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2010 Home

 

 

A WORLD WAR I MEMORIAL

 

in Kansas City

 

May 1, 2010

 

 

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round@rationalsys.com

A World War I Memorial in Kansas City ...

A German U-Boat sunk the British passenger liner, The Lusitania, in 1915.  Aboard were 128 Americans.  All perished.

President Woodrow Wilson declared, "America is too proud to fight".

Germans were suspected of bombings along the eastern seaboard, and President Woodrow Wilson, running on a campaign of neutrality, did nothing.

Fortunately, British cryptoanalysts broke the German code, and uncovered German communications to Mexico, requesting the Mexicans ally themselves with the Germans against the United States.

Only after all this did President Wilson call for war on Germany, which the US Congress declared April 6, 1917.

Kansas Citian William T. Fitzsimons accepted commission as First Lieutenant, Medical Officers’ Reserve Corps, March 27, 1917, and entered on active duty under the commission on April 27, 1917.

He had already been overseas, however.

Prior to the war, he was an intern in Kansas City, and then later at Roosevelt Hospital in New York. With the start of the war in 1914, he went to England as a Red Cross volunteer and served fifteen months at a hospital in South Devon. He returned to Kansas City to private practice, but was commissioned a First Lieutenant in the U.S. Army Medical Corps in 1917 and left for France in June as part of the Harvard University medical unit.

He sailed from New York City July 23 for duty with the American Expeditionary Forces in France and on arrival was assigned to duty with the United States Army Base Hospital No. 5 operating with the British Expeditionary Force at Dannes, Camiers, France.

He served there until he was killed on September 4, 1917 by explosive bombs dropped by hostile air craft on that hospital.

When you hear the words "World War I Memorial", do you think of the "Liberty Memorial"?

 

This is the only United States memorial commemorating the deaths of all servicemen in World War I:

But the first American killed in World War I was William T. Fitzsimons, and the William T. Fitzsimons Memorial Fountain, at 12th and the Paseo, commemorates his life - and death.

 

And, remarkably, these aren't the only two memorials to those serving in World War I.  Here's another:

 

American War Mothers Memorial Fountain

 

 

Problem-Solving and Communication Breakdown

 

 

May 2, 2010

 

 

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round@rationalsys.com

A friend, "Fred", called the other day:  "Can you help me calculate my Rate of Return?"

I hate questions like this, because the relevant data is always missing from the question.  Further, I'm not sure how the data will be used, so I'm hesitant to give an answer, and there's an interesting dilemma:

answer / don't answer.

Why "answer"?  Obviously, because a friend has asked a seemingly simple question.

Why not?  Too often, I've seen my "right" answers not so right, when, after the fact, I'm given a lot more data.  I've found when I ask reasonable questions, I'm suddenly confronted with a negative attitude - JUST ANSWER THIS QUESTION.  There's a ton of negative experiences gleaned over the years about "simple questions".

My problem, in wanting to be a helpful friend, may be summarized as:

 

Here's the dialogue that transpired, on how I handle most situations like this now ...

 

Fred:  "Can you help me calculate my rate of return?"

Mike:  "Sure.  What's your starting and ending balance?"

Fred:  "Starting was $100, and ending was $103"?

Mike:  "Over what period?"

Fred:  "What do you mean?"

(Note to self - be careful here - I've only got one shot at asking a question.  It's got to be the most relevant one, to my answer.  And it's got to be phrased in such a way this part of the dialogue terminates quickly, else "Fred" will start to get angry.  Really.  Here it is!

If I say, "Most rates of return are on an annual basis", so I need the time period, this may or may not work.  For all I know, "Fred" is only interested in the rate of return over his period - whatever that is!  Maybe it's annual.  My fear is talking - theoretically - like this will not help.  I need something concrete!

I've found a simple example works best.  Think, Mike!  What's a simple example that will demonstrate my need for more information?

Mike:  "Well, if you earned three dollars over three years, that's not so good.  However, if you earned three dollars over three days, that's really good!"

Fred:  "I see.  This was for 2010, ending 3/31/2010".

(I quickly create the following in a spreadsheet).

Mike: "So you've earned 3% over this three month period ..."

(Here's another crucial point - I don't want Fred to say, "So my rate of return is 3%?", because that doesn't sound very good.  If I translate this into an annual rate, the response is going to be "How'd you get that", and Fred will not understand the math.  I've got to quickly jump in and add more context).

I quickly modify the spreadsheet above ...

and continue talking before Fred has a chance to say anything ...

Mike: "... And if you earn this same rate over the second quarter, you'd expect to have about $106 by the end of June.  And if this holds for the last two quarters of 2010, you'd have about $109, and then end the year with $112.55."

"So your annual rate of return right now is 12.55%."

An Operational Explanation -

 

the "Operational Syllogism" ...

 

 

Systemic Personality Mismatch

 

May 3, 2010

 

 

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round@rationalsys.com

Different classification systems abound - "what is the nature of a person"?  Here are a few:

Left-brained / right-brained ...

 

Multiple Intelligences ...

 

Myers-Briggs ...

 

Systems abound on how to classify people, and part of me thinks this is useful.  "Know your audience" might be crude summarization of the attempts to classify people, and this makes sense.  Strategic people, for example, may get bored in a meeting with tactical programmers.  Those who see "the forest" are often bothered by those working in "the trees", though both are important!

Additionally, we know people learn different ways.

This doesn't mean, of course, we're all different - though we are - but understanding these differences may help in communicating, understanding, and learning.

But something strikes me as odd - perhaps missing - from these classification systems.

The repetition of problems.

Or the maintenance of problems.

Why do problems not only exist - but persist?

For example, consider math education.  We know - and have known - the math system is poor in our country.  It has been for over half a century.  From the "New Math" to a new learning system every decade to new things coming out on a seemingly monthly basis.

What's going on here?

Scratch that.

What should be done to fix it?

Let's ask two groups of people. 

Group 1

"Here's what we decided it would take to have a great math education system":

1. show the relevance of math;

2. Teach math from an interdisciplinary perspective;

3. Put kids in content-relevant classes rather than grade relevant classes.

4. There were others.

Let's diagram this process ...

 

 

Group 2

"We focused on the obstacles to achieving a good math education - that is, what's preventing us from having a great education system.  Here are three obstacles we found:

And here we end up - don't we end up here often? In trying to achieve a goal, there are (at least) two different ways to go about the process ...

Those who say "Here's what we need to do to get the job done", and those who say, "Here's the reasons the job isn't getting done!"

Both are good.

In context.

But what is the context?

And what happens when someone - thinking of the positives - is working with someone pointing out the obstacles?

It's awful. But is it necessarily awful.  Is this a personality mismatch or a systemic personality mismatch?

I said both methods are good - in context - but what context?

And what should be done - from a problem-solving perspective - in making sure all parties are aligned to the nature of the problem-solving process?

Or is such alignment even necessary?

You may have noticed, though the methods are different, the similarity between the "Necessary Conditions" of "Method 1" and the "Obstacles" of "Method 2".  Suppose, for each obstacle, we write - essentially - the opposite, and create an "Intermediate Objective".  What do we have?  Really, Method 1!

That is:

Stay tuned for Part II ...

 

 

JOY IN LIVING

 

The Meaning of Structure

 

May 4, 2010

 

 

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round@rationalsys.com

In the previous series of letters, we started with the painting - what could it mean?  What was the artist's intent?  What was the context of the painting? 

Let's start from a different perspective:  that of the creator.

Let's create a theme - a goal:  let's suppose it is some recognition of Kansas City as an important point in moving westward.

How can we cast this very abstract idea - concretely?

It's not easy.

What's the essence of what we're trying to communicate?  Maybe it's "opening up of the west".  Does the Arch in St. Louis do this?

Maybe a literal image of Louis and Clark would work.

How about a bridge - spanning the Missouri?

If we decide a bridge, will our sculpture be a replication of the first bridge spanning the Missouri, or perhaps a semi-circle, from point A to point B?

And if the idea of a semi-circle from Point A to Point B sounds interesting, what if we made the semi-circle a rainbow?

Lots of options.

And let's suppose we chose a rainbow.  We know the meaning of the sculpture.  Would we be offended if people misinterpreted the sculpture?

Probably.

So we might ask the question "What can I do?" and modify the sculpture to ensure it not only concretizes our abstraction, but cannot be misunderstood.

Fountains and Sculptures.

Kansas City has more fountains, its said, than any city in the world except Rome.

And I've been looking at many recently.

There's a theme running through many of them:

mythology

war memorials

local history

tributes

 

But another theme emerged as well, and the idea that comes to mind is "celebration of life" or "joy in living".  Here are three such fountains - fountains of youth, happiness, and life!

 

 

 

 

Summer Programs

 

May 5, 2010

 

 

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round@rationalsys.com

 

A Variety of Projects in the works for the summer - some involved, some quick-hitting, and some you can make as big as you want! 

 

More information to come -  CHECK BACK!

 

ONE PROGRAM PULLING BITS AND PIECES FROM ALL OF THESE I'M TENTATIVELY CALLING "ABOUT TOWN" ...

 

SPECIFIC PROJECTS WILL INCLUDE

Santa Fe, Oregon, and California Trails

Art

Fountains and Sculptures

Cemeteries

City and Street Names

The Shakespeare Festival (King Richard III)

Photographs

A Biography

 

 

                                                      

 

The Fountain Project

 

Geocoding Neat Fountains I've Come Across

 

May 6, 2010

 

 

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round@rationalsys.com

 

 

The Spectacular Stradivarius

 

Mother Nature and Beautiful Sounds

 

May 7, 2010

 

 

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round@rationalsys.com

The Spectacular Stradivarius

Mother Nature and Beautiful Sounds

Something that has bothered me for years is the wonderful violin.  A magnificent instrument.  My daughter has played now for about 7 years, and my son played for one before stopping.  We rented violins for a while, and frequented a marvelous store:  KC Strings.

www.kcstrings.com

 

 

Peer through this “digital” window, and look at the instruments.  The violins on the left range in price from hundreds to thousands of dollars.  Thousands!  This got me thinking about the famed “Stradivarius”:

 

 

 

But not just in name, but in value.  A Stradivarius now sells for hundreds of thousands of dollars.

 

Why?

 

One thought was, many things old are valuable because they are old.  That is:

 

 

 

However, there are many things old that are not valuable.  It’s likely “value” here has something more to do than mere age.

 

Let’s ask the musical experts.  They claim a Stradivarius violin sounds better than any violins ever made.

 

How can this be?

 

With existing technology and knowledge, why can’t we make something that sounds as good as that made by hand hundreds of years ago?

 

I think I now know the answer.

 

Antonio Stradivarius

by Edgar Bundy, 1893

 

The quality sound of the Stradivarius violin, it’s believed, is due to the wood used.  Why would this wood be different than wood today?  What has the type of wood to do with the sound at all?  Stradivarius wood was particularly dense.

 

How do we know this?  Why would this be?  We know, from the period, the trees in his part of the world were particularly dense, because of tree-ring growth.

 

 

 

You can liken tree-ring growth to reading a book.  When the reading is easy, and the pictures many, you can go through 40 pages quickly.  On the other hand, when the dialogue is hard to follow and the pictures few, the amount of pages covered is slim. Such is the case with tree-ring growth.

 

But what’s the equivalent thought in circumstances for the tree leading to “slow growth”?  What would cause a tree to grow slowly?  Lack of water?  Lack of warmth?  Either?

 

 

Were either of these the case during the time of Stradivarius?  What was the time – and place – of Stradivarius?   Italy.  1636 – 1737.

 

 

Edward Maunder can help, in this regard.  Maunder (1851 – 1928) was an English astronomer best remembered for his study of sunspots.

 

 

 

But how can sunspot data be irregular?  I’ve always thought of the sun as being this big, round thing in the sky.  There must be a ton of irregularity to it for such data to be the results.  Maunder showed there was.

 

In fact, during the 17th century, there was a remarkable absence of sunspots.   The era has come to be known as the “Maunder Minimum”.  At this time, there also was the “Little Ice Age” that swept Europe.

 

Might these two have something in common?  Causally?  That is:

 

 

 

Let’s put all this together, as we now have beautiful sounds, stressed woods, ice ages, sun spots:

 

More to come on violins - their structure - their music - their history!

 

 

The Territorial Evolution of the United States

 

a New Project - Part of "The autoSocratic Scrolls" Library

 

May 8, 2010

 

 

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round@rationalsys.com

The presentation of data like the one here fascinates me - and frustrates me - both for the same reasons.

It provides an awesome array of material, organized in one layout, for one to see the chronologic and visual change over time ...

It's fascinating.

But because one is limited by space in including material, it necessarily makes choices about what data to include, and within that selection process a great deal of context is lost.

For example:

We're told on April 2, 1790, "Congress accepts North Carolina's cession of its western counties, which had initially been ceded on December 22, 1789. The land became unorganized territory..

This is the explanation for the geographical / visual change in North Carolina.

Read that first sentence again.

North Carolina ceded its western counties.

Why would a state cede any of its parts?

Surrender?

Are you kidding me?

What's this all about?

There's a ton of context missing from this statement.  It includes the "WHAT" but excludes the "WHY"?

And why does the "narrative", the verbal explanation, have to lag behind the visual?  Why is this the default historical method of displaying text? 

What can we do about it?

That's the goal of this initial write-up for a new series called "The autoSocratic Scrolls" ...

You'll see why this name applies when you see the first three examples below.

When printed out in their entirety - and continuously - they span a number of sheets.

And viewing them is best when they're unrolled - as a scroll.

And even under the "operational / contextual syllogism" giving rise to the change from a "present state" to a "future state", there's a ton of research.  Did you know, for example, when North Carolina decided to cede its area between the Mississippi River and Appalachian Mountains, there was a war - between the states?  Between "Franklin" and "North Carolina"?  Franklin?  Yes - the lost state of "Franklin", formed by individuals for the same reason the colonies themselves broke free from England!

Here we go - Installment 1 of about 40 (meaning when this is continuously printed out, it reaches 120 pages laid end to end, sideways.  Approximately 120 feet.  40 yards.  Almost 1/2 a football field!

(A note about these images - they've been reduced to fit on this screen - but in reality, each image fits landscape on 8.5 x 11 ...

These will be included on a site in the near future ...

 

 

A Note from Morris Kline

 

Part I

 

May 9, 2010

 

 

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round@rationalsys.com

PEA SOUP, TRIPE, and MATHEMATICS

By Professor Morris Kline

November 26, 1955.

Talk given at a meeting of the

Mathematical Association of America

Shortly after the title of this talk was announced, I received some threats on my life. I have therefore decided to change the subject of this talk from Pea Soup, Tripe and Mathematics to Tripe, Pea Soup and Mathematics. In more conventional language I wish to discuss the mechanical, meaningless mathematics that is still being taught in 90% of the colleges and universities, the mathematics that many professors would like to substitute for this established material, and finally what I believe mathematics is and therefore should be taught. My concern today is primarily with the freshman courses but many of the remarks apply to the entire undergraduate curriculum.

Let us look for a moment at the status of mathematics education. I believe that I do not have to convince anyone here that we are failing to put mathematics across. One only has to note the reactions of students to the subject, for example, their grim countenances in class, to see that we are failing. One can check this conclusion by asking his colleagues in other departments – surely an intelligent group – how they feel about the mathematics they took at school.

In trying to locate the source of the trouble, one first recognizes that students, teachers, curricula, and texts all enter the picture. The trouble may lie in any one of these quarters. Well, there can be some criticism of the students. But since about 95% of the students feel that they get nothing from their study of mathematics, the trouble can hardly be there. Criticism can be made of many teachers but since the most knowledgeable of the professors have the same trouble, this factor too can’t be more than a part of the difficulty. We come therefore to curricula and texts and these may be discussed together because the texts reflect the curricula, at least these days when almost anyone can get a text published.

I proceed therefore to examine the standard college curriculum for freshmen: algebra and trigonometry. Let me consider first whether the material we teach is knowledge in any significant sense. Does it give us any understanding of the physical world? Does it teach us anything about human physiology or social institutions? Does it help us to get along with our fellow man? Does it teach young people how to choose their mates or even the food they should eat every day? You may regard these questions as ridiculous but what I am getting at is that Horner’s method, trigonometric identities, and partial fractions seem to have no bearing at all on the knowledge and problems with which even educated men should be concerned. This material has no relationship at all to human affairs in the broadest sense. In and for itself, it is meaningless material.

Of course we could be teaching something which has little or no bearing on human affairs and yet possesses intrinsic interest and beauty. The subject of ceramics might be an example. Well, I believe that I can honestly say that I like mathematics. But I hate manipulation of fractions. The laws of exponents fail to thrill me. The quadratic formula, the supposed shining light of algebra, is a huge disappointment. Partial fractions are insufferably dull. The ambiguous case is not ambiguous to me; it is decidedly disagreeable. Triangle identities keep me amused for a short time until the thought crosses my mind that I ought not to waste time and better do something significant. There is beauty in mathematics but there is no topic and no proof in college algebra or trigonometry which possesses it. These subjects are dry as dust; they are mathematics at its worst.

Because students are uninformed and a captive audience, they can be gotten to absorb rubbish. But even rubbish has to be motivated. The topics we teach in college algebra and trigonometry not only are not motivated but cannot be motivated because in and for themselves they serve no purpose. We can tell students that they will use this material if they continue with mathematics.  But who would want to continue with mathematics after such an introduction to it? You know the answer as well as I do. Very few. The students who reject mathematics after being exposed to algebra and trigonometry are wiser than the teachers.

I repeat that from algebra, geometry and trigonometry as such, nothing follows for the students. My thought here was best expressed by Alfred North Whitehead in an address made many years ago to a group of British teachers of mathematics:

. . . . elementary mathematics . . . must be purged of every element which can only be justified by reference to a more prolonged course of study. There can be nothing more destructive of true education than to spend long hours in the acquirement of ideas and methods which lead nowhere. . . . [T]here is a widely-spread sense of boredom with the very idea of learning. I attribute this to the fact that they (the students) have been taught too many things merely in the air, things which have no coherence with any train of thought such as would naturally occur to anyone, however intellectual, who has his being in this modern world, . . . the elements of mathematics should be treated as a set of fundamental ideas, the importance of which the student can immediately appreciate: that every proposition and method which cannot pass this test, however important for a more advanced study, should be ruthlessly cut out. . .

Over and above these objections to the standard material there is another; the topics are disconnected. From the manipulation of fractions we shift to exponents, from exponents to factoring, from factoring and perhaps the solution of equations, to complex numbers, from complex numbers to mathematical induction, from induction to permutations and combinations, from these to progressions, to binomial theorem, to partial fractions, etc. Even the trigonometry material has only an apparent coherence. What has triangle solving to do with identities, identities with trigonometric equations, the equations with trigonometric functions, the functions with the polar form of complex numbers? Surely sin theta and cos theta are involved in all of these trigonometric topics but this underlying thread is a trivial one and a technical one. From the standpoint of motivating students and large ideas there is no unity in trigonometry. How can this welter of unrelated or superficially related topics taught in college algebra and trigonometry produce more than confusion in the minds of the students.

What I have been trying to point out thus far is that the material we have been teaching to almost all of the freshman course of the past 100 years is meaningless, unmotivated, ugly and disconnected. We have taught processes which 95% of the students will never use, and even those who do go on to use it will not be effective because the material is taught mechanically. Starting with fractions in the elementary school the students learn to perform like martinets. As the students attempt to master process after process, the meaninglessness of the material frustrates them. As the years go by, the pile of meaningless operation becomes too large to bear, the entire structure collapses, and the students’ progress is hopelessly blocked. Because the material has been meaningless to them, they forget readily and willingly.

I can sharpen the distinction between what we have been teaching and mathematics. The Greeks, you know, distinguished between arithmetic, the science of number, and logistica, the practice of commercial arithmetic. An analogous distinction should be made today. There is mathematics, the science and art, and there is mathematics, the craft or trade. Trade mathematics is to mathematics as plumbing is to hydrodynamics and as electrical wiring is to electromagnetic theory. We have been teaching the trade and neglecting the science and art. We have been teaching the tripe and neglecting the nourishing meat.

 

 

A Note from Morris Kline

 

Part II

 

May 10, 2010

 

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round@rationalsys.com

Unfortunately many teachers do not understand the distinction between mathematics as a trade and mathematics as an art. They themselves learned the trade as an apprentice to some journeyman and hence they know only the trade. They are the victims of a curriculum now over 100 years old and their understanding is limited to manipulative mathematics. They are entrapped by walls and tradition, educational practices, and systems and the walls are so high they can’t see over them. After their indoctrination into the union of mathematical craftsmen these teachers grow old and die. Perhaps they have heard that mathematics is a gift of the Greeks and therefore fear it – in fact fear it more than their students. At any rate they never venture into mathematics proper.

The “new” books, endless repetitions of algebra and trigonometry, which appear by the dozens each year, cater to these teachers and fail to challenge their narrow horizon. Ultimately, the texts become masters of the teachers and these men follow the books slavishly. Though I do not wish today to digress into the subject of mathematical texts, when I think of them, I am reminded of a remark which William Gilbert, the famous seventeenth century scientist, makes in his De Magnete. After pointing out that Cardan in his writings described a perpetual motion machine and that many other writers did likewise, he exclaims, “May the gods damn all such shame, pilfered, distorted works, which do not but muddle the minds of the students!” May I add, and the teachers.

Up to this point, I suspect that I still have a few friends and sympathizers in the audience because fortunately, a small but interesting group of mathematics teachers has become convinced that the conventional curriculum is bad and is trying to do something about it. But I am afraid I shall lose these friends within a few minutes.

The group of people I have in mind who wish to reform the freshman curriculum have this much in their favor. They do not want to teach ideas; they do wish to exhibit and practice the reasoning processes of mathematics; and they are ready, willing, and able to break with the tradition of techniques for the sake of techniques. But I fear they have gone to the opposite extreme, for their recommendation is that we teach modern abstract mathematics. And so we find in some of the newer texts such topics as symbolic logic and Boolean algebra, postulational systems, set theory, rigorous establishment of the real numbers as Dedekind cuts, and of the complex numbers, as couples, abstract algebra, e.g., groups and fields, functions as transformations from one domain to another, and the like.

Here indeed we do find ideas and clean-cut proofs. There are just a few difficulties. This material is completely over the heads of the students. It is as meaningless to them as the mechanical techniques.

The students are not prepared for such material. How can anyone understand the rigorous establishment of the real number system who can’t add fractions or distinguish rational from irrational numbers? How can anyone appreciate symbolic logic who confuses all A is B with all B is A? Of what significance is Boolean algebra to students who can’t square (a + b) or believe that the square root of (a2 + b2) is equal to a + b? What can an abstract postulational systems mean to students who have yet to understand deductive proof?

Advocates of the new material say that students will learn these things through the abstract approach. But the concrete – indeed, a thorough understanding of the concrete – must come before the abstract. This is the first principle of the psychology of learning. A collection of formulae such as (p > q)×(q > r) > (p > r) will not teach deductive reasoning. Examples of groups such as finite groups with multiplication tables will not make the concept of a real number any clearer. Students who have learned the field concept and some of its theorems will not necessarily be able to add 6 and –7 or to add fractions. Why with a perfect knowledge of the field concept these students couldn’t make change in a grocery store. They would be tied helplessly and hopelessly to a lot of, to them, meaningless assertions. Abstraction is not the first stage but the last stage of development. It may give new insight but only into concrete subject matter already learned. It may unify but it must unify what one already knows.

Whether or not the students can absorb these abstract topics, I would object to them on the additional ground that abstract mathematics is empty mathematics – it is pea soup as opposed to steak. It is the form without the substance, the shell without the kernel. One does not get something for nothing – even in mathematics. Certainly the concept of a field includes the rational, real and complex numbers and these distinctions are all important for any understanding of elementary mathematics.

Perhaps I can make my point clearer by suggesting that we look at the corresponding problem in geometry. Why don’t we abandon triangles, circles, rectangles, parabolas, etc. and just study the concept of a geometrical figure? Hah, say the abstractionists, now you are talking my language. Let’s teach topology. Yes, but topology will not teach us how to obtain the area of a rectangle.

The claim has been made that the abstract approach is more efficient because several topics of conventional mathematics are encompassed in one approach. But the claim is illusory. The concrete cases must still be taught. The time that is wasted is the time spent in teaching the abstract concepts, for when the concrete cases are understood, the abstractions are readily made.

Implicit in the preceding arguments is another objection to the abstract rigorous topics listed above. This knowledge is useless knowledge, something we can’t afford in today’s world. The student who learns all about postulational systems will not be prepared to make the simplest use of mathematics. He will be at a loss in solving even a linear equation. We cannot afford the criticism that will be leveled at such training by the physicists, chemists, engineers, and the industrial world.

Finally, even if the students learned the abstract mathematics and its interpretations, I would still object because this material is not representative of mathematics. One indispensable element has been omitted – the physical world. Mathematics is above all an idealized formulation of physical objects and phenomena and mathematics is significant and vital because it has something to say about the physical world.

The abstractionists apparently want to keep their subject pure. They don’t wish to sully it or they desire to remove the dross of the earth from which mathematics has arisen. But as they wash the ore, they keep the iron and lose the gold. No man is an island unto himself and no subject can exist in isolation. A perfect command of the English language is useless if a man has nothing to say. And pure mathematics has nothing to say. I may appropriate here Russell’s famous dictum: “Pure mathematics is the subject in which we never know what we are talking about nor whether what we are saying is true.” And if we don’t know what we are talking about, the students surely won’t.

Some may say that of course the physical world is there. One has to interpret the mathematics. Perhaps so. The modern abstract painters tell us that the physical world, people, and emotions are all in their works. But I defy you to find them.

 

 

An Open Letter

 

to Supreme Court nominee Elana Kagan

 

May 11, 2010

 

 

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round@rationalsys.com

Supreme Court nominee Kagan ...

You'll be inundated with questions from both parties about your position on specific issues.  Specific issues are important, of course, because they're the concrete implementation of a legal decision in action.

But all legal decisions are based on certain principles, and it's these principles I'd like to quickly explore.

Please define "right":

What is the source of "rights":

What is the proper role of the government:

What is the relationship between the Supreme Court and Federal, State, and Local judicial environments:

What is the relationship between the three branches of government:

What recourse  is afforded the sheep who, with two wolves, take a vote on what to eat for dinner?

I look forward to your honest responses.

Michael Round

Center for autoSocratic Excellence

 

 

King Richard III

Part 1

 

May 12, 2010

 

 

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round@rationalsys.com

You can't imagine how long it took me to put together this little "family tree".  I've ready summary after summary of Richard III, and not been able to follow the cast of characters.

The mere act of creating this - whether it's right or not - now has put me in a position to do some real work.

A starting point - a foothold - and off we go!

 

 

The First Phase of his Journey into Quality

 

Robert Pirsig - and Zen and the Art of Motorcycle Maintenance

 

May 13, 2010

 

 

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"The First Phase of his Journey into Quality"

 

Much of my recent work keeps coming back - metaphorically - to this story ...

 

"Today now I want to take up the first phase of his journey into Quality, the nonmetaphysical phase, and this will be pleasant. It's nice to start journeys pleasantly, even when you know they won't end that way. Using his class notes as reference material I want to reconstruct the way in which Quality became a working concept for him in the teaching of rhetoric. His second phase, the metaphysical one, was tenuous and speculative, but this first phase, in which he simply taught rhetoric, was by all accounts solid and pragmatic and probably deserves to be judged on its own merits, independently of the second phase.

 

He'd been innovating extensively. He'd been having trouble with students who had nothing to say. At first he thought it was laziness but later it became apparent that it wasn't. They just couldn't think of anything to say.

 

One of them, a girl with strong-lensed glasses, wanted to write a five-hundred-word essay about the United States. He was used to the sinking feeling that comes from statements like this, and suggested without disparagement that she narrow it down to just Bozeman.

 

When the paper came due she didn't have it and was quite upset. She had tried and tried but she just couldn't think of anything to say.

 

He had already discussed her with her previous instructors and they'd confirmed his impressions of her. She was very serious, disciplined and hardworking, but extremely dull. Not a spark of creativity in her anywhere. Her eyes, behind the thick-lensed glasses, were the eyes of a drudge. She wasn't bluffing him, she really couldn't think of anything to say, and was upset by her inability to do as she was told.

 

It just stumped him. Now he couldn't think of anything to say. A silence occurred, and then a peculiar answer: ``Narrow it down to the main street of Bozeman.'' It was a stroke of insight.

 

She nodded dutifully and went out. But just before her next class she came back in real distress, tears this time, distress that had obviously been there for a long time. She still couldn't think of anything to say, and couldn't understand why, if she couldn't think of anything about all of Bozeman, she should be able to think of something about just one street.

 

He was furious. ``You're not looking!'' he said. A memory came back of his own dismissal from the University for having too much to say. For every fact there is an infinity of hypotheses. The more you look the more you see. She really wasn't looking and yet somehow didn't understand this.

 

He told her angrily, ``Narrow it down to the front of one building on the main street of Bozeman. The Opera House. Start with the upper left-hand brick.''

 

Her eyes, behind the thick-lensed glasses, opened wide. She came in the next class with a puzzled look and handed him a five-thousand-word essay on the front of the Opera House on the main street of Bozeman, Montana. ``I sat in the hamburger stand across the street,'' she said, ``and started writing about the first brick, and the second brick, and then by the third brick it all started to come and I couldn't stop. They thought I was crazy, and they kept kidding me, but here it all is. I don't understand it.''

 

Neither did he, but on long walks through the streets of town he thought about it and concluded she was evidently stopped with the same kind of blockage that had paralyzed him on his first day of teaching. She was blocked because she was trying to repeat, in her writing, things she had already heard, just as on the first day he had tried to repeat things he had already decided to say. She couldn't think of anything to write about Bozeman because she couldn't recall anything she had heard worth repeating. She was strangely unaware that she could look and see freshly for herself, as she wrote, without primary regard for what had been said before. The narrowing down to one brick destroyed the blockage because it was so obvious she had to do some original and direct seeing."

 

===========================

 

There are (at least) two powerful thoughts here ...

1. cliches - even saying that word may be a "cliche"!  What does it mean to "see" something?  What do you "really" see - if you look?

2. focus - many tend to "see the forest instead of the trees", while others are great at "seeing the trees and neglecting the forest".  Focus may be a great injection to leverage sight of the trees to gain insight into the forest.

 

 

 

ON PAPER ONLY

 

"A Capital Idea" Story

Wisconsin Part III

 

May 14, 2010

 

 

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The story continues, with Territorial Governor Dodge now taking the stand.

Senator:  Mr. Dodge - is it true you presided over Madison being named territorial capital of the Wisconsin Territory?

Dodge:  No.

Senator:  (obviously taken aback) No?  You were Territorial Governor?

Dodge:  Yes.

Senator:  And Madison was named Territorial Capital?

Dodge:  Yes.

Senator:  So what do you mean "no" earlier?

Dodge:  I mean "no".  By "no", I mean I presided over a process whereby ultimately a territorial capital was chosen.

Senator:  (obviously not understanding what's been said), tries a different track:  "Mr. Dodge, is it true you picked Belmont as the first territorial capital because of your relationship with John Atchison?

Dodge:  No.

Senator:  Obviously flustered.  No?  Can you tell us how Belmont, in the corner of the state and with no population, became territorial capital?

Dodge:  Sure.  It was in the middle of the territory, and I knew John as a man who could have the meeting buildings built in time.

Senator:  In the middle of the territory?  Belmont?

Dodge:  You little punk - you have no sense of history of your own area, do you?  You think Wisconsin - as a state - has always been this same shape?  Shut your mouth and pay attention, while I draw you out a history lesson.

(goes to the chalkboard).

Here's us now - and here's Belmont, down in the corner.  Looks out of the way, doesn't it ...

 

In 1835, however, it was clear Michigan was on its way to statewood.  You did know we were once part of Michigan Territory, didn't you sonny?

We could hardly stay Michigan Territory if Michigan was going to become a state!

So they split us off, into the Wisconsin Territory, with the directive to set a meeting place.  This "council" was to meet at a place specified by Acting Governor Stevens Mason.  He called for the meeting to be in Green Bay January 1, 1836, but before the meeting even took place, President Jackson replaced him with John Horner, who moved the meeting up to December 1, 1835.

But Horner never showed up for any of the meetings, the little coward!

The representatives who did show up there, of course, all bickered about where the seat of the new government would sit.

Can you imagine all these folks, all whining their city was the best for the job?

Cassville, just down river from Prairie de Chien, was the front runner.  Remember Cassville?

Vineyard wanted Cassville.  Slaughter wanted Fond du Lac, Knapp wanted Racine, Slaughter changed his mind and recommended Green Bay.  Whine!  Whine!  Whine!  You see Vineyard over there (pointing in the corner)?  He eventually shot an opponent on the chamber floor during a dispute!  You think these hotheads would ever make a decision?

And on April 20, 1836, the government officially created the "Territory of Wisconsin", but without specifying the territorial capital.

We needed a capital, and the decision wasn't going to come from these clowns!

 

Senator:  So how did you come into the picture?  How did you become Territorial Governor?

Dodge:  Jackson knew me, and knew I was someone who could get the process going.  He told me to do a survey of the population, pick the middle, hold a meeting, and then choose a spot for the territorial capital.  That's what I did.

Senator:  But Belmont?

Dodge:  You ignorant fool.  Maybe I should put you under oath.  Here's the Wisconsin Territory created in 1836.  It's quite a bit bigger than our state is now, which, for your information, only became a state in 1848:

It puts a different spin on your thoughts, doesn't it?

Senator:  (embarrassed):  It does.

Dodge: But the story doesn't end there. Yes, I chose Belmont because it was in the center of the territorial population.  Yes, it's true there wasn't much in Belmont.  But I knew if I chose any other city, there'd be trouble.  I also knew Atchison could get the job done, and he did.

Senator:  So you met in Belmont?

Dodge:  Yes.

Senator:  So how did Madison become capital?

Dodge:  You're missing Burlington!

Senator:  Burlington?  What does Burlington, Iowa have to do with anything?

Dodge:  (stepping up to the podium, grabbing the Senator firmly by the collar, and carrying him to the witness' chair.  Dodge then took the gavel.  "You sit there for a while and keep your mouth shut, and I'll do the talking."

Stay tuned for the 4th - and Final - episode!

 

 

PASCAL'S TRIANGLE

 

Miscellaneous Color Renderings - in Excel

 

May 15, 2010

 

 

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A Quick Presentation on "The Santa Fe Trail"

 

Of the United States

 

May 16, 2010

 

 

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A Short Presentation on the Santa Fe Trail, integrating the following items - and many more:

 

And closing with the remark - this is NOT the Santa Fe Trail ...

 

... This is:

 

 

MATHEMATICAL SCULPTURES

 

In the Kansas City Area

 

May 17, 2010

 

 

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The coming summer project on fountains and sculptures gave rise to several general categories:

memorials

historic celebration

mythology

local considerations.

 

But there's another category of spectacular prominence in our area - mathematical sculptures.

 

Here's four:

 

 

Brent Collins

Pax Mundi - at H&R Block

 

Brent Collins

Millennium Arc - at Overland Park Community Center

 

Brent Collins

Double Helix - at the Kauffman Foundation

 

Kenneth Snelson

Triple Crown - at Crown Center

 

 

THE SIERPINSKI GASKET

 

and Cancer ---

 

May 23, 2010

 

 

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Stay tuned for more on a pretty cool project ...

 

BRITISH PETROLEUM

 

and the limits of liability

 

May 24, 2010

 

 

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The oil continues to flow, 5,000 barrels or 200,000 galloons a day.  Even these estimates are now questioned ...

The oil is now threatening all coasts in the gulf.

And there seems no end in sight to the oil spewing from the Gulf floor.

You may wonder how could a oil rig make the coastlines so vulnerable?  Why are there no back-up plans?  This seems an unbelievably vulnerable occupation.

 

You may also not know there are approximately 4,000 other rigs in the gulf, operating year after year, without incident.

 

This may put things in perspective, but doesn't negate the damage caused by the BP rig right now.

And then we learned BP's liability is capped at $75 million.

Congress - and the President - rushed legislation raising that limit to $10 billion.  Everybody applauded.

Except me.

In this country, laws are to be objective.  Playing poker is impossible if, half-way through the game, you discover the deuces are suddenly wild.

Instead of raising the liability limit, a better question might have been:  where did the limit come from in the first place?

You wouldn't be surprised to know it's from the Oil Pollution Act of 1990,

Key Provisions of the Oil Pollution Act

§1002(a) Provides that the responsible party for a vessel or facility from which oil is discharged, or which poses a substantial threat of a discharge, is liable for: (1) certain specified damages resulting from the discharged oil; and (2) removal costs incurred in a manner consistent with the National Contingency Plan (NCP).

§1002(c) Exceptions to the Clean Water Act (CWA) liability provisions include: (1) discharges of oil authorized by a permit under Federal, State, or local law; (2) discharges of oil from a public vessel; or (3) discharges of oil from onshore facilities covered by the liability provisions of the Trans-Alaska Pipeline Authorization Act.

§1002(d) Provides that if a responsible party can establish that the removal costs and damages resulting from an incident were caused solely by an act or omission by a third party, the third party will be held liable for such costs and damages.

§1004 The liability for tank vessels larger than 3,000 gross tons is increased to $1,200 per gross ton or $10 million, whichever is greater. Responsible parties at onshore facilities and deepwater ports are liable for up to $350 millon per spill; holders of leases or permits for offshore facilities, except deepwater ports, are liable for up to $75 million per spill, plus removal costs. The Federal government has the authority to adjust, by regulation, the $350 million liability limit established for onshore facilities.

 

When a liability limit is in place, it's reasonable to ask what happens to the cost above that liability limit?

The Congress created a fund, created via an oil tax, to pay for these costs.

The money is suppose to be set aside already!

Mr. President?  Congress?  Is the money there?

 

A further thought regarding liability maximums.  Responsible parties seek to limit damages by careful execution of a plan.  Back-up plans are essential.  Money is spent to minimize the exposure to spills, leaks, or otherwise adverse events.

However, when the risk of costly mistakes is removed, what incentive is there to "go the extra mile" to make sure "you've covered all bases"?

What role did the government play, in creating the OPA and setting a liability maximum, in causing this accident in the first place?

How would a company act differently, knowing they were entirely liable for the ultimate costs incurred by adverse events?

Of course, companies might not choose to maintain that risk.  Is there another option?  Of course.  This is the role of insurance companies.

But insurance companies don't merely accept risk - they analyze it.  They rate for it.  They recognize good practices, and penalize bad.

If you choose to live in a flood plain, expect to pay a lot for flood insurance - if you can get it at all.  If not, recognize the risk is all yours.  Nobody sees it as a profit-making venture.

In most instances, a policy does not even pay out.  It's not suppose to.  It takes many good years to offset the catastrophic events of one bad year.

But this is the job of the insurance company.

In the case of the oil industry, the government has mandated itself the insurance company.

And we see the results.

They've eliminated the need for anyone to "go the extra mile" to ensure safety at all costs!  They've collected money to pay for the damage, but spent it already. 

The well is dry - financially and intellectually.

 

 

3-DIMENSIONAL GRAPHING IN EXCEL

 

 

May 25, 2010

 

 

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If you've ever tried to graph 3-dimensionally in Excel, you know there are no options in Excel.

If you know at all the Spreadsheet community, you also know thousands of people have found work-a-rounds to solve the problem of graphing in three dimensions.

When you search through these work-a-rounds, you will be disappointed.  The results are poor, cumbersome, and hardly inspiring.

Why is this?

As always, let's "get something on the table":

2-Dimensional Axis:

 

3-Dimensional Axis:

Let's plot something in three dimensions to get something more on the table.  And doing this, an amazing thing happens:  the answer is so damn obvious it's ridiculous - and embarrassing!

The absurdity of the situation - EVEN THE QUESTION - is evident, now!  How do I graph in 3-dimensions - WHEN EVERYTHING BEING VIEWED IS IN 2-DIMENSIONS?

Some transformations are necessary.

Some trigonometry.

But three-dimensional graphing in Excel is a possibility!

 

 

A TRIP TO PARKVILLE, MO

 

a few things we plan on researching on our trip

 

May 26, 2010

 

 

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The Waddell "A" Truss Bridge

Waddell?

Yes - that Waddell, who designed and built the remarkable ASB Bridge crossing the Missouri ...

 

This set of monolithic domes on the Park University Campus ...

 

The Benjamin Banneker School (in the restoration process) - built in 1885 ...

 

Remember the Alamo!  Remember Goliad!  Goliad?

The Goliad Massacre.

But what has this to do with Parkville, Missouri?  George Park, founder of Parkville, MO, was one of the few survivors of the Goliad Massacre!

 

 

ACES OVER EIGHTS

 

a quick biography of Wild Bill Hickok

 

May 27, 2010

 

 

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Wild Bill Hickok.

 

The name may conjure images of the "West".  It should.  Wild Bill Hickok, it seems was the epitome of what we consider the west.

He was shot and killed August 2, 1876 in Deadwood, which had yet to become South Dakota, and was at the time Dakota Territory.

Playing poker, he was approached from behind by John McCall.  This in itself was odd -Hickok always sat with his back to a wall.

He died holding aces over eights - the "dead man's hand".

 

But it's not how he died I want to talk briefly about, but rather how he lived.

He came to Deadwood in search of gold.

No, he wasn't married to Calamity Jane.  That's what she claimed.  It's not true.

Before Deadwood, he held a series of Sheriffs positions.  In fact, it's thought McCall was paid by professional gamblers to kill Hickok because Hickok had a reputation for cleaning up towns.

Before this, he sometimes served as a scout for Custer's 7th Cavalry.

Before this, he briefly rode for the Pony Express.

Gunfights.  The first recorded duel. 

Hickok was born this day, May 27th, in 1837, in Troy Grove, Illinois.

But he left Illinois when he thought, during a fair fight, he'd killed a man.  The man was still alive, but Hickok was on his way west.

To the Kansas Territory.

There's not always a monument left for what's come before.  Not seeing such a monument, you're likely to walk right over a spot, feeling nothing for what's come before.

Such is the case with this plot of land just northwest of us - 83rd and Clare Road, in Lenexa, Kansas.

 

Hickok, you see, plotted this land in 1857.

 

 

I LOVE THE PIANO

 

The Piano and Pi

 

May 28, 2010

 

 

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As Judy Garland said in Easter Parade ...

 

I love a piano

I love a piano

I love to hear somebody play

Upon a piano

A grand piano

It simply carries me away

I know a fine way

To treat a Steinway

I love to run my fingers o’er the keys

The ivories

 

When with the pedals

I love to meddle

When Paderewski comes this way

I’m so delighted

If I’m invited

To hear the long-haired genius play.

So you can keep your fiddle and your bow

Give me a p-i-a-n-o-o-o

I love to stop right

Beside an upright

Or a high-toned baby gray.

 

I love to stop right

Beside an upright

Or a high-toned baby gray.

 

The piano.  Music.

Music and Math.  We've been told for a long time there's a relationship.  There probably is.  I like both, though only one - the latter - do I really understand.  The former I just like to listen to.

A friend has composed a piano symphony based on p.  I wondered how he did it.  How would you map piano keys to numbers?  But more than that, how might I, a non-musician, take a bunch of numbers and translate them into a musical score?

Let's look at p:

Of course, it goes on for ever - and ever!  But that's OK, because at first glance, it seems obvious what to do: let each number represent a key.

For example:

C = 1

D = 2

E = 3

F = 4

G = 5

A = 6

B = 7

and ... then what?  And what about the black keys?  In between C and B, there are five black keys in addition to the seven white!

 

In fact, in looking at the actual keyboard, I see other problems immediately ... there's not just one "C", but eight!

 

That's just one problem - giving the issue a moment's thought brings to mind a couple others:

1. it's often the case several keys are played at once.  How does a number-to-key mapping take this into account?

2. some notes are held for 2 counts, 4 counts, or there is the absence of a sound.  How does a number-to-key mapping take this into account?

 

Let's take a shot at organizing what it would take to accomplish all this - I need to know how many keys are being played simultaneously, how long the note is held, and what key is being played.  Let's get something on the table:

Will this work?

Let's consider the first field.  In this system, I've got only the possibility of playing four keys simultaneously.  If this digit in p is 1,2,3,or 4, I know what to do.  But what happens if the digit is a 5? 9?  What happens then?

Let's use a function called modulus, which returns the remainder of a number when it's divided by the modulus.

For example:

when the digit is an eight, we calculate 8 / 5 = 1 r 3 and write '3' instead

when the digit is a seven we calculate 7 / 5 = 1 r 2 and write '2' instead.

Here's our table of mapped values:

What about the duration the note is held?  Let's learn from what we did with "# of keys played simultaneously".  Possible values might be "1 count, 2 counts, 3 counts, 4 counts."  If the possible values are 1,2,3,4, then I've really got the same mapping as with "# of keys".

We're moving right along, when a thought comes to mind:  what about pauses?  We may be lucky here, since we really didn't do anything about with '0'.  What does '0' mean with respect to "# of keys played simultaneously"?  Maybe that's our pause! 

Now, how long shall we hold that note or pause?

Here, maybe we're not so lucky, since '0' doesn't mean anything.  What can be done to modify this function to result in the values 1,2,3,4 only, with no zero? 

 

and our new table looks like this:

 

Of course, we still haven't done anything with what key we're playing!  How do we translate (or map) this?

Next time!

 

 

I LOVE THE PIANO

 

The Piano and Pi

Part II

 

May 29, 2010

 

 

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We're moving right along, and now I want to figure out what note to play.

It seems possible values are C, D, E, F, G, A, B.  But there's also the five black keys C#, D#, F#, G#, and A#.

That's 12 possibilities, and I only have 10 numbers available.

Moreover, as I said earlier, there's 8 possible Cs to choose from, so not only do I have to map 12 notes onto 10 numbers, but I have to specify what sector I'm considering.

One thought is this:

the first digit tells me what sector of the piano I'm considering, with possible values 1 - 8.

Within each sector, I still have the issue of 12 keys and 10 numbers.  Let's break this down into white keys (7) and black keys (5).  This would work.  So maybe the next digit tells me whether to play a white key or a black key.  Maybe it's an odd / even indicator.

If even, what white key?  Since the possible values are 1,2,3,4,5,6,7, the mapping might be 1 + mod(digit,7).

If odd, what black key?  Since the possible values are 1,2,3,4,5, the mapping might be 1 + mod(digit,5).

That is:

 

This seems to work, but it's a change to our overall table, which now is growing rapidly.

 

Let's put this all together, and apply it to the p:

That's a lot of work!  For merely one count, I've used 18 digits!  Is this plausible? 

Of course it's plausible - remember, p goes on to ∞!

But is it a good mapping?  It works, so, in some respects, it's good.

Can it be better?

Let's look again at all the keys on the piano:  52 white keys, 36 black.

88 keys total.

What if I took the digits, two at a time, and merely mapped numbers 1 - 88 to the keys on the piano as you work across the keyboard left to right?

Of course, I need to account for numbers 89 - 99, but we already know how to do this:  1 + mod (two digits, 88).  The layout is much simplified - and intuitive!

and putting it into practice much more concise:

 

This may seem unnatural, but is it plausible?  Are there other examples where this type of mapping takes place?

Of course. 

This type of mapping system is how the computer interacts with the keyboard.  For example, when we type "hello", what really takes place inside the computer is this:

 

Or barcodes ...

 

This, of course, doesn't make the digit mapping of p right.  It just makes it plausible.

Now, to find someone to actually play a few notes!

 

 

CONVERTING THIS TO THAT ...

 

The Lost Art of Unit Fractions

 

May 30, 2010

 

 

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Metric conversions.  Quarts to gallons.  Do I multiply - or divide - by 4?  Miles / gallon converted to liters. 

And more and more complicated things.

Students guess.

And it's frustrating.

I came upon a question recently as rare as it was odd:

"Convert the speed of light into furlongs / fortnight".

Could you?

Take a moment ... then scroll down.

 

 

 

 

 

 

 

 

 

 

What to do?

Let's get something on the table:

     

Now, what's a furlong?

     

How about a fortnight?

     

These two have interesting histories, which I leave to the reader.  Fortnight?  Why have something stand for 14 days?  Of course, in America we do many things on a bi-weekly basis, so the idea isn't so far-fetched.

I digress.

What now?  Let's establish one more item. 

     

No big revelation there, right?  Let's apply it to one of our equations above:

      

Now, let's get to work.  Let's write a non-remarkable equation to get started:

         

Something equals ... itself!  Big deal.  But I know I can multiply the right side by '1' and the result is unchanged.  There are many definitions of '1'.  We're going to work our way across the "unit" spectrum:

Now it's just a matter of filling in the blanks ...

which reduces to ...

 

And the thing about this is there's really 1,000 ways to do it, depending on what you know!  For example, suppose I didn't know there were 1,760 yards in a mile.  Am I stuck?  The key question is: what do I know about a mile?  4 times around the track?  And each time is 440 yards? 

And the key ... keep integrating this into the model - working left to right.

Canceling along the way.  Units in the numerator canceling units in the denominator.  Filling in the blanks.

There's not a thing I can't convert.

Try me.

 

 

MEMORIAL DAY

 

A Kansas City Fountain / Sculpture / Monument Tribute

 

May 31, 2010

 

 

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The Liberty Memorial of World War I.

 

 

American War Mothers Memorial Fountain

World War I

 

 

William T. Fitzsimons Memorial Fountain

(First US Officer killed in WWI)

 

 

The Vietnam Memorial

 

 

The Korean War Memorial

 

 

Three Civil War Memorials

 

 

The Hiker

The Spanish-American War

 ... a memorial dedicated to the veterans of the Spanish-American War, the Philippine Insurrection and the Chinese Relief Expedition (1898-1902).

 

 

 

Veterans of Foreign Wars Centennial Plaza

 

 

There's more, I'm sure.  I'll be adding these in the future.  But one thing stands out - several Civil War memorials, several in memory to WWI, Vietnam, Korea ... even the Spanish-American War. 

 

BUT WHERE ARE THE MEMORIALS TO THE BRAVE MEN AND WOMEN SOLDIERS, LIVING AND DEAD, OF WORLD WAR II?