Outside the Box: From Sudoku to recreational mathematics

By Moristotle

Hardly anything calms me more than sitting down alone in a quiet place to solve a fresh Sudoku puzzle. At least, it calms me when I don’t screw up the puzzle. Let me recast the opening statement: Hardly anything calms me more than sitting down alone in a quiet place and flawlessly solving a Sudoku puzzle.

Poem taken down on the inside of a Lean Cuisine box

Mornings in July start slowly—and early, because of the heat.
Coffee and a heaping bowl of granola—with kiwi fruit,
Mango, grapes, Greek yogurt, and skim milk—and one
Or two Sudokus speedily done arouse my brain,

And sometimes, if I'm lucky, worded thoughts begin to flow,
And sometimes flow so fast and full I despair to know
How I can remember them until chores are done
And computer on. The recycle basket yields a scrap to pen on.

Today I blitzed a gold-rated Sudoku

"Jim," I said to a friend and colleague at work, "something really wonderful happened this morning. More often than not, when I attempt a gold-rated Sudoku, I give up before I manage to solve it. But this morning—"
    "What do you mean, a gold-rated Sudoku?"
    I explained that different suppliers use different rating systems for easy, moderate, hard. "There's the 1-2-3-4 rating system, for example, and the bronze-silver-gold system."
    Jim nodded his understanding.
    "Anyway, this morning I did this gold-rated Sudoku about as quickly as I've ever done a bronze or a 1."
    I said, "Now, I figure that this means one of two things."
    "At least," Jim said.
    "Right. It means either that they mis-categorized the Sudoku, and it was really a bronze, or—" I made fists, drew up my arms, and wiggled my body like a football player after scoring a touchdown. "Or I'm really clicking today!"
    "And, of course, you're going to go with the second possibility."
    "You know I am, Jim. How empowering that is! If that's what it means, then today I can succeed in my most difficult tasks, I can—"
    "But doesn't this call for you to carefully consider which difficult task you ought to focus on? You don't want to waste today's brilliance on a relatively unimportant goal."
    "Jim! You're a brilliant consultant! Of course, you're right."
    "Maybe you shouldn't be here at work today. Maybe you should—"
    "Maybe I should look at my life goals and choose something that could make a much bigger difference in my life than anything I might do here at work today?"
    "Exactly."

Is it true, then, as it appears, that producing a self-satisfying daily blog post might be one of my main life goals?

Spiritual connectedness

Riding with Bill yesterday to join Ralph for a walk at Johnston Mill, a couple of miles from where my wife and I lived for twenty-five years before moving to Mebane, I took the opportunity to try to find out whether Bill's term spiritual applies to me. I asked him how he would characterize it.
    "Connectedness."
    I instantly saw that indeed, in Bill's sense of the term, I am spiritual. I acknowledge, intellectually, that I am related to all other living creatures and to very "star stuff," as cosmologist Carl Sagan (1934-1996) termed the matter of the Universe. And I feel the connectedness, sometimes profoundly, but more often only latently, out of the neglect of taking for granted. And I mean to honor the connection by humility and compassion.

Ralph and his dog arrived at the entrance to the trail a minute after us. On the walk, we all three chatted about no fewer or less significant things than Ralph and I alone would have done. Bob Dylan. Yoga instruction. The logic of grammar. Growing old, losing one's memory. Julie Christie (from her 2006 movie, Away from Her, in which she played a woman being institutionalized because of Alzheimer's disease). Zen Buddhism. Philosophy scholarship (Ralph had discovered Peter Kingsley, a new name for me). Later, Bill told me that Ralph had demonstrated his own spirituality by picking up a piece of paper on the trail.
    And of course spirituality and religion came up. I told them about Mert's retort Friday to my statement that I didn't believe any of that about the Good Lord's working in mysterious ways. "And I don't believe that!" Mert had said.

    I mentioned that my wife and I had the night before watched a film about the child evangelist Marjoe Gortner on the tent revivalist circuit. I was surprised to learn that I had apparently never told Ralph that in my childhood my mother had taken me to the same sorts of church events at which Marjoe as a child and young man had preached.
    But it wasn't until this morning that it occurred to me that, since Marjoe was starting to preach in 1948 (at age four), precisely when my mother was beginning to take me to revivals, where I witnessed people apparently ecstatically "speaking in tongues," it is likely my mother had heard of him. Could it be that my mother's oft-spoken wish that I would "become a preacher" was influenced by reports of that fabulous child preacher?
    Perhaps Marjoe, with whom I only just became familiar from the movie's being mentioned in a book I'm reading by Daniel Dennett¹, influenced the very trajectory of my "religious life." I told Bill on the ride home that I've always thought I majored in philosophy because of my desperate "search for God" informed by those early church experiences. In fact, I likely chose to apply to Yale because of that interest, since it was Yale's catalog of undergraduate academic programs that most appealed to me because of its "Directed Studies" program, then centered around philosophy and the humanities.
    What a world.

Ralph had asked me how, then, I'd become an atheist. I guess I must not have told him before because I had depended on his reading the answer here on my blog—even though he's told me that he spends so much time on the Internet in his work at IBM that he doesn't spend much or any on it outside work. (Because I go onto the Internet both at work and at home, I must not have believed him.)
    So I summarized my Sudoku analogy for him. I had rejected theism as a "forced move" after eliminating the pertinent possibilities.
    Ralph recounted the Zen parable about the fish in water who reasoned logically that water didn't exist.
    I laughed. "Ralph, that's about the same as Mert's retort, isn't it? He didn't believe that I couldn't believe in water."
    Ralph said that Mert's retort was different; it sounded like a trick of the evangelical trade. Mert might have been trying to convert me. Ralph said I was free not to believe, and recommended Zen Buddhism. "Zen Buddhists don't believe in God," he said.
    On the ride home, Bill pointed out that Zen teaches letting go, detachment. "That's the very thing you do when you accept things as they are and laugh."
    I like it.
_______________

1. From Breaking the Spell: Religion as a Natural Phenomenon, pp. 167-168:

   Every good doctor knows that a few simple tricks of self-presentation that compose a good "bedside manner" can make a huge difference. It isn't really dishonest, is it? Every priest and minister, every imam and rabbi, every guru knows the same thing, and the same gradation from knowingness to innocence can be found today in the practices of revival preachers, as vividly revealed in Marjoe, the Oscar-winning 1972 documentary film that followed Marjoe Gortner, a charismatic young evangelical preacher who lost his faith but made a comeback as a preacher in order to reveal the tricks of the trade. In this disturbing and unforgettable film, he shows how he makes people faint when he does the laying on of hands, how he rouses them to passionate declarations of their love for Jesus, how he gets them to empty their wallets into the collection basket.

Sudoku koan

Today's word from dictionary.com is:

koan \KOH-ahn\, noun:
A nonsensical or paradoxical question to a student for which an answer is demanded, the stress of meditation on the question often being illuminating.
Koan is Japanese, ko "public" and -an, "matter for thought." It enters English through Zen Buddhism before achieving a more general sense.

Maybe the only way I'm going to essay my announced analogy between Sudoku and religion is to exploit the stress of just throwing caution to the wind and publicly meditate the question. It'll either be illuminating, or not.
    What would a Sudoku koan be, though? Maybe the following question is nonsensical enough:

What is puzzling about the analogy between Sudoku puzzling and puzzling over religion?

At any rate, after my announcement eight days ago, the idea of an "elaborate analogy" between Sudoku and religion has at times seemed elusive. (Maybe that's why I've been procrastinating.)

The heady feeling that comes from the numbers quickly snapping into place on a Sudoku board resembles the confident, in-control feeling that accompanies one's sense that one has seen to the bottom of religion and there's nothing there.
    But that's just the dessert. The main course of the analogy is that Sukoku puzzling and religion puzzling both involve combinations of strategies of elimination that lead to forced moves.

In Sudoku, the simplest forced move is the gimmes that are usually offered in the easier puzzles. For example, you look across the middle array of three 9-cell squares and see:

   5  |     9|   1
 7   6|      | 9   8
   9  | 8 5  |   2

[Let's stipulate that each of the nine 9-cell squares is a quadrant, in its general sense of "major part," even when there are not four major parts.] Without looking at any other part of the board, you can see that the middle cell in the third quadrant must contain a 5, because each of the three quadrants must contain a 5, but each row can have only one, and there's nowhere else for the 5 to go but in the middle row of the third quadrant:

   5  |     9|   1
 7   6|      | 9 5 8
   9  | 8 5  |   2

    Ticking off the "gimmes" in a puzzle is like being able to immediately dismiss religious statements that are obviously wishful and without substance. "I prayed that we'd land safely." Praying or not praying will have no effect on the landing. "Everything happens according to God's plan." There is no such plan.

But in the case of the 8 in the array:

      |     3|   9
      |   2  | 8
 6 8  |      | 3

Either of two cells (x) could host it:

      | x x 3|   9
      |   2  | 8
 6 8  |      | 3

...until we look at the quadrant immediately below it:

 - - -|     9| - - -
 - - -|      | - - -
 - - -| 8 5  | - - -

The 8 in the first column of that quadrant forces the 8 in the quadrant above into the second column:

      |   8 3|   9
      |   2  | 8
 6 8  |      | 3

    Sudoku strategy must widen itself in that way to account for constraints at all levels.

My "Sudoku breakthrough" reminded me that I had been able to see to the bottom of religion in much the same way I had become able to solve more difficult Sudoku puzzles: by looking at various levels of the religion question in combination:
    Lack of evidence for it. I've seen no objective confirmation that any miracle has occurred. No one has demonstrated that a prayer was answered. Etc.
    Its absurdity. The most absurd belief of religion is probably the one that "sinners" will be subjected to unspeakable torments that will last forever and ever.
    Its irrelevance to morality. Religious people come in all varieties of good and bad, the same as atheists.
    Its logical contradictions. Each of the three Abrahamic religions consider adherents of the other two to be unbelievers, or infidels.
    Naturalistic explanations for it. The belief in a Day of Judgment satisfies the wish that good people will be rewarded and bad people punished. For example. Evolutionary investigations into the roots of religion are fascinating, and I've only begun to familiarize myself with them.
    I may be forgetting a level that I considered at some point over the past years, but the result in any case was that my conclusion about religion was a forced move. What Gertrude Stein said of Oakland applies even more accurately to religion: There's no there there. In a state of religion, people inhabit a vast vacuity of their own (or, more often, someone else's) imagining.

In the scheme of things, though, Sudoku puzzling is like puzzling over religion in that both are really just trivial pastimes, diversions. There are other, productive ways to spend one's time, as I realized the other day, when Sudoku puzzling had made me stale and I reminded myself to get back to reading a good book.

Breakthrough?

Today, Tuesday's brave words about a "Sudoku breakthrough" feel hollow. It's as though the skills I thought I'd learned on those long flights have deserted me. I'm currently stymied at an early point in two Sudokus, and I'm getting none of that glad reinforcement anymore that comes with the numbers' quickly clicking into place.
    I trust that I still actually have my Sudoku skills, but am just too tired today to access them. I've been spending too much time on puzzles lately, time that would be better spent reading Ayaan Hirsi Ali's passionate, informative book.
    Maybe the Reading God is punishing me? <wink>

Welcomed home

Soon after we returned home from celebrating the 2010 Pacific Cup Sailboat Race in Hawaii, my wife noticed that a lovely green-headed, wide-mouthed creature had taken up residence in our fountain pool. I got my first look at him this evening (click on the photo to see him much enlarged), and the look was enough to smile me out of my doldrums, back to Moristotle. I feel welcomed home.
    Hey, you have to start somewhere. I've been ruminating an elaborate analogy between doing Sudoku puzzles and puzzling over religion, but I have a few more "pencils to sharpen" and walks around the block to take before I'll be ready to essay it.
    Suffice it for now that I had a Sudoku breakthrough on the flight over to Honolulu on July 18. You know, the typical flight magazine has a puzzles page....Anyway, I solved the two Sudokus I found there, then later found a fresh copy of the magazine and solved them again. I even took a third fresh copy off the plane at HNL and solved them again sometime during the week. (And I think I may have solved them yet again at the beginning of the late July 25 flight home— before I fell asleep for a six-hour nap before arriving in Atlanta the next day.)
    I know, they were becoming easier and easier—but not only because I had become familiar with these particular puzzles, but also because I was practicing my technique. Somehow, I was acquiring the power to take in more combinations than just the horizontal and vertical sweeps across or down each set of three nine-square cells to pick off the gimmes. I found myself working combinations of the nine numbers in a cell with the nine numbers in selected rows or columns running through the cell. Oh, glory, how heady was the feeling! My wife was no longer the only proficient Sudoku solver in the house.

And addictive. Not unlike my continuing to rake the dead coals of the fire to which I consigned religion.
    Let that be my preamble. [I wrote up the analogy on August 11.]

Smile, frog! Open that musing mouth. Sing!