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.  

Number Sense: Insights from Ratios

HS #46 2019.5.9

Number Sense: Insights from Ratios

A few years ago while singing with the College Chorus at a Hope College Vespers, I got wondering how many Dimnent Chapel’s filled with sand are needed to fill St. Peters Basilica. So I counted the blocks to the ceiling, paced off the length and width, and returning home looked up the volume of St. Peters. You might be surprised - the answer is 147.

And sitting in the Hope Church choir loft during a children’s sermon, I wondered how I might illustrate to children the 250 million year age of my colorful petrified rock (which I call “God’s artwork”).  It turns out that’s how long it would take to fill the sanctuary if a person brought a quarter teaspoon of sand with them each Sunday. 

Number sense, in particular understanding the relative ratios of things, helps give an appreciation for the world around us. For example, Lake Michigan would fill the Grand Canyon with a little left over. And bottled water costs about 2000 times as much as tap water – without the prophylactic benefits of fluoride. 

Relative rates are interesting: How long does it take a top athlete to go a mile? Swimming: 10 minutes. Walking and kayaking: 6 minutes. Running, cross-country skiing, and roller blading: 4 minutes. Bicycling and ice-skating: 2 minutes. A bit slower, the rate the continents are drifting apart is about the same rate your fingernails grow. They take about 40,000 years to go a mile. 

Relative distances are also interesting: One late night walking home from the office I noticed the blinking lights of a jetliner, the moon, a comet by the sun, and some stars. Extending my arm, I estimated the jet is 25,000 times farther from my eye than my hand, and the moon is also 25,000 times farther than the plane. In contrast, the sun is only 400 times farther than the moon. But then the next nearest star, Alpha Centari, is 15 million times farther away than the sun, and the farthest thing we can see in the night sky, the Andromeda Galaxy, is almost a million times farther than that. 

Owen Gingerich, Harvard University and Smithsonian astronomer, once told me that if your hand were a star, the next nearest star would be in Washington, DC. But if your hand were a galaxy, the next nearest galaxy would be the distance of your other outstretched hand. 

Music is all about ratios. From one C to the next (an octave) the higher note vibrates exactly twice as fast as the lower: a 2:1 ratio. Since there are twelve notes between them, each of those notes is the same ratio higher than its neighbor.  

So that ratio must be the number that when multiplied by itself 12 times gives 2. That number is about 1.06. Multiplying this number by itself, you can see that the frequency of G (fifth of the chord) is almost exactly in a 3:2 ratio with the root (C). The F (the fourth) is almost exactly in a 4:3 ratio with the root, and E (third of the chord) is almost exactly in a 5:4 ratio with the root. These nice ratios mean that the wave vibrations match up often. (If one visitor comes every 4 days and another comes every 3 days, they will meet every 12 days.) That is why C-E, C-F, and C-E-G sound so nice together. It is entirely serendipitous that twelve steps from C to C give such nice results, and is undoubtedly why we use the twelve-tone system. How cool is that. 

But most enlightening is what ratios reveal about the place of humans in the universe.  Imagine a number line with equally spaced tics. The leftmost tic is the smallest possible (quantum) distance and each subsequent tic represents the number 10 times larger than the previous until the rightmost tic is the distance across the universe. It turns out the size of the human body falls exactly halfway along the line. That is, by ratios, our body size is halfway between the smallest thing and the largest.  

However when the same is done with the shortest (quantum) time and the longest time (the age of the universe), the human lifespan is a full three-quarters of the way towards the longest. That is, in terms of ratios, each person reading this has lived or can expect to live three quarters of the age of the universe.  That’s enough time to make a difference in the world. 

Two Visonaries: The Mission of Higher Education

HS #45 2019.4.11

Two visionaries: The Mission of Higher Education 

 I first arrived in Holland Michigan in April 1987.  I was a fresh Ph.D. recipient in mathematics and Hope College had a position open. It was late in the hiring season, so I was likely the final candidate interviewed by the president that spring – and thus likely the last person Gordon Van Wylen interviewed during his presidency. 

I remember the discussion well.  President Van Wylen didn’t tell me he had put a troubled institution on solid footing. He didn’t mention the campus expansion under his leadership, or his previous illustrious careers in the Navy and at the U of M. 

Instead, he proudly showed me a brochure with a statement he had written and honed during the final year of his presidency: The mission of Hope College is to offer, with recognized excellence, academic programs in liberal arts, in the setting of a residential, undergraduate, coeducational college, and in the context of the historic Christian faith. 

Hope College’s mission statement has been modified somewhat since then, but – in my opinion – not improved. A mission statement should be short enough to be easily memorized. It should hang together with an integrity that differentiates from others, while providing a clear path forward. The wisdom that led to that statement was the fruit of a lifetime of thoughtful experience in higher education. Gladly, it wasn’t the end of Gordon’s contribution to the community. Who knew that he’d have yet another successful  “career” developing downtown Holland. 

Although I didn’t know the namesake of Davenport University (which was founded the same year as Hope College), I am just as impressed with him upon seeing the mission statement he provided. It is succinct and powerful, and unique because it is a mission for the students rather than for the institution: “Make a Living. Make a Life. Make a Contribution.” M.E. Davenport didn’t realize it, but he was well ahead of his time – a real visionary. 

Make a Living: Gone are the days (if they ever existed) when an eighteen year old matriculates to a college, majors in an area of interest, and then is all-but-assured of a career with an income that sustains an individual or family.  Prospective students – and their parents – are now intentional about choosing a major and career which makes good on their educational investment. This is good; it’s perhaps too easy for comfortably tenured professors to challenge students to follow their dreams, trusting that a career will follow. Like most else in life, balance is needed. Dreams shouldn’t be ignored, but thoughtful planning is prudent – especially if graduating with a large debt. 

Make a Life: This is the other side of the balance. A college education should provide more than training for a career. President John Adams wrote to Abigail,  “I must study politics and war that my sons may study mathematics and philosophy. My sons ought to study mathematics and philosophy, geography, natural history, navigation, commerce, and agriculture, in order that their children might study painting, poetry, music, architecture, statuary, tapestry, and porcelain.” Yes, if education does not lead to a richer, more thoughtful, insightful, reflective, more pleasurable life, it has failed. 

Even more important, education should make the student hungry for more. Ideally, students should leave college self-engaged in music, reading novels, poetry, history – and yes, even playing thought-provoking, artistically-engaging video games. I am presently in a reading group with former Hope College students and present DU students. That’s good living. 

Make a Contribution: Are you familiar with Maslow’s hierarchy of needs? From bottom up: physiological (food and shelter), safety, love, esteem, and finally self-actualization. This loftiest need involves fulfilling one’s potential in the arts and other creative activities – essentially Davenport’s “Make a Life.”  However, later in life Maslow realized that there was yet a higher intrinsic need, “The self only finds its full actualization in giving itself to some goal outside oneself, in altruism and spirituality.” Davenport realized this all along. 

Indeed, M.E. Davenport and Gordon Van Wylen both felt this truth deep in their bones and their respective institutions reflect their values.  Hope College students and faculty contribute by bringing the performance arts to the Holland community. Davenport students and faculty provide free tax help for 6500 families in need, and STEM Days and free summer math and science camps for junior high students. Making these contributions is good for society, but moreover, it leads to healthy, full individuals.  Van Wylen and Davenport knew it, lived it and passed it on – and we are in their debt. 

Turning Dreams into Reality

HS #44 2019.3.14

Turning Dreams into Reality

“Who do men say that I am?” That’s a question asked by even the best among us. We all want to know how are we viewed by others.  As the saying goes,  “The 20 year old is concerned with what others think, at 40 no longer cares, and by 60 realizes that no one has been thinking about them in the first place.” 

Yes, a teaspoon of recognition is all most of us need. As a college professor, I am never too alarmed when students complain about an instructor who riles them, but  am concerned if they don’t know their professor’s name. 

But an exceptional few notables generate widespread attention and percolate controversy. The poser of the question above has divided people for two thousand years. Some called him the Prince of Peace, but look at his record – he didn’t bring peace, but a sword. 

Others come to mind. Remember Howard Cosell – provocative sports commentator, civil rights opiner, and close friend of Mohammed Ali? When a poll was taken asking people to rank sport announcers, he got both the most first place and the most last place votes. 

Spend a couple hours at the innovative state-of-the-art Lincoln Museum in Springfield Illinois (easily the best historical museum I have ever visited), and you come away knowing that Honest Abe was a polarizer. Nineteenth century Americans loved him or hated him. 

I recently finished Walter Isaacson’s biography of Albert Einstein. In 1938 Einstein won second place in a Princeton University poll asking freshmen to name the greatest living person. Who got the most votes?  You won’t believe it. Yes, he’s the one. You’re still doubting yourself, but you’re right. Let that thought settle for a bit. 

Jesus, Cosell, Lincoln, and Hitler. What do these folk have in common that divides people? At least one thing: They were visionaries. Either you buy into their vision or you don’t. Moreover, their vision preceded and helped create the reality. 

What did Bobby Kennedy say? “Some men see things as they are and ask why.  I dream of things that never were and ask why not.” The author of Proverbs agrees, “Where there is no vision, the people perish.” 

This came to mind recently while listening to an interview with Secretary of State Mike Pompeo. “Do you believe that North Korea is still a nuclear threat?” “Yes, of course.” “But Trump doesn’t – he said they no longer are.” “That’s not what he said – well, yes, he said it, but . . . “

Love him or hate him, Trump viscerally comprehends that vision drives and determines reality. His worldview was forged in economics and the market place. Why does the stock market rise and fall daily? Expectation. What drives the economy? Perception.  How did Trump become a billionaire other than by selling his name? Modern physics concurs that in some mysterious way perception can create reality. 

If Trump deals in “alternative facts” so does every good coach and general. Military commanders and coaches create a vision for victory in order to achieve the victory.  It’s the job of others to report the outcome. 

So when Trump describes that the threat of nuclear war with North Korea is over, that we are no longer in conflict, that there is no need for a military presence in South Korea, that North Korea’s future can and will be like that of (former) North Vietnam which, posing no threat to its neighbors, is now thriving, his words are intended to bring about that reality.

There are limits, of course. If Puerto Ricans are suffering and dying from the after-effects of a hurricane, a rosy report is of little consequence. 

If Mexico realizes it’s not in their interest to foot the bill for a wall on their northern border, promises to the contrary make no difference. 

If the aggregate temperature of the earth is rising even faster than scientific models have predicted – the fastest since human civilization has existed – with the same effects as when the human body rises several degrees, then the visionary is setting himself up for derision and condemnation by future generations. 

What determines then whether visionaries eventually turn their dreams into reality? We honor folk like Jefferson, Lincoln and King and many others who helped make America great. Their visions were not crushed in the crucible of reality, but created a new and better reality. The dreams of other dreamers, unworthy and vacuous, are carried away as dust in the wind. The crucible is heating.

Wind Chill

 HS #43 2019.2.14

Wind Chill

Whether bragging or complaining, wind chill adds sensationalism to the forecast, just as does its summer equivalent – the dreaded heat index. As a youngster, the Twin Cities weather forecaster simply said, “Tomorrow the high temperature will be 0 degrees with a 20 mile/hour northwest wind.  That’s all we needed. We could take it from there. Didn’t need a meteorologist instructing us how to dress, when to stock up on groceries, or whether to venture out. We embraced Emerson’s “Self-Reliance” essay without having read it. Heck, Minnesotans don’t need a New Englander telling them how to live. 

Now with melodramatic air, forecasters provide ostensibly crucial new information:  the wind chill will be . What good is that?   Who in Michigan has felt , so what value is the comparison?  

I, on the other hand, as a proud ex-Minnesotan, DO know what feels like.  As a teenager, I occasionally stood out on the front sidewalk in my shirtsleeves just to experience it. Not even a hint of breeze when it’s that cold – the very wind is frozen.  The sky is deep deep blue – bluer than ever a summer sky can be.  The sun pierces through the blue and you can feel it in your eyes in its futile attempt to warm you.  Low in the sky, on each side of the sun, there are two bright spots – sundogs, they are called – the winter equivalent of rainbows, as sunlight reflects off the ice crystals in the air.  

Each inhaled breath – and you breath very slowly – tingles the nostrils. You blink often to keep your eyeballs from freezing. Each step sounds like you are walking on broken glass as you crunch the brittle snow.  Several blocks away two men are talking, and (due to downward-bending of sound waves by the warmer air above) you can hear them as if they are standing beside you.  Another quick glance at the sundogs and then back inside, being careful not to touch the metal doorknob with your bare hands. 

Why the rich experience of cold? After all, the cold we acutely feel is just the absence of heat energy - our ears don’t acutely hear the absence of sound energy.  What we actually feel is the rate at which the body loses (or gains) heat energy. That is why you can safely touch a wooden object in a hot oven, but not a metal one. They are both the same temperature, but metal transfers thermal energy more readily so it feels hotter. 

Isaac Newton was the first to explain how thermal energy moves.   “Newton’s Law of Cooling” states that the rate an object loses heat is proportional to thedifferencein temperature between the object and the surrounding medium. That’s why a pan hot from the oven will quickly cool to warm, but takes a while cooling all the way to room temperature. 

When expressed succinctly and precisely in mathematical symbols, Newton’s discovery is called a differential equation. These describe how something changes with time. My former Hope College colleague, John Van Iwaarden, wrote a textbook explaining them. It’s no stretch to say that differential equations are the single most important way that mathematics is used to describe and predict natural phenomena. Meteorologists give us advanced warning of weather because of differential equations. 

So, now we can better understand wind chill.   Consider standing outside in still air at . Because of the larger difference in temperature between your body and the  air, heat will leave your body faster than in the air, so it feels colder. However, if there is no wind, then that lost body heat warms the air surrounding your body. Since the difference in temperature between your body and the surrounding air is now not quite so extreme, the rate of cooling decreases.  But wind removes that warm blanket of air, so the full difference in temperature is back in effect, and hence the body cools faster. 

So, if the air temperature is  and the wind chill is , then, like your body, a hot car engine will cool faster because of the wind, but it still will never go below the actual air temperature.  Also, wind chill is more pronounced for someone in shirtsleeves or with bare skin than bundled up. (So there are multiple formulas for calculating wind chill.)

Everything make sense? Good. Then on a cold day why will a bowl of boiling water freeze faster than a bowl of lukewarm water?   Try it – it does. 

Life is a Joke

HS #42  2019.1.10

Life is a Joke

Watching GHW Bush’s funeral last month reminded me of a story he told at the funeral of Ronald Reagan. After Reagan met with Bishop Desmond Tutu of South Africa, Bush asked Reagan, “How was the meeting with Tutu?” Reagan, “So so.”

How funny.  In fact, all the U.S. presidents I have known except the present one have shown a sense of humor. They were able to see humor in situations and – more importantly – in themselves. Lyndon Johnson, satirized often by the Smothers Brothers, wrote them a letter they read on their final show: "It is part of the price of leadership of this great and free nation to be the target of clever satirists. You have given the gift of laughter to our people. May we never grow so somber or self-important that we fail to appreciate the humor in our lives.”

Of course none had the self-deprecating humor of Lincoln who when accused of being two-faced replied, “Sir, if I had another face, do you think I’d wear this one?” When Taft, over 300 pounds, took a recreational vacation in the Philippines, he cabled the Secretary of State that he had just finished a three hour horse ride and was feeling great. Return cable, “How is the horse?”  

No one matched Churchill. Once a young MP came to his estate to apologize for having insulted him that morning in Parliament. Churchill’s servant took the message, and returned a minute later with the reply, “Mr. Churchill says that he is sitting on the john, and he can only take one shit at a time.” 

When I left for college, my father advised no kidding around with college professors.  

I tried, but walked into an argument between my physics professor and a (know-it-all) student as to how thick of a lead wall was needed to stop a high-energy gamma ray. The student was claiming that a million miles of lead would do, but the professor was disagreeing - it would require 4 million miles.

I chimed in, “I agree with the prof - it’s obvious that 4 million miles will stop it, but clearly one million miles would be insufficient.”  The professor, realizing I was poking fun at the absurdity of the disagreement, prophesied, “Pennings, your sense of humor will get you through life.”

As a teacher I get my share of opportunities to have a bit of fun with students.  Sometimes when one is tardy, I’ll instruct the others that after the student arrives, I will ask the class the area of a 2 by 3 rectangle. They are to unanimously respond, “17.”  Then we all watch the reaction.  

Some of the best humor is unintentional. While in graduate school, I dutifully took a break from my studies each day to lift weights at the gym. Although not a body builder, I took it rather seriously. One day when returning from the gym, I met a new friend, a sincere and kind-hearted leader in the Campus Church.  “Hi – where are you coming from?” “The gym.” “Oh, what were you doing there?” “I was lifting weights.” Quickly glancing at my body, “You just start?” 

And I still laugh remembering how my parents, devotees of 8^thStreet Russ’ Restaurant, once told me enthusiastically that they had recently found a restaurant they liked much better. Curious, I asked the name of their newly discovered favorite.  “South Side Russ’.” 

But for finding humor in everything, no one matched my Grandma Pennings. When visiting our home and sewing in the easy chair, she would occasionally call out, "Has anyone seen my needle?" No one ever paid attention. Twenty minutes later, she'd call out again, "I found it - you can all stop looking now." 

Even from her wheel chair, grandma delivered.  Once on a family outing through the great forests of northern Minnesota, we stopped at a trail to a fire lookout station. My younger brother, Daniel, ran ahead as we pushed grandma along the asphalt path. By the time we arrived at the 200-foot-high structure, Daniel had climbed the winding stairs to the top observation deck. Noticing a sign by the entrance, dad hollered, “Dan! Did you see this sign?”  “No.”  “It says, “Dangerous – not permitted on the tower!”  Recognizing the scolding voice, my brother was at a loss for words.” It was grandma who saved the moment.   She cupped her hands, filled her lungs, and called out the logical solution, “You jump down from there right now!”