Bruce Hardy has kidney cancer that has metastasized to his lungs. Pfizer has a drug shown in clinical trials to delay the progression of the cancer for about six months at a cost of $54,000. The British National Institute for Health and Clinical Excellence (NICE) has determined that six additional months of life is worth only about $22,750, so they have denied Mr. Hardy the drug.
I don't disagree with the British. They seek to ensure medical care is both cost effective and effective. A full course of immunizations for a child costs $1200, so Mr. Hardy's recommended course of treatment is equivalent to vaccinating 45 children. Which is worth more, six months of additional life for a 54 year old man or 45 immunized children?
I disagree with the notion that we can value every moment of every individual's life and make meaningful comparisons with the value we set on another person's life.
I need to look more closely at the mechanics of how value is established, but I have some immediate questions:
Is value based purely upon the economic value of the individual? I believe this is at least partly true in litigation.
How do we reconcile the value an individual places on their life with the value of that life to society?
How do we establish the limit of what we are willing to pay to keep someone alive? Does society have a moral obligation to allow individuals to live as long as possible? Do individuals have a moral obligation to not burden society?
How do we reconcile the profit motive of the health care industry with our obligation to provide for individual's health? How do we keep industry from profiteering, while ensuring that some entity has the incentive to provide quality health care and develop new (effective) medical techniques.
Clearly, I need to perform a great deal of research to answer these questions intelligently (or even to ask intelligent questions.) However, I wanted to at least begin listing some of the public health issues that have been bothering me.
Wednesday, June 24, 2009
Tuesday, June 23, 2009
Decision Analysis
I have taught a business statistics course for about two years at Southern New Hampshire University, a small private school in Manchester. The course covers confidence intervals, hypothesis testing, regression analysis, forecasting, etc. All of these techniques have been applied poorly, even disastrously, at times. I try to stress to my students that a quantitative technique pointing to a nonsensical decision may be wrong, and they should check their assumptions and their arithmetic again. (They should be very skeptical of a quantitative analysis that seems to justify an immoral decision.) However, the lecture which always makes me feel dirtiest is when I explain decision analysis.
One aspect of decision analysis lays out the choices which face you on the left side of a table and the possible futures you envision on the top of the table. For every entry, corresponding to a particular decision and a particular future, you determine a cost or a payoff. There are a number of methods for deciding which choice will most likely lead to the best outcome. These methods can take into account how much risk you are willing to accept or how probable you view a particular outcome. There are alternate methods for laying out more complex decision paths, but at its heart, decision analysis quantifies the payoff or cost of your decisions.
It is very hard to argue that a careful ordering and consideration of your choices and their likely outcomes is a bad way to approach decision making. In fact, when Israel was readying for negotiations after the 1973 War, they used decision analysis to prepare the negotiating team. The participants didn't view the payoffs listed in their tables as particularly useful; however, the process of preparing such a table also forced careful consideration of all options and what their global and regional implications were. The decision analysis was constantly updated during negotiations, and the participants also discovered a lot of value in seeing how their estimations of payoffs changed as decisions were made and events moved forward.
So why don't I like decision analysis?
I find it objectionable to reduce a complex process to a single quantity. There are many reasons as a mathematician I find this incorrect and unjustifiable. The claim/caveat is that you shouldn't pay too much attention to the exact numbers you get when performing decision analysis and that the process is the important part. It is even provable that you will reach the optimal decision when your payoffs are accurate. However, accuracy is very hard to guarantee when you are estimating the impact of an advertising campaign on potential market share. If people spend significant time on an analysis leading to a particular number, then it is hard to argue that number should be ignored. It also appears very easy to structure the analysis so that the favored decision is the one with the highest score.
I explain to my students that they should always document their analyses thoroughly, so that others can look at their assumptions and see whether they agree with the inputs, and therefore the outcome. For decision analysis, this documentation seems most useful as a way to show why you made an incorrect decision when things go wrong. Just as it seemed wrong for judges to choose nits in the statutory language to justify a ruling, it seems wrong for an analyst to justify their decisions with an easily gamed process whose documentation serves mostly as cover if your decision is wrong.
I try to find examples of improper use of all the techniques I teach, so that I can make students wary of non-intuitive decisions justified solely by a single numerical method. I have yet to find a documented instance of badly used Decision Analysis. There are a huge number of websites, organizations, and consultants extolling the virtues of Decision Analysis. This also bothers me, since I don't believe any technique is infallible.
We should also keep in mind the comment of an Israeli friend. He said the government spends a lot of effort on Game Theory and Decision Analysis to determine how to deal with the other players in the region. However, it is not at all clear that their adversaries are playing the same game.
One aspect of decision analysis lays out the choices which face you on the left side of a table and the possible futures you envision on the top of the table. For every entry, corresponding to a particular decision and a particular future, you determine a cost or a payoff. There are a number of methods for deciding which choice will most likely lead to the best outcome. These methods can take into account how much risk you are willing to accept or how probable you view a particular outcome. There are alternate methods for laying out more complex decision paths, but at its heart, decision analysis quantifies the payoff or cost of your decisions.
It is very hard to argue that a careful ordering and consideration of your choices and their likely outcomes is a bad way to approach decision making. In fact, when Israel was readying for negotiations after the 1973 War, they used decision analysis to prepare the negotiating team. The participants didn't view the payoffs listed in their tables as particularly useful; however, the process of preparing such a table also forced careful consideration of all options and what their global and regional implications were. The decision analysis was constantly updated during negotiations, and the participants also discovered a lot of value in seeing how their estimations of payoffs changed as decisions were made and events moved forward.
So why don't I like decision analysis?
I find it objectionable to reduce a complex process to a single quantity. There are many reasons as a mathematician I find this incorrect and unjustifiable. The claim/caveat is that you shouldn't pay too much attention to the exact numbers you get when performing decision analysis and that the process is the important part. It is even provable that you will reach the optimal decision when your payoffs are accurate. However, accuracy is very hard to guarantee when you are estimating the impact of an advertising campaign on potential market share. If people spend significant time on an analysis leading to a particular number, then it is hard to argue that number should be ignored. It also appears very easy to structure the analysis so that the favored decision is the one with the highest score.
I explain to my students that they should always document their analyses thoroughly, so that others can look at their assumptions and see whether they agree with the inputs, and therefore the outcome. For decision analysis, this documentation seems most useful as a way to show why you made an incorrect decision when things go wrong. Just as it seemed wrong for judges to choose nits in the statutory language to justify a ruling, it seems wrong for an analyst to justify their decisions with an easily gamed process whose documentation serves mostly as cover if your decision is wrong.
I try to find examples of improper use of all the techniques I teach, so that I can make students wary of non-intuitive decisions justified solely by a single numerical method. I have yet to find a documented instance of badly used Decision Analysis. There are a huge number of websites, organizations, and consultants extolling the virtues of Decision Analysis. This also bothers me, since I don't believe any technique is infallible.
We should also keep in mind the comment of an Israeli friend. He said the government spends a lot of effort on Game Theory and Decision Analysis to determine how to deal with the other players in the region. However, it is not at all clear that their adversaries are playing the same game.
Monday, June 22, 2009
Word Association
My son got me an annotated copy of The Wind In The Willows for Father's Day. This is one of my favorite books. I insisted that my wife read it when we first met, and I read it to both of my children. My father gave it to me as a Christmas present. I know that he liked the book a great deal, and that he insisted that my mother read it when they first met. In my mother's bookcases is an older copy of the book, that I imagine was my father's. My grandfather was born in 1905, three years before the book was published. I believe that it must have been one of his favorite books growing up, and he must have insisted that my grandmother read it when they first met. Certainly, he must have introduced it to my father.
I don't believe everyone is enthusiastic for The Wind In The Willows, but there are too many emotions tied into the book for me to consider it very critically. I have similar feelings for The Chronicles Of Narnia and Where The Red Fern Grows. My Aunt Electa sent me a boxed edition of The Chronicles Of Narnia for Christmas when I was probably in third or fourth grade. My Aunt Joyce gave me Where The Red Fern Grows about the same Christmas. I remember a wild combination of gifts from favorite aunts, Christmas, and stories that were beyond anything that I could imagine. I made my wife and children read these books as well, but they only got the story part of the mix.
When I was in fifth or sixth grade, my family drove from Kansas City, Missouri, to the East Coast where all of my father's relatives lived. Boston and the rest of New England were unimaginably exotic and sophisticated to me. We stayed for a few days with my Aunt Jo and her family in their home in the Berkshires. I slept in a spare room, most likely a library or overflow from a libray. When Aunt Jo showed me my room, she said I should feel free to read anything there. My Uncle Tom pointed out A Clockwork Orange and tried to explain the importance of the corrupt language used by the characters. I certainly didn't understand the book that first time, but the opportunity to read it in such a setting and to have it explained to me by Aunt Jo and Uncle Tom keep me returning to try and understand it.
When I met my wife, (she wasn't actually my wife at the time,) she had a few books that she insisted I read as well. The Princess Bride has been the one that I return to most often. It is a fundamentally silly story, but it hasn't grown stale. I can read it and recall the feeling of being very young and desperately in love with the woman who wasn't my wife yet. The children had to read this story as well, this time at the insistence of both parents.
There are books still waiting to be bound to me by friends and relatives not yet born, just as there are people unaware they will some day be forced to read The Wind In The Willows. For now, I will enjoy the books that were given to me on this Father's Day.
I don't believe everyone is enthusiastic for The Wind In The Willows, but there are too many emotions tied into the book for me to consider it very critically. I have similar feelings for The Chronicles Of Narnia and Where The Red Fern Grows. My Aunt Electa sent me a boxed edition of The Chronicles Of Narnia for Christmas when I was probably in third or fourth grade. My Aunt Joyce gave me Where The Red Fern Grows about the same Christmas. I remember a wild combination of gifts from favorite aunts, Christmas, and stories that were beyond anything that I could imagine. I made my wife and children read these books as well, but they only got the story part of the mix.
When I was in fifth or sixth grade, my family drove from Kansas City, Missouri, to the East Coast where all of my father's relatives lived. Boston and the rest of New England were unimaginably exotic and sophisticated to me. We stayed for a few days with my Aunt Jo and her family in their home in the Berkshires. I slept in a spare room, most likely a library or overflow from a libray. When Aunt Jo showed me my room, she said I should feel free to read anything there. My Uncle Tom pointed out A Clockwork Orange and tried to explain the importance of the corrupt language used by the characters. I certainly didn't understand the book that first time, but the opportunity to read it in such a setting and to have it explained to me by Aunt Jo and Uncle Tom keep me returning to try and understand it.
When I met my wife, (she wasn't actually my wife at the time,) she had a few books that she insisted I read as well. The Princess Bride has been the one that I return to most often. It is a fundamentally silly story, but it hasn't grown stale. I can read it and recall the feeling of being very young and desperately in love with the woman who wasn't my wife yet. The children had to read this story as well, this time at the insistence of both parents.
There are books still waiting to be bound to me by friends and relatives not yet born, just as there are people unaware they will some day be forced to read The Wind In The Willows. For now, I will enjoy the books that were given to me on this Father's Day.
Saturday, June 20, 2009
Making Decisions
One of my favorite lecturers at Michigan was Professor Igor Dolgachev. He was one of the many talented people we were fortunate enough to inherit from the former Soviet Union (and its allies.) He seemed unsure of the US approach to education and its wide ranging requirements. "In Moscow," he told us, "once we decided we were studying math, we studied math. Nothing else!" Then he looked a bit sheepish and bobbed his head, "OK, also Marxism-Leninism, but the rest was math!"
I think what upset him was Michigan's requirement that you take two senior or graduate level courses in a department other than the one granting you your degree. The first course I took to fulfill this requirement was Southeast Asian History. Interestingly, it was taught by a Czech who studied that region because it was one of the few places sufficiently far removed from the concerns of the Czechoslovakian Communist party that he could engage in reasonably honest historical inquiry. It seems that one of the reasons why former Soviet professors and students were such excellent physicists and mathematicians is that it was relatively hard to politicize these disciplines, so the brightest people who wanted intellectual freedom were attracted.
The second course I took was in Industrial and Environmental Health Policy. This course was part of the School of Public Health, and the professor had actually been one of the architects of the Material Safety Data Sheet approach to dealing with toxic industrial chemicals. He contrasted this approach favorably with the more draconian and bureaucratic tack taken by the Superfund Legislation.
At one point in the class, we were talking about the process of legislation, rule making, and inevitably litigation which characterizes health policy in the US. When a rule finally makes it to court, the judge looks at precedent, and then he looks at the legislative history to determine whether the Government's interpretation of a rule is legal (and appropriate.) The actual phrasing of the legislation is also very important when there are confusing, ambiguous, or missing elements for interpreting the law.
When I heard this, I was thunderstruck. I don't spend a great deal of care on choosing prepositions when I write, but this could have a huge effect on how a judge interprets a rule. When you consider the size of some bills, or the generic patriotic, Mom and apple pie style of much legislation, I can't believe that Congress spends as much time as it should choosing its words carefully.
I was studying to be a mathematician when I heard this. My time was spent developing exacting proofs of the truth of exact statements. Natural language is too fluffy and ambiguous to easily lead to an understanding of truth (try reading the original statements of Newton's Laws), yet words carelessly chosen ten or twenty years earlier by a Congressional staffer at 2AM would decide the outcome of a $10billion lawsuit or the fate of a land preserve bigger than Rhode Island.
When I expressed this sentiment to the professor, he was sympathetic, but he pointed out that judges don't have the luxury of not making decisions. All parties expect a resolution in the courts, and the judge has to find some justification for their decision. If all else fails, they will fix on the wording and its legal interpretation, whether or not that was the interpretation of Congress.
I am still uncomfortable with this approach to making decisions, and I will return to it in the future. There are times when we are forced to make decisions without having all of the knowledge we require. This was just the first approach to making a choice I encountered where the goal seemed to be providing a plausible cover for the choice made.
I think what upset him was Michigan's requirement that you take two senior or graduate level courses in a department other than the one granting you your degree. The first course I took to fulfill this requirement was Southeast Asian History. Interestingly, it was taught by a Czech who studied that region because it was one of the few places sufficiently far removed from the concerns of the Czechoslovakian Communist party that he could engage in reasonably honest historical inquiry. It seems that one of the reasons why former Soviet professors and students were such excellent physicists and mathematicians is that it was relatively hard to politicize these disciplines, so the brightest people who wanted intellectual freedom were attracted.
The second course I took was in Industrial and Environmental Health Policy. This course was part of the School of Public Health, and the professor had actually been one of the architects of the Material Safety Data Sheet approach to dealing with toxic industrial chemicals. He contrasted this approach favorably with the more draconian and bureaucratic tack taken by the Superfund Legislation.
At one point in the class, we were talking about the process of legislation, rule making, and inevitably litigation which characterizes health policy in the US. When a rule finally makes it to court, the judge looks at precedent, and then he looks at the legislative history to determine whether the Government's interpretation of a rule is legal (and appropriate.) The actual phrasing of the legislation is also very important when there are confusing, ambiguous, or missing elements for interpreting the law.
When I heard this, I was thunderstruck. I don't spend a great deal of care on choosing prepositions when I write, but this could have a huge effect on how a judge interprets a rule. When you consider the size of some bills, or the generic patriotic, Mom and apple pie style of much legislation, I can't believe that Congress spends as much time as it should choosing its words carefully.
I was studying to be a mathematician when I heard this. My time was spent developing exacting proofs of the truth of exact statements. Natural language is too fluffy and ambiguous to easily lead to an understanding of truth (try reading the original statements of Newton's Laws), yet words carelessly chosen ten or twenty years earlier by a Congressional staffer at 2AM would decide the outcome of a $10billion lawsuit or the fate of a land preserve bigger than Rhode Island.
When I expressed this sentiment to the professor, he was sympathetic, but he pointed out that judges don't have the luxury of not making decisions. All parties expect a resolution in the courts, and the judge has to find some justification for their decision. If all else fails, they will fix on the wording and its legal interpretation, whether or not that was the interpretation of Congress.
I am still uncomfortable with this approach to making decisions, and I will return to it in the future. There are times when we are forced to make decisions without having all of the knowledge we require. This was just the first approach to making a choice I encountered where the goal seemed to be providing a plausible cover for the choice made.
Thursday, June 18, 2009
I, For One, Snicker At Our New Robot Overlords
Inigo was chasing his tail last night. Amusement is another perk of dog ownership. He wanted to chew on an itchy spot on his back, but the temptation of the waving, fluffy tail was too much for his hunter instinct.
I don't think Inigo is a stupid dog. A robot capable of all that Inigo could do would be worth a fortune. The state of the art robot can roughly approximate Inigo's ability to walk over rough ground, but it has none of his grace or speed (although Inigo has a hard time on wooden floors.) In addition, Inigo has cognitive abilities we don't understand well enough to teach to a robot. He can smell and eat old dog poop before I even see it is there. He recognizes people who should be greeted enthusiastically. He knows how to sneak food off of the counter without my noticing.
Computers and algorithms are good enough to now beat pretty much anyone at chess; however, Go masters are still unchallenged by computer programs. The robot soccer tournament is interesting, but still mostly silly.
I believe that even when robots become clever and mobile enough to take over, we can still expect them to be stupid in a lot of ways. They will likely be stupid in the same ways that we are.
I have worked on human directed balancing wheelchairs. Every person who sees one wants to know when we were going to add a vision system and give more autonomy to the machine. But before we give autonomy to the machine, we have to figure out how it will detect when the family cat is twining around the wheels (or more importantly, when a grandchild is underfoot.) Vision systems can make balancing more stable, just as your eyes help keep you stable. (If you doubt how important your eyes are to balance, try to stand up strait with your eyes closed.) But if we use vision for balance, we need to figure out that we are next to a moving truck. This unexpected motion would cause the same dizziness in the machine that it does when you are stopped next to a moving truck at a stoplight.
A lot of human (and canine) stupidity is tied to carrying around an incorrect model for too long. I talk to my mother about iced tea, and when she picks up her soda, she is disturbed by the fact it doesn't taste like tea. I turn onto the highway on a Saturday morning, because I pull onto the highway every morning to go to work. I pick up the book I am bringing home from the front seat of the car, and leave my keys in the ignition, because I have already taken one thing from the car and I always take just one thing from the car.
I believe a lot of professions requiring quick, life and death decisions, e.g. doctors and soldiers, mitigate this through constant and extensive training. Young doctors are presented with a ludicrous number of patients during their training so that twenty years later, they have pathways in their brain to recognize symptoms and to apply treatment. Pilots supplement their training with procedures and a controlled environment. When something is wrong in an airplane, it disturbs the meticulous arrangement of the environment and calls attention to itself. Yet pilots, abetted by the automated systems of their planes still make fatal mistakes.
Our robot overlords will also have to face this problem of when does its current model of the world no longer apply. I watched a talk by Marvin Minsky. His thought was that it is stupid to think that computers won't be able to think, just because all they can do is perform billions of logical operations in a second with perfect accuracy. He also thought that it is stupid to believe that there will be a single approach to artificial intelligence. Sometimes the computer will be an expert system, sometimes a neural net, and sometimes a decision tree.
Computers will have to decide to when to switch between approaches and when to alter its model of the world. They will be just as dependent as we are upon the world providing them the clues that things have changed. They will have the advantage that they can more consistently monitor their environment and they can calculate the relative errors in all of the models they are using. But even they will be limited to the amount of information they can process and the number of predictions they can make. They will likely be better than us in almost every way, but we can still expect a fair amount of tail chasing.
I don't think Inigo is a stupid dog. A robot capable of all that Inigo could do would be worth a fortune. The state of the art robot can roughly approximate Inigo's ability to walk over rough ground, but it has none of his grace or speed (although Inigo has a hard time on wooden floors.) In addition, Inigo has cognitive abilities we don't understand well enough to teach to a robot. He can smell and eat old dog poop before I even see it is there. He recognizes people who should be greeted enthusiastically. He knows how to sneak food off of the counter without my noticing.
Computers and algorithms are good enough to now beat pretty much anyone at chess; however, Go masters are still unchallenged by computer programs. The robot soccer tournament is interesting, but still mostly silly.
I believe that even when robots become clever and mobile enough to take over, we can still expect them to be stupid in a lot of ways. They will likely be stupid in the same ways that we are.
I have worked on human directed balancing wheelchairs. Every person who sees one wants to know when we were going to add a vision system and give more autonomy to the machine. But before we give autonomy to the machine, we have to figure out how it will detect when the family cat is twining around the wheels (or more importantly, when a grandchild is underfoot.) Vision systems can make balancing more stable, just as your eyes help keep you stable. (If you doubt how important your eyes are to balance, try to stand up strait with your eyes closed.) But if we use vision for balance, we need to figure out that we are next to a moving truck. This unexpected motion would cause the same dizziness in the machine that it does when you are stopped next to a moving truck at a stoplight.
A lot of human (and canine) stupidity is tied to carrying around an incorrect model for too long. I talk to my mother about iced tea, and when she picks up her soda, she is disturbed by the fact it doesn't taste like tea. I turn onto the highway on a Saturday morning, because I pull onto the highway every morning to go to work. I pick up the book I am bringing home from the front seat of the car, and leave my keys in the ignition, because I have already taken one thing from the car and I always take just one thing from the car.
I believe a lot of professions requiring quick, life and death decisions, e.g. doctors and soldiers, mitigate this through constant and extensive training. Young doctors are presented with a ludicrous number of patients during their training so that twenty years later, they have pathways in their brain to recognize symptoms and to apply treatment. Pilots supplement their training with procedures and a controlled environment. When something is wrong in an airplane, it disturbs the meticulous arrangement of the environment and calls attention to itself. Yet pilots, abetted by the automated systems of their planes still make fatal mistakes.
Our robot overlords will also have to face this problem of when does its current model of the world no longer apply. I watched a talk by Marvin Minsky. His thought was that it is stupid to think that computers won't be able to think, just because all they can do is perform billions of logical operations in a second with perfect accuracy. He also thought that it is stupid to believe that there will be a single approach to artificial intelligence. Sometimes the computer will be an expert system, sometimes a neural net, and sometimes a decision tree.
Computers will have to decide to when to switch between approaches and when to alter its model of the world. They will be just as dependent as we are upon the world providing them the clues that things have changed. They will have the advantage that they can more consistently monitor their environment and they can calculate the relative errors in all of the models they are using. But even they will be limited to the amount of information they can process and the number of predictions they can make. They will likely be better than us in almost every way, but we can still expect a fair amount of tail chasing.
Wednesday, June 17, 2009
Best friends
This morning our dog Inigo woke Jess and I up at 5:00. Yesterday, he woke up at 4:30AM, but we didn't have to pay attention to him until 5:00.
We got a dog about two months ago, because Brendan really wanted one. I did the same thing to my parents, so karma seems to be working properly. Inigo is about 35lbs and looks mostly like a black lab. He has white on his chest, and a few other spots, and his ears cock like the ears of the dog on the RCA record. He is about a year old.
Inigo is much like having a third baby. He is very loud if ignored for too long. You risk the carpet if you delay taking him outside. We find our conversations once again revolve around bodily functions. He has the single-minded insanity and self-absorption of your typical three-year old.
I don't have the intense affection for him that I had for my children when they were in the same stage of development. This is most likely healthy, but it does mean that attending to his needs is motivated by duty and the need to keep the house in decent shape.
I suspect that I will develop deep feelings for him. Certainly, I have for various cats. Emma has always been a paragon of catly virtue. She never gave a damn for any of us, and I believe she would cheerfully murder us in our sleep and eat us, if only she were bigger. Yet Emma will also climb into my lap and purr the loudest of any of our cats. When she is finished, she will bite me and hop off. Flit, on the other hand, is desperately affectionate. I protect her from the horrible things the world (mostly Emma) does to her.
Despite the work and annoyance of a dog, and they are a lot more work and annoyance than cats, I have already noticed some benefits. Inigo is the creature most obviously glad to see me in the evening. I haven't been greeted at the door like this, since my children were toddlers. My cardio health is also improving. We take Inigo on a lot of long walks. Our neighbors laugh at how much time we spend walking, but it keeps him from destroying things in the house, and I hope it exhausts him to the point where he will be content to sit on the couch for a while.
I have never been motivated to leave the house and walk through the neighborhood. Inigo provides the motivation. He also provides a good excuse. I feel goofy walking around by myself, but people see you with a dog, and they understand what you are up to. I would like to be able to walk him without a leash. He has amazing athletic ability, but my ambling pace restrains his attempts to catch butterflies and chase squirrels. We are taking him to obedience school, so maybe in the future.
According to Brendan, Labrador Retrievers have about four years of acting like a puppy. Inigo should be done when Brendan graduates. My cardio health will likely suffer as a result of Inigo's entry into middle age, but I am looking forward to sitting on the couch with him.
We got a dog about two months ago, because Brendan really wanted one. I did the same thing to my parents, so karma seems to be working properly. Inigo is about 35lbs and looks mostly like a black lab. He has white on his chest, and a few other spots, and his ears cock like the ears of the dog on the RCA record. He is about a year old.
Inigo is much like having a third baby. He is very loud if ignored for too long. You risk the carpet if you delay taking him outside. We find our conversations once again revolve around bodily functions. He has the single-minded insanity and self-absorption of your typical three-year old.
I don't have the intense affection for him that I had for my children when they were in the same stage of development. This is most likely healthy, but it does mean that attending to his needs is motivated by duty and the need to keep the house in decent shape.
I suspect that I will develop deep feelings for him. Certainly, I have for various cats. Emma has always been a paragon of catly virtue. She never gave a damn for any of us, and I believe she would cheerfully murder us in our sleep and eat us, if only she were bigger. Yet Emma will also climb into my lap and purr the loudest of any of our cats. When she is finished, she will bite me and hop off. Flit, on the other hand, is desperately affectionate. I protect her from the horrible things the world (mostly Emma) does to her.
Despite the work and annoyance of a dog, and they are a lot more work and annoyance than cats, I have already noticed some benefits. Inigo is the creature most obviously glad to see me in the evening. I haven't been greeted at the door like this, since my children were toddlers. My cardio health is also improving. We take Inigo on a lot of long walks. Our neighbors laugh at how much time we spend walking, but it keeps him from destroying things in the house, and I hope it exhausts him to the point where he will be content to sit on the couch for a while.
I have never been motivated to leave the house and walk through the neighborhood. Inigo provides the motivation. He also provides a good excuse. I feel goofy walking around by myself, but people see you with a dog, and they understand what you are up to. I would like to be able to walk him without a leash. He has amazing athletic ability, but my ambling pace restrains his attempts to catch butterflies and chase squirrels. We are taking him to obedience school, so maybe in the future.
According to Brendan, Labrador Retrievers have about four years of acting like a puppy. Inigo should be done when Brendan graduates. My cardio health will likely suffer as a result of Inigo's entry into middle age, but I am looking forward to sitting on the couch with him.
Algorithm Efficiency
I made a first pass through Charles Bennett's paper "The Thermodynamics of Computation - A Review." There are a number of interesting parts.
One that is just cool, is a description of how to make a computer out of billiard balls and rigid walls which theoretically dissipates no energy for computation. It is capable of this performance while actually making measurable progress on the computations. It has a few disadvantages. It is vulnerable to outside influence, so it must be thermally isolated, or the computations cease to be accurate after a handful of iterations. It is actually sensitive enough that the tidal forces from the atmospheric turbulence of nearby extra-solar stars will destroy the algorithm in a few hundred computations.
Bennett and others also have proposed a Brownian motion computer (Turing machine). In the presence of a weak driving force, an algorithm will progress toward its conclusion. The higher the speed, the more energy is dissipated by the computer, but in the limit, it is a lossless computer. The chemical actions of RNA polymerase synthesis can act as the elements of a Brownian motion Turing machine.
Bennet measures the energy dissipated by a computation in kT, the order of energy contained in a single molecule of the system. At room temperature, kT~10^-21J. RNA polymerase synthesis dissipates about 20kT per computation, while a digital computer dissipates about 10^11kT (at least in 1982.)
Bennett's paper demonstrates that the measurement required by Maxwell's Demon does not increase the entropy of the system (or its environment), provided the measuring device starts in a known state. The entropy change in the system arises from the necessity to return the measurement device to a known state. The entropy change is ln(2)kT and it matches the work extracted by Maxwell's Demon.
I need to read through the article more carefully, but I believe that we can consider the minimum entropy added to a system to be the change in entropy of all of the information encoded by the algorithm, the computer's memory, and the information stream feeding the algorithm from when the algorithm starts until it finishes. We may not actually have to consider the entropy of the input stream. The complexity of the algorithm required to extract the answer from input streams with a variety of entropies may already book this value. It may also be that the complexity of the algorithm can be predicted from the entropy change in going from the input data stream to the output data stream. This is probably related to why programs for handling free-form data entry are much more complicated than programs which handle data entered with a rigid format.
We can look at the efficiency of an algorithm by determining how much extra entropy is created to execute the algorithm than is strictly required to solve the problem. Efficiency of an algorithm should be directly measurable, since there should be a correspondance between the entropy created by a processor and the entropy of the algorithm it is executing. It also appears that the speed of computation has an effect on the entropy dissipation. Certainly, for the Brownian motion computers, speed of computation is related to the amount of energy expended per computation.
I wonder if ultra-low temperature computers would be slow? The kT term is small, but molecular interaction/velocity should be correspondingly small.
One that is just cool, is a description of how to make a computer out of billiard balls and rigid walls which theoretically dissipates no energy for computation. It is capable of this performance while actually making measurable progress on the computations. It has a few disadvantages. It is vulnerable to outside influence, so it must be thermally isolated, or the computations cease to be accurate after a handful of iterations. It is actually sensitive enough that the tidal forces from the atmospheric turbulence of nearby extra-solar stars will destroy the algorithm in a few hundred computations.
Bennett and others also have proposed a Brownian motion computer (Turing machine). In the presence of a weak driving force, an algorithm will progress toward its conclusion. The higher the speed, the more energy is dissipated by the computer, but in the limit, it is a lossless computer. The chemical actions of RNA polymerase synthesis can act as the elements of a Brownian motion Turing machine.
Bennet measures the energy dissipated by a computation in kT, the order of energy contained in a single molecule of the system. At room temperature, kT~10^-21J. RNA polymerase synthesis dissipates about 20kT per computation, while a digital computer dissipates about 10^11kT (at least in 1982.)
Bennett's paper demonstrates that the measurement required by Maxwell's Demon does not increase the entropy of the system (or its environment), provided the measuring device starts in a known state. The entropy change in the system arises from the necessity to return the measurement device to a known state. The entropy change is ln(2)kT and it matches the work extracted by Maxwell's Demon.
I need to read through the article more carefully, but I believe that we can consider the minimum entropy added to a system to be the change in entropy of all of the information encoded by the algorithm, the computer's memory, and the information stream feeding the algorithm from when the algorithm starts until it finishes. We may not actually have to consider the entropy of the input stream. The complexity of the algorithm required to extract the answer from input streams with a variety of entropies may already book this value. It may also be that the complexity of the algorithm can be predicted from the entropy change in going from the input data stream to the output data stream. This is probably related to why programs for handling free-form data entry are much more complicated than programs which handle data entered with a rigid format.
We can look at the efficiency of an algorithm by determining how much extra entropy is created to execute the algorithm than is strictly required to solve the problem. Efficiency of an algorithm should be directly measurable, since there should be a correspondance between the entropy created by a processor and the entropy of the algorithm it is executing. It also appears that the speed of computation has an effect on the entropy dissipation. Certainly, for the Brownian motion computers, speed of computation is related to the amount of energy expended per computation.
I wonder if ultra-low temperature computers would be slow? The kT term is small, but molecular interaction/velocity should be correspondingly small.
Tuesday, June 16, 2009
Photography
About two years ago, I bought myself a digital SLR camera. My grandfather was a nature photographer of some reputation. My father showed me several pictures that he took when he was young, which I think show a great deal of talent. My brother has several photographs he has taken in his home, which I find very cool.
I have irregularly taken pictures, and I find that I like several of them. However, when I entered some of them into a WIRED photo-contest, they attracted less than no attention. As I looked back at what I submitted, I agree with the crowd's opinion. I have some interesting pictures of Portsmouth, NH, but they look pretty much like any picture of a seaside. My pictures of the Manchester, NH, mills look very much like any picture of industrial architecture. Since I have only nodding acquaintance with the technical aspects of photography, they are only accidentally competent
Margret Bourke-White has magnificent pictures of industry. Henri Cartier creates amazing city-scapes. Annie Leibovitz's portraits are compelling. When I take pictures, I end up seeing the world as it is portrayed in their photographs. What results is a marginally competent photograph which looks vaguely like something you have already seen.
I find my photographs interesting, because I know the people in the picture and I know the locations where they are taken. They are certainly good enough to decorate my house, but they won't have any connection or drama for other people. Truly great photographers seem to create a universal connection. Their photographs become symbolic of an object or place or time. In Annie Leibovitz's case, the subject is already well-known, so we are interested in the person in her snapshot. Her talent somehow makes her snapshot the iconic image of that celebrity.
It is still possible to take significant photographs. Not all of human experience has been codified into an image. One of the winners of a WIRED photo-contest submitted a picture of his five year old daughter in a fur-lined parka, that I still recall for its perfection of light and texture and composition. This was someone else's family portrait, yet I find it particularly compelling.
Human drama also provides endless opportunity for taking the perfect picture. Robert Capa said, "If your pictures aren't good enough, you aren't close enough." He gives hope that I can still take a perfect picture if I am just prepared to plunge into the world around me. I will try to take pictures more regularly. Hopefully, familiarity with the camera will allow me to capture the "decisive moment" when I see it.
I have irregularly taken pictures, and I find that I like several of them. However, when I entered some of them into a WIRED photo-contest, they attracted less than no attention. As I looked back at what I submitted, I agree with the crowd's opinion. I have some interesting pictures of Portsmouth, NH, but they look pretty much like any picture of a seaside. My pictures of the Manchester, NH, mills look very much like any picture of industrial architecture. Since I have only nodding acquaintance with the technical aspects of photography, they are only accidentally competent
Margret Bourke-White has magnificent pictures of industry. Henri Cartier creates amazing city-scapes. Annie Leibovitz's portraits are compelling. When I take pictures, I end up seeing the world as it is portrayed in their photographs. What results is a marginally competent photograph which looks vaguely like something you have already seen.
I find my photographs interesting, because I know the people in the picture and I know the locations where they are taken. They are certainly good enough to decorate my house, but they won't have any connection or drama for other people. Truly great photographers seem to create a universal connection. Their photographs become symbolic of an object or place or time. In Annie Leibovitz's case, the subject is already well-known, so we are interested in the person in her snapshot. Her talent somehow makes her snapshot the iconic image of that celebrity.
It is still possible to take significant photographs. Not all of human experience has been codified into an image. One of the winners of a WIRED photo-contest submitted a picture of his five year old daughter in a fur-lined parka, that I still recall for its perfection of light and texture and composition. This was someone else's family portrait, yet I find it particularly compelling.
Human drama also provides endless opportunity for taking the perfect picture. Robert Capa said, "If your pictures aren't good enough, you aren't close enough." He gives hope that I can still take a perfect picture if I am just prepared to plunge into the world around me. I will try to take pictures more regularly. Hopefully, familiarity with the camera will allow me to capture the "decisive moment" when I see it.
Monday, June 15, 2009
Autopilot
I was making my sandwich this morning, and it looked as if I would not have enough cheese for tomorrow's sandwich, even though I have enough baloney. My immediate thought was that I should stop at the grocery store after class tonight and pick-up some more cheese. (Swiss is on sale. It did not occur to me until just now that I should also pick up some more baloney, which is also on sale.) My next thought was, "Why do I need to have cheese on my baloney sandwich?" It won't improve the flavor, but I always put cheese on my sandwiches.
After moving past the baloney sandwich, I rinsed a bunch of grapes and added them to my lunch. Maybe because I was primed to note my own inanity, I wondered why I was rinsing my grapes. There is some guarantee of safety by purchasing the grapes from a grocery store. Even if the grapes are not actually safe, rinsing them for a few seconds in cold water is unlikely to make them safer. However, my mom always rinsed the grapes, so I do too.
I appear to live much of my life on autopilot. My naive understanding of Zen leads me to think they view this as negative, and that you should strive to live in every moment. I am ambivalent.
I don't know that I want to spend much time thinking about lunch. If I did, I would likely make better choices than baloney. Would these choices lead me to spend more time shopping for healthy and tasty foods to put in my lunch? Would I need to spend more time on creating a suitable environment for eating lunch? I imagine that answering these questions positively would lead me to a more contemplative life where I am required to participate in the production of what I eat.
What I really want to think about, which is why I don't spend time thinking about lunch, is: how can the algorithm efficiency question be resolved? how can I ensure my son is reaching toward happiness and is aware that I love him? how can I make my wife happier? how do I continue to connect with my daughter as her life separates further and further from mine?
However, as I write out the implications of thinking more about my lunch, I begin to wonder if my naive understanding of Zen is better suited to letting me think about what I want. A measured and contemplative life absorbed by ensuring that all moments and actions are noted, appreciated, and performed well, must lead to easier resolution of difficult questions than the quick tossing together of lunch so that I can beat the traffic jam where 495 crosses Route 3.
After moving past the baloney sandwich, I rinsed a bunch of grapes and added them to my lunch. Maybe because I was primed to note my own inanity, I wondered why I was rinsing my grapes. There is some guarantee of safety by purchasing the grapes from a grocery store. Even if the grapes are not actually safe, rinsing them for a few seconds in cold water is unlikely to make them safer. However, my mom always rinsed the grapes, so I do too.
I appear to live much of my life on autopilot. My naive understanding of Zen leads me to think they view this as negative, and that you should strive to live in every moment. I am ambivalent.
I don't know that I want to spend much time thinking about lunch. If I did, I would likely make better choices than baloney. Would these choices lead me to spend more time shopping for healthy and tasty foods to put in my lunch? Would I need to spend more time on creating a suitable environment for eating lunch? I imagine that answering these questions positively would lead me to a more contemplative life where I am required to participate in the production of what I eat.
What I really want to think about, which is why I don't spend time thinking about lunch, is: how can the algorithm efficiency question be resolved? how can I ensure my son is reaching toward happiness and is aware that I love him? how can I make my wife happier? how do I continue to connect with my daughter as her life separates further and further from mine?
However, as I write out the implications of thinking more about my lunch, I begin to wonder if my naive understanding of Zen is better suited to letting me think about what I want. A measured and contemplative life absorbed by ensuring that all moments and actions are noted, appreciated, and performed well, must lead to easier resolution of difficult questions than the quick tossing together of lunch so that I can beat the traffic jam where 495 crosses Route 3.
Saturday, June 13, 2009
Algorithm efficiency
I did a little research. The latest thought on information entropy and Maxwell's Demon appear to have been developed by Charles Bennett in 1982. The irreversible part of the process arises from the need to erase memory about the state of the system.
I haven't found whether anyone has developed an equivalence between this and the work done by an algorithm.
I haven't found whether anyone has developed an equivalence between this and the work done by an algorithm.
Friday, June 12, 2009
Algorithm Efficiency
Is there a theoretically most efficient algorithm for performing a particular task?
I began wondering about this question while working on a signal processing project using a processor with very limited computation and memory. Inefficiency in design limits the system's ability to perform other tasks, so it would be useful to know how close to ideal an algorithm is. Furthermore, such a measure would bound the tasks a system is capable of performing.
Driving home last night, I thought about Maxwell's Demon. I remember reading that the missing work in the description of the system is contained in the intelligence of the demon and its measurement of the environment. I am also tentatively aware that information, data, and information transmission have associated entropy measures.
Is it be possible to express a task as a Maxwell's Demon lowering the entropy of information. The optimal efficiency in performing the task would be related to the minimal work required to change the entropy.
If I recall my statistical physics properly, the work required to change the entropy of a system also depends upon the temperature of the system. In statistical physics, the temperature is related to the speed of the gas molecules making up the system. Is it possible to define an analogous notion for information related to the rate of information arriving or the speed of computation?
I began wondering about this question while working on a signal processing project using a processor with very limited computation and memory. Inefficiency in design limits the system's ability to perform other tasks, so it would be useful to know how close to ideal an algorithm is. Furthermore, such a measure would bound the tasks a system is capable of performing.
Driving home last night, I thought about Maxwell's Demon. I remember reading that the missing work in the description of the system is contained in the intelligence of the demon and its measurement of the environment. I am also tentatively aware that information, data, and information transmission have associated entropy measures.
Is it be possible to express a task as a Maxwell's Demon lowering the entropy of information. The optimal efficiency in performing the task would be related to the minimal work required to change the entropy.
If I recall my statistical physics properly, the work required to change the entropy of a system also depends upon the temperature of the system. In statistical physics, the temperature is related to the speed of the gas molecules making up the system. Is it possible to define an analogous notion for information related to the rate of information arriving or the speed of computation?
Wednesday, June 10, 2009
Why Am I Here
My daughter leaves for Kenya on Friday.
She will graduate from college in December, and my son finishes his freshman year of high school in two weeks. My children won't really need me for too much longer.
As this part of my life ends, fundamental questions start intruding. I wonder, "Is my life serving a purpose?" I wonder, "Is my presence a net gain for the world?" I wonder, "Is there anything I can still contribute?"
Less obviously self-absorbed questions also occur to me. Can you have an economy in a refugee camp or a slum which benefits the inhabitants? Can you determine a limiting efficiency for implementing an algorithm in the same way that you can define Carnot efficiency for a heat engine? Can you make good choices in the absence of knowledge about the problem?
Finally, I stumble across interesting objects, sites, books and music. This morning, MetaFilter pointed me to a website about Goths in Hot Weather. I have been working my way through Magnum's collection of photographers for a few years. I think the last, most interesting book I read was Graceling, by Kristin Cashore.
I would like to share my questions and my discoveries with people who will take them with some seriousness, or at least gentle disdain. I would like these people to share their questions and discoveries. We are unlikely to discover anything original for the world, but hopefully, our discoveries will be original for us.
She will graduate from college in December, and my son finishes his freshman year of high school in two weeks. My children won't really need me for too much longer.
As this part of my life ends, fundamental questions start intruding. I wonder, "Is my life serving a purpose?" I wonder, "Is my presence a net gain for the world?" I wonder, "Is there anything I can still contribute?"
Less obviously self-absorbed questions also occur to me. Can you have an economy in a refugee camp or a slum which benefits the inhabitants? Can you determine a limiting efficiency for implementing an algorithm in the same way that you can define Carnot efficiency for a heat engine? Can you make good choices in the absence of knowledge about the problem?
Finally, I stumble across interesting objects, sites, books and music. This morning, MetaFilter pointed me to a website about Goths in Hot Weather. I have been working my way through Magnum's collection of photographers for a few years. I think the last, most interesting book I read was Graceling, by Kristin Cashore.
I would like to share my questions and my discoveries with people who will take them with some seriousness, or at least gentle disdain. I would like these people to share their questions and discoveries. We are unlikely to discover anything original for the world, but hopefully, our discoveries will be original for us.
Subscribe to:
Posts (Atom)