob, a dog-collar (but no dog), the handle of a knife, four pieces of orange-peel, and a dilapidated old window sash, the idle but rich Tom sauntered off to inform Aunt Polly the job was complete.

The unbelieving Aunt, unaware of the shenanigans behind the whitewashing, lavished praise on the gleaming young lad, and let him off to the water hole.

About an hour later, Aunt Polly, while doing dishes, spied Billy Fisher moping down the lane, occasionally but violently winging rocks at squirrels scrambling for cover up the trees.  "Billy Fisher!", she yelled, "What's wrong you picking on those innocent squirrels?"

"I borrowed my older brother's kite this morning, and now that Tom's got it, I'm sure-enough in for a licking!"
 

"Tom stole your kite?  I'll fix him good.  And here I sent him off to the watering hole thinking he was a good boy!"

"That's just it, Mamm ... he didn't steal nothing.  I gave it to him on account he let me take a turn whitewashing the fence."

Aunt Polly took it in at once.  Tom hadn't done a drop o' work.  He'd tricked the other kids into doing the fence-work, probably charging them for the privilege!  She marched up to Tom's room, and removed the case covering the secret opening in Tom's closet, knowing what treasures lay concealed in the darkness.  Down the stairs she came, kite in hand.

"Don't you say nothing about this to nobody, Billy.  You understand me?  You take this kite home to your brother, ask your mom if you can do a little work for me, and then come back here with a good appetite.  We're going to do a bit of work, have some apple pie, and set a trip ol' Tom Sawyer will fall right into!

Revenge is a mighty sweet motivator, and Billy was off right quick.

 

The Plan

Billy Fisher returned, relieved with the kite now back in the hands of its rightful owner.  He saw Aunt Polly in the backyard, standing in the middle of a well-worn garden in need of repair.  "Hurry, child: we don't have much time.  Likely Tom will be strutting down the road in about an hour."  She stood in the middle of the garden, string in hand, and told Billy to take one end.  "Go out until the string is tight, and then walk in a circle.  As you walk, scratch your feet into the ground, leaving a mark."

 

The rough circle complete,  Aunt Polly continued.  "You ready to do a bit of work for half an apple pie?"  The lad eagerly agreed.  "Take this rake and hoe, and first hoe all around the circle.  After you're done, rake it all into a pile, and then we'll wheel it out into the forest.  I'll get to cooking your apple pie.  I reckon it will take you about an hour.   Think you can do it?"

"Yes, mamm," and off he went.

You'd have thought there was treasure under that garden, with Billy Fisher hacking and raking and digging and tugging at the dirt.  With sweat dripping from his forehead, he knocked at the door, and was greeted by Aunt Polly, holding an apple pie fresh the stove, steam rising from the crust.

"You've done a great job, son - sit down here at the picnic table and have yourself half a pie.  Think you can eat that much?"

Again, the young boy responded simply, "Yes, mamm!"

 

The Get-Back Plan

Aunt Polly smiled.  Here came Tom, ambling up the walk just as Billy was finishing his half of the pie.  Tom peered at the apple-pie-stained face of his grinning friend, and filed his protest verbally.  "What's it all about, Aunt Polly.  What's Billy Fisher doing eating a pie from our house?"

 

"I needed work done in the garden, and you weren't around.  I saw Billy walking a'ways and told him if he did a bit of digging in the garden, I'd give him half-a-pie."

 

"Half a pie for digging in the dirt?"  Why didn't you save some of the work for me?"

 

"Well, I do have a bit more to dig, and Billy has to get home.  I told his mom he'd be back by 3:00."

 

"You mean if I do what digging is left, I'll get some pie?"

 

"That's it, Tom - but I have to tell you, Billy worked that rake like there's pirates attacking him.  Can you do the same?"

 

Tom started to smell a trap.  Sure, there was work to be done, and pie as the reward.  Could it be Billy did just a part of the work, leaving the most for Tom himself?  That's how Tom would play it if he were laying a trap for Billy!

 

"Let's just see how much work there's left," the suspicious Tom chimed.  "I wouldn't want Billy feeling cheated I did more than him, you know."

 

"That's kind of you, Tom," Aunt Polly said, innocently.  After sending Billy home with a "thanks", she took Tom to the garden, and stood in the middle, and told Tom to take the string and walk to where Billy's footprints ended.  "That's how far Billy went out.  You stay right there - I'm comin' to you."  Aunt Polly approached Tom, and then told him to go out until the string was again taught.

 

"That's the same distance as Billy, right, 'cause the string's the same length?"  "Sure enough," the still-skeptical boy responded.  "Now, let me walk back to the center of the circle.  You hold your end tight."  He did, and the string was again taught, one end at the middle of the circle, one end held by Tom.

 

"Now you walk walk in a circle, scratching your feet like Billy did."  Tom responded, and a new outer circle resulted.

 

"Billy stretched out the string a'ways, made a circle, and then did all the work inside that circle.  You did the same thing, right, Tom?  Now, with this new circle, you just do the rest of the diggin' Billy didn't."  The logic was infallible, and he admitted to himself maybe Aunt Polly was a good person after all, despite the thrashing he sometimes gets.

 

"You get to work, Tom, whilst I keep this half-a-pie steamin' for you"

 

 

 

The Sweet Taste of Justice

Three hours later, a weary Tom Sawyer presented himself to the front door of the house and pounded.  Aunt Polly answered, pie in hand.  "If I live to be a hundred," Tom said, "I don't think I'll be as dog-tired as I am right now."

 

"You did a good-bit of work, boy.  Let's go out back and you finish that pie, while I wheel some of that trash out into the forest.

 

The hungry Tom Sawyer clawed at the pie, watching his Aunt and thinking of Billy Fisher.  "How long was Billy here?"  "Just under an hour," she replied.

 

Tom Sawyer thought ...

 

 

 

An Aerial View of the Circular Garden

A pictorial and mathematical analysis of what exactly took place that sunny Saturday afternoon.

 

 

 

 

 

 

 

Communication Breakdown

 

Having Another Breakdown - Drives Me Insane!

 

PART II

 

 

April 29, 2008

 

 

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The Flow of Information: III

Earlier, we talked about the origins of many "communication breakdowns", and the nature of communications in organization.  The Message, we recognized, between simply two parties, contains at least three elements:

1. At each interaction between two people, someone is making a request of someone else;

2. At each interaction between two people, someone is interpreting the message they are being given;

3. At each interaction between two people, there is a number of ways the message can be transmitted.

 

 

The Flow of Information: IV

And if any one of the three variables fail (the request, the interpretation, the message) - the other two fail as well.  This interaction, then, can be viewed as a CHAIN WITH THREE LINKS.

 

 

 

 

The Flow of Information: V

But let's remember, usually when someone is making a request for information, it's not for them, but for their boss, and possibly their boss.  And let's also remember, this flow of data goes both directions - from the request to the delivery of the message.  That is:

 

 

and because, in a Decision Chain, all interactions are dependent on preceding events, once the chain is weakened at a link, all subsequent links can AT BEST be as strong as that weakest link - and the chain can only get weaker!!  INFORMATION ENTROPY!

 

 

 

A CURRENT EVENTS EXAMPLE

In this issue of 366, the policy of Law Enforcement and Racial Profiling was addressed.  The important issue of documenting stops by race has been going on for seven years.  The following graphic was displayed, showing the relationship between time and "race" ...

 

LAW ENFORCEMENT and RACIAL PROFILING

 

Contrary to what one should expect, things have gotten much worse!  How can this be?  What improvement initiatives have been put in place by the Missouri Attorney General to counter this ominous trend?

 

None.

 

But why?

 

Because there's nothing to be done from the data - and the AG knows this - as does every policy commissioner in the state.

 

Why?

 

Let's look at a simple example:  our goal, as KCMO residents, is to track the status of pull-overs by race.  Easy enough.  We've done that.  Now, is there profiling going on in these stops?  There are more white pull-overs than black, so the answer is "no".  Or is it?  Don't we have to take into account the populations?  If 10 whites are pulled over out of 100 white residents, this is different than 8 blacks pulled over out of 10 black residents.  So a "population" needs to be considered. 

 

What population do we use?

 

Should we use the census data?  A quick visualization of KCMO reveals this tells us nothing.  We live at the intersection of three national interstates.  People drive in from the suburbs every day.  The city population is meaningless - and this simple fact undercuts all data collected over the last seven years.

 

 

 

 

So the analyst gets data and does what with it?  Produces reports.  The AG gets the results and does what with it?  Announces it.  What improvements have taken place?  None.  And it's no wonder - the decision chain here was weakened at the outset of the project!

 

Is there a way to strengthen this chain?  Yes - but it must start at the weakest link - here, the data collection process, and rethink the relationship between data and information, information being "the answer to the question asked".

 

It's possible!

 

 

 

A PREDICTION

The AG will announce 2007 data in two days (May 1st).  My prediction?

 

 

 

It will be painful!  Likely 2007 data will show a slight decrease, and why not?  2006 rocketed up far above the previous years (which themselves had been creeping up).  Notice, nothing was done to address this large increase.  But 2007 will likely fall back in line with 2004 and 2005 data, and the AG will announce the "decrease" as evidence the system is working (though there's still ways to go).

 

 

 

A Few Degrees of Separation

 

 

April 30, 2008

 

 

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LET'S SEE HOW!

Pascal's Triangle, I know, is merely a triangle where each number is formed by adding the two numbers directly above it.  That is:

 

 

 

What possible relationship can this have with the line designs I so like?

 

 

 

Let's see by drawing several designs, each varying only by the number of points about the circle.

 

 

A SPECIFIC EXAMPLE:  n = 5 points

Where are the numbers coming from above?  Where do the "triangles", "quadrilaterals", etc., come from?  Let's use our circle with 5 points as an example and see.

 

Clearly, I've drawn but one circle.   I've next disbursed 5 points equally about the circle.  Fine.  What happens when I connect each point to the other points on the circle?  I get 10 lines.  With all these diagonals formed, I can now concentrate on polygons.  How many triangles have I?  10.  How many quadrilaterals can I form?  5.  How about polygons?  Just the lone one in the middle.

 

 

 

FURTHER FOOD FOR THOUGHT

Before I get too excited about this wonderful find, an anomaly seems to have crept in.  Above, in my example of the 5-pointed figure, the prediction was there would be 10 triangles.  I found 10 triangles.  But are there only 10?  For example, the figure is also a triangle, but it's not one of my 10!

 

 

Does this invalidate the relationship above?  In a word: "yes".  More probably, it likely means there's a relevant definition of "figure" I'm just not taking into account.  For example:  since this new "anomaly" triangle covers entirely one of my triangles, perhaps this new triangle is deemed "not relevant".  Maybe there's something else.  What I do know is our theory, once thought "good", is not so good after all; at least, not until we can clear up the following contradiction!