Einstein: Foil for Quantum Physics

 HS #119 2025.6.12

 

Einstein: Foil for Quantum Physics

 

 

Do you remember Vivian Vance, Lucy’s friend on “I Love Lucy”? Vivian was crazy and trouble-prone, but not to the extent of Lucy. As such, Vivian served as a literary foil for Lucy. Her presence (Lucy! You can’t do that!) highlighted Lucy’s defining characteristics. A foil highlights (by contrast or comparison) the qualities of another central character. 

 

In the tavern scene of “Raiders of the Lost Ark” the enormous tough man was a foil for the girlfriend of Indiana Jones. She outdrank him. Then she in turn served as a foil for Jones (Harrison Ford). As tough as she was, Jones was tougher. Then in the sequel, “Indiana Jones and the Last Crusade”, in a stroke of cinematic genius, instead of finding another foil for Indiana, they instead used him as a foil for his father (played by Sean Connery). 

 

How about “Frazier”? The two brothers were foils for each other. 

 

Foils highlight. And none other than Albert Einstein served as a foil to highlight the inconceivable mind-boggling strangeness of modern quantum physics.

 

Einstein ushered in the 20^th century with his own mind-boggling discoveries: i) Light is neither just a particle nor just a wave, but both – simultaneously. ii) Nothing can go faster than the speed of light (seven times around the earth in a second). iii) If an eastbound train and a westbound train are approaching the station at 50 miles/hour, how fast are they approaching each other? 100 miles/hour is the obvious answer. It took Einstein to realize the obvious answer is not the correct one. iv) As an object’s speed increases, its length decreases, its mass increases, and its time moves more slowly. v) Gravity bends a light beam passing an object. vi) Gravity, stranger than Newton described, affects time. Essentially, matter tells space how to bend, and space tells matter how to move. (See a graduate physics course for details.) vii) Forget what you learned in junior high, matter and energy are not distinct categories. Instead, take a little matter, stir in the speed of light, stir it in again, and you’ve just made (a lot of) energy. 

 

It took the imagination and open-mindedness of Einstein to conceive these bewildering results. His cognitive nimbleness stood him head and shoulders above other scientists. 

 

But with quantum physics, Einstein met his match. As the saying goes, “Not only is the universe stranger than we imagine; it is stranger than we CAN imagine.” 

 

Einstein, serving as foil, described quantum physics as “spooky.” What was he objecting to? Read on. 

 

One claim of quantum physics is that it is impossible to know both the exact velocity and the exact position of a particle. It’s not just that we don’t have precise enough instruments; it is theoretically impossible to exactly determine both. Why?  To find the position, you have to observe it; to observe it, you have to shine light on it. And photons of light energize the particle, affecting its velocity. Thus, by observing something, we affect it. So all we can know is its probable location (like a weather forecast).

 

That inherent probability-of-nature bothered Einstein, thus claiming that “God doesn’t play dice with the universe.”  He pictured a pool table. If you hit two balls simultaneously with the cue ball, then, using conservation of momentum, knowing the velocity of the cue ball and of one of the struck balls allows you to determine the exact velocity and position of the second ball. 

 

Einstein reasoned the same technique could be done with atomic particles.  Hit a particle so that it breaks into two pieces moving apart. Then by measuring the velocity of one of the moving pieces, even though you altered it, you can use conservation of momentum to exactly determine the velocity of the other piece. 

 

Neils Bohr said, “Nope.” The two pieces are mysteriously connected via “quantum entanglement.” Observing one piece INSTANTLY affects the velocity of the other piece as well. 

However, this “spooky action at a distance” does not let useful information travel faster than the speed of light, so Einstein’s claim that nothing goes faster than the speed of light still holds (sort of).   

 

Though inconceivable to Einstein, this spooky action has now been experimentally verified. In fact, predictions of quantum physics, accurate to one part per trillion, are the most precise in science, and are relied upon for much of modern technology including GPS, MRIs, and the computer on which you are reading this column.

 

Mind-boggling, but true.  

 

 

Tragedy of the Commons

 HS #118 2025.5.8

 

Tragedy of the Commons

 

Imagine a pasture dedicated to the production of wool which optimally feeds 1000 sheep. Less sheep than that, and some grass goes uneaten. More than 1000, and the total wool produced decreases because the underfed sheep are not as robust.

 

Suppose that the pasture is shared by ten shepherds, each with 100 sheep. All goes well until one shepherd realizes that by doubling his herd to 200, although the total wool output decreases, his own wool production will increase. So he acts in his own self-interest. 

 

Soon the other shepherds realize what he has done and so increase their herds to 200 as well. What’s the final result? By each shepherd acting in his own best interest, they all lose. 

This truth is called “Tragedy of the Commons.”

 

A corollary is that to optimize the general welfare, folks need to form agreements, to compromise, to work together. This was a central theme of W. E. Deming (Japan’s Deming Prize) when he visited Hope College in 1993 shortly before his death. His point: Instead of competing for limited resources, work together to “enlarge the pie.” That is, “win-win” situations are possible through innovative thinking and cooperation.  

 

Sadly, in the last few years, we have seen many (local and national) who don’t understand and appreciate this truth.

 

Any politician who claims, “Your money is best kept in your own pocket” doesn’t understand Tragedy of the Commons. Here in Ottawa County our lives are better because we all contribute a little towards our great county parks. If we kept all our money to ourselves, we’d all lose. 

 

Wearing masks during COVID provided a great example. Those who wore masks were protecting the community by i) reducing their own risk of illness, ii) reducing the risk of spreading it, and iii) serving as a role model for others to do the same. However, masks were uncomfortable and bothersome. Thus it would have been in my own selfish best-interest for everyone else to wear a mask, but not me. Those who wore masks, then, showed they understood Tragedy of the Commons – everyone acting unselfishly for the greater good. 

 

Firearms is another example. In nations which outlaw handguns, the number of violent deaths is a fraction of that in the U.S. where we are trained to think selfishly of our own rights.  However, admittedly, it might be optimal for an individual if he were the only one to carry a firearm for protection. Thus, we have seen Tragedy of the Commons play out in tragic fashion in the U.S. as everyone acts in their own self-interest rather than as part of a greater community.

 

Those who don’t understand Tragedy of the Commons, but instead act in their own selfish interest, hurt everyone. It’s no coincidence that those opposed to wearing masks during the COVID pandemic are largely the same as those who promote carrying firearms.  And it’s no coincidence that Ottawa County is now spending a million dollars and counting in lawsuits and litigation because of the decisions of those who didn’t understand the wisdom of compromise and working together. Lose-lose. 

 

Nationally, vaccinations is a prime example. Whether it be measles, COVID, or other communicable diseases, our entire population benefits by everyone having vaccine resistance. Yes, there is a miniscule chance of a slight reaction when inoculated. Thus, it’s best for me if everyone but myself got vaccinated.  Then disease won’t spread, but I incur no personal risk or inconvenience. But if everyone made that choice, we’d all lose. Only by living and acting in community do we win. 

 

Taxes provide yet another case in point. A strong and effective IRS ensures that everyone (especially the rich) pays their share of taxes. Reducing IRS personnel invites Tragedy of the Commons as people may act with impunity by shrinking from their responsibility. 

 

Internationally, free trade and curbing CO2 emissions via renewable energy are ways nations can work together for the world’s betterment. Tariffs and continuing fossil fuel (especially coal) production leads to everyone losing as each nation looks to itself. 

 

This is why after the collapse of the USSR, George H. W. Bush spoke eloquently of the “New World Order.” He realized we could all be winners if we acted cooperatively. 

 

Indeed, we will all live better when we understand the truth of John Donne that no man is an island. Our lives are interwoven. Maybe, just maybe, like the shepherds, we all win or we all lose together. 

 

Memories of Hope College President John Jacobson

 HS #117 2025.4.10

 

Memories of Hope President John Jacobson

 

 

When James Bultman came to Holland in 1999 to assume the office of President of Hope College, I clearly remember a front-page Holland Sentinel picture showing him being greeted by former President Gordon Van Wylen.  But just as with the Sherlock Holmes’ story involving the curious incident of the dog who didn’t bark, I found the picture most significant for what it didn’t show: John Jacobson, who had been Hope’s president for the previous dozen years. 

 

It wasn’t totally surprising since President Jacobson had chosen to officially leave Hope on July 4 – Independence Day. As the son of a minister, I can appreciate that those in positions of leadership with varied constituencies can often leave their posts under a bit of a cloud. 

 

Also, John didn’t live and hadn’t grown up in the Hope/Holland community. Even after being at Hope for a decade, he would greet crowds by saying, “Perhaps you’re a long-term member of the Hope family, or a new member as myself . . . “ 

 

But certainly, another reason for his absence was the person. John Jacobson was understated, and self-effacing. Ironically, his lack of drawing attention to himself caused him to get more attention than he intended when he first came to Hope. Responding to a report of a strange middle-aged man walking around campus, Hope Campus Safety discovered it was the new president.

 

So, in recognition of the man who came to Hope College the same year I did, and who shares my fashion sense (he usually wore a rumpled blue striped suit), and since he hasn’t been recognized via a named building, I’d like to give a man I admired some well-deserved recognition. 

 

Any who drive by the Hope campus on 9^th Street will see one of his accomplishments. Jacobson was responsible for the Haworth Center and adjoining Cook Hall which serves as a “front door” to the campus, both via its location and its function. It helps to house and feed Hope students, and provides hotel space for college guests in a downtown which – at that time – had no alternatives. 

 

But certainly, the largest accomplishment – one which affects many students significantly - that happened during his tenure was the institution of the Dean of the Chapel and the accompanying new chapel program. Formerly, Hope had a program – including organ music and homily – which well served the 30-40 students and faculty who attended. Nothing wrong with it – I rather enjoyed it. But certainly the new program, with several new staff including fulltime musician, transformed not only the chapel program, but also the college. One thousand  students now fill the chapel for M W F Chapel and Sunday evening “Gathering”. In warm weather the sound of instruments and singing floats from the open windows. 

 

But change does not happen without some discomfort – especially to the faculty. So to provide opportunity for Hope faculty to voice concerns, President Jacobson hosted several dinners for groups of 15-20 faculty to meet with him. The dinner I attended had a robust, at times cantankerous, discussion. So to provide a balm for the evening, John asked German professor Sander de Haan if he’d give a closing prayer. Although given no advanced notice, Sander offered a beautiful graceful prayer encapsulating the thoughts expressed and asking for God’s blessing. At the “Amen”, one of the professors gibed, “Sounds like he’s been working on that prayer all day.”  President Jacobson immediately countered, “Sander has been working on that prayer his entire life.”  I still get goosebumps when I think of it. Wisdom. 

 

Drs. John and Jeanne Jacobson also gave dinners at their home on campus. Noticing from their choice of artwork that the Dutch master, Rembrandt, was a favorite, and owning volumes of Old Testament and New Testament paintings of Rembrandt, I delivered them unseen to the Hope mailroom addressed “To the Jacobsons from a faculty friend.” Alas, Jeanne brought my note to the provost asking, “Whose handwriting is this?”  and was promptly given the answer. 

 

Being discovered provided an opportunity for the Jacobsons to be guests at my home – together with several Hope students. In the dinner conversation, I remember being impressed as John pondered why people spend so much time watching television even though they admit it is not especially satisfying. He suggested it was because, compared to other pursuits, there was little risk or investment. 

 

Another insight from Hope’s philosopher president. Long may his memory live. 

 

 

 

 

Mathematics in the Sauna

 HS #116 2025.3.13

 

Mathematics in the Sauna

 

This time of year, I make good use of my Priority Health (Medicare) free admission to 

MVP and the Holland Aquatic Center. The main course for a good workout is some aerobics and weightlifting, and the dessert is the sauna and whirlpool. But, as the saying goes, “Life is short – eat dessert first.” So I sometimes bypass the workout (since my opportunity as a professional athlete is lessening daily), and head straight for the reward. 

 

And there I find not only a great break from Michigan’s cold winter, but also some great conversations. It’s the non-coffee-drinker’s substitute for LemonJellos. Sometimes conversations happen spontaneously. Recently, asking a couple young fellows if they were in college, they responded that they were in a Leadership Bible class. This led to a six-way conversation among all the occupants about all things scriptural (complete with memorized verses and references). I was concerned when new people entered the sauna that they would be overwhelmed by the conversation, but, (much to my surprise – but perhaps it shouldn’t have been) the newcomers jumped right in with their own opinions and scriptural references. Only in West Michigan!

 

However, if no conversation is forthcoming, then, as I did last evening with a Black River sophomore, I ask if they want to play a math game. Haven’t been turned down yet. My favorite is “Don’t say 21”. Here are the rules. Two players take turns counting from 1 to 21. Starting at 1, they alternate, each counting the next one, two or three consecutive numbers. So, for example, if I start by saying “one, two”, then my opponent may say “three” or “three, four” or “three, four, five.” Then, starting where he stopped,  I say the next one, two or three numbers. Whoever is forced to say “21” is the loser. 

 

Try it with a fellow nerd and see who can be the first to discover the strategy to win. Hint: If both players know the strategy, then the second one to play will always win. (Solutions at the end, but don’t spoil the fun – try to figure it out first.) 

 

Here’s another one: Using a belt, strap, or shoelace, or even a towel if necessary, lay it C-shaped in front of you. Then, picking it up, one end firmly in each hand, tie a simple under-over knot in it between your outstretched hands WITHOUT LETTING GO OF EITHER END. 

 

By the way, these challenges work well even outside of a sauna. They are great ways to entertain children or grandchildren around the holiday table. Indeed, I give math talks in which I demonstrate these and others.  All promote creative thought and tenacity – two essential ingredients for success in many careers and life in general. 

 

Here’s another: Using six coins (or other small uniform objects), place them in the form of a cross with four in the vertical row and three in the horizonal row, so that a line passes over four coins in one direction and three coins in the other direction. Challenge them to move one coin so that a line passes over four coins in one direction AND four coins in the other direction as well. 

 

Another:  Position a rubber band (an elastic hair band can almost always be found on the sidewalk entrance to an athletic club), around the base of your index and middle fingers of your clenched hand. Then by quickly opening your hand, the band is instantly transferred to your ring and little fingers. 

 

Solutions: “Don’t Say 21”: Notice that for my opponent to lose, I must say 20. In order to guarantee saying 20, I need to say 16. To guarantee that, I must say 12, then 8, then 4. So 4, 8, 12, 16, 20 are safe lily pads from which to jump. Try it. If you go second, you will always be able to say those numbers. 

 

Knot in Belt: The trick is to transfer a knot in your arms to a knot in the belt. So first cross your arms into an over-under knot, and then, bending over as needed, pick up the ends of the belt. Then merely untie your arms, and the knot will transfer to the belt. 

 

Six Coins: Notice that the coin at the intersection of the rows counts twice. So just place another coin from the vertical row ON TOP OF the coin at the intersection. 

 

Last one:  I’ll show you when I see you in the sauna. Have fun. 

 

 

The Soul

 HS #115 2025.2.13

 

The Soul

 

Last month at the funeral of President Jimmy Carter, several speakers mentioned that Jimmy was now with his dear wife, Rosalynn. Married seventy-seven years on earth, and now together again in heaven. Very comforting and reassuring.  But true? 

 

Everyone agrees that their bodies are buried in caskets in Plains, Georgia. Christians believe also that these bodies will one day be resurrected and their lives will then continue on. But no matter what happens in the future, are they together now? If so, how? In what way? 

 

Some would say, “Perhaps it is their souls which are in heaven – conscious but waiting for reunion with their bodies.” Seems possible.  But if so, it doesn’t conjure up quite as satisfying a picture: The souls of Jimmy and Rosalynn communicating – perhaps telepathically. No vocal cords. Obviously no embracing. No smiling at each other. No looking into each other’s eyes. 

 

But even this raises questions for the Christian. Older Bible translations occasionally refer to the soul (newer use “being”), but give no indication that the soul is something that inhabits the body and then leaves upon death. That notion is gotten from Plato, not Jesus. 

 

So this raises the question: Am I a soul that inhabits my physical body, or am I a physical body from which a soul emerges?

 

What does that even mean?  I vividly remember from whom I first heard the notion of an emergent soul.  It was from Professor Leon Kass, M.D. of the University of Chicago. Kass was the person chosen by George W. Bush to head the discussion of stem-cell research. But long before gaining that prominence, he was invited (in the mid 1990’s) to give a talk to the senior seminar faculty at Hope College. In that presentation, Kass posited that humans are physical beings and that our soul emerges as we (gain ability to) interact with the world – both affecting and being affected by the world. So the soul is not a thing, it is a state of being. As a person develops in the womb and then as an infant and child, one’s soul (i.e., one’s depth and breadth of interaction) grows.  Then the soul diminishes as one ages, having less ability to interact – physically and mentally – with the world. I was fascinated by the simplicity of the idea. It rang true.

 

This conception of the soul was reinforced by Paul Davies, physicist and author who, along with Billy Graham, Mother Teresa, The Dalai Lama, and Professor Alvin Plantinga (philosopher from Calvin University), received the John Templeton Prize in Science and Religion. In his book, God and the New Physics, Davies describes the soul as being like a newspaper picture. Up close (perhaps with a magnifying glass), it’s just an arranged collection of black dots. But as you back away, an image (perhaps a familiar face) emerges. 

 

 

Culture is another example of an emergent thing. What does it mean to experience the culture of Paris? One might describe the food, the wine, the music, the art, the language being spoken, the clothes, the way Parisians walk, the smells, the sound of the traffic. All of these contribute to the culture, but it’s only when all are together in a seamless whole that one experiences Parisian Culture. It’s essentially the idea of Gestalt: The organized whole greater than the sum of the parts. 

 

Similarly, Davies explains that one’s soul (or mind) is the wholistic “YOU” which emerges as your physical body and brain interact with the world. This explains why YOU are affected by too little sleep, or too much sugar or alcohol. It explains why YOU lose awareness when your brain is in sleep mode. This perspective does not say that YOU are MERELY a body, but it DOES say that once your body is dead, your soul no longer exists. Just as the image in the newspaper or the culture of Paris disappears when all the parts are removed. 

 

Notice that this conception of the soul provides that animals have a soul too since they also have ability to interact with the world. 

 

 Moreover, this understanding of the soul solves the conundrum:  If the soul were put within the zygote at conception, then if the zygote divides into identical twins, which twin gets the soul? It also mitigates the humorous-profound charge from Matthew McConaughey’s character in “True Detective” upon hearing of a friend becoming pregnant, “The HUBRIS is must take to YANK a soul out of nonexistence.” Think about that one!

 

 

 

 

The Next Four Years

 HS #114 2025.1.9

 

The Next Four Years

 

 I begin this month’s column by borrowing two paragraphs from what I wrote in February 2018 on the occasion of Presidents Day towards the beginning of President Trump’s first term: 

 

What does it take to lead a country? Is it possible, for example, to have an effective leader who i) is unpolished, with no prior political experience, ii) seems focused on his own needs and situation, iii) gets into fights regularly, hitting back hard - and often unfairly - because it is an effective way to win, iv) can’t control his tongue – gets himself into trouble repeatedly because he can’t just keep quiet, v) has his career threatened momentarily by the way he treats women but still wins in the end, vi) is impulsive and erratic, apparently giving little deep or reflective thought to his actions, vii) is excessively concerned about keeping his hair, viii)  marries a foreign wife, ix)  lives this sort of a life even without drinking alcohol?

 

Unlikely leader to be sure, but Sampson was the leader of Israel for twenty years. And even though an unsavory character personally, he was able to accomplish some things and help Israel in certain ways not only in spite of, but because of his rather unique “skill set.” Indeed, his self-centered, vindictive temperament was crucial to his success. Had he not taken a hard line on his enemies and sought revenge, his extraordinary strength would have been of no use.  Gladly, his type of leadership was not needed for long, so it eventually passed on to those with different temperaments and value systems.  Shows the wisdom and value of limiting the terms of leaders. 

 

Looking back, it would be easy to finish this column by listing actions and behaviors of Trump with which I disagree and/or find abhorrent. I mention only two: Should a president be reelected who i) watched a mob invade and damage the U.S. Capital yelling “Hang Mike Pence” for three hours before taking action, ii) spent the last four years claiming he won the 2020 election in spite of total overwhelming evidence to the contrary? Given my moral/value system, the answer is a clear “no.” 

 

However, like Sampson, that does not mean that he has not and cannot not again be an effective president. So, in the interest of giving every reader something to ponder, I make the following points: 

 

President Trump’s 2017 Inauguration Speech was one of the best I have ever heard. He called Americans to come together – actually using the word “love.” Only one other politician in my lifetime have I heard use that word: Bobby Kennedy – in his great speech in Indianapolis on the occasion of Martin Luther King’s assassination. As are all such speeches, Trump enumerated present faults with America which needed addressing. Yet the press lambasted the speech as dark and violent. 

I wonder how Trump may have responded had the press (and Democratic leadership) reacted instead by saying, “What a pleasant surprise! – we’ll work with you!” The sociologist Charles Horton Cooley explained, “I am not what I think I am, I am not what you think I am, I am what I think you think I am.”  Understand? We become the people we think others see us to be. When chair of Mathematics Departments, I made sure that new professors got positive reinforcement from their students, so that they would “live into” that identity. Same is true of Trump, and, unfortunately, the initial negative feedback he got helped define his first term. 

 

So let’s look ahead. Do you agree that since we are a nation under the rule of law, those who join us should come lawfully? True? 

 

Do you agree that our national debt is spiraling ever greater, and that this can kicked down the road will one day be a great burden affecting the quality of life of future generations? If so, isn’t the answer BOTH tax increases and spending cuts? If Trump successfully works on the second, the Democrats can then do the first. 

 

Isn’t it true that tariffs will bring in income while also protecting American jobs and somewhat curbing American consumption. All sound good to me. 

 

Trump hates killing. He compliments when he can and develops relationships with enemies. Sounds like something I once read in a Gospel (not assuming that Trump has). That’s not a bad place to start in foreign policy. 

 

So, as with the new leadership in Syria, let’s give the guy a chance. 

 

 

 

 

 

 

Christmas Lesson: Ode to the Hydrogen Bond

  

HS #113 2024.12.12

 

Christmas Lesson: Ode to the Hydrogen Bond

 

We in West Michigan are blessed by the presence of two noted institutions of Higher Education: Hope College here in Holland, and Calvin University in Grand Rapids. As iron sharpens iron, these two institutions have brought out the best in each other over the decades. A former Hope president (VanderWerf) said the definition of an atheist is someone who doesn’t care who wins a Hope – Calvin basketball game. 

 

Indeed, the U.S. News & World Report recently recognized again the excellence of these two institutions. Their 2025 College Ranking edition puts Hope College as 31^st in the nation among ALL colleges and universities in Undergraduate Research and the 23^rd most innovative National Liberal Arts College. 

 

Calvin University was ranked among Regional Universities in the Midwest as the very best (Number 1) university for undergraduate teaching and as the second most innovative.  

 

Impressive indeed. 

 

But, as I tell my students, numbers, scores and rankings aren’t as important as qualities that can’t be quantified. 

 

And I discovered a testament to such recently on the Calvin University campus. Outside of the Science Building, stands a pedestal with a plaque on which is inscribed a poem, “Ode to the Hydrogen Bond” by Thomas Dykstra ‘57. The very existence of this plaque makes Calvin stand out. The only other university where I have seen an inspired inscription is in the Rockefeller Chapel at the University of Chicago. (See my July 2024 column.) I tell Calvin students that they can be proud to belong to an institution that not only inspired these words, but also puts them front and center for all to see. Here is the poem, “Ode to the Hydrogen Bond” (read it aloud): 

 

Simple in structure, profound in effect // You order our DNA, cause ice to float, give us jello. //

Weak alone, strong in crystalline array // You rend mountains, sink ships, split oak. // 

Echo of your Maker made flesh // Simple in the manger, profound in purpose // 

Weak on the cross, strong to save. 

 

The author who died in 2022 was an organic chemist (Ph.D., U of Illinois), and served for years as his church choir director. An avid woodworker, he described his life and death as having been hewn and molded by the Master Carpenter, “But, now, finally, I am to be conformed to my Maker. And in such congruence, there is pure, everlasting Joy."

 

Dykstra’s poem certainly reveals the heart of Calvin University more than any numbers or stats. Enfolded in these simple words are humor, thrill of discovery, mystery, awe, gratefulness, and reverence.

 

First, note that the poem carries the spirit of John Calvin himself. Calvin wrote in his Institutes, “If we regard the Spirit of God as the sole fountain of truth, we shall neither reject the truth itself, nor despise it wherever it shall appear, unless we wish to dishonor the Spirit of God.” 

 

This quote, and the poem, captures John Calvin’s conviction of the integrity of truth. Truth cannot be separated into distinct domains. The same God who made the hydrogen bond also came to earth and lay in a manger. No reason to separate the study of truth artificially into spiritual and secular. This, of course, is the reason for educational institutions – both K-12 and higher ed – which tie all truth together into one cohesive and coherent world view. 

 

A corollary of this realization is that careers, whether studying chemical bonds or felling trees or even making jello, have dignity.  When John Calvin’s contemporary, Martin Luther, was asked by a spiritually-converted cobbler how he could serve God, Luther replied, “Make better shoes.” 

 

But the main point of the poem is captured by the surprising turn it takes midway. Plato is famous for his illustration of shadows on the cave wall. As shadows are not the real thing, so also, according to Plato, all we see around us are mere shadows of the true things that exist beyond this life. 

 

However, Dykstra goes a step further. All we see around us is (not a shadow but) an echo of its creator – a creator who Himself came to live among us in the flesh, profound in purpose. A Creator weak on the cross, so as to be strong to save. As such, the awe-inspiring echoes – the mysteries of our natural world – deserve zealous study, even as these mysteries point to their Source. And the Source, giver and redeemer of life, is worthy of reverence and gratitude.