Here is a math problem for you, from the 1971 edition of Polya's How to Solve It, a classic on mathematical problem-solving:
Bob has ten pockets and 44 silver dollars. He wants to put his dollars into his pockets so distributed that each pocket contains a different number of dollars. Can he do so?
Monday, June 11, 2007
Wednesday, June 06, 2007
Lord of the Flies
I recently finished listening to Lord of the Flies, by William Golding. I had read it many years ago (probably in high school) but remembered it always as a dark and violent picture of how bad anarchy is. I was not wrong. It is a violent tragedy.
Brief plot summary and spoiler: an undefined number of British schoolboys (ages 5 to 12) survive their plane crashing into a deserted island (resembling something in the South Pacific). Ralph, initially elected the leader, tries to organize them in building shelters and keeping a fire going to attract rescue, but most of the other boys don't want to do that and eventually leave to form a tribe of hunters. The resulting violent conflict ends when they are suddenly rescued.
In thinking about Ralph's efforts to form a society, I kept thinking of how the family is the basic unit of society. The collegial, democratic model sounds wonderful, but it will work only if there is an authority to set the rules, enforce them, and punish lawbreakers. In the book that was absent - the little ones were interested only in playing and eating, and the bigger ones felt no responsibility to help Ralph, and Ralph didn't try to punish anyone. Another model would have been to setup little family-like groups, with two older boys (like big brothers) sharing the responsibilities of caring for a small number of little ones. Perhaps the big brothers would have formed an attachment to their little brothers and worked to provide for them. Having two big brothers would enable them to share that work and the community work of tending the fire and hunting. (The way two parents share the work of child-rearing and income-earning?)
Ultimately, despite Ralph's attempts to create a social order, the boys' downfall is that, in some of them, the evil part of them (which exists in all of us, thanks to original sin) overcomes friendship and cooperation and leads to selfishness and pride and fear and jealousy and hate and senseless violence.
It becomes a world without rules, without authority; a world where everyone does what they want without considering the long-term consequences; a violent tragedy.
Brief plot summary and spoiler: an undefined number of British schoolboys (ages 5 to 12) survive their plane crashing into a deserted island (resembling something in the South Pacific). Ralph, initially elected the leader, tries to organize them in building shelters and keeping a fire going to attract rescue, but most of the other boys don't want to do that and eventually leave to form a tribe of hunters. The resulting violent conflict ends when they are suddenly rescued.
In thinking about Ralph's efforts to form a society, I kept thinking of how the family is the basic unit of society. The collegial, democratic model sounds wonderful, but it will work only if there is an authority to set the rules, enforce them, and punish lawbreakers. In the book that was absent - the little ones were interested only in playing and eating, and the bigger ones felt no responsibility to help Ralph, and Ralph didn't try to punish anyone. Another model would have been to setup little family-like groups, with two older boys (like big brothers) sharing the responsibilities of caring for a small number of little ones. Perhaps the big brothers would have formed an attachment to their little brothers and worked to provide for them. Having two big brothers would enable them to share that work and the community work of tending the fire and hunting. (The way two parents share the work of child-rearing and income-earning?)
Ultimately, despite Ralph's attempts to create a social order, the boys' downfall is that, in some of them, the evil part of them (which exists in all of us, thanks to original sin) overcomes friendship and cooperation and leads to selfishness and pride and fear and jealousy and hate and senseless violence.
It becomes a world without rules, without authority; a world where everyone does what they want without considering the long-term consequences; a violent tragedy.
Thursday, May 31, 2007
A Day of Queueing
On Thursday, May 31, I went to Atlanta, Georgia, and back with Kay Aaby from Montgomery County to tape interviews for an upcoming CDC satellite broadcast on Mass Antibiotic Dispensing:
Taking the Guesswork out of POD Design. It was an honor to be invited to participate, and I appreciate the opportunity to talk about our research on clinic planning models, which include queueing models.
The first photo is me under the lights in the studio. (They have first-class studio facilities.) I worked at CDC 20 years ago as a co-op student, so it was a bit of a homecoming, but the place has changed dramatically - almost all of the old buildings are gone, and I never went near the one remaining building where I worked.
The day was, appropriately, full of queueing. Following are items from the log I kept for the day:
6:30 am: Leave home
7:03 am: Waiting in line to check in at the AirTran ticket counter (there are only five people in front of me; over at United, the queue is overflowing the waiting area lines).
7:15 am: Waiting all through security, first for the ID check, then to get a plastic bin for my shoes and coat, then to put the stuff through the X-ray, then to get the stuff when it exits.
7:25 am: Arrive at the gate and begin waiting to board.
7:30 am: Waiting at the coffee and doughnut shop. I don't get coffee, so I have to wait only once (those getting coffee have to wait again for their coffee to be prepared).
7:36 am: Waiting in a queue to have gate agent check boarding pass, then waiting in jetway to get my seat.
8:00 am: Plane departs and lands in Atlanta at 9:30.
9:38 am: Plane stops on taxiway; pilot explains that we're waiting for an open path to our gate. (Atlanta is extremely hazy - see photo, and we can smell smoke once we're outside - must be from the wildfires.)
9:50 am: Waiting for the next train to the terminal.
10:05 am: Get cab (no line) to CDC and arrive around 10:35 to wait for our contact to appear.
11:00 am: Meet our contacts, go downstairs to do interviews (I, Kay, and Leah Matteson from New York) until 2:45.
2:50 pm: Waiting upstairs at the front desk for a cab.
3:15 pm: Depart in cab. Trip to airport takes over 35 minutes due to traffic congestion, especially at a stoplight that was blinking red.
3:58 pm: Waiting at the AirTran ticket counter (because we switched to an earlier flight and needed new boarding passes).
4:07 pm: Waiting in security (again). Exit at 4:19 and take train to Concourse C, arriving at gate at 4:30 to wait for 5:46 flight.
5:12 pm: Waiting in line to order sandwich, then waiting while sandwich is prepared.
6:00 pm: Plane is waiting on taxiway in a queue of planes that want to take off.
6:15 pm: Plane takes off and arrives at BWI at 7:40.
8:02 pm: Waiting at parking garage exit (3 cars in front of me).
8:30 pm: Home!
All together, it was a 14-hour trip comprising (roughly) 3.5 hours of interviews, 5 hours of transportation, and 5.5 hours of waiting!
Taking the Guesswork out of POD Design. It was an honor to be invited to participate, and I appreciate the opportunity to talk about our research on clinic planning models, which include queueing models.
The first photo is me under the lights in the studio. (They have first-class studio facilities.) I worked at CDC 20 years ago as a co-op student, so it was a bit of a homecoming, but the place has changed dramatically - almost all of the old buildings are gone, and I never went near the one remaining building where I worked.
The day was, appropriately, full of queueing. Following are items from the log I kept for the day:
6:30 am: Leave home
7:03 am: Waiting in line to check in at the AirTran ticket counter (there are only five people in front of me; over at United, the queue is overflowing the waiting area lines).
7:15 am: Waiting all through security, first for the ID check, then to get a plastic bin for my shoes and coat, then to put the stuff through the X-ray, then to get the stuff when it exits.
7:25 am: Arrive at the gate and begin waiting to board.
7:30 am: Waiting at the coffee and doughnut shop. I don't get coffee, so I have to wait only once (those getting coffee have to wait again for their coffee to be prepared).
7:36 am: Waiting in a queue to have gate agent check boarding pass, then waiting in jetway to get my seat.
8:00 am: Plane departs and lands in Atlanta at 9:30.
9:38 am: Plane stops on taxiway; pilot explains that we're waiting for an open path to our gate. (Atlanta is extremely hazy - see photo, and we can smell smoke once we're outside - must be from the wildfires.)
9:50 am: Waiting for the next train to the terminal.
10:05 am: Get cab (no line) to CDC and arrive around 10:35 to wait for our contact to appear.
11:00 am: Meet our contacts, go downstairs to do interviews (I, Kay, and Leah Matteson from New York) until 2:45.
2:50 pm: Waiting upstairs at the front desk for a cab.
3:15 pm: Depart in cab. Trip to airport takes over 35 minutes due to traffic congestion, especially at a stoplight that was blinking red.
3:58 pm: Waiting at the AirTran ticket counter (because we switched to an earlier flight and needed new boarding passes).
4:07 pm: Waiting in security (again). Exit at 4:19 and take train to Concourse C, arriving at gate at 4:30 to wait for 5:46 flight.
5:12 pm: Waiting in line to order sandwich, then waiting while sandwich is prepared.
6:00 pm: Plane is waiting on taxiway in a queue of planes that want to take off.
6:15 pm: Plane takes off and arrives at BWI at 7:40.
8:02 pm: Waiting at parking garage exit (3 cars in front of me).
8:30 pm: Home!
All together, it was a 14-hour trip comprising (roughly) 3.5 hours of interviews, 5 hours of transportation, and 5.5 hours of waiting!
Monday, May 28, 2007
Engineering History
In the Summer 2007 issue of Prism, the magazine of the American Society for Engineering Education, Henry Petroski writes about the fact that engineers don't get much recognition. People see the things that engineers designed but don't think about the men and women who did the designing. Very true: who designed the car you drive? the appliances you use to cook? I have no idea.
Of course, Petroski has attempted to overcome this with some of his writing about famous bridges and other engineering marvels. In this column he reiterates the need to include the history and heritage of engineering in the engineering body of knowledge (he specifically refers to a debate within the civil engineering profession). Petroski laments that young engineers don't know the names of the engineers responsible for outstanding engineering achievements and encourages engineering faculty to teach history as part of their courses.
I fully agree. I do cover history in my Production Management course because Hopp and Spearman's Factory Physics text includes a chapter on history. I also wrote some history for a chapter of the Handbook of Production Scheduling. See also my earlier post on the history of manufacturing.
The American Society of Mechanical Engineers has a History Center; among the listed landmarks is the FMC Citrus Juice Extractor, invented in 1947 by the FMC Corporation of Lakeland, Florida, and now used worldwide for squeezing oranges.
You can find the story of extractor in this PDF document.
Of course, Petroski has attempted to overcome this with some of his writing about famous bridges and other engineering marvels. In this column he reiterates the need to include the history and heritage of engineering in the engineering body of knowledge (he specifically refers to a debate within the civil engineering profession). Petroski laments that young engineers don't know the names of the engineers responsible for outstanding engineering achievements and encourages engineering faculty to teach history as part of their courses.
I fully agree. I do cover history in my Production Management course because Hopp and Spearman's Factory Physics text includes a chapter on history. I also wrote some history for a chapter of the Handbook of Production Scheduling. See also my earlier post on the history of manufacturing.
The American Society of Mechanical Engineers has a History Center; among the listed landmarks is the FMC Citrus Juice Extractor, invented in 1947 by the FMC Corporation of Lakeland, Florida, and now used worldwide for squeezing oranges.
You can find the story of extractor in this PDF document.
Thursday, May 24, 2007
Tender is the Night
I just finished listening to the audiobook version of Tender is the Night by F. Scott Fitzgerald. It tells the story of a psychoanalyst (Richard) in the period after World War I. He is married, and his wife Nicole was the victim of child abuse at the hands of her wealthy father and is now schizophrenic. They are rich Americans, they have two children, and they live in the south of France.
Here is a brief plot summary: The couple's life consists of travel and entertaining. He is trying to write another book; she gardens. They care about their children but leave the childcare to a governess. They care about each other, but he eventually feels trapped and has an affair. Then he starts drinking. Her illness disappears, she has an affair, and they divorce. Richard leaves the family and goes back to America.
It is a great but sad picture of how empty life can be, even for people who have money and leisure, when it has no purpose. Once Nicole is well, Richard no longer has to help her and protect her. And Nicole finds that being a wife and mother is not enough. Neither has any thought of asking God for help or has a faith on which to rely.
Here is a brief plot summary: The couple's life consists of travel and entertaining. He is trying to write another book; she gardens. They care about their children but leave the childcare to a governess. They care about each other, but he eventually feels trapped and has an affair. Then he starts drinking. Her illness disappears, she has an affair, and they divorce. Richard leaves the family and goes back to America.
It is a great but sad picture of how empty life can be, even for people who have money and leisure, when it has no purpose. Once Nicole is well, Richard no longer has to help her and protect her. And Nicole finds that being a wife and mother is not enough. Neither has any thought of asking God for help or has a faith on which to rely.
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