A Model of the Trinity

A true cornerstone

Introduction

Is it possible to have three distinct persons in one nature? If your response is affirmative, I ask the following? “Is it possible for the three persons to be co-equal?” Recall Robert Louis Stevenson’s Dr. Jekyll and Mr. Hyde, your answer is likely “NO!” But wait, an informed Christian’s answers is, “Absolutely, yes!”

This post supports the answer of the informed Christian? The path-to-clarity is a non-threatening model in mathematics that exhibits three distinct co-equal sets.

What will co-equal mean? When I think of co-equal individuals, I think of individuals with the same moral capacity who can accomplish the tasks. Their skillset/attributes need not be exactly the same, but they operate under the same rules and they can accomplish the same goals.

Our Takeaway: Co-equal individuals have the same moral capacity and they can accomplish the tasks.

What is a model?

A model is a story that attempts to explain how a part of God’s world operates by using symbolic assignments.

As an example, consider the famous story that Jesus told about seeds sown in a field. Seeds, their function, as well as how to activate them were known and understood by Jesus’ audience. Jesus likened Sewing(casting) seeds into different soils in a field, to the Word of God being preached to the different peoples(the different soils). Jesus’ symbolic assignments are the sown seeds, the different soils, and the casting of the seeds.

Our Takeaway: Symbolic assignments bridge the gap between the known and unknown or between what is concrete and what is abstract.

In Jesus’ story, the symbolic assignments are realities found in the world but He corresponds them to objects in God’s world ( the story).

Jesus’ model of the seeds is a useful story because it reveals patterns of behavior. Some seeds will germinate and produce like-kind while other seeds will not produce.

Our Takeaway: Useful models reveal patterns.

Patterns are important because they are signs of “order”. Scriptures assets that order replaces chaos when God intervenes. Hence observed patterns are flashings of God’s intervention.

Childhood counting story

The core of my family unit consisted of my mother, my father, my sister, and me. Occasionally on his way home, my father stopped at the neighborhood store to purchase a treat for my sister and me. Usually, it was a hand full of hard rock candy. I suspect he grabbed a hand full of candy from the candy barrel because the counts were often random – or he ate some of the pieces on the way home.

As the older, my sister appointed herself to divide the treat. Having been bitten by “her counting” I imposed the requirement that two separate piles be formed saying out loud, “one for you, one for me as a piece is placed in each pile. Even counts presented no problems. They yielded the same number of pieces in each pile. However odd counts designated the last recipient to have more. In mathematical terms, if the contents in each pile can be evenly paired, the piles have the same number of pieces. However, if this pairing cannot be evenly established, one pile contains more pieces than the other.

The Takeaway: Two collections have the same number of elements when each element in the first collection can be paired with only one element in the second collection without having any unpaired elements in the second collection. This will be our meaning of co-equal piles.

Christians believe God is three distinct persons( the Father, the Son, Holy Spirit) in one nature, love. This unit is called the Trinity.

A Model of the Trinity

Designate the person of the Father by the infinite collection: {0,3,6,9,12,15,18, …}

Designate the person of the Son by the infinite collection: {1,4,7,10,13,16,19 …}

Finally, designate the person of the Holy Spirit by the infinite collection: {2,5,8,11,14,17,20 … }

Using the “one for you and one for me” – counting method, the Son and the Holy Spirit have the same number of elements.

Pairing “1” in the Son is with “2” in the Holy Spirit then;

Pairing “4” in the Son is paired with “5” in the Holy Spirit then; etc. continued indefinitely.

Each element in the Son has the form by $latex (3p+1)$ for $latex p=0,1,2,….$

And each element in the Holy Spirit has the form $latex (3p+2)$ for $p=0,1,2,....$ .

The pairing rule between the Son and the Holy Spirit is pair:

(3p+1) in the Son with (3p+2) in the Holy Spirit, for p=0,1,2 …

This rule pairs each element of the Son to only one element of the Holy Spirit and it leaves no element of the Holy Spirit unpaired. Therefore the Son and the Holy Spirit have the same number of elements.

What do the elements in these collections (the Son, the Father, and the Holy Spirit) represent? They represent the divine attributes of the Son, the Father and the Holy Spirit possess.

Remember how Jesus used “seed” to represent the Word of God and its power. The one-to-one pairing between the Son and the Holy Spirit asserts these two persons have “comparable” attributes in the divine world.

The collections representing the Father and the Son also have the same number of elements, thereby reminding us of Jesus’ statement, “I and the Father are one”. One can see the pairing as follows:

“0” in the Father is paired with “1” in the Son,

“3” in the Father is paired with “4” in the Son, etc. continued indefinitely.

The pairing rule between the Father and the Son is:

Pair (3p) in the Father is paired with (3p+1) in the Son, for p=0,1,2, …

The Trinity is the unit: the Father, the Son, and the Holy Spirit. Hence represent the Trinity by the collection: {0,1,2,3,4,5,6,7,8,9,… }.

Although not obvious, the Trinity has the same number of elements as the Son. This is not evident because the Trinity contains all the elements found in the Son, the Holy Spirit, and the Father. Let’s demonstrate that Trinity does have the same number of elements as the Son.

Pair each (p) in the Trinity with (3p+1) in the Son, for p=0,1,2,…

For example, the fourth element in the Trinity is represented by “3”. So pair it with (33+1=10), the fourth element in the Son.

In this manner, every element in the Trinity is paired with exactly one element in the Son having no elements of the Son left unpaired.

Thus the Trinity has the same number of elements as the Son.

A similar argument demonstrates the Trinity and the Father have the same number of elements by the pairing:

(p) of the Trinity to (3p) of the Father, for p=0,1,2,…

How are these numbers, symbolic representations to be interpreted?

The nature of God is LOVE. If the elements in each person represent a love attribute of that person. The elements in the Trinity might be interpreted as the illimited indescribable love of God.

The interpretations, therefore depend on the assignments given to the elements in the (persons) and the meaning given to the word “pair”.

For example, Jesus tells the story of a man who builds his house on a deep rock foundation. Then He concludes the man’s house does not fall during a flood because the house was built on a firm foundation(rock). The story symbolic assignments are the man’s wise decision and follow-through to build his house on a solid foundation, thereby protecting it from destructive worldly phenomena. Jesus used the rock foundation, an unyielding stratum, to represent the Word of God as the man’s daily directive(choice) to follow, making him impervious to worldly calamities. So it is in our case. The elements in a model and their function determines the pattern’s interpretations.

Consider this interpretation. Each element in the person of the Trinity represents one of his special powers. The operation “pairing” identifies comparable power in another person of the Trinity. The interpretation will be the two persons have comparable powers to accomplish a given task. The comparable powers need not be the “same” powers.

Also, pairing can mean identical powers.

A DNA Model of the Trinity

Interpret the elements of the Father to be a molecule of the Father’s Divine DNA. Then each molecule of the Father’s DNA is (3p) for p=1,2,3,… The Son chose complete obedience to the Father. To show the complete obedience gene, assign one gene of obedience to each of the Father’s molecule, thus (3p+1).

The Holy Spirit flows from the mutual love between the Father and the Son. Hence set Holy Spirit’s DNA to contain the tissue from the Father and the Son. The Spirit is given power to teach and guide all within creation. Show this special love for the creation augmenting one gene to the DNA of the Father and Son. Thus each molecule of the Holy Spirit’s DNA is 3p+2=(3p+1)+1.

quartic

Solving quartic equations

Solving the quartic (by radicals) isn’t taught in high school because it requires solving a cubic called the resolvent cubic. Solving by radicals means finding the solution using standard operations of arithmetic and taking roots. Though not taught in high school, solving the quartic is within the skill set of a second year high school algebra student, when the resolvent cubic is easily factored. This post illustrated the method to solve the quartic. The resolvent cubic easily factors, thereby opening the student to the deeper problem solving techniques of this solution. Consider

$x^4+4x^3-7x^2-22x+24=0.$

Make the left side of the equal sign a square by putting all terms on the right side of the equal sign except the third and fourth degree terms, then complete the square on the left side.

$x^4+4x^3=7x^2+22x-24.$

Since

$x^4+4x^3= x^2(x^2+4x) .$

Complete the square of the factored expression, adjust the right side to the equation appropriately and get

$x^2(x^2+4x+4) = 11x^2+22x-24 .$

The left side of the equal sign is a square. Thus the right side is a square, but it is not easily identified as a square. So we make the left side a larger square that reveals the right side as a square.

Do this by expanding the left side to a trinomial that is also a square with the help of a number “y”, yet to be determined.

$((x^2+2x)^2 +y(x^2+2x)+frac{y^2}{4})^2 = (11+y)x^2 +(22+2y)x+(frac{y^2}{4} -24).$

The right hand member is a square. Hence its discriminate is zero. Thus,

$(22+2y)^2 - 4(11+y)(frac{y^2}{4} -24)=0.$

$4(11+y)^2 - 4(11+y)(frac{y^2}{4} -24)=0.$

Simplifying and get

$(11+y)(y^2-4y-140)=0.$

Solutions:

$y_1 = 14,$

$y_2 = -10,$

$y_3= -11.$

When

$y_1=14$

get

$(x^2+2x +frac{14}{2})^2= 25x^2+50x+25,$

This means solving

$(x^2+2x +7)= 5(x+1).$

and

$(x^2+2x +7)= -5(x+1).$

Solutions to the quartic are:

$1,2 , -3, -4.$

NOT FINISHED!

REVELATIONS: Visions, Prophecy, & Politics in the Book of Revelation

Elaine Pagels is a gifted expositor. What is often boring to me, she expresses an interesting narrative. Since my last post, I have been following paths that she has laid over the past 15 years.

Ms. Pagels is the Harrington Pierce Professor at Princeton University. Her interest is early Christianity history. The Gnostic Gospels, one of her bestsellers, is presently joined by another that is the focus of his post: Revelations: Visions, Prophecy, & Politics in the Book of Revelations.

If you’ve ever said to yourself that you will read the Bible or the book of Revelations, after having second thoughts, felt the task too boring or overwhelming for lack of a scholarly background in spiritual readings. I invite you to read Elaine Pagels’ latest volume, Revelations. It’s an assessable read filled with drama, intrigue and it contains an excellent history of early Christianity.

A great storyteller and scholar

Before I begin, I declare that I am not an agent for Professor Pagels. My motivations for the post are twofold. My first motivation: I admire how the professor presents her research interest to the non-scholar. She has more than forty years of research experience, yet she communicates like a great storyteller. My second motivation: Having been one of the first scholars to help deliver a complete English translation of the Hag Hammadi in the United States – the 1945 discovery of secret gnostic writings that electrified the world, Professor Pagels is among those who help to unlock the history of how Christianity spread, why it was successful, and why Christians believe what they believe.

John the Apostle, writer of Revelation?

Early in her book, Professor Pagels resurrects a still debated mystery. Is the author of the book of Revelations, John the Apostle? She recalls three undisputed observations.

The Gospel of John is a treatise that declares Jesus is God.
The book of Revelations deals with cosmic war, dragons, beasts, a whore, a mother, plagues, earthquakes, cosmic disintegrations and the salvation of Jesus’ followers has a drastically different style than the Gospel of John.
Further, the writer of Revelations fails to declare himself an apostle, which was the practice of an apostle.

Dr. Pagels makes no attempt to resolve this mystery.

Many revelations

John’s Revelations was written during a time when many were writing a book of revelations. Peter, Mary Magdalene, Paul, Phillip, and James wrote their own revelations. A Revelations of Ezra had been written, although the author was not the prophet Ezra. Even non-Christians were writing their own revelations.

Writers of a revelation tended to write two: a secret revelation and a public revelation. Apostle Paul is an example. In Paul’s public revelations, he declares that Jesus called him to minister to the Gentiles. Then Jesus revealed those things that he wished Paul to tell the Gentiles. Paul’s zealous pursuit of his public revelation kindled a wide spreading of the new religion. But, it was the Revelations of John, that was highlighted in the Christian canon.

My takeaways from this read

A plausible explanation of why John’s revelation entering the Christian Canon over the other revelations,
A long but interesting chapter on church history,
Professor Pagels’ details of an intense rivalry between Apostle Paul and John, the writer of Revelations,
A short introduction to Gnostic history and the Gnostic gospels,
The existence of other revelations, and finally
Encouraging an initiate to question was the major focus of secret revelations writers

Conclusion

Today we are bombarded with messages through multiple channels. Those who seldom question are prey to messages that are harmful to our society. In Revelations Pagels alerts us to the importance gnostic writers placed on questioning in their secret revelations. My hope is that this observation ignites readers to forsake blind followings and adopt questioning the “politics, beliefs and wisdom ” of all with the power to spread their views.

Big Willie street racer

Remembering Big Willie: Peacemaker/American Hero

On May 19, 2012, Willie Andrew Robinson III, departed this life.

Family and friends gathered on June 2, 2012, at Faithful Central Bible Church, Inglewood, CA to celebrate his life. Many thanks and acclaims were offered for his guidance to advance personal, local, state and national interests. More importantly, the family to which he was the patron proudly attested his impact on their lives.

At death, Big Willie’s life spoke loudest of two devotions. Devotion to his wife, Tomika, and to the organization he founded: the National and International Brotherhood of Street Racers (INBSR). Through this organization, Big Willie attained fame as a visionary and a peacemaker. At death, he was its patron of INBSR and its only president.

Prologue

in 1960 Willie Andrew Robinson and I graduated from Walter Louis Cohen High School in New Orleans, Louisiana.

In high school, he had two obvious passions: devotion to a long-time girlfriend, whom he often claimed that he would marry, and street racing a fully primed but never painted 1957 Olds. Which had the strong pull on him I could not determine.

After graduation, I did not see Willie again until we attended our 50th high school class reunion in 2010.

In 2004 through a chance encounter, I got the opportunity to have a phone conversation, Willie. With much enthusiasm, he talked about his street racing organization.

In 2006 Willie surprised me with a phone call a surprising call to wish me a speedy recovery from a tumor extraction. Then he mused about the possibility of bringing racing to Sacramento.

The next time I had contact with him was at the closing program of our 50th class reunion. Sharing an eight-person round we exchanged greetings. To me, he looked frail and appeared to be spiritually depleted – unlike the Willie of high school and the telephone chats I had had. Our exchange was minimum.

I was scheduled to deliver some thoughts to the class. My practice before speaking is never to go into myself and orchestrate how I will deliver my presentation to this audience. After the program, He told me about his breakdown in route to the reunion.

May 19, 2012

I arrived at the church two hours before the celebration began. Peoples of all races, genders, and ages began to arrive at the church as early as 11:00 am. The ages spanned from twenty years to sixty-plus years. Many were clad in a colorful black leather vest or a well-worn jacket. The rear of the vests showed a large picture of a car frantically trying to outrun a pursuing a police cruiser. The phrase, STREET RACERS INTERNATIONAL, encircled the picture.

On the rear of the jackets, the picture showed a police cruiser chasing a car modified for racing. STREET RACERS INTERNATIONAL encircled this chase. The picture on the jackets back distinguished members inducted into the membership called the old breed while those wearing the vests were the new breed.

Church Preparations

The right side of the church’s dais stood a wreath bearing the message:

Rest Big Willie

You are with

Tomika

To the right of the wreath was a collection of awards, memorabilia, and event photos documenting some highlights of the life and work of Willie Andrew Robinson. Below is a small sample of the many awards:

Outstanding Citizen of the Year
American Body Building Coordination Committee
Awarded
to
Willie Robinson
for
leadership and service to the community.

Willie had taken 6th place in the American Body Building contest. He proclaimed himself the strongest street racer in the world.

Certificate of Special Congressional Recognition
Big Willie Andrew III
Outstanding and Invaluable Service to the Community
August 19,1955
Signed Steve Horn
Member of Congress
38th District of California

Tomika also received the same proclamation.

City of Los Angeles
Los Angeles Human Relation Commission
Certificate of Appreciation for Special Services
Bill and Tomika Robinson
04/07/1994
Signed Ivan Houston

Los Angeles Police Department
Southeast Community Police District
Certificate of Appreciation
To
Willie Robinson
Support “We Do Care Picnic”
September 9, 1995
At
Imperial House
Signed Kenneth Small, Captain

City of Los Angeles
Certificate of Appreciation
Mr. and Mrs. Big Willie Robinson
The National and International Brotherhood of Street Racers
September 8,1995
Signed Rudy Svorinic
Council Member 15th District

I interviewed many and I asked each the following questions.

• What was your life situation when you met Big Willie?
• What is your present life situation?
• Why was Willie important to you?
• What are you doing now to carry on his ideals?

All respondents spoke of the positive effect Willie had on their lives.

Interviews

Donald Galaz

Donald Galaz was the first person I interviewed. He bore the title of Lieutenant in International and National Brotherhood of Street Racers.
I asked him to explain the functions of the Lieutenant. He gave me the Senior Hierarchy: President, Executive Vice President, Captain, Lieutenant, Sergeant-At-Arms, Public Relations Officer, Racing Control. Then he explained the organization functioned in paramilitary-style and that non-senior positions exist.

Galaz: Life before meeting Big Willie:

I had an alcohol problem. In 1993 I learned about the racing on Terminal Island. I went to observe. I listen to Big Willie speaking to the racers. He had a positive outlook. One, (an outlook) other than gangs and drugs. He spoke about reaching your full potential.

I interjected, “How was this message different from the message your parents told you?” He said,” I never listened to my parents. Big Willie spoke my language. He spoke with heart, earnest … his words pierced my heart. ”

To my question, “How have you used what Willie has given to you?” He said,” I fell back into alcohol. I sort Big Willie again. He advised me to man up. Now I’m active in the organization. I am all right now. I know where I am going. I make a living restoring classic cars of the ’30s to ’60s. I have a garage. I park some of my restored cars outside. The young guys come in and ask what going on. I talk to them like Big Willie talked to me.”

At this point, Galaz insisted that I meet Angel. He said that Angel as one of the first member of the organization.

Angel Nieves
Angel identified himself as a member since 1968 when the organization was organized. “When I joined I was in high school and I had a passion for racing. The message Big Willie delivered attracted me. He preached elimination of race and that racers are a brotherhood.”
Angel interjected:

In those days, Big Willie wore a derby. The derby and his positive messages attracted me. He became my father figure.

“What now?” I asked.

With confidence and certainty, Angel responded without hesitation, ” We continue the fight for legal street racing in a supervised environment. The formula is not changed.”

John Nardella
John is a 12-year member. He is one who Angel calls the new breed. John summarized my questions with the phrases: I love racing, Big Willie had heart and that captured me. Big Willie thought it important to bring all people together. His messages stressed peace and happiness. Willie’s goals were my goals also.

‘Final Call Tyrone’ was standing alone. He is one of those whom Angle calls the new breed. The designation on his vest is Vice President.

Tyrone eulogized:

Big Willie was a good happy soul, a happy heart always had open arms, willing to lend a hand to solve a problem.

The phrase ‘Safe Racing Control’ on the vest of a young racer attracted my attention. I asked him to explain the phrase. He said:

I inform the neighborhood that a race was about to begin. Do not back out of your driveway. I watch for stray youth and I promote a safe racing environment.

Suddenly the church sound system blasted:

Fe-Fe-Fi-Fi-Fo-Fo-Fum.

I smell smoke in the auditorium.

Charlie Brown, Charlie Brown.

The Prelude
Charlie Brown signaled the beginning of the celebration program. It was the first song of a medley of old tunes. The medley enlivened the church. People began to circulate and the chatter became louder. The second song was, Why do fools fall in love? …. Most of the tunes were popular during our high school days.

The Celebration Service
During a repeat of Why Do Fools Fall In Love, the sound system went silent and the procession entered the church.

Rev. Jordan Allen, the minister-charge, followed by the body, the family and selected officials of the Brotherhood.

Dr. Jean Davis

Big Willie’s youngest sibling, welcomed everyone to the family’s celebration of Big Willie’s life.

After an emotional moment, she began to share her oldest brother value to her life, his spirit, and his life’s mission.

The value to her life: She described a caring, protective and ever-encouraging brother. Always proud of her accomplishments as a physician and he was a good person.” He lifted me up in all my endeavors.”

Describing his spirit, she told of his gentleness, his large arm of protection around his extended family members, and his desire for peace and reduction in crime.

Of his love for his wife: She spoke of his loyalty and love for her as unquestionable. As if to offer proof she said, Willie changed his birthday to Tomika’s to celebrate their marriage was the beginning of “the two becoming one.”

Of Willie’s altruistic spirit, she gave his short-term goal to eliminate race in the racing environment and of his long-term goal he long to bring all peoples together in Los Angeles.

Of Tomika’s value to him, she said in health, they were always together. He directs all references of his success to her, the source of his strength. The young physician described her brother as a giant who draws strength from his wife.

When Tomika suffered the stroke, Davis described how Willie meticulously cared for her and struggled to give his strength for recovery. Successful in many things, he was unsuccessful in this attempt.

Dr. Dee

The multi-ranged lyrical voice of Diane White-Clayton (Dr. Dee) followed a reading of John 14:1 – 6. Her selection, “You raised me up to be more that I can be…” explains the source Willie Robinson’s earthly success. His obedience to his spirit quieted him so he was able to do the work of the master – preach brotherhood and to teach peace. Now he can claim the promised room John 14:2 scripture.

James T. Butts

Mayor of Inglewood, CA: Said of Willie Robinson, “Very few will be fortunate enough to do something that changes the life of someone. You are one.”

Other family member spoke about things Willie told only to them. All emphasized the effect he had on their lives.

A Congressional Delegation from the Office of Janice Hahn, U.S. House of Representatives, California 36th District read the Congressional Recognition and Service to the Community honoring Willie Andrew Robinson III as a Peace Keeper.

Representative Hahn ‘s speech on the House floor labeled Willie Andrew Robinson III as an American Hero. On the day of her speech, the flag that had flown over the U.S. House of Representatives and the Congressional Recognition was presented to the family.

Fabian Arroyo, a Sergeant of Sheriff Patrol overcome by resurging emotion from the death of his friend and father figure, told of Willie’s guidance during the early days of the Brotherhood. He detailed how their relationship developed into more than friendship.

Steve Sokoloff, the newly appointed Harbor Commissioner told that he was warned to expect Big Willie at his meetings. Willie and supporters attended Sokoroff’s first Harbor Commission meeting.

Sokoloff described this meeting:

Big Willie told us his vision to allow street racers to use Terminal Island for racing. He touted themes of public safety and the need to provide a place for this marginalized group to meet and to pursue their passion. He asserted that permitting street racers to use Terminal Island would be a means through which brotherhood would be developed. I(the commissioner) left the meeting completely in support of his vision for Terminal Island.

Politics delayed the vision for two years. But it came.

During the racing days on Terminal Island, no property was destroyed or damaged. None of the predicted riots materialized. And racers of every ethnic background treated each other as brothers.

The commissioner held up his gold shield and said,” Willie, you were the commissioner. ” then he presented his shield to the family.

Dr. Dee closed the speaking segment with an emotional Amazing Grace. The color of her voice was sweet, my spirit bathed in it, and it enlivened me. When she ended, I could hear other spirits responding, “Yes Lord and “Amen.”

Rev. Allen eulogized Big Willie was the person who Los Angeles needed at that time. His efforts help to dismantle the racial and physical barriers between Los Angeles’ peoples. Inglewood began to accept blacks. East Los Angeles was no longer the only haven for people of Mexican descent and the city prospered.

The U.S. Army Honor Guard led by Lt. O. Estrada, ceremonially played taps. The guard folded the American flag that draped the coffin and respectfully presented it to the family. They saluted the deceased for the service he gave for his country.

Click picture for taps.

Epilogue

When I read the email announcing Willie’s death, an unexplainable need to attend his dismissal services grew within me. Except for the two chance phone calls and the short visit at the reunion, our lives barely intersected. So I could not account the need I attempted to satisfy driving 380 plus mile to attend Big Willie’s dismissal service.

Making the trip was a good decision. First, attending it reminded me of an important life principle. Second I learned the answer to a question I asked myself in high school.

The testimonies of the people who Big Willie helped, reminded me that a good life is one devoted to helping others overcome barriers that deny their full potential.

Having seen Big Willie’s accomplishments and his response to Tomika’s, I feel the most important element in his life was his life partner. Losing her was the beginning of his downward spiral into frail health and a depleted spirit – that not even the brotherhood could arrest.

Now,

Rest in Peace

Willie Andrew Robinson, III

Peacemaker and American Hero

Big Willie at the reunion.

A video detailing the growth of street racing can be found at this site

In the vestibule of the church

Leaving the celebration

Preparing the Next Leaders

The flyer, Summer, announces a collaboration between Christopher Givens and me. There is no mention in the flyer of the python coding component that he will direct. This is our first collaboration to give back to the young in our community, Enrollment is brisk and we are excited and prayful.

A Love Affair

Against the wishes of her sister, I was to see her again.

It had been twenty years since our last meeting.

She was always logical and cogent, now,

– in a cryptic letter, she reveals she’s going to the motherhouse.

Having never questioned her about personal matters,

I responded with this simple sentence,“Are you in pain?”

Days later, I got a letter from one of her sisters,

reporting her condition and St. Elizabeth hospital’s phone number.

I called the hospital about her condition three times.

Always, the response was, “she’s resting.”

About a week later, her sister called to say,

“She has been a coma for a week.”

Without thought, I immediately said, “I am coming.”

The voice at the other end of the line said,

“Don’t, you can’t do anything.”

But responding to an internal juggernaut,

I found myself on a United flight from Sacramento to Philadelphia.

Upon arrival, I called her sister for directions.

She said, “Wait I will come and get you.”

She arrived about forty minutes later.

We drove.

Then she reiterated the folly of my trip.

I didn’t respond to her argument.

We arrived at the hospital and began the walk down

a long dimly lit gray corridor.

Halfway into the corridor,

we turned into a shorter hall leading to her room.

A nurse entering the wing’s nursing station spotted us and summoned the other nurses at the station.

They entered the hall and observed our approach.

As we advanced, I felt their positive feelings towards us.

It warmed me.

Apparently they surmised I was the consistent caller from California.

I sensed that they wanted to reach out and touch me.

I felt like a conquering hero.

We passed the station;

my guide entered her room.

I followed her, but stopped in the doorway – frozen with anxiety.

An inner voice shouted: “Why are you here?”

Her sister approached her bedside and looked at her.

The room was barely lit.

The window coverings admitted no outside light.

The only sources of light in her room were

a small night light in a distant corner and

a ray of hall lighting slicing through the darkness of her room and

dimly illuminated her uncovered head.

A small audio recorder poured a soft spiritual rendition of my university’s alma mater into her room.

In the Mississippi valley, in the crescent bend …

Her sister turned to me,

frozen in the doorway and in a gentle tone said,

“Come in.” To me, her demeanor of my presence seemed to have changed.

I enter the room and she said, ”talk to her”

The sounds of her microchipped I-Vee and

her respirator seemed suddenly to boldly voice their function – forestall the inevitable.

My inner voice greatly demand of me,

“What do you say to a comatose person?”

With a quick breathe behind me

I began to tell her our news,

I told her that David was lecturing in the Soviet Union, then

I began to tell her about students she had taught:

I said, “Chuck is lecturing in Oslo”,

“Ella is completing her Master degree at LSU,

Shellie is lecturing at the University of Kentucky,

Ronald is completing his PhD at the University of Miami.”

Now less anxious, and donning 210 pounds I said, “I now weight 210 pounds.”

Her left eye opened!

The last time she was me, I weighted about 165 pounds.

My weight had always been a source for her jabbing.

A nurse had entered the room, to check on the patient and her machines noticed the opened eye.

She asked,” What is your relationship to her?”

I said, “She is the mother of my academic life.”

Apparently, the response pleased her,

because an ear-to-ear smile inched onto her face.

But racked with the pain of bone cancer,

she slowly closed her eye, and the smile melted from her face.

I told her I would return to see her.

The next morning her sister told me she died about 3:00 AM.

Lying before me, was Sister Miriam Friancis Quinn.

She was a nun, an Irish American, a mathematician, and my college mentor,

She was concluding the final hours of her life.

The last 40 years of her life having taught young black men and women at the Xavier University of Louisiana.

Observing her I learned:

How to be a teacher;

How to be patient with struggling students;

How to wait and for a gifted student to discover his/her core to success.

Most importantly, I learned the importance of “knowing why one exists”.

She believed her Creator pleasured to bring her into existence.

So moved by that action,

she devoted her life to praising Him by teaching downtrodden youth in Louisiana.

She died in pain but in peace.

Rest in Peace, good and faithful servant of the Most High God.

Do you know “Why do you exist?”

Universities don’t teach the reason for your existence.

Universities teach how science and logic can make life comfortable.

I encourage you to master the lessons of science and logic.

BUT Seek!

Seek the reason for your existence.

Then you also, will inherit a peace beyond understanding.

The invaluable gift, I got from my university.

Convergence in a Topological Space

$\textbf{7.1 }$

$\mathfrak{M}$ is a maximal filterbase on $Y$ , $A,B \subset Y$ disjoint subsets, and $A \cup B \in \mathfrak{M}$ . Then either $A \in \mathfrak{M}$ or $B \in \mathfrak{M}$ .

$\textbf{Proof: }$ Let $A, B \subset Y$ such that $A \cap B =\phi, \; A \cup B = M_{\gamma} \in \mathfrak{M}$ . As $A \cup B \subset Y$ , there exists $M_{\alpha} \in \mathfrak{M}$ such that $M_{\alpha} \subset A \cup B$ . Or $M_{\alpha} \subset \complement (A \cup B)$ . The latter condition implies $M_{\gamma} \cap M_{\alpha} \subset (A \cup B) \cap \complement (A \cup B)= \phi$ .This is a contradiction.

So assume for all $M_{t} \in \mathfrak{M}, M_{t} \nsubseteq A$ . Then $M_{t} \cap \complement A \ne \phi$ for all $t$ and $\mathfrak{B} = \mathfrak{M} \cap \complement A$ is a filterbase.

For any $t,\; M_{t} \cap \complement A \subset M_{t}$ . Thus $\mathfrak{B} \vdash \mathfrak{M}$ which implies $\mathfrak{M} \vdash \mathfrak{B}$ .

Hence for $M_{\alpha} \cap \complement A \in \mathfrak{B}$ there exists $M_{\delta} \in \mathfrak{M}$ , such that $M_{\delta} \subset M_{\alpha} \cap \complement A \subset (A \cup B) \cap \complement A =B \subset M_{\gamma}$ .

Thus $\mathfrak{M*}=\mathfrak{M} \cup \{B\}$ is a filterbase that contains $\mathfrak{M}$ .

By the maximality of $\mathfrak{M}, \; \mathfrak{M*}=\mathfrak{M}$ . Hence $B \in \mathfrak{M}$ .

A Canadian’s View On Our Disrespect Of President Obama’s Presidency

The Fifth Column

EgbertoWillies.com

America – He’s Your President for Goodness Sake!

By William Thomas

There was a time not so long ago when Americans, regardless of their political stripes, rallied round their president. Once elected, the man who won the White House was no longer viewed as a republican or democrat, but the President of the United States. The oath of office was taken, the wagons were circled around the country’s borders and it was America versus the rest of the world with the president of all the people at the helm.
Suddenly President Barack Obama, with the potential to become an exceptional president has become the glaring exception to that unwritten, patriotic rule.
Four days before President Obama’s inauguration, before he officially took charge of the American government, Rush Limbaugh boasted publicly that he hoped the president would fail. Of course, when the president fails the country flounders. Wishing harm upon…

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algebra appreciating mathematics content attainment education lesson plan prealgebra preparation primary grades mathematics proportion ratios

A Content Attainment Lesson Plan for Ratios Part 3

This is third post in the series A Content Attainment Lesson Plan for Ratios. It gives suggestions to an alternative approach to teach proportions.

I give two guided presentations (situations). Each has everything students need to attain (discovery) the definition of a proportion. Encourage students to study both situations before attempting to give a final definition of proportion.

For this study adopt, the definition: A proportion is a statement that says two ratios are equal.

Situation 1

We wish to make predictions. Good predictions require knowledge of the world where the predictions apply. Our first task is to seek condition(s) that ensures good predictions.

Let’s begin.

Assume a world in which only two conditions affect events. Call the conditions, controlling conditions. If the behavior of these conditions are completely understood, good predictions are possible.

Below choose responses to the numbered statements that makes a “good” prediction possible?

1. The controlling conditions do not change. ][ The controlling conditions change.

2. Controlling conditions that are not changing can indicate world events are not changing. ][

Changing controlling conditions indicate world events are not changing.

Assume a number on a common scale summarizes each controlling conditions. Ratios are ideal measure to compare two things of the same type.

So choose a ratio of the controlling conditions numerical summaries. Call the ratio, the controlling ratio, since it is a numerical measure of the controlling conditions at a particular time. The only restriction place on the ratio is that its denominator cannot be zero.

If world conditions are not changing, which choice in the following do you expect to be true.

3. The controlling ratio is probably not changing. ][

The controlling ratio is changing.

Have students to discuss of this statement and then write a summary of the discussion.

Exercise.

ABC Manufacturing Company reported the following information:

On June 30, 2013, free cash flow was $284,867 and dividends paid were $99,851.

On March 31, 2013, free cash flow was $206,207 and dividends paid were $99,812.

On June 30, 2012, free cash flow were $175,837 and dividends paid were $100,054.

Your task is to predict whether this company can pay a good dividend. Free cash flow and dividends paid are the only information available.

Take the ratio of dividends paid to free cash flow to be your controlling ratio. Is it a good predictor? If so why, and give a prediction. If not, why not.

Teachers: With this exercise experience, have students rewrite their summary statements to mention the controlling ratio and to say whether it can or can not give reasonable predictions.

Some students may need a hint.

Hint : If the controlling ratios are not changing over time, good predictions are likely.

Situation 2:

A red dot is 1/4 of the distance from the center of a DVD disk. On the outer edge of the same radius is a green dot. The disk spins about its center.

Ask students to compute:

Compute the distance the red dot travels in one revolution. (A)__________________

Hint: C = 2 π r, where r is the radius of the circle the point describes.

Compute the distance the green dots travels in one revolution. (B)_______________

Give the ratio of the distance that the red dot travels to the distance that the green dot travels in one revolution. (C)_____________________________

What is the ratio when the disc rotates half of a revolution? a quarter of a revolution?

What do you think is the ratio for a partial revolution?

Can you compute the ratio for any partial travel about the center? ___________________

Are the disk sizes relevant to the ratio? _________________

Is the speed of the disk relevant to the ratio? __________

In the final analyses what was(were) the important factor(s) needed to compute the ratio?_____________

How do these answers make you feel about ratio?

Give your definition of proportion.__________________

A Problem

A disk of radius of 5 feet has a red dot 5 inches from its center. On the outer edge of a second disk of diameter 4 yards is a green dot. Where on the second disk should the red dot be placed to have a proportion between these two disks?

Writing proportions

Symbolically a : b represents the ratio of a to b.

a : b : : c : d is the symbolic representation of a proportion. The symbol “: : “ is read “as”. a : b : : c : d reads , a is to b as c is to d.

If the terms of the ratios are numbers, write a / b = c / d.

Exercises

1. Over a three months period, the insider of a company bought about 120,000 shares of stock, compared with insider sales of 96,495 shares. Last year, insider purchases had been two million shares of stock, compared with insider sales of around 800,000.

Using these numbers to form two ratios. Do they form a proportion?

2. In 2010 The United States boasted one of the best health care systems in the world. It had an estimated 246 000 primary care physicians [1] and 256,000,000 citizens with health care coverage [2]. The Affordable Health Care Act will add 30,000,000 who are not able to afford the cost of coverage. If the ratio of physicians to those covered must be maintained to have the system’s quality, How many new doctors must the system have to cover the 30,000,000 increase?

3. Jackie bakes cupcakes for her church’s bake sales. For Sunday’s bake sale, Jackie will bake 45 cupcakes. After checking her available ingredients, she has only 3 tablespoons of the sugar. The recipe requires 23 tablespoons of sugar for 45 cupcakes. In her cupboard, Jackie has a 40-ounce bottle of agave, a sweetener. The agave manufacturer claims 4 tablespoons of agave has the same sweetening power as 5 tablespoons of sugar. How much agave must Jackie add to her sugar in order to bake 45 cupcakes?

4. The City of Sacramento CA has a sales tax. Assume all purchase items have the same tax rate – not true. Is the following true? Total price of any purchase in the City of Sacramento : the sum of the prices of the purchased : : the total purchase price of a nine-volt battery : the price of two nine-volt batteries. [5]

Describing concepts with proportions

The ancient Greeks believed numbers could describe natural concepts. To visualize a number they used line segments. This enabling them to visualize concepts with line segments.

To represent a given concept that is not as extreme as either of two given concepts, a number between the assigned numbers of the extreme concepts is chosen.

A favored choice between two numbers is the midpoint of a line segment is the Arithmetic Mean of the two numbers.

A concept associated with the arithmetic mean has the balanced blend of the extreme concepts.

The Greeks used the proportion (a-m) : (m-b) :: a : a to describe the arithmetic mean, m, of a and b where a > b.

Another favored choice is the Geometric Mean, m, satisfying the proportion: (a-m) : (m-b) :: (m-b) : b where a > b.

A third choice to represent betweenness is the Harmonic Mean, m, it satisfies (a – m) : (m – b) :: a : b for a > b.

Problems. (Requires elementary algebra)

1. Express m, the means in the three proportions, in terms of a and b.

2. Given x, y > 0. What is x : y, if x² – 6 y² = xy ?

3. For what value(s) of x is the proportion (x+3) : (x +4) : : 5 : 6 true?

4. For a > x > 0, show that a² – x² : a² + x² > a-x : a+x.

5. If a : b = c : d prove a³/b + b³/a : c³/d + d³/c = ab : cd.

Hint: Let x = a : b = c : d .

6. If a : b = b : c , solve for b in terms of a and c.

7. Give numbers a, b, c such that b is the geometric mean of a and b.

Plato used the proportion in problem 6 to explain his divided line theory [3].

References:

[1] http://www.cnn.com/2012/06/27/politics/btn-health-care

[2] http://www.kevinmd.com/blog/2012/03/onethird-hospitals-close-2020.htm

[3] Plato Republic, Translated by Benjamin Jowett, Barnes and Noble Classic, 2004.

[4] Edward Maziarz and Thomas Greenwood, Greek Mathematical Philosophy, Mathematics People, Problem, Results Volume I, p 22-23.

[5] Dick Stanley, Proportionality, SUMMAC FORUM , September 1993, pages 5,6.

Published by Lloyd Gavin

Laughter Was God’s Idea: Stories About Healing Humor by Chaplain Jack Hinson

Today I visited my new hospice patient. He’s 94 years old. His frame tells of a once fit physique. Aging has robbed him of strength, but his spirit testifies age has no power over spirit.

During our time together, he kept things light. Never did he emitted a whimper of despair nor take anything about himself seriously. He is the model person described in Laughter Was God’s Idea: Stories About Healing Humor by Chaplain Jack Hinson.

The objectives of the book are:

Humor is a good medicine.

Humor is God’s gift to us to navigate life with joy.

We must be taken with the word “joy”. For joy according to Hinson grants us peace, openness to others, and it allows us to bond with others. It does not have the usual meaning of ‘

“a state of laughter and fun”.

In one of the early chapters, Hinson writes, “Taking oneself seriously leads us to believe that we are responsibility for our personal well-being and our future.” He continues,”Only when we accept of our human frailty, can we naturally accept God’s grace.”

His obvious corollary is, “Don’t take yourself seriously. For it builds a wall around you that keeps you from the joy that awaits you.”

Hinson writes that these views were his takeaways from four Conrad Hyers lectures. They changed my perception on the healing power of humor, joy and laugher.

Having embraced at these beliefs, Hinson realized that a hospital deserves a joyful chaplain. His daily prayer became, “God, if you will furnish the joy, I will spread it all over the hospital …”

My new hospice client is another example of a person who believes and adopted this “joy” to navigate life.

Hinson’s book contains many experiences and profession wisdom gained from his life as a chaplain. These two arrested me:

Go, eat your food with gladness, and drink your wine with a joyful heart, for God has already approved what you do. Always be clothed in white, and always anoint your head with oil. Enjoy life with your wife, whom you love, all the days of this meaningless life that God has given you under the sun—all your meaningless days. For this is your lot in life and in your toilsome labor under the sun. Whatever your hand finds to do, do it with all your might, for in the realm of the dead, where you are going, there is neither working nor planning nor knowledge nor wisdom. Ecclesiastics 9:7-10.

Thus is another way to say life is a one-time gift, let nothing (particularly seriousness) keep you from the joy God has already approved for you.

Love thy neighbor as thyself. Phil 1:3-4.

Chaplain Jack interprets this to mean: Do something for your neighbor that you would do for yourself, for your neighbor is just like you.

To support his joy/humor in healing theory, Hinson laces his book with scientific studies from the halls of research, from sayings by famous historical figures and from recognized medical stalwarts. They make interesting readings. For me, the tone of his stories convinced me. For conviction is hard to sell when there is no belief.

Jack Hinson is a husband, father, pastor, writer and chaplain of various hospital chaplaincy committee. Further, he served as interim pastor in a number of international locations and delivered numerous addresses on Humor in Healing.

My thoughts at the time . . .

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