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Showing posts with label dreaming. Show all posts
Showing posts with label dreaming. Show all posts

Monday, November 2, 2015

Dear Young Ones


Parents, step-parents, and grandparents, we have come to an age where the greater length of the path lies behind us. It is a strange realization, one that prompts me to tell you a story. Isn’t that what old folks do? Tell stories to the young ones? Here’s mine, and I make no excuse for its rambling nature or scanty conclusion.

A couple of decades ago, David and I made an expedition to the other side of Michigan, “the sunrise side,” where both his parents were born. Out in the countryside beyond Tawas we found his father’s old one-room school. We explored on foot the nearby area where his grandfather’s farm had been, though no trace of it remained. A short drive away, we found his grandparents’ graves in a little country cemetery. 

By chance, also, in a restaurant on the shore of Lake Huron , we ran into one of his distant cousins, a bald man with the unforgettable name Waldemar. He was sitting in a booth next to ours, and when the waitress addressed him by name, David said, “I wonder if that could be my cousin Waldemar.” It was, conversation ensued, and in the end Waldemar gave us directions to the homes of a couple more cousins on nearby farms. All these cousins, I should say, were of the first-cousin- once-removed or second-cousin relation.

The first old farmer we tracked down, Howard, lived with his wife at the end of a tree-lined dirt road in a most picturesque setting. Their farmyard featured among its outbuildings an old log barn like nothing I’d ever seen before, and to the north of that barn, concealed by a pretty line of trees, was a charming small brook. Howard and his wife make us welcome, and Howard climbed up into the loft of a newer barn to retrieve a piece of furniture put aside for David years before, a rustic twig table made by David’s paternal grandmother, who died before he was born. (We still have that table. You all have seen it.) I always thought we might return to Howard’s farm, so steeped in family history. We never have, but we sometimes speak of it, and David tells me stories of going there as a little boy, stories of fish-head skulls nailed to a shed wall, of driving a horse-drawn sulky (is there another kind?) down the dirt road when a wheel came off – but those are not my stories, not what I want to tell you today.

The other old farmer, Herman, a man well into his 80s, lived at the end of a long driveway going straight south off the east-west two-lane highway. Herman’s house and outbuildings sat out in the open, exposed to the sky like farms on the central Illinois prairie. We were not invited into the house but kept standing outside to talk with Herman, who stood on the stoop, just outside the doorway, his wife standing behind him, inside the door, silent. Herman might have invited us in (or he might not), but he was on his way out, hot on the trail , he told us, of a neighbor’s spotted pony he wanted to buy, and so we took our leave.

Our memory of Herman and the spotted pony entertained us for years. We would laugh and shake our heads and ask each other what that old man in his 80s thought he needed with a spotted pony! Lately we understand better and no longer laugh, although we still smile.

And this is what I want to tell you. It will probably come as quite a surprise, and you may have trouble believing it’s true. No one , no matter how old, ever gets over wanting that spotted pony.

David watches the special features that come with movies on DVDs , telling me, “I learned a lot,” as if he will be directing a movie in the near future, and I read farming magazines as if I’ll very soon be bringing worn-out soil back to fertility and breeding livestock. When we travel together, we assess strange towns and wild landscapes as if we might start new lives there. We picture to ourselves and to one another the wilderness cabins where our novels will be conceived and birthed. In conversations in strange motels we imagine the furniture re-arranged, paintings and bookshelves added, picturing a whole life we might put together in that one room. You have no idea how many parallel lives we have going!

No doubt you see us as completely settled into our chosen grooves, the dreamy painter and bookseller, content to be what we are and as we are for the rest of our lives, not at all busy launching new careers or building new houses or setting off for distant parts of the country. (Maybe even another country! A houseboat on the Seine!) Not very likely, is it? After all, how much energy do we have to make serious changes, to make new beginnings? How much savings do we have socked away for acquisition and startups?

We’re not deluded, young ones. We know what’s real and what’s feasible, and we do not regret the lives we have made. At the same time, our fantasies continue to blossom in ways that would astound you. It’s a jungle in there, fertile and crowded with possibilities of all kinds, and in that largely shared space – because a shared life is built on conversation -the two of us are still young and vibrant and full of dreams.

You cannot fully grasp what I’m trying to tell you, never having been as old as we are now, but I thought I should give you at least this little hint. It will better explain, perhaps, my excitement over that old scythe from the farm auction and David’s satisfaction in buying the bright-orange rowing scull. In his mind, he is skimming over Lake Leelanau, you see, and in mine I am mowing our back meadow by hand, like one of Tolstoy’s peasants. And it goes way beyond that! In imagination we are writing and directing movies together and applauding one another’s published novels. Every road we drive down leads through towns and past houses we look at with an eye to their possibilities for us. Can we see ourselves there? Could we make a life there? What would that life look like? He envisions a smooth, empty road in front of his Hayabusa as he cruises at 100 mph, and I become the world's oldest jockey on my lightning-fast Apaloosa.

Our projects at home may appear small to you these days – insignificant and barely there. You may puzzle over my modest pile of old bricks and David’s four stout wooden posts and wonder, if you even notice them, what we hope to make of such small beginnings. Ah, but if you could only see our future with our minds’ eyes!

Spotted ponies! Spotted ponies by the thousands, still out there on the horizon, thundering along the ridge, raising clouds of dust!

11/1/2015

Saturday, February 22, 2014

A Math Dream That Was Not a Nightmare


Why would my dream life be invaded by a geometry problem? The setup was a line segment, and the question that invaded my dream life was, how many lines could intersect that line segment? At first I imagined the intersecting lines to be all perpendicular and parallel, and my dream thinking was that the number of possible intersecting lines could not be infinite because (1) the original line was only a line segment, and so not itself infinite; and (2) while lines have no breadth or thickness, it seemed to me (but this could be only commonsense thinking, which doesn’t always translate to mathematics) that there would have to be space between the lines or they would simply fill in -- ??? But they would not turn the group of lines into a solid, because there would still be no thickness, or depth.... Does plane geometry care at all if a surface is blank or filled in, or (and if I had to bet, I’d put my money on this second disjunct) does it only care about lines and points?

Ah, but points have no length, breadth, or thickness! A point is not an object but a location. So even the line segment could have, it seems, an infinite number of intersecting, parallel, perpendicular lines. Do you buy it?

Next (still in my dream) I started wondering about intersecting oblique lines. (What would be the smallest conceivable angle? Would there be such a thing?) Would this generate a larger infinity of intersecting lines? Can infinity come in different sizes, bigger and smaller, or is infinity just always that -- infinity?

Finally, dragging myself out of the dream and into wakeful consciousness, I searched around for a way to ask the question that my geometry dream had posed, and here's what I came up with: What is the maximum number of lines that can intersect any given line segment?

Here’s a question and answer I found online that has bearing on my dream, but before following the link you might enjoy thinking about the question yourself. I mean, there's no exam involved here, not even a pop quiz.