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!”

Molded by Experiences

HS #33  2018.4.3

Molded by Experiences 

Perhaps the cleverest sermon I ever heard was April 1, 1988 while attending Hope College’s Good Friday service. Jerry VanHeest, Hope’s chaplain, offered a meditation on I Corinthians 1:18, “For the word of the cross is folly to those who are perishing, but to us who are being saved, it is the power of God.”  As he proceeded with his thoughts, I eventually caught on that he had chosen a text that perfectly tied together April Fools Day and Good Friday. Very clever indeed. 

Maybe only the Apostle Paul could have written such a statement. He had lived both sides – dramatically. For a good portion of his life, he ravaged the Christian church believing the Christian message was not only foolish but dangerous. Then after an experience he vividly described as an encounter with the risen Christ, his point of view – and as a result, his life mission - did a complete turnabout. 

This all happened even though Paul’s values and personality remained essentially the same. He was a gung-ho, Type A personality before his conversion, and he certainly was after it. He loved and wanted to serve God before, and just as much afterwards. 

Paul’s story shows us that life experiences are often central to our beliefs and consequently our life’s trajectory. 

A few years back, Hope College psychology professor David Myers gave a talk on homosexuality. Taking comments after the talk, a middle-aged man – bleached crew-cut and bronze from working in the sun – stood up and repudiated all that Myers had just said. Homosexuality was wrong – plain and simple. As he sat down, another man of similar description stood up, “Last year I would have said exactly the same. But last winter my son told me he is gay - and I love my son.” 

Dick Cheney provides another example. He is solidly conservative on most every issue except the LGBT one. No coincidence that his daughter is a lesbian.  So life experiences certainly seem to influence our life perspective. 

Or is it the other way around? Is it our perspective that colors our experiences?

There’s a joke about a shoe salesman who was sent to a remote tribe in the rainforest. He wrote back, “No market here – no one wears shoes.” Another salesman was sent, who immediately telegrammed, “Unlimited market here – No one has shoes!” 

As a real counterpart, I remember once hearing a moderator interview two Nobel Laureate economists. He asked them to predict the world economy over the next 5-10 years. One gave a rosy forecast, the other’s was bleak. The moderator was perplexed, “You are both experts and you both see the same data – why the difference?” Rather sheepishly, they explained that one was an optimist and the other a pessimist. 

For a Biblical example, see John 12: 27-29. Some heard angel voices, others heard thunder. 

Same experiences, but different interpretations. What causes the difference? Does seeing cause believing, or does believing cause seeing? Do experiences make us, or do we determine our experiences?

C.S. Lewis thought the former. His book “Miracles” begins “What we learn from experience depends on the kind of philosophy we bring to experience.” 

My father agreed, but with a twist. I remember his sermon, “Butter and Eggs” in which he noted that when heated, the first melts while the other hardens. He reasoned by analogy that a person’s character determines how one reacts to experience. So while the experience (heat) affects the individual, it’s the individual who determines what the effect is. (Immanuel Kant’s epistemology is similar:  Experiences happen to us, but WHAT we experience depends on us.) 

The PBS documentary “Faith and Doubt at Ground Zero” – made a year after 9/11, seems to support this view. The two-hour special included interviews of a dozen people who had lost loved ones in the attack.  Some had a severely damaged faith in God as a result; others experienced an enhanced belief and experience of God. 

My own take on the matter is informed by the recent forest fires out west. These fires are affected by the existing weather – dry wind versus rain makes all the difference. But meteorologists are also finding that large fires actually influence and create their own weather.  Our brains likely have similar feedback systems. Like M.C. Escher’s illustration of two hands drawing each other, our experiences mold us as we in turn interpret and mold our experiences. 

Mindboggling, and leaves me wondering:  If I had been with Paul, what would I have seen?

The Infinite and our Place in the Universe

HS #41 2018.12.13

The Infinite and Our Place in the Universe

Let’s listen to Immanuel Kant on one of his evening walks about Konigsberg:

 “Two things fill the mind with wonder and awe the more steadily I reflect upon them: the starry heavens above me and the moral law within me. The starry heavens begin at the place I occupy in the external world of sense.  The moral law begins at my invisible self, my personality, which has true infinity. 

The former annihilates my importance as an “animal” which must give back to the planet (a mere speck in the universe) the matter from which it came. The latter, on the contrary, infinitely raises my worth as that of an “intelligence” independent of animality with a final destination not restricted by the boundaries of this life, but reaching into the infinite.”

Three thousand years ago, a shepherd boy destined to become the King of Israel gazed into the night sky, took his lute and composed something quite similar: “When I look at thy heavens, the work of thy fingers, what is man that thou art mindful of him? Yet Thou hast made him a little less than God.“

Theologian, astrophysicist and WTS emeritus professor, Chris Kaiser, with the benefit of modern scientific knowledge, still asked the same,  “Scientific theories will always leave us with the perplexing question of the relationship between humanity and nature, history and cosmology. Which is the real drama? Is it the evolution of the universe, with the rise of life on earth and the history of humanity a mere curiosity, a freak sideshow doomed to extinction and oblivion? Or is the story of humanity the real drama with the vast panorama of the universe merely a background?”

Why do we humans ponder our place in the universe?  Is it because, as the writer of Ecclesiastes said, “He has put eternity into man’s mind“?  Why did Kant keep referring to the infinite?  What does the infinite have to do with our understanding of ourselves?

Thirty years ago, as a new professor at Hope College, I wrote a paper: “Infinity and the Absolute: Insights into our World, Our Faith and Ourselves.” I began, “The more I ponder the infinite, the more I question my ability to know, because I become increasingly aware of the limitations of my own mind. On the other hand, contemplating the infinite and endeavoring to understand its connection to the world outside of me and the faith within me, serves me by clarifying my position in the scheme of things. Thus in grappling with the infinite, the mind is at once humbled by the inability to fully understand, while enriched by the very attempt to understand.”

David Hilbert, perhaps the greatest mathematician of the twentieth century, observed, “The Infinite. No other question has ever moved so profoundly the spirit of man, no other idea has so fruitfully stimulated his intellect.” 

For thousands of years, mathematicians and philosophers wrestled with the meaning of the infinite. For some it was a pejorative term, others associated it with the divine. Then Georg Cantor singlehandedly ripped the curtain from top to bottom revealing the infinite’s inner sanctum. 

Cantor successfully defined the infinite. Essentially, an infinite collection is one in which after removing some, there are still as many as before. John Newton, the author of “Amazing Grace”, captured the idea exactly: “When we’ve been there ten thousand years . . . we’ve no less days to sing God’s praise than when we first begun.”

Cantor also proved that there are different sizes of infinity - - in fact there are an infinite number of sizes.  But he was humbled by it as well. Cantor could not answer a vexing question: Are the sizes of infinity discrete (like the numbers 1, 2, 3) or are they all bunched together (like the possible distances along a ruler). Cantor, obsessed with this question and taunted by mathematicians who rejected his ideas, died in an insane asylum. 

But Hilbert recognized the significance of his findings. In 1900, Hilbert, the key-note speaker at the International Congress of Mathematicians, listed 23 problems for mathematicians to solve in the next century. Cantor’s problem was number one.  The answer, in 1963, shocked everyone.  It was totally unexpected. 

No wonder Cantor associated this unknowable, otherworldly infinite with the divine, envisioning the different sizes of infinity as angels leading to the very throne of the inscrutable Absolute Infinite. The Infinite: humbling, mysterious, and surprising – almost as surprising as an infant lying in a manger. 

SDIC

HS #40  2018.11.8

SDIC

Last Christmas, Kids’ Hope had a party for the children including Bingo with an assortment of prizes. Jon (I’ll call him) was excited when he saw two hot rod cars among the toys. His expression of hope fell when another boy yelled BINGO! and chose one of them. Three turns later, the same boy shouted bingo again and took the second car. Jon quietly sobbed. As mentors consoled him, it occurred to me that bingo is a good game for children to play. It shows them that life is not fair and that the difference between winning and losing sometimes depends on the luck of the draw. 

Do you remember the opening and closing scenes of “Forrest Gump”?  A feather flitters in the wind – tossing and turning aimlessly. That, of course, was the point of the movie. The outcome of our lives is an unpredictable amalgam of intention and inherent randomness. 

In high school I read a short story about a flea that hatches and develops into an adult all on a single leaf. The flea sits on that leaf waiting – waiting – waiting until a mammal passes by. Then it leaps. If successful, it lands on a furry back, burrows down to a nourishment of blood, finds a leaf and lays eggs – completing the cycle of life. If it misses, it falls to the ground and dies. Its entire existence lay in the success or failure of a single leap. 

Stark pathos. The story resonates deep in the soul – perhaps because we realize the truth of it.  We plan and prepare, doing everything in our power to succeed. But the outcome? Who knows.  The quality Napoleon most wanted in his generals? Lucky. 

Perhaps that’s why American Ninja Warrior is a favorite TV show for millions. Men and women run a three minute obstacle course involving jumping, balancing, climbing, and hanging on. Some have dedicated their lives to finishing the event, building elaborate backyard courses and practicing for hours each week. 

In the Jumping Spider obstacle, contestants leap from a trampoline and must catch themselves with outstretched arms and legs between two parallel walls. If their timing is slightly off, they fall into a watery pit. Like Jon, some break down in tears. But others, stoically accepting the uncertainty of life, promise they will redouble their efforts and try again the next year. 

Life often turns on a dime, determined by minute circumstances. Mathematicians have a term for situations where a slight difference leads to drastically different outcomes: Sensitive Dependence on Initial Conditions (SDIC). One example is the Continental Divide. Spit and it will eventually find its way to the Atlantic Ocean. Give your head a slight twist and spit again – its destiny is the Pacific. 

SDIC is why physicists can determine exactly where the planets will be in 10,000 years, but cannot predict where a fluttering feather will land.  Indeed, in order to calculate the position of an air molecule just one-ten-billionth of a second into the future, a physicist would need to take into account the gravitational force from each electron on the other side of the universe. That’s sensitive!

Meteorologists call it the “butterfly effect” because mathematical models show that the flap of a butterfly’s wings at just the right time and place in, say, Australia could produce a totally different weather system in North America two weeks later. 

A poem from antiquity captures the idea: For want of a nail, a shoe was lost. For want of a shoe, a horse was lost. For want of a horse, a rider was lost. For want of a rider, a battle was lost. For want of a battle, the kingdom was lost. 

 Al Gore understands it. He meticulously tended to every detail in the 2000 presidential election, but didn’t think to inspect the Florida ballots. A misleading design caused thousands to mistakenly vote for the wrong candidate. U.S. and world history has changed as a result. In David McCullough’s “1776”, the author explains that the outcome of the Revolutionary War depended on rolling fog hiding Washington’s army on one critical evening.  

In 334 BC, Alexander III of Mecedon narrowly escaped a death blow.  According to Princeton historian, Josiah Ober, had Alexander the Great been killed – goodbye to the Roman Empire, Christianity, Hellenism, and Western culture. Safe to say you wouldn’t be reading my column right now because neither of us would exist. 

All rather mind-blowing. But rather wonderful. In all likelihood, you will change the world. 

What is true faith?

HS #39 2018.10.11

What is true faith?

“Faith” is a word I have never understood. 

Part of the confusion occurs because the word is used in opposing ways.  This occurred recently at a conference.  One speaker explained that as evidence grows, our faith – that is our confidence – grows in proportion. The more supporting evidence one has, the more faith one has. Seemed reasonable. But then another speaker explained that “faith” fills the gap left by having incomplete evidence.  So the more evidence one has, the less faith one needs. 

As an example, consider a mother who sends her son and daughter to a store each with a grocery list and $20. The daughter has always returned with the correct items. The son sometimes loses the money or buys the wrong things.  

In which child does she have more faith?  Her confidence in her daughter is higher than in her son. Is this what "faith" means?  Or is she putting more faith in her son because the faith makes up – fills the gap - for the lack of confidence? 

Or is the verb significant: Does she HAVE more faith in her daughter, but PUT more faith in her son? 

Or is it incorrect to quantify faith? She has faith in both, never mind “how much.” 

These seem important questions for Christians in particular, since faith is central in Christianity. 

Jesus was comfortable quantifying faith; he talked about having the tiny faith of a mustard seed. 

The Apostle Paul claimed, “by grace are ye saved through faith.“  The Heidelberg Catechism (HC) agrees that only those with “true faith” are saved. But this, of course, raises the next question, “What is true faith?”

The HC’s answer: “True faith is a sure knowledge whereby I accept as true ALL [my emphasis] that God has revealed to us in his word. At the same time it is a firm confidence … ” But alas, this just raises more questions. 

 Does “all” really mean “all”? So then a person who doesn’t accept as true that the sun stood still for Joshua or that Jonah was swallowed by a fish is not saved? Seems severe. 

The HC also seems confused, even self-contradictory, as to whether faith is an active choice one makes or a state of mind not under one’s control.  

Consider the phrase, "a sure knowledge whereby I accept as true."  “Accept as true” implies making a choice. But what choice to believe is needed if the thing is already known for sure?   I have a sure knowledge that a bowl of Hudsonville Toasted Coconut ice cream (the best flavor ever invented) is on my lap.  I see it.  I smell it.  I taste it.  I feel the weight and the coolness, I hear the clunk when I knock it with my spoon. My friend confirms that it is there. So I am compelled to believe it (unless like George Berkeley or the solipsists I assert that the physical world doesn’t really exist). Conclusion:  No choice is needed to “accept as true” if one already has “a sure knowledge.” 

The confusion continues with the phrase  “a firm confidence.”   Whereas “accept as true” implies that faith is an act of volition,  “a firm confidence” implies that faith is a   state of mind not under one’s control, since one can’t choose to have confidence any more than one can choose to like ice cream.   So is faith a state of mind or an act of volition?   

Indeed, can a person choose to believe?  If I offered you $1000 for believing that I could levitate, would you believe it? COULD you believe it? The incentive is there, but can you choose to have faith? Perhaps the choice is whether you are honest with yourself and others concerning if you have faith. But whether or not you believe seems outside of your control.

Or suppose an entrepreneur advises four friends to invest their savings in a new company. One is confident and invests; one is skeptical, but invests nonetheless; the third believes it will likely be successful, but still doesn’t take the chance; and the fourth has no confidence and doesn’t invest. Which of these has faith? Is faith essentially an action one takes, or is it a state of mind?

So, does faith increase or decrease with supporting evidence? Is faith a matter of choice? If so does it require action?  Or is faith a state of mind not under our volition?  All questions to ponder. Thoughts are welcome.

Song Birds and Pedagogy

2018.9.13

Song Birds and Pedagogy

It’s a memory indelibly imprinted in my mind. My fifth-grade teacher, Mrs. Reeves, was entertaining several of us after school until the school bus came.  That day in class we had learned how to add fractions such as 1/5 + 2/5. She cut a pie into 5 pieces, took one piece and then two more, and we had 3/5 of the pie. Easy. 

Now she asked, “What is 1/3 + 1/2?”  I drew half a pie and a third of a pie and put them together, but that didn’t help. The denominators (bottoms of the fractions) were different, so the earlier method didn’t work. I was stumped. 

After letting us struggle a while, she gave a hint: Cut the 1/2 and the 1/3 into 6ths.

 Then I got it!   1/2 is the same amount as 3/6, and 1/3 is the same as 2/6, so we add 2/6 + 3/6 to get the answer: 5/6.  What a feeling of satisfaction.  The next day when she taught that lesson, I proudly displayed my superior intellect to the class. 

The next year my science teacher asked: Why isn’t it self-sustaining for a burner to heat water, steam from the water to spin a rotor, and the rotor create friction to heat the burner?  He let us think about it overnight before giving us the hint: Not ALL of the heat from the burner heats the water. Not ALL of the steam hits the blades. My hand shot up to give the answer: Energy is lost at each step in the process.  

Those truths of math and nature have stayed with me my entire life. But more importantly, I still use their method of teaching. Shamelessly taking the credit, I describe it to my students as Pennings Pedagogy Theory. 

Drawing a circle on the board, I explain to my students, “This is your brain. When I teach you something that you haven’t yet pondered, it’s like a stream of water [which I then draw above the circle] running over the top of the circle. A little seeps into the brain, but most runs off the sides.”

However, I continue to explain, if students become invested in the problem either via a teacher’s challenge or from their own inherent interest (the advantage of teaching sex education), then a divot is formed in the top of the circle – their brain - so the material collects and sinks in.

So that is how I teach. As I explain new material, the lecture is pitted with silent periods where I ask students to solve the next step. Either they figure it out, confirming that they fully understand, or else they get stumped, thereby forming a mental divot.  Then they are (hopefully) all ears and get a satisfying “ah ha!” sensation when I give the solution. 

This summer I taught a graduate course in Urban Education in Mathematics at Davenport University.  The K-12 teachers and I together explored the challenges of teaching students who may come from homes where they have not been exposed to the rich learning environment that others have experienced. These students have not formed as many mental divots. For example, as a child I learned about area and volume by playing with wooden blocks. A rectangle of 4 by 7 requires 28 blocks  (the area), and if I stacked them three high, then the volume is 4x7x3=84. It’s also clear by re-orientating that 4x7x3=7x3x4, so the order of multiplication doesn’t change the answer.  Children self-discover these important mathematical concepts just by playing with block towers. Their minds are now primed – divots formed - to formalize the concepts in school. 

It’s just as fun as we grow older. When I was advisor for the Hope College Outdoor Adventure Club, I kept vanloads of college students entertained for hours asking them math and logic puzzles. Just like Mrs. Reeves, I posed the questions and their natural curiosity and competitive spirit did the rest. 

The method was applied to me this summer when I camped and fished in the BWCA (Boundary Water Canoe Area) with my college friend of 40 years.  Tom knew each bird we encountered – either by appearance or song – and kept asking me if I knew.  I have enjoyed bird songs all my life, but never had the curiosity to determine the name of the bird. Now, thanks to Tom’s enthusiasm and prodding, I have started forming and filling my own mental divots and consequently my life has just become richer.