Neither Rhyme Nor Reason

Robert Frost, Mending Wall, and Poetry

March 1, 2008

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round@rationalsys.com

Have you ever heard the expression, “Good fences make good neighbors”?  When I hear this phrase, I imagine the author is in favor of fences.  On the other hand, I've heard the following as well:  “Something there is that doesn’t like a wall”. This author seems to be saying the opposite!

It's common, of course, for authors to differ on a theme.  However, the above quotes are both from Robert Frost, and they are from the same poem:  Mending Wall!

How can this be?

It's easy enough to clear up this issue:  go to the source and read the poem for myself.  What was Frost saying?

And here I run into problems.

You see, I cannot read poetry.  I've never been able to read poetry.   

Why not?  I can read novels with ease, but here in front of me lies one page of paper and I am stuck.

Why?

Much of the problem, I suspect, lies in the nature poetry is often written - it's very abstract.  Being absent from the "abstracting" process, I have nothing to ground my thoughts as I read. 

What if could ground myself?  What would it take to establish a foothold?

A STARTING POINT

For a moment, imagine the closing scene in The Shawshank Redemption where Morgan Freeman (Redd) is walking in the field towards the large tree, in search of a rock where a message was placed by Tim Robbins (Andy).

It was a wall similar to this:

Keep this image in mind when reading further ...

THE CONTEXT OF THE PLAY

CONSTRUCTING THE WALL

IMPROVING OUR SITUATION

MY INABILITY TO CONVINCE MY NEIGHBOR

VERBALIZING THE CONFLICT

“MAINTAIN THE WALL versus DESTROY THE WALL”

"MENDING WALL" by Robert Frost

With the above background and story, NOW let's read what Mr. Frost has to say ...

Something there is that doesn't love a wall,

That sends the frozen-ground-swell under it,

And spills the upper boulders in the sun;

And makes gaps even two can pass abreast.

The work of hunters is another thing:

I have come after them and made repair

Where they have left not one stone on stone,

But they would have the rabbit out of hiding,

To please the yelping dogs. The gaps I mean,

No one has seen them made or heard them made,

But at spring mending-time we find them there.

I let my neighbor know beyond the hill;

And on a day we meet to walk the line

And set the wall between us once again.

We keep the wall between us as we go.

To each the boulders that have fallen to each.

And some are loaves and some so nearly balls

We have to use a spell to make them balance:

"Stay where you are until our backs are turned!"

We wear our fingers rough with handling them.

Oh, just another kind of outdoor game,

One on a side. It comes to little more:

He is all pine and I am apple-orchard.

My apple trees will never get across

And eat the cones under his pines, I tell him.

He only says, "Good fences make good neighbors."

Spring is the mischief in me, and I wonder

If I could put a notion in his head:

"Why do they make good neighbors? Isn't it

Where there are cows? But here there are no cows.

Before I built a wall I'd ask to know

What I was walling in or walling out,

And to whom I was like to give offence.

Something there is that doesn't love a wall,

That wants it down!" I could say "Elves" to him,

But it's not elves exactly, and I'd rather

He said it for himself. I see him there,

Bringing a stone grasped firmly by the top

In each hand, like an old-stone savage armed.

He moves in darkness as it seems to me,

Not of woods only and the shade of trees.

He will not go behind his father's saying,

And he likes having thought of it so well

He says again, "Good fences make good neighbors."

BREAKING THE CONFLICT

Now I understand what Frost was saying, I am not a lethargic reader, but rather an active participant.  But not just this - I can envision what the problem is, and in doing so, advance solutions!  Build a Wall / Don't Build a Wall ...

What to do? Our yards don’t have anything needing enclosing, and I certainly don’t want to continue the hard work of maintaining the wall annually. Given my neighbor’s blind conformity to tradition, it will be a “cold day in hell” before he changes his mind! Should I just continue on fixing the wall, albeit reluctantly?

Before abandoning my pursuit of tearing down the wall together, let’s look at the wall itself. Why is there a wall in the first place? What gives rise to a wall? There must be some reason it’s there, otherwise it would not!

Defense and security? The wall is only 4-feet high. This wall could not hold back anybody who thought ill of me, and besides, we are friendly neighbors!

Property lines? How does anybody know where my property ends and his begins? There must be a physical barrier marking this boundary. Perhaps there is something to what his father says, though it’s clear he himself knows not the reason why.

Let me think further on this. Suppose a physical boundary is necessary to mark property lines. Must it be this crumbling and ugly wall we have now? What alternatives are there?

He’s got children, as do I. Children love to run, to play, to hide ... to enjoy life. Suppose, rather than this failing rock wall continually needing mending, we instead plant bushes a few feet apart. Yes! Let’s walk through the future reality of this injection.

THE FUTURE REALITY OF THE “BUSHES” INJECTION

CLOSING THOUGHTS

In the next issue of "Neither Rhyme Nor Reason", I'll explore the starting point of this "foothold" process, as this is the leverage point to generate "intellectual throughput".

The Supreme Count - Visually - Through the Year

March 2, 2008

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round@rationalsys.com

My January 29^th post touched on "Political Power", and the accumulative relationship between the legislative and executive branches - two of the three foundations of our "Separation of Powers".  The third is, of course, the judicial branch.  This tri-partite ruling system of "checks-and-balances" forms the basis governing basis of our constitutional republic.

The Judicial Branch - The Supreme Court

To ensure this branch is "non-political", the following justices are appointed for life.  But appointed by whom?  Ginsberg and Breyer were appointed by Clinton, Roberts and Alito by Bush, with others appointments ranging from GHW Bush, Reagan, and even Ford!

This hardly seems "non-political".  Is it possible to have all nine justices appointed by one president?  One party?  How has the distribution of justices by political party looked over the last century?  How long does the average justice serve?  Brennan and Black seem to have been justices forever, and the impact of FDR's 4-terms are evident in the domination of "Democratic-appointees" during the Truman administration.

Perhaps surprisingly, though the Executive and Legislative branches have seen an alternating ebb and flow of control - punctuated by extreme control during the FDR and LBJ presidencies, the Supreme Court seems to be largely a Republican establishment during the last century.

The Sub-Prime Fiasco

from a different perspective

March 3, 2008

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round@rationalsys.com

What is a "sub-prime" mortgage causing all the problems?

It's a loan made to a person who doesn't qualify for the "best available interest rate", due mostly to credit history.

Why would a lender issue a loan to a "bad risk"?  Why would a person with "bad risk" want a loan?  Good questions - to be addressed in a different article.  Needless to say, the government is not without blame here, pushing lending institutions to make loans available to "marginal risk", as well as the artificial enticement in owning a house of having the interest tax deductible.

THE ADJUSTABLE-RATE FIASCO

Obviously, if sub-prime loans are made to a less-desirable risk, and if risk is really the interest charged on the loan, then sub-prime loans will be subject to a higher rate than "prime" risk.  But if the potential loanee is a marginal risk, be it for financial considerations, credit history, or other issues, who will apply?  Likely, not many.  Not unless they are enticed by artificially low rates.

Clearly, however, if the risk is bad but the loanee gets a low rate, there must be some catch.  After all, one "can't have his cake and eat it too."  What is the catch?  These teaser rates are bundled under the umbrella of an "adjustable rate mortgage".

AMPLE BLAME TO GO AROUND

Was there predatory lending?  Obviously.  Was there predatory "borrowing", where people lied on the applications to become eligible for the loan?  This is well documented.  Is government intervention in the housing market an issue?  Clearly.

However, I don't want to focus on any of these.  Instead, I want to focus my attention on those borrowees who didn't understand the ARM-process, and now find themselves in an unfavorable light.

Why didn't they?

THE FINE PRINT

Watch any ad on TV ultimately financial in nature.  Car ads are wonderful in this regard.  Big bold print about the price - and at the bottom of the screen:  6-point font "fine-print" about the details of the loan.  This flashes for a moment - and is gone.

Likely no one in the history of television has read this - ever.

Why, then, do the commercials use it?  Government regulations mandate this "full-disclosure".

Likely, one outcome of the sub-prime fiasco will be a clarion call for "non-legalese" print.  If only the loanees knew the full details of the ARM, they would have made a more fully-informed decision.

But what happens when "non-legalese" hits a snag, and "not everything" is disclosed?  We know the results.  You likely get examples in the mail everyday from your 401(k) institutions - massive books that contain everything.  Has anyone ever read these?  Of course not.

And the pendulum effect of these actions is a back-and-forth between extremes:  add fine print.  Something bad happens.  Legislate readability.  Something bad happens.  Mandate full-disclosure. 

THE CURSIVE INJECTION

Observe, in this process, there is only one perspective: the lending institution's.  How can we make sure the borrowee themself really knows the terms of their loans?  Why not allow part of the overall agreement include a signed statement by the borrowee - in their own words - regarding the details of the contract - signed by them and a representative of the company?  Such a statement would move great distances in making sure the borrowee knew the terms of the loans.

An American Grammar

simple changes to the "grammar" code

March 4, 2008

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round@rationalsys.com

There - I've included all four of my recommendations (for now) in one brief paragraph: three I've put in my recommended format, the fourth I've left in place to demonstrate the rule.

Change 1:  Every sentence DOES NOT need a subject and a predicate.

Wonderful!   There - I just violated the rule!  Why do we insist on a rule contrary to the way we speak?  Our ordinary speech is peppered with complete sentences interrupted by one-word thoughts.  Why is this OK when we speak but not when we write?

Fine.

Change 2: Avoid like the plague the use of the word "that".

"Redundant" doesn't do this rule justice - simply eliminating the word does not change the meaning of the sentence, but at the same time, it does.  Sentences become sharper and crisper.  And in proofing your own work, when you find you are stuck in how to jettison the word, you think more deeply about the sentence and paragraph you're writing.

Here are a number of examples from just a portion of an article on the Liberty Memorial in today's KC Star:

Brian Alexander, executive director of the Liberty Memorial Association, said that he would be open to exploring a partnership with the federal government but that it was premature to talk about turning the monument over to the federal agency.

But he was not optimistic that the federal government would be any more interested now in acquiring the memorial.

But Funkhouser and others are annoyed that memorial officials continue to ask for more city money.

Councilwoman Cindy Circo said Liberty Memorial was a phenomenal museum that needed to be protected beyond the city’s ability.

Change 3:  Quotation marks should include only what is being quoted.

Regardless of standards and traditions, I've never liked the idea of including the quotation marks around closing punctuation marks.  Pardon the expression, but I think it "stinks."

There - I just did it.  The job of the period is to close out the sentence; the job of the quotation marks are to enclose a thought.  The above sentence should be written:  Pardon the expression, but it think it "stinks". 

Change 4:  The "Serial Comma" is NOT optional.

I'm agitated when I read about lions, tigers and bears.  Why?  Because later I may read about lions, cats and kittens, and tigers.  Do you see the difference?  The absence of the comma after "tigers" in the first sentence leaves the reader in doubt: is the next object the last object, or does it belong to the prior object?

As was the case in "Change 3" above, the comma is not merely a grammatical convention here; it serves a purpose.  It isolates entities from one another. 

Architects of Their Own Future

Chapter 12

March 5, 2008

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round@rationalsys.com

Chapter 12

THE CHALLENGE

The reading and science tests are each 35 minutes in length (40 questions). In the 2004 / 2005 school year, nearly 1.2 million students took this exam, and the average score was 20.9 out of a possible score of 36. The ACT–representatives knew the average student got slightly more than ˝ of the problems correct. They did not know the purpose of them being in the library with the students, but they were certain if it were for the sake of a contest, the kids were in for a surprise. Each representative had post–graduate degrees, Mr. Anderson an MBA, and Mr. Jones an MS in Math, both from respected institutions.

The students and representatives were seated around differing tables, the proctor certain no students taking similar parts of the exam were seated at the same table.

“The purpose of this little exercise is to demonstrate to these gentlemen how it was possible for all our kids who took the exam in September to have done so well. However, don’t feel any anxiety over this. You’re here voluntarily, so do your best. You’re only going to work on one section, so once you’re finished, you may go back to your classroom or lunch. I’ll take you gentlemen back to the Principal’s office with the exams.”

With that, the students and ACT–representatives began.

After the 35–minute period ended, those students and ACT–representatives left their material and went to the hallway. Mr. Anderson was about to say something about the exam when he overheard one student say, “What did you write for the ‘social science’ passage?”

He listened in, curious. “What did you write?” he thought? These were questions where you color in a circle to record your answer. What were they talking about? The second student continued. “That was an easy one – the hard one for me was the Humanities passage. I had no idea what they were talking about. I had to read through that one entirely before I could write my first statement! I started to panic, but remembered our material – structure with confidence – and then everything went OK.”

This was odd talk! What were these kids talking about? He turned to his colleague. “How do you think you did?

“Those first two passages I did fine. I knew most of the answers right off, and a couple I had to go back, but I think I did fine. Those last two …” he added embarrassedly, “… through me a bit. I’m not so confident with those, but I’m certain I did better than those kids! How about you?”

“Same thing for me, except I had more problems with that second passage, the Humanities item. I took quite a bit of time on that one, but I think I did OK.”

“Funny thing about that Humanities passage,” said Mr. Anderson, “I heard those kids talking about it too, but they were saying some strange stuff about writing things down. I couldn’t follow what they were saying.”

The receptionist appeared from the library, exams in hand, and escorted the gentlemen back to the principal’s office.

“Well,” said Principal Ragnar happily, “Let’s see how we did.”

“Why don’t you grade the students papers, and I’ll grade yours. Ms. Taggert: will you read through the correct answers, and we’ll all grade accordingly?”

Ms. Taggert proceeded rhythmically: “1–A, 2–B, 3–C …” with a cadence pausing only to allow everyone to turn the pages in their books. Jones and Anderson looked at each other as page 1 became page 2: in the first reading passage, these students had scored perfectly – all three of them! Passage 1 became passage 2, and the cadence continued. Relieved, Anderson checked two questions incorrect in the second passage, Jones marking one. The performance continued, until Ms. Taggert concluded: “39–D, and 40–A”.

The two men looked at each other, astonished and bewildered. They knew what the average was on a test like this – and they knew what the distribution of scores looked like. But this? Their thoughts were interrupted.

“Very good”, said the principal. Now let’s tabulate all the scores and see what we’ve got. He went to the white board and wrote everybody’s name. Consulting his own sheet, the Principal wrote "34" next to Mr. Jones name.  Flipping over the sheet, he noted "32" for Mr. Anderson and wrote it on the board.  Though surprised at missing 4 and 8 questions respectively, they knew these scores put them in the top ten percent. They also knew what was coming, because they had graded the student's sheets.  The scores were recorded:

“OK – OK”, said Mr. Jones. “We give up! What’s your secret?”

“Over the summer, a few teachers and I got together to talk about the school's future. We had been handed a death sentence by the district. They were going to take away our charter status after the upcoming year!

“Who would come to our school, knowing it was certain to close after another year? What hope had we? The only hope we had was to demonstrate massive improvement immediately – to show parents and the district we should not be shut down.”

“But massive improvement immediately? How could we do this? In our profession, improvement is tracked over 5–year periods, and here we needed something now!”

“This is where your test and organization came in. Is there anymore respected metric than either the ACT or the SAT? The scores are very stable over time, kids have a vested interest in doing well – in order to get into college – and we could leverage improvement into news stories about a turn–a–round at our school.”

“But it’s one thing to have a plan like this – another to act on it. How could we achieve massive improvement immediately? Your organization writes the test. Your organization also writes the best–selling materials to pass the test! And yet the scores are stagnant over time!”

“This ‘anomaly’ – this “gap between what we’d expect to see in reality and what we actually see” is where we focused our efforts. How could this be? We read your materials on how to take the reading test, and it was shocking: here you say to browse, here read carefully, here skip to the questions, and here read first. Your own recommendations were all over the board!”

“Moreover, look at this passage. Principal Ragnar pulled one of the tests from the table and opened randomly to Passage IV. Look at this reading material. One page. And all 10 of these questions relate to this one page of material. One actually does little thinking here – all you have to do is find the answer. And yet the average student scores only 20 out of 40 on this test! How can this be?”

“That’s what we were thinking this summer – that one question – because it made no sense. And the tragedy of the situation is you yourselves have created a conflict everybody takes for granted?”

“What do you mean?”

“Skimming makes sense, right? We all do it. But we also read carefully, at times, right? So there are legitimate reasons to do these things. But you tell students to do BOTH of these things! 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.

“Look at what you’ve created!”

“And what do students do – in fact? Do they stick with a specific strategy? Of course not. Everybody panics, and immediately switches back–and–forth from “strategy” to “strategy”. Your material, far from helping students, perpetuates the stagnating scores I showed you earlier.”

“And you’ve found a more powerful strategy, if I understand you? What’s your secret?”

“There’s sadly no secret at all, and it’s hardly a strategy.  But not so fast.  What we realized was there's no sense teaching our kids your strategies when everybody else is already using them, and your scores are stagnant.  So we backed up and just took a look at the test in general.

What we saw was this: at least in two of the four subjects (reading and science), all of the information is there to answer the question. Now, if all of the information is there, why does one even need to study before hand - at all? But even though all of the information is there, students still don’t score well – even using your material. How can this be explained?”

“The answer was obvious. The students, given lots of ‘stuff’ to organize, did not know to organize it. You all made things worse by using terms like ‘summarize’, ‘skim’, etc., but all these multiple and conflicting tools do is confuse the student. If they have no idea what a passage means, have you helped them by telling them to ‘summarize’ the passage, or outline ‘key words’?”

“So your mission became: ‘How do you organize a block of material you know nothing about?’”

“That’s the majority of it – and the practical tools we developed differ a little bit, based on the subject matter. The exciting thing about the use of these simple tools is they do apply to all aspects of the curriculum – that’s what you saw this morning when I was talking about the electoral college!”

Our Own Writing System

March 6, 2008

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round@rationalsys.com

What would it take to invent our own system?

Consider the grid below.  Our goal is to populate it with - something, and this "image" will be our new "hieroglyphic system".  But populate it with what?  I want the image to look elegant, and in doing so, I recognize a number of "symmetries" possibly existing.

Consider the image on the right: if I populate sector 1, I can fold this over, and I have sector 2.  Taking these two sectors together and folding them across the vertical, I have sectors 7 and 8.  Taking these four sectors and folding them over the horizontal, I have the remaining 4 sectors.  Therefore, to populate this grid with complete symmetry, all I need are elements in sector 1.

Let's go ahead and randomly populate "sector 1", sprinkling black cells throughout it.  This being done, and remembering the 7 remaining sectors are merely copies of this one sector, I can create the entire grid.

LETTING THE ROUTINE RUN

OK - I've done this for one pattern - what about other patterns?  What happens if I just let the algorithm "run", and see what happens:

ADDING SOME STRUCTURE

This looks great!  Now let's see if I can add some structure to it.  Let's suppose a black cell is equal to a "1", and a white cell a "0".  If I have all these 1s and 0s, surely I can aggregate them to make sense.  And if I can generate a string of 1s and 0s, is this not binary?  So if I have a binary representation of my visual structure, I can then translate it into a familiar decimal number.  That is;

 "BINARY SYMMETRIC HIEROGLYPHICS"

AN INTRODUCTION

A structured set of "binary symmetric hieroglyphics" looks as follows (from 1 to 40), with the second image starting at a much higher number to give an idea of how the image changes:

The Origins of Logical Haiku

March 7, 2008

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round@rationalsys.com

I've included a weekly haiku throughout the year.  It's time to put some structure to what exactly is going on here ...

FUNCTIONAL HAIKU

From Syllogism to Poetry

Interdisciplinary Education and the Japanese Haiku

The teacher excitedly prepared the main English lesson for the day. Finally, she thought, a subject I really like: poetry! And not just any poetry, but the Japanese Haiku! She thought of the many themes and experiences the young kids could use as the foundation for their haikus. She thought of the rich variety of explanations to come forward. She thought of …

… She pondered. What happened? How did what was suppose to be so good become so bad? Why had so many kids struggled with this simple exercise? How can it be so difficult, coming up with five and seven syllable sentences? And what of the work done by those who did finish the work, she thought, looking at the work - ugh! Students despise the structured fill-in-the-blank lesson plans, yet here they struggled more when there was a great deal of freedom! What to do?

Indeed!

A STATEMENT OF MY PROBLEM

The Japanese poetry of Haiku is introduced to young children as a means of experiencing nature and describing this experience via a structured 3-line description, the three lines consisting of 5, 7, and 5 syllables.

I have tried this many times and, despite the ease at which the process sounds, I’ve never liked any of my work. It addition to sounding extremely artificial, I fight very hard to describe things in the manner noted above.

Is such poetry open only to the “creative” people, while such freedom is anathema to those of us desiring more explicit algorithms to achieve a result? Is there a dilemma between structure and freedom? Can creativity be a learned behavior?

Let’s see.

Part of my problem, I believe, stems from trying to write poetically about something – from the start. In fact, I think I’m like this when I read poetry. Since I usually have no idea what the poet is talking about, it doesn’t help to read on, because the poem becomes mere words – no meaning.

A DIRECTION OF MY SOLUTION

Establish meaning. Let’s focus on this – both in writing poetry and in reading poetry.

But how?

To maintain the spirit of Haiku, let’s start with something we experience – any experience – and see where we can get to.

I see a rainbow. I see a cloud. I see a line of smoke trailing an airplane. I see something that interests me. I like that start, but is it enough? Why have I chosen this experience? What is it about this that interests me? Let’s remember our goal: establish meaning. How can I explain these experiences? Let’s start with the rainbow. Why is there a rainbow? Let’s posit a cause: sunlight hits water droplets.

Is this reasonable logic? Does it explain what I’m seeing?

Let’s see: IF: sunlight hits water droplets, THEN: I see a rainbow in the sky. Does this make sense? I don’t think so. There are many times when I see the sun and the rain, yet I don’t see a rainbow. Also, what has light hitting rain have to do with a rainbow? I can think of a number of problems with this logic.

The missing link, here, deals with the dispersion of light when light hits water. How does this work? I’m not sure.

Is it OK to leave it at this level – for now? Let’s see where we’re at: if sunlight hits water droplets, and if water droplets disperse the light into spectrum colors, then I see a rainbow. This makes sense to me.

But can I add to this – because now there are a lot of facts on the table. Let’s visually organize our understanding thus far.

Of course, there are still a lot of unanswered questions, but nonetheless, I think this is a reasonable starting point.

INTRODUCING HAIKU

to the Causal Logical Structure

But what has this to do with the Japanese Haiku? Here’s where the union of structure and freedom comes into play. With reasonable statements in place, I can now look to summarize each statement in terms of the 5 / 7 / 5 syllable structure of the traditional Haiku:

For example:

I need a 5-syllable statement to reflect: “sunlight hits water droplets”: Here’s one: Union: sun and rain.

I need a 7-syllable statement to reflect: “The water droplets disperse the light into spectrum colors”: Here’s one: Droplets disbursing colors.

I need a 5-syllable statement to reflect: “I see a rainbow in the sky”: Here’s one: Wonderful rainbow!

Let’s pause for a moment: where did these “haiku-equivalent” statements come from? With my mind now focused like a laser beam on a specific topic (sunlight hits water droplets) and a specific goal (5 syllables), they came from me – naturally!

But why stop here: before, I visually arranged my statements to better organize my thoughts and understanding. Now, I’ve got three more statements hanging out there. Why not integrate all of these elements? The result (with my own “causal logic” haiku title added):

This may not strike others as a beautiful haiku, but to me, it’s the best one I’ve ever written! And look how the structure has not hindered freedom, it has expanded it – from scratch on a piece of paper (and frustration in the mind) to a poetic detective undertaking.

Let’s try a few more before describing further the theory. One I like: on our counter is a candle in a jar. I place the lid on the jar and the candle goes out. How can I explain this, and translate this into a Haiku?

Let’s try one more: I’m fascinated by an article in our paper describing the likely result of the coming census, and the impact to the House of Representatives. What has this to do with Haiku?

In fact, what has this to do with “directly experiencing nature”? If I could create the same logical and haiku structure with a “current event”, this would extend the application of Haiku not just to experiencing nature, but understanding reality!

But let’s not get too theoretical here – let’s just do it and see what happens:

LOGICAL HAIKU

A Description of the Process

So what have I found? Let’s start with where Haiku is typically taught: English. Above, it’s been brought out into the open, where all the understanding of reality is taking place! Science, current events, math, etc. We talk of making education relevant. Haven’t we addressed that problem above? How does this apply to the real world? We’ve started with the real world! Where, precisely, do we start, given reality is infinite and so are our experiences. Start with something that interests you, and explain it causally. If you’re like me, you’ll find this is not so easy. Happily, however, this hard work pays off. The structure above I call the “context syllogism”, and it forms the foundation for developing the 5/7/5 Haiku.

With the structure in place, I found a wonderful starting point with boundaries from which to develop the accompanying Haiku statements. The search for relevant synonyms, varying methods of describing reality, phrases I never would have come up with out of the blue, now are so plentiful the variety is amazing! Have I explained reality? You bet. Have I improved my English? Immensely!

Structure VERSUS Freedom? I think not! Right-brained versus left-brained? Let’s abandon this artificial classification immediately!

A closing thought or two: is this Haiku? Haiku is traditionally thought of as directly experiencing nature. Isn’t that what I’ve done above? I think so. And if it’s not technically Haiku, it seems to me to be in the spirit of Haiku. However, for those caught challenging the nomenclature and therefore the process, let’s remove this objection up front. Don’t think of this as Haiku, but perhaps causal poetry, or applied English.

Secondly, in the above examples the logic can certainly be tightened. In fact, in any logical structure, the firmness of the logical connections can be improved. Improve as you wish. In fact, extend the Haiku into further Haiku and create a sequence of 5/7/5 explanations.

The Functional Haiku Process

Step #1: record an experience – anything very interesting to you – as a complete sentence.

Step #2: why does this experience exist? What causes it? Write this cause as a complete sentence.

Step #3: read these two sentences as follows: if (step 2), then (step 1). You’ll probably note there is something missing, that the sentence does not make sense. Add another statement to make the logic better.

Step #4-#6: translate each of the above sentences into the appropriate Haiku statements. It does not matter which order you take here.

Step #7: name the Haiku.

A Letter to the Philamath Society Regarding Morris Kline

March 8, 2008

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round@rationalsys.com

A COMMEMORATIVE STAMP CAMPAIGN

The great 20th century mathematician Morris Kline is well known for his amazing works on math history and pedagogy.

With an intense interest in mathematical history, pedagogy, and application, Morris Kline was, to me, one of the most dominant mathematical figures in the 20th century. ‘Mathematical Thought From Ancient to Modern Times', 'Why Johnny Can't Add', 'Mathematics and the Physical World', and 'Mathematics and the Search for Knowledge' are but a few of the tremendous works authored by Kline. Were volume alone a criteria for greatness, he stands alone.

But more impressive than volume was the content, the focus, the drive, the joy with which each of these books shouts to the reader. Nature and the world is screaming to be understood, and it is mathematics that can - and should - lead the charge! Though he passed away in 1992, the message he left behind is an inspiring one. A clarion call? You bet!

Among many of the exciting initiatives of the “Morris Kline Society" is a campaign for a commemorative stamp in his honor, and I write in this regard, soliciting thoughts, advice from those who have been through such a process, pitfalls to avoid, etc.

A “Philamath” member for about two years now, I’m still a novice at stamp collecting, but enjoy everything about the group! So thanks!

Michael Round

Center for autoSocratic Excellence

www.rationalsys.com

WHO WAS MORRIS KLINE?

Who was Morris Kline? To many, Morris Kline was the author of one of the most definitive books (now a series of three books) on the history of mathematics: Mathematical Thought from Ancient to Modern Times:

To others, Morris Kline was the author of several books on the application of math to reality, understanding nature, and making math comfortable for many who have been traditionally labeled as “mathematically illiterate”:

To others, Morris Kline was the reformist, concerned with the proper teaching of math, the status of math in curriculum, of what math means, and pedagogic considerations. According to Siobhan Roberts in “King of Infinite Space”, a biography of Donald Coxeter, Morris Kline was the leading antagonist of “The New Math” revolution in the 1960s:

These are several of the books authored by Morris Kline. There were many more.

Volume and diversity of thought alone places Morris Kline in a very select classification of mathematical genius. The pedagogic considerations in how to teach math, the curriculum considerations in what to teach, and the logical considerations as to why things are the way they are, with reasonable steps to correct the mistakes of the past – to me, this is the total package.

Quoting and paraphrasing from the obituary first appearing in The New York Times, June 10, 1992:

In a 1986 editorial in Focus, a Journal of the Mathematical Association of America, he [Morris Kline] summarized some of his views: "On all levels primary, and secondary and undergraduate - mathematics is taught as an isolated subject with few, if any, ties to the real world. To students, mathematics appears to deal almost entirely with things which are of no concern at all to man".

The error, he contended, was that "mathematics is expected either to be immediately attractive to students on its own merits or to be accepted by students solely on the basis of the teacher's assurance that it will be helpful in later life." And yet, he wrote," mathematics is the key to understanding and mastering our physical, social and biological worlds."

He argued that teachers should stress useful applications of mathematics in various other fields: that they could have elementary schoolchildren deal with baseball batting averages and puzzles, get high school students work with statistics and probability, and bring college students to apply mathematics to computers and physics.

But, he said, many schoolteachers are simply unfamiliar with such teaching techniques, and the same is true of numerous college professors who were under "pressure to write research papers." He called on professional mathematics journals to print articles that instructed school and college teachers about ways of presenting such applications to their pupils and students.

"The greatest contribution mathematics has made and should continue to make was to help man understand the world about him."

Challenging Intuition Directly

March 9, 2008

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2,500 Years Too Late

Cleaning Up the Mess of Zeno

“THE PARADOX” PARADOX

Zeno of Elea is well known from ancient times for formulating interesting paradoxes regarding motion. Perhaps his most famous paradox is the “Tortoise and the Hare”, where he purportedly demonstrates a slow-moving tortoise, if given a head start, can never be overcome by a speedy hare.

How can this be?

Well, we’re told, surely the hare, in pursuing the tortoise, must move half the distance to the tortoise.

But in the time it takes the hare to move this distance, the tortoise itself has moved. Hence, when the hare again attempts to overtake the tortoise, it must again move halfway to the tortoise. Clearly, every time the hare moves halfway, the tortoise has moved, albeit slightly.

Hence, we’re told, the always-moving tortoise will never be overtaken by the rapidly-approaching hare, which must infinitely make up “half-distances”.

Of course, we know in reality the hare does overtake the tortoise, just as a fast-moving runner overtakes the plodding jogger. Why did Zeno himself not recognize his logic did not conform with reality, and wonder himself where he went wrong?

Richard Feynman, the great physicist, verbalized this wonderfully in “Surely You’re Joking, Mr. Feynman!”. While at Princeton pursing his graduate degree, Feynman was talking with the mathematicians, who claimed you could cut up an orange into a finite number of pieces, and, putting it back together, arrive at something as big as the sun.

“Impossible”, claimed Feynman.

When given the mathematical explanation about cutting the orange, Feynman interjected: “But you said an orange! You can’t cut an orange peel any thinner than the atoms.”

When given further mathematical justification about being able to cut continuously, Feynman concluded, “No, you said an orange, so I assumed that you meant a real orange.”

Indeed – dealing with reality.

A GEOMETRICAL PARADOXICAL PERSPECTIVE

Rather than deal with this specific paradox, let’s modify the behavior of the tortoise, and say he doesn’t move at all. What of the course of action of the hare? How can we visualize it? With the ending point stable, we need only graph the halfway point between the ever-changing starting point and the stable ending point. Let’s see:

This certainly gives me a visual idea of what’s going on, but now I’d like to change the rules a bit. Rather than continuing in the same direction, always halving my distance to the goal, what would happen if I go halfway, and then wherever I am, I choose randomly to continue on in the same direction, or turn around, going in my new direction half the distance to the starting point in that direction. What would this look like? Let’s graph a few points:

This new rule seems to have me going back and forth to many, many different points. What happens if I continue the pattern for a 1,000 movements? Let’s see:

As expected! I eventually hit every spot between the starting point and the ending point.

SHIFTING TO TWO DIMENSIONS

I’ve focused on only one direction. What happens if instead I can go in two dimensions? What happens if I have a square? My intuition tells me if, in one dimension I eventually landed on every point on the line, in two dimensions I should cover every point on the square.

Carrying out the procedure, I get exactly what I expected – a completely filled square:

This seems natural and intuitive: if I bounce around randomly within a certain area, eventually I will hit every point. As this was confirmed by both a straight line and a box, I suspect every shape follows suit. To be safe in confirming my theory, I decide to try the method with a triangle, and am astounded by the result:

How can this be?

Rivers and Dams

March 10, 2008

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To set the stage: rivers have always contributed sediment along the river-route.  What happens to the sediment when a dam is erected?  Does it ever make it past the dam walls?  No. 

The water release at the Glen Canyon Dam, upstream of the Grand Canyon, had a goal of restoring beach sediment.  Likely, such an experiment will not work - nature does this naturally over time - slowly - and not with the release of torrents of water.

But what has this to do with the Nile?

Watching a documentary on the construction of the Aswan Dam on the Nile is where my first thought on this idea of sediment build-up began.

You see, the Aswan Dam sits on the Nile River in southern Egypt, and we're all taught about the "Delta" in the Nile region - the flooding that historically dropped rich soil onto the banks of the Nile, affording tremendous agricultural.  What happens to this marvelous "delta" in a river system affected not solely by one dam, but many?

Well. up to this point, there does not seem a grand thought giving rise to my story.  Dams built for irrigation and electricity.  Pros and cons.  People striving to conquer nature to live better lives.  Where's the story?

When I first started researching the Aswan Dam, one element stood out:  the effects of the Dam were damaging sea-life in the Mediterranean!  The Mediterranean?  How can that be?

And then I realized:  THE NILE FLOWS NORTH!

All my years of education - of seeing pictures of the Nile and maps of Egypt - and not one had depicted the actual flow of the river.  Where did my notion come from?  Likely, the simple bias of most rivers seemingly flowing to the south, coupled with a bias on viewing maps.

What a revelation:  The Nile flows North!

In Search of Simplicity

March 11, 2008

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In Search of Simplicity

Overcoming Math Anxiety in the Teacher and the Student

The idea of “math anxiety” is not new, and a low-performing K-12 math student can feel nothing but anxiety when faced with questions they either do not know how to answer, or do answer – but with uncertainty.

What’s less talked about is math-anxiety relative to the elementary and junior-high teacher who’ve not received a great deal of math education, and instead rely on the materials and lesson plans of others. Faced with questions regarding division of fractions, multiplication of radicals, etc., what recourse do they have? It’s no wonder they too often feel anxious!

Does the continued rigor demanded of teachers and students alleviate this anxiety – or accelerate it? Do lesson plans and manipulatives aid in learning – or become an obstacle – for both the student and the teacher?

An odd question: aren’t manipulatives and hands-on learning good? Aren’t “tried-and-true” lesson plans better than “starting from scratch”? After all, aren’t we told “there’s no reason to reinvent the wheel?”

Let’s look at a few simple examples to make this concrete:

Do these errors look familiar? How can such errors persist in an atmosphere of manipulatives, hands-on activities, critical thinking, etc? The answer is obvious: guessing, but the cause of the problem is less clear.

A more thorough analysis of the constraint and core-problem in our math system will come in future issues. Here, I’d like to focus on one issue relevant to every math classroom in the K-12 environment: manipulatives / hands-on materials.

A Philosophy of Manipulatives

What constitutes a good manipulative? Their use permeates the classroom in all forms of computation, so they must be good. Aren’t they? But why? To what end? For what purpose?

Let’s see if we can address these questions by way of an example: subtraction. Our goal: teach lower elementary students subtraction. How would we do this?

What is the basic idea to be communicated in subtraction? We want to recognize “something being taken away from something else” … three chairs and you remove one chair; 6 books and you remove 2 books; 8 blocks and you remove 1 block; something – and you remove something. The creation of simple blocks or squares, then, moves us in the proper direction.

Will these blocks work? We’re trying to focus on the removal of same things – and these are not the same! We introduced another variable, perhaps a confusing variable: color. Might the child not say “Should I remove any two blocks – or red blocks? Can we avoid such confusion?

We can then proceed to a number of problems using our simple yet good manipulatives:

Is this appropriate for all subtractions – or just some? For example: what about 23 subtract 12? Here we encounter a problem, because there’s likely to arise an error in simply counting the 23 blocks out, a second error removing the 12, and finally a third likely error is counting the remainder. What to do? We see above our simple manipulatives are perfect for single-digit subtraction, but beyond that, they are not only inappropriate, they do harm to the mathematical development of the child! What, then, can be done to extend the lesson to help?

Thinking through the logic of subtraction, we realize we’ve jumped into the concept of 10s and 1s. Let’s not be hasty here, because success here is dependent on success at the earlier stage. Has the student mastered that earlier stage, because such mastery is a prerequisite to success at this higher stage?

What exactly is this higher stage? How do I represent 10s and 1s separately? One way:

Does this isolate the idea to be communicated; namely 10s and 1s? Intuitively, it seems of course! Reds are 10s and whites are 1s. However, more fundamental of 10s is the geometric difference between “10 and 1”; have we made this differentiation? No. Further: in such a presentation, we require the child to make one mental calculation (red=10, white=1) prior to any computation. How can we isolate and focus on the concept at hand, namely representing “10s and 1s” separately? The answer is obvious: have one item 10 times as big as the other. Geometrically and visually, we give the student the correct mapping.

Are these simple manipulatives “good”; that is, do they achieve our goal of differentiating 10s and 1s? The former “looks” like it’s much bigger, but have we communicated effectively it is 10 times bigger? Of course not. How can we improve on our manipulative?

Here we have made explicit that which we wanted to communicate … one thing is in reality 10 of the other.

Now, do we simply throw problems at the child, now that we have proper manipulatives for them to deal with? Perhaps. 23-12? Reasonable. 44-33? Reasonable. What about 88-77? We start to get a lot of stuff on the table here, don’t we? And let’s think what we do in such subtraction problems as adults: we simply align numbers and carry out the subtraction? Don’t we? Therefore, at some point here, we want to integrate the manipulative calculation with the arithmetic calculation. At what point? At such a point the manipulatives do not dominate the process, and instead the calculation and the manipulatives as “error-checking” can be employed …

Once this back-and-forth is mastered … actual calculation in conjunction with manipulatives as error-checking, we can move on to higher order numbers – without the manipulatives, which was our goal at this point.

Wait! A further consideration! All of these examples have been chosen because you can take away the ones from a larger group of ones. That is, no borrowing has been necessary. Why were those examples above chosen, excluding the concept of borrowing? Because borrowing is a higher-level of thinking, where “take-away” is a necessary condition to solve the problem. Borrowing requires “exchange” from another place value. Once those prior problems have been mastered, we can move on – to borrowing!

What about “borrowing”? How do we integrate this?

What is the crucial conceptual element regarding “borrowing”? We, as adults, do it with money, we do it with poker chips, and we do it in asking for 5 ones for a five: it’s exchanging one item of equal value for another. We’ve already developed the good manipulatives demonstrating visually and geometrically equality here, so let’s continue with that idea.

Would we start with 94 – 78? Of course not. As noted earlier, such large numbers invite counting error, and we want to isolate “equal value exchange” here. Therefore, lets’ start with an easy one: 23-15. We see, via our good manipulatives, I cannot take five 1s from three; therefore, I must perform a “good trade” trading in one 10 for 10 1s. The simple manipulation can then be performed – here with our manipulatives only, to ensure the idea of quantity being exchanged is reinforced.

Finally, we want to move beyond the use of manipulatives as the method of computing “exchange”, and move on to the borrowing idea we as adults take for granted. Using the same examples as above, with the manipulatives as error-checking, we demonstrate how to perform arithmetically the “good trade” of borrowing:

Once this back-and-forth is mastered … actual calculation in conjunction with manipulatives as error-checking, we can move on to higher order numbers – without the manipulatives, which was our goal at this point.

Now, we’ve mastered all subtraction problems: up to 2-digit – 2-digit. What about larger numbers? How do we create manipulatives for 100s, 1000s, etc.? Do we have to? The goal was to use manipulatives as a means to an end. At this point, we’ve mastered the art of “good trade”, of borrowing, etc. At this point do manipulatives at higher level calculations help – or hinder – the process? At this point, the child should be able to perform the following calculations:

Subtraction Conclusion:

What’s interesting about this process is the majority of the work is done by the teacher – and it’s intellectual work! The thought process necessary to achieve one goal, build on that goal, etc., of what constitutes “goodness” at each stage and what constitutes “badness” are revealing. Most important here is this realization: in doing the work in developing these processes, we realize, especially at the younger levels, we’re cheated when someone hands us a “math box” or a “tried-and-true” lesson plan. Further, we realize the construction of good manipulatives can cost literally nothing! All of the above can be done with simple paper and cutting in the classroom, if necessary.

A last note: the above structure appears very logical and sequential. That’s the goal. Logic and structure are necessary conditions to an effective learning environment. Does this limit the teacher? On the contrary, I believe such an environment invites extraordinary freedom in using a great deal of other materials – or the development of one’s own materials, because now we have criteria to judge what constitutes appropriate materials! Structure and freedom indeed operating simultaneously!

Going back to our original question: now – and only now – does the idea of “manipulatives, hands-on learning, and ‘tried-and-true’ lesson plans” make sense!

A Philosophy of Manipulatives: Summary

Though the Montessori Method is a comprehensive approach to education, it is to many simply “manipulatives”. It is from this movement many of the manipulatives on the market today originated. Have you priced Montessori manipulatives lately? Wow! And the manipulatives themselves assume quality training in the Montessori Method. Both issues make such an effective math environment outside the reach of most schools, given the resource issues faced by many. Do we need to mimic in fact the work of Ms. Montessori? What was the powerful method of Ms. Montessori giving rise to quality education? Was it in the “manipulatives”? Clearly not, as we’ve seen above. Manipulatives outside of context do not help. However, manipulatives with context provide for the foundation for an effective mathematical environment where quality learning can flourish, and it is this environment that is the key to the Montessori Method – or any good method!

Finally, with such an environment detailed above, there are a variety of student learning levels that can be addressed simultaneously … the outstanding math student working with 4-digit calculations need not be constrained by the lower achieving student who is working with manipulatives. Both are afforded the opportunity to proceed at their own speed.

In Search of Simplicity

I started this article with the simple theme: In search of simplicity. Has this process been “simple”? It’s certainly been a lot of work, but “hard” work? I think not! On the contrary, we can see all of this is within the realm of the ordinary adult – provided there is an underlying philosophy of how to create quality materials.

And the result? To what end? Students doing things right the first time? Students proceeding at their own pace? Good materials existing in the classroom at affordable prices being used – rather than sitting unorganized in a box? All of the above, but most importantly, realization the elementary and junior-high math teacher has the ability to generate all of this themselves – this, and many other manipulatives and thinking processes – as we shall see in the next feature.

In Search of Simplicity

The Audible-Ready Tree – A Renaissance in Lesson Planning

The astute reader shall notice the intellectual structure extending from ground to sky, a logical girder system of proper action coupled with behaviors to avoid ... the "audible ready tree" first mentioned here.  It's structure is reminiscent of  Louis Sullivan's "tall office building - artistically considered":

The Simplest Equation in the World

The Mandelbrot Set

March 12, 2008

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What comes to mind when I say “geometry”? Triangles? Spheres? Generally, shapes – and maybe proofs regarding the similarity of triangles, distance formulas, and the Pythagorean Theorem? What shape is a basketball? Sphere. What shape is a football field or basketball count? Rectangle. How do planets orbit the sun? Elliptically. The answers come so quickly I’m certain I know quite a lot about geometry. What about a fern? The clouds? A snowflake? Do these have “shapes”?

These are all the result of nature, and they’re not “math-related”? I didn’t initially believe so – until I saw the following created by a very simple math formula:

What I’ve found, however, is an amazing story about an amazing man who developed the word “fractals” and discovered the above graphic using a very simple mathematical process. Until the discovery of the computer, such a process was theoretical only; the shear amount of computations required to do this was insurmountable. However, in 1979, Benoit Mandelbrot undertook this problem with the aid of computers. What exactly did he do? More importantly, can I do it?

The Nature of "Complex Numbers"

Normally, we view numbers as behaving "regularly".  For example, if I continue to double a number, I go from 1 - 2 - 4 - 8 - 16 ... No mystery here.  What happens if I multiply two complex numbers?  Odd things!  Sometimes!  Infinitely!  Unexpectedly!

Here is not the place for how the images below come into being - that's done more practically at =EQUALS=, located here.  Here, I'd just like to show a little of what's possible with a simple formula, iteration, and massive computing power at the fingertips of the average person.  Below are pictures of "the Mandelbrot Set", zooming in to great magnification.

Neither Rhyme Nor Reason

Understanding Shakespeare and Hamlet

March 13, 2008

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 A Starting Point - ANY Starting Point

The King of Denmark has unexpectedly died, and Hamlet, believing the death was accidental, is confronted by the Ghost of the King.  The Ghost tells Hamlet the death is no accident - it was murder - and the murderer no less than the King's own brother!  What would you do in such a situation?  How would you feel?  Hamlet clearly wants to avenge his father's murder.

Not exciting stuff for the good reader, but for myself?  This bit of work was in fact a great deal of work!  To merely build this little scenario provides me the "foothold" necessary to "get into the book":

A Second Point

But here I've merely used my logical thinking processes to launch myself into the book - is this what Shakespeare actually said?  Now that I have an idea what the story is about, I can "read with meaning", and see if this is what Shakespeare did say.

But more than this, I can put my logical language into narrative format - and create my own "summary" along the way ...

Narrative Summary: A Brief Outline

The King of Denmark has died, and his ghost has appeared to tell the surviving son Hamlet the death was no accident! Death by murder, is the charge, with the King's own brother the murderer! Hamlet devises a plan to reveal the murderer for all to see. In the following pursuit of justice, Hamlet ends up killing a man (Polonius), another man (Laertus), and the King, while his girlfriend (Ophelia) kills herself, and his mother (Queen Gertrude) accidentally dies drinking a glass of poisoned wine meant for Hamlet.

Narrative Summary: A Detailed Outline

The Context of the Play: The guards at the palace gates are confronted by the Ghost of the King of Denmark. The King has died, and the King's brother, Claudius, has ascended to the throne. The King's death was believed accidental, but now the ghost tells his son, Hamlet, the death was murder, and Claudius the murderer! With this information, the justice-seeking Hamlet seeks to avenge his father's murder.

Hamlet’s Problem: Learning of his father's fate, the furious Hamlet wants to avenge his father's murder. What son would not? Yet, how has Hamlet learned of his father's fate? By a ghost? His fellow Denmarkians, on the other hand, still believe the King's death was an accident. Should Hamlet avenge his father's death, he realizes he himself will not be viewed favorably by his fellow Denmarkians. However, Hamlet - as a Denmarkian - wants to be viewed favorably by his fellow countrymen! Therefore, Hamlet must devise a way to reveal the death of his father as murder for all to see. Only then can justice prevail - in all eyes.

Hamlet’s Problem Reconsidered: What should Hamlet do? Only he knows of the words of the ghost. But are these words to be believed? Who would consider the testimony of an apparition reasonable? Should I take the advice, or not take the advice of the apparition? What to do, what to do, what to do? Let's think deeper: why would I not follow the advice? Clearly, because ghosts do not exist, and Hamlet wants to act rationally. On the other hand, why would I follow the advice? Again, the obvious reason: if a murder has been committed, the murderer need be brought to justice. Is there a common goal here, between these two legitimate needs – justice and rationality? Let's choose a general goal: I want to lead a virtuous life. Where does this lead us? A good goal, implying legitimate needs, yet leading to a dilemma. What should I do?

Hamlet’s Solution (Injection): "Think, Hamlet, think", Hamlet says to himself. "How can I find out if this apparition tells the truth?" I've got it! Suppose I somehow devise a plan that makes my uncle reveal himself as a murderer for all to see? That would do it. But how can I do this? What murderer reveals himself? There is a play coming to town. I shall speak to the actors, and change the play "The Murder of Gonzago" so the plot is consistent with my father's murder - as told me by the ghost. Seeing the plot unfold, surely my uncle will display discomfort - deja vu if you will - and he will therefore reveal himself as the murderer.

Consequences of the Play: Hamlet has a talk with the actors regarding their past great performances, and wonders if they can modify the play, "The Murder of Gonzago", which they do. Expectedly, the King shows great discomfort at the revised plan, and Hamlet now knows the Ghost has spoken the truth! His uncle is a murderer. Hamlet reasons, because a murderer, a quick death is inappropriate and non-equivalent to the evil done his father. Hamlet therefore decides he will wait until the greatest harm can be done the king.

The Tragic Consequences of the Play: Hamlet also does not want to let his mother off easy; after all, she has taken up marriage with the murderer of his father! Surely, his mother knows nothing about the murder, and Hamlet decides to confront her with the wickedness of the situation. Seeing his rage, she cries for help, and Polonius (hiding in the room behind curtains), too cries for help! Hamlet, believing the second cry is from his uncle, stabs through the curtains only to see it is Polonius he has killed - and not his uncle!

The King’s Ambitious Target: The King learns of the accidental death, and sees a way out of his problem. I will send Hamlet away, and have him killed by others! How can I make this happen, reasons the king? I will send two couriers - his trusted friends Rosencrantz and Guildenstern - with Hamlet with letters to deliver to the King of England. These letters will detail the murder of Polonius, and request England take Hamlet's life! All my problems are solved!

Hamlet’s Response: Hamlet, realizing something sinister is going on, instead takes charge of the letters, and realizes his fate. Not wanting the couriers to realize he knows all, Hamlet simply changes the wording to say "Kill the couriers", rather than "Kill Hamlet". Of course, once reaching England, the couriers are immediately killed, and Hamlet decides to return to Denmark to avenge his father's death. The King, hearing of his failed plan and Hamlet's goal, must think of another way of having Hamlet taken care of.

Poor Ophelia: In the meantime, let us recall Hamlet has accidentally killed Polonius, believing Polonius' cry for help was that of the King. Ophelia, understandably, is saddened by her father's death, and becomes despondent. Climbing a tree one day, she accidentally falls into a brook, but tries not to save herself. Ophelia has killed herself.

The Angry Laertus: What of Ophelia's brother and Polonius' son, Laertus? He too learns of the murder of HIS father, and, rather than the despondency of Ophelia feels extreme rage, and demands vengeance on the King. The King explains it was Hamlet, and not the King, who has killed Polonius. Hamlet! Learning of Ophelia's death, he blames Hamlet all the more, and demands Hamlet be dealt with appropriately.

The King’s Ambitious Target: The King, seeing a second chance to fix his problem, reasons as such with Laertus: let us prepare a fencing match with Hamlet, with the prelude it being a friendly match. Surely, in such a match, his expectation can be used to your advantage. To ensure we win and Hamlet is killed, we shall poison your rapier. Finally, let's assume Hamlet is not killed by your rapier. What can we do to ensure he ends up dead nonetheless? Let's poison his wine, for in the celebration of possible victory, he shall surely drink his wine. Surely, this will ensure his death!

The Duel and Tragic Outcome: The fencing commences, and Hamlet realizes the match is more competitive than he was led to believe. The king seizes the opportunity, during a break in the action, to offer Hamlet a drink from the poisoned wine. Hamlet refuses, and the duel continues. Queen Gertrude, however, sees the wine, and takes a drink. Her fate is sealed, and she slowly starts to die.

The Duel and Tragic Outcome: As the match continues, the rapiers fall to the ground and, in the struggle and confusion, change hands. Hamlet, unknown to him, is in charge of the poisonous rapier! Being a good dueler, he eventually strikes Laertus. Both Laertus and Queen Gertrude now are in the dying process.

The Duel and Tragic Outcome: Laertus' last words reveal the plot to poison Hamlet, and Hamlet now really seeks vengeance on the King. He stabs his uncle, and makes him also drink the poisonous wine. Tragically, Hamlet has been nicked by the poisonous napier, and he too is on his deathbed. The play ends, with the Uncle, Hamlet, Queen Gertrude, and Laertus all killed in this tragic duel gone awry.

Resolution: Hamlet gains the vengeance sought the entire story, but has failed to tell fellow Denmarkians of his father's murder! The witnesses to the act, of course, yell "Treason!", for all they have seen is one man kill the King. Only Hamlet and Horatio know the truth, and Hamlet now is on his deathbed. He convinces Horatio to report to the crowd the circumstances surrounding the death, and to tell Hamlet's story.

Integrity

March 14, 2008

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round@rationalsys.com

Former Chairman of the Federal Reserve wrote of the nature of capitalism in 1963, and of the inevitable result of government intervention in the economy ...

THE ASSAULT ON INTEGRITY

An Article by Alan Greenspan, written in 1963

Capitalism: The Unknown Ideal by Ayn Rand

Protection of the consumer against “dishonest and unscrupulous business practices” has become a cardinal ingredient of welfare statism. Left to their own devices, it is alleged, businessmen would attempt to sell unsafe food and drugs, fraudulent securities, and shoddy buildings. Thus, it is argued, the Pure Food and Drug Administration, the Securities and Exchange Commission, and the numerous building regulatory agencies are indispensable if the consumer is to be protected from the “greed” of the businessman.

But it is precisely the “greed” of the businessman, or, more appropriately, his profit-seeking, which is the unexcelled protector of the consumer.

What collectivists refuse to recognize is that it is in the self-interest of every businessman to have a reputation for honest dealings and a quality product. Since the market value of a going business is measured by its money-making potential, reputation or “good-will” is as much an asset as its physical plant and equipment. For many a drug company, the value of its reputation, as reflected in the salability of its brand name, is often its major asset. The loss of reputation through the sale of a shoddy or dangerous product would sharply reduce the market value of the drug company, though its physical resources would remain intact. The market value of a brokerage firm is even more closely tied to its goodwill assets. Securities worth hundreds of millions of dollars are traded every day over the telephone. The slightest doubt as to the trustworthiness of a broker’s word or commitment would put him out of business overnight.

Reputation, in an unregulated economy, is thus a major competitive tool. Builders who have acquired a reputation for top quality construction take the market away from their less scrupulous or less conscientious competitors. The most reputable securities dealers get the bulk of the commission business. Drug manufacturers and food processors vie with one another to make their brand names synonymous with fine quality.

Physicians have to be just as scrupulous in judging the quality of the drugs they prescribe. They, too, are in business and compete for trustworthiness. Even the corner grocer is involved: he cannot afford to sell unhealthy foods if he wants to make money. In fact, in one way or another, every producer and distributor of goods or services is caught up in the competition for reputation.

It requires years of consistently excellent performance to acquire a reputation and to establish it as a financial asset. Thereafter, a still gr