Summary
Russell's paradox describes a fundemental conundrum with set theory that is sometimes illustrated by way of a story about a barber.
Paradox
This presentation is a modified version of Russell's original presentation.
There once was a platoon of men who were very punctilious about following orders. One day, the commander decided that the men needed to look less disheveled. One of the men, a barber named Bob, proposed that he shave everyone everyday. Some of the men complained and asked if they could shave themselves instead. As a compromise, the commander ordered Bob to shave all and only the men who do not shave themselves.
The paradox is this: who shaves Bob? If he shaves himself, then he ends up being prohibited from shaving himself. In which case he must shave himself. Continue ad infinitum.
Commentary
The significance of this paradox was that it undermined the existence of certain types of sets, potentially undermining all of set theory. There were some interesting responses, but ultimately Gödel showed the inescapable nature of such paradoxes for most logical systems.
Friday, November 27, 2009
Wednesday, November 25, 2009
The Importance of Numeracy
Definition
Numeracy is a portmanteau of "numerical literacy" and refers to the understanding of mathematical concepts such as orders of magnitude, probability, and statistics.
Conjecture
Certain concepts in math are necessary for critical thinking. Many people, however, struggle to learn these concepts well thereby reducing the effectiveness of their policy choices.
Commentary
In a country of over $12 trillion dollars deficit (and counting), about 80% of people cannot concieve of the magnitude of a trillion. Very small quantities are equally confusing, because people are unaccustomed to seeing them in their everyday lives. However, thanks to wonderful videos and interactive comparisons you can get a better sense of how orders of magnitude work.
Of course, that's only a very small part of overall numeracy. Probability and statistics, it can be argued, play an important role in everyday discourse, especially as we continue to be bombarded by facts and figures of every sort. When I was younger, someone told me a joke:
I currently do not have any solutions to this problem, yet I do not believe it unsolvable. Part of the issue may lie with trying to solve the wrong problem. But that will have to be another post.
More on this later.
Numeracy is a portmanteau of "numerical literacy" and refers to the understanding of mathematical concepts such as orders of magnitude, probability, and statistics.
Conjecture
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Certain concepts in math are necessary for critical thinking. Many people, however, struggle to learn these concepts well thereby reducing the effectiveness of their policy choices.
Commentary
In a country of over $12 trillion dollars deficit (and counting), about 80% of people cannot concieve of the magnitude of a trillion. Very small quantities are equally confusing, because people are unaccustomed to seeing them in their everyday lives. However, thanks to wonderful videos and interactive comparisons you can get a better sense of how orders of magnitude work.
Of course, that's only a very small part of overall numeracy. Probability and statistics, it can be argued, play an important role in everyday discourse, especially as we continue to be bombarded by facts and figures of every sort. When I was younger, someone told me a joke:
Two boys are walking home from school and one asks the other,At the time I recall laughing very hard. As I got older, this joke became less funny for I encountered more and more people who surprised me with their ignorance and actually maintain variations of this sort of thinking.
"What's the chance that I'll see a man riding a dinosaur in the street?"
His friend thinks for a moment, and responds,
"Fifty percent. Either you will or you won't."
I currently do not have any solutions to this problem, yet I do not believe it unsolvable. Part of the issue may lie with trying to solve the wrong problem. But that will have to be another post.
Tuesday, November 24, 2009
Computational Theory for Lawyers
Definition
Computational Theory is a branch of mathematics that morphed into computer science. Among its goals is to look at a problem and ask: Is there a series of steps that will solve this problem? Those steps are also known as an algorithm, and finding a fast & efficient algorithm for something people care about, such as searching for a piece of information, is often a great way to start a business.
Commentary
Groklaw has an interesting (and very long) discussion about computational theory and how it applies to patent law. From the article:
(Disclosure: the author is a friend of mine.)
Meta
The basic question is how can we say that two items or methods "are the same?" In what way are they the same? Computational theory suggests that two methods are the same if they are reducible to each other. That is, if under the same circumstances they both produce the same result, the methods are considered the same.
More on this later.
See Also (Updated 2010-02-24)
Computational Theory is a branch of mathematics that morphed into computer science. Among its goals is to look at a problem and ask: Is there a series of steps that will solve this problem? Those steps are also known as an algorithm, and finding a fast & efficient algorithm for something people care about, such as searching for a piece of information, is often a great way to start a business.
Commentary
Groklaw has an interesting (and very long) discussion about computational theory and how it applies to patent law. From the article:
For example consider I write a program. Some outside party has written a similar program. This party sees my program and thinks I infringe on his proprietary rights. There are two scenarios depending on whether he makes his claim according to copyright law or patent law.The notion of an intensional and extensional perspectives is actually an amazing insight into the world of mathematics that I hope to discuss more as I make my way through the excellent book Autonomy of Mathematical Knowledge by Curtis Franks.
For claims of copyright infringement the text of the source code matters. If I wrote my program independently and I can prove the texts are different, I don't infringe on his rights. This is an intensional point of view.
For claims of patent infringement then differences in the text of the source code won't matter. It won't even matter if the code is written in a different programming language. If my program uses the same method that is covered by the patent according to whatever legal test of "same method" is applicable, I will infringe. This is an extensional perspective.
(Disclosure: the author is a friend of mine.)Meta
The basic question is how can we say that two items or methods "are the same?" In what way are they the same? Computational theory suggests that two methods are the same if they are reducible to each other. That is, if under the same circumstances they both produce the same result, the methods are considered the same.
See Also (Updated 2010-02-24)
- Review: The Autonomy of Mathematical Knowledge for my review of that book.
Monday, November 23, 2009
Review: I Will Teach You To Be Rich
Review
Ramit Sethi (that I guy I quote a lot), author of the website IWillTeachYouToBeRich.com, published a book by the same name about personal finance for twentysomethings.
Although I knew the book would not differ much from the content available on his website, it was pleasant to have Ramit's thoughts presented in close proximity to each other rather than spread out across the years I've been following his blog.
Most of his advice revolves around a single theme: stop loosing money by doing nothing. It occurred to me that while in the world of economics, such appeals to opportunity cost are customary, the world of twentysomethings would much rather feel guilty about doing nothing rather than actually figuring out what needs to be done and doing it. (Please pardon the gross oversimplifications; there are many responsible twenty year-olds, but few who think they can do anything about their finances.)
The blog contains much, if not all, of the advice in the book, but the book highlighted three things I had failed to implement (though I read them on the blog). First, I finally took Ramit's advice about negotiation, and negotiated a bill. I clearly have more work to do in that department, but it was good to have a plan of how to approach the conversation, and not feel weird about talking about money. To Ramit's credit, he portrays negotiation as asymmetric warfare: you, a novice in negotiation, are battling with experts who negotiate with people every day. However, you needn't become a Spartan to negotiate effectively. In fact, being pleasant (and smiling) makes it even easier. Negotiation is a fascinating phenomenon in the world of human interaction; it has elements of conflict, optimization and compromise. Each party seeks to optimize results that favor him or her, yet done right both parties can win. A critical part of Ramit's advise is to avoid yes-or-no questions when you really want to ask "how can we make this work?" That one question saved me $180 (over six months) for 2 minutes worth of effort.
The next piece of advise I had failed to implement was to synchronize your bills with your paycheck (to the extent possible). The idea is to have a more predictable and automated flow of money. While I've got much of the flow nailed down, I never thought to change the billing date to a common date; we'll see how this works out over the coming months and years.
Lastly, the book provided a clearer perspective on what it takes to buy a house. Again, this isn't anything that Ramit hadn't said previously about buying a house. It was just easier to focus on his points when I was reading a book (about finance!) rather than reading my daily blogs. The only change in behavior this created was creating a little "dashboard" for important goals. Previously the goals were general (house, travel, etc.); now they are very specific (20% down payment, trip to California, etc.). This small change forced me to also estimate the cost and, by extension, the date of fulfillment of each of the goals. Again, the payoff is mostly psychological, but it helps take down some psychological barriers.
Overall, I recommend this book to most people as an example of how to set up an automatic system that helps alleviate certain kinds of stress. It's an excellent short read and his good humored presentation doesn't hurt either.
Ramit Sethi (that I guy I quote a lot), author of the website IWillTeachYouToBeRich.com, published a book by the same name about personal finance for twentysomethings.
Although I knew the book would not differ much from the content available on his website, it was pleasant to have Ramit's thoughts presented in close proximity to each other rather than spread out across the years I've been following his blog.
Most of his advice revolves around a single theme: stop loosing money by doing nothing. It occurred to me that while in the world of economics, such appeals to opportunity cost are customary, the world of twentysomethings would much rather feel guilty about doing nothing rather than actually figuring out what needs to be done and doing it. (Please pardon the gross oversimplifications; there are many responsible twenty year-olds, but few who think they can do anything about their finances.)
The blog contains much, if not all, of the advice in the book, but the book highlighted three things I had failed to implement (though I read them on the blog). First, I finally took Ramit's advice about negotiation, and negotiated a bill. I clearly have more work to do in that department, but it was good to have a plan of how to approach the conversation, and not feel weird about talking about money. To Ramit's credit, he portrays negotiation as asymmetric warfare: you, a novice in negotiation, are battling with experts who negotiate with people every day. However, you needn't become a Spartan to negotiate effectively. In fact, being pleasant (and smiling) makes it even easier. Negotiation is a fascinating phenomenon in the world of human interaction; it has elements of conflict, optimization and compromise. Each party seeks to optimize results that favor him or her, yet done right both parties can win. A critical part of Ramit's advise is to avoid yes-or-no questions when you really want to ask "how can we make this work?" That one question saved me $180 (over six months) for 2 minutes worth of effort.
The next piece of advise I had failed to implement was to synchronize your bills with your paycheck (to the extent possible). The idea is to have a more predictable and automated flow of money. While I've got much of the flow nailed down, I never thought to change the billing date to a common date; we'll see how this works out over the coming months and years.
Lastly, the book provided a clearer perspective on what it takes to buy a house. Again, this isn't anything that Ramit hadn't said previously about buying a house. It was just easier to focus on his points when I was reading a book (about finance!) rather than reading my daily blogs. The only change in behavior this created was creating a little "dashboard" for important goals. Previously the goals were general (house, travel, etc.); now they are very specific (20% down payment, trip to California, etc.). This small change forced me to also estimate the cost and, by extension, the date of fulfillment of each of the goals. Again, the payoff is mostly psychological, but it helps take down some psychological barriers.
Overall, I recommend this book to most people as an example of how to set up an automatic system that helps alleviate certain kinds of stress. It's an excellent short read and his good humored presentation doesn't hurt either.
Sunday, November 22, 2009
Advances in Printer Ink
Summary
A recent IEEE Spectrum featured an article about an advance in ink-less printing called ZINK.
Commentary
As consumers, we're familiar with the high price of ink. If you think gasoline is expensive, how's $8,000 a gallon for HP ink? And it doesn't help that many printers have been "designed" to produce false out-of-ink messages.
There have been several attempts at lowering the cost of printer ink. In 2007, Kodak introduced a printer that used their "pigment-based ink" and was supposed to revolutionize the printer world. I'm not sure how successful, they've been, but it put the issue of ink pricing at the forefront of many consumers minds.
The most recent attempt at overcoming printer ink pricing comes from a Polaroid spin-off called ZINK (for Zero-ink) that has been working for decades on creating colorless, ink-less paper that uses localized heat to change the color at each point. Several companies have cameras that also print 2x3 inch photos using ZINK: the Polaroid PoGo, Dell Wasabi, and the TOMY xiao.
It's fascinating to see the old fallen giants Kodak and Polaroid wake from their slumber and try to compete in their former markets adapting to the digital realities of today. If their technologies advance and expand, we may see a disruption in the printer market similar to that of the '80s.
A recent IEEE Spectrum featured an article about an advance in ink-less printing called ZINK.
Commentary
As consumers, we're familiar with the high price of ink. If you think gasoline is expensive, how's $8,000 a gallon for HP ink? And it doesn't help that many printers have been "designed" to produce false out-of-ink messages.
There have been several attempts at lowering the cost of printer ink. In 2007, Kodak introduced a printer that used their "pigment-based ink" and was supposed to revolutionize the printer world. I'm not sure how successful, they've been, but it put the issue of ink pricing at the forefront of many consumers minds.
The most recent attempt at overcoming printer ink pricing comes from a Polaroid spin-off called ZINK (for Zero-ink) that has been working for decades on creating colorless, ink-less paper that uses localized heat to change the color at each point. Several companies have cameras that also print 2x3 inch photos using ZINK: the Polaroid PoGo, Dell Wasabi, and the TOMY xiao.
It's fascinating to see the old fallen giants Kodak and Polaroid wake from their slumber and try to compete in their former markets adapting to the digital realities of today. If their technologies advance and expand, we may see a disruption in the printer market similar to that of the '80s.
Friday, November 20, 2009
Maslow's Hierarchy of Needs
Definition
An structure that describes human desires and motivations in terms of tiers of fulfillment.
Commentary
The basic premise behind Maslow's hierarchy is that people's needs are organized in such a way that when lower needs (e.g., sleep) are unfulfilled, it is impossible to focus on higher needs (e.g., self-esteem). Recently, a friend questioned the nature of this hierarchy citing examples of religious people who clearly appear to be fulfilled at the highest level (self-actualization), yet lacked many of the securities provided by the lower levels (e.g., food, employment, health).
Alderfer proposed a revised version known as ERG Theory in which needs are also grouped into Existence, Relatedness, and Growth categories. However, neither of these theories explains how people could work on higher levels while lower levels remain unfulfilled.
Conjecture
A possible explanation might be the inverse of the "regression" theory that Alderfer proposed. He suggested that when a higher need was unfulfilled, lower needs received more attention. I propose that if a higher need is over-fulfilled, lower needs can be (temporarily) ignored.
Update (2009-11-23) A friend suggested that perhaps only people who have had lower levels satisfied in the past are able to refocus efforts into higher levels when those lower levels are subsequently unfulfilled because they at least experienced those levels.
Meta
Is it useful to organize human needs in this way? I'm aware of some applications in education and business, are there any others? Do you know of alternatives?
An structure that describes human desires and motivations in terms of tiers of fulfillment.
Commentary
The basic premise behind Maslow's hierarchy is that people's needs are organized in such a way that when lower needs (e.g., sleep) are unfulfilled, it is impossible to focus on higher needs (e.g., self-esteem). Recently, a friend questioned the nature of this hierarchy citing examples of religious people who clearly appear to be fulfilled at the highest level (self-actualization), yet lacked many of the securities provided by the lower levels (e.g., food, employment, health).
Alderfer proposed a revised version known as ERG Theory in which needs are also grouped into Existence, Relatedness, and Growth categories. However, neither of these theories explains how people could work on higher levels while lower levels remain unfulfilled.
Conjecture
A possible explanation might be the inverse of the "regression" theory that Alderfer proposed. He suggested that when a higher need was unfulfilled, lower needs received more attention. I propose that if a higher need is over-fulfilled, lower needs can be (temporarily) ignored.
Update (2009-11-23) A friend suggested that perhaps only people who have had lower levels satisfied in the past are able to refocus efforts into higher levels when those lower levels are subsequently unfulfilled because they at least experienced those levels.
Meta
Is it useful to organize human needs in this way? I'm aware of some applications in education and business, are there any others? Do you know of alternatives?
Thursday, November 19, 2009
Pomodoro Technique
Technique
The Pomodoro Technique is a method for improving productivity by creating focused periods of attention as well as forcing breaks at regular intervals.
Definition
A pomodoro is an indivisible unit of time (usually 25 minutes), plus a short break (3-5 minutes). Also the word for tomato in Italian. (The inventor, Francesco Cirillo, used a tomato kitchen timer when he came up with this technique.)
Commentary
Although I've only been using this technique for several months, I'm finding it an increasingly pleasant way to organize my day. In particular, I enjoy the focus on the down-time and context switching. Here's my adapted version:
The Pomodoro Technique is a method for improving productivity by creating focused periods of attention as well as forcing breaks at regular intervals.
Definition
A pomodoro is an indivisible unit of time (usually 25 minutes), plus a short break (3-5 minutes). Also the word for tomato in Italian. (The inventor, Francesco Cirillo, used a tomato kitchen timer when he came up with this technique.)
Commentary
Although I've only been using this technique for several months, I'm finding it an increasingly pleasant way to organize my day. In particular, I enjoy the focus on the down-time and context switching. Here's my adapted version:
- Task Lists - Believe it or not, I use a plain text file. In fact, I make a new text file every month for all the things that need to be done (unfinished items from previous months carry over). This text file is split into two parts: the top part has all the unscheduled tasks (i.e., tasks that have not been assigned to a day) and the bottom is a reverse-chronological list of tasks by date.
- Scheduling - Most days start by selecting which unscheduled tasks I'll do today. Occasionally, I create a "check-on-the-status" tasks which are derived from special unscheduled tasks that indicate that I'm waiting for something (e.g., someone needs to get back to me). Tasks are organized roughly in the order I want to accomplish them, and I add estimates for the number of pomodoros I anticipate certain tasks to take. Since pomodoros are indivisible I group small tasks together and estimate the total time for all of them.
- Countdown - I use an online stopwatch to count-down 25 minutes during which time I work on the next task in the list. If I finish early, I try to look over my work. When the bell rings I force myself to stop immediately.
- Recordkeeping - I use a variant of the notation in the book. Instead of "X"'s, I record the pomodoro number. This way, if I accomplish multiple tasks, I record the pomodoro during which they were accomplished. Internal interruptions (e.g., hunger, tiredness) are indicated by an apostrophe ('), external interruptions by a dash (-), and a lost pomodoro by a slash (/). (Pomodoros are considered indivisible, so if you get really off-track, you have to reset the clock.)
- Break - When the stopwatch rings, I usually take a three minute break, and take care of most of the interruptions that occurred during the previous pomodoro.
Wednesday, November 18, 2009
Discontent Grows with Google: Wave, Colsure and Go
Commentary
Recently, programmers have been grumbling about Google on several fronts, although none of the issues seem unsurmountable. Complaints about (the currently invite-only) Google Wave and, more recently, Google's Closure Library and Go programming language, all seem to wonder at how these formerly Google-internal technologies could lack Google's characteristic polish.
For example, Lukas Mathis is concerned about Wave's scrollbars, while others seem to have more general concerns. Similarly, while Closure seems to be providing the world with Google's internal toolset, Dmitry Baranovskiy points out that the library is riddled with poorly written code leaving many scratching their heads thinking "how could this come from Google?"
And then there's Go. Go is Google's new programming language that is attracting a lot of attention. Aside from the previously used name (a surprisingly lively discussion), apparently many of its advantages (namely its compiled, concurrent nature) are apparently not as stellar as Google supposes.
Yet unlike other companies that dig themselves into a hole, Google has a great escape plan: outsource the work to the community, and with enough interest, they'll polish your product for you. This only works, of course, as long as Google continues to give off the impression that they care about the communal input. Without that respect, Google is stuck under an avalanche.
Recently, programmers have been grumbling about Google on several fronts, although none of the issues seem unsurmountable. Complaints about (the currently invite-only) Google Wave and, more recently, Google's Closure Library and Go programming language, all seem to wonder at how these formerly Google-internal technologies could lack Google's characteristic polish.
For example, Lukas Mathis is concerned about Wave's scrollbars, while others seem to have more general concerns. Similarly, while Closure seems to be providing the world with Google's internal toolset, Dmitry Baranovskiy points out that the library is riddled with poorly written code leaving many scratching their heads thinking "how could this come from Google?"
And then there's Go. Go is Google's new programming language that is attracting a lot of attention. Aside from the previously used name (a surprisingly lively discussion), apparently many of its advantages (namely its compiled, concurrent nature) are apparently not as stellar as Google supposes.
Yet unlike other companies that dig themselves into a hole, Google has a great escape plan: outsource the work to the community, and with enough interest, they'll polish your product for you. This only works, of course, as long as Google continues to give off the impression that they care about the communal input. Without that respect, Google is stuck under an avalanche.
Tuesday, November 17, 2009
Inbox Zero
Technique
Inbox Zero is a technique for processing your email and somewhat related to the concepts David Allen put forth in Getting Things Done.
I have found Inbox Zero effective at dealing with the psychological barriers around checking and responding to email. I've adapted the process so that for every email (starting with the oldest) I choose one of the following actions:
In the past two years, I have maintained an empty inbox at home and at work and have found that I spend more time doing what needs to be done rather then trying to keep it all in my head.
Inbox Zero is a technique for processing your email and somewhat related to the concepts David Allen put forth in Getting Things Done.
(Video: YouTube)
CommentaryI have found Inbox Zero effective at dealing with the psychological barriers around checking and responding to email. I've adapted the process so that for every email (starting with the oldest) I choose one of the following actions:
- Label & Archive - This is the most common action since most of my email is purely information. By using filters, most the email is pre-labeled and I usually just archive it (or delete it if it's an unsolicited advertisement).
- Star It - I choose this for emails that require me either do something or that indicate that I'm waiting for something to happen (e.g., receipts for an order).
- Respond - Usually to acknowledge receipt of an email, or provide someone with a particular piece of information. This must take less than two minutes.
In the past two years, I have maintained an empty inbox at home and at work and have found that I spend more time doing what needs to be done rather then trying to keep it all in my head.
Monday, November 16, 2009
Psychological Barriers
Definition
A psychological barrier is a perception that impedes an action usually by creating a sense that the activity is overly burdensome or that some unstated prerequisite is unfulfilled. The result is often procrastination.
Example
In a study of 401(k) enrollment, only 40% of employees took advantage of matching programs (note that this is basically free money). Most employees viewed the task of enrolling as annoying and simply took the passive do-nothing route.
Ramit Sethi likes to talk about psychological barries and how to overcome them. In that post, he also mentions how one could use psychological barriers to intentionally prevent oneself from doing an action. For example, people who have trouble using credit cards responsibly can freeze it in a block of ice so that it is available for emergencies, but is otherwise annoying to access.
Commentary
Psychological barriers provide insight into the origin of responses such as "I didn't have a pen at the time" in response to why someone might forfeit thousands of dollars in matched retirement income-- the perception of complexity (no matter how small) can shift one's decision away from even ridiculously beneficial activities.
Moreover, we gain insight into the world of advertising. Note how advertisers try to tear down the barriers between you and an order for their product ("order today", "act now", "call now", "but wait there's more") and how they try to create barriers for the "problem" that their product "solves". Of course we always knew that television is the opiate of the masses.
A psychological barrier is a perception that impedes an action usually by creating a sense that the activity is overly burdensome or that some unstated prerequisite is unfulfilled. The result is often procrastination.
Example
In a study of 401(k) enrollment, only 40% of employees took advantage of matching programs (note that this is basically free money). Most employees viewed the task of enrolling as annoying and simply took the passive do-nothing route.
Ramit Sethi likes to talk about psychological barries and how to overcome them. In that post, he also mentions how one could use psychological barriers to intentionally prevent oneself from doing an action. For example, people who have trouble using credit cards responsibly can freeze it in a block of ice so that it is available for emergencies, but is otherwise annoying to access.
Commentary
Psychological barriers provide insight into the origin of responses such as "I didn't have a pen at the time" in response to why someone might forfeit thousands of dollars in matched retirement income-- the perception of complexity (no matter how small) can shift one's decision away from even ridiculously beneficial activities.
Moreover, we gain insight into the world of advertising. Note how advertisers try to tear down the barriers between you and an order for their product ("order today", "act now", "call now", "but wait there's more") and how they try to create barriers for the "problem" that their product "solves". Of course we always knew that television is the opiate of the masses.
Sunday, November 15, 2009
Easy Big Wins
Conjecture
Optimizations that are easier to implement and that have a higher return on investment are better than the alternative optimizations. Furthermore, most popular optimizations do not deliver high returns on investment.
Technique
Ramit Sethi outlines (in eye-catching ways) how one can figure out which optimizations are worth your effort. Mostly, his advice hinges on differentiating yourself from everyone else:
Optimizations that are easier to implement and that have a higher return on investment are better than the alternative optimizations. Furthermore, most popular optimizations do not deliver high returns on investment.
Technique
Ramit Sethi outlines (in eye-catching ways) how one can figure out which optimizations are worth your effort. Mostly, his advice hinges on differentiating yourself from everyone else:
As you can see, many Big Wins are actually easily within reach — if you choose the right targets and differentiate yourself from others. While you’ll have a few areas of life where you’ll have to go up against formidable competition, many other areas of life are wide open.
Friday, November 13, 2009
Pre-Weekend Summary (2009-11-13)
Have a good weekend.
Summary
This week Schneier taught us that thieves prefer black luggage, that anti-virus is still a good idea (despite it's moderate effectiveness), and that there are new access control mechanisms as well as methods to mitigate rootkits.
Reddit was full of cappuccino drawings (e.g., Saturn, a dragon, and the Mona Lisa). Speaking of coffee, Matthew Inman taught us some interesting facts about its origins and how it works.
XKCD was sympathetic and political; Wondermark was apiarian; Abstruse Goose was psychological.
Lukas Mathis explained why people don't realize their camcorders have touch screens, and Techdirt exposed Murdoch's ridiculous, not-connected-to-reality thinking.
Summary
This week Schneier taught us that thieves prefer black luggage, that anti-virus is still a good idea (despite it's moderate effectiveness), and that there are new access control mechanisms as well as methods to mitigate rootkits.
Reddit was full of cappuccino drawings (e.g., Saturn, a dragon, and the Mona Lisa). Speaking of coffee, Matthew Inman taught us some interesting facts about its origins and how it works.
XKCD was sympathetic and political; Wondermark was apiarian; Abstruse Goose was psychological.
Lukas Mathis explained why people don't realize their camcorders have touch screens, and Techdirt exposed Murdoch's ridiculous, not-connected-to-reality thinking.
Thursday, November 12, 2009
Zombies in Math and Literature
Definition
A zombie is typically a reanimated corpse. Also known as the "un-dead."
Commentary
While zombies are not as popular as brains, the former are increasingly the subject of discussion. For example, the recent film Zombieland and the video game Left 4 Dead
both feature zombies. Various defenses and survival guides exist to help you deal with potential zombie attacks.
However, the emergence of zombies in non-entertainment fields is interesting. David Sirota of In These Times has an interesting article on The Zombie Zeitgeist which discusses this new/old phenomenon and how society is dealing with "apocalyptic anxiety".
See Also
A zombie is typically a reanimated corpse. Also known as the "un-dead."
Commentary
While zombies are not as popular as brains, the former are increasingly the subject of discussion. For example, the recent film Zombieland and the video game Left 4 Dead
both feature zombies. Various defenses and survival guides exist to help you deal with potential zombie attacks.
However, the emergence of zombies in non-entertainment fields is interesting. David Sirota of In These Times has an interesting article on The Zombie Zeitgeist which discusses this new/old phenomenon and how society is dealing with "apocalyptic anxiety".
See Also
- When Zombies Attack!: Mathematical Modelling of an Outbreak of Zombie Infection (via Schneier)
- Pride and Prejudice and Zombies
- Sense and Sensibility and Sea Monsters
(not about zombies, but related)
Wednesday, November 11, 2009
Fairness: Equity, Equality and Relative Need
Conjecture
When people discuss "fairness" they are actually referring to either equity, equality or relative need. Or (like children) they mean "it's not what I want."
Definitions
Equity is how a checkout line (queue) works: people line up and are served in order. This is also know as "first-come, first-serve." Notice that we don't randomly select among the customers waiting to be served (equality) nor do we order the customers by the number of items in their cart (relative need).
Equality is how a one-ticket-per-person raffle works. Assuming the winning ticket is chosen at random, the probability of winning is the same for each ticket-holder. We don't award the prize to the first person who buys a ticket (equity), nor do we award the prize to whomever wants or needs it the most (relative need).
Relative need is how an emergency room works. If Alice is waiting to have a splinter removed and Bob needs immediate surgery, the relative needs of Bob take priority over the needs of Alice and Bob is served first. While in some cases, we'd process patients in the order in which they arrived (equity), it seems rather arbitrary to select patients at random (equality).
Example
A simple example is affirmative action. Both sides of the debate tend to complain about "fairness," yet both refer to different policies. One side demands equality or equity, while the other wants a policy of relative need. Of course, such realizations do not solve the problems involved, but they do clarify the locus of dispute.
Meta
How do we decide which policy of "fairness" to apply in a given situation?
When people discuss "fairness" they are actually referring to either equity, equality or relative need. Or (like children) they mean "it's not what I want."
Definitions
Equity is how a checkout line (queue) works: people line up and are served in order. This is also know as "first-come, first-serve." Notice that we don't randomly select among the customers waiting to be served (equality) nor do we order the customers by the number of items in their cart (relative need).
Equality is how a one-ticket-per-person raffle works. Assuming the winning ticket is chosen at random, the probability of winning is the same for each ticket-holder. We don't award the prize to the first person who buys a ticket (equity), nor do we award the prize to whomever wants or needs it the most (relative need).
Relative need is how an emergency room works. If Alice is waiting to have a splinter removed and Bob needs immediate surgery, the relative needs of Bob take priority over the needs of Alice and Bob is served first. While in some cases, we'd process patients in the order in which they arrived (equity), it seems rather arbitrary to select patients at random (equality).
Example
A simple example is affirmative action. Both sides of the debate tend to complain about "fairness," yet both refer to different policies. One side demands equality or equity, while the other wants a policy of relative need. Of course, such realizations do not solve the problems involved, but they do clarify the locus of dispute.
Meta
How do we decide which policy of "fairness" to apply in a given situation?
Tuesday, November 10, 2009
Pareto Efficiency
Definition
If a change from X to Y results in at least one agent better off without making any agents worse off, we call Y a Pareto improvement relative to X. If no more Pareto improvements are possible, the situation is said to be Pareto efficient or Pareto optimal.
Meta
When thinking about a proposed Pareto improvement, consider the resistance to change on the part of the people who will implement your proposal. You may realize that your proposal is no longer a Pareto improvement because of the non-monetary costs involved.
If a change from X to Y results in at least one agent better off without making any agents worse off, we call Y a Pareto improvement relative to X. If no more Pareto improvements are possible, the situation is said to be Pareto efficient or Pareto optimal.
Meta
When thinking about a proposed Pareto improvement, consider the resistance to change on the part of the people who will implement your proposal. You may realize that your proposal is no longer a Pareto improvement because of the non-monetary costs involved.
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