Wedding Gifts and Living in Community

HS #52 2019.12.12

Wedding Gifts and Living in Community

While in graduate school I regularly received wedding invitations from former college friends. Since I was living on a grad student stipend, I typically sent just a card.  However, for one good-humored friend, I included a $1 bill and also taped in a quarter. I explained that he was such a good friend that I wanted to include money in his card - and sending just a dollar seemed rather cheap. 

He has never forgotten. 

Back up five years when I graduated from high school. Being a preacher’s kid, we invited the entire congregation. Most folk put $3-$5 in a card. One elderly widow lady gave me a pair of socks. That is the only gift and giver I remember.

Keep those stories in mind and answer this question: Why do folks give gift cards rather than cash/check? Gift cards restrict the purchase to a certain place and often within a certain time, it takes extra effort to buy them, and sometimes there is an extra fee attached. All negatives. What's the advantage? The advantage is something folk feel in their bones, but likely have not elucidated in their thinking: By giving a gift card, you are demonstrating that you put effort into the gift and are causing the recipient to think of you when they use it. A $50 bill is added to the pile and deposited in the bank. But a Target gift card reminds them that this deck chair is from Aunt Milly and Uncle Joe, and hopefully Milly and Joe will be lovingly remembered when the chair is bought and used. 

And why do we want to be remembered? Biologists tell us that it’s to our benefit because the relationship will be strengthened. Perhaps the recipient will reciprocate. After all, Milly and Joe have a golden retriever who needs care when they go to Chicago for the weekend. 

As a Dutch pragmatist, I want to both optimize value and minimize effort, 

so I put checks into wedding cards for some arbitrary amount, say, $52.38. Then  several weeks later I get a thank you card explaining that the couple spent an evening discussing the significance of the amount. Mission accomplished. They will never forget me and my gift. 

We bestow medals for similar reasons.  It’s to our benefit to have others in our group act valiantly. Their bravery and risk of life and limb serves our purpose – it keeps us safe. A medal is a small price to encourage others to follow their lead. Ironically, we selfishly encourage others to be unselfish.

Let’s call a spade a spade: Whether in the way we give gifts, or the way we honor our heroes, our “unselfish” acts are likely motivated at the core by our own self-interest. But no self-flagellation needed. That’s the way we evolved. We are hard-wired to form group relationships so others will help take care of us.  

Proof? A famous psychology experiment gathered a collection of strangers and arbitrarily put them into two groups.  Then each group was offered a choice: They get $3 and members of the other group get $5, or they get $2 and members of the  other group get $1. Most chose the later. In that short time, a “we-they” competition had developed, and folk’s priority was getting more than the other group.

This clumping together which aids survival helps explain birthday parties, tree houses (password required for entry), sororities and the Masonic Lodge. Significantly, since we have evolved to live in groups, it also explains why taking others into account leads to good living. 

Dale Carnegie’s classic, “How to Win Friends and Influence People” explains how to take full advantage of our social nature. He writes, “There is one all important law of human conduct which will bring us constant happiness: Always make the other person feel important.” 

The most successful contestant in the twenty years of the reality TV show “Survivor” is Boston Rob. He explains his recipe for being chosen by others as the winner: “Others go to bed thinking, ‘What do I need to do to win?’ I go to bed thinking, ‘What does each of them need to do to win.’ – then I help them achieve it.” 

Rob realized that in helping others, he ultimately helped himself. 

Indeed! Five years ago when my retired neighbor moved next door with a broken mower, I mowed his lawn. He hasn’t let me mow my own lawn since. 

The Beauty of Mathematics

HS #51 2019.11.14

The Beauty of Mathematics

This past summer while enjoying Thursday Street Performers on 8^th Street, I stopped into Readers World and found myself captivated by Jim Holt’s, “When Einstein Walked with Godel.” I have seldom read a book that so skillfully interweaves history, biography, and mathematics. 

One theme running through it is the beauty of mathematics. The great mathematician, G.H. Hardy, declared that beauty, not usefulness, is the true justification for mathematics.  Bertrand Russell observed, "Mathematics possesses not only truth but supreme beauty."  

How can mathematics be beautiful? Anyone who asks that question has never seen the Mandelbrot Set – certainly the most intricate and stunning thing in mathematics. Yet even simple things can contain hidden beauty. Case in point: consider the prime numbers, those like 2,3,5,7,11,13,17,19,23 that have no factors. (15, for example, is not prime since 15 can be divided by its factors 3 and 5.) 

These innocuous primes hide deep mysteries. For example, every even number ever checked is the sum of two primes (12=5+7, 20=17+3). Although no exception has ever been found, is this true for all even numbers? No one has been able to prove it. 

But the most elegant result involving the primes dates back to antiquity. Although they thin out as they grow in size, Euclid proved that there is no largest prime – that is, there are an infinite number of primes. His proof is the mathematical equivalent of Hamlet’s Soliloquy  or Pachelbel’s Canon or Michelangelo’s “David.”  And amazingly, it can be understood by anyone willing to put in a bit of effort. Are you game? Let’s start. 

First a bit of motivation. This past summer a tech friend explained to me that the security of email messages, credit cards, and bank statements relies on big prime numbers. Each user (person or computer) has their own personal prime number as part of their security key. That requires a lot of primes! Are there enough to go around? And the prime number needs to be large enough that others can’t easily discover it. So it’s reassuring to know that there is an inexhaustible number of big primes.  

Second, a bit of detail work: Consider (2x3x5)+1=31. Notice that 31 does not have the first three primes 2 or 3 or 5 as factors, because dividing 31 by any of them will result in a remainder of 1. Check it out. Similarly, 2, 3, 5, and 7 are not factors of (2x3x5x7)+1=211;  for example, 211 divided by 7 gives 2x3x5=30 with a remainder of 1. 

Another detail: Notice that if a counting number (1,2,3,4,5, . . ) is not prime, then it is the product of primes. For example, 15=3x5, 84=2x2x3x7. This fact is called the Fundamental Theorem of Arithmetic because it essentially shows that the primes are the building blocks of all the counting numbers. (What are the prime factors of 70?)

OK, let’s get started on the clever proof that Euclid discovered 2300 years ago. We begin by assuming for sake of argument that there are just a finite number of primes. Then there is a last and largest one – we’ll call it N. So let’s form a new number, much bigger than N, by multiplying all the primes together and then adding 1.  We’ll call it P. So P=(2x3x5x7x11x13x17x . . . xN)+1. 

Now we assumed that N was the largest prime number, but look at the fix that P puts us in: Either P is a prime number or P is not a prime number. (That’s from Aristotle’s logic.) If P is a prime number, then since P is larger than N, N is NOT the largest prime number after all. So our initial assumption was wrong. 

If P is not a prime number, then, according to the Fundamental Theorem of Arithmetic, P can be written as the product of prime factors.  But notice, just as 31 divided by 2, 3, or 5 leaves a remainder of 1, so also P divided by ANY of the entire list of primes all the way up to N leaves a remainder of 1.  So if P is not prime, then the prime factors of P must be larger than N. Again, our initial assumption was wrong.  

Since assuming that there is a largest prime number, N, leads inexorably to the contradictory conclusion that N is not the largest prime, that initial assumption must have been wrong. Thus, there is no largest prime – they go on forever. 

How cool is that! Give yourself a pat on the back. 

A Wedding Reflection

HS #50 2019.10.10

A Wedding Reflection  

 Officiating a wedding recently brought some new thoughts: 

As a single man with single siblings, I can think of no one with less experience in weddings than I.  But I’ll take heart from an Old Testament story - the story of Balaam who was confronted – in fact rebuked – by a talking ass. Well, to avoid confusion, let’s call it a talking donkey. The point of the story seems to be that advice and even wisdom can sometimes come from unlikely places - so I’ll play the part of the ass for this occasion. 

What I do know about marriage, I have learned – as with much else - from scientific research. In 1994 there was a cover story of a TIME magazine: “Infidelity: It may be in our Genes.” The researchers looked at the various primates – apes, gorillas, chimps – all those in the same family with Homo sapiens. They noted the phenotypes - the outward physical bodies - of these apes and then also observed their mating behaviors. In particular, some are monogamous and others polygamous. Then they asked: Given the phenotype of humans, what behavior would we expect? The answer: humans appear to be designed NOT to be monogamous. 

That explains much we see in society. But it raises a more compelling question: Given our natural proclivities, why do so many human couples remain faithful?

For many, the reason is their religious beliefs. Dr. Leon Kass, of the University of Chicago and chosen by GWB to steer the study of stem cell research, once remarked that the purpose of the Jewish scripture was to keep humans faithful to their spouses. 

That’s surprising, given the 750 wives of Solomon, but consider the first couple chapters of the Pentateuch.  Good stories and poems are sometimes achieved by setting up a pattern and then breaking it. This is exactly what we see in chapters 1&2 of Genesis. The author repeatedly says, “And God made - and it was good.” Over and over. But these phrases lead to the climax: It is NOT good that man should be alone – so God made Eve. The reason given was not for Eve to be a sexual partner nor even the mother of offspring – although these of course are understood. Instead, Eve was made to be a helper, a life partner – someone with whom to walk through life. 

Is this story literally true?  It doesn’t matter. This story has survived 4000 years. Chaff – lesser stories - have long since blown away. This story – among others from antiquity – remains because it contains deep wisdom about the human condition.  Namely, humans are made to be completed by another. In Greek mythology, the notion of soul mate expresses the same wisdom.  My late father, a minister, used to say, “A man is not complete until he’s married - then he’s finished.” 

However, many of my friends from past and present have little regard for religious beliefs and traditions.  Yet many of them have – from what I see – good marriages and raise wonderful children. One was my thesis advisor.   He once invited me to his home for dinner, and I noticed a plaque on his living room coffee table that I have never forgotten. It said simply:  “Choose your Love. Love your Choice.” 

Powerful!  Why? It is making a claim on human conduct not dependent on the will of God or law of man, but a claim almost mathematical in its logical simplicity and symmetry. 

Each person has total freedom to make their choice of a life mate. The recent Supreme Court ruling allowing same-sex marriage underlines that freedom.  No hindrances, no encumbrances - make your choice. 

But, with that choice comes an awful responsibility. The choosing is over – those days are past. Now Love your Choice. 

And THAT is why we are all gathered here today – to solemnize your choices via your vows to each other in front of all of us. It is not to be made lightly. There should be a little trepidation even now. You are going through a doorway. It is meant to be a semipermeable membrane. You are taking vows freely – you came here as two individuals, you will be leaving as one couple – a man and his partner, a woman and her partner. It is a holy moment. “Holy” means “set apart”  - something special. This is. Even the words used are special.  Again quoting my father, “Marriage is one big “I do” followed by a lifetime of  “uh-huhs.” 

Excelling at Teaching

HS #50 2019.9.12

Excelling at Teaching

Anyone know the name Dan Gable? He was an Iowa State University two-time NCAA Division I national wrestling champion and Olympic gold medalist with a college record of 117-1 (he beat the guy the next year). I remember Gable not so much because of his record or because we share the same alma mater, but for something he once said. After becoming the wrestling coach at rival University of Iowa, he commented that he got more satisfaction from training others to wrestle than wrestling himself. 

Amazing!  A 117-1 Olympic gold medalist gets greater satisfaction from training others.

I can relate - just a bit. My success as a teacher doesn't compare to Gable’s, and being chair of an academic department is not training others as much as facilitating "iron sharpening iron" as we all work to improve. However, I share his pride and sense of accomplishment when department members succeed in their teaching. 

So it was a high point of my academic life recently when I wrote and read a citation about a colleague who won the Teacher of the Year award at Davenport University. The citation contained a student quote: “You are the best math teacher I’ve ever had.  The thing that ignited my passion and curiosity is the realization that everything contains math at its core. Once you dig deep and find the math, it gives the most amazing feeling in the world.”

What causes that sort of thrill from students? Such comments are certainly the best award or reward a teacher can receive. Good teachers are passionate about their discipline and pass that love and excitement on to others. If the goal of higher education is to produce life-long learners, then sharing one’s love of the subject is perhaps the single most important thing a teacher can do. 

Another Davenport colleague recently found and shared this quote from the American writer, Alice Rollins: “The test of a good teacher is not how many questions he can ask his pupils that they will answer readily, but how many questions he inspires them to ask which he finds hard to answer.” Yes. Yes. Yes. 

Ironically, my high school physics teacher passed this test, but unfortunately he viewed it as a sign of weakness. I would ask him questions to which he could have legitimately said, “Good question – I don’t know – let’s explore that together.” But instead he made up answers that were clearly wrong. With a little shame, I admit that I once brought a piece of paper to him on which I had written, “I don’t know” and asked him to read it. Knowing me and wary of some trick, he refused. Then he asked the reason for my request. I explained that I thought he was afraid to say those words and just wanted to check.  Score one for Pennings.

Yes, the best teachers are those who love the subject so much that they themselves are lifelong learners, and they share the experience with their students. Indeed, I challenge my colleagues to be engaged in mathematical research not because they will necessarily find some new theorem, but so that they can identify with their own students in the challenge and frustration of learning. Einstein once received a letter from a young girl complaining about her problems with math. He replied, “Do not worry about your difficulties with mathematics. I can assure you mine are still greater.” That’s good mentoring. 

However, the pinnacle of teaching is the ability to motivate ALL students to excel. That’s a very high standard – one I have not personally attained. 

One teacher who has come close is a recent acquaintance, Luke Wilcox, statistics teacher at East Kentwood High School. Luke was the 2017-18 Michigan Teacher of Year.  EKHS is the most diverse high school in the state, yet Luke’s class scored better on the AP test than the east coast preparatory class of his idol – the author of the textbook he uses. His explanation? He takes personal responsibility to motivate his students. 

 Just some of his ideas: He exchanges student-teacher contracts detailing mutual expectations at the beginning of the year – he can alter theirs, they can adjust his. He greets them all personally when they enter the classroom. On and around his desk he has trophies and ribbons for his various athletic victories – ANYTHING to model to his students what it means to excel. Fascinating. 

The best part of being a teacher: there is always more to learn.

A Parable of Moving Blocks

HS #49 2019.8.8

A Parable of Moving Blocks

 Imagine exploring a basement and finding two identical massive wooden blocks resting on a concrete floor. You try to move them, but neither will budge.  Then, using a hose from a fire hydrant, you begin filling the basement with water. Half submerged, you try again. One block remains stuck in place, but the other seems a bit loosened. More water. No change in the first, but now the second groans as it shifts slightly. More water. The first shows no sign of movement, but the second slides a couple inches. Finally, when the blocks are totally submerged the second can be easily repositioned, while the first, apparently bolted in place, holds fast. 

Those who have ears to hear, let them hear.  Consider two siblings growing up in the same home, being taught the same lessons, accepting the same truths. 

Early on, their life views seem identical and remain steadfast. But then they grow, leave home, meet new people, have new experiences, learn new things. These have no discernable effect on the worldview of the one, while the other sibling’s worldview shifts to a new position. 

Blocks that appeared to be identical turn out to be totally different. The first was fixed in place; the second, seemingly just as immovable, just needed enough buoyancy from new life experiences to change considerably. Why the difference? Personalities? Life experiences? Likely a combination of both.

Is one preferred? Aristotle, true to his golden mean, finds middle ground. He said the mark of an educated mind is the ability to entertain a thought without accepting it.  Perhaps similar to a block that is free to move, but after honest consideration remains in the same position. The key for Aristotle is not the new position, but the true freedom to move.

This analogy came to mind recently while listening to a TED talk about an astronomer who proved that other stars have their own planet systems. Since the planets are too distant to be seen, the scientist inferred their presence by precisely measuring a minute wobble of the star as the alleged planets circled it.  However, after the announcement had gone public and a lecture had been planned, the astronomer realized that he had not taken into account the earth’s varying position around the sun as he took his measurements. When he accounted for the earth’s changing position, he realized that his claim was unjustified. 

So, with regret and embarrassment, the scientist reported his error to the assembly who had come to hear of his discovery. To his surprise, they rose in applause. Truth, the pure, unadulterated search for truth, was so highly valued among his colleagues that they honored his commitment to being led solely by the evidence.  (His technique was later used to successfully show the existence of other stars with planet systems.)

This commitment to honestly seeking the truth by following the evidence is the mark of a good scientist. Commitment to searching for the truth takes courage. It may result in altered beliefs. Nietzsche wrote, “The surest way to corrupt a youth is to instruct him to hold in higher esteem those who think alike than those who think differently.”  

Jesus of Nazareth might agree. He certainly challenged folks by upending the worldview of his time. He brought new wine requiring wineskins that stretched and flexed.

How should we then live? As G.K. Chesterton remarked, the reason to keep an open mind is to close on truth.  Yes, indeed! But how long and to what extent should one search before closing?  When I was in college I was active in evangelism and would often start conversations, “Let’s talk only if our objective is to seek the truth.” Later, in graduate school, I turned that question on myself, “Am I willing to examine my own world view with a willingness to move?”

 I now challenge others with the question:  Are you a Seeker of Truth or a Child of God? Of course these are not mutually exclusive, but that’s not the point. Which is at your core?  Wittgenstein said one’s core belief is the hinge around which others move. How do you self-identify? Is one preferred? 

 A related question:  Why do churches encourage young people to make lifelong pledges of faith and commitment while still in their teens?  Shouldn’t  a religion centered on the Person of Truth encourage adherents to take their time in discerning it?  What other decisions of such magnitude are made so young? Something to ponder. 

Our Evolving Language

HS #48 2019.7.11

Our Evolving Language

I am scarred for life. I’m speaking of the abuse of my father  - a lover of the English language and devotee of its proper use. Even now, I feel him looking over my shoulder as I write this. I am trying not to split any infinitives. 

The words “darn, heck, golly, and gee” did not occur in the Pennings’ household. “Halfway houses to profanity” they were called. I could see the angst in my father’s face when I read a book to my younger brother containing one of those words. Dad’s desire for language purity conflicted with his desire for accurate reading.  

But those were lessons easily learned. More difficult was the distinction between “lie” and “lay”. For those who don’t know, the following – and only the following – are correct: “I am lying on the bed.” “I am laying my body on the bed.” “Yesterday I lay on the bed.”  No wonder folks go crazy. 

Dad drove the lesson deep. When I said, “I am laying on the floor” he would gently – but unfailingly – correct, “I am lying on the floor.” I once put a couple eggs under me so that when he corrected, I could show him that indeed, I WAS laying on the floor.  

But learn I did, and now I can’t hear anyone use “lay” incorrectly without aching to correct them. But I have formed rules. Never correct a boss or subordinate. Friends are OK if the subject being discussed is less important than that I help them become a better person. OK to correct siblings under all circumstances. 

Unfortunately the sins of the father have perpetuated and expanded. I have developed my own peeves. Chief among them is “compose” versus “comprise.” For the record, it is NEVER correct to say, “is comprised of.“ NPR announcers regularly make this mistake. Feels good to inwardly correct those stuck-up prigs. 

“I am doing good” shows the speaker doesn’t know an adjective from an adverb. 

But the worst offense is “Me and John are eating.“ Wrong. Wrong. Wrong. One doesn’t say “”Me is eating,” so why change the form of the subject when adding another?  I have considered jettisoning candidates for professor positions when I heard that mistake. 

The logic is simple: “I” is the subject or predicate nominative. (This is I.)  “Me” is the direct object. (He hit me.) “Myself“ is used only sparingly when self-referencing. (I hit myself.) 

But I am having second thoughts. Way back in the 50’s, Andy Griffith would regularly tell Aunt Bee, “Me and Opie are going fishing.” Why is incorrect grammar so enduring and increasingly common? 

Perhaps language evolves to improve communication. When listening to BBC, I sometimes miss hearing a murder victim’s name because they report the full identity and personal details before saying "was killed," Once I hear "killed" I perk up, but it's too late.

Similarly, to begin a sentence "John and I are going to the gym" gives identity information at the beginning, but no context for it. In contrast, "Me and John are going to the gym" has several advantages. Beginning with "me" communicates instantly that someone else is included. Else one would say, "I am going to the gym." Secondly, it gives the listener opportunity to pay attention by the time the companion’s name is mentioned. 

There is an area of mathematics called constructivism that studies how natural systems evolve towards optimal states. For example, a mass of people exiting a ballpark will organically form flow lines. Is this perhaps what is happening in language?  Are we unconsciously changing our grammar so it becomes more efficient: maximum understanding with minimum number of words?

Case in point: To say “I am lying” could be confused with telling fibs. 

Another: Using the word “comprise” eliminates need for the word “compose” with no loss of understanding.  

No one says, "That is behavior up with which I shall not put." Instead, it’s more efficient to flaunt the formal rules and end sentences with propositions. 

Even the increasing prevalence of profanity may be an evolution towards efficiency. During the intensely frustrating years of my graduate work in mathematics, I had a Mark Twain quote over my desk, “In desperate times, profanity provides a balm denied even by prayer.”

Profanity is also an effective way to bond friendships. Making oneself vulnerable affirms relationships and is more convenient and less fattening than getting a beer together. 

Heck, dear readers, it’s even useful when writing darn newspaper columns. 

Kids Hope USA

HS #47 2019.6.13

Kids Hope USA

A while back I learned how elephants are trained in rural Thailand. Young elephants are chained to a stake pounded deep into the ground. The youngster will pull for several days until finally giving up. With this experience deep in mind, the adult (weighing up to 10,000 pounds) will remain in place when attached to a small stake it could easily pop out with a single tug. 

Parents who recently brought their precocious preteen to me for some mathematical guidance recounted another interesting natural phenomena. When the University of Arizona designed and built the enclosed, self-contained biosphere in 1990, they planted palm trees inside it. Without environmental strains to hamper the growth, these trees quickly grew straight and tall. Then, unexpectedly, they snapped in two. Apparently in the natural environment, stress from wind causes the wood fiber of palm trees to form strong, knurly, interconnected fibers. Without that strain, the fibers grew in isolated parallel strands that were unable to support the tree. 

These two examples from the natural world share a lesson – one that is also contained in the ancient wisdom of Buddhism. This philosophy of life uses the notion of karma to explain that the quality of one’s life depends on one’s choices together with the advantages or disadvantages from birth. True enough. 

 Experiences from early life are crucially important in determining the caliber of the future life of the adult. 

 I learned that lesson yearly teaching senior seminars at Hope College. Towards the end of the course, students shared life-view papers describing their values and beliefs. These were often deeply personal – reaching back into their childhood.  I often left those classes amazed and dismayed that seemingly similar students had such disparate life stories – some filled with trauma, others with kindness, love and opportunity. I was shaken because I realized that no matter how good life might be in the future, no matter how much love, kindness and opportunity, lives malnourished during childhood will forever bear the marks. 

And that is why I am a mentor with Kids Hope USA, an organization conceived by Virgil Gulker of Holland 25 years ago and now spread throughout the nation.  Forming partnerships between churches and schools, Kids Hope provides academic and relational mentoring to young at-risk children. With more than 1400 church-school partnerships reaching over 25,000 children, the leadership remains in West Michigan with the recent appointment of Karen Pearson of Holland as president.

Over the past twenty years I have mentored six children. One memorable moment was in 2014 when I met with a newly assigned first grader.  At our very first meeting he greeted me with two questions: Am I your only child? Will you be with me next year?  The first time we met!  What a testament to his acute need for a relationship. For the next four years, I’d come every Tuesday to find him with one eye watching the door, and leaping out of his seat when he saw me. 

My present child is not so effusive, but I see the fruits of our relationship as well. Recently the fifth grader pouted as he was prone to do when I didn’t give him the answers for his worksheet. Judging that our relationship had adequately deepened, I told him sternly, “Either stop that behavior, or I’m going home and you’re going back to class – it’s up to you.” His attitude changed instantly. I raised the bar for his behavior, and he rose to it.  Our relationship and his life will be the better for it.  

Having taught for almost forty years, I am convinced that the three crucial personal qualities needed for successful living are:  i) grit (perseverance), ii) imagination (creative thinking), and iii) people skills (ability to relate to, empathize with, and understand people).  Significantly, I can work on and see progress in all of these areas with my Kids Hope children.

Today while loading my groceries from the cart into my car at Meijer, it occurred to me that there are three kinds of people:  i) those who don’t return their cart to the cart corral, ii) those who bring back their own cart, and iii) those who bring back another cart as well. The world desperately needs more of this third type of person – those who are not satisfied with doing just what is required of them, but go the extra mile to leave the world a better place. The world needs them, and, more importantly, a child needs them.