Are You Sick of Both (Snow and Probability)?

The sky is cloudy again, and it’s snowing again, too. “The snow was beautiful this morning!” exclaimed Denise Holland before quickly admitting, “but I wish it would go away!” Today’s picture is from yesterday’s weather, a shot south-southeast from Omena across the icy bay, Arctic in appearance but bathed in sunshine.

Bob Bergdoll from Omena (who most recently finished and highly recommends PEOPLE OF THE BOOK, by Geraldine Brooks) stopped in to distract me from the puzzle on Monday afternoon with his clear, simple, stunningly elegant proof of the probability problem. In essence, Bob’s chart is a truth table, of the sort beginning formal logic students learn to construct, with WIN and LOSE in place of TRUE and FALSE. There are three doors, therefore nine possible combinations. Where is the car, and what door is selected? Bob’s introduces columns are for “Stick with Selection” and “Switch Selection,” and all you have to do is add up the WINs in each column to see the result: three in one, six in the other. He made up the chart in preparation for writing a computer program, but the chart itself tells the story, making the program redundant.



Oh, the joys of logic! Teaching my first class in the subject at the University of Illinois when only a nervous graduate assistant, I first realized the power and comfort of this dry field. Three smart young men sat together by the windows, waiting for me to stumble. When one of them doubted that affirming the consequent was a fallacy (“Are you sure?” he pressed, eyes narrowed challengingly), what wonderful calm settled over me as I said to him, nodding, “Do the truth table.”

More Odds Than Ends

Today David fixed a big breakfast for us, I did a little laundry and fixed roast chicken for dinner, but basically we’ve had a day of rest, and I’ve been commuting mentally (my usual armchair travel) between northern Michigan and southern Louisiana. The sun was out for a while, air warm, and Sarah and I had a good ramble in the fields. Afterward she was content to lie on the rug and work over a big rawhide bone while David enjoyed ROAD FEVER, by Tim Cahilll, and I lost myself in James Lee Burke’s CRUSADER’S CROSS. More another day about the allure of murder mysteries in romantic places and the back-and-forth from violent crime to pastoral Eden.

My picture today is from the last February sunset. But now, it’s March, oh, it’s March! Only three weeks to the spring equinox! But did yesterday count as a lion or a lamb? And let’s not forget that it’s April, not March, that is the cruelest month. The perfection of May and June are nearer than they were but still a long, chilly, snowy, rainy, windy, muddy way off.

As for the probability problem, Ben W. thought it made a difference that the game show host knows where the prize is, but I don't see why. As long as the door he opens is not the door with the prize, so that the contestant has a chance to stick with his first choice or switch doors, how would the host’s knowledge affect the odds, any more than the odds are affected (not at all) by the lack of knowledge of the second competitor I introduced after the third door was eliminated? After all, if you’re betting on a racehorse, the odds for that horse in that race are what they are, whether you know the odds or not.

At least the problem has animated coffee conversation at the Treasure Chest this past week, and what with ever-new topics to chew over and Donna’s cheerful welcome and good breakfasts (the home-fried potatoes warm body and spirit these blustery days), Northport will make it through to spring. But then, we always do.

P.S. I’ve been asked about winter carnival, specifically about the outhouse race. There were five outhouses in competition this year, and if you go to the Chamber of Commerce site (in the links list) you can click from there to a site with videos. Sally Coohon, President of the Northport-Omena Chamber of Commerce, thought there were about 500 participants at this year’s winter carnival.

Weekend Begins

Tomorrow is Sunday! “Sunday, Sunday, SUNDAY at beautiful U.S. 30 drag strip!” went the manic radio commercial of my youth. David heard a similar one on Detroit radio, featuring a different drag strip. Saturday’s excitement this week (that would be today) was a continuation of the probability problem discussion with coffee drinkers and, later, with Ben Wetherbee (I asked him how the host’s knowledge of where the prize was changed the odds, and what if the host picked a door at random, revealing no car behind it—how would that make the odds any different?); a discussion on Kant and Schopenhauer with friend Big Steve; the arrival of a splendiferous (one of my father’s favorite terms) new dog bed for Sarah from friends Kathie and Amanda; and a late afternoon burst of sunshine to make Sarah’s and my homecoming even more fun than usual. Frisbee tossing and chasing! Oh, frabjus day!

Lest I give a false impression of my recreational reading, I should report that Thursday evening I was laughing so loudly and uncontrollably, weeping and choking and gasping for breath, over Bill Bryson’s THE LIFE AND TIMES OF THE THUNDERBOLT KID that David had to close a door between us to carry on his long-distance telephone conversation. I’m not always wandering the corridors of philosophical speculation. In fact, tonight I’m planning to get back to that James Lee Burke murder mystery I started last week. It’s the weekend! Time for self-indulgence! Not only has a week past, but this latest month of February, longest in seven years, is over! Can spring be far behind?

Pretzel Recipe

It was a magical, sparkly world out there this morning, one that I traveled with many starts and stops, even backtracking twice. We’ve had an entire week of (mostly) sunshine, and it’s done wonders for people’s spirits. If we change the elements of the game of “rock, paper, scissors” to "cold, light, precipitation," what would beat what? Some things need a period of cold, and there are spells in which we do “need rain,” but when is sunlight unwelcome?

But I promised that brain-twister that has my thinking thing knotted into a pretzel, so here’s the setup: There are three closed doors. Behind one of them is a big prize—say it’s a car—while there’s nothing behind the other two. You get to choose one door, and let’s say you choose Door A. What are your odds of winning the car? One in three, obviously. But all three doors are still closed. All is yet uncertainty and probability. You haven’t won yet.

Now your game show host opens Door C, and you learn that there was nothing behind it. Doors A (your first choice) and B are still closed, and behind one of them is the hot new car. Question to you: Are you better off sticking with your first choice or, when the host gives you the option, switching to Door B? Most people’s intuition is either to stick with A or that it makes no difference, since with only two choices (comparable to heads-or-tails), they reason, they have a 50/50 chance either way.

But probability experts who have worked on this problem say you’re better off switching. They say you initially had one in three odds (granted) but with one door eliminated, your original choice remains at one in three, while the unopened and unchosen door’s odds have jumped to two in three. Scream all you want. They’ll smile at you condescendingly.For a heated, lengthy explanation and discussion of this problem (ultimately humiliating for all the smart people now eating crow), take a look at Marilyn’s claim and subsequent shouting and murmuring.

Being very stubborn (just ask David), I can’t give up yet. Taking a new approach, I imagine a second contestant taking the place of the first at this point. The second contestant's choice is A or B, hence his odds (I think you’ll agree) 50/50. And now my question to the experts is, with two doors still closed, how can the odds be different for two different contestants? What I’m pushing for here (going way out on a limb I have no reason to dare to explore, given my history with math) is that maybe this problem presents a mathematical paradox, as opposed to truth vs. naïvete. But I’m over my head and need help on this one. Tom? Mark? Steve? Walt? ...Anyone?

Meanwhile, a friend out in Cherry Home (north of town), George Carpenter, writes about "Harbingers of Spring" he's noted in the last few days:

"Sunset on the far shore of Grand Traverse Bay (shadow covering the ridge across the bay from us) about 6:10 pm. Crows doing the 'aerial kiss,' both red bellied and hairy woodpeckers paired up (technically this is a partial cheat since they tend to stay in proximitity of each other year round), about 30 starlings back from the south, and an adult bald eagle carrying nesting material in his talons near Woolsey Airport. I probably shouldn't count the cut daffodils I bought today at Tom's because the label says they came from the UK."

Thank you, George, for that cheery report!

One last note on what I'm calling the paradox of the doors: When I said to David and Al, "Now suppose that Al steps out of the game and lets David take his place," David interrupted with a serious car-guy objection. "Why would he do that? Why would he give up his chance to win the car?" "For the sake of the problem!" I answered, and that made perfect sense to Al. Oh, we have fun here at Dog Ears Books!