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 greater effort is required to maintain it: a company cannot afford to risk its years of investment by letting down its standards of quality for one moment or one inferior product; nor would it be tempted by any potential “quick killing”. Newcomers entering the field cannot compete immediately with the established, reputable companies, and have to spend years working on a more modest scale in order to earn an equal reputation. Thus the incentive to scrupulous performance operates on all levels of a given field of production. It is a built-in safeguard of a free enterprise system and the only real protection of consumers against business dishonesty.

Government regulation is not an alternative means of protecting the consumer. It does not build quality into goods, or accuracy into information. Its sole “contribution” is to substitute force and fear for incentive as the “protector” of the consumer. The euphemisms of government press releases to the contrary notwithstanding, the basis of regulation is armed force. At the bottom of the endless pile of paper work which characterizes all regulation lies a gun. What are the results?

To paraphrase Gresham’s Law: bad “protection” drives out good. The attempt to protect the consumer by force undercuts the protection he gets from incentive. First, it undercuts the value of reputation by placing the reputable company on the same basis as the unknown, the newcomer, or the fly-by-nighter. It declares, in effect, that all are equally suspect and that years of evidence to the contrary do not free a man from that suspicion. Second, it grants an automatic (though, in fact, unachievable) guarantee of safety to the products of any company that complies with its arbitrarily set minimum standards. The value of a reputation rested on the fact that it was necessary for the consumers to exercise judgment in the choice of the goods and services they purchased. The government’s “guarantee” undermines this necessity; it declares to the consumers, in effect, that no choice or judgment is required – and that a company’s record, its years of achievement, is irrelevant.

The minimum standards, which are the basis of regulation, gradually tend to become the maximums as well. If the building codes set minimum standards of construction, a builder does not get very much competitive advantage by exceeding those standards and, accordingly, he tends to meet only the minimums. If minimum specifications are set for vitamins, there is little profit in producing something of above-average quality. Gradually, even the attempt to maintain minimum standards becomes impossible, since the draining of incentives to improve quality ultimately undermines even the minimums.

The guiding purpose of the government regulator is to prevent rather than to create something. He gets no credit if a new miraculous drug is discovered by drug company scientists; he does if he bans thalidomide. Such emphasis on the negative sets the framework under which even the most conscientious regulators must operate. The result is a growing body of restrictive legislation on drug experimentation, testing, and distribution. As in all research, it is impossible to add restrictions to the development of new drugs without simultaneously cutting off the secondary rewards of such research – the improvement of existing drugs. Quality improvement and innovation are inseparable.

Building codes are supposed to protect the public. But by being forced to adhere to standards of construction long after they have been surpassed by new technological discoveries, builders divert their efforts to maintaining the old rather than adopting new and safer techniques of construction.

Regulation – which is based on force and fear – undermines the moral base of business dealings. It becomes cheaper to bribe a building inspector than to meet his standards of construction. A fly-by-night securities operator can quickly meet all the S.E.C. requirements, gain the inference of respectability, and proceed to fleece the public. In an unregulated economy, the operator would have had to spend a number of years in reputable dealings before he could earn a position of trust sufficient to induce a number of investors to place funds with him.

Protection of the consumer by regulation is thus illusory. Rather than isolating the consumer from the dishonest businessman, it is gradually destroying the only reliable protection the consumer has: competition for reputation.

While the consumer is thus endangered, the major victim of “protective” regulation is the producer: the businessmen for reputation undermines the market value of the good will which businessmen have built up over the years. It is an act of expropriation of wealth created by integrity. Since the value of a business – its wealth – rests on its ability to make money, the acts of a government seizing a company’s plant or devaluing its reputation are in the same category: both are acts of expropriation.

Moreover, “protective” legislation falls in the category of preventive law. Businessmen are being subjected to governmental coercion prior to the commission of any crime. In a free economy, the government may step in only when a fraud has been perpetrated, or a demonstrable damage has been done to a consumer; in such cases the only protection required is that of criminal law.

Government regulations do not eliminate potentially dishonest individuals, but merely make their activities harder to detect or easier to hush up. Furthermore, the possibility of individual dishonesty applies to government employees fully as much as to any other group of men. There is nothing to guarantee the superior judgment, knowledge, and integrity of an inspector of a bureaucrat – and the deadly consequences of entrusting him with arbitrary power are obvious.

The hallmark of collectivists is their deep-rooted distrust of freedom and of the free-market processes; but it is their advocacy of so-called “consumer protection” that exposes the nature of their basic premises with particular clarity. By preferring force and fear to incentive and reward as a means of human motivation, they confess their view of man as a mindless brute functioning on the range of the moment, whose actual self-interest lies in “flying-by-night” and making “quick kills”. They confess their ignorance of the role of intelligence in the production process, of the wide intellectual context and long-range vision required to maintain a modern industry. They confess their inability to grasp the crucial importance of the moral values which are the motive power of capitalism. Capitalism is based on self-interest and self-esteem; it holds integrity and trustworthiness as cardinal virtues and makes them pay off in the marketplace, thus demanding that men survive by means of virtues, not of vices. It is this superlatively moral system that the welfare statists propose to improve upon by means of preventive law, snooping bureaucrats, and the chronic goad of fear.

The Incredible Bread Machine

March 15, 2008

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round@rationalsys.com

The "Rise and Fall" of NY Governor Spitzer may seem a "tragedy" to commentators.  This commentator instead sees government at its worst - using laws as silly putty, non-objectively and selectively attacking businesses for personal gain, all-the-while violating the same laws.

The great R.W Grant wrote the following poem regarding the nature of "improper" laws and a government running wild ...

The Incredible Bread Machine

By R.W. Grant

This is the story of a man whose name

Was a household word: a man whose fame

Burst on the world like an atom bomb;

Smith was his last name; first name Tom.

Now, Smith, an inventor, had specialized

In toys, so people were surprized,

When they found that he instead

Of making toys, was BAKING BREAD!

The way to make bread he'd conceived

Cost less than people could believe!

And not just make it! This device,

Could in addition, wrap and slice!

The price per loaf, one loaf or many,

The miniscule sum of under a penny!

Can you imagine what this meant?

Can you comprehend the consequent?

The first time yet the world well fed,

And all because of Tom Smith's bread.

A citation from the President,

For Smith's amazing bread,

This and other honours too,

Were heaped upon his head!

But isn't it a wonderous thing,

How quickly fame is flown?

Smith, the hero of today,

Tomorrow, scarcely known!

Yes, the fickle years passed by,

Smith was a millionaire,

But Smith himself was now forgot,

Though bread was everywhere...

People, asked from where it came,

Would very seldom know.

They would simple eat and ask,

"Was not it always so?"

However, Smith cared not a bit,

For millions ate his bread . . .

And everything is fine, thought he,

I am rich, and they are fed!

Everything was fine, he thought,

He reckoned not with fate.

Note the sequence of events,

Starting on the date,

On which the business tax went up.

Then, to a slight extent,

The price on every loaf rose too -

Up to one full cent!

"What's going on?" the public cried,

"He's guilty of pure plunder!

He has no right to get so rich

on other peoples hunger!"

(A Prize cartoon depicted Smith,

With fat and drooping jowls,

Snatching bread from hungry babes,

indifferent to their howls!)

Well, since the public does come first,

It could not be denied

That in matters such as this,

The Public must decide!

So Anti-Trust now took a hand,

Of course, it was appalled

At what it found was going on.

The "Bread Trust" it was called.

Now this was getting serious,

So Smith felt that he must

Have a friendly interview

With the men in Anti-Trust.

So hat in hand, he went to them.

They'd surely been misled;

No Rule of Law had he defied.

But then their lawyer said:

"The Rule of Law, in complex times,

Has proved itself deficient.

We much prefer the Rule of Men,

It's vastly more efficient!"

"Now let me state the present rules,"

The lawyer then went on,

"These very simple guidelines,

You can rely upon:"

"You're gouging on your prices if

You charge more than the rest.

But it's unfair competition if

You think you can charge less!"

"A second point that we would make

To help avoid confusion . . .

Don't try to charge the same amount,

That would be Collusion!"

"You must compete. But not too much,

For if you do you see,

Then the market would be yours -

And that's Monopoly!"

Price too high?

Or Price too low?

Now, which charge did they make?

Well, they weren't loath to charging both,

With Public Good at stake!

In fact, they went one better!

They charged "Monopoly!"

No muss, no fuss, oh, woe is us!

Egad, they charged ALL THREE!

Five Years in jail, The Judge then said

"You're lucky it's not worse!

Robber Barrons must be taught,

Society comes first!"

Now bread is baked by government.

And as might be expected,

Everything is well controlled.

The Public well protected.

True, loaves cost a dollar each,

But our leaders do their best!

The selling price is half a cent..

Taxes pay the rest.

Three Layers of Causality

March 16, 2008

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round@rationalsys.com

Why is this?  One thing that stands out is the amount of daylight / sunlight throughout the year.  During the summer, it seems to stay bright forever, while during the winter, it seems the sun is going down as soon as the kids are home from school.  Does this have anything to do with the above graph?  Let's graph the amount of sunlight and see:

The causality is clear - when there is maximum sunlight, we see the highest temperatures.  On the other end of the spectrum, where sunlight is at a minimum, we see the lowest temperatures.  Not a startling statement, but neat to see the relationships visually.  In fact, the definition of "solstice" (maximum) and "equinox" now also have a visual interpretation - we can see, about 3/26, the sun rises about 5:45 in the morning and sets at 5:45 in the evening, meaning there is equal amounts of sunlight and nighttime; i.e., the equinox!

But why stop here?  Why is it there are unequal amounts of sunlight throughout the year?  The earth revolving about the sun?  The axis of rotation?  Yes.  Therefore, let's show it:

A Good Man

Lew Anderson:  Part 1

March 17, 2008

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round@rationalsys.com

Lew Anderson: My Friend

A Logical Biography

The second world war was in full force, with battles raging across Europe, when a young man of 20 entered the military office on the campus of Gustavus-Adolphus College in St. Peter, Minnesota, to enlist in the Army Air-Force. Lew Anderson was entering the war.

“I thought if I were drafted, I would go into the regular army, and I really wanted to go into the Navy Air-Force, so I volunteered.”

The draft? To many of us, it’s just a word with little meaning. The draft was discontinued in 1981, but was in place during WWII. It has an interesting origin.

The Union had instituted the draft in the Civil War, but allowing draftees to opt out if they could find a substitute led to the perception of unfairness. The draft was discontinued, and not reinstated until 1917 during WWI.

But the army air-force? I thought there was only the air-force. Where did the idea of “army” and “navy” air-force come from?

After the Wright Brothers invented the airplane at Kittyhawk, North Carolina, both the Army and Naval branches of the military sought to enhance their fighting capabilities with air force. This gave rise to the dual branches of the Air Force: the Army Air-Force and the Naval Air-Force. These forces were consolidated into one unit, the Air Force, we know today.

“I wanted to join the Navy Air Force, but my friend’s father would only allow his son to join the Army Air Force, so that’s the direction we took.” Why the desire to join the Navy Air Force? “Landing on a carrier really excited me. I thought it neat these people could take off and land on a carrier.”

Fly he did.

The War

After five months of ground training at Washington University in St. Louis, three months primary training at Uvalde, Texas, three months basic and three months _______ training at Waco, Lew was stationed at Grottaglia, Italy in 1943.

How did the US come to establish a foothold in Italy for staging operations in the European campaign?

The Italian dictator Benito Mussolini had fallen in 1943, and the new Italian government was secretly conducting negotiation meetings with the Allies. This proved advantageous to the allies. With a base of operations south of German-held territory, the allies could effectively engage the axis in Europe. Italy was “the soft underbelly of Europe”.

Staging Operations

Operating out of the Naval Base at Taranto, Italy (just inside of the ‘heel of the boot’), Lew was stationed at Grottaglie (just north of Taranto), Lew began operations as a B-24 co-pilot.

Things quickly changed.

On the 7th mission, the pilot was shot. Lew took command and was the pilot for the remainder of the 33 bombing runs on Austria and Southern Germany. The 8-hour round trip about this B-24 took Lew over the Alps.

A typical mission began with a mission-briefing at 5:30 AM. Take-off was about 8:00 AM, returning anywhere from 3:00-5:00 in the afternoon, followed by a briefing by a senior officer.

Lew recalls the slight celebration of the crew upon landing from a successful mission: “We were served a shot of bourbon. There were some crew-members, of course, who did not drink, so we were glad to take their shot for them.”

“And then we heard back home some woman’s group against drinking raised hell because their boys were being served liquor!”

Lew recalls one mission where his smoking habit didn’t mix well with flight gear. Below 10,000 feet, one can breathe regular air, but above 10,000, you must wear your mask. On the return flight back to base, those of us who were smokers were so anxious to smoke at about 12,000-14,000 feet, we’d take off our oxygen masks, take a drag, and immediately get a blinding, splitting headache. We knew it was going to happen, but the need for the smoke was so great we couldn’t resist! Just horrible!”

Returning to the USA after the war’s conclusion, Lew was stationed at Chandler Air Base in Chandler, Arizona, and received his discharge in Sioux Falls, South Dakota.

Imagine his surprise, when, after his physical during the discharge process, he was told he was color-blind, and couldn’t be a pilot!

Good Intentions Gone Bad

The Philosophical Origins of "The New Math"

March 18, 2008

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round@rationalsys.com

The story of the rise and fall of the “new math” has been told so many times, it’s tempting to think of it as a fad occurring nearly ˝ century ago, with little to do with modern mathematics. Whether or not that’s true, we shall see, but to be certain we’re reasonably thorough in our understanding of history, let’s take a brief look.

The New Math, implemented in the 1960s, had noble origins and good intentions. The 19th and early-20th centuries had seen the erosion of “certainty” from the once-solid foundations of math. Euclidean geometry, the calculus, and set theory were under assault at the ground level for inconsistencies, contradictions, and non-intuitive results. As a result, a paradigm shift in mathematics took place, the goal: shore up the foundations of math.

When the Soviet Sputnik created the USA mathematical / scientific panic igniting the New Math movement, the above curriculum paradigm shift was put into action. The strategy and tactic? In order to achieve good mathematical results, we must start our kids on the road to certainty at an early age.

Of course, it did not take long to realize we were not achieving that noble goal with that tactic, and it also did not take long to realize why not! There was a crucial assumption that had not been considered: the pedagogy is sound.

We quickly realized the flaw in the “new-math” implementation plan: our kids were not ready for the material. It was no surprise. It had taken thousands of years to reveal the inconsistencies, contradictions, and non-intuitive results in math, we sought to restructure the math, and we did not give a moment’s thought to whether this was good – for kids? We knew, having practiced it in academia for ˝ century it was good for adults, and assumed what’s good for adults is also good for children. This was the underlying assumption in judging the pedagogy of the New Math.

This part of the story is well-known.

A less pursued angle of this tragic story is the following question: “The Sputnik incidence launched the ‘new math’ principles. Why were these the new principles that were launched?”

As the great mathematician Morris Kline has so well pointed out, math through the ages had been considered the apex of logical thought and consistency. As in many sciences, when issues arose challenging the status quo, the issues are dealt with on an ad hoc basis, and the underlying philosophy left unchanged.

However, as Thomas Kuhn points out in The Structure of Scientific Revolutions, infrequently an anomaly arises challenging the philosophical status quo, and cannot be explained away.

THE ORIGINS OF “SOUND PRINCIPLES”

The Geometric Anomaly

Such was the case with Euclidean Geometry. In the creation of the systematic understanding of geometry, Euclid had sought to start with sound principles – postulates – and reason deductively. These postulates were as follows:

1. A straight line may be drawn between any two points;

2. A piece of straight line may be extended indefinitely;

3. A circle may be drawn with any given radius and an arbitrary center;

4. All right angles are equal;

5. If a straight line crossing two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if extended indefinitely, meet on that side on which are the angles less than the two right angles.

This fifth postulate, the so-called “parallel postulate”, so differed from the others in clarity, mathematicians throughout the ages sought to prove the theorems of geometry without reference to it. This postulate equated to saying the sum of the degrees in a triangle equal 180 degrees.

We now know there are other geometries where this assumption IS NOT valid – these “non-Euclidean geometries” were as consistent as Euclidean geometry.

The troubling aspect of this discovery, of course, was the revolution it sparked. After all, it was believed, Euclidean Geometry was believed to be the apex of consistency in a discipline itself at the apex of consistency – and now, to realize the foundations were in fact not as solid as believed?

THE ORIGINS OF “SOUND PRINCIPLES”

The Calculus Anomaly

Of course, one issue does not destroy a movement, and such is the case with geometry. In the 17th century, the formulation of the calculus – by Newton and Leibniz – gave rise to a new method of the analysis of nature. How did this method move forward? The controversy really is as old as the study of math, and can be traced, analogically, to the well-known paradoxes of Zeno.

If I say it’s impossible to fill a cup with water, intuition tells us that’s nonsense, and, placing the cup under the faucet, the claim is quickly disproved, as the water reaches the top of the cup, eventually pouring over.

However, if I point out to you in order to fill the whole cup, you must first fill ˝ the cup. Obviously. However, once ˝ the cup is filled, the cup must again fill the remaining ˝ cup ˝ the way. Continuing the process, we see there is an infinite progression of “one-halves”, getting ever-and-ever closer to a full cup, but not quite getting to the rim of the cup.

What has this to do with the calculus? The notion of the calculus rests on the concept of change over time. We’re accustomed to averages such as miles / hour, the common metric being a certain distance traveled over a certain period of time. Of course, with stoplights, and reststops, the average time does not necessarily refer to the average speed at a particular point, but generally over the entire trip.

What happens if we want to know what the speed is at a particular point in time? It would seem we would be dividing by zero time, because there seems to be no change.

However, certain mathematical manipulations by both Newton and Leibniz gave rise to right answers, despite the awkwardness of the “divide by zero” issue.

As with the issue in Euclidean Geometry, this “lack of rigor” troubled the math profession, and consequent issues regarding this issue of limits and infinity tore away at the fabric of certainty once covering the profession.

THE ORIGINS OF “SOUND PRINCIPLES”

The Set Theory Anomaly

In the 19th century, the notion of dealing with mathematics by way of “sets” was seen as a possible method of dealing with the inconsistencies plaguing the once certain profession of mathematics. Set theory is the mathematical theory of sets, which represent collections of abstract objects. It encompasses the everyday notions, introduced in primary school, of collections of objects, and the elements of, and membership in, such collections. In most modern mathematical formalisms, set theory provides the language in which mathematical objects are described.

In this regard, the simple notion of “counting” took on a new look. If one wanted to know if there were enough chairs for participants in a conference, for example, one could align each person with a chair to answer the question. Is there a 1-1 correspondence between “participants” and “chairs”? If so, the “sets” are equal.

Intuitively, this notion of “equality” is consistent with our ordinary experience.

However, let’s extend this idea of “correspondence” and “equality” a step further. Are there as many even numbers as there are integers? Of course, the answer is no. But is it? Using our previous definition of “equality”, we see the following:

There IS a 1-1 correspondence, and therefore, by the definition of set theory, the two sets are equal! Yet this seems inconsistent with our everyday reasoning. What’s going on here?

RE-ESTABLISHING CERTAINTY

It’s hard to imagine what this set of crises did to the mathematicians in that age. A once-certain profession, faced with major attacks on the foundations of their subject, had to rethink what exactly was going on. What would you do if faced with such a crisis of confidence?

But what is the problem? The lack of logical consistency. It makes sense, then, to shore up the foundations of the branches of math via rigorous methods to ensure the result is logical consistency.

But what constitutes rigor in this regard?

A PARADIGM SHIFT IN EDUCATION

Is it any wonder there was a concerted effort to change math as it was once conceived? With the erosion of certainty and the emergence of logical contradictions, it’s natural to rethink – rigorously – what exactly the science is. If numbers lie at the core of the profession, for example, and the results of the 19th century application of math yields inconsistencies, it makes perfect sense to rethink what exactly a number is.

If logical inconsistency lies at the heart of the problem, it makes sense to rededicate oneself to understanding what exactly constitutes logical reasoning. Moreover, can a system of logic be developed and applied at the core of the “new math” to ensure logical consistency is achieved?

Finally, the fear in any industry is though something may work in one circumstance, it may fail in another. This belief held as well for mathematicians at the turn of the 18th-19th centuries. How does one ensure logical consistency is maintained in all contexts? We make our mathematical systems independent of all objects – and simultaneously applicable to all objects!

How was this rigor actually applied?  Is it still being applied?

Cars, Trains, and Systems

March 19, 2008

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round@rationalsys.com

As the price of gas creeps towards $3.50 / gallon, for example, one thought is: do driving habits really change?  I'm certain I've not curtailed any habit because of the price of gas.  "Have I?" is one question.  Another is: "Would I ever?"  If the price soared to $10 / gallon, would this change my habits?  $20?  Of course.  Of course there's a point where I would carpool or put off a trip. 

But even this logic needs to be clarified, I believe.  Ask a person two years ago if they'd pay $3.50 / gallon, and would they change habits, and the likely response would be "yes".  Here we are, and they're not.  Why not?  Likely it's because the price of gas has crept up, and we find ourselves like the proverbial frog in the pan.

Does it take abrupt changes in the system to extract change from the system? 

A Thought About Change

For the time-being, I'd like to concentrate on light-rail, and more generally, about change - in demographics and logistics.  "Suburban-sprawl" is a term said with denigration.  That's neither here nor there; what I want to take a peek at is why it happens.

A starting point may be this: there are many people in the city.  We were an agricultural society.  We became an industrial one.  People flocked to the cities for work.  Now they're in the city, and it's a new day.  Crowded.  Dirty.  Yes - dirty.  People want openness.  To get away from this.  To have a yard.  To live in - the suburbs.

Of course, it's one thing to want to live in the suburbs.  It's another to make it happen.  Let's not forget our job is still in the city.  We need to get back and forth to our job in the city, which means meaningful transportation.  A good highway system.

But does the "system" stop here?  Of course not.  With a better highway system, more urbanites see an opportunity to move to the suburbs effortlessly!  The highways are bigger and more convenient.  And with this - what happens - inevitably?  More people move to the suburb!  But with more people living in the suburb, what is the natural and clarion call?  Better highways to get us to the city! 

Closing Thoughts

Does such a system ever reach an "equilibrium"?  Probably.  All systems with feedback loops do - I think.  But what constitutes "equilibrium"?  Maybe that's not the right word, because great Roman cities of millions of people were vacant decades later.  Gold towns in the west become deserted.  Cities can dry up.  "Equilibrium" is not the right word.  This feedback loop cannot continue infinitely - that's what I'm searching for.

But what are the costs?  Are there any?  Is a grand 6-lane highway system careening from city to city what we want?  Are the suburbs what we want?  Is a deserted downtown what we want? Were there alternatives to "suburban-sprawl"?  How many people would flee the city if they had to pay for the upkeep of the highway system?  How many people would have moved to the city in the first place if they had to pay for the development of those costs?

What constitutes a "good city"?  What are we looking for?  And is highway transportation the only means to get from here to there?  And here we end up, rethinking the initial consideration in today's article:  what about light-rail?

In the process of researching this issue, and cable, trolley, and interurban rail in the Kansas City area, I came upon an extraordinary item:  there once was a light-rail system extending from Olathe to downtown Kansas City - 100 YEARS AGO!  The Strang Line Interurban ...

Sadly, where does the political discussion of the above start - and stop?  Suburban sprawl is a bad thing - and it must be fixed.  Is it bad?  Must it be fixed?  The above discussion was simply one of logistics.  By what standard is it bad?  Where should the discussion even start?  The questions seem similar - and are similar - to the discussion here ...

The Federal Reserve, the DJIA, and the Visual Display of Quantitative Information

March 20, 2008

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round@rationalsys.com

The KC Star had a wonderful opportunity to lead by example in today's paper.  The Federal Reserve announced a huge rate reduction, hoping to kick-start the economy.  Measurably, this is often viewed - successfully or not - via the performance of the stock market.

The lead article title, "FED DOES HEAVY LIFTING TO PROP UP THE MARKET", suggests the Fed action worked.  Perhaps it merely meant to suggest this was the theory behind the Federal Reserve action.

In either case, here's how the article played out:

Is there a relationship between the DJIA performance and the Federal Fund rate?  It's hard to tell, because the two graphs are side-by-side, rather than superimposed.  Notice too how the y-axis of the "federal fund rate" graph extends from 2.000 to 5.000 (why the third decimal place I don't know), close to the actual data, whereas the y-axis of the "DJIA" graph ranges up to 15,000, though the high point in the 12-month period is only slightly more than 14,000.  This change makes the graph artificially level.  Minor points, but points any graphic designer should consider.  Let's make them here, just for the record, and see what the above graph might look like:

A Deeper Consideration

What I want to consider deeply is the question, "IS THERE any relation between the action of the Federal Reserve and the performance of the market?"

Let's see.

But some considerations:  why stop at 1-year of data.  Let's use a few more to ensure we're not looking at data anomalies.  As we said earlier, the "side-by-side" comparison leaves us guessing as to the relationship.  Let's superimpose the two items.

Well?  What can be concluded from this graph?  It's hard to say anything - at least, to me.  I see a great deal of Fed action, then none, followed by drastic action.  Perhaps this, in itself, is revealing.  What on earth are they doing - what should they be doing?  As to a relationship between their action and the performance of the market, it's not clear to me, even superimposing the two graphs above.

What if we concentrate on the specific dates of the fed policy change?  Will that provide any additional information?  This seems to be what the KC Star article above is saying.  Having said this, we quickly realize this may not be a good barometer.  After all, if a 400-point increase one day is offset by a 400-point decrease the next, has the policy worked?  Has the market rebounded? 

Let's include this cautionary note in our index of change - not solely the performance of the market immediately after the change, but the 2-day average (after versus before) of the market.  What does the graph of the 18 Federal Reserve Fund Rate changes since 1/1/2005 look like?

Let's see.

There seems to be NO relationship!  For example, there were 12 instances where the rate was increased a quarter of a point.  How did the market respond?  You see the results.  What of the Federal Reserve lowering the rate?  Again, the scatter-plot tells us the market is not as "predictable" as the article - or the Federal Reserve - wants.

Closing Thoughts

My article here discussed the theoretical operation of the Federal Reserve and the economy.  One of several logic-graphics there went as follows. 

Is this what we see in reality?  I think not! 

Rethinking Pi-Day

March 21, 2008

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round@rationalsys.com

Pi, most people know, as 3.14... something.  Older people may remember it as 22/7.  Younger people are taught it's something called a transcendental number, meaning it's a number going on forever, non-repeating and non-terminating.

Contests are held, seeing who can remember the most decimal places.  Why not?  If it goes on forever, it's a neat contest, right?

3.141592653589793238462643383279502884197169399375105820974 ... ...

Big Deal.

I'm more interested in what "pi" really means - and not memorizing someone else's digits, but figuring this out for myself.

The concept is as easy as looking at a bike tire.  If I've got a spoke in my tire, how big do I need to make the rim?  It depends!  On what?  The size of the spoke.  The bigger the spoke, the bigger the rim.  But how much bigger?  There's the question:  how much bigger?

If you actually measure, with a tape-measure or a string, you'll see it's about "3 spokes"; that is, 3 spokes laid end to end about equal the size of the rim.  But not exactly.  It's a bit more than three spokes.  We know the relationship now as: C = πd.

How can we approximate this ourselves?  Sure, we could use more precise means of measuring, and we'd get more and more precise results.

What can we do on the computer?

Suppose I draw a circle, and than add a couple items I know the answer to.  I'll draw a square about the circle, and one inside.  It's easy enough for me to calculated the areas of each square.  Here, I've assumed the radius of my circle is one unit, so the length of each of the outside lines is 2 units.  Therefore, the area of the outside square is 4 square units.  I can also find the area of the inside square as 2 units.  (The specific math will show up in the next edition of =EQUALS=).

But so what?  What has this to do with π?  I see the area of the circle is somewhere between two and four, and I also know the area of a circle is:  A=πr² (which is why I chose my radius as '1').

Fine.  I know the value of π is between 2 and 4.  Big deal.  I already knew that.

But what happens if, instead of a square, we use a hexagon?  Let's see:

What's going on here?  The two polygons, as the number of sides grow, are getting closer to each other.  But if they're getting closer to each other, and if the circle is in between them, then I should be getting a better and better approximation of π.  I am.

Let's continue!

Clearly, my approximation becomes much better as the number of sides of the polygon increases.  Having perfected the method, let's increase the number of sides of the polygon.

I've always thought of π as 3.14159.  I've never memorized more digits than that.  What size polygon generates my idea of π?  A 2,500-sided polygon!

Logical Haiku of the Week

This method above - a modification of the "Method of Exhaustion" of Eudoxus and Archimedes from ancient times - gives rise to the "Logical Haiku" of the week ...

POLITE DISCUSSION

A Play About Rational Discourse

March 22, 2008

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round@rationalsys.com

The scene: Smith and Jones, workers at a software company, their cubicles side-by-side.  Smith, the diligent worker, is back from lunch on a Friday afternoon (though reading a newspaper), and Jones, a bit late, now arrives, irritated.  It’s Friday, approximately 1:00.

Jones: “AHHH … I don’t know why I continue to talk with him – he’s impossible!”

Smith: “What happened?  Who are you talking about?”

Jones: “Bob – he works across the street, and we meet for lunch every other Friday.”

Smith: “So what happened?”

Jones: “What always happens!  We start to talk about an issue – any issue – and I don’t know how it happens, but I leave so angry I could explode!”

Smith: “What did you talk about this time?”

Jones: “He brought up the Bush-policy in Iraq, and how it’s such a failure.  I asked him what else could the US have done, given the number of UN resolutions violated, and anyways, was it reasonable to sit back and wait to be attacked like we did at 9/11?”

Smith: “And what did he say?”

Jones: “Who knows what he said!  He’s always all over the board.  He started talking about a conspiracy to invade the Middle East for their oil, how the weapons-documents were all forged, stuff like that.  Nonsense.”

Smith: “And in two weeks you’re going to lunch again with him and talk about something else?”

Jones: “Probably.”

Smith: “… knowing you’ll probably leave the lunch as angry then as you are now?”

Jones: “Well – now that you put it that way, it really doesn’t make much sense.”

Smith: laughing softly.

Jones: “What’s so funny?”

Smith: “I was just picturing the news talk shows – people – EXPERTS – yelling at each other for 30 minutes – and then the show ends.  In fact, far from any problems being solved, I’m not even sure there’s been movement towards a solution.  And what you said sounded just like that!”

Jones: “That does sound like me – not that it makes me feel any better.”

Smith: (scratching his head, thinking) “Do you remember when we played football together in high school?”

Jones: “Sure!  That was a long time ago.  What has that to do with anything?”

Smith: “I was thinking about my days as quarterback.  I always approached the line of scrimmage with a play called, and I was wondering what it would have been like to go to the line with no play called.”

Jones: “And?”

Smith: “And I was wondering if it was possible to construct some type of play – or plan – for conversations.”

Jones: “I don’t know.”

Smith: “Let’s call it a ‘conversational plan’.”

Jones: “I like it!”

Smith: (pointing at his newspaper)  “Something comes to mind as I was reading this article on housing sales.  It says here the housing market is down 3%.  What do you think of that?”

Jones: “I’d say that’s sounds pretty bad.”

Smith: “Now what if I told you there are many ways to calculate this, they all make sense, yet they all give different answers.”

Jones: “I’d say that’s nuts.  How can there be so many different ways?”

Smith: “Here, we’re apparently talking about new home sales.  What about existing homes?  What if the average price is up?  And here we’re talking about the metro area.  Surely, this average doesn’t apply to the whole area, but probably parts.  See here – look at this area.  It looks like new home sales are exploding!  The point is how can one even have a conversation unless one is talking about the same thing with the other person?”

Jones: “You’re exactly right – and that’s what happened with me!  I heard this Democrat bashing Bush about a ‘failure’ in Iraq, and I immediately went on the offensive.  That’s it!  Next time I’ll ask more questions.  In fact, isn’t that what we’re told to do: ‘Seek first to understand?’”

Smith: “It seems a reasonable starting point.”

Jones: “Starting point, nothing – that’s what I’ve been missing!  In fact, I’m going to call Bob right now and invite his family over tomorrow for lunch.  His kids like to play with my kids, and it’ll be a great chance to try our new strategy!”

      (looks at his watch and realizes he needs to leave)

“Oh, man – I forgot I’ve got an off-site meeting at 2:00.  I’ve got to get going.  I’ll call Bob on the way.  See you Monday!”

Smith: (with Jones departing) … “Wait – Mike – don’t you remember ….” 

To the audience:  oh well – I guess he’ll learn the hard way. Continuing … “asking questions seems like a good thing, doesn’t it?  Isn’t that a powerful strategy we’ve been taught?  “Seek first to understand?”  “You can’t know where you’re going unless you know where you’ve been?”  “Make sure you’re both talking about the same thing?”  etc.  But how are all these things achieved?  You’ve got to ask questions.  Have you ever been asked questions you thought were ridiculous?  Off-topic?  Simply pestering?  How do they leave you feeling?  I hope things go well for Mike – but I’m not very optimistic.

  (transition:  Monday morning.  Mike is reading the paper)

Jones: “You know, I’m starting to believe Patton was right: everybody in the world is an SOB – except me!”

Smith: “I take it the family lunch didn’t go so well.”

Jones: “That’s an understatement!  What an idiot he is.  We were watching the college football game, and during a commercial time-out, Bob says to me.  ‘Look at all the money being made off these athletes.  I can’t believe the NCAA still will not allow colleges to pay the athletes.’”

Jones: (continuing)  “So here was my chance.  I’m against paying athletes, but rather than simply saying that, I instead tried our new method.  ‘What do you mean by paying?’, I said.”

Smith: “And?”

Jones: “And he talked at me like I was a high-school student.  ‘What do you mean, what do I mean by ‘paying’.  I mean just that.  You get a salary for working at your company.  So do I.  Why can’t college athletes get a salary as well?’”

Smith: After a short pause … “And?”

Jones: “So I said they do get paid – they get scholarships that pay for everything, plus when they travel, everything is paid for.”

Smith: “And …?”

Jones: “And what do you think happened?  Our discussion disintegrated like it always does! I thought asking a question would be a good thing, but it sure didn’t work for me!”

Smith: “I thought it might not work.”

Jones: “What do you mean ‘You thought it might not work!’  This is what we talked about Friday, wasn’t it?”

Smith: “We talked about asking questions being effective, but we didn’t say it would always work.  Don’t you remember our own conversation last week about abortion?  You said you didn’t believe so many people could be in favor of third-trimester abortions, and I asked you what your definition of ‘life’ was.  Do you remember how mad you got?  You couldn’t even answer the question, and I meant it as a legitimate one.   Forget that one: let me give you another example:  suppose you tell me it’s cool today.”

Jones:  “OK.”

Smith:  “No – you tell me.”

Jones:  “OK – I got it.  “It sure is cool today.”

Smith:  “What do you mean by cool?”

Jones:  “Mean by cool?  Literally?  The thermostat says it’s cool.”

Smith:  “The thermostat talked to you?  Really?”

Jones:  “No – the thermostat reads 52 degrees.”

Smith:  “Great – now, what do you mean by today?”

Jones:  “What?”

Smith:  “I mean just that – what do you mean by today?”

Jones:  “OK – I get it.  It’s October 28, 2006.”

Smith:  “Everywhere it’s that date, or only in some places, and not others?”

Jones:  “OK – in Arlington, the calendar reads October 28, 2006.”

Smith:  “Great:  now I understand your phrase ‘It’s cool today’.  You really meant ‘In Arlington, when the calendar reads October 28, 2006, the thermostat reads 52 degrees.’  Now, how do you feel about my clarifying your statement via a rigorous question process?”

Jones:  “I want to literally punch you, that’s how!”

Smith:  “Exactly – that’s what I meant by “sometimes questions are good – sometimes maybe not.”

Jones: “But then we’re back to where we started – how to have a good conversation?”

Smith: “Maybe – maybe not.  We’ve learned some things, haven’t we?  We know something seems reasonable – sometimes, yet other times it doesn’t.  That’s a start.”

Jones: “Yeah – but how do you know when something is reasonable and when it’s not?”

Smith: “What about our own business.  We sell software, right? And what did we do for so long in selling?  We’d go into a client and boast about how great our product was, how many fabulous things it can do, and then tell them our cost.  Do you remember our hit rates?  It’s a wonder we stayed in business!”

Jones: “That sure changed a few years ago with the changes didn’t it?  I can’t even imagine trying that strategy anymore.  It doesn’t make sense.  Now, we make an unbelievable effort to find out what the problems of the client are before we even talk about the features of our products.”

Smith: “Yes.  We get their side of the story.  What sense is there in presenting a solution to a problem they might not have?”

Jones: “Ah – the good old days of closing 2% of our deals.”

Smith: “This is why I brought it up.  I was wondering if there’s any similarity between this and what we’ve been talking about?”

Jones: “How so?”

Smith: “Look what happened in both your examples:  you start talking about the Iraq war, and both of you instantly present – well, maybe not a solution – but something not far from it.  ‘Iraq is a failure’ versus ‘Iraq is not a failure’, and ‘College athletes should be paid’ versus ‘College athletes should not be paid’.  And what happens.  You’re immediately confrontational, butting heads like billy goats.  Neither has time to hear any discussion from the other, you’re so busy guarding your own side of the story.”

Jones: “So what’s the alternative?  I already tried ‘asking questions’ to get his side, and you saw how well that worked!”

Smith: “Wait a minute: it didn’t work well in that case, but I can think of many instances where it does work.  Remember when you and I were talking about stem-cells, and you asked me what I thought about research on stem-cells?  I had no idea what they were, so that was how I responded.  It turned out you didn’t know anything either, so in that case, a simple question was a great introduction, wasn’t it?”

Jones: “So there are times when questions are good and times when they work poorly.  My ‘road-map to a good conversation’ is getting complicated.  How am I to know when to ask and when not to ask?”

Smith: “Slow down – let’s not get ahead of ourselves.  All we said was many conversations instantly deteriorate, because each lays claim to a side of the issue, and then guards their side.”

Jones: “Yes.”

Smith: “So let’s quit focusing on solving problems in a conversation, and instead focus only on the ‘deteriorating instantly’ part.”

Jones: “But aren’t they the same thing?”

Smith: “Maybe / maybe not.  Going back to our high-school football days, though the goal was to win the game, there are times in the game where the immediate goal is a first-down.  Without first-downs, there is no winning.”

Jones: “I got’cha.  So if we can avoid the ‘instant deterioration’ right off, we can have a good conversation.”

Smith: “Wait a minute … let’s back up a second and see why we’re even doing this.  We’re conversing for a reason, right?  Presumably we both want to benefit, else we would not be talking.  Will we agree?  Maybe.  Or we may not agree on anything – or we may agree – or we may change our minds.  A thousand things can happen.  But they only can happen if we get past that first step, and establish some form of foundation – let’s call it a FOOTHOLD – a mindset, if you will – from which we can hear each other talk.”

Jones: “I’m still not sure what this will look like.  Let’s try an example.  Suppose we go back to the Iraq conversation with Bob.”

Smith: “Sounds good.  Bob immediately says the Bush policy is a failure.  How do you respond?”

Jones: “I … I don’t know?”

Smith: “Well (thinking about the conversation between Bob and Mike) you need to say something – it’s your turn.  You can’t – in this case – question him because he’ll explode, and you can’t – in this case – simply say the opposite – because that leads to the deterioration.”

Jones: “Suppose I say something neutral – like – ‘President Bush faces many problems dealing with a 21^st century global economy.’  It’s neither pro-Bush nor anti-Bush.  What do you think?”

Smith: “The question isn’t what would I think, it’s what would Bob think?”

Jones: “I think Bob would immediately jump all over it, perceiving it as ‘Pro-Bush’, and therefore ‘pro Iraq policy’.”

Smith: “But I like the ‘neutrality’ idea, though it – in this case – may not have worked because Bob would not have perceived it as being neutral.  What else could you say?”

Jones: “Well, suppose I generalize ‘President Bush’, yet still make it specific to war.  How’s this:  ‘Many countries have trouble articulating a rational foreign policy.  How’s that?’”

Smith: “You tell me – how would Bob perceive it?”

Jones: “He’d probably ask me what I meant by that.  Boy, if he asks me that question, I’d better be thinking about an answer!”

Smith: “That’s true – but that’s good, isn’t it?  Who says we have to come to the table with all the answers.  The key thing is the dialogue made it past the first step – and we’ve got our FOOTHOLD.   Let’s say you have no idea what a good foreign policy is.  You could say to him, ‘I don’t know – what do you think.’”

Jones: “Yes – and now we’re not talking about Bush and Iraq, but rather foreign policy in general, of which the Bush/Iraq issue is a specific example.”

Smith: “I like it – I like it a lot.  Say again what you said.”

Jones: “Many countries have trouble articulating a rational foreign policy.”

Smith: “So let’s see what it is we like about this answer – but not in the other example.  In this case, you’ve not entered into the is/is-not trap.  What else?”

Jones: “Let’s not forget we also tried another answer and did not think it would work so well.  That one also did not go into the is/is-not trap, so it must be more than that.”

Smith: “That’s right – because we had a criteria for good and bad, and the one response was bad because it did not advance us to our goal of achieving a foothold – a position where reasoned discussion can take place.”

Jones: “So an effective response avoids the is/is-not trap to allow us to achieve a foothold.  The foothold is our goal.  Yes?”

Smith: “IN THIS CASE!”

Jones: “Why do you keep saying that?”

Smith: “Let’s say I ask you what’s the capital in Texas?”

Jones: “Austin.”

Smith: “So we’re having a conversation?”

Jones: “Sure.”

Smith: “And you answered directly?”

Jones: “I see where you’re going – there are some instances where a direct response is good – and others where it’s not.”

Smith: “Exactly – that’s why I added ‘IN THIS CASE’.  What we’re looking for is not the specific strategy to use in all conversations, but a good method of getting us to the foothold – the foothold’s the key to many conversations!”

Jones: “So if I’m asked about stem-cell research, what should I say?”

Smith: “IT DEPENDS!”

Jones: “Depends on what?”

Smith: “On who is asking – on the company – the environment – everything!  For example, if a Priest is asking, you might say one thing.  If Bob is, you might say something else.  If you’re asking me, you’d probably say something different and we’d both start doing Google searches.  Remembering the goal is the establishment of the foothold, let’s suppose Bob was asking.  What would you say?”

Jones: (thinking) “Science now-a-days makes the idea of ‘life’ tricky.”

Smith: “I like it!  What could Bob possibly say to that?  It’s neither pro-nor-anti stem cell research.  The likely response is what?”

Jones: “That’s a good question!  I’m sure Bob is just like me, and we hear a lot of things in the news about it, but I know I don’t know a thing about it!”

Smith: “Which is a great place to start – from a foothold point of view!  Can you imagine another argument where you’re both arguing about it, yet neither knows what it is?”

Jones: “I was just thinking about the earlier talk on the Iraq policy, and my response:  ‘Many countries have a problem articulating a rational foreign policy?’”

Smith: “And?”

Jones: “And I didn’t say a thing about war – all I said was ‘foreign policy’.”

Smith: “So?”

Jones: “Well, think about these questions:  ‘What should the USA do about the issue in the Sudan.  Maybe that’s a humanitarian issue – maybe war.  Either way, my response works great to that question.’”

Smith: “You’re right.”

Jones: “And what about these:  ‘What should the USA do about illegal immigration?  Foreign trade?  The same statement works great for those as well!’”

Smith: “And even staying on war, it works well for all countries.  What should the USA do in the Iraq situation?  What about North Korea?  What about Iran?  It seems to work well everywhere!”

Jones: “That makes sense – and now that I think about it, it’s frustrating to see experts discuss one issue, and then move on the next issue, and onto the next issue, etc., like they’re all separate issues.”

Smith: “You’re right – though they are separate issues – it’d be nice to see some common theme – or philosophy – running through the argument.”

Jones: “So where are we?”

Smith: “You’re right – we do need to get back to work.  I’ve got that project to finish this afternoon.”

Jones: (giggling – and looking at a pretend screen) “I see my program’s still running, so I’m technically still working.”

Smith: “You seem to get all the easy projects.”

Jones: “Enough.  All right, the goal was …”

Smith: (interrupting)  “Wait a minute:  what’s the problem?”

Jones: “You’re right.  The problem I’ve found with many of my conversations is they deteriorate quickly.”

Smith: “And the goal is what?”

Jones: “I’d like to have good conversations.”

Smith: “In order to achieve that we …”

Jones: “Try for a response – any response – that establishes the foothold.”

Smith: “And the foothold is …?”

Jones: “The foothold is simply a position where reasoned discussion between both people can take place.  Imagine that?”

Smith: “Slow down, funny-man.  A powerful method of establishing the foothold is …”

Jones: “By avoiding the is/is-not trap.”

Smith: “Right, but as we saw, even if we avoid with trap with a good statement, all such statements are not equal.”

Jones: “That raises a good question:  is there a way we can immediately know what statement to use to establish the foothold?”

Smith: “That is a good question.  Everything we’ve been saying is based on the expected response of the person we’re talking with.  Is that the answer?  ‘IF I say ‘x’, THEN I think they’ll respond with ‘y’?’”

Jones: “I think you’re right – it’s all about the predicted effect our response has on the other person.”

Smith: “Should we try a few more?”

Jones: “Sounds good – so long as you’ve got a few free minutes!”

Smith:   “So let’s practice a bit:  You start.”

Jones:  “OK:  here’s one:  ‘I can’t believe we’re considering an amendment to the constitution allowing for gay-marriage.’”

Smith: “The government does seem to frequently involve itself in the private matters of many adults.”

Jones: “What do you mean by that?”

Smith: “Just talking about marriage: many things are allowed and many things not.  Gay-marriage?  Polygamy?  Family-marriages?  Age-requirements?”

Jones: “I like your answer too.  There are a lot of things I didn’t even think about.  Let’s try one more.”

Smith:   “OK: here’s a popular one:  ‘What should be done about global warming?’”

Jones: (prolonged hesitation)  “The earth’s weather certainly changes a lot.”

Smith: “Why’d you say that?”

Jones: “Because I honestly don’t know if the changes are due to natural changes occurring all the time, or if the changes are due to man-made things, are if there are even changes at all!”

Smith: “I like it.”

Jones: “And I really like the idea of talking about all these topics not as isolated incidents, but rather as they’re all connected.”

Smith:  “You’re right – and I was just thinking about something else.  You took quite a while to answer that time.  How come?”

Jones:  “It took me a while to think of a good response.  Why do you ask?”

Smith:  “I was thinking the same thing myself.  Look what we’ve told ourselves.  To effectively answer the question, there’s lots of things to consider.  My goal in the conversation.  The nature of the question.  The predicted effects of the person to my response…”

Jones:  (rudely interrupting)  “And not just that, but of course the subject we’re talking about!”

Smith:  “So earlier we described the good response as the foothold, right?  Isn’t that exactly what we’re doing – to ourselves – when considering a quality response?”

Jones:  “You’re exactly right!  And another thing about all of this thinking one has to do.  What really ticks me off many times is how people spout right off on a subject – you can tell they haven’t done a whole lot of thinking on the subject.  What’s wrong with some ‘reflective time’ to think and respond?”

Smith:  “I like it – the use of the foothold to create the foothold!”

Jones: (puzzled look on face – scratches neck).

Smith:  “What’s wrong now?”

Jones:  “I was just thinking – when you formalize it like we have, it sounds so ‘robotic’ – maybe even manipulative – all this thinking, determining what the other person is thinking, etc.”

Smith: “When you put it like that, I don’t like the sound of it either!  Sure we’ve got a process – but is it so mechanical?  Look at our examples.  Reasonable answers do come pretty quick, don’t they?”

Jones: “I guess – it’s just so different, isn’t it?”

Smith: “You bet it is!  Let’s not forget where we started.  Arguing, not having good conversations, anger on your part.  One thing we haven’t talked about is Bob – the other person.  Do you think he enjoyed any of those conversations?”

Jones: “You’re right.  It’s hard to say why I call us ‘friends’ when all we did was argue.”

Smith: “So what have we created while we’re supposed to be working:  a great process for effective communication – in addition to building long-term friendships.  That’s not bad!”

Jones: “So how do I put this talk on my timesheet?”

Smith: “How about under ‘miscellaneous’, with the details:  ‘the Foothold: Building a foundation for Rational Discourse?’”

"Candy Cane" Pipes "about town"

March 23, 2008

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round@rationalsys.com

An astute observer has noticed a series of odd-shaped pipes along Quivera, stretching from 135th to 119th Street.  Green and yellow and shaped like candy-canes, they look as follows:

The Candy-Cane Anomaly

The Candy-Cane Anomaly

What's going on here?  My first thought was these were pipes similar to the exhaust pipes in cars, or venting pipes from houses, taking unwanted fumes from one place and venting them into the air.

But what is vented to the air?  Natural gas?  That's my initial guess, and as dangerous as it sounds, I think it must be pretty safe; otherwise the gas company would not do it.

Rather than guess, let's just ask them!

My guess is partially correct: they are pipes related to the natural gas distribution system.  But they are not for venting gas into the air; they are for venting air INTO the ground to prevent corrosion of the pipes.  That is:

The Candy-Cane Anomaly

This seems reasonable (again, my understanding of what's being said), but I know something is not right here.  You see, there are natural gas pipes all over the city, but I've only seen the above venting pipes along Quivera, in this short 16-block corridor.  If the above explanation is valid, I ought to see candy-cane venting pipes everywhere - and I don't.

The Candy-Cane Anomaly Continued

Where have I gone wrong?  Is it the idea of bringing in outside air to the underground via the curved pipes as a means of drying moisture to prevent corrosion?  Is that part correct, but the reason there are so few odd-shaped pipes is because of the alignment of the natural gas pipes underground on this straight-line corridor?  How might this be the case?  If natural gas pipes ran parallel to water pipes, and if the water pipes created excessive underground moisture, then here there might be need to bring in outside air to prevent the corrosion.

It's my next guess.

Architects of Their Own Future

Chapter 13

March 24, 2008

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Chapter 13

A BRIGHT FUTURE IS POSSIBLE

Coach Thompson sat upright in bed, unable to sleep, thinking about his situation.  His Generals were now 4–3, riding a 3–game winning streak.  Coaches were talking.  Heck, everybody was talking!  How could this team of average players now lead the conference – at 3-0?  Two weeks ago, he would have asked himself the same question.

He knew it would not take long for other teams to notice what was taking place at Washington.  But he had the upper hand on these coaches, he knew, because they were looking for gimmicks, tricks, and things of this nature.  They would practice not committing to the ball fakes of his players. He knew it wasn’t the ball fake that had made them successful against Jackson Central.  Sure, the ball fake is what they used in the game, but the key was focusing on what was preventing his team from scoring.  The ball fake helped them achieve this goal.  Other teams will catch on, but does that mean there aren’t other ways to improve scoring immediately?  What else was he missing?

Another thought came to mind:  suppose other teams did come around defensively and not commit to the ball fake.  Isn’t that what defense is all about?  Aren’t his own players better offensive players because of this?  Isn’t this what basketball is about – becoming a better basketball player?

He went downstairs, grabbed a glass of milk from the refrigerator and an old basketball video off the shelf.  What else had he been missing?  What else was preventing his team from scoring?

He watched the Jackson Central game a while as the game went back and forth, making mental notes of what he was watching. 

“Pass to the corner, and the center is supposed to come out here and set a pick.  We draw it up so this frees up the dribbler for an open jumpshot.  Why does it not work like this in the game?”  He hit the rewind button to watch the play again.  The answer was obvious.  “A pick is supposed to stop the defensive player.  This defensive player hardly stops at all.  What a terrible pick!”

The irony was not lost on him, given the circumstances surrounding the “relearning” of the ball fake.  Yelling “ball fake” is one thing – teaching the players to actually do it properly quite another.  Was the same true here?  Of course.  He could see himself yelling at the player, “Set a good pick.”  Had he shown the player how to effectively set the pick?  He chuckled to himself. 

"What else is there here?”, he thought to himself, continuing on, making notes.

The video was paused moments later, to the scream of the referees whistle, signifying a blocking foul.  In the attempt to draw a charge on the opposing player, a Washington player had not established proper position; hence the blocking foul.  “Get in front of him,” Coach Thompson could hear himself saying, though no words came from the video.  “Do these words have meaning?  Have I showed them how to really draw a charge?  How to really get into proper position?”  He again chuckled to himself, knowing the answer.  As in the example of the ball fake, he had provided simple examples and verbal exhortations to get the job done.  “How ridiculous these slogans!”, he thought to himself.

He thought more about the charge.  It was an effective way to draw a foul, but how else could it be used?  He was thinking of the upcoming game against Wilson Academy.  Academy had one of the best players in the state, and at 6’9”, was 6” taller than any player on Washington High.  How could we stop him?

The Coach wondered to himself:  suppose we try to draw a charge on him wherever he is on the court.  As soon as he turns around, we’ll be there.  I’ve never seen a charge attempted like this!

Doubt rang in his head, however.  Is this basketball, doing something like this?  Sure it would help us win, but is the goal to win at any cost?  He had seen coaches with this mentality, and he did not like what he saw.  At the professional level?  Of course.  Collegiate?  High School?  These are different arenas, aren’t they?  The goal is to win, but not at any price.  But at what price?  To play a good game, he decided. 

This went on for another hour, the coach making notes, jotting down examples where what was thought of as “basketball” was not – at least not “good” basketball.

The following three days of practice were sure to be fun ones.  He could not remember having as much fun coaching as he was now.

Counter-Intuition

Revisiting the TOC P-Q Game

March 25, 2008

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round@rationalsys.com

My first Board meeting is minutes away, and I'm excited about the possibilities - and challenges -  for this company.

We make two products, and employ four willing workers to manufacture the products.  The production work-flow is as follows:

For example: to build Product P, workers A and B start the process, and then hand their work to worker C.  Worker C then passes on the results of their work to worker D. 

The numbers in each box represent minutes at each work-station.

Note also there are materials' costs involved.  Product P starts with $40 materials, assembly follows, $5 of materials are added, and the product is ready to ship.  The selling price of Product P:  $90.  The cost of materials is $45.  Therefore, the profit/piece (Product P) is $45.

Similarly, for Product Q, the cost of materials is $40, and we sell this product for $100/piece, thus clearing $60/piece.

The demand for the products is P = 100; Q = 50.

The real issue, to me, for the meeting is to what level of detail should I explain the operation of the plant?

Salary costs, the building, utilities - overhead - is $6000 / week, and these are the only overhead costs.  This is important.  What else?  How about I promise no more overtime.  Overtime was killing the previous manager, but he had left himself no choice.  He made unrealistic delivery promises, and then had to pay workers time-and-a-half to produce them.  Of course, this meant he was losing money on every part produced.  What a ruthless spiral that was!

How am I going to explain expected profit?  That should be easy enough - do it visually ...

A stab of uncertainty runs through my spine.  Is my promise realistic?  There's no magic in this calculation, but it's too easy.  Likely my predecessor did the same thing, and look where he is now.  Is this right?

I've got a few minutes:  build a quick model and see:

Applying the minutes of each work-station against the production of 100 Ps and 50 Qs, I see Worker B is being asked to work 3,000 minutes.  Poor Worker B.  Moreover, poor me!  I was about to promise the Board a profit of $1,500, and now I see it's not even possible - at least not with the production schedule I'm recommending (no overtime)!  It's no wonder there was so much overtime previously.  They, whether they knew it or not, had predicted it!

No need to panic - at least not yet.  Have some composure and think!  The board meeting is in 10 minutes, and I've just discovered the error.  How to correct it? 

Start with the obvious: if our profit is $60 / piece on Q, and only $45 / piece on P, we've got to build all 50 Qs first.  That's $3,000 in profit.  Because worker B was the over-worked worker above, let's keep track of his time.  At 30 minutes / piece, we've used 1,500 minutes from his work-week in building 50 Qs.  Therefore, he has 900 minutes left, and if it takes 15 minutes of his time in building Product P, then we can only make 60 of these.  At a profit of $45 / piece, this yields a profit of $2,700.  I frown, doubting my numbers I know are correct.  Taking into account the overhead, I'm about to go into the Board meeting forecasting a loss of $300 / week! 

I begin to feel weak, hoping this "illness" will allow me to skip the meeting.  OK, I think, if building as many Qs as possible, and then determining how many Ps can be built leads to a horrible bottom-line, how about reversing the strategy: build as many Ps as possible, and then figure out how many Qs can be built.  I pound away at the keyboard to "run the numbers":

OK - I breathe a sigh of relief:  I can report a forecasted profit of $300 / week.  I hope I won't be asked how this will be accomplished, because I'll have to say we're going to build all 100 of the less profitable pieces first, and then spend time building only 30 of those pieces MOST profitable.

I dread explaining that recommendation.

But at least I can recommend a profit!

Five minutes to meeting time, I'm at least recovering from my temporary illness when my eyes fall upon the number "2,650", for "minutes worked by Worker D"!  What's this?  Now I've got him working overtime?

The upset stomach returns, this time literally.  Feeling the need to excuse myself, I change my mind: I might as well resign now.  This company cannot be profitable.  OK: give it a couple minutes.  Is there any combination of products generating a profit?

I'm proficient in writing quick programs, so I decide to simply simulate every conceivable combination of products to be built.  Maybe it's not even possible to make a profit in this company.  Why did I sign on to this dog?  OK - first things first.  Get my program written.  Let's capture only those combinations where worker hours are all under 2,400 minutes for the week.  Those are the realistic combinations.  Let's also eliminate "trivial" results (like building only 1 of each).  Graph the combination of products, and the resulting profits. 

Go!

88 Ps and 36 Qs.  A new profit of $120.  No workers working overtime.  I again breathe a sigh of relief.  A huge one.  It's not much of a profit, but at least it's a profit.  I still hope I won't be asked why we're not building to the demand of the extremely profitable Product Q.  On second thought, I hope I will be asked this.  I'm not sure why the results lead to a gain of $120; I'm just sure they do, and there's no greater proof than the one "in the pudding"!

I also realize the danger of "common sense".  "Common sense" had me running into the Board meeting initially recommending a $1,500 gain, followed by a $300 loss - both the result of "common sense", and finally advocating a $120 profit, created only by brute-force initially, substantiated by logic only later.  This answer was far from common sense!

Walking into the Board room, I decide on another tactic: tell the Board the obvious strategy - and wrong one.  Get them to actually realize the job of the foreman - of the company - is not merely one of pushing buttons and barking orders.  To do it right requires thinking!  "What order to bark?" is much different than "Barking orders".  Get them to see me not merely as a "% increase in profit" statistic, but a person using his mind to solve problems in the company!

It's weeks later, when I've been given time to consider constraints, interactive constraints, linear programming, profit per constraint minute, etc., I'm able to make sense of it all. 

And there is sense here - a lot of it!

A Bright Future

But is this structure complete?  Have I taken into account the variables properly?  Has my theory taken into account the constraint, the constraint dollar / minute, and other considerations properly?  In all instances?

And not only this, but other considerations come to mind: here, I'm trying to maximize profit in this system.  Why is the plant layout as it is?  Why is Worker C working so little, while we fight to manage the times of Workers B and D?  Is it possible to use the excess time of C to help B and D?  Maybe.  There's got a market out there of 100 Ps and 50 Qs, with a profit of $1,500.  Wouldn't it be sweet to tap into known demand! 

Instead of fighting for the 10% and 15% profit increases that make Boards happy, think of the future when I could report a 1,150% increase!

But how to manage the plant to get there - that's the question.

That's a question.

Suppose I do "produce to market", and show this remarkable increase.  What then?  That then becomes the new benchmark - and the Board will be demanding increases from that point.  Ugh.

Maybe it's best to temper increases and show a "mere" 20-25% increase, and I alone will know the truth of what's possible.  I'd be a hero in their eyes.  But not my own.

"Be true to thyself", I say to myself.  I'm not going to temper anything.  If I can produce a $1,500 profit, I will!  The new question becomes: how can I create more demand for my product?  The constraint is no longer the time of Worker B or Worker D - it is the market!

The work has just begun.

My new message to the Board, bought into by the Board, is one of no longer setting arbitrarily mindless and repetitious single-digit profit objectives.  Rather, it is in the spirit of Jonathan Livingston Seagull:  "For a thousand years we have scrabbled after fish heads, but now we have a reason to live - to learn, to discover, to be free!" 

Neither Rhyme Nor Reason

O Captain! My Captain! and the Metaphor

March 26, 2008

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round@rationalsys.com

Whitman's Ambitious Target

The context of this play is the United States Civil War, lasting from 1861-1865. The war has just ended, and President Abraham Lincoln has been assassinated by John Wilkes Booth.

Whitman, wanting to write a poem on this, believes he can best describe these events metaphorically. Therefore, he seeks to write a metaphorical poem on the War, Lincoln's death, and Whitman's reaction to the death.

The metaphor Whitman has in mind is a sea-going vessel returning from war, with the President as Ship Captain, to a shore lined with cheering citizens.

Necessary Conditions for a Successful Poem

OK … I will write a sea-going metaphorical poem about the Civil War, the assassination of the President, and my reaction to the President’s sudden death. What is it going to take to make this a success? Clearly, I must write about the Civil War, and the reuniting of the Union and Confederate States. Is this sufficient to make a good poem? I think not. What else? The celebration is a huge part of my image of the War; therefore, an accounting of it must be present. Most importantly, I must include an account of President Lincoln's death. But what about his death stands out? It was my reaction to it - ranging from Denial to Acceptance - that really strikes me, and will therefore be included in the poem.

Therefore, to have a successful poem, I must write about the Civil War and the reuniting of the states, I must write about the celebration of war's conclusion, and I must account for President Lincoln's death, and my reaction to it.

The Poetic Transition … Necessary Condition #1

If I must write about the Civil War and the reuniting of the Union and Confederate States, and the nature of this poem is metaphorical - relating the sea to war, then I shall equate the Civil War with a FEARFUL TRIP, the reuniting of the states with the PRIZE, the USA with a SHIP, and the President of the United States being the CAPTAIN OF THE SHIP.

"Does this make sense?"" I ask myself? The captain of the ship? Of course. A fearful trip? I believe a good analogy. The prize? That works, because that's the goal of the war - to reunite the ceded states. What about the USA as a 'ship'? Is this good? The poem's goal is to describe the fearful trip - taking by what? The Union states alone, or the confederate states alone? Nonsense ... the USA will be my ship!

Now, I simply need to put to actuate this analogy poetically:

O CAPTAIN! My Captain! our fearful trip is done;

The ship has weather’d every rack, the prize we sought is won;

The ship is anchor’d safe and sound, its voyage closed and done;

From fearful trip, the victor ship, comes in with object won;

The Poetic Transition … Necessary Condition #2

What do all people feel at the conclusion of a war? Exuberance? Celebration? Joy? Relief? I need to capture this sense of ""conclusion"" in order for my poem to portray accurately the Civil War … the specific sense being one where ""Crowds of people display immense enthusiasm at the conclusion (and victory) of a hard-fought battle.

And who is the crowd cheering? The President, of course - and how are they cheering him? How does a parade meet the honoree? Shouting! Bells! Ringing!

Actuating this sense poetically gives me ...

The port is near, the bells I hear, the people all exulting,

While follow eyes the steady keel, the vessel grim and daring:

Rise up (Captain)—for you the flag is flung—for you the bugle trills;

For you bouquets and ribbon’d wreaths—for you the shores a-crowding;

Exult, O shores, and ring, O bells!

The Poetic Transition … Necessary Condition #3

The conclusion of war and the celebration of victory are completed, and now I must move on to the assassination of President Lincoln … what do I write? It was a shock, an unexpected death, and my initial belief was one of disbelief … I shall write of this: my denial of death, in order to capture my thoughts following the death.

How do I actuate this context, given my ""ship is coming to port, and the crowds are cheering?"" As follows:

But O heart! heart! heart!

O the bleeding drops of red,

Where on the deck my Captain lies,

Fallen cold and dead.

Captain! my Captain! rise up and hear the bells;

Here Captain! dear father!

This arm beneath your head;

It is some dream that on the deck,

You’ve fallen cold and dead.

The Poetic Transition … Necessary Condition #3

The war is won, the celebration on, and my President has been murdered. I cannot believe it - I won't believe it! But alas, it is true. How does one capture mourning, when acceptance is the successor to denial? That's the one thing missing from this poem ... this poem, remember, is about ME and how I felt regarding the Civil War and the assassination.

Poetically, I shall capture this grim mood as follows:

My Captain does not answer, his lips are pale and still;

My father does not feel my arm, he has no pulse nor will;

But I, with mournful tread,

Walk the deck my Captain lies,

Fallen cold and dead.

Poetic Creation

What to do with all these lines - these wonderful and metaphorical lines?  How should I arrange them?  Just in the order they appear above?  Possibly.  The events are occurring simultaneously; why not intermix the prose, as the events themselves are intermixed.  What would that look like?

Strangers in the Night

The "Magic" of Fuel - "I Push a Button and Out It Comes"

March 27, 2008

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round@rationalsys.com

Today's journal entry was going to focus on the "unit-verse", capturing relevant examples of math and science in the world as easy entry points into "applied" math.  Filling the van up with gas, I was going to use the receipt from the gas station to demonstrate how there are a number of items right there

But lucky me!

The above tanker truck was at the station!  One rarely sees them, as they appear as "strangers in the night", refueling the station tanks, affording us the ability to push a button and fill our tanks on our way to work, not stopping a second to ask "How does this happen?"

Where do they come from?  How many are there?  How much do they hold?  Where do they fill up?  What is the relationship between the oil we hear about in the news and the fuel these trucks deliver? 

So many questions.

Here, I want to focus on a single question:  this truck is filled with fuel, and I'm at the station to fill my tank with fuel.  How much fuel do I use - how many "trucks" of fuel?

Well, I need to know how much fuel is in the trailer.  Fortunately, the driver was in the station, so I asked him:  9,500 gallons.  Actually, the capacity is 10,000 gallons, but because temperature causes gas to expand, he told me the most they fill the trailers in 9,500 gallons.

Fine:  let's find out how many miles this provides my car.  My car gets about 20 miles / gallon, so with this trailer I could get about 190,000 miles. I average about 10,000 miles per year, so the trailer provides me about 19 years worth of travel.

That sounds like a long time time, but an alternate explanation suggests otherwise.  If I took a small group of 18 other adults with similar driving habits and vehicles, we as a group use a trailer of fuel like this every year.  Wow!

Even though I like this format of moving from fact to fact, there are instances where I get lost - even here.  Is there an alternative way to format knowledge - and also simultaneously ensuring my units are being applied properly? 

I like this "unit multiplier" structure - at times.  I like the logical structure above - at times.  In this instance, the latter works better for me.  It allows me to move systematically from the known to the unknown, each step with a known starting point: a "unit" of measurement in the denominator canceling the same unit in the previous numerator.

I asked the driver how long the trailer was: 40'.  Let's see if I can calculate the other dimensions of the trailer.  It's more an ellipse than a circle, but knowing the formula for the area of a circle, I'll start with that to get an approximation.  This should be easy enough: I seem to have all the data - or do I?

Maybe I don't!  The "volume" I have from the driver is in gallons, and my other unit of measurement is in inches!  I can't do anything here.  A quick internet search reveals the volume of a gallon of gas to be 231 cubic inches.  That sounds pretty big, considering my car tank holds 15 gallons.  Another issue - another time.  I'm back on track, comparing units-to-units!

(A side note:  The choice above was not between using the logic branches or the unit-multipliers; I can use both!  I can have my cake and eat it too!)

Wonderful!  And now I can equate my two descriptions for the volume of my trailer-cylinder to generate a formula allowing me to solve for the radius of my "circle":

More Work

I use a fuel-trailer once ever 19 years.  Wow!  That in itself is revealing!  Moreover, the dimensions of the trailer seem to be 40 feet in length, and about 6.5 feet in width.  I'll call today to check this.  Note in this latter calculation I've used the 10,000 gallon capacity, instead of 9,500.  There seems to be a principal at work here similar to why hot air rises - I'll investigate that in future thoughts as well.  The size of the fuel tank intrigues me as well.  231 cubic inches for one gallon?  Let's get a picture of this - it seems like there must be a tank the size of a moose under my car, though I know that's not right!

And what of my assumption above of substituting a circle for the obvious elliptical nature of the trailer. 

These three shapes all have the same area - how can I tell how close my approximation is?

And is there a reason the trailer is elliptical - I see it is, but why is it this way - and not a circle?  Is there a physical reason?  Enough for one sitting!  Maybe. 

For the next journal entry on this issue, we'll look focus on the logical follow-up issue of me at the station.  I'm putting gas in my car in order to ... go!  How and why does gas make my car "go"?

No Season Better

Sports Forensics

March 28, 2008

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round@rationalsys.com

But how would one gauge "the best season"?  Sure, one could rank annual batting champions, and search for the highest average.  That'd be easy - maybe even right.  Let's see:

Clearly, by the table, Nap Lajoie's 426 average makes this the best hitting season, followed by the great Rogers Hornsby at 424, and George Sisler and Ty Cobb, each with 420 seasons.  But is this right?

Has a 400 hitter with 400 at-bats, for example, had a better season than a player hitting 380 with 600 at-bats?  As noted above, several players have flirted with the magical "400", only to fall off as the season progresses.  Is our 400 hitter above any different?  These are only two variables - average and # of at-bats.  Surely, there are others: on-base %, slugging %, home-runs, etc. 

Let's assume, for the sake of this argument, I'm interested only in batting average.  Wouldn't it be nice, before answering the question above of who's best, to look at the performance of all batters over the years?  That is, plot all players' statistics.

But to make sure the data is not skewed by a player getting 10 hits in 20 at-bats, let's limit the number of at-bats:  choose a random number:  50.

The information used here was obtained free of charge from and is copyrighted by Retrosheet.  Interested parties may contact Retrosheet at "www.retrosheet.org".

With average on the x-axis and at-bats along the y-axis, some interesting things show up:  few players last long if they're not hitting well.  If you're only hitting 100, you're not likely to get many at-bats.  One can easily see how hard it is to hit 400!

To my question, the points in the upper-right become individually distinctive - and they show # of hits as the product of at-bats and average.

The Great George Sisler

Two of these individual points are the great George Sisler, in 1920 and 1922.  In 1920, he had 257 hits in only 154 games!  Both points, being individually distinguishable and upper-most towards the right, tell me these are among the two greatest batting-average seasons ever. 

But are they the best?

In Search of a Quality Algorithm

A method is to find out which point is in the "upper-right-most" sector of the grid.  One way to determine this is to establish a new grid, and see which is "closest" to the intersection of these two axis.

Let's establish an "optimal" year as having a 430 batting average with 710 at-bats.  No one has ever done both simultaneously, but both levels themselves have been approached separately.  Perhaps a reasonably good "optimal" starting point.

Now, how can I establish which points are "closest"?  I could calculate the distance by way of the Pythagorean Theorem - that would be pretty easy.  Time-consuming as well.  What if I simply draw a circle from the intersection of the two axis, and see which point I hit first - that would show me which point is closer to the optimal point than any other.

Indeed, the 1920 season of Sisler, coupling at-bats with average (producing 257 hits), was the greatest batting season of all time!  What are some of the others?

Sadly, Sisler missed the entire 1923 season with poisonous sinusitis.  More sadly, despite a career average of 340 and 2,812 hits, he initially received only 34% of the votes for entry to the Hall-of-Fame (75% is required to be inducted), and it wasn't until the fourth try before he finally gained entrance to the Hall.

Surprisingly, those listed above as potential candidates for "greatest season" are nowhere on our table.  Why?  Those great seasons were the result of fewer at-bats than those seasons of the players in our table.

But does this mean "greatest season" is just a measure of "hits"?  Partly - and why not?  "Number of hits" is a good barometer of both hitting ability and season-longevity.  The table above, however, is a blend of the two, as evidenced by the sixth-place ranking of Ichiro Suzuki and his phenomenal year of 2004, where he had 262 hits while batting 372!

By Decade

I've got all this data well-organized - what else can I do with it?  Above, I looked at the history of baseball, lumping everything together.  How do the individual decades compare?  To make sure there is an available comparison, let's superimpose each decade with the totals above.

Notice the 60s: this was the "pitcher's decade", where Yastrzemski won the triple crown in 1968 with a meager 301 average.  The 1920s, on the other hand, was a hitter's decade: compare the 20s with the 60s and you can easily see the number of "great hitters".  You can also start to see the introduction of the 162 game schedule in the 60s.

Finally, the similarity of the decades, despite flickers of change, are remarkably similar.

Let's continue!

By Year

The strike-shortened seasons of 1981 and 1994 are obvious, as is the continuation of the self-similar nature of performance over more than a century!

Looking further at the "top-10" list, three of the ten are from 1930!  What a spectacular hitting year that was - as is demonstrated in the graphic above.  Compare 1930 with 1968, the year of the pitcher, to see remarkable differences.

Of course, there's many ways to describe "best hitting" season - on base %, slugging percentage, batting average, etc.  In future editions of "Sports Forensics", I'll present an interesting graph of all three, which have Baby Ruth and Barry Bonds head-and-shoulders above the crowd.

Sediment Revisited

March 29, 2008

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round@rationalsys.com

This tremendous fish, between 3 and 5 feet in length and weighing up to 85 pounds, has been on the endangered-species list for nearly two decades.  It's environmental-spawning needs require certain sediments, which have changed due to the construction of dams along the Missouri.

In order to restore the water-content balance to the river, making the river more conducive to the needs of the pallid sturgeon, the Army Corp of Engineers, in accordance with the Environmental Protection Agency, is creating channels along the river to divert and slow part of the river flow.  The KC Star article states "Channels are designed so that further erosion will occur over time, the way river erosion used to occur naturally."  (sidenote: a clear violation of the 'that' rule)

In creating these channels, you can imagine the amount of soil dredged.  What do you do with this soil?  The Army Corp is going to put it in the Missouri river.

However, an objection to this practice has come from another government agency - the Clean Water Commission.  Missouri's Clean Water Commission says this sediment contains high levels of nitrogen and phosphorous that cause pollution.

Clearly there is a conflict here ...

Before searching for a compromise, as the two entities are doing now, I'd like to better understand the issue.  The CWC claims, as I understand it, this dredged soil should not be added to the river because this adds pollutants to the water.  That's their claim, though I don't understand it.

But the implication of their claim seems to be they would be OK with the Army Corp proceeding if the dredged soil were placed on land.

I think.

Why, again, is the Army Corp doing this?  They want sediment added to the river over time, restoring the water content to a previous state.  Will this sediment do it?  I'm not sure how, as the CWC has already told us this sediment contains pollutants!

"Water is not Water"

It is amazing to see how "water is not water" - that every bit of water is unique.  This image below shows the confluence of the eastward flowing Missouri (left) with the southernly flowing Mississippi (right).  The lighter color of the Missouri shows its high sediment content, one reason the river is known as "The Big Muddy".

Prime Numbers from a "Manipulative" Perspective

The Absence of Geometric Rectangularization

March 30, 2008

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round@rationalsys.com

Let's see it now.

Prime numbers are mostly thought of from an arithmetic perspective.  The definition itself speaks to formulas and numbers:  "a prime number is a number divisible only by itself and 'one'."

So 24 is not prime, because 24 = 1 x 24, 2 x 12, 3 x 8, and 4 x 6, but 29 is prime, because the only way to get to 29 multiplying integers is 1 x 29.

Fine.

What about '2'?  Well, we're told, it is prime - the only even prime - but '1' is not.  These are presented as though they're self-evident definitions.

In Search of an Intuitive Understanding of Prime Numbers

Suppose there were no such things as numbers, and I ask you to break these blocks into even units.

Easy enough - there are two ways:

Fine.  How about this one?

Again, easy enough.  Once again, there are two ways:

Let's try one more: 

This time, there are three ways:

Sensing you're tiring of the exercise, I ask one more:

Playing around with this one for a moment, I see the only way is

because

does not make a "rectangle" - the blocks are not broken into even units.

Fine:  let's call the size of these blocks where the only rectangle to be made from them is the original set of blocks themselves prime - literally "of the first order (or row)".

That's a geometric interpretation of "prime numbers"; "of the first order".  Nary a number in sight!

But what of '2'?  Clearly, we see it is prime, because the only way to arrange the '2-block':

is this set of blocks itself.

Fine:  but what about a '1' block?

Above, I was talking about "blocks" (plural), and rearranging blocks (plural) in making (or not making) rectangles.  We don't have blocks here - we have a block (singular).  This falls outside the realm of consideration for "prime-ness", since we're not dealing with blocks (plural). 

A New Definition of "Prime Numbers"

with worked examples from 2 - 40

The Geometric Mind

This "geometric" interpretation / method will serve us well in dealing with binary numbers, which shall come up in the next issue of "The Geometric Mind".  In the meantime, I dedicate today's "logical haiku" to prime numbers.

Why I Could / Would Never Go Back to School

March 31, 2008

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round@rationalsys.com

"Penguins (order Sphenisciformes, family Spheniscidae) are a group of aquatic, flightless birds living almost exclusively in the Southern Hemisphere."

Really.  This is what penguins are?

Three immediate questions come to mind:

1. if they cannot fly, why are they called birds?  I know the ostrich is similarly described, which doesn't address the question.

2. penguins could once fly, but are now entirely aquatic.  How did this change come about?

3. why are they almost exclusively in the Southern Hemisphere?

The class would go on, all students drawing a line from the name to the correct description, and there I would be, sitting in my chair, stewing over these simple questions where all the meat really is!

Can't these types of things be better embedded in children's books?

Let's try.

But before we try, the Antarctic was rocked by a large chunk of ice, the Wilkins Ice Shelf,  collapsing into the waters surrounding Antarctica last week.

What are the implications to global sea levels to such a collapse?  Let's take it to the extreme: what would happen to global sea levels if all of Antarctica melted?

The United States Geological Survey has produced the following table, telling us:

Does this mean, if the entire Antarctic melted, the sea would rise 73 meters - or 219 feet?  Can that be?  That is:

An Experimental Simulation

It's tough to say, because one can't do an experiment to see if this is the case - or can we?  Suppose I fill a bowl with water, and then add a lot of ice.  Does this simulate the situation at the Antarctic?  Let's say it's close enough.

Let's call the water level in my bowl the "sea level".  Now, the question is: what happens to this "sea level" when the water melts?

We could hazard a guess, perhaps a logical one, to determine what will happen.  "Hypothesize", if you will.  That's part of the "scientific method".  But not mine.  I just want to see what will happen.  Then I'll start to reason as to what I've seen.

My Antarctic Simulation

My ice melted, there's not been a change at all in my "sea-level".  As you can see, the water-line remained the same (I've photographed this just prior to the last bit of ice melting, to demonstrate this is the same bowl).  How can this be?  Logically, we'll look in a moment. 

For the time being, let's note the problem here.  According to the USGS, the sea-level will rise consistent with the melting of the ice.  I'd expect to see the water-level in my bowl rise as well - but it didn't.  Does this mean the USGS is wrong?  Are there circumstances my experiment is not accounting for?  What's going on here?  Something!  Here's where the real work starts!

More Thoughts

The logic of why my experiment ended the way it did is coming in a future write-of of Archimedes.  The logic of why I differ from the USGS is being researched.