Noesis

The Journal of the Mega Society

June 2004 Issue 170

Officers

Editor and Publisher: Ron Yannone

189 Ash Street #2

Nashua, NH 03060

Administrator: Jeff Ward

13155 Wimberly Square

San Diego, CA 92128

Internet Officer: Kevin Langdon

P.O. Box 795

Berkeley, CA 94701

Founder: Ronald K. Hoeflin

P.O. Box 539

New York, NY 10101

no·e·sis – Greek Þ understanding – to perceive. Psychology Þ the cognitive process

The Mega Society was founded in 1982 and has been documented in the GUINNESS BOOK OF WORLD RECORDS during the 1980s as the most exclusive society. Mega means million and denotes the one-in-a-million status of its members. Presently, the only viable adult-level admissions test is the Titan Test, developed by its founder, Ron Hoeflin – where 43/48 correct answers corresponds to the minimum accepted IQ level of 176. See www.megasociety.org Since its GUINNESS “distinction” in the 1980’s, the Mega Society with its 99.9999 percentile member status, remains “the most elite ultra-high IQ Society.”

Editorial Introduction to NOESIS Issue #170 – June 2004

By the time readers receive Noesis issue #170, it’ll be close to July. To get our mindset in tune, we exude our Patriotic Flair – and wish our Nation – The United States of America – a hearty Happy Birthday! – July 4^th 1776 . . . “. . . one nation, under God, indivisible, with liberty and justice for all.” I hope our readers from England and Australia will celebrate with us!

We want to extend a Happy Birthday to Bill Corley over in Texas! Bill is engaged in an exciting part of his life – and the avid readers of Noesis want to wish you all the best! If there is something you feel the members of the Mega Society can do to lighten your load, please send your requests to the editor – and he can present them to our readers. Bill sent the following encouraging email on May 28, 2004:

“You are doing a terrific job as editor. Sorry I'm not contributing more, but this is the most creative phase and busiest time of my life. Plus, with 4 daughters, I just had a grandson here for 5 day, etc. It's terrific to be 60 (on June 12 to be celebrated in the Caribbean) and still feel 35. . . . I'll eventually get you a biography (and picture of townhouse). As for other stuff, I'm now using LaTeX for all my papers. Many journals demand it.” Godspeed! Bill Corley

In this patriotic issue, we first present the Declaration of Independence. We hope our readers will contemplate the many sacrifices made by our Forefathers to secure INDEPENDENCE for our Nation.

We next list the signers of the Declaration of Independence. Take a moment to visualize these pioneers – and the era in which they lived.

“A picture is worth a thousand words.” Here, the editor selects photographs of some former Presidents of the United States of America. We have nothing to fear for the future, lest we forget the past, and remember the way in which God has led us.

To get the brain cells churning, we next present famous quotes by different U.S. presidents. Here we team with Bryan Curtis – the editor of the book used.

Hot topics were raised in March Noesis issue #167. Two of these are the war in IRAQ and same-sex marriage. Both topics bombard us daily via diverse media. The editor presents one view of the same-sex marriage issue. He invites other views.

“All work and no play can make Jack a dull boy” – so here we present some jokes and puns the editor recalls during his life. May these quips bring a chuckle to your countenance.

Back to our patriotic theme, we present the Star-Spangled Banner – by Francis Scott Key. Contemplating the historical setting brings a lump to one’s throat.

Next, we revert back to mental stimulation for our young and novice readers – with recreational problems by Michael Holt.

Bill Corley provided his 2003 DIRTY DOZEN exercise set for more mental stimulation. Mega Society member Eric Erlandson will be in his glory – and the editor requests that Eric develop an intriguing set of mathematical recreations for an exciting forthcoming issue of Noesis.

Next, among the many exciting products provided by Dr. Layman E. Allen’s WFF ‘N PROOF website, one item is the topological puzzle by J. R. O’Neil. We present this puzzle on paper, and provide the ‘800’ number to order it as well.

Back to the light side, we present a few chess jokes. We welcome your favorites for publication!

We next move to a serious technical area – that of language translation to thwart terrorism – and the 9/11 saga. We tap Michael Erard, and his article that appeared in a recent MIT Technology Review magazine issue.

Next, we present an excellent book on practical engineering math applications for our children’s stimulation – by teaming with Holbrook Horton. Our avid readers would also greatly benefit from reading through this book!

Next, we present a condensed sample of the fascinating Wonderlic Personnel Test by Wonderlic, Inc. More than 120 million people at thousands of organizations worldwide have taken the 12-minute, 50-question test.

By request of Ron Hoeflin, we present an article in memory of the late Dr. Lewis Aiken on commercially available performance tests. Dr. Aiken is author of about 10 books in areas that span psychometrics.

Next, we move into futuristic robotics research for the U.S. Army – engaged by DARPA (Defense Advanced Research Projects Agency) – with prize money that even our creative readers can consider winning – DARPA’s “Grand Challenge”!

The editor is a lover of WWII history and as such – the exciting article on The Secret in Building 26 will captivate readers – young and old.

We next present a reply article to Brian Schwartz’ articles on psychometric testing and the SAT (Noesis #169) prepared by Mega Society’s Internet officer, Kevin Langdon.

The editor likes Fibonacci numbers and shares a fantastic, award-winning website by Ron Knott – aimed at all levels of mathematical ability.

Along the lines of the previous article, we share the intriguing Fibonacci Journal by Gerald E. Bergum (editor). We add a few exercises that appeared in earlier issues to spark your brain cells.

Next, we return to our patriotic flair by paying tribute to the late President Ronald Reagan. Here, David von Drehle’s article is the source of the warm sentiments presented. The editor vividly recalls President Reagan’s Strategic Defense Initiative (SDI), or Star Wars, program.

The editor next shares some of his favorite nursery rhymes – with the hope that readers will develop complementary mathematical nursery rhymes – that can be used to instill a love for mathematics in children.

The editor presents a rendition of Ron’s MATH-O-DAY for the upcoming American holiday. The last one the editor prepared was in the late 1980s.

We close this patriotic issue with The Man of Few Words.

STATISTICS for June Noesis issue #170: 719 revisions; 25 hours actual editing time (at the PC); approximately 21,000 words; and over a 1000 paragraphs.

NOESIS Journal – June 2004 – Issue #170

CONTENTS
#	TITLE	AUTHOR	PAGE
1	July 4^th – Independence Day	Forefathers	5
2	Signer’s of the Declaration of Independence	Forefathers	8
3	Some of America’s Well-Appreciated Presidents	Editor	9
4	Name that President	Editor/Bryan Curtis	10
5	Same-Sex Marriage – A Biblical and Sympathetic View	Editor	14
6	The Pledge of Allegiance	Forefathers	17
7	Simple Math Quickies for Young and Novice Readers	Editor/Mike Holt	17
8	On the Light Side	Editor	18
9	The Star-Spangled Banner	Francis Scott Key	19
10	Simple Math Quickies for Young and Novice Readers - continued	Editor/Mike Holt	20
11	Name that President - Answers	Editor/Bryan Curtis	21
12	Puzzles – DIRTY DOZEN	Bill Corley	24
13	Simple Math Quickies for Young and Novice Readers - Answers	Editor/Mike Holt	28
14	Chess-Lover Jokes	Editor	28
15	A Topological Puzzle	J. R. O’Neil	29
16	Solicitation for Foreign Language Translation Ideas	Editor/Mike Erard	30
17	DIRTY DOZEN - answers	Bill Corley	32
18	Practical Engineering Applications of Math for Children	Editor/Horton	35
19	Wonderlic Personnel Test^TM (WPT^TM)	Editor/Wonderlic Inc.	36
20	Commercially Available Performance Tests	Dr. Lewis R. Aiken	39
21	DARPA’s Dust-busters – “Grand Challenge”	Jean Kumagai	41
22	The Secret in Building 26	DeBrosse/Burke	42
23	Reply to Brian Schwartz' Articles on Psychometric Testing and the SAT in Noesis #169	Kevin Langdon	45
24	Fibonacci Numbers	Editor/Ron Knott	51
25	About the Fibonacci Quarterly	Gerald E. Bergum	52
26	President Ronald Wilson Reagan (1911-2004)	David von Drehle	57
27	Some of my Favorite Nursery Rhymes	Editor	58
28	Ron’s MATH-O-DAY	Editor	60
29	The Man of Few Words	Editor	61
30	Ron’s MATH-O-DAY - solution	Editor	62

July 4^th – Independence Day

The Declaration of Independence of the Thirteen Colonies In CONGRESS, July 4, 1776

When in the Course of human events, it becomes necessary for one people to dissolve the political bands which have connected them with another, and to assume among the powers of the earth, the separate and equal station to which the Laws of Nature and of Nature's God entitle them, a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation.

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness. --That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, --That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness. Prudence, indeed, will dictate that Governments long established should not be changed for light and transient causes; and accordingly all experience hath shewn, that mankind are more disposed to suffer, while evils are sufferable, than to right themselves by abolishing the forms to which they are accustomed. But when a long train of abuses and usurpations, pursuing invariably the same Object evinces a design to reduce them under absolute Despotism, it is their right, it is their duty, to throw off such Government, and to provide new Guards for their future security. --Such has been the patient sufferance of these Colonies; and such is now the necessity which constrains them to alter their former Systems of Government. The history of the present King of Great Britain [George III] is a history of repeated injuries and usurpations, all having in direct object the establishment of an absolute Tyranny over these States. To prove this, let Facts be submitted to a candid world.

He has refused his Assent to Laws, the most wholesome and necessary for the public good.

He has forbidden his Governors to pass Laws of immediate and pressing importance, unless suspended in their operation till his Assent should be obtained; and when so suspended, he has utterly neglected to attend to them.

He has refused to pass other Laws for the accommodation of large districts of people, unless those people would relinquish the right of Representation in the Legislature, a right inestimable to them and formidable to tyrants only.

He has called together legislative bodies at places unusual, uncomfortable, and distant from the depository of their public Records, for the sole purpose of fatiguing them into compliance with his measures.

He has dissolved Representative Houses repeatedly, for opposing with manly firmness his invasions on the rights of the people.

He has refused for a long time, after such dissolutions, to cause others to be elected; whereby the Legislative powers, incapable of Annihilation, have returned to the People at large for their exercise; the State remaining in the mean time exposed to all the dangers of invasion from without, and convulsions within.

He has endeavoured to prevent the population of these States; for that purpose obstructing the Laws for Naturalization of Foreigners; refusing to pass others to encourage their migrations hither, and raising the conditions of new Appropriations of Lands.

He has obstructed the Administration of Justice, by refusing his Assent to Laws for establishing Judiciary powers.

He has made Judges dependent on his Will alone, for the tenure of their offices, and the amount and payment of their salaries.

He has erected a multitude of New Offices, and sent hither swarms of Officers to harass our people, and eat out their substance.

He has kept among us, in times of peace, Standing Armies without the consent of our legislatures.

He has affected to render the Military independent of and superior to the Civil power.

He has combined with others to subject us to a jurisdiction foreign to our constitution and unacknowledged by our laws; giving his Assent to their Acts of pretended Legislation:

For Quartering large bodies of armed troops among us:

For protecting them, by a mock Trial, from punishment for any Murders which they should commit on the Inhabitants of these States:

For cutting off our Trade with all parts of the world:

For imposing Taxes on us without our Consent:

For depriving us, in many cases, of the benefits of Trial by Jury:

For transporting us beyond Seas to be tried for pretended offences:

For abolishing the free System of English Laws in a neighbouring Province, establishing therein an Arbitrary government, and enlarging its Boundaries so as to render it at once an example and fit instrument for introducing the same absolute rule into these Colonies:

For taking away our Charters, abolishing our most valuable Laws, and altering fundamentally the Forms of our Governments:

For suspending our own Legislatures, and declaring themselves invested with power to legislate for us in all cases whatsoever.

He has abdicated Government here, by declaring us out of his Protection and waging War against us.

He has plundered our seas, ravaged our Coasts, burnt our towns, and destroyed the lives of our people.

He is at this time transporting large Armies of foreign Mercenaries to compleat the works of death, desolation and tyranny, already begun with circumstances of Cruelty and perfidy scarcely paralleled in the most barbarous ages, and totally unworthy the Head of a civilized nation.

He has constrained our fellow Citizens taken Captive on the high Seas to bear Arms against their Country, to become the executioners of their friends and Brethren, or to fall themselves by their Hands.

He has excited domestic insurrections amongst us, and has endeavoured to bring on the inhabitants of our frontiers, the merciless Indian Savages, whose known rule of warfare, is an undistinguished destruction of all ages, sexes and conditions.

In every stage of these Oppressions We have Petitioned for Redress in the most humble terms: Our repeated Petitions have been answered only by repeated injury. A Prince, whose character is thus marked by every act which may define a Tyrant, is unfit to be the ruler of a free people.

Nor have We been wanting in attentions to our British brethren. We have warned them from time to time of attempts by their legislature to extend an unwarrantable jurisdiction over us. We have reminded them of the circumstances of our emigration and settlement here. We have appealed to their native justice and magnanimity, and we have conjured them by the ties of our common kindred to disavow these usurpations, which would inevitably interrupt our connections and correspondence. They too have been deaf to the voice of justice and of consanguinity. We must, therefore, acquiesce in the necessity, which denounces our Separation, and hold them, as we hold the rest of mankind, Enemies in War, in Peace Friends.

We, therefore, the Representatives of the united States of America, in General Congress, Assembled, appealing to the Supreme Judge of the world for the rectitude of our intentions, do, in the Name, and by the Authority of the good People of these Colonies, solemnly publish and declare, That these United Colonies are, and of Right ought to be Free and Independent States; that they are Absolved from all Allegiance to the British Crown, and that all political connection between them and the State of Great Britain, is and ought to be totally dissolved; and that as Free and Independent States, they have full Power to levy War, conclude Peace, contract Alliances, establish Commerce, and to do all other Acts and Things which Independent States may of right do. And for the support of this Declaration, with a firm reliance on the protection of divine Providence, we mutually pledge to each other our Lives, our Fortunes and our sacred Honor.

The Signers of the Declaration Represented

the New States as follows:

New Hampshire:

Josiah Bartlett, William Whipple, Matthew Thornton

Massachusetts:

John Hancock, Samual Adams, John Adams, Robert Treat Paine, Elbridge Gerry

Rhode Island:

Stephen Hopkins, William Ellery

Connecticut:

Roger Sherman, Samuel Huntington, William Williams, Oliver Wolcott

New York:

William Floyd, Philip Livingston, Francis Lewis, Lewis Morris

New Jersey:

Richard Stockton, John Witherspoon, Francis Hopkinson, John Hart, Abraham Clark

Pennsylvania:

Robert Morris, Benjamin Rush, Benjamin Franklin, John Morton, George Clymer, James Smith, George Taylor, James Wilson, George Ross

Delaware:

Caesar Rodney, George Read, Thomas McKean

Maryland:

Samuel Chase, William Paca, Thomas Stone, Charles Carroll of Carrollton

Virginia:

George Wythe, Richard Henry Lee, Thomas Jefferson, Benjamin Harrison, Thomas Nelson, Jr., Francis Lightfoot Lee, Carter Braxton

North Carolina:

William Hooper, Joseph Hewes, John Penn

South Carolina:

Edward Rutledge, Thomas Heyward, Jr., Thomas Lynch, Jr., Arthur Middleton

Georgia:

Button Gwinnett, Lyman Hall, George Walton

Some of America’s Well-Appreciated Presidents

Abraham Lincoln, kind and good, honored and loved by many. To help us remember this president, we put his face on our penny!

Name that President

by Editor and Bryan Curtis

Material from a bargain book at Barnes & Noble – Bryan Curtis, editor of “A Call to America – Inspiring and Empowering Quotations from the Presidents of the United States,” Rutledge Hill Press, 2002, ISBN 1-55853-996-4

Ninety-nine percent of the failures come from people who have the habit of making excuses. _______
Discipline is the soul of an army. It makes small numbers formidable, procures success to the weak, and esteem to all. _______
Old minds are like old horses: you must exercise them if you wish to keep them in working order. _______
Genius is sorrow’s child. _______
When angry, count to ten before you speak. If very angry, a hundred. _______
Those who desire to give up freedom in order to gain Security will not have, nor do they deserve, either one. _______
It is universally admitted that a well-instructed people alone can be permanently a free people. _______
The right of self-defense never ceases. It is among the most sacred, and alike necessary to nations and to individuals. _______
A little flattery will support a man through great fatigue. _______
Duty is ours; results are God’s. _______
Courage and perseverance have a magical talisman, before which difficulties disappear and obstacles vanish into air. _______
One man with courage makes a majority. _______
I hope and trust to meet you in Heaven, both white and black – both white and black. ___
Ignorance and vice breed poverty which was as immutable as the seasons. _______
A decent and manly examination of the acts of government should not only be tolerated, but encouraged. _______
I can never consent to being dictated to. _______
No president who performs his duties faithfully and conscientiously can have any leisure. _______
It would be judicious to act with magnanimity towards a prostrate foe. _______
We should act to other countries as we wish them to act towards us. _______
I had not the advantage of a classical education, and no man should, in my judgment, accept a degree he cannot read. _______
The stars upon your banner have become nearly threefold their original number; your densely populated possessions skirt the shores of the two great oceans. _______
What sir, prevent the American people from crossing the Rocky Mountains? You might as well command Niagara not to flow. We must fulfill our destiny. _______
I am a slow walker, but I never walk back. _______
Nearly all men can stand adversity, but if you want to test a man’s character, give him power. _______
Tact is the ability to describe others as they see themselves. _______
The ballot is stronger than the bullet. _______
The goal is to strive for a poor government but a rich people. _______
There never was a time when, in my opinion, some way could not be found to prevent the drawing of the sword. _______
My policy is trust – peace, and to put aside the bayonet. _______
A pound of pluck is worth a ton of luck. _______
Ideas control the world. _______
Men may die, but the fabrics of our free institutions remain unshaken. _______
The ship of democracy which has weathered all storms may sink through the mutiny of those aboard. _______
Officeholders are the agents of the people, not their masters. _______
I believe also in the American opportunity which puts the starry sky above every boy’s head, and sets his foot upon a ladder which he may climb until his strength gives out. ___
That’s all a man can hope for during his lifetime – to set an example – and when he is dead, to be an inspiration for history. _______
Speak softly and carry a big stick; you will go far. _______
We cannot do great deeds unless we are willing to do the small things that make up the sum of greatness. _______
Courtesy is as much a mark of a gentleman as courage. _______
Anti-Semitism is a noxious weed that should be cut out. It has no place in America. ____
Friendship is the only cement that will hold the world together. _______
One cool judgment is worth a thousand hasty counsels. The thing to be supplied is light, not heat. _______
Character is a by-product; it is produced in the great manufacture of daily duty. _______
Never murder a man who is committing suicide. _______
A regret for the mistakes of yesterday must not, however, blind us of the tasks of today. _
Four-fifths of all our troubles would disappear, if we would only sit down and keep still. __
The slogan “press on” has solved and always will solve the problems of the human race._
Christmas is not a time nor a season, but a state of mind. To cherish peace and goodwill, to be plenteous in mercy, is to have the real spirit of Christmas. _______
If you see ten troubles coming down the road, you can be sure that nine will run into the ditch before they reach you. _______
It takes a great man to be a good listener. _______
The durability of free speech and free press rests on the simple concept that it search for the truth and tell the truth. _______
When you come to the end of your rope, tie a knot and hang on. _______
The United States Constitution has proved itself the most marvelously elastic compilation of rules of government ever written. _______
Men are not prisoners of fate, but only prisoners of their own mind. _______
Selfishness is the only real atheism; aspiration, unselfishness, the only real religion. ____
The ablest man I ever met is the man you think you are. _______
It is amazing what you can accomplish if you do not care who gets the credit. _______
If you can’t stand the heat, get out of the kitchen. _______
Actions are the seeds of fate. Deeds grow into destiny. _______
Accomplishments will prove to be a journey, not a destination. _______
America is best described by one word, freedom. _______
I’m saving the rocker for the day when I feel as old as I really am. _______
Peace and justice are two sides of the same coin. _______
The only way to win WW III is to prevent it. _______
Forgive our enemies, but never forget their names. _______
Man is still the most extraordinary computer of all. _______
Change is the law of life. And those who look only to the past or present are certain to miss the future. _______
The greater our knowledge increases, the more our ignorance unfolds. _______
And so, my fellow Americans: ask not what your country can do for you—ask what you can do for your country. _______
Yesterday is not ours to recover, but tomorrow is ours to win or lose. _______
Peace is a journey of a thousand miles and it must be taken one step at a time. _______
The greatest honor history can bestow is that of a peacemaker. _______
The finest steel has to go through the hottest fire. _______
If an individual wants to be a leader and isn’t controversial, that means he never stood for anything. _______
I believe that truth is the glue that holds government together. Compromise is the oil that makes governments go. _______
We must adjust to changing times and still hold to unchanging principles. _______
America is too great for small dreams. _______
Excellence demands competition. Without a race there can be no champion, no records broken, no excellence – in education or in any other walk of life. _______
America must remain freedom’s staunchest friend, for freedom is our best ally. _______
Great nations like great men must keep their word. When America says something, America means it, whether a treaty or an agreement or a vow made on marble steps. We will always try to speak clearly, for candor is a compliment, but subtlety, too, is good and has its place. _______
Building one America is our most important mission – “the foundation for many generations,” of every other strength we must build for this new century. Money cannot by it. Power cannot compel it. Technology cannot create it. It can only come from the human spirit. _______
Encouraging responsibility is not a search for scapegoats; it is a call to conscience. And though it requires sacrifice, it brings a deeper fulfillment. _______

Same-Sex Marriage – A Biblical and Sympathetic View

by Editor

The local Nashua, NH newspaper The Telegraph headlines for Tuesday, May 18, 2004 read: “Gay weddings begin – Massachusetts becomes first state to allow same-sex marriages.” On the same page was a second article: “Hudson couple one step closer – Longtime partners get Massachusetts license, but still want recognition in NH” – relating to a male couple. In USA Today, the front-page headlines included “First Weddings Intensify Gay-Marriage Debate – Massachusetts sets stage for battles elsewhere.”

Certainly many average Americans look at a gay or lesbian couple holding hands and walking down the street as if they were aliens from another planet.

And yet compared to God’s original Garden-of-Eden, all 6-plus billion people on planet Earth are aliens in God’s eyes. When Adam and Eve sinned, the Divine plan God established began to slowly disintegrate. Over the centuries, fallen man deviated further and further away from the harmony God designed.

Very simple cases to pause-and-reflect on include:

1. we’re not supposed to spill milk at the dinner table, but we do

2. we’re not supposed to get angry, but we do

3. we’re not supposed to have automobile accidents, but we do

4. we’re not supposed to make errors, but we have still erasers

5. we’re not supposed to “think angry thoughts,” but we do

6. we’re not supposed to get impatient, but we do

7. we’re not supposed to commit suicide, but people do

8. we’re not supposed to break the ten commandments, but we do

9. we’re not supposed to overeat and DWI, but we do

10. we’re not supposed to pass through a stop sign without stopping, but we do

11. we’re not supposed to offend people, but we do

12. nothing was supposed to die, but mankind and animals do

13. humans and nature are not supposed to do a lot of things, but they do

From a Biblical account, we see marriage was designed for a man and a woman. A short list of texts are summarized in the following table. The Bible covers the account of Sodom where sexual relations between men was prevalent – Genesis 19:4-5 – where Lot is approached by men who wanted to have a sexual relationship with the two “men” they knew Lot had in the house. The men Lot was hosting were angels – but this fact was not known to the men who knocked on Lot’s door. Lot, in a merciful act, tried to persuade the men to take his two daughters instead – that they are “appropriate” for the passionate desires the men had (Genesis 19:6-8). The men were not interested in Lot’s two daughters – they wanted the men Lot was hosting inside his home. The story continues where God destroys Sodom.

Same-sex couples may appear as aliens as our mind conjures up sex with a similar-gender partner. We may recall the Bible texts referenced above – and realize same-sex partners cannot conceive offspring – and that God rained down fire-and-brimstone on the evil-doers (“Then the Lord rained brimstone and fire on Sodom and Gomorrah, from the Lord out of the heavens." Genesis 19:24. "Turning the cities of Sodom and Gomorrah into ashes, condemned them to destruction, making them an example to those who afterward would live ungodly." II Peter 2:6).

Heaven Approves Marriage

1^st Marriage – Adam and Eve ------------------- Genesis 2:18, 20-25

Jesus approved marriage ------------------------ John 2:1-11

Facts about Marriage

Marriage for the continuance of the race ---- Genesis 1:28

Marriage is honorable ----------------------------- Hebrews 13:4

Man is to cleave to his wife ---------------------- Matthew 19:5,6

Marriage is to last until death of spouse ------ Romans 7:2,3

Husband is the head of the wife ---------------- Ephesians 5:23

Marriage relations ---------------------------------- 1 Corinthians 7:1-40

Choice of Partner

Be not unequally yoked --------------------------- 2 Corinthians 6:14

Marital Problems

Relation of believer and non-believer --------- 1 Corinthians 7:10-17

Divorce allowed because ------------------------- Matthew 5:27-32

Paul says partners not under bondage if ----- 1 Corinthians 7:12-15

Jesus said fornication reason for divorce ---- Matthew 19:3-9

Adultery ----------------------------------------------- Mark 10:2,11

Adultress women forgiven ----------------------- John 8:3-11

Marriage in Heaven

No marriage in heaven --------------------------- Matthew 22:30; Mark 12:25

Thus, our tolerance level, coupled with the pressure society places upon our thinking on the same-sex issue, is greatly reduced. We, in effect, alienate ourselves from the same-sex couple – and not the other way around. How might we conduct ourselves in such a heated topic area?

Books, daily news broadcasts, and daily newspapers/magazines continue to cover the same-sex saga – but one simple chapter in the Bible can be a source of help – The Love Chapter – 1 Corinthians 13:1-3. Please prayerfully read this chapter, reproduced on the next page.

One way to look at the same-sex issue is to realize not every same-sex couple have passionate sex. As we become familiar with same-sex couple situations, we learn that some partners of a same-sex relationship have had childhood experiences where they were molested by their opposite-sex parent; or opposite-sex friend, or with the spouse they were formerly married to – having been abused, beaten, and other complications.

Any number of tangible reasons can, and do, drive a person towards a same-sex partner for comfort. Even the passionate segment may be “safer” in their mind – over the tumultuous experiences they had with the opposite sex. Many same-sex couples are as close as actual brothers or sisters. For other same-sex couples, mutual sympathetic hearts are exercised toward one another as they both realize the “common” set-backs experienced in their lives. These “common” items strengthen their bond through understanding and trust – understanding and trust they lost with former opposite-sex relationships. Many same-sex couples, with these deep, personal issues raised above, are crying out for love and understanding – in a world where many will never take the time to prayerfully contemplate, and exercise, The Love Chapter in their lives.

The Love Chapter – 1 Corinthians 13:1-13

(King James Version)

13:1 Though I speak with the tongues of men and of angels, and have not charity, I am become as sounding brass, or a tinkling cymbal.

13:2 And though I have the gift of prophecy, and understand all mysteries, and all knowledge; and though I have all faith, so that I could remove mountains, and have not charity, I am nothing.

13:3 And though I bestow all my goods to feed the poor, and though I give my body to be burned, and have not charity, it profiteth me nothing.

13:4 Charity suffereth long, and is kind; charity envieth not; charity vaunteth not itself, is not puffed up,

13:5 Doth not behave itself unseemly, seeketh not her own, is not easily provoked, thinketh no evil;

13:6 Rejoiceth not in iniquity, but rejoiceth in the truth;

13:7 Beareth all things, believeth all things, hopeth all things, endureth all things.

13:8 Charity never faileth: but whether there be prophecies, they shall fail; whether there be tongues, they shall cease; whether there be knowledge, it shall vanish away.

13:9 For we know in part, and we prophesy in part.

13:10 But when that which is perfect is come, then that which is in part shall be done away.

13:11 When I was a child, I spake as a child, I understood as a child, I thought as a child: but when I became a man, I put away childish things.

13:12 For now we see through a glass, darkly; but then face to face: now I know in part; but then shall I know even as also I am known.

13:13 And now abideth faith, hope, charity, these three; but the greatest of these is charity.

I know that if you learned that a family member (brother, sister, parent) were gay, you’d go through “preliminary” feelings – possibly of anger, fright, disappointment, shock, rebellion, segregation, embarrassment, etc. After the “dust” settled, wouldn’t you try to manage your emotions – and realizing you still love the person deeply – proceed to understand and accept them? See 1 Corinthians 13:7 in The Love Chapter above.

I realize no single article exhaustively covers this controversial topic, but I feel The Love Chapter, appropriately applied in our individual lives, will provide the anchor to allow us to reason through the same-sex issue and interface with these couples in a manner God would encourage. Same-sex marriage raises other concerns that relate to income tax impacts to the American people – and maybe someone can contribute an article in this area.

The Pledge of Allegiance

I pledge Allegiance to the flag

of the United States of America

and to the Republic for which it stands,

one nation under God, indivisible,

with Liberty and Justice for all.

Simple Math Quickies for Young and Novice Readers

by Editor and Michael Holt

Tug of War. In a tug of war, four boys can tug as hard as five girls. And two girls and one boy can tug as hard as one dog. The dog and three girls tug against four boys. Which side will win the last tug of war?
4-Box Code Template. Given the 4-box CODE template below, how many different combinations of BLACK (filled) and WHITE (unfilled) combinations can you form? Two combinations are shown afterward.

SAMPLE 4-box CODE Template ¯

All 4 are WHITE (unfilled) ¯

Two are WHITE (unfilled) and two BLACK (filled) ¯

Guilty Party. Vinnie, Gary and Faye are the suspects in a robbery case. Their trial reveals the following facts: Either Faye is innocent or Gary is guilty. If Gary is guilty, then Faye is innocent. Vinnie and Faye never work together and Vinnie never does a job on his own. Also, if Gary is guilty, so is Vinnie. Who is guilty?

On the Light Side

by Editor

Life certainly can get pretty hectic and unbearable at times. One prescription the Bible gives us is that “A merry heart doeth good like a medicine.” Proverbs 17:22

So, in this section, I list some jokes and puns I recall over the years that will help bring a chuckle to your countenance – and get the blood circulation going.

It worries me, I’m getting so absent-minded. I mean, sometimes in the middle of a sentence I . . .
I’m a writer. Well, what a coincidence. I’m a reader!
It takes him an hour to get to work – after he’s got there.
Why did I become a baker? Because I kneaded the dough!
Don’t get me wrong. I love the job. It’s the work I hate.
The billionaire built himself a house so large, it was in four area codes.
He’s got a BA, an MA, and a PhD. The only thing he doesn’t have is a JOB.
It’s lonely at the top – but you eat better.
A statistician is someone who can put his head in the oven and his feet in the freezer and tell you, “On average, I feel just fine.”
Ladies and gentlemen – I guess that takes care of most of you . . .
If there were people on other planets, why don’t they contact us? Would you?
The trouble with that restaurant is, it’s so crowded nobody goes there any more.
What do you call the cabs lined up outside Dallas-Fort Worth airport? The Yellow Rows of Texas.
I’ve changed my mind. Good. Does it work any better now?
I must be getting old. I can’t take yes for an answer.
I’m calling about the announcement of my death in your paper this morning. I see. Can you tell me where you’re calling from?
Good morning, I’m the piano tuner. But I didn’t send for you. No, but the neighbors did.
He was born with a silver spoon in his mouth – and he hasn’t stirred since.
It takes a thief to catch a thief – and a jury to let him go.
No matter how bad the in-flight movie, you still shouldn’t walk out on it.
An electrician is a man who wires homes for money.
A diplomat is a man who always remembers a woman’s birthday but never remembers her age.
I said to my dentist, “Do you promise to pull the tooth, the whole tooth, and nothing but the tooth?”
My car is for four people – one driving and three pushing.
If money doesn’t grow on trees, how come the banks have so many branches?

The Star-Spangled Banner

Francis Scott Key, 1814

O say, can you see, by the dawn's early light,
What so proudly we hail'd at the twilight's last gleaming?
Whose broad stripes and bright stars, thro' the perilous fight,
O'er the ramparts we watch'd, were so gallantly streaming?
And the rockets' red glare, the bombs bursting in air,
Gave proof thro' the night that our flag was still there.
O say, does that star-spangled banner yet wave
O'er the land of the free and the home of the brave?

On the shore dimly seen thro' the mists of the deep,
Where the foe's haughty host in dread silence reposes,
What is that which the breeze, o'er the towering steep,
As it fitfully blows, half conceals, half discloses?
Now it catches the gleam of the morning's first beam,
In full glory reflected, now shines on the stream:
'Tis the star-spangled banner: O, long may it wave
O'er the land of the free and the home of the brave!

And where is that band who so vauntingly swore
That the havoc of war and the battle's confusion,
A home and a country should leave us no more?
Their blood has wash'd out their foul footsteps' pollution.
No refuge could save the hireling and slave
From the terror of flight or the gloom of the grave:
And the star-spangled banner in triumph doth wave
O'er the land of the free and the home of the brave.

O thus be it ever when free-men shall stand
Between their lov'd home and the war's desolation;
Blest with vict'ry and peace, may the heav'n-rescued land
Praise the Pow'r that hath made and preserv'd us a nation!
Then conquer we must, when our cause it is just,
And this be our motto: “In God is our trust!”
And the star-spangled banner in triumph shall wave
O'er the land of the free and the home of the brave!

Simple Math Quickies for Young and Novice Readers - continued

by Editor and Michael Holt

Here are a few more Math Quickies for our young and novice readers.

The Twelve Days of Christmas

On the twelfth day of Christmas my true love sent to me

12 drummers drumming, 11 pipers piping,

10 lords aleaping, 9 ladies dancing,

8 maids amilking, 7 swans aswimming,

6 geese alaying, 5 gold rings,

4 calling birds, 3 French hens,

2 turtledoves, and a partridge in a pear tree.

How many things did my true love send to me?

Encoded Frame

Encoded in the frame below is a well-known saying. Try to “read” it. Begin at one of the letters. Reading every other letter, go twice around the frame. What is it saying?

Infamous 100

Try to make the number 100 out of the numbers 1 through 9, using the arithmetic operations +, -, x, ¸, and parentheses ( ). Try to complete the following four cases. Use the digits 1 through 9 only once in any of these cases – and for cases 1-3 use 1-9 in sequence as you write your expression left-to-right.

100 = 1 + 2 + 3 + . . .

100 = 123 – 45 . . .

100 = 123 – 4 – 5 . . .

100 = 1/2 + 6/4 + . . .

Name that President - Answers

by Editor

Ninety-nine percent of the failures come from people who have the habit of making excuses. George Washington
Discipline is the soul of an army. It makes small numbers formidable, procures success to the weak, and esteem to all. George Washington
Old minds are like old horses: you must exercise them if you wish to keep them in working order. John Adams
Genius is sorrow’s child. John Adams
When angry, count to ten before you speak. If very angry, a hundred. Thomas Jefferson
Those who desire to give up freedom in order to gain Security will not have, nor do they deserve, either one. Thomas Jefferson
It is universally admitted that a well-instructed people alone can be permanently a free people. James Madison
The right of self-defense never ceases. It is among the most sacred, and alike necessary to nations and to individuals. James Monroe
A little flattery will support a man through great fatigue. James Monroe
Duty is ours; results are God’s. John Quincy Adams
Courage and perseverance have a magical talisman, before which difficulties disappear and obstacles vanish into air. John Quincy Adams
One man with courage makes a majority. Andrew Jackson
I hope and trust to meet you in Heaven, both white and black – both white and black. Andrew Jackson
Ignorance and vice breed poverty which was as immutable as the seasons. Martin Van Buren
A decent and manly examination of the acts of government should not only be tolerated, but encouraged. William Henry Harrison
I can never consent to being dictated to. John Taylor
No president who performs his duties faithfully and conscientiously can have any leisure. James K. Polk
It would be judicious to act with magnanimity towards a prostrate foe. Zachary Taylor
We should act to other countries as we wish them to act towards us. Millard Fillmore
I had not the advantage of a classical education, and no man should, in my judgment, accept a degree he cannot read. Millard Fillmore
The stars upon your banner have become nearly threefold their original number; your densely populated possessions skirt the shores of the two great oceans. Franklin Pierce
What sir, prevent the American people from crossing the Rocky Mountains? You might as well command Niagara not to flow. We must fulfill our destiny. James Buchanan
I am a slow walker, but I never walk back. Abraham Lincoln
Nearly all men can stand adversity, but if you want to test a man’s character, give him power. Abraham Lincoln
Tact is the ability to describe others as they see themselves. Abraham Lincoln
The ballot is stronger than the bullet. Abraham Lincoln
The goal is to strive for a poor government but a rich people. Andrew Johnson
There never was a time when, in my opinion, some way could not be found to prevent the drawing of the sword. Ulysses S. Grant
My policy is trust – peace, and to put aside the bayonet. Rutherford B. Hayes
A pound of pluck is worth a ton of luck. James A. Garfield
Ideas control the world. James A. Garfield
Men may die, but the fabrics of our free institutions remain unshaken. Chester A. Arthur
The ship of democracy which has weathered all storms may sink through the mutiny of those aboard. Grover Cleveland
Officeholders are the agents of the people, not their masters. Grover Cleveland
I believe also in the American opportunity which puts the starry sky above every boy’s head, and sets his foot upon a ladder which he may climb until his strength gives out. Benjamin Harrison
That’s all a man can hope for during his lifetime – to set an example – and when he is dead, to be an inspiration for history. William McKinley
Speak softly and carry a big stick; you will go far. Theodore Roosevelt
We cannot do great deeds unless we are willing to do the small things that make up the sum of greatness. Theodore Roosevelt
Courtesy is as much a mark of a gentleman as courage. Theodore Roosevelt
Anti-Semitism is a noxious weed that should be cut out. It has no place in America. William H. Taft
Friendship is the only cement that will hold the world together. Woodrow Wilson
One cool judgment is worth a thousand hasty counsels. The thing to be supplied is light, not heat. Woodrow Wilson
Character is a by-product; it is produced in the great manufacture of daily duty. Woodrow Wilson
Never murder a man who is committing suicide. Woodrow Wilson
A regret for the mistakes of yesterday must not, however, blind us of the tasks of today. Warren G. Harding
Four-fifths of all our troubles would disappear, if we would only sit down and keep still. Calvin Coolidge
The slogan “press on” has solved and always will solve the problems of the human race. Calvin Coolidge
Christmas is not a time nor a season, but a state of mind. To cherish peace and goodwill, to be plenteous in mercy, is to have the real spirit of Christmas. Calvin Coolidge
If you see ten troubles coming down the road, you can be sure that nine will run into the ditch before they reach you. Calvin Coolidge
It takes a great man to be a good listener. Calvin Coolidge
The durability of free speech and free press rests on the simple concept that it search for the truth and tell the truth. Herbert Hoover
When you come to the end of your rope, tie a knot and hang on. Franklin D. Roosevelt
The United States Constitution has proved itself the most marvelously elastic compilation of rules of government ever written. Franklin D. Roosevelt
Men are not prisoners of fate, but only prisoners of their own mind. Franklin D. Roosevelt
Selfishness is the only real atheism; aspiration, unselfishness, the only real religion. Franklin D. Roosevelt
The ablest man I ever met is the man you think you are. Franklin D. Roosevelt
It is amazing what you can accomplish if you do not care who gets the credit. Harry S. Truman
If you can’t stand the heat, get out of the kitchen. Harry S. Truman
Actions are the seeds of fate. Deeds grow into destiny. Harry S. Truman
Accomplishments will prove to be a journey, not a destination. Dwight D. Eisenhower
America is best described by one word, freedom. Dwight D. Eisenhower
I’m saving the rocker for the day when I feel as old as I really am. Dwight D. Eisenhower
Peace and justice are two sides of the same coin. Dwight D. Eisenhower
The only way to win WW III is to prevent it. Dwight D. Eisenhower
Forgive our enemies, but never forget their names. John F. Kennedy
Man is still the most extraordinary computer of all. John F. Kennedy
Change is the law of life. And those who look only to the past or present are certain to miss the future. John F. Kennedy
The greater our knowledge increases, the more our ignorance unfolds. John F. Kennedy
And so, my fellow Americans: ask not what your country can do for you—ask what you can do for your country. John F. Kennedy
Yesterday is not ours to recover, but tomorrow is ours to win or lose. Lyndon B. Johnson
Peace is a journey of a thousand miles and it must be taken one step at a time. Lyndon B. Johnson
The greatest honor history can bestow is that of a peacemaker. Richard M. Nixon
The finest steel has to go through the hottest fire. Richard M. Nixon
If an individual wants to be a leader and isn’t controversial, that means he never stood for anything. Richard M. Nixon
I believe that truth is the glue that holds government together. Compromise is the oil that makes governments go. Gerald Ford
We must adjust to changing times and still hold to unchanging principles. Jimmy Carter
America is too great for small dreams. Ronald Reagan
Excellence demands competition. Without a race there can be no champion, no records broken, no excellence – in education or in any other walk of life. Ronald Reagan
America must remain freedom’s staunchest friend, for freedom is our best ally. Ronald Reagan
Great nations like great men must keep their word. When America says something, America means it, whether a treaty or an agreement or a vow made on marble steps. We will always try to speak clearly, for candor is a compliment, but subtlety, too, is good and has its place. George Bush
Building one America is our most important mission – “the foundation for many generations,” of every other strength we must build for this new century. Money cannot by it. Power cannot compel it. Technology cannot create it. It can only come from the human spirit. Bill Clinton
Encouraging responsibility is not a search for scapegoats; it is a call to conscience. And though it requires sacrifice, it brings a deeper fulfillment. George W. Bush

BONUS: Chess-Lover Jokes:

“How do chess players begin a game?” ⇔ “______________”

“What makes a chess player happy?” ⇔ “______________”

“What do chess players like for breakfast?” ⇔ “______________”

PUZZLES – DIRTY DOZEN

copyright Ó 2003 by H.W. Corley

1. On a biomedical engineering examination a student named Syed computes in feet and inches the maximum distance that a certain artificial heart design could pump blood upward against gravity. Unfortunately, in recording this distance on his examination paper, he reverses the numbers for feet and inches. As a result, his recorded answer is only 30% of the computed length, which was less than 10 feet with no fractional feet or inches. What length did Syed compute in feet and inches?

2. A female IE student named Aruna jogs north across a bridge used for both a road and a train track. Three-eighths across the bridge, she hears a train coming north toward the bridge from behind her. Aruna calculates that if she keeps running, she will reach the north end of the bridge at the same instant as the train. She also calculates that if she turns around and runs back south, she will reach the south end of the bridge at the same instant as the train. If Aruna jogs at a constant speed of 8 mph, what is the speed of the train to the nearest two decimal places?

3. An ME named Eduardo uses some three-dimensional CAD/CAM software to draw a right circular cone with a height of 3 feet and with a base of radius 1 foot. Next he inscribes a cube in the cone so that the face of the cube is contained in the base of the cone. What is the length of the cube’s side in feet to the nearest three decimal places?

4. The UTA student chapter of SWE (Society of Women Engineers) has noted that the proportion of the IMSE faculty members at UTA who are female is greater than the proportion of all engineering faculty members at UTA who are female. Let P denote the proportion of female IMSE faculty to female engineering faculty at UTA, and let Q denote the proportion of all IMSE faculty members to all engineering faculty at UTA. With no further information or numerical data, exactly one of the following statements is true.

(a) P > Q

(b) P < Q

(d) The relation between P and Q cannot be determined.

Select the correct answer and submit only the corresponding letter.

5. A fabrication engineer named Dave lies a lot. In fact, he tells the truth only one day a week and always on the same day. One day he said, “I lie on Mondays and Thursdays.” The next day he said, “Today is either Thursday, Saturday, or Sunday.” And then the following day he said, “I lie on Wednesdays and Fridays.” On what day of the week does Dave tell the truth?

6. The nation of Griddonesia consists of eighty-one equally-spaced islands represented by intersections of the lines in the grid below, where north is up and east is right as on a standard map. Each island is connected to all its adjacent islands by horizontal and vertical bridges exactly one-mile long. There are no diagonal bridges.

A native environmental engineer named caizb lives on the northwest island and must drive to the southeast island to assess the damage from an oil spill. The shortest driving distance on bridges between the northwest and southeast islands is obviously 16 miles. How many different such shortest routes could she take?

7. A CE graduate student named Masoud has a grant to study construction methods of the ancient Egyptians. One day in the Valley of the Kings he discovers an odd structure whose stone walls form a square spiral as indicated in the figure below, which is obviously not to scale. The sides of the outside square measure 102 feet by 102 feet. The interior spiral path is 2 feet wide and spirals through the entire structure. To the nearest tenth of a foot, what is the distance along the exact middle of the path from the entrance to the center of the structure?

102 feet

8. One day Masoud, the CE of problem 7, stops for lunch in the center of the square spiral. Then he discovers that he brought water to drink but nothing to eat. So Masoud offers to pay his two Bedouin assistants, Al-Fahl and Gamal, to share their lunches with him. Al-Fahl has five loaves of bread and Gamal has three loaves, all identical. The two Bedouins agree to divide up their eight loaves equally among the three men. After eating, Masoud lays down 8 one-piaster coins. To be fair, how many coins should Gamal receive?

9. Four EE students have formed a string quartet called the Ohms. One dark night they are warming up for a concert in Trinity River Park in Fort Worth. Suddenly the four musicians realize that it’s almost time for the concert, and they must all cross a small bridge over the river to reach the stage. At most two people can cross this bridge at one time, and any such group crossing the river must have a flashlight. The four musicians have only one flashlight, however, and it must be carried back and forth across the bridge. Moreover, each EE walks at a different speed, and a pair must walk together at the rate of the slower one. The time required for each musician to cross the bridge is given as follows, where they are identified by their instruments:

· Cello – 1 minute to cross

· First violin – 2 minutes to cross

· Second violin – 5 minutes to cross

· Viola – 10 minutes to cross.

What is the minimum time in minutes required for all the Ohms to cross the bridge?

10. A CSE named Olga uses a computer simulation program to generate three numbers in the interval (0,1), where each number is equally likely to have any value in the interval and is independent of the other two. What is the probability that three lines with lengths in feet equal to these three numbers would form a nondegenerate triangle (one with nonzero area)? Express your answer as a reduced fraction.

11. An Arlington High School senior named Jamal is a finalist for two scholarships at UTA – a university-wide scholarship worth $15,000 per year for four years and an engineering scholarship worth $10,000 per year for four years. The recipients for each type of scholarship are decided independently. However, a student can win only one scholarship and must take the university award if offered both types. There are 15 finalists for 8 engineering scholarships, and 3 finalists for 1 university scholarship. Exactly one other student besides Jamal is a finalist for both the university and engineering scholarships. If all the finalists for each type are equally likely to win, to the nearest three decimals what is the probability that Jamal wins one of these scholarships?

12. A materials science graduate student named Hsu Wen has taken several CSE courses offered by Dr. Frank N. Stein. For this reason Hsu has asked the eminent AI guru to be on his Ph.D. supervisory committee. As part of the written portion of Hsu’s comprehensive examination, Dr. Stein e-mails Hsu a drawing on Friday afternoon with the following instructions. By Stein’s return on Monday, Hsu must produce the minimum integer number of cubic feet (i.e., 1, 2, 3, …) of composite material required to cast an object formed by plane surfaces with both a top and front view as shown below. Then Dr. Stein flies off to an applied probability workshop in Las Vegas. Determine the integer number of cubic feet of composite material that Hsu must produce by Monday.

3′

9′

1. (Remember, it’s a dirty dozen.) A petite five-foot AE named Kim weighs 95 pounds normally. During the past two week, however, she has gained weight from eating pizza at midnight while studying. A revolutionary way to lose weight occurs to her. She would weigh less standing on a scale at the equator than standing on the same scale at the geographic north pole (i.e., on the earth’s axis of rotation). If Kim weighs exactly 100 pounds at the North Pole, to the nearest tenth of a pound how much would she weigh at the equator? Assume the earth is a perfect sphere of radius 6370 kilometers.

Simple Math Quickies for Young and Novice Readers - Answers

by Editor and Michael Holt

Tug of War – In the last tug of war, we can replace the dog with two girls and a boy because, as we see in the second tug of war, they are equally matched. The last tug of war then becomes a contest between the five girls and a boy on the left against the four boys on the right. But the first tug of war showed that the five girls are as strong as four boys. Namely, a boy is stronger than a girl. The tug of war reduces to a contest between five boys on the left and five girls on the right. So the team on the left will win. This is predicated on the fact that each girl pulls equally hard as the other girls, and similarly for the boys.

4-Box Code Template – Here we notice we have either WHITE (unfilled) or BLACK (filled) color options in each of the 4 box slots. There are 4 box slots. Thus, there are 2 raised to the fourth power = 2x2x2x2 = 16 unique patterns.

Guilty Party – Vinnie and Gary are guilty.

The Twelve Days of Christmas – The sum of the first N integers is simply N x (N+1)/2. So, with N = 12, we get

1+2+3+ . . . +12 = (12) x (12+1) / 2 = 6 x 13 = 78 gifts

Encoded Frame – Beginning at the bottom left corner: “A rolling stone gathers much speed.”

Infamous 100 –

100 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + (8 x 9)

100 = 123 – 45 – 67 + 89

100 = 123 – 4 – 5 – 6 – 7 + 8 – 9

100 = 1/2 + 6/4 + (5+3)/8 + 97

If you enjoyed these simple mathematical recreations, you might want to purchase the inexpensive bargain double-volume (originally published in 1977, 1978, respectively) hardcover book by Michael Holt titled: “Math Puzzles & Games,” Barnes & Noble Books (1996), ISBN 0-88029-948-7.

BONUS: Chess-Lover Jokes:

“How do chess players begin a game?” ⇔ “Once a pawn a time!”

“What makes a chess player happy?” ⇔ “Taking the knight off!”

“What do chess players like for breakfast?” ⇔ “Pawn cakes!”

A Topological Puzzle

by Editor and J. R. O’Neil

Readers will never forget the two stimulating problems we posed in the Noesis May issue #169 by Dr. Layman E. Allen in the WFF ‘N PROOF Tardy Bus Problem and the game EQUATIONS Elementary Problem E1. These two games, WFF ‘N PROOF and EQUATIONS, teach logical thinking – to young and old alike!

In the same series of innovative problems, Dr. Allen carried a topological puzzle developed by J. R. O’Neil called QWIK-SANE – A Topological Puzzle for Thinkers. Unfortunately, J. R. O’Neil is deceased. I would like to see topology “spark” at least one of our young readers (maybe the child or nephew/niece of one of our avid readers) into possibly pursuing a career in mathematics – along the lines of topology. As such, I include the puzzle (on paper) here to entice our readers to purchase several of these inexpensive ($3.50) puzzles for youngsters they know. This enjoyable puzzle is still available for only $3.50 through Dr. Allen at:

http://www.wff-n-proof.com/www-wff-n-proof-com/QWIKSANE.chk?AOLHelp=40bb338c.37a.388.1&ServerName=www.wff-n-proof.com

The 13 multicolored wooden pieces are crafted in Germany.

QWIK-

SANE

♥

MAN

WFF ‘N PROOF

In the upper row of the tray, place lettered blocks THINK in that order, followed by the shorter of the two long blocks (QWIK-SANE), then the “♥” yellow block, thus filling out that row, Place the yellow “MAN” block at the extreme left in the lower row, then the long block (WFF ‘N PROOF), then the letters HARD. This fills the tray, with lettered blocks in the relative positions shown above.

To “set” the puzzle, remove and put aside the “♥” block, then, without disturbing the other blocks, pick up and transfer the “MAN” block to the space from which the “♥” was removed. With pieces “set,” the puzzle consists of sliding the “MAN” back to the lower left corner and still have THINK and HARD intact in their original starting positions, then replacing, as a final move, the “♥” block at the right end of the upper row. It can be done in TBD moves. Can you do it? A “move” consists of the sliding of one or as many blocks as can be shifted simultaneously in one direction.

You will find the complete shopping list of Educational Gifts at:

http://www.wff-n-proof.com/www-wff-n-proof-com/Eductnal.chk?AOLHelp=40bb338c.37a.388.1&ServerName=www.wff-n-proof.com

Solicitation for Foreign Language Translation Ideas

by Editor and Michael Erard

In the spirit of the United States of America and the war against terrorism, we entreat our avid readers to consider solutions for the foreign language translation problem. I do this by capturing some high points in an article by Michael Erard (www.technologyreview.com) I read in the March 2004 issue of MIT’s Technology Review, pages 54-60, titled “Translation in an Age of Terror.” The “preface” and disconcerting “opener” sentences given on pages 54 and 56 follow.

The September 11 attacks exposed the flaws in the U.S. intelligence community’s approach to translation. Now, the new federal National Virtual Translation Center seeks to dramatically increase the chances of preventing the next attack by using technology to leverage – rather than replace – crucial human skills.

Page 54, MIT’s Technology Review – March 2004

In Washington, DC, conference room soundproofed to thwart eavesdropping, five linguists working for the government – speaking on condition their names not be published – describe the monumental task they face analyzing foreign-language intercepts in the age of terror.

Page 56, MIT’s Technology Review – March 2004

▶ The editor entreats avid readers of Noesis to possibly think of ideas and forward them to, say, Michael Erard (author of the article) or U.S. Government agencies. In light of the 9/11 event, I close with this sobering material presented in the article, page 56.

“The costs of failing to clarify what adversaries mean in a timely manner are high. That was made clear during Congressional investigations into the intelligence lapses that led up to the September 11 attacks. In perhaps the most glaring example, on September 10, 2001, according to June 2002 news reports, the NSA intercepted two Arabic-language messages, one that said “Tomorrow is zero hour” and another that said: “The match is about to begin.” The sentences weren’t translated until September 12, 2001. The revelation underscored the fact that the U.S. government faces a serious crisis in its ability to store, analyze, search, and translate data in dozens of foreign languages. . . . Consider that every three hours, NSA satellites sweep up enough information to fill the Library of Congress.”

The Library of Congress is the largest library in the world, with nearly 128 million items on approximately 530 miles of bookshelves. The collections include more than 29 million books and other printed materials, 2.7 million recordings, 12 million photographs, 4.8 million maps, and 57 million manuscripts. (http://www.loc.gov/about/ )

If you have ideas to help fight the language translation problem – contact your local government officials!

The National Security Agency/Central Security Service is America’s cryptologic organization. It coordinates, directs, and performs highly specialized activities to protect U.S. information systems and produce foreign intelligence information. A high technology organization, NSA is on the frontiers of communications and data processing. It is also one of the most important centers of foreign language analysis and research within the government.

NSA's early interest in cryptanalytic research led to the first large-scale computer and the first solid-state computer, predecessors to the modern computer. NSA pioneered efforts in flexible storage capabilities, which led to the development of the tape cassette. NSA also made ground-breaking developments in semiconductor technology and remains a world leader in many technological fields.

NSA employs the country's premier cryptologists. It is said to be the largest employer of mathematicians in the United States and perhaps the world. Its mathematicians contribute directly to the two missions of the Agency: designing cipher systems that will protect the integrity of U.S. information systems and searching for weaknesses in adversaries' systems and codes.

ANSWERS – Dirty Dozen

copyright Ó 2003 by H.W. Corley

1. 9 feet, 2 inches. Let x = computed feet, y = computed inches. Then 0.30(12x + y) = 12y + x in inches. Thus x = (9/2)y. Let y take on 0, 1, 2, …,11 since y must be an integer. Only y = 2 yields a nonzero integer number of feet x under 10. Thus he records 2 feet, 9 inches on his test.

2. 32.00 mph. From the two possibilities, it is apparent that Aruna can run one-fourth the bridge’s length in the same time that the train can go the entire length. Thus the train’s speed is four times Aruna’s.

3. 0.961 feet. Consider the plane containing both the axis of the cone and two opposite vertices of the cube’s bottom face. Let s be the length of the cube’s side. Then the cross section of the cone and the cube in this plane consists of a rectangle of sides s and s inscribed in an isosceles triangle of base 2 and height 3, where the s side of the rectangle lies on the base of the triangle. Similar triangles now yield s/3 = (1 – s/2) /1. Thus s = (9 - 6)/7.

4. (a) Let f = IMSE female faculty, t = IMSE total faculty, F = COE female faculty, T = COE total faculty. Then f/t > F/T, so P = f/F > Q = t/T.

5. Thursday. One of the statements: “I lie on Mondays and Thursdays” and “I lie on Wednesdays and Fridays” must be false. Hence, Dave must tell the truth on either Monday, Wednesday, Thursday, or Friday. All except Thursday yield a contradiction to Dave’s statements.

6. 12,870. There are 16 bridges to traverse - 8 east and 8 south in some order. Then the number of shortest paths is the simply the number of ways to select 8 of 16 to go south (and hence 8 to go east). This number is simply 16!/8!8! = 12,870. Incidentally, the number 2¹⁶ = 65,532 doesn’t account for situations when there are not two choices, such the case from the northeast corner.

7. 5201.0. Any foot forward results in 2 square feet of area along the path. The distance to the end of the spiral path is (102)²/2 = 10,404/2 = 5202 feet. But the center of the structure is 1 foot from the end.

8. 1 coin. Al-Fahl ate 8/3 loaves and contributed 7/3 loaves. Gamal 8/3 loaves and contributed 1/3 loaf. Hence, Al-Fahl gets 7 coins, and Gamal gets 1 coin.

9. 17 minutes. C + FV = 2. Return C = 1. SV + V = 10. Return FV = 2. C + FV = 2. Alternately, C + FV = 2. Return F = 2. S + V = 10. Return C = 1. C + FV = 2.

10. 1/2. Denote the lengths by x, y, z. To form a nondegenerate triangle, the largest side must be less than the sum of the other two. There are 6 mutually exclusive orderings of the sides. To simplify, we ignore any equality in an ordering such as x < y < z since its probability is zero. Now by the law of total probability

P[x,y,z form ] = P[x,y,z form | ordering of x,y,z] P[ordering of x,y,z],

where the sum is over the six possible orderings. By the symmetry involved, each

P[x,y,z form | ordering of x,y,z] is equal and each P[ordering of x,y,z] = 1/6. In particular, choose x < y < z and compute

P[x,y,z form | x < y < z] = = 1/2.

Substitution now yields the result.

11. 0.702. Define events as follows. Let S = Jamal wins a scholarship, U = Jamal wins the university scholarship, = Jamal does not win it, C = the other common finalist wins the university scholarship, = the other common finalist does not win it. We condition on U since the university scholarship will always be taken by a student. From the law of total probability

P(S) = P(S | U)P(U) + P(S |)P() = 1(1/3) + P(S |)(2/3).

In this equation, compute

= (8/14)(1/2) +(8/15(1/2) = 116/210.

Thus P(S) = 221/315 = 0.702.

12. 1 cubic foot. Consider the object shown below, where a flat sheet of composite material has been bent to form a triangle in the side view. The hypotenuse portion has a hole in it as shown in the problem’s figure. By making the sheet sufficiently thinner than the width of a line, less than 1 cubic foot of composite material would be required. Obviously zero cubic feet would not work.

13. 99.7 pounds. From the physics of circular motion, mrω² = mg – N, where ω is the angular velocity, r is the earth’s radius, and N is the net normal force exerted by the scale. Then N = mg - mrω² = mg[1 – (r/g)(2πf)²]= (0.997)mg = 99.7 pounds for the frequency f = 1/24 revolution per hour.

Practical Engineering Applications of Math for Children

by Editor and Holbrook L. Horton

As your children, grandchildren, nephews, nieces, and children of friends plow through math in school, they may begin to question why they need to learn math – and further, where is it used in everyday life. I recommend a very practical mathematics book that children will appreciate as they learn diverse engineering applications of mathematics.

The book is “Mathematics at Work” by Holbrook L. Horton, edited by Henry H. Ryffel, published by Industrial Press, Inc., 200 Madison Avenue, New York, NY 10016, copyright 1990, 3^rd edition (1^st edition – 1907), ISBN 0-8311-3029-6. Cost is around USD $24. Many problems discuss actual machining processes!

The math subjects span arithmetic, algebra, geometry, trigonometry, and logarithms. The contents:

· Basic mathematical principles

· Right- and Oblique-angled triangle problems

· Problems relating to tapers and angles

· Problems involving arcs, circles and vees

· Use of approximate formulas

· Problems in mechanics and strength of materials

· Gear ratio problems

· Methods and formulas for special conditions

· Miscellaneous problems and refresher questions

· Mathematical tables

· Index

There are 28 “sections” in the 1¼-inch thick, 5-inch wide, 7-inch long paperback – so it is easily handled by children and attractive to carry around (not bulky). The book is written in tutorial style, with many intermediate steps explained in the derivation of the formulas presented. An outstanding feature is the author presents a problem to be solved (say a formula), then proceeds through the step-by-step derivation with clearly marked illustrations, and then, the piece de resistance – he walks through an application of the formula with actual numbers. A sample problem statement given in Section 25-14, with neither the worked solution nor the illustration, follows. The solution is 3 pages. The example uses D = 4.82 inches, with the goal to remove one-sixth the original weight.

“To determine the diameter d in Figure 5. A hole is to be drilled through a sphere of diameter D in order to reduce its weight W by a given amount w. What is the diameter d of the hole in terms of the diameter D of the sphere and weights W and w?”

The answer to the numerical example above is d = 1.63 inches.

Wonderlic Personnel Test^TM (WPT^TM)

by Editor and Wonderlic Inc.

Are you an employer looking to hire high-potential candidates? Are you considering applying for a job that requires a certain skill set? Are you simply curious in your personal aptitude? Then you might wish to consider the Wonderlic Personnel Test. Since 1937, more than 120 million people at thousands of organizations worldwide have taken the WPT employment test for cognitive ability testing and aptitude testing purposes.

http://www.wonderlic.com/products/product.asp?prod_id=4

Measure cognitive ability - the most accurate predictor of employment success.

Description
The WPT is a short form measure of cognitive ability designed for simple administration and interpretation. Cognitive ability testing – or aptitude testing - is a crucial component of any successful employment testing program.

Content
Research has proven that cognitive ability, or general intelligence, is the single greatest predictor of job success - for any position. More effective than resumes, education, references or interviews, cognitive ability testing gives employers the objective information they need to make the right hiring decision.

The WPT employment test takes only 12 minutes to complete. It accurately measures a candidate's ability to:

Learn a specific job
Solve problems
Understand instructions
Apply knowledge to new situations
Benefit from specific job training
Be satisfied with a particular job

Using the WPT for employment testing enables you to match people with positions that suit their learning speed and aptitude. The Wonderlic Hire Results process combines research information from the U.S. Department of Labor with an analysis of your specific job to establish an appropriate minimum score for your position.

Since 1937, more than 120 million people at thousands of organizations worldwide have taken the WPT employment test for cognitive ability testing and aptitude testing purposes.

Implementation
The WPT employment test is aptitude testing that can be used to match job candidates or employees to jobs in which they will be effective and satisfied. WPT employment testing information shortens training time and reduces turnover from employees who are over- or under-challenged in a given position.

RELIABILITY: The manual reports odd-even reliabilities, which are not appropriate for speeded tests; however, it also reports test-retest reliabilities of .82 to .94, and interform reliabilities of .73 to .95. NORMS: White adults across all occupational categories.

The Wonderlic Personnel Test (WPT), so named to reduce the possibility that job applicants will think they are taking an intelligence test, was originally a revision of the Otis Self-Administering Tests of Mental Ability. The WPT is a 50-item, 12-minute omnibus test of intelligence. The items and the order in which they are presented provide a broad range of problem types (e.g., analogies, analysis of geometric figures, disarranged sentences, definitions) intermingled and arranged to become increasingly difficult. The WPT exists in 16 forms, and was designed for testing adult job applicants in business and industrial situations.

So, how do you score? http://espn.go.com/page2/s/closer/020228test.html

See how you score on some examples from a Wonderlic IQ test. Set your clock for five minutes, don't peek at the answers.

The Wonderlic Personnel Test ™
WPT ™ Sample Questions

Question 6

1. Look at the row of numbers below. What number should come next?
8	4	2	1	½	¼	?

2. Assume the first two statements are true. Is the final one:

1. true,

2. false,

3. not certain?

The boy plays baseball. All baseball players wear hats. The boy wears a hat.

3. Paper sells for 21 cents per pad. What will four pads cost?

4. How many of the five pairs of items listed below are exact duplicates?

Nieman, K.M.	Neiman, K.M.
Thomas, G.K.	Thomas, C.K.
Hoff, J.P.	Hoff, J.P.
Pino, L.R.	Pina, L.R.
Warner, T.S.	Wanner, T.S.

5. RESENT RESERVE • Do these words
1. have similar meanings, 2. have contradictory meanings, 3. mean neither the same nor opposite?

6. One of the numbered figures in the drawing at the top is most different from the others.

What is the number in that figure?

7. A train travels 20 feet in 1/5 second. At this same speed, how many feet will it travel in three seconds?

8. When rope is selling at $.10 a foot, how many feet can you buy for sixty cents?

9. The ninth month of the year is

1. October,

2. January,

3. June,

4. September,

5 May.

10. Which number in the following group of numbers represents the smallest amount?

.33

11. In printing an article of 48,000 words, a printer decides to use two sizes of type. Using the larger type,

a printed page contains 1,800 words. Using smaller type, a page contains 2,400 words. The article is

allotted 21 full pages in a magazine. How many pages must be in smaller type?

12. The hours of daylight and darkness in SEPTEMBER are nearest equal to the hours of daylight and

darkness in:

1. June,

2. March,

3. May,

4. November.

13. Three individuals form a partnership and agree to divide the profits equally. X invests $9,000,

Y invests $7,000, Z invests $4,000. If the profits are $4,800, how much less does X receive than if the

profits were divided in proportion to the amount invested?

14. Assume the first two statements are true. Is the final one:

1. true,

2. false,

3. not certain?

Tom greeted Beth. Beth greeted Dawn. Tom did not greet Dawn.

15. A boy is 17 years old and his sister is twice as old. When the boy is 23 years old, what will be the age

of his sister?

These are sample test questions and are intended for demonstration purposes only.

The Wonderlic Personnel Test is published by Wonderlic, Inc.; 1795 N. Butterfield Road, Libertyville, IL 60048

1-800-323-3742

Answers

1. 1/8
2. true
3. 84 cents
4. 1
5. 3
6. 4
7. 300 feet
8. 6 feet
9. September
10. .33
11. 17
12. March
13. $560
14. not certain
15. 40 years old

Commercially Available Performance Tests

for Dr. Lewis R. Aiken by Editor

Dr. Aiken passed away in January this year according to his wife, Dorothy. In memory of his prolific contributions to psychometrics, we present this article. So often knowing what resources are available for testing can be a tremendous help. In the area of psychometrics and related areas, the following table is provided by Dr. Lewis R. Aiken, in his book titled “Tests & Examinations – Measuring Abilities and Performance” by John Wiley & Sons, 1998, ISBN 0-471-19263-5, USD $110.00, [Table 5.1, page 129].

“Several performance test batteries or supplements to standardized achievement test batteries are available from CTB/McGraw-Hill, the Riverside Publishing Company, and The Psychological Corporation. Table 5.1 is an illustrative list of such instruments, including a brief description, the grade levels for which they are appropriate, and the publishers. These are open-ended instruments involving reasoning exercises in basic skill areas that are designed to test examinees’ strategic thinking and problem-solving abilities either alone or in small groups. Many exercises involve making extended responses to meaningful, “real-world” problems in which the examinee does something with the information that is provided. Both norm-referenced and criterion-referenced interpretations are available on certain instruments, some of which are limited in scope to reading, language arts, mathematics, science, or social science. Other instruments, such as the CTB Performance Assessment, GOALS, the New Standards Reference Examinations, Performance Assessments for ITBS and TAP & ITED, and the Riverside Performance Assessment Series, measure performance in two or more subject areas.” [pages 128, 130]

The information on the back cover of Dr. Aiken’s book, as well as a short biography follow.

Everything you need to select, design, construct, administer, score, and evaluate tests of cognitive abilities and performance

This book provides brief but complete coverage of concepts, methods, and materials for selecting, designing, and using tests of achievement, aptitudes, and special abilities. Dr. Lewis R. Aiken provides step-by-step guidelines along with a set of computer programs for planning, constructing, administering, scoring, and evaluating tests in educational, clinical, business/industrial, and government/military settings. The coverage includes:

· Psychometric concepts and methods

· Test construction, administration, and scoring

· Standardized achievement tests

· Oral and performance achievement tests

· Tests of single and multiple aptitudes

· Tests of general mental ability

· Assessment of cognitive development and disorders

Dr. Aiken received his doctorate in psychometrics and clinical psychology from the University of North Carolina. He has taught at the University of North Carolina at Greensboro, the University of Illinois, the University of the Pacific, and most recently at Pepperdine University. Among his nine other books are Psychological Testing and Assessment – 9^th edition; Assessment of Intellectual Functioning; Personality Assessment Methods and Practices; Assessment of Adult Personality; Rating Scales and Checklists; Questionnaires and Inventories; Human Development in Adulthood; Later Life; and Death, Dying, and Bereavement.

TABLE 5.1 Some Commercially Available Performance Tests [1]

AMAP Language Arts Performance Assessment. Grades 3-10. The Psychological Corporation. Real-life tasks involving reading, reflecting on, and responding to literature questions alone and in small groups.

AMAP Mathematics Performance Assessment Investigations. Grades 3-10. The Psychological Corporation. Real-life tasks involving investigations designed to help students understand and appreciate the value of mathematics.

Constructed-Response Supplement to The Iowa Tests. Grades 3-11/12 (Levels 9-17/18). The Riverside Publishing Company. Performance assessments in reading, language, and mathematics.

CTB Performance Assessment. Grades 2-11. CTB/McGraw-Hill. Exercises in Reading/Language Arts, Mathematics, Science, and Social Studies.

GOALS: A Performance-Based Measurement of Achievement. Grades 1.5-12. The Psychological Corporation. Content areas include Reading (narrative, informational), Mathematics (problem solving, procedures), Language (narrative, expository), Science (life, physical earth/space), Social Science (geographic, economic and cultural foundations of society, history and political bases of society).

IAS – Language Arts Performance Assessment (English). Grades 1-8. Also Spanish language version. The Psychological Corporation. Consists of a series of Reading Passages and Guided Writing Activities to assess reading comprehension, writing performance, and higher-level thinking.

IAS – Mathematics Performance Assessment. Grades 1-8. The Psychological Corporation. Consists of problems or situations requiring the use of mathematics for their solutions.

IAS – Science Performance Assessment. Grades 1-8. The Psychological Corporation. Consists of pictures and brief descriptions of problem tasks; respondents are supposed to devise their own methods for exploring the problem.

New Standards Reference Examinations. Elementary, Middle, High School. The Psychological Corporation. English, Language Arts and Mathematics.

Performance Assessments for ITBS and TAP & ITED. Grades 1-12. The Riverside Publishing Company. Language Arts, Mathematics, Social Studies, and Science.

Riverside Performance Assessment Series. Grades 1-12. The Riverside Publishing Company. Constructed-response assessments in Reading, Writing, and Mathematics.

Stanford 9 Open-ended Mathematics Assessment. Grades 1.5-13. The Psychological Corporation. Consists of nine questions or tasks developed around a single theme. Answers to questions scored on a 4-point scale according to one of three rubrics: communication, reasoning, problem solving.

Stanford 9 Open-ended Reading Assessment. Grades 1.5-13. The Psychological Corporation. Narrative reading selection followed by 9 open-ended questions.

Stanford 9 Open-ended Science Assessment. Grades 1.5-13. The Psychological Corporation. Nine tasks with items on life, earth, and physical sciences that address applications of concepts, decision-making, and problem solving, and scientific inquiry.

Stanford 9 Open-ended Social Science Assessment. Grades 1.5-13. The Psychological Corporation. Real life questions designed to measure student’s understanding of history, geography, economics, civics and government, and culture.

[1] from page 129 of Dr. Lewis R. Aiken’s book “Tests & Examinations – Measuring Abilities and Performance”

I’d like to mention, too, that an 11-page Appendix is supplied to describe the included computer diskette which contains several dozen programs to provide experience in selecting, using, and evaluating tests.

DARPA’s Dust-busters – “Grand Challenge”

by Editor and Jean Kumagai

The Defense Advanced Research Projects Agency (DARPA) is the central research and development organization for the Department of Defense (DoD). DARPA manages and directs selected basic and applied research and development projects for DoD, and pursues research and technology where risk and payoff are both very high and where success may provide dramatic advances for traditional military roles and missions. [See: http://www.darpa.mil/ ]

In the June 2004 issue of IEEE Spectrum magazine, we read a fascinating article by Jean Kumagai titled “SAND TRAP - DARPA's 320-kilometer robotic race across the Mojave Desert yields no winners, but plenty of new ideas.” DARPA conducted its first Grand Challenge, a field test of autonomous ground vehicles, March 8 to 13, 2004. Its purpose was to encourage the accelerated development of autonomous vehicle technologies that could be applied to military requirements.

SAND TRAP – IEEE Spectrum – June 2004 – pages 44-50

http://www.grandchallenge.org

"THE BATTLEFIELD OF THE FUTURE," and the anticipated key role on it for autonomous vehicles, was what DARPA had in mind when it set aside an estimated $13 million for this rally. A few years back, Congress had mandated that by 2015, one-third of U.S. armed forces would be robotic, but the lawmakers didn't say how that might happen. Though DARPA could have simply awarded robot developers R&D contracts, which typically run well in excess of a million bucks, the agency's director, Anthony Tether, decided that a more public competition would draw forth entrants who had never considered working with the Department of Defense.

It's a stupendously difficult challenge — DARPA itself has decided it is a Grand Challenge —and yet hundreds of engineers, inventors, robotics experts, computer scientists, garage monkeys, students, and others have gathered here today to take up the agency's gauntlet. Many have devoted the better part of a year to this undertaking, forgoing jobs, family, regular sleeping hours, and less technologically intensive pastimes. To sweeten the pot, DARPA (or, rather, U.S. taxpayers with Congress's approval) has ponied up a $1 million prize for the vehicle that can cover the distance in under 10 hours. But there's no mistaking the looks on people's faces: anxious, excited, sleep-deprived, and slightly obsessed. This is clearly not about the money.

AMONG THE 22 FINALISTS AT THE SPEEDWAY, many are simply modified SUVs or trucks, with a few sensors and GPS antennas tacked on top. But a few are custom built and puzzlingly complex, as if the prize will go not to the vehicle that can complete the course but to the vehicle that looks most like a robot.

In the end, there are no winners. Fulfilling its destiny, Sandstorm travels farthest, covering 12 km, or about 5 percent of the course. Earlier, the Humvee had struck a couple of fence posts, which seemed to damage its steering. After making it to a series of hairpin turns at Dagget Ridge, it gets stuck on a large rock—"high-centered" in off-road lingo—and its front tires continue to spin until the rubber has burned off and both drive shafts break.

The agency (DARPA) has funding to continue the event through 2007 and is rumored to have doubled the prize money to $2 million for next year's race.

The Secret in Building 26

by Editor, Jim DeBrosse and Colin Burke

“The SECRET is hidden in plain sight: a nondescript glass-and-panel box of a building standing four stories high, flanked by parking lots and set back far enough from the busy intersection of South Patterson Boulevard and West Stewart Street that few motorists even notice it, much less wonder what might have transpired there some sixty years ago. Inside the now empty structure is another empty building of tan brick and glazed cinder block, a far more interesting art-deco design that has been nearly encapsulated by the newer addition and can be seen only from the rear.

A granite boulder emblazoned with a small bronze plaque is all that testifies to the building’s proud history. It sits along a nearby sidewalk that few people traverse even by day. The plaque reads:

‘In 1942, the United States Navy joined with the National Cash Register Company to design and manufacture a series of codebreaking machines. This project was located at the U.S. Naval Computing Machine Laboratory in Building 26, near this site. The machines built here, including the American “Bombes,” incorporated advanced electronics and significantly influenced the course of World War II.’

October 2001

Institute of Electrical and Electronics Engineers

Nearly one thousand people worked on the Navy’s top secret project in Building 26 between 1942 and 1945. They were sworn never to divulge the nature of their work.

The full story of their struggle, sacrifice, and ultimate triumph has never been told – until now.”

The editor, since 7 years old, has always been fascinated by the cloak-and-dagger facets of WW II, and when his eye caught this new book on the Barnes & Noble display table – it was “love at first sight.” The editor shares enticing glimpses of the extremely well written, co-authored book, that readers – young and old – who have interests in cryptography – will either buy the USD $26.95 book for themselves or have their local libraries order it. Our youth should read this book – to initiate a love for cryptography and to appreciate the extreme dedication this field demands in an ever-changing military landscape.

The title of the book “The Secret in Building 26 – The Untold Story of America’s Ultra War Against the U-Boat ENIGMA Codes,” by Jim DeBrosse and Colin Burke; Random House publishing company; 2004; ISBN 0-375-50807-4; 272 pages; with 16 glossy B&W photos.

On the inside jacket of this intriguing book:

“Reams have been written about the success of the British “Ultra” program in cracking the Germans’ Enigma code early in World War II, but few people know what happened in 1942 when the Germans added a fourth rotor to the machine that created the already challenging naval code – and tracking German U-boats once again became impossible.

Joe Desch, an unassuming but brilliant thirty-five-year-old engineer at the National Cash Register Company in Dayton, Ohio, was given the task of creating a machine to break the new Enigma settings – an assignment whose secrecy rivaled that of the atom bomb [i.e., the Manhattan] project, and that was perhaps just as daunting. Not only was Desch under unrelenting pressure to build the machine before the Battle of the Atlantic was lost, but because he was the son of a German immigrant mother, his own life was pinned under a microscope.

The Desch Bombe, as the codebreaking machine was called, was a mammoth electromechanical marvel that stood seven feet high, eleven feet long, and two feet wide. Row upon row of commutator wheels imitated the rotors of the Enigma machine at extremely high speeds, attempting to crack the code. But an earthshaking scandal erupted late in 1943, when it was discovered that one of the engineers at NCR was in touch with German and Japanese embassies. This engineer and his wife were seized immediately, but the story of what happened to them has never been revealed until now.

Joe Desch suffered a nervous breakdown from the pressure of his work; still, he was given the National Medal of Merit, our country’s highest civilian honor. When he died in 1987, even his daughter had no idea how important his career had been to the Allied victory in World War II. The Secret in Building 26 brings Desch’s story, and the entire story of the war against Enigma, to vivid, thrilling life.”

Some excerpts from the mesmerizing Prologue:

“The Germans were confident that their coding system was impenetrable – even if their machines were captured – and they had good reason to be. Theoretically, at least, the number of ciphering possibilities generated by the advanced naval Enigma of 1942 was far greater than the number of all the atoms in the observable universe – an incredible 2 x 10¹⁴⁵ possible encryption settings compared to a mere 1 x 10⁸⁰ known atoms. After purchasing the rights to the commercial version of the Enigma Cipher Machine in the 1920s, the German military began adding its own bedeviling improvements and innovations and continued to do so throughout most of the war. [xxi]

. . . As a result, the naval Enigma would never repeat the same position of its scrambling wheels for hundreds of thousands of keystrokes (26 x 26 x 26 x 26 = 456,976; however, a complex feature of the Enigma, a double turnover of one of the rotors, reduced the number of positions by some 18,000). [xxii]

. . . The fourth and final disk, called the Umkehrwalze, or reflector, served to reroute the current back through the first three wheels, ensuring that the plain text and the scrambled text were always reciprocal at the same settings. [xxii]

. . . The different wirings for the rotors and the different orders for placing each rotor inside the machine created another staggering set of enciphering possibilities – 26 x 10¹⁰⁵ – again, far greater than all the atoms in the known universe. [xxiii]

. . . But the hurdles for the codebreakers didn’t stop there. Each of the four rotors could be set manually to a different starting position, at letter A and on through Z, with the starting letters visible through small windows on the Enigma casing. The total number of possible initial settings for the four rotors was, again, 456,976. Likewise, the tumbler rings on each of the first three rotors, which caused the adjacent rotor to advance, could also be set to different starting positions, multiplying the possibilities by yet another 456,976. [xxiii]

. . . If all that weren’t enough to drive codebreakers mad, the Germans added what looked like a tiny telephone switchboard to the front of the machine, on which double-ended wires, called Steckers in German, could be plugged into jacks for swapping individual letters, so that A became E, for instance, and vice versa. Anywhere from one to thirteen different letters could be steckered in this way. The stecker board proved to be one of the biggest headaches in breaking the Enigma. With twenty letters steckered to one another and six letters unplugged, the standard practice during the war, the number of plugboard possibilities alone was nearly 533 trillion. [xxiii]

. . . Under the most stringent security measures of the war, the codebreaking machine would be designed and produced in Dayton, Ohio, at the National Cash Register Company, then a world leader in electronics. Only two companies in the United States had the technical capability at that time to produce such a marvel: IBM and Dayton’s NCR. The obvious choice for the Navy at that time was NCR, where chairman of the board Colonel Edward A. Deeds had a long working relationship with Vannevar Bush, the famed MIT scientist who had forged an alliance between military and academic researchers through his National Defense Research Committee. [xxvii]

. . . The project would be entirely self-contained inside NCR’s Building 26, so named because it was the twenty-sixth structure to rise on the company’s ninety-acre business campus. It was only a coincidence, noted by researchers at the time, that the work in Building 26 would revolve around the seemingly endless possibilities in scrambling the twenty-six letters of the alphabet.” [xxvii]

A question by the Editor (Ron Yannone) to readers of Noesis: What were the stakes back then – for such a crucial push for a solution against Enigma?

“As a U.S. Navy training manual pointed out as the time:

If a submarine sinks two 6,000-ton ships and one 3,000-ton tanker, here is a typical account of what we have totally lost: 42 tanks, 8 six-inch howitzers, 88 twenty-five-pound guns, 40 two-pound guns, 24 armored cars, 50 Bren carriers, 5,210 tons of ammunition, 600 rifles, 428 tons of tank supplies, 2,000 tons of stores and 1,000 tanks of gasoline. . . . In order to knock out the same amount of equipment by air bombing (if all this material were on land and normally dispersed) the enemy would have to make three thousand successful bombing sorties.” [xx]

Reply to Brian Schwartz' Articles on

Psychometric Testing and the SAT in Noesis #169

Kevin Langdon

In his article, "Reply to Kevin Langdon -- Relative to SAT Topic Noesis Issue #167," Brian wrote:

In Noesis #167, Kevin says that only 6 people get a top score every year, and that's too small a sample. But you're always going to get a small sample at the 99.9998 level! The SAT has been taken by upwards of 50 million people. How much larger sample can you have?

Brian misunderstands the thrust of my argument. I am talking about how the meaning of very high scores is established. There are not enough of the very highest scores to reliably extract a pattern from, but when they are grouped with other high scores statistically and the overall distribution is examined the statistical meaning of the particular scores in question can be determined more reliably.

And can one really say, as Kevin does, that since there are 200 SAT points between 2- sigma and 3-sigma, there must be another 200 points between 3-and 4-sigma? Kevin treats SAT scores like deviation IQ scores.

Ratio IQ scores and deviation IQ scores are essentially identical near the middle of the bell curve. Further from the mean, SAT scores behave more like deviation IQ scores than like ratio IQ scores; the tails of the distributions are nowhere near as widely spread out.

Equating means and standard deviations is the usual method for establishing the correspondence between two distributions.

The burden of proof is on those advocating different methods.

He adds them, multiplies them by 1.11, ends up with the bizarre result that an impossible SAT score of 1750 is below Prometheus level.

An impossible score on a test for mental retardation won't get you into a lot of high-IQ societies. So what?

You can do this sort of thing with deviation scores, but not with SAT scores. If the outdoor temperature reaches 70 Fahrenheit once every 50 days (sigma 2), and 108 Fahrenheit once every thousand days (sigma=3), Kevin would (using his exact same reasoning) say it would reach 146 once every 30,000 days! Eeek!

That isn't the same reasoning at all. There you have a system involving many variables; with regard to IQ testing, we're dealing with a system composed of one variable of interest and various sources of noise. If a test measures g it should be possible to place scores on it along the g scale--IQ.

Test score extrapolation can be done -- but it's a lot more complicated. Predictions made by calculating the standard deviation and simply adding it to get to the next sigma level are almost never accurate (except, of course for deviation IQ scores).

Predictions are reasonably accurate up to the point where the test runs out of ceiling. Unfortunately, the SAT runs out of steam long before it reaches the Mega level, even for a 14-year-old.

Indeed, Ron Hoeflin cleverly used this fact when he normed the Mega Test; check out Table 6 of his 6th norming, entitled "Table T6. Extrapolations to higher percentiles based on changes in the ratios of observed to expected participants scoring above five selected percentiles."

It's a little too clever. Hoeflin's methodology in the sixth norming is flawed. There is no statistical justification for claiming to be able to discriminate at progressively further extrapolated levels with progressively less data. Talk about Voodoo statistics!

Later on Kevin argues that a 14 year old who is equal to a normal 17 year old has an IQ, not of 120 but of 111. I question this figure. I can't find it in the pages cited.

You have to interpolate, but it's clearly implied. See also pp. 104-105 of Jensen's Bias in Mental Testing.

Indeed, the Educational Testing Service estimates that a SAT score of a high school junior is equivalent to a score 65 points higher obtained by a senior. Extrapolating this -- and here extrapolation is valid, since the point difference per year probably increases the younger one goes -- this would add 195 points to my score.

I included a figure showing how scores converge toward their adult level in the late teen years. It should be clear enough that the ratio method has to leave off somewhere. And, in fact, a 14-year-old is not going to get 14/17 the score a 17-year-old gets on an IQ test; they're much closer together than that.

But let's assume Kevin's 111 figure is correct. The correct procedure is quite straightforward. Simply check a table to determine the rarity of a 111 IQ. If a 14 year old who is equivalent to a normal 17 year old has an IQ of 111, then that 14 year old is in the 75% percentile. This figure is more than enough to boost my score way over the 99.9999 level. If a million 14-year-olds took the test, less than one will [sic] equal my score.

Does not compute. Maybe you could take us through the math.

What Kevin does with that 111 figure, however, is to multiply my SAT score by it (which is wrong) and then use the fact that he multiplied the SAT with a ratio to conclude that the result is a ratio IQ . . . even though he got it from a table wrongly calculated by treating the SAT as a deviation IQ. This is doubly wrong. Voodoo psychometrics.

SAT total scores are conventionally considered to be (roughly) IQs with an extra digit, and the ratios between mean scores at different ages can only meaningfully be made use of to compare distances from the mean in standard deviations.

In his article "Reply to Chris Cole -- Relative to SAT Topic Noesis Issue #167," Brian wrote:

Chris Cole has, using mathematical simulations, made some rather strong arguments against the reliability of the SAT at the 99.9999 level. But these arguments are not limited to the SAT. They apply to all tests and especially to all multiple-choice tests. So if you accept Chris's proof that the SAT is not a good test for Mega, you will have to throw out the L.A.I.T. as well. (And possibly the Mega and Titan test too, since many of the math questions are in effect multiple choice.)

In fact, I believe that Chris' critique would apply even more to the L.A.I.T. than it does to the SAT for 2 reasons.

1. The SAT, unlike the L.A.I.T., has a 1/n penalty for incorrect answers, where n = the number of choices for each question.

Wrong on two counts:

A. The correct formula is 1/(n-1); if there are n items, the testee will get an item right by chance 1/n of the time and wrong (n-1)/n of the time. This will produce a score of 1 for the right answer and of - (n-1) * (1/(n-1)) = -1 for the n-1 wrong answers, yielding a net score of 0 for guessing.

B. The LAIT corrects for guessing, just like most of the items on the SAT.

However, corrections for guessing make very little difference at the extreme high end, where the testees have missed only a very few items.

2. The SAT has more questions than the L.A.I.T. Now of course the L.A.I.T. has a much higher mean, but that's not what is relevant. What matters is the number of questions that stand between a very high score -- say 3-sigma, or 99.9 -- and the Mega level.

Not necessarily; beyond a certain point there are enough to yield high-quality statistics. The SAT has way more than enough, but at 56 items (reduced by a few bad items that are not scored) the LAIT isn't a short test, either.

Psychometricians generally want to see at least 30-40 items for this purpose.

The SAT reaches the 3-sigma level at about 1450. The top 3/28 of its range, about 15 items, is above this point.

The LAIT reaches the 3-sigma level at a scaled score of 53/100; about two dozen items are above this point.

But the SAT has no items above the midpoint of this range and the LAIT has a dozen.

And there both tests are, I believe, equal. In fact, now that I think of it, the SAT has quite a few more questions standing between a 99.9er and the top -- at least 15 --

That number's just about right, but the LAIT has more items in the range of interest.

So the odds of a 3-sigma fellow guessing his way to a perfect score are infinitesimal (4^15).

Even very bright testees wind up "guessing," in the sense that they can't adequately check their work due to time pressure. That's why there are so few of the very highest scores. That doesn't mean that such scores genuinely indicate that degree of rarity of intellectual ability. This is simply ceiling-bumping.

So, suppose your fondest dreams are realized and every college in the US drops the SAT and requires the L.A.I.T. for admission. The next year, over a million high school seniors take the L.A.I.T. What are the chances that the most intelligent person gets the highest score? Wouldn't it be (as Chris calculated for the SAT) less than 1%...and possibly a lot less?

Kevin apparently recognizes this. In Noesis #135, he wrote "In my opinion, it's stretching things considerably to claim that these tests [L.A.I.T. and Mega] are accurate at their ceilings or a couple of points below them. The one-per-million level occurs at 176 on the LAIT and 46 on the Mega. Even if we allow one point for ceiling bumping, fewer than fifteen people have made scores this high on my tests or Ron's. I suggest that we lower our percentile cutoff to 99.9997, one in 300,000, or 4.5-sigma."

There are major uncertainties in measurements at very high levels. The Mega Society is pushing the limits of what is possible at the present state of the art of high-range testing.

What is not possible is to estimate mega-level scores using a test that doesn't even reach the four-sigma level.

And even for a 14-year-old the SAT doesn't reach the Mega level, as I made clear in my article in Noesis #167.

In his article "How 'Selective Tests' Select," Brian wrote:

I think a lot of people have the intuitive feeling that a timed test with a lot of relatively easy questions cannot have a very high ceiling. (Of course, they are wrong to think the SAT questions are easy, but that's another matter.)

None of the SAT questions are difficult, by the standard of problems on tests like the LAIT and the Mega.

But what makes an IQ test question good is not its high difficulty (which could well be due to s, specific math ability which may come as the result of study, such as that required for an advanced math diploma) but its correlation with that factor common to all problem-solving . . . g.

In order for a test to be usable for Mega admissions it must be highly g-loaded and have a high ceiling.

Many easier problems can substitute for one slightly harder one, but it isn't possible to measure Mega-level IQ's with tests designed to be accurate only up to the three-sigma level.

Furthermore, researchers studying chronometrics have shown that reaction times are strongly correlated with g. (See the papers published in the mid-1980s by Philip Vernon, L.T. Miller, F. Nador and L. Kantor.) And if this is granted, then it IS possible to have a lot of easy, but timed, questions measuring g, with a high ceiling, because what you would then be doing is measuring reaction time.

But if a test is highly g loaded it should not come as a big surprise that its items correlate well with one another. And the aggregation of the items facilitates a simple comparison between a harder item and a set of easier ones.

If many easy items are used in an attempt to measure very high levels of ability there will be a lot of scores bunched up at the high end and the signal will get lost in the noise (careless errors, time pressure, defects in the test items, etc.).

From Paul Cooijmans' page, http://members.chello.nl/p.cooijmans/gliaweb/morefaq.html :

What’s the correlation between chronometrics and intelligence? Depending on what measure or combination of measures is considered this varies from about .2 to about .7. Also, as mentioned by Chris Brand in his book The G Factor (not to be confused with A. Jensen's book of the same title), the correlation is not constant over the entire range, but highest in the low range and lower in the above-average range; in the very high range there may be no correlation at all.

Back to Brian Schwartz:

Of course, such a test does not directly measure speed of neuronal processing . . . but, since millions of reaction times are involved in completing such a test, someone who cannot achieve the highest processing speed also cannot get a perfect score.

Chronometric tests do not measure "millions" of reaction times; they measure the speed of simple responses to simple stimuli.

In fact, there is some evidence that even the most notoriously difficult IQ test questions might work in similar fashion. Fred Vaughan's study of the distribution of correct answers to Question 36 on the Mega Test found a striking similarity with the distribution of answers to a test composed of 6 easier questions on which a testee's score is zero unless he answers all 6 correctly.

The exact same performance (ability to select at a very high level) as a tough problem can be achieved by grouping easier problems such that you must get all of a set correct. That is in essence what someone who gets an extreme score on a test like the SAT has done -- gotten them correct in every set.

What is the justification for this scoring procedure? It is always more accurate to use more separate items; grouping the items just lowers the effective length of the test, and therefore its reliability.

Fibonacci Numbers

by Editor and Ron Knott

The editor recalls learning about Fibonacci numbers in high school. There were interesting properties of this number set. See this URL for a wealth of hands-on, colorful, information:

http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibmaths.html#patt

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, ...

Here are some patterns people have already noticed in the final digits of the Fibonacci numbers:

Look at the final digit in each Fibonacci number - the units digit:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, ...

Is there a pattern in the final digits?

0, 1, 1, 2, 3, 5, 8, 3, 1, 4, 5, 9, 4, 3, 7, 0, 7, ...

Yes! It takes a while before it is noticeable. In fact, the series is just 60 numbers long and then it repeats the same sequence again and again all the way through the Fibonacci series - for ever. We say the series of final digits repeats with a cycle length of 60.

Suppose we look at the final two digits in the Fibonacci numbers. Do they have a pattern?

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, ...

Yes, there is a pattern here too. After Fib(300) the last two digits repeat the same sequence again and again. The cycle length is 300 this time. So what about the last three digits? and the last four digits? and so on??

For the last three digits, the cycle length is 1,500; for the last four digits, the cycle length is 15,000 and for the last five digits the cycle length is 150,000 and so on...

Petals on flowers

On many plants, the number of petals is a Fibonacci number: buttercups have 5 petals; lilies and iris have 3 petals; some delphiniums have 8; corn marigolds have 13 petals; some asters have 21 whereas daisies can be found with 34, 55 or even 89 petals. 13 petals: ragwort, corn marigold, cineraria, some daisies 21 petals: aster, black-eyed susan, chicory 34 petals: plantain, pyrethrum 55, 89 petals: michaelmas daisies, the asteraceae family. Some species are very precise about the number of petals they have – e.g., buttercups, but others have petals that are very near those above, with the average being a Fibonacci number. Pine cones show the Fibonacci Spirals clearly.

About The Fibonacci Quarterly

by Gerald E. Bergum

http://www.mathpropress.com/problemColumns/fq/fqInfo.html

The Fibonacci Quarterly is normally published four times a year: in February, May, August, and November. The primary function of the journal is to serve as a focal point for widespread interest in the Fibonacci numbers (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,...) and related numbers, especially with respect to new results, research proposals, challenging problems, and innovative proofs of old ideas.

Editorial Policy

The Fibonacci Quarterly seeks articles that are intelligible, yet stimulating, to its readers, most of whom are university teachers and students. These articles should be lively and well motivated, with new ideas that develop enthusiasm for number sequences or the exploration of number facts. Illustrations and tables should be wisely used to clarify the ideas of the manuscript. Unanswered questions are encouraged, and a complete list of references is absolutely necessary.

Problem Columns

The journal contains two problem columns, one for Elementary Problems and one for Advanced Problems. Problems from the elementary column are maintained in an electronic archive. Solutions can be found in the printed issues of the journal, approximately one year after the appearance of the problem, together with the names of the people who solved the problem correctly. The best solution to each problem from those submitted is published in the journal.

All correspondence related to the elementary problem column should be sent to

Stanley Rabinowitz

12 Vine Brook Road

Westford, MA 01886-4212  USA

Fibonacci@MathProPress.com

All correspondence related to the advanced problem column should be sent to

Raymond E. Whitney

Mathematics Department

Lock Haven University

Lock Haven, PA 17745  USA

Submitting an Article

Articles should be submitted in the format of the current issue of The Fibonacci Quarterly. They should be typewritten or reproduced typewritten copies, that are clearly readable, double spaced with wide margins and on only one side of the paper. The full name and address of the author must appear at the beginning of the paper directly under the title. Illustrations should be carefully drawn in India ink on separate sheets of bond paper or vellum, approximately twice the size they are to appear in print. Since the Fibonacci Association has adopted standard definitions for the Fibonacci and Lucas sequences, these definitions must be used and need not be a part of the paper. One to three complete AMS classification numbers must be given directly after the references or on the bottom of the last page. Papers without classification numbers will be returned.

Submission of Manuscripts

Two copies of the manuscript should be submitted to

Gerald E. Bergum

Editor, The Fibonacci Quarterly

Department of Computer Science

South Dakota State University

Box 2201

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Authors are encouraged to keep a copy of their manuscripts for their own files as protection against loss. The editor will give immediate acknowledgment of all manuscripts received.

Subscriptions:

Address all subscription correspondence, including notification of address change, to:

Richard Vine

Subscription Manager

The Fibonacci Association

Santa Clara University

Santa Clara, CA 95053  USA

Annual domestic Fibonacci Association membership dues, which include a subscription to The Fibonacci Quarterly, are US $35 for Regular Membership, $40 for Libraries, $45 for Sustaining Membership, and $70 for Institutional Membership. Foreign rates, which are based on international mailing rates, are somewhat higher than US domestic rates; please write for details.

Reprint Permission

Requests for reprint permission should be directed to the editor, Gerald Bergum. However, general permission is granted to members of the Fibonacci Association for noncommercial reproduction of a limited quantity of individual articles (in whole or in part) provided complete reference is made to the source.

Permission to download and print the problems given on these web pages for personal or educational use is granted provided that the copyright notice remains with the text. Commercial use is prohibited.

Back Issues

All back issues of The Fibonacci Quarterly are available in microfilm or hard copy format from

University Microfilms International

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Dept. P.R.

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Reprints can also be purchased from the UMI Clearing House at the same address. Back issues are available from many university libraries.

A sample set of problems from Volume 30 (1992) and Volume 31 (1993) follow.

President Ronald Wilson Reagan (1911-2004)

by Editor and David von Drehle

As we converge to Independence Day (July 4^th) this year, we cannot help but pause a moment on the late former President Ronald Reagan – an American “original.” Ronald Reagan, the 40^th president of the United States passed away June 5^th at age 93.

A condensed history of former President Reagan’s life, extracted from David von Drehle’s (The Washington Post) article that appeared in our local Sunday (June 5^th) Nashua Telegraph newspaper, follows.

Amazing Story – It was an almost unbelievable life, a melodrama, a rags-to-riches tale, a multi-part saga written by someone with boundless imagination and an infinite sense of the possible. Born in tiny Tampico, Ill., educated at Eureka College, Reagan was a radio sportscaster, a Hollywood B-movie star, host of a TV variety show, a soap salesman, a motivational speaker, governor of California, and starting at age 53 – arguably the most important American political figure since Franklin D. Roosevelt. . . . Reagan was a champion salesman of the American dream, mayor-for-life of the land he called “a shining city on a hill.” . . . Like all forceful leaders, Reagan made some people very angry – but his gift for communication and his bedrock optimism attracted far more supporters than critics. In 1984, he was reelected with the largest number of electoral votes in U.S. history. Though the nation has added some 50 million people since then, no candidate has surpassed his record. . . . “He got the country to believe in itself again,” his longtime aide Michael Deaver said in an interview before Reagan’s death. Reagan held office between 1981-1989, the first in a generation to serve two complete terms. Former President Reagan was coined the nickname “The Great Communicator.” Unquestioned was Reagan’s ability to connect with the American public through formal speeches, offhand remarks, even mere gestures. He was the most effective presidential communicator since Roosevelt and probably one of three greatest to hold the office – Lincoln, master of the written speech, Roosevelt, master of the radio address and Reagan, master of television. . . . Wounded in an assassination attempt shortly after taking office in 1981, he quipped “I forgot to duck.” . . . Crystallizing the final stage of the Cold War confrontation between Western liberties and Soviet repression, he visited the Berlin Wall in 1987 and challenged Soviet premier Mikhail Gorbachev to tear it down. In a perfect summary of his core faith, Reagan declared: “After these four decades, then, there stands before the entire world one great and inescapable conclusion: Freedom leads to prosperity. Freedom replaces the ancient hatreds among the nations with comity and peace. Freedom is the victor.” . . . Reagan wrote ten years ago: “In closing let me thank you, the American people for giving me the great honor of allowing me to serve as your President.” . . . . “When the Lord calls me home, whenever that may be, I will leave with the greatest love for this country of ours and eternal optimism for its future.”

Some of my Favorite Nursery Rhymes

by Editor

Some of my favorite nursery rhymes follow. For purposes of teaching math and/or physics, the editor would appreciate readers transforming any of these nursery rhymes into mathematical nursery rhymes. Submittals will be published in a future issue of Noesis.

See-saw, Margery Daw,

Johnny shall have a new master;

Johnny shall have but a penny a day,

Because he can’t work any faster.

Georgie Porgie, pudding and pie,

Kissed the girls and made them cry;

When the boys came out to play,

Georgie Porgie ran away.

Jack be nimble,

Jack be quick,

Jack jump over

The candlestick.

Baa, baa, black sheep,

Have you any wool?

Yes sir, yes sir,

Three bags full;

One for the master,

And one for the dame,

And one for the little boy

Who lives down the lane.

Old Mother Hubbard

Went to the cupboard,

To fetch her poor dog a bone;

But when she got there

The cupboard was bare

And so the poor dog had none.

Sing a song of sixpence,

A pocket full of rye;

Four and twenty blackbirds,

Baked in a pie.

When the pie was opened,

The birds began to sing;

Was not that a dainty dish,

To set before the King?

The King was in his counting-house,

Counting out his money;

The Queen was in the parlor,

Eating bread and honey.

The maid was in the garden,

Hanging out the clothes,

When down came a blackbird

And pecked off her nose.

Ron’s Math-O-Day

by Editor

Back in my freshman year at college (1972), I started developing a math puzzle for each major holiday, called Ron’s Math-O-Day. I continued developing these puzzles until around the mid-1980s, but unfortunately, I never archived these hand-written exercises. To help revive the art, I will try to present one here for our avid readers.

The idea is to solve the pieces, and then assign an alphanumerical value to them. Evaluate the “pieces” below, and then transform them into the corresponding letters of the alphabet. A = 1, B = 2, . . . Z = 26. CAUTION: Some numbers are used as is!

The slope (m₁) of the line perpendicular to the line 3x – 5y – 25 = 0; then compute the rounded up {[-(m₁)^t] } plus where , where t is defined (computed) in (4) below
The area A_R of the region R bounded by the graphs of the functions f(x) = 2x – 1 and g(x) = – (2x – 1)² and the lines x = 1 and x = 2; multiplied by 3, and augmented by 3!
Precious perfume is escaping from a spherical balloon so that its radius r is decreasing at the rate of 2 inches per minute. Find the rate of change of the volume V as a function of time if we are given that r = 10 inches when t = 0, and the volume V₁ of the balloon when t = 2 minutes, and the time, t when V = 0? Then divide V₁ by
The value of (for n = integer), rounded to the nearest integer
The approximate area of the bounded curve defined by , multiplied by 10p, rounded down to the nearest integer

The Man of Few Words

by Editor

As I scanned through more than two decades of the Mega Society’s journals (The Megarian and Noesis), I noticed that Administrator Jeff Ward only published ballot reports, some legal-oriented reports, and one chess problem. My personal experience with Jeff since February 2004 is that he is “quiet” – and a “number-cruncher” – via his profession – Income Tax Services.

Interfacing with Jeff on the Brian Schwartz and SIGMA VI Test ballot results, true-to-his-nature, Jeff only emailed the ballot numbers. To spruce Jeff’s “article debut” on the ballot results in the recent Noesis May issue #169 (page 37), I added the diplomatic words. Jeff, again, true-to-his-nature, emailed a request that I inform our avid readers that I contributed the words. Jeff wants credit only for the ballot numbers.

BACKGROUND: Brian Schwartz sent Dr. Ron Hoeflin his SAT scores back in September 2003 – for admission into the Mega Society. It wasn’t until I became editor/publisher that we accelerated addressing Brian’s inquiry. With mountainous enthusiasm, and I believe now, earnest hope, Brian must have felt that I had some extra, magical clout as editor – because his email stream and Pony Express mail were frequent. I know the SAT saga isn’t as trivial as some feel. Personally, the highest IQ ceiling anyone vouched for years ago was 160 – for 17-year-old SAT test takers. I mentored a 12-year-old boy who got 800 (Math) and 730 (Verbal) back in 1995 – and when I inquired with Dr. Hoeflin then – Ron desired a 1600 combined score. I personally engaged in contacting several gifted program experts for insight on behalf of Brian – like the Johns Hopkins Center for Talented Youth (http://www.cty.jhu.edu/ ). I did not get a solid yea/nay. The ballot results were 4 YES, 6 NO, and 4 UNDECIDED – so it was not a slam-dunk in the negative. I took on the editor/publisher role for several reasons – two of which are to provide an informative journal and because I truly care about each member and non-member subscriber. Since high school I have been coined as diplomat, ambassador, negotiator, and mediator – always attempting to s-m-o-o-t-h out the rough edges in tight, touchy situations. “Everyone is a saint” is my motto. As ballot results came in Brian was anxious – but I told him the results will soon be published – but nevertheless – to not be disappointed if they turn out “gray.” As Brian has been on tender-hooks for 6 months, I felt some healing balm should accompany the, otherwise, “cold” numbers in the ballot outcome. Since the March issue was released, I have not heard from Brian Schwartz. Brian – you can still take the Titan Test after warming up with the Mega Test.

I’d like to present an award to Administrator, Jeff Ward and a Roman poem each reader can continue to implement in their lives: “Take one hundred and one, and to it affix, the half of a dozen, or if you please, six. Add fifty to this, and then you will see, what every good lad to others should be.” I encourage Jeff to share his wealth of knowledge by way of a regular column titled: “Income Tax Tips.” Every reader, as well as Administrator Jeff Ward, will benefit!

This Award is presented to Mega Society Administrator

Jeff Ward, EA PhD

For his undying service as Administrator, dealing only with numbers, as

The Man of Few Words

Editor/Publisher: Ron Yannone June 13, 2004

Ron’s Math-O-Day – Tentative Solution

by Editor

3x – 5y – 25 = 0 can be written as –5y = 25 – 3x and so y = (3/5) x – 5. The slope of the original line is 3/5, therefore the slope of the line perpendicular to this line is m₁ = -1/ m = - 5/3 ; and the time (t) computed in item (4) below is t=5; thus rounded up {[-(m₁)^t] } + where Û U
The , so that Û L
Since g(x) £ 0, for every x, and f(x) ³ 0, if 1 £ x £ 2, it follows that g(x) £ f(x) on the interval [1, 2]. Both functions are continuous and hence integrable, and so . Since f(x) – g(x) = (2x – 1) + (2x -1)² = 4x² – 2x, the answer is area(R) = (partial answer)
The volume of a sphere is given by V = (4/3)pr³, and we are given that . Hence, . Setting t=0, we see that the constant of integration c is the value of the radius at t=0, namely, 10 inches. Thus, r = -2t + 10. And since , we obtain for the answer to the first part of the problem, , where t is measured in minutes and dV/dt in cubic inches per minute. Hence, . The volume of the balloon when t=2 minutes is therefore cubic inches, and the volume will be zero when , i.e., when t=5 minutes.
is the famous math constant, e @ 2.71828, thus = e² @ 7.4 and adding e to this, 7.4 + e @ 10.11, rounded down, is 10 Û J
This is the standard form for the equation of an ellipse, , where a and b are the semi-major and semi-minor axes of the ellipse, respectively. The area of an ellipse is approximately A = pab; thus A = p(3)(6) = 18p square units.