Changing Colors

 HS #81 2022.4.14

 

Changing Colors

 

I heard recently that a common mistake middle aged folk make in planning for the future is assuming their interests won’t change. For the young, it’s expected that changes occur. One of the richest verses from scripture is Luke 2:52: “Jesus grew in wisdom and stature and in favor with God and man.” Getting annual Christmas cards each year, it’s clear (especially from the pictures) that attention and pride resides with the growth and development of children and grandchildren. 

 

But once we become adults and pass into and through middle age, it’s easy to suppose that our interests and passions will remain constant, even if our bodies give out a bit. Indeed, as adults our desire is to remain the same. Middle age and beyond might be defined as that period of life where we are jealous of our former selves. 

 

Poets certainly have expressed this thought. I’ve had this poem by Yeats on my refrigerator for years: “I thought no more was needed // Youth to prolong // Than dumbbell and foil // To keep the body young. // Oh, who could have foretold // That the heart grows old?” Yeats realized that our noble ambitions wane as we age. 

 

Counterexamples exist. The great Hungarian mathematician Paul Erdos, the most prolific of the 20^th century with 1500 articles, continued publishing until his death at age 83.  Similar to the Kevin Bacon Number among actors, mathematicians have an Erdos Number depending on whether they coauthored an article with Erdos (#1), coauthored with someone who coauthored with Erdos (#2) and so on. Driven by his love of mathematics, Erdos described fellow mathematicians who stopped researching as “they died.” When someone truly died, he said simply, “They left.” 

 

My 93-year-old aunt (Wanda Hendrickson) who learned how to roller blade at 75 and still takes classes at Calvin University is a personal counterexample and inspiration. Our regular visits provide an intellectual challenge. 

 

Robert Frost also contrasted between the glory of youth versus the sameness of middle age in his poem, “Nature’s first green is gold. Her hardest hue to hold. Her early leaf’s a flower, But only so an hour. Then leaf subsides to leaf. So Eden sank to grief. So dawn goes down to day. Nothing gold can stay.” 

 

Indeed, each Tulip Time reminds us that the “early leaf” – the petals of tulips – are appreciated just because we know they won’t last. In early May my front yard is gorgeous as the dogwood tree blossoms in pink and white. Then leaf subsides to leaf – to the necessary chlorophyll-green leaves which drink up the sun’s energy. 

 

 

Garrison Keiller (Prairie Home Companion) once said he’d trade his entire decade of 40’s to be 19 again. As a mathematician, I think he was on to something. Since each new year of life adds just a fraction to the memory of our past years, an alternative way to determine our age is by adding: 1 + ½ + 1/3 + 1/4 + . . . That is, early years of life are the most colorful and rich, we learn more than in our later years. High school seniors missed much more during the COVID down shutdown than did us 60-somethings. 

 

Mark Twain caught the idea with his usual wit: “Youth is so precious, it’s a shame it’s wasted on the young.” 

 

However, nature has one more lesson for us. Not only is the “early leaf” colorful, so also is the autumn leaf, albeit for a different reason. The brilliant fall pigments of red, orange and yellow are contained in the leaf all along, but they are dominated by the green chlorophyll. With less sunlight in the fall, the unneeded chlorophyll subsides, and the other colors – just as rich but not as assertive – have opportunity to express themselves. 

 

Similarly, as the passion of youth and focus of middle age subside due to changes in body chemistry and the accumulation of life experiences, perhaps that allows some subtleties in our personality – there all along – to be revealed. All of which shows that, indeed, even as we age, we continue to change – new colors, long muted, being revealed in our personalities. 

 

Is death the end of this process? Are other colors waiting to be expressed? Even the most creative among us cannot imagine the other colors in the electromagnetic spectrum left of red (infrared) and right of violet (ultraviolet). So also, any color changes to come are beyond 

ours to know and even imagine.

 

Travels with Elvis

 HS #80 2022.3.10

 

Travels with Elvis

 

I listen to audio books from Herrick District Library when driving. Biographies are my favorite. Ben Franklin, Thomas Jefferson, Theodore Roosevelt, and Leonardo da Vinci inspire and help keep one’s life in perspective. Presently I’m reading John Steinbeck’s “Travels with Charlie.” Whoever has not read his “East of Eden” should put it on their bucket list. Nothing better. 

 

Listening to Steinbeck’s adventures touring the country with his pet dog spurs me to tell adventures I had with my Welsh corgi, Elvis. When climbing the Laketown Beach steps between a friend and me, my friend observed, “He thinks he’s human, doesn’t he?” Indeed, it never occurred to Elvis that he wasn’t. 

 

It was at Laketown Beach that Elvis answered the question, “Do Dogs Know Calculus?” the title of my research paper co-authored with him. Essentially, Elvis, starting on shore, retrieved a stick thrown into Lake Michigan by first running and then swimming to fetch it as quickly as possible. The paper provided fame for both of us and gained his picture on the cover of numerous journals and several front pages of the Holland Sentinel.  I met one of his biographers (Keith Devlin, NPR’s Science Guy) at a national math convention.  Introducing myself after his talk, he exclaimed, “Tim Pennings! – I didn’t recognize you with your clothes on!” He then explained to the curious crowd (and me!) that he had sought a picture of Elvis and me for his book, but only found ones of us at the beach – me sans shirt. 

 

I readily admit that Elvis was the star of our dog and pony show – or as I’d describe, “Dog and Jack-ass Show.” A former student asked how it felt to be famous just because “you have a dog who is better looking than you even when he is running away?”  No argument. 

 

I sent two copies of the Elvis-covered math journal to fellow-corgi-lover Queen Elizabeth – one signed by me and the other requesting her signature. I received the journal from Buckingham Palace a month later with a note from her “Lady in Waiting” assuring me the Queen found our story interesting, but that she gave her signature only to those she personally knew.  Not having that rule for myself, I’m assuming she still appreciates having my signature in her library.  I kept the returned unsigned journal – after all, how many have been spurned by Her Majesty? 

 

That article led to another, “Do Dogs Know Bifurcations?” describing how Elvis, when starting in the water, would first swim to shore, then run along the shore, then swim to the stick, so that the resulting trek was the quickest. Not only did that paper earn me my highest professional honor (MAA George Polya Award), it also earned Elvis an honorary doctor’s degree from Hope College, awarded by Provost Jim Boelkins. The certificate was inscribed with the proper Latin phrase, which I shortened when I made Elvis business cards. I was later told that the abbreviated phrase had a different meaning – it conveyed “doctor” and “dog”, and because of the feminine sense of the Latin word was perhaps best translated, “Dog Gynecologist.” I’ve given away thousands. 

 

Elvis and I gave close to 300 talks all around the country, and I’ve lost count of the number of newspaper articles about him. Colleges would often invite the local press, so as we’d traveled through the state, I’d see his picture on the front page of newspapers at rest stops.  

 

He contributed to recreation trips too. As the advisor for Hope College Outdoor Adventure Club, Elvis and I led groups of students to Pictured Rocks for Fall Break. In lieu of an alarm clock, I’d unzip the tents, gently usher Elvis in among the sleeping students, then quietly command, “Speak. Speak.” Always worked. 

 

He was also fun at home. I once mistakenly fed him an Easter ham bone which plugged up his digestive track. Per the vet’s instructions, I put him on the back porch that night with the door open accessing the back yard. Feeling sorry for him, I bundled in a sleeping bag and joined him. After a chilly night’s sleep, I awoke shivering to find him warm and cozy INSIDE the house. He had pottied, gone to the front door, barked, and my neighbor let him in. 

 

What a guy. Initially Elvis was my dog who was a good friend.  Before he died Elvis was my good friend who just happened to be a dog.  Good memories. 

Three Mysterious Numbers

 HS #79 2022.2.10

 

Three Mysterious Numbers

 

 When I teach precalculus, I bring rope of various lengths to class and invite students to pair up. One holds an end stationery, and the partner – holding the other end and keeping the rope taught –  counts paces around the circumference of the resulting circle, and then across its diameter. When I did it, I counted 50 paces around, and 16 across. The ratio: 50/16 = 3.125 is an approximation of pi. The Greek letter pi represents the ratio of the length of circumference to the length of diameter. 

 

This number, so easily understood, is mysterious.  If you try to write it out as a decimal, it never stops and never starts repeating. Is there a place in the decimal expansion where there are 1000 sevens in a row? Most certainly. 

 

Pi shows up other places as well. If you continue the pattern: 1 - 1/3 + 1/5 - 1/7 + 1/9 – 1/11 + . .  and multiply the result by 4, you’ll get pi. 

 

Or try this:  Snip a piece of paper clip to the length of the distance between the lines of ruled paper. Then randomly spin and drop the clip onto the paper T times, counting the number of times (C) the clip crosses one of the lines. Then pi = 2T/C. How cool is that! 

 

Perhaps the most surprising result involving pi is also the simplest. A 25,000 mile length of string will lay around the equator of the earth.  How much longer does the string need to be if the string is raised one foot above the earth along the entire equator? I guessed 10,000 miles.  Answer: If r is the length of the radius of the earth in feet, then the equator is 2(pi)r feet. The circumference of the larger circle is 2(pi)(r+1) feet. The difference in lengths is 2(pi) feet – just over 6 feet longer! Blows my mind.

 

Here’s another mysterious number: If you have a calculator, multiply (1+1/2) by itself twice. Then multiply (1+1/3) by itself three times. Then multiply (1+1/4) by itself four times, etc. What happens to this sequence of numbers? As the sequence continues, the portion inside the parenthesis decreases to 1, but since it is multiplied by itself more times, the resulting number grows larger. So there is tension – a struggle. Some students think the resulting numbers will get closer to 1. Others think they will get arbitrarily large. Turns out that neither happens. The struggle ends in compromise.  The numbers get closer and closer to e = 2.718 . .  It’s another number that never stops. 

 

The number e is at the heart of the “normal distribution” or “bell shaped curve” which is used extensively in statistics. So, like pi, it is super important in understanding the world. 

 

One other mysterious – beautiful – number:   Consider the sequence: 1, 1, 2, 3, 5, 8, 13, 21, . . where each successive number is gained by adding the previous two. This is the famous Fibonacci Sequence. These numbers are found throughout nature – count the petals on a flower or the seeds in an arch of a sunflower, or the knobs in a row of a pineapple and you will often get a Fibonacci number. If you divide a Fibonacci number by its predecessor, the result will be about phi = 1.618 . .  Yet another number that goes on forever. This number is called the Golden Ratio. If you construct a rectangle so that the length of the longer side is phi times the length of the shorter side, you get a Golden Rectangle. Remove a square from a Golden Rectangle, and the remainder is another Golden Rectangle. When I ask 5^thgraders how many times this can be done, they shout “Infinite!” Their response gives me goosebumps; how interesting that even children imagine infinity.  (See Ecclesiastes 3:11.) Golden Rectangles are found throughout art and architecture. da Vinci used them extensively. Google it and see for yourself. 

 

On the other side of the interesting-spectrum of numbers are 0 and 1 - the most basic and ordinary numbers around. Adding 0 doesn’t change a number, and multiplying by 1 doesn’t change it. 1 has a counterpart, i, which is its imaginary cousin. How eerie then that 0, 1, i, e, and pi can all be combined in one simple equation – called Euler’s Equation, perhaps the Holy Grail of Mathematics. Yet one more surprise: “Euler” is pronounced, “oiler.” Pronouncing it correctly will impress any mathematician. 

Secrets Make You Sick

 HS #78 2022.1.13

 

Secrets Make You Sick

 

 “Life can only be understood backwards, but it must be lived forwards.”- Soren Kierkegaard.

 

For the last thirty years, my “home away from home” has been the Au Train Beach on the south shore of Lake Superior, ten miles from Pictured Rocks. Many good times of fires, frisbee, new friends, and watching shooting stars while sleeping on the beach. Best spot on earth!

 

Highway 28 passes over the Au Train River as it enters the beach, so there is a bridge locals and tourists use for jumping. Fathers encourage timorous children to leap – standing in the water ready to catch them. I’ve jumped a few times myself. Life doesn’t get any better. 

 

So it strikes me strange that the most prominent graffiti on the concrete side of the bridge is the bold, black-painted phrase, “SECRETS MAKE YOU SICK.”   I’ve contemplated who wrote it and why. Most likely a teenager. Filled with angst. Betrayed by a friend? Jilted? 

 

Whoever and whatever, one thing is evident: The author discovered a deep truth. Secrets do make one sick – I should know. 

 

Until ten years ago, I carried a secret. As a child, when the family was safely across the street at church on Sunday morning, I’d open the family Bible to the picture of Sampson at the treadmill – muscular in a loin cloth. I was fascinated by the brawny physique. 

 

In third grade I had a secret crush on a couple 6^th graders. I admired their poise and athleticism. 

 

My secret took a name six years later when reading an article in TIME magazine about homosexuals – a new word for me. But the description rang true. I shuddered realizing the article was describing me. 

 

Continuing through high school, my fears were confirmed. Friends would point out a cute girl and I would agree, keeping my true thoughts to myself – that I had noticed instead the guy she was with.  

 

I went on to college and leadership in Campus Crusade for Christ. I considered joining the staff after college, but the application form had a question, “Are you physically attracted to those of the same sex?” This forced me, at age 20, to reveal my secret for the first time – to a CCC Director. He reassured me that “You are not gay in Christ.” I so wanted to believe him. 

 

I finished undergrad, six years of grad school, and six years pre-tenure at Hope College without telling anyone. I lied only a couple times when, then in my thirties, friends asked why I wasn’t in a relationship. I envied those who could enjoy beer/wine without fear of revealing guarded thoughts.

 

After getting tenure, I bought a house, and furniture from Ten Harmsel on 8^th Street. I remember my quandary deciding what size bed to buy, and choking up when the salesperson counseled, “You’re single now, but shouldn’t you buy for the future?” 

 

In 2008, I spent two weeks in Tokyo. On the subway, the young man next to me fell asleep and his head lay on my shoulder for 15 minutes. I soaked up the experience – the longest duration of human contact I had since childhood. 

 

I was 53 when my parents died. I never told them. I’ve wondered the reaction had I told my minister-father when in high school/college.  I discovered the answer when sorting through his letters after he died.  In 1977 he wrote “strongest possible opposition” to a state legislator who voted to extend rights to homosexuals. Dad called homosexuality a highly pernicious destructive force and spiritual illness from which society needs protection. 

 

I sometimes wonder how life would have differed had I told my secret earlier. Would I have lost my college friends? Perhaps. Would I have gotten a faculty position at the alma mater of my father and grandfather? Tenure?  Tough choices.

 

Nathaniel Hawthorne captured the double-edged poison of secrets in “The Scarlet Letter.” The truth of Hester Prynne was known, and she bore the results of rejection daily. But even worse was the internal damage, the soul-sickness, done to her lover who kept the secret within. The former may bring loneliness and isolation. The latter will for sure. 

 

The world is still a tough place for those who are caught in Kierkegaard’s dilemma and forced to decide whether and when to leap – as from the Au Train bridge – by revealing their secret. Hopefully, they have trustworthy friends and relatives – as I did – standing ready to catch them. 

Ecclesiastes and Leaf Cutter Ants

 HS #77 2021.12.9

 

Ecclesiastes and Leaf Cutter Ants

 

 

I have long been inspired by the sage wisdom of Ecclesiastes. Several years ago, I attended a wedding where the couple wove three strands of cord together representing their lives being joined together with God. It was inspired, no doubt, by Eccl 4:11 “A threefold cord is not quickly broken.” 

 

It inspired me to compose a song, “Bound and Woven,” for such occasions: “AS we bind our hearts together, Asking God to make us one, May the union of our spirits, Glorify thy Son.   AS we weave our live’s ambitions, Into a single common dream, May your purpose and your pleasure, Ever be our theme. AS our lives grow bound and woven, Intertwined oh God with thee, A three-fold cord not quickly broken, Union of mystery.” (Song at my YouTube channel: timothy j pennings)

 

Indeed, it’s an interesting topological truth that while a rope of two strands twisted together and fastened at the ends can be unraveled and pulled apart, this cannot be done when three strands are woven together. Three strands woven together and secured at the ends is inseparable. What an insight – from 3000 years ago!

 

Such gems of wisdom from Ecclesiastes have inspired much music and poetry: “To everything – turn, turn, turn, there is a season - -“ (The Byrds, 1962).  “Dust in the Wind - all we are is dust in the wind“ (Kansas, 1977). 

 

But while such nuggets of wisdom resonate with all, there is less consensus about the overriding themes of Ecclesiastes.  

 

As I read the book, the theme of the first several chapters is living with contentment. The key is to lower one’s expectations.  Though not discussing Ecclesiastes, C.S. Lewis made the same point in one of his essays. If two people are forced to live in a poor quality hotel for a month, the first having been told s/he was going to prison, while the second told s/he was going to a luxury retreat, then the first will be satisfied, and the second not. All depends on one’s expectations.

 

How does the author of Ecclesiastes lower our expectations? He first tells us (Chapter 1) not to expect anything better in the future than what we presently have. There is nothing new under the sun.

 

Then (Chapter 2) he tells us (we who has not had his rich life experiences) that the things we imagine might bring us pleasure and fulfillment all fail to satisfy: wine, achievements, gardens, slaves, flocks and herds, treasure, concubines.  We have to take his word for some of those! (My high school English teacher said his doctor warned that he was getting too much “wine, women and song” - so he stopped whistling.)

 

Then at the end of Chapter 2, after showing us that nothing present and nothing to come will bring fulfillment and happiness, he gives the bottom line: “There is nothing better than that one should eat and drink and find enjoyment in his toil.”  That’s it. “This is from the hand of God.” Don’t expect more. 

 

In Chapter 3, the author underscores this point by reminding us that, although we have a sense of eternity, we have no assurance of life beyond this one (vs 18-22). Concluding, he emphasizes yet again, “Enjoy your work – that is your lot. For who can see what will come after?”  Don’t expect more – there is no guarantee of anything better. 

 

Fascinating that our Founding Fathers (especially Jefferson) understood this wisdom. The Declaration of Independence asserts that rights given by our Creator include life, liberty and THE PURSUIT OF happiness. Life and liberty are rights in and of themselves. But we have no right to happiness. There is no such guarantee. We are granted only the opportunity to pursue it. 

 

Can one be content with the daily routine of work and activity? The author of Ecclesiastes may also have written the proverb exhorting us to learn from the ant.   When touring the Amazon rainforest, I was fascinated by the 100 foot stream of leaf-cutter ants, one line heading away from the denuded tree each with a portion of cut leaf, the other line heading back for another. 

The most complex animal society functioning because each is content to do their part. 

 

Martin Luther seemed to agree with this approach to life. When a cobbler asked him how he could serve God, Luther replied, “Make better shoes.”  

Veterans Day - Our Obligation

 HS #76 2021.11.11

 

Veterans Day – Our Obligation

 

Today is Veterans Day. My fifth grade teacher helped me appreciate the sacrifice of veterans by requiring that we memorize the Gettysburg Address. I still recite it – trying to say it as I think Lincoln would have. 

 

Its memorization is worth the effort.  Lincoln was the secondary speaker at Gettysburg. The main speech - given by Edward Everett, a famous orator and former Secretary of State, was two hours long. Then Lincoln spoke - giving his speech in two minutes.  Everett wrote to Lincoln the next day, "I should be glad if I could flatter myself that I came as near to the central idea of the occasion in two hours as you did in two minutes."

 

Lincoln was able to distill the essence of the U.S. experiment in democracy into 273 words because he had been thinking and living it nonstop in the crucible of a conflict – a conflict which threatened to tear the union apart. The vision of our country – past, present and future – crystalized in his mind. 

 

If you find it and read it, you’ll notice something strange. In this elegant, succinct, smooth-flowing address, there is a pair of sentences which seems awkward and redundant. The reason, I think, is that these two sentences form the focal point and the focal joint of the address. This transitional thought was so important to Lincoln, that he essentially said it twice. 

 

The first part of the speech tells of the sacrifice of the soldiers and the ceremony to honor them. Then comes “BUT”. “BUT in a larger sense, WE cannot dedicate, WE cannot consecrate, WE cannot hollow this ground. The brave men, living and dead, who struggled here have consecrated it far about OUR poor power to add or detract. The world will little note nor long remember what we say here (turned out to be false!), but it can never forget what they did here.” So Lincoln is making the point that ceremony and speeches and gravestones are not adequate. He does not allow the listeners - then or now - to get easily off the hook with a simple day of remembrance. Observing Veterans Day is not enough. What then is our obligation? 

 

Then comes his answer – repeated twice for emphasis: “It is for us the living, rather, to be dedicated here to the unfinished work which they who fought here have thus far so nobly advanced. It is rather for us to be here dedicated to the great task remaining before us.”  

 

For Lincoln, the essential way to honor the sacrifice of veterans was not by giving speeches and putting flowers on their graves, but by resolving to devote ourselves to “the great task remaining before us.” 

 

But what is that great task? And how do we devote ourselves to it?

 

Lincoln answered the first question. Quite simply, the great task is that we keep government of the people, by the people, for the people from perishing. This is no small task. At the time of Lincoln’s speech, these United States had been a nation for less than a century. In fact, before the Civil War, the “United States” was considered a plural. Folks said, “The United States ARE . .  “ Only after the War of the Rebellion did people begin to say “The United States IS . . “ The Civil War welded us together. 

 

We have now been a union for over two centuries, but we still should not take our existence for granted. It is clear from history that democracy is not necessarily a stable state. It needs to be conscientiously groomed and maintained. 

 

How? Having just finished Walter Isaacson’s biography of Ben Franklin, it’s striking that the essential element that Franklin brought to the Constitutional Convention which laid our foundation is the same quality of mind that we vitally need now: The moral duty to consider opposing views and to compromise. It stemmed simply from his realization that he was fallible. 

 

Franklin also had unwavering faith in the middleclass. Power should reside with the people – with ALL the people, not just the wealthy and elite.  He likely would have approved of our recent election of the first president in forty years who didn’t attend an Ivy League school. Indeed, it was Franklin’s sort of vision which eventually brought a self-educated rail-splitter from the Midwest to the White House. A gangly commoner who charges us to take the torch from the veterans and carry it forward. 

 

 

 

Long Live Liberal Arts

  

HS #75 2021.10.14

 

Long Live Liberal Arts

 

Introductions first: 

 

I met Andrew while waiting for a stalled train by Hope College. I asked him the dinner question I have asked such Hope seniors for 30 years: How are you a different person now than when you arrived at Hope College? 

 

I have heard many thoughtful answers, but his brought a lump to my throat: “Professor Ortiz taught me how to see beauty. He showed me how to slow down when I read Augustine’s “City of God” and appreciate the beauty.” 

 

I can’t think of a better testimony to the liberal arts – disciplines meant to liberate the mind. 

 

Meet Yamir - my 18-year-old Hispanic housemate who responded to my Craigslist room-for-rent ad.  Yamir recently graduated from high school in Tulsa OK and is seeking a way to get a college degree in psychology. He brought two suitcases with him – the larger one filled with favorite novels. He recently received an Amazon package: “The Best Poems of the English Language” and a favorite epic DVD: “Ben Hur.”   We take turns showing our favorites. Last evening, he had the privilege of watching “Casablanca” for the first time.  Unlike most of his generation, he watches movies without his phone on his lap. In our subsequent discussion, he stumped me, “If Lazlo had to choose between his wife and his cause, which would he choose? (If you haven’t yet seen “Casablanca” put it on your bucket list.)

 

Yamir loves the liberal arts. 

 

Let me introduce you to “Floor Fienz Family.” If you frequent Holland’s Thursday 8^th Street Entertainers, you have likely seen them. They are the break-dancers who draw the overflowing crowds and represent Holland as they travel the country. Break dancing is the improv “jazz” version of dance. Mastering their art requires athleticism, appreciation of music and dance, understanding of the body, engagement with the audience, and tenacious practice.  Hope College should sponsor a joint Hope - Floor Fienz dance concert. Spanning cultures, it would be the very best of the liberal arts. 

 

I don’t know his name, but this past weekend I got into a conversation with a 26-year-old skateboarder at Smallenburg Park who was jumping OVER picnic tables on his board. Except for a couple missing teeth, he was unscathed from his years of practice. No money. No medals. No audience. Just the thrill of perfecting his leaping much as Jonathan Livingston Seagull perfected his flying. He may not know the term, but he is a pure liberal artist – as pure as they come. 

 

As are those who paint the colorful murals on railroad cars. As was the 10-year-old African American boy who coming out of a Hope College violin recital exclaimed, “That made my throat dance!” As are my computer game-design students at Davenport University who – know it or not – are engaged in perhaps the newest form of artistry. 

 

Of course, there is also value in studying the liberal arts.  When I give math talks in high schools, I explain that one can get a great education and learn about life by traveling, or getting a job, or joining the military, or, for that matter, living on the street. But one can only learn the greatest things ever discovered by the human mind via study of the liberal arts. 

 

But learning  ABOUT the liberal arts is not as valuable as actually DOING them. Emerson admonished young men to be out in the world creating their own adventures rather than sitting in a library reading the adventures of others. C.S. Lewis explained that while a map is needed in finding a mountain lake, it is not as valuable as sitting by the lake. 

 

However, there is no need to choose betwixt them. A life is enriched both by studying the liberal arts and by being engaged in them. This is what led President John Adams to reflect, “I am a revolutionary so my son can be a farmer, so his son can be a poet.” Or the counsel of my college physics professor, “If you only know what you have to know, you are just one step from being ignorant.” 

 

More broadly, a life is enriched by engaging in what Bertrand Russell sarcastically termed “useless knowledge.” In his essay, “In Praise of Idleness” Russell argued that during WWII, England devoted half of its energy to the war and still produced enough for all to live. So he suggested a 20 hour work week for all with the balance devoted to living rich lives. Something to ponder.