God, Mathematics, and Beauty

I’ve wondered recently about beauty. Why are some things beautiful and other things aren’t? Why is it that a thing can be beautiful to one person, but hideous to another? Why is it that beauty often defies definition, yet we know exactly what it means? How come immaterial things can be beautiful?

One oft-cited immaterial bearer of beauty is mathematics. Physicists and mathematicians reportedly wept over the beauty of Einstein’s proofs. Paul Erdős, the late mathematician, has said, “Why are numbers beautiful? It’s like asking why Beethoven’s Ninth Symphony is beautiful. If you don’t see why, someone can’t tell you. I know numbers are beautiful. If they aren’t beautiful, nothing is.”

The sublime beauty of mathematics is lost on those of us who have not paid the high price of admission to join the elite fraternity that includes men like Isaac Newton, John Nash, and countless others you’ve never heard of. This makes me sad, because it doesn’t take long before mathematicians turn into theologians when they behold the elegance of the way numbers relate to one another.

Exhibit A: Euler’s Identity. It is simply this: eiπ+1=0. Impressed? Are you slack-jawed at the astonishing beauty of this equation? Few people are, but blessed are those who “get it,” I say. A mathematics professor at MIT, an atheist, has said of Euler’s Identity, “There is no God, but if there were, this formula would be proof of his existence.” I wish I could appreciate that. I feel like I’m missing out.

Erdős, also an atheist, said, “God may not play dice with the universe, but something strange is going on with the prime numbers.” Here’s what he means: look at this picture of the prime numbers, plotted graphically. The white dots are primes; the black dots are non-primes. Notice a pattern? Click the image to see all the primes from 1 to 1,299,827 plotted like this.

Prime Numbers

Why should prime numbers line up like this? When numbers—which are uncreated and necessary (in the sense of “it could not be otherwise”)—exhibit an aesthetic like this, I can understand why mathematicians turn into theologians. Galileo reportedly claimed that “mathematics is the language with which God wrote the universe.”

I have a faint idea of why he might say such a thing. But I daresay a musician could say the same thing about his art; C.S. Lewis had Aslan sing Narnia into existence. Similar claims could be advanced by a programmer or a painter or any manner of craftsman, I suppose. Whatever form beauty takes for a person, it stirs within the soul a desire for the One who possesses beauty without limit.

(Before we leave Galileo, let me digress from mathematics into astronomy to present Spiral Galaxy IC342. As @BadAstronomer put it, “If that doesn’t impress you, close this window, shut down your computer, go find a nice hole in the ground and lie down. You have no pulse.” And Yuri Gagarin went up there and claimed he didn’t see God. Like Ellie Arroway said in Contact, “They should have sent a poet.”)

Spiral Galaxy IC342

Spiral Galaxy IC342

In the end, I think beauty is an apologetic for God’s existence, a signal of transcendence that leads us home. As Lewis reasoned, “If I find in myself a desire which no experience in this world can satisfy, the most probable explanation is that I was made for another world.” We desire beauty and we never tire of it; we never have our fill. Our appetite for beauty is never satisfied in this world, so the most probable explanation is that the beauty we desire resides elsewhere.

Augustine knew where to find it: “You have made us for Yourself, and our hearts are restless until they rest in Thee.”

See also: God by the Numbers

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Life is a highway? More like mowing a lawn.

I love being able to devote long blocks of time to one thing. Interruptions really throw me. So the idea that “life is a highway” sounds great — cruise control, no turns, put it in high gear and leave it there, and make lots of progress really fast.

Unfortunately, real life is more like mowing my lawn. I might get 100 feet of straightaway now and then, but mostly it’s a matter of frequent turns with an inadequate turning radius, lots of noise, bumps, backing up & moving forward, and generally inconvenient monotony for long periods of time.

However…

What about a trucker who sees nothing but mile after mile of asphalt, stretching as far as the eye can see? I’m sure the thought of just mowing his lawn must sound delightful. What about the guy who just bought a sports coupe and finds himself getting bored with seeing how fast it can go? Taking some corners with a finely engineered suspension would probably sound really attractive.

We’re designed to be good at lots of things, not great at just one thing.

Where’s all this coming from? I got to thinking about this blog… should I just focus on programming? Or religion? Or maybe entertainment… or science geek stuff. But the thing is, I’m about all that stuff. The way I write software is informed by the way I think through my faith, and vice-versa. The things I find entertaining are often scientific, and I’m often entertained by learning about science and technology. It’s all about being an authentic, well-integrated person.

What’s more, you never know how worlds will collide. It’s perhaps odd that I, an evangelical Christian, get such a kick out of so much stuff that’s so appealing to atheists. I love reading tweets & blogs from folks like @BadAstronomer and the @MythBusters crew. Or consider this thoughtful riff from Penn Jillette:

So, without apology, this blog isn’t going to be a highway of single-subject information; it’s more like mowing the lawn of my scary little mind, weeds and all. I hope that’s more interesting and makes my little corner of the internet a little more attractive too.

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I’m Making This Up As I Go (Just Like I Planned)

Thoughts on serendipity and planning…

Happy As A Dog Chasing Cars

My favorite part of The Dark Knight is when the Joker is talking to Harvey Dent in the hospital, and he says: “Do I really look like a guy with a plan? You know what I am? I’m a dog chasing cars. I wouldn’t know what to do with one if I caught it! You know, I just DO things… I’m not a schemer. I try to show the schemers how pathetic their attempts to control things really are.”

And therein lies the best career advice I could possibly dispense: just DO things.  Chase after the things that interest you and make you happy.  Stop acting like you have a set path, because you don’t.  No one does.  You shouldn’t be trying to check off the boxes of life; they aren’t real and they were created by other people, not you.  There is no explicit path I’m following, and I’m not walking in anyone else’s footsteps.  I’m making it up as I go.

(via Charlie Hoehn)

Brilliant or insane? It depends on what interests you and what makes you happy. There’s a big difference between “do what makes you happy” and Augustine’s counsel to “Love God and do as you please.” The latter offers healthy constraints. The former endorses the likes of Hannibal Lecter. But there is a healthy dose of wisdom in Mr. Hoehn’s advice. (See also Just Do Something.)

Planning is Useless, But Do It Anyway

Plans are worthless, but planning is everything. There is a very great distinction because when you are planning for an emergency you must start with this one thing: the very definition of “emergency” is that it is unexpected, therefore it is not going to happen the way you are planning.

Dwight D. Eisenhower

Nothing ever goes according to plan, but planning gives you the mental categories for handling the way things actually do go. It reminds me of college, when I was sometimes permitted to bring a one-page crib sheet to some exams. Invariably, I never used the crib sheets during the exams: the act of preparing it got me ready for whatever the test threw at me.

Build One To Throw Away

The management question, therefore, is not whether to build a pilot system and throw it away. You will do that… Hence plan to throw one away; you will, anyhow.

Fred Brooks

That’s great advice for software engineering, but not so great for life. You only get one of these things… you don’t want to end up like this:

Mistakes

It could be that the purpose of your life is only to serve as a warning to others.

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A Heaven Worth Looking Forward To

“I have come home at last! This is my real country! I belong here. This is the land I have been looking for all my life, though I never knew it till now. The reason why we loved the old Narnia is that it sometimes looked a little like this… Come further up, come further in!”

— C.S. Lewis, The Last Battle

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Why Software Defies Intuition (and why my wife “gets it” now)

Let’s say you’re creating a website. Your customer comes with his hat in his hand, saying, “I know you built out the whole website using Comic Sans, but now we need the whole thing redone using Arial. It turns out Comic Sans makes it look like we’re running a kindergarten or something. Just let me know how long it’s going to take and I’ll make sure we get the funding to redo the whole thing.”

You reply with good news. “No problem, it’ll just take a minute. There’s this thing called a ‘stylesheet’ that controls the fonts and colors for the whole site. I’ll just change it there and we’ll be done.” Your customer worships you.

The next day, your customer says, “Oh, one more thing. On the data entry page, where the user puts in all their information… we just need to add a date of birth there. And don’t let them use the ‘chat’ feature if they’re under 16.”

“Whoa, cowboy,” you reply. “That’s going to take a couple of weeks.”

“How come? Yesterday you changed the whole site in under a minute! This only adds one thing to the data entry form!”

(Here’s where my wife said, “Oh, I get it now.”)

“True. But I need to add a field in the database for the user’s date of birth. I need to change all the code that handles user input on that form to put the date of birth in the right field in the database. Anything that shows user information needs to get that date of birth out of the database now. We also need to make sure they don’t put in invalid dates, like ‘February 31’ or something. And the biggest thing is changing the whole ‘chat’ feature so that it doesn’t allow the user access if their date of birth is less than 16 years ago.”

What your customer says next determines whether you hate your job or not.

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A warehouse of beliefs, or a workshop of faith?

D. A. Carson:

Christian beliefs are not to be stacked in the warehouse of the mind; they are to be handled and applied to the challenges of life and discipleship.

How Long, O Lord? Reflections on Suffering and Evil, p. 20

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If You Live Long Enough, You Will Suffer

Suffering shouldn’t surprise me anymore, but it still does.

Word came this morning that a great guy at church has cancer. Bad cancer.

Earlier this month, my wife’s best friend lost her dad to pancreatic cancer. There was a devastating earthquake in Haiti. Going back to Thanksgiving, there was a young family driving home when a highway accident claimed a 3-year-old girl’s life and her mother’s ability to walk. There’s @mattchandler74 and his brain cancer. There’s little Kate McRae. I could go on, but I don’t want to.

As a thoughtful Christian, I have to be able to make sense of that most difficult of questions: how do you reconcile the reality of suffering and evil with the existence of an all-good, all-powerful God? At the risk of sounding academic and sterile, I’m going to address that the only way I know how: by breaking it down. I see two questions there.

The first is philosophical: are those two ideas even compatible? The short answer is yes. First, on God’s existence in the first place: If there is no God, there can be no such thing as real suffering and real evil; they are just ideas we’ve created that have no grounding in objective reality (see yesterday’s post, Ideas Have Consequences, for more on that).

Second, if God is all-good, does his tolerance of suffering and evil prove that he is not all-powerful? Conversely, if he is all-powerful, does his tolerance of suffering and evil prove that he is not all-good? The Christian worldview supplies defeaters to both objections. The Bible’s storyline tells us about a God who created a good universe with good people who used their freedom to rebel against him: the fact that he didn’t wipe out the rebels straight away speaks to his mercy and patience; the fact that he came in the flesh to atone for man’s rebellion by living a perfect life, dying for the crimes of others, and ultimately rising from the dead speaks to his grace and power; and the advance warning that he is going to return to set everything straight one day speaks to his justice. Whether you like that story or not, it takes away the opportunity to say that suffering and evil logically disproves God’s simultaneous goodness and power.

That’s the philosophical answer. But what do you say to the existential question? As the atheist philosopher Bertrand Russell famously asked, “what are you going to say as you kneel next to a dying child?”

Bringing logic to bear on that situation is, for most people, simply a case study in using the wrong tool for the job. Instead, comfort comes from understanding that God is familiar with suffering through first-hand experience of the real thing.

Jesus was not just a man; he was God. And he was not just God; he was a man. This is the most mind-boggling mystery of the Christian faith to me. Everything that is true about mankind is true about Jesus. And everything that is true about God is true about Jesus. But in his humanity, he didn’t “cheat” by playing his “God card” whenever things got tough. People suffered and died all around him. He lost people close to him. And eventually, when it was his turn to suffer and die, he didn’t rage against it as though something disruptive to the whole universe were happening.

The best explanation I’ve ever heard about these questions comes from D. A. Carson in his two messages titled On Being Prepared for Suffering and Evil (part 1, part 2). He begins with these words:

If you live long enough, you will suffer. (And these two talks go downhill from there.) The only alternative is not to live long enough. If you live long enough, you will face bereavement, severe illness, loss, disappointment; you, or your children, or your children’s children, will face loss, death, war… suffering.

When Jesus came in the flesh, he knew those sobering facts better than we do, and he signed up for it all the same. There’s something about the fellowship of sufferings that speaks louder and more powerfully than any moral dilemma or logical challenge can do. So to answer Russell’s challenge, all I can offer in answer to the existential question is “Jesus understands.”

Thankfully, for now, despite all the tragedy that’s come to my attention, I do not find myself kneeling at the side of a dying child. For now, my job is to settle the questions that make “Jesus understands” worth anything as an answer: was he really who he claimed to be? Is he really the only way to get right with God? Does he offer something that no one else does? Do I need what he offers? Is this hope real, or just therapeutic wishful thinking? Is sin real, or just a useful fiction to make sense of all this? And maybe the ultimate question: is sin a big enough problem that it’s worth enduring all this evil and suffering to rescue as many people as possible from it?

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