Zebras and Original Sin

  

 

HS #112 2024.11.14

 

Zebras and Original Sin

 

Recently I discovered a YouTube video showing a zebra stallion on a river bank holding in its mouth the hoof of a foal and suspending it upside down so that its head was submerged in the water. The stallion was stomping on its head to drown it. When the foal broke free, the stallion chased it, kicking and stomping it, hindered only by the mother trying to protect it. Check out “Zebra tries to kill foal” on YouTube if interested. A comment explained the stallion was protecting its genetics. Apparently, this foal, born to one of his mares, was not his offspring. 

 

Other animals do the same – lions and grizzly bears in particular. I had come to terms somewhat with this behavior from aggressive carnivores, but it was more shocking to see it from a handsome, benign-looking zebra. 

 

When I teach calculus to engineering students, I explain that the process of using mathematics and scientific principles to understand and predict natural-world phenomena is called modeling. The fewer and more universal the principles, the better. 

 

For example, before Copernicus, the apparent motion of the planets was explained via cycles and epicycles. These are the motions of The Scrambler at an amusement park – seats spin around a small circle, and these in turn spin around larger circles. Since we observe planets seemingly going backwards and forwards in the night sky, and since we supposed the earth to be sitting motionless in the center of the universe, these small circles attached to bigger circles was the best way to explain what we saw. 

 

Then along came the giants of modern science including Newton, Kepler, Galileo, and Copernicus. By the end of this period of rich discovery and mathematics, we had a new model for the heavens. The planetary movement we see is due to the planets – including the earth – revolving around the sun at different speeds. Thus, from our perspective, some seem to be going backwards at various times. 

 

This explanation – this model – was far simpler than the one it replaced. Furthermore, it explained everything using only an understanding of the force due to gravity. One simple idea explained everything – and explained it more accurately than the previous model. 

 

It has parsimony and beauty.  It sits well. As Occam (Occam’s Razor) advanced, the simplest explanation is the most likely to be true. That is a guiding principle of science. 

 

Indeed, is this not a guiding principle for anyone wanting to find the truth? For detectives, the usual suspect is often guilty. 

 

Now, back to the zebra – and us humans. I grew up learning an explanation for human behavior from the Heidelberg Catechism. It asserts that humans were created good, but the disobedience of Adam and Eve brought death, and all humans became wicked, corrupt and prone to hate each other (Original Sin). But those who believe the Christian Gospel live a New Life free from the bondage of sin and bringing forth fruits of righteousness. 

 

This model offers some challenges. Is there a clear difference in behavior among those with the New Life? Also, how does this model explain the death and pain found among other animals? C.S. Lewis (The Problem of Pain) suggested that perhaps the same Evil Being who tempted humans to fall into sin had (before humans came on the scene) already corrupted the animals. That, of course, is extra-biblical, but give Lewis credit for wrestling with it. Given the model he was trying to defend, it’s one solution. 

 

But take my point: The model of human behavior offered by orthodox Christianity leaves much to be explained and gets rather messy and complicated in its attempt. 

 

Another model: Naturalism. As can be shown mathematically, a person who steps randomly to the left or right will stay centered about the original point. But if there is a wall hindering movement in one direction, the person’s random steps will eventually take them far in the other direction. 

 

 Similarly, the model built on naturalism predicts that life, begun at the wall of simplest-possible-living organisms, will – via randomness built on mutations – eventually advance to increasingly complex lifeforms. That’s in fact what we find in nature. 

 

The randomly mutated genes which outcompete their colleagues continue on – causing animals to behave as we observe in zebras, lions, and – yes – humans. Indeed, watch the squirrels around town compete and fight over food, mates, and territory. Then watch the evening news. 

 

Does this prove naturalism true?  Nope – but it’s worth pondering. 

Is more better?

  

HS #111 2024.10.10

 

Is More Better?

 

Don’t get me wrong. I’m a pickleball player. I play lots. So it might seem surprising that I’m against Park Township constructing ten more pickleball courts at the site of the former airport in Park Township. It’s just that I’ve learned from experience that more of a good thing is not necessarily better. Sometimes it’s a negative. 

 

This runs counter to the American mindset. As I write this, I’m watching the story of the journey of Lewis and Clark on Story Television (great channel – available at 54.4 with antennae). Washington, Jefferson – our founding leaders wanted more. More land, more room, more opportunities. Daniel Boone moved to Kentucky when he felt crowded by a neighbor 20 miles away. 

 

This mindset runs through modern affluent Americans. Ever notice how easy it is to spot a group of Americans at international airports? How do we give ourselves away? We walk in groups all spread out, we swing our arms wide, we speak loudly. We take up lots of room. 

 

Check out Laketown Beach south of Holland at the end of 142^nd Ave.  Looking in either direction, you’ll see an army of signs warning everyone that they are trespassing on private land. The houses aren’t even visible, but the land owners want their expanse to themselves. The beach has been there for thousands of years – shared by Native Americans and wild animals, but now it is owned by us who came late to the North American continent and claim the land for ourselves. Stay off – give us our room. 

 

“More is better” is seen as one walks into many West Michigan churches. Sanctuaries have been replaced by auditoriums. Know the difference? If you’ve ever gone there alone to reflect, pray and meditate because it has an ambience which suggests God’s presence, that’s a sanctuary. There are a few in Holland. Some old, such as Grace Episcopal Church, some new such as the chapel of Western Theological Seminary. Zeeland has one at 2^nd Reformed Church. But increasingly, churches instead have large auditoriums to hold lots of people in spacious comfort. 

 

Indeed, visiting one such church, the entrance hallway/mingling area is so large that there is no need to be close to anyone you don’t know.  Doing so feels like needlessly standing next to a person in an elevator – it is invading their space. Entering the auditorium, there are circular tables and chairs, so families can sit together with no need to mingle with strangers. Thus copious space hinders fellowship. 

 

Sitting in the center of Holland is Hope College which shows this principle in spades. Hope is a residential college, most students living on campus or within easy walking distance. Unlike GVSU for example, there is little need for expansive lounges for commuting students who drive to campus and need a place to relax between classes. But Hope has lounges in abundance – several more large ones in their two newest buildings. More yet to come in the 8^th street expansion. The more the better; no need to sit close to anyone. Living on East 12^th Street, Hope has five training rooms within 1000 feet of me. If one is good, five are better. Newest residence accommodations at Cook Village are palatial. 

 

Before Hope College tore down the old Nykerk Hall for a spacious lounge-filled building, students used to arrive 45 minutes early to get a seat for their homegrown VanderProv comedy show. Crowded in the small auditorium, every seat full and aisles bursting, the students found ways to amuse themselves until the show began. By the time it did, they were primed and ready. The limited, tight space added immensely to the atmosphere and fun.

 

Yes, we Americans behave like electrons on a conducting sphere – we spread out from each other as far as possible. We want room – more room, even though experience shows that the opposite often is more satisfying. How fun is it to see the opening of a movie in an empty theatre? Why do young people love rock concerts where they are squeezed together?  

 

So, back to the pickleball courts, what’s wrong with having crowded courts with a few people waiting - visiting and getting to know each other? Also, it’s easier to find fellow players around town without so many court locations. Why the need for ten more when the present courts around Holland are easily handling the demand with ample free time and courts available? Too much of a good thing isn’t always better. 

 

 

What's in a Name? A rose . . .

  

HS #110 2024.9.12

What’s in a Name? A Rose . . . 

 

What the f**k are you reading? I assume you fully understand the sentence I just wrote. A thought – in particular, a word - has passed surely and exactly from my mind to yours. You may well have mouthed the word as you read. All legit since I didn’t include the middle two letters. But writing the actual word is taboo – in fact not even allowed. The word itself has potency even more than its meaning. 

 

We make similar use of the phrase “the n-word.” We use that phrase since the word it replaces has a power of its own. Somehow, just making those vibrations in the air, just putting the ink in that particular pattern of letters is the source of the trouble. When I was in junior high, one vocabulary word I learned was “niggardly” – meaning miserly. It has an entirely different etymology from the racial slur, but because of the similarity of pronunciation, its use causes trouble. 

Interesting,  a word itself may be more objectionable than what it references. My mother wryly observed that the prudish Dutch of her home in West Michigan were more offended by the “f-bomb” word than by the action. Remember the lyric from the musical “My Fair Lady”? Professor Henry Higgins observed, “The French don’t care what they do actually, as long as they pronounce it correctly.” 

 

“Sticks and stone may break my bones, but words will never hurt me!” is a bit of childhood wisdom which is, in fact, false. Certain words – just the words themselves – pack a punch. 

 

Some words originally considered legit become tainted because they are associated with things which, if we are honest with ourselves, are undesirable. Hence “graveyard” has been replaced by “cemetery.”  “Nursing homes” are now called “Senior Assisted Living.” “Crippled” became “handicapped” became “disabled” became “challenged.” Most recently (on NPR, of course) I heard another phrase, “adaptive sports” to signify sports which have been adapted via the use of tools so that folks with a disability can participate.  And yet a new name “parasports” has been coined to refer to them. 

 

When I first came to teach at Hope College, I also took the position of “Head Resident” in a “dormitory.” But by the time I left five years later, I was a “Resident Director” in a “Residence Hall.” I often wondered if someone earned their Ph.D. in something or another by arguing for that change. 

 

The words we use date us and also sometimes show that which goes around comes around. My mother never changed from the phrase, “colored people” (a habit which rankled my father). I grew up with “Blacks” and “African Americans” with which I am comfortable. But, the current phrase, “people of color” becomes almost indistinguishable (in terminology but not in effect) from mom’s generation. 

 

I recently read that many of the common names of animals and plants are being renamed so as not to offend. “Gypsy moth” is now “spongy moth.” The Audubon Society was involved in many of the changes, but then, ironically, it got caught in its own quagmire because of its own name;  John James Audubon apparently owned and sold slaves. 

 

Blood-toil-tears-and-sweat Winston Churchill appreciated the power of words. The original code names for the British D-Day beaches were Gold, Sword, and Jelly (as in goldfish, swordfish, and jellyfish). But Churchill, a veteran himself, thought the word “jelly” had insufficient dignity to inspire courage and sacrifice, so he renamed it “Juno.” 

 

Of course Shakespeare, the master of words, weighed in. “What’s in a name? That which we call a rose by any other word would smell as sweet.” Yes indeed, Juliet knew all too well that if the last name of her lover had been “Smith” rather than “Montague” life would have been – rosy. She fell in love with the man without knowing his name, while her parents rejected the name without knowing the man. 

 

Shakespeare may not have been surprised had he recalled the Jewish Torah – the Third Commandment in particular. The other commandments forbid harmful activity, but the Third concerns itself with the proper use of words – giving due honor to the word representing the creator Yahweh.  Indeed, John the Apostle took this understanding even further as he began his gospel, “In the beginning was the Word . . .  and the Word became flesh . . “

 

Surely, words clearly have a power – even a life – of their own. 

Why elephants have big ears

 HS #109 2024.8.8

 

Why Elephants Have Big Ears

 

This time of year finds me at my cabin in the Upper Peninsula surrounded by nature. And appreciating nature is enhanced by understanding the underlying mathematics and physics. 

 

For example, Einstein was once walking on a beach with a friend and asked him, “Why do our feet sink into the dry sand, and also into the sand under the water, but the moist sand at the water’s edge holds firm? Einstein then explained that the water molecules in the moist sand form a molecular table-top of sorts giving rise to surface tension.  Dry sand has no such water, and sand under the water has water above it as well, so there is no “table-top.” This is also why I see lots of spiders and other bugs skimming along the surface of the water when I kayak. 

 

Here's another one: Why do the waves easily move sand about, but larger stones and boulders remain still? “They are heavier” is a ready reply, but whether the rock moves depends on the rock’s weight compared to the force of the moving water on its surface. As the rock grows, both its weight and its surface area increase, but (here’s the key!) the weight grows more than the surface area. 

 

This is apparent for anyone (such as I) who built things with square blocks as a child. Suppose you have a bunch of one-inch cubic blocks. One block by itself has a volume of 1 cubic inch, and a total surface area of 6 square inches. Agreed? So the ratio of volume to surface area is 1:6.  Now let’s make the cube bigger: 2 by 2 by 2. The volume is now 8 cubic inches, and the total surface area is 6 x 4 = 24 square inches. So the ratio of volume to surface area is 8:24 = 1:3. 

 

What happens when it grows to 6 by 6 by 6? Now (calculate), the volume is 6 x 6 x 6 AND the surface area is 6 x 6 x 6, so the ratio of volume to surface area is 1:1. 

 

One more: A 10 by 10 by 10 cube has a volume of 1000, and surface area of 600, so now the ratio of volume to surface area is 1000:600 = 5:3.  

 

See what is happening? As the object grows (keeping the same shape) the ratio of its volume to its surface area increases. That is, although they both grow, the volume grows more than the surface area. 

 

So, as a rock increases in size keeping the same shape, its volume (hence its weight) grows faster than its surface area – on which the water pushes. Eventually, the weight-to-push ratio becomes so large that the boulder doesn’t budge. 

 

Another example: Why do elephants have big ears? Every cell in a mammal’s body is a little furnace, giving off heat. So the amount of heat produced by a mammal is proportional to its overall volume. 

 

Mammal’s release heat through their skin which covers their body. So the amount of heat released is proportional to the animal’s surface area. For mammals of human size, the ratio of generated heat to released heat is about equal. But for large elephants, the generated heat due to their volume has overgrown their ability to shed their heat through the surface area. Thus, they need some extra surface area (without much volume). Hence the large floppy ears. 

 

Understand? Here’s a nature-question for you to answer using the same principle: Why do our cells divide as they grow? Why do they stay so small? 

 

Let me get you started. Our cells are living things which need food and oxygen to live. These are gained passively by letting them soak through the outer cell wall. There is no active pump, they just seep through. Thus the amount of nutrients and oxygen that a cell gets depends directly on its surface area. 

 

On the other hand, since everything inside the cell needs food and oxygen to live, the amount of food and oxygen that a cell NEEDS depends directly on the volume of the cell. 

 

Can you take it from here?  A small cell can get its food and oxygen through its cell wall at a sufficient rate to feed all the living material inside. But as it grows, the volume (hence the need) grows faster than the surface area (supply), so the cell divides to reestablish the correct ratio. 

 

Neat! Go forth in wonder!

Holland and Chicago: Great Living in Sister Cities

  

HS #108 2024.7.11

 

Holland and Chicago: Great Living in Sister Cities

 

Do you remember Paul Harvey, the popular conservative radio personality who broadcast “The Rest of the Story” from Chicago?

 

Once, well into his 70s, he was asked, “Why stay in Chicago instead of broadcasting from some warm southern city?” His answer: “NYC with Wall Street thinks it’s the center of things. So does Washington DC, and L.A. struts its importance as entertainment capital. But when I’m inside the Loop of Chicago, I’m at the productive heart of our nation and I can feel its pulse.”  

 

I agree. Once I spent a day in Chicago sitting by Buckingham Fountain and the Bean, taking a tour of the Chicago River, and strolling the shoreline and Navy Pier. Riding back to Holland on Amtrack, I wrote Chicago’s Chamber of Commerce, “A great city is one after which spending a day touring, one leaves refreshed and energized. By that measure, Chicago is a great city.” 

 

And that is why Holland, Chicago’s little sister, is also a great city on a smaller scale.  

 

These cities lying on the shore of Lake Michigan have much in common. Historically, on October 8, 1871, after a dry, windy stretch of weather, they both burned to the ground.  And as a phoenix from the ashes, they both rose to new prominence. 

 

They both are abounding in the arts. Chicago has its theatres and symphony, and The Bean. Holland has the world class Jack Miller Music Center, and the Kruizenga Art Museum surrounded by the Nyenhuis Sculpture Garden, not to mention Kollen Park’s outdoor shell at which hundreds gather on Tuesday evenings for the American Legion Band. 

 

Both are also grounded in heavy industry giving foundation and backbone to their existence. When I ride my bike past Padnos, I find myself proud that Holland’s heavy industry has the  mission of recycling earth’s resources.

 

Chicago has its outstanding University of Chicago. Prominently engraved at the front of its John D. Rockefeller Chapel one finds his words, “As the spirit of religion should penetrate and control the University,so that building which represents religion ought to be the central and
dominant feature of the University group. Thus, it will be proclaimed that the University in its ideal isdominated by the spirit of religion, all its departments are inspired by religious feeling, and its work isdirected to the highest ends.” Holland’s Hope College embodies that in structure (Dimnent Chapel) and in spirit. 

 

Both cities have their own newspapers which inform and well-serve their citizenry. 

 

But mostly, Chicago and Holland are similar in offering great living. 

 

What other small Midwest city offers a vibrant heated-sidewalk downtown with local eateries, a cheese-lover’s Mario’s Pizza, one of the best Aquatic Centers in the nation, an Outdoor Discovery Center with innovative educational opportunities, a Farmers Market that attracts folk even from Indiana, Evergreen Commons for seniors, an abundance of pickleball courts for enthusiasts of all ages, a first-rate library and city hall, a beautiful central park (albeit with a less-than-impressive fountain) and two weeks of hosting the nation to Tulip Time, our nation’s third largest city celebration. Impressive list. 

 

More?  Bountiful beaches. Holland’s flat topography perfect for riding bikes around town. Even the nearby cities of Grand Rapids and Kalamazoo are filled with hills. Also, being on the extreme western side of a time zone. The sun goes down at about the same time in Chicago, but there it’s 8:30 p.m., while here it’s 9:30 p.m. giving us an extra hour of sunlight in the evening. 

 

I recently returned from a hiking-camping-hosteling trip to Maine and the Canadian Maritime provinces. Granted, they have a richer history - if you haven’t seen FDR’s retreat home on Campobello Island, the only jointly managed national park in the world, or the Titanic gravestones in Halifax, put those on a future vacation list. But the street performers on Halifax’s oceanfront were no better than Holland’s Thursday evening 8^th Street performers. The forests and ocean views of Acadia were reminiscent of the beauty of forest and water in West Michigan (without the salt and jellyfish). And with Maine’s median home price at $395,000, Canadian gas at $5/gallon, and high-priced groceries, living the good life in Holland is easier on the wallet. 

 

Finally, as the many booths at the recent annual PRIDE celebration in Centennial Park demonstrated, Holland is filled with organizations and churches which are available to help its residents live life to the fullest. Holland – a good city, a good home. 

 

 

 

 

Greatness and Vulnerability

  

HS #107 2024.6.13

 

Greatness and Vulnerability

 

In today’s column I discuss one of the most profoundly true sayings I have ever known. I don’t remember where I heard it, but it has stayed with me for decades. 

 

A man is as great as his noblest ambition, as weak as his controlling desire. 

 

I use the sexist language because i) that’s the way I heard it, ii) it packs a bigger punch, iii) I suspect (but don’t know) that it may apply more to men than to women. I will be talking primarily about men. 

 

First, a mathematical explanation. Consider a beam with dimensions of 12 feet by 10 inches by ½ inch which is being used to support a 12-foot deck or bridge. As I explain to my calculus classes, the strength of the board is proportional to its width and proportional to the square of its height. Mathematically,  strength = width x height x height. Thus the height is more important. Suppose the board is “flat” so that its width is 10 inch and height is ½ inch, enabling it to hold 100 pounds. Then if it is turned so that the height is 10 inches and the width is ½ inch, it could support a ton – 2000 pounds! Try the experiment with a ruler or yardstick. Held flat, a small force will bend or crack it. But turned so that it has a greater height, and it is rigid and unbreakable.  

 

Thus the same object is strong or weak depending on its position – on the situation.  

 

True also with people. 

 

Countless people come to mind – both those I know personally, and the famous and well known. I’m guessing for you too. 

 

One such person is Bill Cosby. I’m confident that he had a genuine, heartfelt  passion for helping  African American young men live better lives. He talked to them and about them regularly. “The Cosby Show”, I’m guessing, was one way he hoped of modelling good living. However, he also had a passion for sex – unrequited sex in particular – and this was, of course, his downfall. 

 

General Petraeus, Elliot Spitzer, Governor Cuomo, President Clinton all come to mind. The Me-Too movement caught many of them. Many others could have been caught – JFK, FDR, MLK Jr. Many of these had noble ambitions. Truly. Nothing insincere or hypocritical about them. They weren’t pretending to be good. But, turn the board over and what is strong becomes vulnerable. Noble ambitions, controlling desires. 

 

One of my Biblical heroes, King David from the Old Testament, had no trouble defeating the massive Philistine warrior, Goliath. He easily routed his enemies and stayed true of intention when challenged by his associates (King Saul). He was fearless and pure. 

 

But, dang it, as he got older – perhaps as he hit 50 – he got soft. His self-discipline sagged. The temptations and weaknesses which he controlled as a fighting youth were exposed. And he blew it – big time. 

 

If Nathan the prophet had come to David accusing him of breaking the 6^th and 7^th commandments (murder and adultery), David would have likely yawned. But Nathan hit David’s soft spot. Hearing Nathan describe a rich man who killed a poor man’s one beloved lamb for dinner rather than take from his own flock, the former shepherd boy exclaimed in anger, “That man shall surely die!” In a scene similar to the climax of “A Few Good Men”, Nathan counters, “Thou art the man!” The heart-rending 51^st Psalm is the result. 

 

Yes indeed, we get soft as we age. The disciple John (I John 2: 16-17) lists i) the lust of the eyes, ii) the lust of the flesh, iii) the pride of life as temptations that mess us up. Indeed, sex, money, pride – not to mention drugs, alcohol, and other traps ensnare. Like David, they often hit in middle age when we get comfortable and lose our edge and our focus. 

 

What can be done? 

 

Don’t be quick to judge. The point of the quote is that BOTH are true parts of the same person – the greatness and the weakness.  And whether a person gets snared is often due to circumstances. Luck. One reason I appreciate helping those in prison is that I realize many there are like the rest of us – except they got caught. 

 

Realize we all have our own weak spots, our own vulnerabilities. To think that one is immune because his is different from others is setting oneself for failure. Be on guard. 

Is Mathematics Invented or Discovered?

  

HS #106 2024.5.9

 

Is Mathematics Invented or Discovered? 

 

Occasionally a reader suggests a topic for my column as with the above title.  My thanks. 

 

This question is important because it applies to more than mathematics. For example, did Michelangelo create (invent) David from a block of marble or discover David in the marble? We typically think of artists using their imagination to create their art, but Michelangelo thought differently. He claimed, “The sculpture is already complete within the marble block before I start my work. It is already there, I just have to chisel away the superfluous material.”  So David was in the block – waiting to be discovered and released. This makes Michelangelo’s sculpture, “Slaves” especially poignant. The figures are only partially carved from the marble. The rest of the slaves’ bodies were not released – they stayed enslaved in the marble block. 

 

It also applies to moral truth. Do we humans invent our own ethical systems through the creative and natural use of our empathy, or do we discover morals truths platonically existing outside our natural world – perhaps given to us by God?

 

Let’s reflect on the meaning of those two words. In my living room I have a favorite piece of petrified wood. It was discovered. In my closet is the board game Monopoly. That game was invented. Which of these two words best describes how we came upon mathematics? 

 

Did not Pythagoras discover that the lengths of a right triangle obey “A squared plus B squared equals C squared”? Could he have chosen otherwise? Seems not. Seven is a prime number because this many things $-$-$-$-$-$-$ can’t be divided into equal piles. Wasn’t this true before humans existed – indeed, before the universe existed? Can 2 plus 3 equal anything but 5? Would a first-grade teacher allow a creative student to answer 7? 

 

So it certainly seems that mathematical truths exist independent of humans and were there to be discovered. 

 

But not so fast. On the other hand, some mathematicians claim that doing math is like playing a game. Once you invent the game of chess, for example, there are all sorts of questions to ask: Can a knight be manipulated to land on any square? What is the fewest number of moves needed to win? Moreover, if someone wishes, they can change the rules to invent a modified game. 

 

Similarly, until the nineteenth century, Euclid’s geometry was considered the one true geometry discovered by ancient humans and organized by Euclid. Then Gauss and others started playing around with the Euclid’s five foundational axioms. By changing them, mathematicians invented new geometries to play with - very much like altering the rules of a board game. Some of these new geometries were fun to play but useless, while another was used by Einstein in formulating his Theory of Relativity, and yet another describes the geometry of the globe on which we live. Useful, but ostensibly invented by humans.

 

So is mathematics invented or discovered? 

 

The 19^th century mathematician, Leopold Kronecker, effectively answered “Both!” Referring to the simple integers {. . . -3, -2, -1, 0,  1,2, 3, . . . }, he famously claimed, “God made the integers, all the rest is the work of man.” That is, the foundational truths already exist for humans to discover. But once discovered, humans can use their imagination to create more. Much like baking bread – the recipe may be your own invention, but your choices are limited by the (discovered) inherent properties of the ingredients. Every yeast bread recipe must include time for it to rise. 

 

The great 20^th century mathematician Paul Erdos likely agreed. Every living mathematician has an “Erdos number”: 1 if they published a paper with Erdos, 2 if they published with someone who published with Erdos, etc.  (My Erdos Number is 4.) Erdos traveled the globe asking mathematical questions and solving mathematical theorems (visiting Hope College a couple times). When an aspiring mathematician showed Erdos a new mathematical proof, Erdos sometimes gave his supreme compliment, “That one is from The Book.” That is, certain proofs were so beautiful – so much like Michelangelo’s David or Beethoven’s Ninth Symphony – that Erdos claimed they had been discovered from God’s book of proofs rather than just invented by human imagination. 

 

Don’t we think the same? Who can listen to Beethoven’s Ode to Joy without sensing that this is a piece discovered from “God’s Book”.  In contrast, the music written by the high school rock band in your neighbor’s garage - most likely invented.