In the opening chapters of (Chisholm, 1977) and (Chisholm, 1982), Chisholm sketches an account of some basic concepts of epistemic justification in terms of the relation `P is more reasonable than Q' (suppressing references to epistemic agents and moments of time since they are not relevant for my purposes here), where P and Q are (roughly) propositional attitudes logically built from the primitives `believing p' and `withholding p', for any proposition p. In particular, Chisholm gives several axioms for the logic of this relation. My purpose here is to prove that these axioms are inconsistent.
January 29, 2007
On the consistency of Chisholm's axioms of epistemic logic
Link!
Another Link From Brottman
This kid is better than me at Guitar Hero. He's better than you at Guitar Hero. This kid is eight. I hate him with the power of a million exploding suns, but he rocks and he rolls.
Superbowl Shuffle
I had been planning on rooting for Chicago because they eliminated Seattle, but Atrios gives me another reason to hope the Colts lose the big game.
January 27, 2007
Well, it's not quite Kim Stanley Robinson
But I'll take it.
 | I am:William GibsonThe chief instigator of the "cyberpunk" wave of the 1980s, his razzle-dazzle futuristic intrigues were, for a while, the most imitated work in science fiction. |
January 24, 2007
"On The Outside, We Run Shit."
There's a documentary in the works chronicling MC Frontalot's "Nerdcore Rising" Tour and among those interviewed are Gabe and Tycho of Penny Arcade. Indeed, in an effort to raise funds to complete the film, the ladies behind it are doing weekly video podcasts featuring interviews from the movie. The first, of couse, is about the Penny Arcade Expo, or PAX. It is my eternal shame that I've yet to make it to a PAX. 2008, baby, that's my year!
"We Used To Swap Shots Between Drinks, Or Drinks Between Shots, Whichever You Like."
Word is that Clive Owen will be playing Raymond Chandler's Phillip Marlowe. Not much word on when, or what story they'll be working on, but that sounds just swell to me. Gotta say, my exposure to noir is actually a bit spotty, but I'm a sucker for Bogey, particulary in The Big Sleep.
January 23, 2007
Go to Barbara Boxer's website to email a petition
to bring home the troops.
Here is her website: http://www.barbaraboxer.com
[And here is the email form.]
Dear Sarah,
Urge President Bush to stop the Iraq escalation!
In just 9 hours, President Bush will stand before Congress and the American people to deliver his State of the Union address and defend his unwise plan to deploy over 20,000 new American troops to Iraq.
Help me stand up to the President by urging him to listen to the American people and turn away from this unwise escalation of the war. Email President Bush before his speech tonight and ask him to listen to reason.
Last November, the American people went into the voting booth and said loud and clear that they wanted a change of course in Iraq. Instead, President Bush ignored the public and the advice of senior military officials by proposing to escalate our commitment in Iraq.
It is so crucial that we all keep up the pressure to start bringing our troops home so the Iraqis know that Iraq is their country, we are not occupiers, and that they must defend themselves. It is also crucial that we keep up the pressure for a political and diplomatic solution to this travesty -- to bring together all of the countries in the region with the coalition President Bush says he has, in order to meet and hammer out the details for bringing about a peaceful Iraq. Instead, the Bush Administration is only offering a military escalation, which means more and more killing, leaving our sons and daughters in the middle of a full-blown civil war.
Enough is enough. Forward an email to President Bush before tonight's State of the Union address. Tell him that America wants our troops to start coming home.
Just this past weekend, 27 American troops lost their lives in Iraq -- one of the deadliest two-day periods for U.S. forces since we first invaded Iraq 4 years ago. Then on Monday, more than 100 Iraqis were killed in car bombing attacks in Baghdad and Khalis. This nonstop violence is sickening, and we must do everything we can to end it.
It is no wonder that recent polls show that 65 percent of the American people oppose the president's plan to send more troops to Iraq. They know that President Bush isn't offering a solution; he's just putting more young Americans in harm's way without taking any serious steps to end the conflict.
President Bush's escalation plan also faces bipartisan opposition in Congress. On Monday, Senator John Warner -- a senior Republican and respected military expert -- proposed a resolution opposing the Bush troop increase. It could not be more clear that President Bush is standing alone -- against even his own party -- in trying to escalate this conflict.
Already, over 17,000 people have emailed President Bush through our PAC for a Change website, urging him to listen to reason and turn away from this foolhardy policy. It is critical that we double this number in the last hours before his speech tonight.
Email President Bush right now, and let him know that it's time for him to listen to the American people and end the war in Iraq.
Thank you for your help to change course and start bringing our brave men and women home so the Iraqis can take responsibility for their own country.
In Friendship,
Barbara Boxer
[Ripped off entirely from my friend Sarah.]
Here is her website: http://www.barbaraboxer.com
[And here is the email form.]
Dear Sarah,
Urge President Bush to stop the Iraq escalation!
In just 9 hours, President Bush will stand before Congress and the American people to deliver his State of the Union address and defend his unwise plan to deploy over 20,000 new American troops to Iraq.
Help me stand up to the President by urging him to listen to the American people and turn away from this unwise escalation of the war. Email President Bush before his speech tonight and ask him to listen to reason.
Last November, the American people went into the voting booth and said loud and clear that they wanted a change of course in Iraq. Instead, President Bush ignored the public and the advice of senior military officials by proposing to escalate our commitment in Iraq.
It is so crucial that we all keep up the pressure to start bringing our troops home so the Iraqis know that Iraq is their country, we are not occupiers, and that they must defend themselves. It is also crucial that we keep up the pressure for a political and diplomatic solution to this travesty -- to bring together all of the countries in the region with the coalition President Bush says he has, in order to meet and hammer out the details for bringing about a peaceful Iraq. Instead, the Bush Administration is only offering a military escalation, which means more and more killing, leaving our sons and daughters in the middle of a full-blown civil war.
Enough is enough. Forward an email to President Bush before tonight's State of the Union address. Tell him that America wants our troops to start coming home.
Just this past weekend, 27 American troops lost their lives in Iraq -- one of the deadliest two-day periods for U.S. forces since we first invaded Iraq 4 years ago. Then on Monday, more than 100 Iraqis were killed in car bombing attacks in Baghdad and Khalis. This nonstop violence is sickening, and we must do everything we can to end it.
It is no wonder that recent polls show that 65 percent of the American people oppose the president's plan to send more troops to Iraq. They know that President Bush isn't offering a solution; he's just putting more young Americans in harm's way without taking any serious steps to end the conflict.
President Bush's escalation plan also faces bipartisan opposition in Congress. On Monday, Senator John Warner -- a senior Republican and respected military expert -- proposed a resolution opposing the Bush troop increase. It could not be more clear that President Bush is standing alone -- against even his own party -- in trying to escalate this conflict.
Already, over 17,000 people have emailed President Bush through our PAC for a Change website, urging him to listen to reason and turn away from this foolhardy policy. It is critical that we double this number in the last hours before his speech tonight.
Email President Bush right now, and let him know that it's time for him to listen to the American people and end the war in Iraq.
Thank you for your help to change course and start bringing our brave men and women home so the Iraqis can take responsibility for their own country.
In Friendship,
Barbara Boxer
[Ripped off entirely from my friend Sarah.]
January 21, 2007
To split yourself into two / is just the most radical thing you can do
Tomorrow is the thirty-fourth anniversary of Roe v. Wade, and that means it's Blog for choice day. This year's theme is the rather dull `Why I am pro-choice'. Dull because my reasons are themselves rather dull and dryly philosophical -- (1) there are no good reasons to think a foetus has a right to life (ie, is a person), and (2) even if it did have such a right to life, there is no reason to think that right supersedes a woman's right to bodily autonomy and integrity.
This is, essentially, the position taken in Judith Jarvis Thomson's famous essay `A defense of abortion'. I don't agree with Jarvis Thomson entirely, though, because she seems to assert that we never have any obligations to aid others. By contrast, I think there's intuitive appeal to Peter Singer's principle that we have obligations to make sacrifices to aid others when the sacrifice is not of `comparable moral significance' (that's a paraphrase, not a direct quotation). Cashing out that phrase is tough, but I think that rights of bodily autonomy and integrity are of comparable moral significance with the right to life.
Let me open the comments thread to you all: Why are you pro-choice?
NB I'd like to reserve substantive comments in this thread for pro-choicers only. If you're opposed to abortion and would like to discuss my reasons or anyone else's, you're welcome to email me or put a link to a post on your own blog in the comments below.
This is, essentially, the position taken in Judith Jarvis Thomson's famous essay `A defense of abortion'. I don't agree with Jarvis Thomson entirely, though, because she seems to assert that we never have any obligations to aid others. By contrast, I think there's intuitive appeal to Peter Singer's principle that we have obligations to make sacrifices to aid others when the sacrifice is not of `comparable moral significance' (that's a paraphrase, not a direct quotation). Cashing out that phrase is tough, but I think that rights of bodily autonomy and integrity are of comparable moral significance with the right to life.
Let me open the comments thread to you all: Why are you pro-choice?
NB I'd like to reserve substantive comments in this thread for pro-choicers only. If you're opposed to abortion and would like to discuss my reasons or anyone else's, you're welcome to email me or put a link to a post on your own blog in the comments below.
January 20, 2007
The Gini coefficient
The Gini coefficient is a measure of the distribution of wealth within a population. The idea is simple: line up the entire population, with the poorest person on the left end and the richest person on the right. As you go down the line, take the total income of everyone to the left (so the first person has just their own income counted, the last person has everyone's income counted). This plots a curve that kind of swoops up from the lower-left corner to the upper-right. Now measure the area between this curve and the straight line from the lower-left corner to the upper-right, and divide that by the triangular area under the straight line. This gives you a ratio between the actual distribution of wealth and the perfectly equal distribution of wealth. Multiply that ratio by 100, and you have the Gini coefficient.
Since a larger ratio means there's more of a gap between reality and the perfectly equal distribution, a coefficient of 0 means perfect equality (everyone's income is exactly the same), while a coefficient of 100 means perfect inequality (one person gets all the money). Here is an alphabetical list of countries and their Gini coefficients, measured in various years.
According to this list, in 2004, the Gini coefficient for the US was 45. Here's a list of the other countries whose most recent Gini coefficient calculation, according to this list, was between 40 and 50: Armenia, Burundi, Cambodia, Cameroon, PRC, Costa Rica, Cote d'Ivoire, Ecuador, Georgia, Guinea, Guinea-Bissau, Iran, Kenya, Madagascar, Malaysia, Mexico, Mongolia, Nicaragua, Nigeria, Philippines, Senegal, Singapore, Thailand, Trinidad and Tobago, Tunisia, Turkey, Turkmenistan, Uruguay, and Venezuela.
Those are our peers. The list of countries with a lower Gini coefficient (remember, lower means more egalitarian) is way too long to list here. But here's a list of countries those coefficients are between 30 and 40: Algeria, Australia, Austria, Bangladesh, Belgium, Burkina Faso, Canada, Egypt, Estonia, Ethiopia, France, Greece, India, Indonesia, Ireland, Italy, Jamaica, Japan, Jordan, Kazakhstan, South Korea, Laos, Latvia, Lithuania, Mauritania, Moldova, Mozambique, Netherlands, New Zealand, Pakistan, Portugal, Romania, Spain, Sri Lanka, Switzerland, Tajikistan, Tanzania, the UK, Vietnam, and Yemen. These are the countries whose incomes are distributed somewhat more equally than in the US.
Since a larger ratio means there's more of a gap between reality and the perfectly equal distribution, a coefficient of 0 means perfect equality (everyone's income is exactly the same), while a coefficient of 100 means perfect inequality (one person gets all the money). Here is an alphabetical list of countries and their Gini coefficients, measured in various years.
According to this list, in 2004, the Gini coefficient for the US was 45. Here's a list of the other countries whose most recent Gini coefficient calculation, according to this list, was between 40 and 50: Armenia, Burundi, Cambodia, Cameroon, PRC, Costa Rica, Cote d'Ivoire, Ecuador, Georgia, Guinea, Guinea-Bissau, Iran, Kenya, Madagascar, Malaysia, Mexico, Mongolia, Nicaragua, Nigeria, Philippines, Senegal, Singapore, Thailand, Trinidad and Tobago, Tunisia, Turkey, Turkmenistan, Uruguay, and Venezuela.
Those are our peers. The list of countries with a lower Gini coefficient (remember, lower means more egalitarian) is way too long to list here. But here's a list of countries those coefficients are between 30 and 40: Algeria, Australia, Austria, Bangladesh, Belgium, Burkina Faso, Canada, Egypt, Estonia, Ethiopia, France, Greece, India, Indonesia, Ireland, Italy, Jamaica, Japan, Jordan, Kazakhstan, South Korea, Laos, Latvia, Lithuania, Mauritania, Moldova, Mozambique, Netherlands, New Zealand, Pakistan, Portugal, Romania, Spain, Sri Lanka, Switzerland, Tajikistan, Tanzania, the UK, Vietnam, and Yemen. These are the countries whose incomes are distributed somewhat more equally than in the US.
Review of Pan's labyrinth
Guillermo del Toro is best well-known in the US as the screenwriter and director of Hellboy, but in the right circles he is much more renowned for The devil's backbone and Cronos. If you're not familiar with either of these, I recommend hunting down some copies before seeing Pan's labyrinth.
Del Toro has called Pan's labyrinth a `sequal in spirit' to The devil's backbone, and the two films share a number of thematic elements. Both take place in Spain towards the end of the Civil War, and have, as protagonist, children of about ten years old whose lives have been severely disrupted by that war. Both live solidly within the Spanish literary genre of magical realism, with two distinct but parallel and sympathetic plotlines. Indeed, it is magical realism that makes these two films so distinctive, and makes Pan's labyrinth so artistically successful.
===== Very, very small spoilers below the fold =====
Briefly, Pan's labyrinth tells the story of Ofelia, a Spanish girl whose father has been killed in the Spanish Civil War. The war is ending, and her mother has become pregnant by a captain in Franco's army. At the beginning of the film, Ofelia and her mother are brought out from the city to an old mill, which is being used as a base for the rebel-clearing mission of the captain. Ofelia discovers an rotting stone labyrinth just inside the forest, and an ancient faun (played by the incredibly talented Doug Jones), the mime who played Abe Sapien in Hellboy and the lead Gentleman in the Buffy episode `Hush') in the centre tells her that she is the reincarnated daughter of the king of the Underworld. To return to the Underworld (`where there is no suffering or death'), she must complete three tasks, with the help of the faun's pet faeries and a magical book.
Meanwhile, the Civil War rages on in the microcosm of the mill household. Giving a more adequate summary of the realist plotline without major spoilers is difficult, so I will just say that it is a mistake, as many of the reviewers on IMDb (both positive and negative) do, to focus more or less exclusively on the supernatural plotline. Magical realism is built on the way the realist and supernatural are used to comment on each other, and you will not be able to understand the film without grasping that basic premise. I will, say, however, that the realist plotline is fairly standard: the captain is almost a two-dimensional villain (as befits a fairy tale), sadistic and misogynist and obsessed with his patrimony; there are Republican sympathisers right under his nose; Ofelia's mother's pregnancy takes a turn for the worst; the main characters are slowly but inevitably isolated; and so on.
===== Spoilers end =====
Del Toro's greatest skill as a storyteller (and he has several; his visual aesthetic, for one, is absolutely breathtaking) lies in his subtle and sophisticated use of allusion, reference, and reflection, and he makes full use of the complex structure of magical realism to this end. Too often `updated' or `modernised' fairy tales collapse under their own weight, and turn into either disappointing action movies (Terry Gilliam's Brother's Grimm) or cheesy and painfully insipid pieces of crap (anything M Night Shyamalan has ever touched). Pan's labyrinth avoids these pitfalls by focussing, not on the fantastic characters and settings, but on the basic iconic elements of fairy tales, in both the supernatural and realist plotlines: items of power, rules and warnings of danger, deception and trust, the powerless facing down the powerful. Don't misunderstand me, some of the most tour de force sequences of the film are encounters with fantastic characters in fantastic settings, but the realist side of the film means it cannot be built around these encounters, and thereby avoids going over the top.
For all its praise, Pan's labyrinth is not quite del Toro's masterpiece. All the characters are, ultimately, rather flat archetypes, and nothing that transpires is ever really all that surprising. It's far from formulaic, but I suspect the rave American reviews have more to do with the novelty of magical realism than any actual innovation on del Toro's part (besides putting magical realism on the screen; I can't think of another film, besides The devil's backbone, that's really done this). Pan's labyrinth is highly recommended, but I'm going to wait another five or ten years before I label del Toro a true genius; at only 42, he still needs some time to mature completely, especially as a writer.
One final note: While undoubtedly a fairy tale, Pan's labyrinth is not for young children. This is a dark and extremely disturbing tale, on the order of, say, something by David Cronenberg. (Though obviously very different in most other respects.) The somber atmosphere settles in from the first frame, and only becomes more and more oppressive -- I don't think there's a single moment where anyone says or does anything that's in any way amusing or light-hearted. It didn't give me nightmares, but I believe it would for anyone younger than about 14.
Del Toro has called Pan's labyrinth a `sequal in spirit' to The devil's backbone, and the two films share a number of thematic elements. Both take place in Spain towards the end of the Civil War, and have, as protagonist, children of about ten years old whose lives have been severely disrupted by that war. Both live solidly within the Spanish literary genre of magical realism, with two distinct but parallel and sympathetic plotlines. Indeed, it is magical realism that makes these two films so distinctive, and makes Pan's labyrinth so artistically successful.
===== Very, very small spoilers below the fold =====
Briefly, Pan's labyrinth tells the story of Ofelia, a Spanish girl whose father has been killed in the Spanish Civil War. The war is ending, and her mother has become pregnant by a captain in Franco's army. At the beginning of the film, Ofelia and her mother are brought out from the city to an old mill, which is being used as a base for the rebel-clearing mission of the captain. Ofelia discovers an rotting stone labyrinth just inside the forest, and an ancient faun (played by the incredibly talented Doug Jones), the mime who played Abe Sapien in Hellboy and the lead Gentleman in the Buffy episode `Hush') in the centre tells her that she is the reincarnated daughter of the king of the Underworld. To return to the Underworld (`where there is no suffering or death'), she must complete three tasks, with the help of the faun's pet faeries and a magical book.
Meanwhile, the Civil War rages on in the microcosm of the mill household. Giving a more adequate summary of the realist plotline without major spoilers is difficult, so I will just say that it is a mistake, as many of the reviewers on IMDb (both positive and negative) do, to focus more or less exclusively on the supernatural plotline. Magical realism is built on the way the realist and supernatural are used to comment on each other, and you will not be able to understand the film without grasping that basic premise. I will, say, however, that the realist plotline is fairly standard: the captain is almost a two-dimensional villain (as befits a fairy tale), sadistic and misogynist and obsessed with his patrimony; there are Republican sympathisers right under his nose; Ofelia's mother's pregnancy takes a turn for the worst; the main characters are slowly but inevitably isolated; and so on.
===== Spoilers end =====
Del Toro's greatest skill as a storyteller (and he has several; his visual aesthetic, for one, is absolutely breathtaking) lies in his subtle and sophisticated use of allusion, reference, and reflection, and he makes full use of the complex structure of magical realism to this end. Too often `updated' or `modernised' fairy tales collapse under their own weight, and turn into either disappointing action movies (Terry Gilliam's Brother's Grimm) or cheesy and painfully insipid pieces of crap (anything M Night Shyamalan has ever touched). Pan's labyrinth avoids these pitfalls by focussing, not on the fantastic characters and settings, but on the basic iconic elements of fairy tales, in both the supernatural and realist plotlines: items of power, rules and warnings of danger, deception and trust, the powerless facing down the powerful. Don't misunderstand me, some of the most tour de force sequences of the film are encounters with fantastic characters in fantastic settings, but the realist side of the film means it cannot be built around these encounters, and thereby avoids going over the top.
For all its praise, Pan's labyrinth is not quite del Toro's masterpiece. All the characters are, ultimately, rather flat archetypes, and nothing that transpires is ever really all that surprising. It's far from formulaic, but I suspect the rave American reviews have more to do with the novelty of magical realism than any actual innovation on del Toro's part (besides putting magical realism on the screen; I can't think of another film, besides The devil's backbone, that's really done this). Pan's labyrinth is highly recommended, but I'm going to wait another five or ten years before I label del Toro a true genius; at only 42, he still needs some time to mature completely, especially as a writer.
One final note: While undoubtedly a fairy tale, Pan's labyrinth is not for young children. This is a dark and extremely disturbing tale, on the order of, say, something by David Cronenberg. (Though obviously very different in most other respects.) The somber atmosphere settles in from the first frame, and only becomes more and more oppressive -- I don't think there's a single moment where anyone says or does anything that's in any way amusing or light-hearted. It didn't give me nightmares, but I believe it would for anyone younger than about 14.
One of the finest legal minds of the day. Or something.
Attorney General Gonzales yesterday: `There is no expressed grant of habeas in the Constitution; there’s a prohibition against taking it away.'
Okay, I suppose he's right in at least one sense. According to Article One, Section 9, `The privilege of the writ of habeas corpus shall not be suspended, unless when in cases of rebellion or invasion the public safety may require it'. The specific wording is that it's a right the state is not allowed to take away, except in certain specific cases. But, if it's a right the state is not usually allowed to take away, this would seem to imply directly that it's a right people usually have. A can't be forbidden from taking X away from B if B never ever has X in the first place.
Maybe one of your lawyerly types can explain this to me?
HT
Okay, I suppose he's right in at least one sense. According to Article One, Section 9, `The privilege of the writ of habeas corpus shall not be suspended, unless when in cases of rebellion or invasion the public safety may require it'. The specific wording is that it's a right the state is not allowed to take away, except in certain specific cases. But, if it's a right the state is not usually allowed to take away, this would seem to imply directly that it's a right people usually have. A can't be forbidden from taking X away from B if B never ever has X in the first place.
Maybe one of your lawyerly types can explain this to me?
HT
Short review of Marie Antoinette
Sophia Coppolla's Marie Antoinette is about the boring, vapid life of the title historical figure. This makes for a boring, vapid film.
January 18, 2007
Bill Simmons
I've written and rewritten this post a couple times because it always ends up way too long and autobiographical. Suffice to say I've never been into sports much, but Bill Simmons makes me want to learn about bit more. After reading that column I've actually considered Tivoing Phoenix Suns games.
January 17, 2007
My Roulette System
Well now, Dan comes back from vacation and steals my spot at the top of the blog! With real posts about minimum wages and such things no less! I'll put a stop to this!
In my last post about gambling I failed to really make clear what my system entails. This really didn't help anybody offer an evaluation of the system. Without further ado:
The game is Roulette*. I play the outside, which means I don't put chips directly on any numbers but play groups. In particular, the roulette board is divided into three collumns. Betting successfully on a collumn pays 3-to-1. You can also bet on half the field(the two zeros are excluded from both the collumns and the evens/odds and red/black) with a pay rate of 2-to-1.
When I play, I bet two equal stacks of chips, one on each of two collumns. This means if I win I receive three stacks of chips back, covering my bet and giving me the same payout as if I had bet half the board. On the one hand this gives me better odds than betting red/black/odd/even as I'm covering slightly less than 2/3 of the board. It also means if I lose I lose twice as much.
Now, when I do lose I double down, placing double the original bet on the same collumns. If I lose again the bet is redoubled and again placed on the same collumns. This process is repeated until one of my two collumns wins, bringing me all the money that I'd lost in that stretch and one stack the size of the original bet. If I win on a particular spin, I move my bets to the other two collumns. I admit that this doesn't effect my odds of winning, but at the very least it gives me something to do and assuages that nagging feeling that it *has* to be more likely to hit on the other two collumns after a string of hits on one of them. I know, not true, but it sure makes sense and if it doesn't hurt my odds than it really doesn't matter.
There are obvious problems with this which were entailed in the Gambler's Falacy and Martingale System pages linked in the previous post. A very long string of losses is not impossible, even if it may be unlikely. Given the doubling of bets, a sufficiently long string of losses would bankrupt the player eventually.
The difference I think between my system and the Martingale system it that the latter seems to assume, based on the Wikipedia page, that the odds of success on a given bet are slightly less than 50%. That being the case it makes sense that over time you would eventually lose all your money. But my system has odds in my favor in execess of 60%. This in particular is where I need help from math inclined folks. Do the higher odds of success in my model make it viable where the Martingale system is not? It is granted that a player using my system needs a bank to draw from far in excess of the minimum bet they are using (I figure that a bank of $400-$500 for a table with a $15 minimum bet is sufficiently "safe"). It is also granted that given limited funds this system could be beated by a bad streak of luck, say hitting the same collumn and/or the zeros four or five times in a row. But I do think that the odds of such a streak are pretty poor and represent probably the best odds you can get in a casino.
Any thoughts?
*It should be noted at the outset that I always play the table with the lowest minimum bet and I *always* bet the minimum, except as specified in the explanation.
In my last post about gambling I failed to really make clear what my system entails. This really didn't help anybody offer an evaluation of the system. Without further ado:
The game is Roulette*. I play the outside, which means I don't put chips directly on any numbers but play groups. In particular, the roulette board is divided into three collumns. Betting successfully on a collumn pays 3-to-1. You can also bet on half the field(the two zeros are excluded from both the collumns and the evens/odds and red/black) with a pay rate of 2-to-1.
When I play, I bet two equal stacks of chips, one on each of two collumns. This means if I win I receive three stacks of chips back, covering my bet and giving me the same payout as if I had bet half the board. On the one hand this gives me better odds than betting red/black/odd/even as I'm covering slightly less than 2/3 of the board. It also means if I lose I lose twice as much.
Now, when I do lose I double down, placing double the original bet on the same collumns. If I lose again the bet is redoubled and again placed on the same collumns. This process is repeated until one of my two collumns wins, bringing me all the money that I'd lost in that stretch and one stack the size of the original bet. If I win on a particular spin, I move my bets to the other two collumns. I admit that this doesn't effect my odds of winning, but at the very least it gives me something to do and assuages that nagging feeling that it *has* to be more likely to hit on the other two collumns after a string of hits on one of them. I know, not true, but it sure makes sense and if it doesn't hurt my odds than it really doesn't matter.
There are obvious problems with this which were entailed in the Gambler's Falacy and Martingale System pages linked in the previous post. A very long string of losses is not impossible, even if it may be unlikely. Given the doubling of bets, a sufficiently long string of losses would bankrupt the player eventually.
The difference I think between my system and the Martingale system it that the latter seems to assume, based on the Wikipedia page, that the odds of success on a given bet are slightly less than 50%. That being the case it makes sense that over time you would eventually lose all your money. But my system has odds in my favor in execess of 60%. This in particular is where I need help from math inclined folks. Do the higher odds of success in my model make it viable where the Martingale system is not? It is granted that a player using my system needs a bank to draw from far in excess of the minimum bet they are using (I figure that a bank of $400-$500 for a table with a $15 minimum bet is sufficiently "safe"). It is also granted that given limited funds this system could be beated by a bad streak of luck, say hitting the same collumn and/or the zeros four or five times in a row. But I do think that the odds of such a streak are pretty poor and represent probably the best odds you can get in a casino.
Any thoughts?
*It should be noted at the outset that I always play the table with the lowest minimum bet and I *always* bet the minimum, except as specified in the explanation.
Feedback from my students
With the start of the new semester, I've gotten the packet of student evaluations from the end of last semester. The best (by which I mean most amusing) answer was to the question `Did you meet your teaching assistant during office hours? If you did, why not? If you did were the meetings helpful?'
More seriously, I've identified a few things I need to work on, and a few things about the format of the course that caused serious problems.
First, as a grader, I'm used to working through math exams, not papers. Grading math exams, you usually only need to identify the point at which the student forgot how to use the method she or he is applying in each particular problem. Paper grading is much more subtle, and I need to take the time to figure out the most time-efficient way to make helpful comments.
Second, I was surprised to see several students say things like `He also never really encouraged us or made us feel positive.' I need to give more positive feedback, even just for answers that are on the right track but not totally right, in both class and papers.
Third, especially with introductory courses, the students need a fair amount of explicit structural guidelines when they go to write their papers. A common strategy I've seen my friends and colleagues use is to have a series of progressively more involved paper assignments. For example, in the first assignment, students just have to summarise an argument in a perspicacious way; in the second, they summarise and formulate a single objection; in the third, they summarise, object, and then rebut the objection. The distribution of the paper assignments is accompanied with discussions on how to summarise arguments and how to formulate objections.
Fourth, students need some variety. Lecture-lecture-discussion gets old, and sometimes they need more lecture or more discussion. That's a flexibility I don't really have as a TA, but I do have some wiggle room: I can sacrifice our discussion time to lecture, and do things like ask students to give presentations or lead discussions.
Fifth, I have learned how not to formulate exam questions. Intro students should be asked to regurgitate major arguments, or briefly compare and contrast what Plato, Descartes, and Perry think about the soul. They should not be asked to recall trivial minutiae about the readings, with virtually no guidelines as to what minutiae they will be asked about.
And sixth, at the introductory level, a `student directed' course is just begging for disaster. I'm not sure that I ever explained the format here, so let me do so briefly now.
Thursday night, the students would finish their assigned reading, and email questions on that reading to their TAs. We sorted through them and put together handouts, and the discussion section on Friday was usually spent working through these questions. We would usually get through 4-6 (out of 20+ or so distinct questions) in the fifty-minute section. At the end of section, the students would identify questions that the TAs would send on to the professor that night. The lecture periods on Monday and Wednesday consisted almost exclusively of the professor answering these questions. Hence, if the students didn't consider it important or interesting or confusing, or important or interesting or confusing enough to warrant being sent up to the professor, it was never discussed in the context of the class. To make matters worse, we were supposed to never give them straight out answers; they were supposed to struggle with answering the questions of their classmates, and get direction but not answers from the lectures.
Unsurprisingly, many students found this immensely frustrating and never achieved even the barest beginnings of understanding of the texts. Incorporating at least a little Textbook Philosophy would have been slightly frustrating for us the professional philosophers, but at least the students have a chance of understanding what's going on.
Yes, they were sort of helpful except he never gave straight answers to my questions. I think that's a philosophy thing though.
More seriously, I've identified a few things I need to work on, and a few things about the format of the course that caused serious problems.
First, as a grader, I'm used to working through math exams, not papers. Grading math exams, you usually only need to identify the point at which the student forgot how to use the method she or he is applying in each particular problem. Paper grading is much more subtle, and I need to take the time to figure out the most time-efficient way to make helpful comments.
Second, I was surprised to see several students say things like `He also never really encouraged us or made us feel positive.' I need to give more positive feedback, even just for answers that are on the right track but not totally right, in both class and papers.
Third, especially with introductory courses, the students need a fair amount of explicit structural guidelines when they go to write their papers. A common strategy I've seen my friends and colleagues use is to have a series of progressively more involved paper assignments. For example, in the first assignment, students just have to summarise an argument in a perspicacious way; in the second, they summarise and formulate a single objection; in the third, they summarise, object, and then rebut the objection. The distribution of the paper assignments is accompanied with discussions on how to summarise arguments and how to formulate objections.
Fourth, students need some variety. Lecture-lecture-discussion gets old, and sometimes they need more lecture or more discussion. That's a flexibility I don't really have as a TA, but I do have some wiggle room: I can sacrifice our discussion time to lecture, and do things like ask students to give presentations or lead discussions.
Fifth, I have learned how not to formulate exam questions. Intro students should be asked to regurgitate major arguments, or briefly compare and contrast what Plato, Descartes, and Perry think about the soul. They should not be asked to recall trivial minutiae about the readings, with virtually no guidelines as to what minutiae they will be asked about.
And sixth, at the introductory level, a `student directed' course is just begging for disaster. I'm not sure that I ever explained the format here, so let me do so briefly now.
Thursday night, the students would finish their assigned reading, and email questions on that reading to their TAs. We sorted through them and put together handouts, and the discussion section on Friday was usually spent working through these questions. We would usually get through 4-6 (out of 20+ or so distinct questions) in the fifty-minute section. At the end of section, the students would identify questions that the TAs would send on to the professor that night. The lecture periods on Monday and Wednesday consisted almost exclusively of the professor answering these questions. Hence, if the students didn't consider it important or interesting or confusing, or important or interesting or confusing enough to warrant being sent up to the professor, it was never discussed in the context of the class. To make matters worse, we were supposed to never give them straight out answers; they were supposed to struggle with answering the questions of their classmates, and get direction but not answers from the lectures.
Unsurprisingly, many students found this immensely frustrating and never achieved even the barest beginnings of understanding of the texts. Incorporating at least a little Textbook Philosophy would have been slightly frustrating for us the professional philosophers, but at least the students have a chance of understanding what's going on.
January 15, 2007
The danger premium
In discussions on the wage gap (women, on average, make less than 75 cents for every dollar than men, on average, earn), one of the cards anti-feminists like to play is the `danger premium'. The idea is that, for whatever reason, women are less likely to take dangerous jobs; and because they are dangerous, these jobs pay more; hence, the wage gap can be explained by the danger premiums that men receive.
Let's grant the first premiss, and ignore the complete lack of analysis needed to reach the conclusion. Is the second premiss true? If you believe supply and demand curves model reality, then it has some intuitive force: in order to attract workers to these more dangerous jobs, you have to provide them with some incentive. On the other hand, if you're remotely familiar with reality, this is intuitively preposterous: obviously the unpleasant, dangerous work is done by the people at the bottom of the socio-economic ladder, while the rich people have nice safe white collar jobs.
For more solid evidence, MSN (that great media critic of the socio-economic status quo) gives us this list of the eleven most life-threatening jobs: fishing workers, logging workers, aircraft pilots, iron and steel workers, refuse collectors, farmers, electrical line workers, truck drivers, `Miscellaneous agricultural workers', and construction workers. We also get fatality rates and average salary, as measured by the Bureau of Labor Statistics. Take a moment to peruse the list.
Notice anything? The only category where the average salary is above $50k a year (roughly speaking, the bare minimum you need to live a comfortable middle-class life for a family of 4) are aircraft pilots and flight engineers, who are by far the most highly educated group in the list. The same goes for the other two lists in this article, of most injury-prone jobs and `Jobs That Could Make You Sick'. In fact, according to a chart produced by the Bureau in 1998 (and reproduced by Ampersand in his discussion of the danger premium as part of the wage gap series), the danger premium is not just the smallest of those investigated, but actually negative, while the corresponding knowledge premium is not just the highest of those investigated, but about three times the magnitude of the second highest. Dangerous jobs actually pay less, on average, not more. The danger premium hypothesis is not only wrong, but the exact opposite of reality.
Let's grant the first premiss, and ignore the complete lack of analysis needed to reach the conclusion. Is the second premiss true? If you believe supply and demand curves model reality, then it has some intuitive force: in order to attract workers to these more dangerous jobs, you have to provide them with some incentive. On the other hand, if you're remotely familiar with reality, this is intuitively preposterous: obviously the unpleasant, dangerous work is done by the people at the bottom of the socio-economic ladder, while the rich people have nice safe white collar jobs.
For more solid evidence, MSN (that great media critic of the socio-economic status quo) gives us this list of the eleven most life-threatening jobs: fishing workers, logging workers, aircraft pilots, iron and steel workers, refuse collectors, farmers, electrical line workers, truck drivers, `Miscellaneous agricultural workers', and construction workers. We also get fatality rates and average salary, as measured by the Bureau of Labor Statistics. Take a moment to peruse the list.
Notice anything? The only category where the average salary is above $50k a year (roughly speaking, the bare minimum you need to live a comfortable middle-class life for a family of 4) are aircraft pilots and flight engineers, who are by far the most highly educated group in the list. The same goes for the other two lists in this article, of most injury-prone jobs and `Jobs That Could Make You Sick'. In fact, according to a chart produced by the Bureau in 1998 (and reproduced by Ampersand in his discussion of the danger premium as part of the wage gap series), the danger premium is not just the smallest of those investigated, but actually negative, while the corresponding knowledge premium is not just the highest of those investigated, but about three times the magnitude of the second highest. Dangerous jobs actually pay less, on average, not more. The danger premium hypothesis is not only wrong, but the exact opposite of reality.
MLK, 2007
You certainly wouldn't know it looking at the homepage of The New York Times, but today we celebrate the life and work of Martin Luther King. Being an ivory tower intellectual, I celebrate not by contributing to the ongoing fight for justice and civil rights for all people everywhere, but instead by reading an essay. If you think this is a crappy way to celebrate, you're probably right, but it's a lot better than sleeping in and watching Comedy Central all day.
King was educated as a theologian, with a heavy dose of philosophy, and his Letter from Birmingham Jail is a beautiful discussion of the legitimacy and necessity of civil disobedience, just and unjust laws, and race consciousness:
Christians will also be interested in King's criticisms of the conventional American church; for more on that, read today's piece on King in The Chron.
The link above has links, in turn, to the Letter, and a brief historical discussion putting the Letter in context. It's not too long; I highly recommend taking a few minutes to read it.
King was educated as a theologian, with a heavy dose of philosophy, and his Letter from Birmingham Jail is a beautiful discussion of the legitimacy and necessity of civil disobedience, just and unjust laws, and race consciousness:
I suppose I should have realized that few members of the oppressor race can understand the deep groans and passionate yearnings of the oppressed race, and still fewer have the vision to see that injustice must be rooted out by strong, persistent and determined action.
Christians will also be interested in King's criticisms of the conventional American church; for more on that, read today's piece on King in The Chron.
The link above has links, in turn, to the Letter, and a brief historical discussion putting the Letter in context. It's not too long; I highly recommend taking a few minutes to read it.
New web album
I'm going to start putting my favourite shots on a Picasa web album. All of the shots in there right now have been posted to this blog in the past, but I expect to add some others that have not been so posted.
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