Wednesday, June 16, 2010


Well, our last days at Woodstock have been full of packing what we need and getting rid of what we don't. The very real constraints of space and weight and their costs have made us sharpen our ideas of what is important among the piles of our papers and clothes and other junk which has become such a burden in the light of our impending move. It is refreshing and liberating, and a bit melancholy. I feel like Ma Joad sitting next to her wood stove, taking one last look and pushing into the flames those papers that need to not make the trip. Quite literally, as this process has included some actual pushing letters into the wood stove.

That is something special about traveling, is a more frequent need to let go, to evaluate. Sometimes I just want a big attic or a garage with the potential to hold on to any box of papers I simply do not want to decide about. And other times I enjoy the healthy feeling of being rid.

And the leaving is very anticlimactic as we say goodbyes and then see people a few more times, or don't say goodbye because we didn't realize we wouldn't run into somebody during these last few frantic days. C'est la vie.

Wednesday, June 9, 2010

5-star challenge: hailstone numbers

Luke asked why I stopped with the math contest questions. As he forms a strong percentage of recent commenters on this blog, I suppose I ought to humour him. The fact is, these questions are tricky to find. I don't want something that just amounts to boring computations, and I don't want something that can be artlessly mined from Google or WolframAlpha.

This is one of the recent 5* challenge problems I ran. It's tied to a set of sequences that could keep me (has kept me) busy for hours. It's not like useful math, it's more the sort that could be warmly amusing and deeply intriguing, the kind of thing I would be thankful for on a desert island.

A hailstone sequence is defined recursively by this equation:

an = { 3*(an-1)+1 if an-1 is odd; (an-1)/2 if an-1 is even}

For example, if we start with 10, the next term (because 10 is even) is 5, the next term (because 5 is odd) is 16, then 8, then 4, then 2, then 1, then 4, 2, 1, 4, 2, 1… for ever and ever. The shortest hailstone sequence starting with 10 and concluding with 1 is 10, 5, 16, 8, 4, 2, 1 and its length is seven.

Find the sum of all positive integers N such that the length of the shortest hailstone sequence starting with N and concluding with 1 is thirteen.

Thursday, June 3, 2010

brainy legos

Two Lego projects for your consideration:
A Lego printer
A Lego Rubik's Cube solver
Oh, the people on that internet. My own obsession with Legos was so much more primitive. The internet brings us all so frighteningly close to some properly obscure endeavors.

Tuesday, May 25, 2010

book: silence

I just finished reading Silence by Shusaku Endo. It was recommended to me by Bryan, an English teacher at my school who described it as one of the only Christian books he really likes for its literary value. It is a novel about Portuguese missionaries in Japan during the 1600's. Japan had outlawed Christianity and the missionaries who were caught were tortured and killed if they did not apostatize.

The novel explores the concept of inter-cultural missions and a claim that Japan's culture would simply not support Christianity as it was presented by the Europeans. Any Christianity that allegedly did take hold was corrupted and confused in translation. The priest Rodrigues steals into Japan to follow up on the reports that his mentor, an older priest, has defected and denied the faith.

My reaction to this book and my interpretation of the author's message has been so muddled, it was such a distressing story at times, and its value lies in a few bright details, a few words in the book that really seemed to make the story right. For much of the book, I could sense that the ending would determine if I joyed in the story or resented it, and that is how it was. But not just the ending, the few days after the ending, it is the pondering which has made me like this book.

The story painted a murky picture of the confused motives, futile hopes, and deniable victories of the Portuguese missionaries. And all the while, through all the pain, after all the sacrifice, God's silence.

The human events of Silence include as an element the claim that Christianity does not translate and should not be translated into certain cultures. This message of course is especially common in the academic world, but by people who also lean on absolute truth. They appeal to some sort of absolute truth to explain that Christianity absolutely cannot be absolutely true. They claim some sort of universally undeniable logic to say that Christianity cannot be undeniably universal. In the end the most common argument presented against Christianity is the failures of those who promote it, and the story shows the rejection of a Christianity that Christians have failed to make relevant.

In Silence, Endo invites the reader to ask: Can a truth exceed in power our ability to express it? Can God take imperfect human efforts and complete the statement? Can we afford to interpret God's silence as his inaction? Can we presume that our designs are the limit and the fullness of God's actions through us?

Monday, May 17, 2010

moving on

We are down to our last month in India. After a quick month in the USA, we will be heading off to Seoul, where I will teach at Yongsan International School. Joie and I are very excited about this new direction in our life. We will miss Woodstock and the people here and life in Redwood Cottage, where we have spent most of our last four years, most of our marriage, and most of our time with Will and Annie.

Monday, May 10, 2010

joie's songs

Joie just finished her CD! You can listen to her 10 songs or download them from her music page. She did a great job with it and I'm so blessed to have such a talented wife.

Friday, May 7, 2010

the doon valley

the rain

I had forgotten about Elijah. This morning I woke up to a drumming rain and a grumbling thunder that didn't stop. I was so deeply grateful for the rain, it means much more to me than it used to. In India on this mountain we have seen every year a dry season building up to the monsoon. Every year the rains come, every year the Lord provides. But before the rain, the dryness builds, the people grow strained, the land starts to die. Many years there are wildfires before the rain finally comes. Sometimes there are clouds that disappoint, or rain that stops after a minute or two. When the rain comes, it is a gift, it is life, it cleans and renews a dry land. When I hear these early rains on our tin roof in redwood cottage, I feel excited for every drop and trickle that soaks through between the dusty pebbles and into this thirsty land, I find myself praising God for his provision for this land. I never took the rain so personally.

It reminded me of Elijah, announcing the end of a severe drought, sending the thirsty servant seven times to look toward the sea, to six times stare wearily at a cloudless horizon before spotting a cloud the size of a man's hand. The hope and hopelessness of that poor servant, and the tension of thirst that so much of the world knows year after year as they wait for the rains. I suffer from a terrible memory, and I think that most of the time I spend waiting for refreshment I have indeed a very dry and distant notion of what refreshment must be, and it is generally better than what I thought I was waiting for.

Friday, April 9, 2010

the dark tower

I just finished reading The Dark Tower by C.S. Lewis. This was a tangent begun serendipitously whilst I was waiting to locate a copy of The Last Battle, to finish my recent trip through the Narnia books. I love his writing, he gives his words so much more meaning than most of us can.

The Dark Tower was gripping from the very first page, promising to be a philosophical story about time travel and souls of men, featuring Dr. Elwin Ransom from the space trilogy. The story centers around a "chronoscope" that reveals to a few professors a sinister semi-parallel Cambridge in some other time. In the end I was sad to find the manuscript come to an abrupt stopping point. Lewis just stopped writing it, apparently not liking it or not knowing how to finish it.

The story (what there was) was a pretty good read, but more along the lines of That Hideous Strength, somewhat disturbing, but with an underlying theme of redemption and clarity. Not as cheery as some of the Narnia books, but rather intriguing. Mostly I was delighted to have found another book with Ransom, it was much like the time I discovered The Club of Queer Trades, featuring another G.K. Chesterton detective that I hadn't known about.

The unfinished story is a perplexing animal of literature, and yet it stands to reason that every great author must leave a few. Some writing is immortalized by publication, but what of that writing that never fully happened? It wasn't really approved and sent out by the writer, does it even count? One could hardly hold the writer responsible if the book did not meet expectations. And yet it was written, and he did hang on to it, perhaps letting it inspire his later books, perhaps waiting to someday return to it. It reminded me of Michelangelo's David statue in Florence, surrounded by half a dozen other huge blocks of marble with partial figures trying to emerge.

Wednesday, April 7, 2010

biblical mathematics

Something got me thinking about mathematics and the Christian world view, and about being a Christian math teacher. I have blogged a bit about this before here.

Ecclesiastes 3:11 tells us that God has set eternity in the hearts of men. This reminder is illuminating as we consider the pursuit of mathematics from a Biblical world view. There are evidences of the eternity in our hearts all around us in the way people live their lives, striving to be close to something bigger, something more permanent, something less bound by the temporal cages that define the edges of our existence.

Our God has created us with inquisitive and creative minds that are hard-wired to pursue the infinite, to wonder about our Maker, to ponder eternity. Mathematics has been moved forward throughout history not by practical people but by seekers and worshippers, artists and philosophers, obsessed, committed, awestruck, determined, half-crazed and wild-eyed people who gave their lives to grasp at the fringe of the robes of the only One who can explain the eternity residing in their hearts.

Many students eventually ask, "Why do people care about math?" and we often fail to dignify this, we respond by explaining that math is used to decide how much grass seed you should buy for your lawn, or to divide a box of cookies between you and your n-1 friends, or to calculate a tip at a restaurant. Or to find the volume of a cone or the number of Mondays in the eighteenth century or the roots of a quadratic equation or a way to ferry our foxes and geese safely across the river. Purely practical skills, right?  In short, we fail to dignify them.  We offer a few empty incentives to learn math, without really addressing their question. We respond almost defensively, as though mathematics would die without our help, or as though we are afraid our students will grow up and be unable to tip at restaurants.

It is in fact a great question deserving of our consideration: why DO people care about math? Instead of reducing the question to something harmless, let students confront it, let it intrigue and inspire them, let it be a context and a backdrop for the math that happens. Let us lead students to questions about knowledge and proof and logic. Let us ask them to think critically when they hear that science and religion should be separate—because they never have been separate. Teaching mathematics is inviting students to enjoy those gems of thought that have no earthly right to be in our minds, whose presence and beauty is only really explained by the eternity that God has set in our hearts.

Why did the Greeks revere a particular number as divine? Why did the Pythagoreans despair at the discovery of irrational numbers? Why did men like Newton give their lives to pursue mathematics and science in tormented seclusion? Why do people gamble? I am not talking merely about a tingly thrill of profundity that drives numerology and superstition, but also the real gripping and consuming rigor of mathematics, the desire to prove and to irrefutably establish the slightest fragment of logically solid ground. Why do we seek such?

If we want our students to think critically about the teaching and learning of mathematics, we might encourage them to look at the people who have been involved through the centuries. They will see that indeed mathematics is the product of earnest attempts to prove or disprove God's existence, to demonstrate the sufficiency of humanity or the greatness of God, to describe the beginning of the universe or predict its end, to map the heavens, to fathom knowledge itself, to experience a moment of the eternity that God has set in the hearts of men.

The Christian world view does offer an explanation for the eternity that we find in our hearts, and it does tell us that people will be obsessed with the study of mathematics and all manner of science. I am not convinced that a God-denying world view offers a satisfactory explanation of these pursuits or the vigor with which humans engage in these pursuits. The motive of math often goes unexplained. Much of Mathematics was built as an altar to an unknown god, and by teaching mathematics I can hope to bring glory to Him who has been worshipped as something unknown.

Wednesday, March 3, 2010

a novel thought

I just finished reading the Count of Monte Cristo by Alexandre Dumas. This is probably the longest book I have ever read, but except for a few slow parts it clipped along nicely. I enjoy reading novels and I like to write as well, but just to try to express myself, to formulate a thought that fails to satisfy until it is written. There certainly is a need to articulate. I have never really tried to write people.

You write to express yourself, sure, but it seems that you write a novel to express a person that lives within you whom you are not really excited to share, that you don't know how to share and to own. I have read novels that do not seem thus inspired, but many are. A person needs to write when once they realize that the thoughts and philosophies that define their beliefs are incongruous with one another and would make more sense if presented as the thoughts and philosophies of half a dozen distinct characters. The novel then is a stage for a writer to play out the people within him, the people who tolerate and despise and resent one another, who challenge and sharpen and object to one another. Each character in a novel is an experiment, the writer tries to prove or fears to allow that the person could exist in a life. In this way, the writer gives voice to his vengeance and mercy alike, his acceptance and rejection of life, his assurance of clarity and his confounded despair, dispensed through the voices of a sufficiently large number of people to make such a noise of thoughts believable to the reader, who in turn fancies himself to be more lucid and coherent than he perhaps is.

Sunday, February 28, 2010

will quotes

So I noticed recently that while nobody really seems interested in my posts about abstract computing theories, it is always a hit when I tell funny stories about Will.

Joie has been diligently teaching Will his numbers and his alphabet, but his progress is slow. Every once in a while he casually takes an interest in the games that we try to encourage and one of his favorite questions for us is, "What number starts with 'car'?"

A few days ago on the return trip from the bazaar we found ourselves about to start walking up Mullingar Hill, a long steep winding climb at the near end of our bazaar. The hill is quite steep and we frequently see drivers stop to let traffic pass and then need to roar their engine like a jet to get moving again. Guys on motorcycles sometimes have to make a few of their friends get off and walk up the hill. Will looked up at the coming climb with an air of weary discouragement. "I'm not gonna like this... upping thing," he said, all the more pathetic for being unable to come up with the word "hill".

That's my boy.

Friday, February 12, 2010

valentine candy

A few days ago we received a package of goodies from Mormor and Morfar. After Will and Annie got a taste of some Valentine's candy we put the box out of reach where they wouldn't be tempted beyond what they can handle, which isn't much. "Pappa, can I please have some more?" "No, you need to wait until later, you've had enough now". Then Will spotted in the package a pack of shiny alphabet stickers, which he recognized as ABCD's but was unable to read. "Pappa, what does this say?" Then Will tried to read it: "Mormor... loves... us... and... we... can... eat... whatever... we... want".

Thanks for the candy, it was a hit.

Sunday, February 7, 2010

game of life

John Conway's Game of Life is not actually a game as there are no players or winners or decisions. Rather, it is a sequence of states that result from a single set of initial conditions by employing a set of a few simple rules. The Game of Life was invented by Cambridge mathematician John Conway in 1970.

Thursday, January 28, 2010


Today my dear wife watched our kids while I went down the hill to Dehra Dun to try to track down George Everest's theodolite. It supposedly resides at the Survey of India museum, but it turns out you have to write a letter to the Survey General at least a few days ahead of time to humbly ask permission to visit the museum, and individuals are not given entry, only groups. I thought it made a lot of sense. I mean, without this reasonable measure of having to seek the permission of a government official, we would just have kids strolling into that museum like nobody's business, learning about cartography and history and who knows what else.

I was able to buy a few maps, which have generally been difficult to find here. A letter was not necessary to buy maps, thankfully. I got a fairly nice 1:10,000 map of Mussoorie and it has my house, Redwood Cottage, marked on it and listed on the margin. Our town is pretty big but has only a few roads, so it is not very descriptive to say what road you live on. Instead the houses have names.

As I do not have any theodolite pictures to post here, I thought I would take this opportunity to show a few pictures that I have encountered which I should have posted (or maybe I did and I'm too lazy to browse the back-issues) earlier. The blog is pretty demanding in that I sometimes have a picture I would like to share, but which is a bit on the mundane side and I can't think of a caption at the time and you know how I hate to bore my readers. To begin, here is a picture of me sitting next to the campfire with my kids. We enjoy our campfire and I will miss it when we leave.
Below is a green beetle.
Here is me in a skirt with Kyle at the staff banquet last June. A lungi, actually. They are very masculine in some cultures, you'll just have to take my word for it.
Here is a pattern in the domed gateway looking into the Taj Mahal enclosure. I wondered how they decided that they would need to go from six-point stars to five-point stars.
Here is my first view of the Taj Mahal, as seen from our hotel's rooftop restaurant.

Here is my darling Annie enjoying the matching dresses that Joie made for her and "baby Dechen".
And here are my Will and Annie in their fancy hats from Auntie Dot.

Thursday, January 14, 2010

jaipur - amber fort

Here Will is looking through one of the many little windows in the fort. It was a maze of a place with little rooms everywhere around a big courtyard. It made us all think of hide and seek.

Here I can see Will, Joie and Eleanor across the courtyard. I think Will is showing his claws here. Lately he has been showing his tiger claws and declaring in a fierce growling voice "I am Shere Khan! Give me my man-cub!"

Monday, January 4, 2010

taj ii

The taj is somewhat photogenic, to be sure.

pine marten

A week or so ago I finally got a nice shot at a pine marten. These animals live somewhere on the mountainside near our house, and we seem to spot them more often than most people. They are pretty shy though, so most of my pine marten pictures are a bit like those out-of-focus shots the loch ness monster. This one was more cooperative than usual.

Saturday, January 2, 2010

the taj mahal

We made it! The Burchells have finally seen the Taj Mahal. I have dozens of other pictures that look like the rest of the pictures that anyone reading this has probably seen. It is certainly a grand spectacle.