Category Archives: failure

On endings

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Unlike beginnings, which are plenty scary by themselves, endings are often poignant and solitary. You drive off, you walk away from an airport, you get on a train or bus, you stroll down a street never to come back. A car door slams, you lock the door and turn away. It’s over. We have all been through our share of endings–a job, a school, a friendship, a life–so we all have our anecdotes about moving on, saying goodbye, and picking up the broken pieces so that we can start again. Endings make us wistful and nostalgic because we are not always sure that the new thing ahead of us is better than what is being left behind. We are plagued by our memories which torture us into remembering all of those great moments in the past when we were, at least for a moment, happy. The constant truth is that all things end, no matter how we feel about them. Change is, perhaps, the only constant in most of our lives. As a teacher, students come and students go, and that’s the way it’s always been. As an ex-pat in another country, my friends have come and gone many times, and now are scattered to the four corners of the world. It is hard to stay in touch, and even with different digital media sites, it is still difficult to maintain a real friendship from seven thousand miles away. And when old friends finally make their last trip, it is equally difficult to say goodbye, especially when you have known them for more than fifty years. Yet those fifty years are also a monument to that friendship which has had to endure a lot of stuff, not all good, much of it very good. Mortality is, in the end, about endings, and that is the way it must be–one of those rules nobody breaks.

On endings

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Unlike beginnings, which are plenty scary by themselves, endings are often poignant and solitary. You drive off, you walk away from an airport, you get on a train or bus, you stroll down a street never to come back. A car door slams, you lock the door and turn away. It’s over. We have all been through our share of endings–a job, a school, a friendship, a life–so we all have our anecdotes about moving on, saying goodbye, and picking up the broken pieces so that we can start again. Endings make us wistful and nostalgic because we are not always sure that the new thing ahead of us is better than what is being left behind. We are plagued by our memories which torture us into remembering all of those great moments in the past when we were, at least for a moment, happy. The constant truth is that all things end, no matter how we feel about them. Change is, perhaps, the only constant in most of our lives. As a teacher, students come and students go, and that’s the way it’s always been. As an ex-pat in another country, my friends have come and gone many times, and now are scattered to the four corners of the world. It is hard to stay in touch, and even with different digital media sites, it is still difficult to maintain a real friendship from seven thousand miles away. And when old friends finally make their last trip, it is equally difficult to say goodbye, especially when you have known them for more than fifty years. Yet those fifty years are also a monument to that friendship which has had to endure a lot of stuff, not all good, much of it very good. Mortality is, in the end, about endings, and that is the way it must be–one of those rules nobody breaks.

On insomnia

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Couldn’t get to sleep at all last night–to coin a phrase. The creepy part of jet-lag is not that you can’t wake up or stay awake, it’s that you can’t get to sleep at night. I tossed and turned last night and nothing was comfortable, not the pillow, not the mattress, nothing. The hours ticked off–one, two, three, four, and I still couldn’t conjure up sweet dreams. The sandman would not visit my house. The worst part is that everyone else in the whole place was sound asleep. Insomnia is a solitary past-time in which the dark hours of the early morning pass slowly and painfully. Oh, one might find something to eat, read a book, or watch an old movie, but you are really missing out on all that rejuvenating sleep which totally eludes you. Sleep is the antidote for the stress and work of the day. To close your eyes and drift into unconsciousness is the only way to deal with being bone-tired, stress out, and sleepy. Yet, when sleep eludes you as if it were tiny fish in big pond, one suffers from a strange sadness, excluded from a world of dreams in which every other human being has taken refuge. Insomnia is a mean, hard, unfriendly sort that makes friends with no one. To sleep the sleep of the just plain tired is one of the priceless luxuries that no one can keep from you, but insomnia can. You can feel tired, you can feel like you should be be asleep, and you can still be wide awake. Every bone and every muscle in your body will ache, but sleep is a foreign country where you don’t have a visa and you’ve lost your map.

On insomnia

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Couldn’t get to sleep at all last night–to coin a phrase. The creepy part of jet-lag is not that you can’t wake up or stay awake, it’s that you can’t get to sleep at night. I tossed and turned last night and nothing was comfortable, not the pillow, not the mattress, nothing. The hours ticked off–one, two, three, four, and I still couldn’t conjure up sweet dreams. The sandman would not visit my house. The worst part is that everyone else in the whole place was sound asleep. Insomnia is a solitary past-time in which the dark hours of the early morning pass slowly and painfully. Oh, one might find something to eat, read a book, or watch an old movie, but you are really missing out on all that rejuvenating sleep which totally eludes you. Sleep is the antidote for the stress and work of the day. To close your eyes and drift into unconsciousness is the only way to deal with being bone-tired, stress out, and sleepy. Yet, when sleep eludes you as if it were tiny fish in big pond, one suffers from a strange sadness, excluded from a world of dreams in which every other human being has taken refuge. Insomnia is a mean, hard, unfriendly sort that makes friends with no one. To sleep the sleep of the just plain tired is one of the priceless luxuries that no one can keep from you, but insomnia can. You can feel tired, you can feel like you should be be asleep, and you can still be wide awake. Every bone and every muscle in your body will ache, but sleep is a foreign country where you don’t have a visa and you’ve lost your map.

On Fermat’s Last Theorem (Conjecture)

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Fermat, a French mathematician of the late 17th century, came up with a conjecture that baffled other mathematicians for three and half centuries until Andrew Wiles published a proof in the mid-nineties. Most of you are familiar from high school geometry with the Pythagorean theorem, that the sum of two integers squared may be equal to another integer squared: a2 + b2 = c2, but Fermat imagined a more general problem for integers where an + bn ≠ cn where n>2: Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et generaliter nullam in infinitum ultra quadratum potestatem in duos eiusdem nominis fas est dividere cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet. That last bit is the mystery—that the margin was too small for his proof. Many mathematicians believe he did not have a proof, but all the same, he did throw down the gauntlet by making the conjecture. He just wrote the conjecture, that an + bn = cn, is not possible. Wiles’ proof is so complex and convoluted, however, that you have to be a brilliant mathematician to even begin to understand his arguments. For as simple as the Pythagorean theorem looks, Fermat’s conjecture is inversely complex, and complex in ways that not even a great mathematician can dream. The conjecture looks simple, but the answer seems to be one of the most complex ever proved in the history of mathematics. The proof, almost as elusive as the Holy Grail, is unintelligible to the average lay person, and difficult for even the gifted. What kind of mind does it take to fathom the dark and profound reaches of Fermat’s conjecture? This conjecture, according to a French academy of math, has the dubious honor of having the highest number of incorrect proofs written about it. In other words, many mathematicians have tried to conquer the proof, but died ignominiously on the battlefield without having succeeded. That fact that Wiles did his work in secret suggests that even he thought the little problem might be paradoxically unsolvable—a no-win scenario, as it were, and a career-ending catastrophe. That there is, after all, a solution to Fermat’s last theorem is of little consolation to all of that failure. (Sorry mathematicians,formatting limitations don’t allow for the little raised numbers in the equations.)

On Fermat’s Last Theorem (Conjecture)

Posted on by

Fermat, a French mathematician of the late 17th century, came up with a conjecture that baffled other mathematicians for three and half centuries until Andrew Wiles published a proof in the mid-nineties. Most of you are familiar from high school geometry with the Pythagorean theorem, that the sum of two integers squared may be equal to another integer squared: a2 + b2 = c2, but Fermat imagined a more general problem for integers where an + bn ≠ cn where n>2: Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et generaliter nullam in infinitum ultra quadratum potestatem in duos eiusdem nominis fas est dividere cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet. That last bit is the mystery—that the margin was too small for his proof. Many mathematicians believe he did not have a proof, but all the same, he did throw down the gauntlet by making the conjecture. He just wrote the conjecture, that an + bn = cn, is not possible. Wiles’ proof is so complex and convoluted, however, that you have to be a brilliant mathematician to even begin to understand his arguments. For as simple as the Pythagorean theorem looks, Fermat’s conjecture is inversely complex, and complex in ways that not even a great mathematician can dream. The conjecture looks simple, but the answer seems to be one of the most complex ever proved in the history of mathematics. The proof, almost as elusive as the Holy Grail, is unintelligible to the average lay person, and difficult for even the gifted. What kind of mind does it take to fathom the dark and profound reaches of Fermat’s conjecture? This conjecture, according to a French academy of math, has the dubious honor of having the highest number of incorrect proofs written about it. In other words, many mathematicians have tried to conquer the proof, but died ignominiously on the battlefield without having succeeded. That fact that Wiles did his work in secret suggests that even he thought the little problem might be paradoxically unsolvable—a no-win scenario, as it were, and a career-ending catastrophe. That there is, after all, a solution to Fermat’s last theorem is of little consolation to all of that failure. (Sorry mathematicians,formatting limitations don’t allow for the little raised numbers in the equations.)