Libertarians are kind of annoying in their purism, but I think it’s a useful political philosophy to use as a thought experiment, at least to highlight the ways in which we are willing to let our liberty be reduced.
The easy argument against strict libertarianism (=no government action except the enforcement of contracts and national defense) is: what will you do when your house catches on fire—or if your neighbors’ house catches on fire. Clearly there are some collective goods that we want government to provide because the market alone will not adequately account for the externalities (positive or negative). That said, we don’t need government to _run_ everything. For example, we think that to ensure equal opportunity, we want every child to have access to a good school. That doesn’t mean the government needs to operate the schools, just that it has to pay for them. Hence the logic of charters. [Aside: I won’t go into the arguments against vouchers here, but I think there are good ones.]
Sandel’s 1st two libertarian requirements: 1) No paternalism, and 2) No moral laws are fairly hard to argue against. Of course, when your actions incur a cost on others, we have a right to restrict them. Heroin addicts tend to steal other people’s property, so we are justified in legislating against heroin use.
The third libertarian requirement, that there be no redistribution of wealth, is a bit tougher. Technically, as soon as you charge one person more in taxes than another person, you are redistributing wealth. Maybe the libertarian would argue for a flat tax instead of progressive tax policy. From a strictly libertarian perspective, it is hard to argue for progressive taxation. But I think once you take a broader look at justice (for example, adopting the veil of ignorance), a progressive tax policy becomes pretty reasonable.
One last point on libertarianism. It basically assumes that every individual is entitled to his own rights to do whatever he wants. However, the reality is that we have only one habitable planet, and we’re all stuck sharing the finite resources we have access to on Earth. The ideal of everybody being able to do whatever they want simply doesn’t work when there are finite resources. So we’re going to have to give up some of our individual rights in order to survive together on this one planet. Surely we can figure out a fair way to do that.
Sunday, January 11, 2009
Sunday, January 4, 2009
Justice Lecture 4: Higher vs. lower pleasures
This lecture really annoyed me. Sandel describes how Mill distinguishes between higher and lower pleasures. Mill’s argument as I understand it is that higher pleasures trump the lower pleasures in terms of the utilitarian calculus. So, for example, the pleasure that I derive from being able to eat a bowl of rice if I’m starving should trump whatever pleasure you derive from tossing that bowl of rice in the mud. It’s been too long since I’ve read Mill, so maybe I’m not accurately representing his position. But if I were drawing distinctions between the utility gained from different kinds of activities, that’s the sort of distinction I would want to draw: one that can be universally agreed upon. Having a shelter over your head, or food to eat, or medicine to make you healthy are all going to trump pleasure gained from entertainment.
However, Sandel polls the class about whether they prefer the Simpson’s or Shakespeare. To me, this is not a very important distinction in matters of ethics. There are reasons to prefer one or the other, but ultimately not all people are going to agree. But who cares? So what if someone prefers watching mass-produced cartoons than live theater? Lots of people would pay more to see a football game than the symphony, or spend more money on their monthly cable bill than they do buying books. We could have a long debate about promoting culture and education and reasoned thinking, but that debate doesn’t really change our moral code. Individuals get to choose what they enjoy doing, whether that’s watching a ballgame or a lecture.
However, we will draw the line when the pleasures of diversion come into conflict with basic human needs like sustenance, shelter, freedom, or health. Let’s not let the other debate about culture be confused with this distinction.
p.s. Are all values commensurable? If they are, we should be able to translate all values into dollar amounts. I think I'll come down with the economists on this one and say that we can assign dollar amounts to all values. We certainly have to make tradeoff decisions; how else can we make those decisions than by comparing different values.
However, Sandel polls the class about whether they prefer the Simpson’s or Shakespeare. To me, this is not a very important distinction in matters of ethics. There are reasons to prefer one or the other, but ultimately not all people are going to agree. But who cares? So what if someone prefers watching mass-produced cartoons than live theater? Lots of people would pay more to see a football game than the symphony, or spend more money on their monthly cable bill than they do buying books. We could have a long debate about promoting culture and education and reasoned thinking, but that debate doesn’t really change our moral code. Individuals get to choose what they enjoy doing, whether that’s watching a ballgame or a lecture.
However, we will draw the line when the pleasures of diversion come into conflict with basic human needs like sustenance, shelter, freedom, or health. Let’s not let the other debate about culture be confused with this distinction.
p.s. Are all values commensurable? If they are, we should be able to translate all values into dollar amounts. I think I'll come down with the economists on this one and say that we can assign dollar amounts to all values. We certainly have to make tradeoff decisions; how else can we make those decisions than by comparing different values.
Sunday, December 28, 2008
Justice Lecture 3: The cost of a life
The case study in this lecture is an internal memo from Ford that assigns a dollar value to a human life in deciding whether or not to issue a recall of its Pinto cars. Most of the students in the class called this move objectionable, but the obvious objection to that position is: how else do you decide whether to do something? For example, we could certainly reduce the number of traffic deaths by imposing a mandatory 25 mph speed limit across the country. If the value of a human life were infinite, we would be compelled to take such an action. However, we don’t think that lives are infinitely valuable. An important point here is that no action can ever be guaranteed to save a life, i.e., we can only take actions that have some statistical probability of saving lives. This probability must enter into the likelihood of the calculation. Resources are scarce. We only have so many bags of rice or vaccines to ship around the world, so we have to make hard choices. I don’t think that we boost our ethical consciousness by ignoring the dollar value that we place on human lives. Rather, I think by talking about the value of a life we will become more aware of how tough ethical decisions have to be made. Also, I think it would expose the dramatically distorted value that we place on human lives in, for example, Congo compared to human lives in California.
Sandel offers a counter argument to the contention that we must assign a dollar value to human lives. He uses the example of the Roman coliseum: maybe the combined utility of all the people enjoying the show would outweigh the loss of life for the slave who gets tortured and murdered in the coliseum. Therefore: killing for sport is justifiable. Here’s another (imaginary) example: Jon Krakauer writes Under the Banner of Heaven, which offends millions of Mormons. Therefore, Krakauer’s book should not be published. In each of these examples, an individual right is overcome by the aggregate utility of a large number of people. How does the rule-based utilitarian face these cases? I think the answer is that we believe in individual rights because over the long run they lead to a maximization of utility. Though there may be some fluke cases in which aggregate utility is increased by violating individual rights, but overall we want to live in a society where we are free from murder or free to express ourselves. So we make those rights near-absolute. When individual rights are violated, as is done for criminals, we want this done by a body (the criminal justice system) that follows fair procedures.
Sandel offers a counter argument to the contention that we must assign a dollar value to human lives. He uses the example of the Roman coliseum: maybe the combined utility of all the people enjoying the show would outweigh the loss of life for the slave who gets tortured and murdered in the coliseum. Therefore: killing for sport is justifiable. Here’s another (imaginary) example: Jon Krakauer writes Under the Banner of Heaven, which offends millions of Mormons. Therefore, Krakauer’s book should not be published. In each of these examples, an individual right is overcome by the aggregate utility of a large number of people. How does the rule-based utilitarian face these cases? I think the answer is that we believe in individual rights because over the long run they lead to a maximization of utility. Though there may be some fluke cases in which aggregate utility is increased by violating individual rights, but overall we want to live in a society where we are free from murder or free to express ourselves. So we make those rights near-absolute. When individual rights are violated, as is done for criminals, we want this done by a body (the criminal justice system) that follows fair procedures.
Sunday, December 21, 2008
Justice Lecture 2: The case of the cabin boy
First, Sandel describes the distinction between consequentialist and categorical approaches to morality. As I see it, any moral code must be consequentialist at its most fundamental level. There are no absolute moral laws in the universe, that is, morality does not exist independently of sentient beings. In a world with no consciousness, there is no right or wrong. The is no way to morally differentiate between, say, Mercury and Pluto. However, once there is consciousness (even if rudimentary), then we can start to make moral evaluations. At this foundational level, what we care about is minimizing suffering and maximizing pleasure and happiness (broadly defined). Again, we do not make moral judgments about inanimate objects, unless they have an impact on the quality of life of living beings.
Thus any moral code must at its most fundamental be utilitarian, in the most general form of the definition. That is to say, a moral code is utilitarian if it is grounded in promoting the quality of life of living beings. I assert that this is the only thing we value. There is nothing else that we really care about. If a moral code is *not* utilitarian, then what does it value? The shape of rocks? The temperature? The periods of planetary revolution?
[ASIDE: Here I am ignoring any moral claims that are derived from religious dogma. The justification for any of these claims is an appeal to authority which is not widely accepted by all people. Even if such an appeal were accepted by a majority (say, a majority in a single nation), I reject any moral argument of the form “I believe X because Y tells me so,” where Y is Moses, Jesus, Muhammad, God, etc. The only defensible arguments that are valid are ones which all reasonable people can accept. Rawls has talked a lot about this (in Political Liberalism), but it’s been awhile since I read it, so I won’t want into it now.
[One might say, well, how are you going to live in a civil society with all those people who derive their morality from moral codes? My goal here is not to describe what morality actually is followed by most people. Instead, I want to lay out my own argument for a justifiable moral code. I think it’s right, and I think people ought to adopt it based on the reasons as I describe them. But I fully understand that many people will not follow this morality. Despite that fact, I still think that democracy is the best political structure, even if many members of the society do not have moral/political values that I subscribe to. Ultimately, I think my moral code—let’s call it limited liberalism for now—will be the one that societies converge toward. END ASIDE.]
So let’s start from the assertion that all reasonable moral codes must be at their most fundamental level motivated by utilitarian values. Now, the question is how to best achieve this. One extreme approach, let’s call it “OCD Utilitarianism,” says that to make a moral judgment, one must perform an extended calculation of all the ramifications of your decision. For example, if I am a doctor and two patients arrive in the ER, I need to do a full background check—family members, career history, resume, etc.—in order to evaluate which one to save. Taken to this logical extreme, OCD utilitarianism is obviously unrealistic. We simply have too many decisions to make every day for this to be realistic. My point is proposing this ridiculous moral code is to demonstrate that we live in a world of complexity, uncertainty, and scarcity (of time and resources). To make decisions, we need to have simplifying rules of thumb. These are not absolute moral laws, but rather moral guidelines.
For example, one moral rule of thumb is to feed kids milk. We break this rule commonly, whenever a child is lactose-intolerant. Another moral rule of thumb that is less commonly broken is to stop at red lights. However, there are certainly some rare cases when it is morally justifiable to violate this rule, e.g., if a passenger is dying of a gunshot wound in the backseat and you’re trying to get to the hospital. Given that we need to make decisions quickly, we need moral rules of thumb to help us make moral decisions. Since we live in a world of uncertainty, sometimes following these rules of thumb will lead us to make decisions that, in hindsight, we regret. Many laws of the state are based on these kinds of moral rules of thumb: do not kill, do not steal, do not prevent people from worshiping as they choose, etc. These are not absolute moral laws but rather very strong rules of thumb which may be justifiably broken only under very rare circumstances.
So any moral code will need a way of deriving moral rules of thumb; OCD utilitarianism is simply untenable. The moral codes which claim to be alternatives to utilitarianism (such as the categorical imperative, or contractualism) really just disagree about how to generate the rules of thumb. The end goal is to create a set of laws that maximizes quality of living.
Now, one of the big outstanding questions to resolve is the distribution question: given scarce resources, the opportunity cost of a marginal addition to my utility is an incremental utility for someone else. This is one of the big questions that Rawls tries to tackle in Theory of Justice. It’s been awhile since I read it, so I can’t describe the argument in detail. But the thrust is that the veil of ignorance is a powerful thought experiment which helps motivate his two basic principles: maximal liberty without infringing on others’ liberty, and supporting differences in income only to the extent that all people benefit. I won’t go into these in any depth now, but I think they’re fundamentally on the right track.
Now (finally!), let’s turn to the case of the cabin boy, described by Sandel in this lecture. As a brief recap, the story is that in the 17th or 18th century a ship sinks and some crew survive in a lifeboat, with almost no provisions. After 19 days, they realize they will die unless they kill someone. So the older guys decide to kill the cabin boy who is in his teens. They kill him with a pen, eat his remains, and several days later are rescued. They are then taken to court and tried for murder.
I think this is a very interesting case because it is an example of humans acting not as moral agents but as animals designed to survive. In the animal world, there is no such thing as moral judgments. We don’t say that a male bird is amoral for abandoning its offspring. We don’t say that a male sea lion is amoral for fighting off other male sea lions. We don’t say a praying mantis is amoral for eating her mate after he fertilizes her. We don’t say pandas are amoral for only wanting to have sex once per year—even if it’s not very good for the survival of their species. Animals are designed in many different ways to propagate their genes. Some strategies are more successful than others, but we don’t attribute moral value to any of their actions. Animals are not moral agents. Humans, by contrast, are not only motivated by survival. We have the capacity to overcome the design of our genes, and thank goodness we do—otherwise our society would be filled with plundering rapists.
Just because we have the capacity to act as moral agents does mean that we always do. When threatened by death, we revert to our instincts for survival. As proof of this fact, we may ponder whether the sailors would have acted differently if they had known they would be convicted guilty of murder. On the brink of starvation, I think most people would act in whatever way necessary to save their own lives. Thus, I don’t think it’s very useful to ponder the morality or even the legality of people’s actions in such a circumstance. What is the use of a moral code for a non-moral agent? I think this example has a lot of lessons. Let me give just two examples. Consider the drug addict who values a high over his family’s and his own safety, security, and comfort. For such an addict, the force of law holds little power of persuasion. There may be reasons to have laws against the use of such powerful drugs, but deterring the hardened addict should not be one of them.
As another example, let us consider the plight of someone like Ishmael Beah, the child in Sierra Leone whose parents were killed by rebels and who was then forced to fight with the rebels. Twelve-year-old Beah may have performed actions (murder, to start with) that would be amoral for most people to commit, but he was doing them in order to survive. Thus he cannot be held morally responsible for those actions.
Thus any moral code must at its most fundamental be utilitarian, in the most general form of the definition. That is to say, a moral code is utilitarian if it is grounded in promoting the quality of life of living beings. I assert that this is the only thing we value. There is nothing else that we really care about. If a moral code is *not* utilitarian, then what does it value? The shape of rocks? The temperature? The periods of planetary revolution?
[ASIDE: Here I am ignoring any moral claims that are derived from religious dogma. The justification for any of these claims is an appeal to authority which is not widely accepted by all people. Even if such an appeal were accepted by a majority (say, a majority in a single nation), I reject any moral argument of the form “I believe X because Y tells me so,” where Y is Moses, Jesus, Muhammad, God, etc. The only defensible arguments that are valid are ones which all reasonable people can accept. Rawls has talked a lot about this (in Political Liberalism), but it’s been awhile since I read it, so I won’t want into it now.
[One might say, well, how are you going to live in a civil society with all those people who derive their morality from moral codes? My goal here is not to describe what morality actually is followed by most people. Instead, I want to lay out my own argument for a justifiable moral code. I think it’s right, and I think people ought to adopt it based on the reasons as I describe them. But I fully understand that many people will not follow this morality. Despite that fact, I still think that democracy is the best political structure, even if many members of the society do not have moral/political values that I subscribe to. Ultimately, I think my moral code—let’s call it limited liberalism for now—will be the one that societies converge toward. END ASIDE.]
So let’s start from the assertion that all reasonable moral codes must be at their most fundamental level motivated by utilitarian values. Now, the question is how to best achieve this. One extreme approach, let’s call it “OCD Utilitarianism,” says that to make a moral judgment, one must perform an extended calculation of all the ramifications of your decision. For example, if I am a doctor and two patients arrive in the ER, I need to do a full background check—family members, career history, resume, etc.—in order to evaluate which one to save. Taken to this logical extreme, OCD utilitarianism is obviously unrealistic. We simply have too many decisions to make every day for this to be realistic. My point is proposing this ridiculous moral code is to demonstrate that we live in a world of complexity, uncertainty, and scarcity (of time and resources). To make decisions, we need to have simplifying rules of thumb. These are not absolute moral laws, but rather moral guidelines.
For example, one moral rule of thumb is to feed kids milk. We break this rule commonly, whenever a child is lactose-intolerant. Another moral rule of thumb that is less commonly broken is to stop at red lights. However, there are certainly some rare cases when it is morally justifiable to violate this rule, e.g., if a passenger is dying of a gunshot wound in the backseat and you’re trying to get to the hospital. Given that we need to make decisions quickly, we need moral rules of thumb to help us make moral decisions. Since we live in a world of uncertainty, sometimes following these rules of thumb will lead us to make decisions that, in hindsight, we regret. Many laws of the state are based on these kinds of moral rules of thumb: do not kill, do not steal, do not prevent people from worshiping as they choose, etc. These are not absolute moral laws but rather very strong rules of thumb which may be justifiably broken only under very rare circumstances.
So any moral code will need a way of deriving moral rules of thumb; OCD utilitarianism is simply untenable. The moral codes which claim to be alternatives to utilitarianism (such as the categorical imperative, or contractualism) really just disagree about how to generate the rules of thumb. The end goal is to create a set of laws that maximizes quality of living.
Now, one of the big outstanding questions to resolve is the distribution question: given scarce resources, the opportunity cost of a marginal addition to my utility is an incremental utility for someone else. This is one of the big questions that Rawls tries to tackle in Theory of Justice. It’s been awhile since I read it, so I can’t describe the argument in detail. But the thrust is that the veil of ignorance is a powerful thought experiment which helps motivate his two basic principles: maximal liberty without infringing on others’ liberty, and supporting differences in income only to the extent that all people benefit. I won’t go into these in any depth now, but I think they’re fundamentally on the right track.
Now (finally!), let’s turn to the case of the cabin boy, described by Sandel in this lecture. As a brief recap, the story is that in the 17th or 18th century a ship sinks and some crew survive in a lifeboat, with almost no provisions. After 19 days, they realize they will die unless they kill someone. So the older guys decide to kill the cabin boy who is in his teens. They kill him with a pen, eat his remains, and several days later are rescued. They are then taken to court and tried for murder.
I think this is a very interesting case because it is an example of humans acting not as moral agents but as animals designed to survive. In the animal world, there is no such thing as moral judgments. We don’t say that a male bird is amoral for abandoning its offspring. We don’t say that a male sea lion is amoral for fighting off other male sea lions. We don’t say a praying mantis is amoral for eating her mate after he fertilizes her. We don’t say pandas are amoral for only wanting to have sex once per year—even if it’s not very good for the survival of their species. Animals are designed in many different ways to propagate their genes. Some strategies are more successful than others, but we don’t attribute moral value to any of their actions. Animals are not moral agents. Humans, by contrast, are not only motivated by survival. We have the capacity to overcome the design of our genes, and thank goodness we do—otherwise our society would be filled with plundering rapists.
Just because we have the capacity to act as moral agents does mean that we always do. When threatened by death, we revert to our instincts for survival. As proof of this fact, we may ponder whether the sailors would have acted differently if they had known they would be convicted guilty of murder. On the brink of starvation, I think most people would act in whatever way necessary to save their own lives. Thus, I don’t think it’s very useful to ponder the morality or even the legality of people’s actions in such a circumstance. What is the use of a moral code for a non-moral agent? I think this example has a lot of lessons. Let me give just two examples. Consider the drug addict who values a high over his family’s and his own safety, security, and comfort. For such an addict, the force of law holds little power of persuasion. There may be reasons to have laws against the use of such powerful drugs, but deterring the hardened addict should not be one of them.
As another example, let us consider the plight of someone like Ishmael Beah, the child in Sierra Leone whose parents were killed by rebels and who was then forced to fight with the rebels. Twelve-year-old Beah may have performed actions (murder, to start with) that would be amoral for most people to commit, but he was doing them in order to survive. Thus he cannot be held morally responsible for those actions.
Sunday, December 7, 2008
Tweaking nature's laws
Dennett's main point in Freedom Evolves is that assuming we live in a deterministic universe, then the interesting question is: how different would things have to be in order to produce a different outcome? I know that I can't run a 2 minute mile--that would require deep physiological changes. I know that I can't speak Mandarin right now--that would require deep neural changes. But I might be able to calculate the differential cross-section for some scattering process. That's within the bounds of my capability, though I may fall short.
I think this approach is also valuable in thinking about science. It's useful to ask the question: "How different would the universe have to be in order for X to be the case?" In biology, we could imagine primates evolving to have 6 limbs. It's harder to imagine them evolving to have 2 on one side and 3 on the other, but not impossible.
In physics, we could imagine the value of G being different (even if it would create a universe that could not support life). It's harder to imagine a universe in which the small oscillations around a point of equilibrium is described by a triangle wave rather than a sinusoidal wave. I think that's about like trying to imagine a universe in which 2 + 2 = 5. You sort of can, but it's very hard to do.
Well, here's my rumination on a question my brother asked me, about why E=mc^2 and not E=m(kc)^2. I imagine that this falls closer to the 2+2=5 case than the different G case, but i'm not fully convinced by my explanation. I haven't seen a more complete explanation anywhere else though.
Hey Stu,
Let me try to do a better job answering your question about why E=mc^2 and not E=m(kc)^2.
I think it really centers on frame-invariant quantities. If you want something to be frame-invariant, it needs to be represented in an appropriate 4-vector. An example is the position 4-vector (t, x, y, z), for which s^2 = t^2 - x^2 - y^2 - z^2 is invariant. If you're on a train and I'm on a platform, we may disagree about the time between 2 events or the space between 2 events, but we'll always agree on the s^2 of the 2 events.
Well, rest-mass is something that is also invariant. You and I will always agree on the rest-mass of an object, even if we disagree on its momentum and energy. We can make a 4-vector that obeys these
properties [is this the only way to get a frame-invariant rest-mass?]: (A/c, px, py, pz), where
m^2*c^2 = A^2/c^2 - px^2 - py^2 - pz^2
= A^2/c^2 - p^2.
What is A? Well, note that p = gamma * m * v, with gamma = (1-v^2/c^2)^(-1/2). [You need the gamma if you want conservation of momentum to hold in different reference frames.] Now, let's take an enlightened guess about what A is:
A = gamma * m * (kc)^2.
Then, we can expand the gamma with a Taylor series (trust me if you forget how to do this):
A = m*(kc)^2 * (1 + v^2/2c^2 + 3v^4/8c^4 + ...)
= m*(kc)^2 + (1/2)m(kv)^2 + (3/8)mv^4(k/c)^2 + ...
The third and higher terms are negligibly small, so let's drop those.
Then if we set k=1, we get
A = mc^2 + (1/2)mv^2
All that we can measure are changes in energy. So what we will measure are changes in (1/2)mv^2, which just happens to be the same as the expression for kinetic energy that we're familiar with. If, however, we had left k not equal to 1 then changes in A would not correspond to changes in Newtonian kinetic energy. And we would not be able to set A = E.
Not sure if that helps. It's a good question, one that hits at some subtle issues in relativity. Most of the time we just use it because we know that it works! :)
I think this approach is also valuable in thinking about science. It's useful to ask the question: "How different would the universe have to be in order for X to be the case?" In biology, we could imagine primates evolving to have 6 limbs. It's harder to imagine them evolving to have 2 on one side and 3 on the other, but not impossible.
In physics, we could imagine the value of G being different (even if it would create a universe that could not support life). It's harder to imagine a universe in which the small oscillations around a point of equilibrium is described by a triangle wave rather than a sinusoidal wave. I think that's about like trying to imagine a universe in which 2 + 2 = 5. You sort of can, but it's very hard to do.
Well, here's my rumination on a question my brother asked me, about why E=mc^2 and not E=m(kc)^2. I imagine that this falls closer to the 2+2=5 case than the different G case, but i'm not fully convinced by my explanation. I haven't seen a more complete explanation anywhere else though.
Hey Stu,
Let me try to do a better job answering your question about why E=mc^2 and not E=m(kc)^2.
I think it really centers on frame-invariant quantities. If you want something to be frame-invariant, it needs to be represented in an appropriate 4-vector. An example is the position 4-vector (t, x, y, z), for which s^2 = t^2 - x^2 - y^2 - z^2 is invariant. If you're on a train and I'm on a platform, we may disagree about the time between 2 events or the space between 2 events, but we'll always agree on the s^2 of the 2 events.
Well, rest-mass is something that is also invariant. You and I will always agree on the rest-mass of an object, even if we disagree on its momentum and energy. We can make a 4-vector that obeys these
properties [is this the only way to get a frame-invariant rest-mass?]: (A/c, px, py, pz), where
m^2*c^2 = A^2/c^2 - px^2 - py^2 - pz^2
= A^2/c^2 - p^2.
What is A? Well, note that p = gamma * m * v, with gamma = (1-v^2/c^2)^(-1/2). [You need the gamma if you want conservation of momentum to hold in different reference frames.] Now, let's take an enlightened guess about what A is:
A = gamma * m * (kc)^2.
Then, we can expand the gamma with a Taylor series (trust me if you forget how to do this):
A = m*(kc)^2 * (1 + v^2/2c^2 + 3v^4/8c^4 + ...)
= m*(kc)^2 + (1/2)m(kv)^2 + (3/8)mv^4(k/c)^2 + ...
The third and higher terms are negligibly small, so let's drop those.
Then if we set k=1, we get
A = mc^2 + (1/2)mv^2
All that we can measure are changes in energy. So what we will measure are changes in (1/2)mv^2, which just happens to be the same as the expression for kinetic energy that we're familiar with. If, however, we had left k not equal to 1 then changes in A would not correspond to changes in Newtonian kinetic energy. And we would not be able to set A = E.
Not sure if that helps. It's a good question, one that hits at some subtle issues in relativity. Most of the time we just use it because we know that it works! :)
Sunday, November 16, 2008
Justice Lecture 1: Trolley Problems
The first in what I hope will become a series of posts based on Michael Sandel's Justice lectures at Harvard (which can be obtained as podcasts from justiceonline.harvard.edu).
In this lecture, Sandel sets up several “Trolley problems,” philosophical thought experiments to probe our moral intuitions.
1. Split track. A train with no brakes is coming down the track. The track splits; on one side is tied one person, while 5 people are tied to the other side. On its current course, the train will kill the 5 people. You can throw a switch to redirect the train so that it kills only the 1 person. Do you throw the switch?
a. A: Yes, you throw the switch. Killing 1 person is better than killing 5. However the rule “Always kill as many lives as possible” should not be followed universally. For example, would you rather save two 90-year-old people both suffering from terminal cancer or one 30 year old single mother who has three children? You save the mother. Do you save two mentally-retarded people or the president of the
2. The pusher. Now the only way to stop a train is to push a fat man (who is much fatter than you are) off a bridge so that he falls on the tracks, stopping the train and saving the 5 lives. Do you push him off?
a. A: No, you don’t push him. That’s what our moral intuition tells us, at least. It seems that it would be more unfair to push a man on the tracks than it would be in case 1 to throw a switch that ends up killing one man. Why does our moral intuition tell us this? Because our moral intuition is based on probable outcomes. We choose what is the right thing to do based on what will usually yield the optimum outcome (let’s say maximum utility), based on our limited knowledge in the real world. In the real world there are lots of ways to solve problems. If you want to stop a train, there are many things you can push into its path—a trash can, a hot dog stand, a car—besides a human being. Furthermore, there are other ways to save the 5 tied victims from a train besides pushing something in the way of it. Maybe there is some emergency braking system on the train or on the tracks. Maybe there is a switch to divert the train. In the real world, there are usually many options, and sacrificing an innocent person’s life hardly seems like the best one. The premise of the thought experiment is that the only way to save the 5 people’s lives is to push the one fat man, but in the real world we are rarely given such clarity of options. Maybe after the fact a careful analysis will reveal the only way to save these lives. But in the moment when we make a decision, we work with imperfect information and therefore have to follow rules that work (i.e., yield optimum outcomes) most of the time. We can explain the principle at work here as the Murder Rule: “Do not cause an innocent person to die unless you can be sure that the death of that one person will allow the saving of many more lives, and there are no other ways of saving those lives.” In this case, we are not sure that there is not another way to save the 5 lives. In the rare cases when it is very obvious in the moment that there are no other ways to save the 5 lives, then we are back to the split track situation of Case 1: Split Track.
3. The triage doctor. You’re a doctor who gets 6 patients. Five of them can be saved relatively quickly, but saving one of them will take so much time that you will not be able to get to any of the others. Who do you save?
a. Of course, you save the 5 people. This is analogous to Case 1: Split Track. You can be relatively confident (assuming, for example, that you’re the only doctor) that there is no other way to save the 5 lives than by operating on them first.
4. The transplant doctor. You’re a doctor with 6 patients. Five need different organ transplants. One is getting his wisdom teeth removed (general anesthesia) but is otherwise healthy. Do you sacrifice the healthy one, take out his organs, and then transplant them to the other 5 patients to save their lives? This is the only way to save their lives.
a. No, you can’t do that because that would violate the fairness of the healthy person. It violates the Murder Rule because in fact, in real life, you would never know that there are no other ways to save these 5 lives. Maybe more organs will come from new organ donors—which could arrive at any minute. Maybe there are other ways to save those 5 lives. One student in class had a brilliant solution: take 4 organs from whichever of the 5 dies first to save the other 4. In real life, these are the kinds of options that have to be considered.
Friday, September 19, 2008
can she persuade them?
This is an interesting PBS piece on Michelle Rhee's drive to institute merit pay in the DC schools, along with ending tenure:
http://www.pbs.org/newshour/bb/education/july-dec08/dcschools_09-18.html
However, the comments of George Parker, the Union chief, suggest that he's not that interested. And given that the straw vote of teachers was 2 to 1 against the new 2-tier merit/no-tenure system, the prospects are not promising.
Fundamentally, I think this is the wrong way to go about it. Pay for performance is almost impossible to implement. I know of hardly any schools that pull it off. That's because there are lots of ways to be a good teacher, and boosting test scores is only one measure. Look at what independent schools do: they let principals make the decision.
So if I were Rhee, I would be taking the extra pot of cash that she has and telling teachers that they can get roughly a 20% boost in pay, if they give up their tenure. If they agree, then the principal gets control of the school budget. I think if you put that offer on the table, there would be a lot of pressure from teachers to sign on to that.
http://www.pbs.org/newshour/bb/education/july-dec08/dcschools_09-18.html
However, the comments of George Parker, the Union chief, suggest that he's not that interested. And given that the straw vote of teachers was 2 to 1 against the new 2-tier merit/no-tenure system, the prospects are not promising.
Fundamentally, I think this is the wrong way to go about it. Pay for performance is almost impossible to implement. I know of hardly any schools that pull it off. That's because there are lots of ways to be a good teacher, and boosting test scores is only one measure. Look at what independent schools do: they let principals make the decision.
So if I were Rhee, I would be taking the extra pot of cash that she has and telling teachers that they can get roughly a 20% boost in pay, if they give up their tenure. If they agree, then the principal gets control of the school budget. I think if you put that offer on the table, there would be a lot of pressure from teachers to sign on to that.
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