Astronomer, inventor, and old friend of the family/distant relative Bob Doyle has begun a project to address old philosophical problems using information theory.
One such problem, as he explained to me at my aunt's 75th birthday last weekend, is free will versus determinism. Philosophers have been arguing for eternity whether free will exists, and if it does, where it comes from. Disconcertingly, free will seems incompatible with the major theories of physics. In Newtonian physics, all future states of the universe are completely determined by its present state, so no choices can ever be made. In quantum physics, events happen randomly according to precise mathematical rules, so the only "choices" are simply rolls of God's dice. Neither one of these theories seem to allow for any human or animal agency in changing world events.
Bob's idea is that the combination of Newtonian determinism and quantum randomness can explain more than either theory separately. Randomness generates new information and ideas in our brains, giving us novel options to choose from. But our brain is deterministic enough to sort through these ideas and choose the ones that are consistent with our character and past experience. In other words, randomness provides the "free" aspect of free will, and determinism provides the "will."
I don't think this theory is complete, because there's no real explanation of what the choice-making process looks like. But it seems beyond dispute that both random and deterministic forces play a role in what we call "human creativity." Currently, Bob is scouring the history of philosophy for all that's been said on the free will question, and how information theory and physics could connect to this. The blog of his efforts is now a proud memeber of the plektix blogroll.
Field of Science
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Change of address1 year ago in Variety of Life
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Change of address1 year ago in Catalogue of Organisms
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Earth Day: Pogo and our responsibility1 year ago in Doc Madhattan
A Mathematician's Apology
First, the apology: I started a summer job last week and it's taking up a huge amount of time. So posts will be infrequent until my job ends in August.
But since it's on my mind, I'd like to share a bit about this job. I'm assisting in the PROMYS for Teachers program. The goal of the program is to give math teachers an experience similar to the way mathematicians do math.
We mathematicians approach math differently from the way anyone else does. Most people learn math by watching a teacher explain a concept and demonstrate some examples. Students then apply these concepts to some practice problems, and that's pretty much it.
Mathematicians are in the business of discovering new mathematics, not reproducing what is known. To do this, we do what all scientists do: we experiment. Except that for us, experimentation involves only a pencil and paper (computers are sometimes used, but not as much as you might think.) We take numbers or shapes or other mathematical objects and play around with them. This can be a frustrating and fruitless process, but eventually we hope to discover something interesting about the way these objects work.
The next step after discovery is to describe our discovery. This is harder than it sounds, because mathematical language is very precise. One's first few attempts to describe a discovery are often wrong in some way; perhaps an important qualifier has been left out. Sometimes we have to invent new language to describe a discovery.
Finally, we try to justify our discovery by proving it from first principles or from other established theorems. This process can range from easy (a few minutes of thinking) to moderately hard (a few weeks) to epic (a few centuries.) The most famous mathematical theorems come from discoveries that are simple to describe but surprisingly difficult to prove.
In the PROMYS for Teachers program, we try to give teachers a taste of this experience. We give them numerical problems that hint at deep mathematical patterns. We then ask them to describe these patterns precisely and prove them if possible. This is often frustrating for them, since they haven't been shown how to do the problems or proofs beforehand. But by making their own discoveries, they take ownership of the mathematics, and when the process works it is tremendously exciting.
This program is modelled on the Ross program at Ohio State University, which I attended as a high school student. That program basically made me into a mathematician, so it is very rewarding to me to be able to share this experience with teachers.
But since it's on my mind, I'd like to share a bit about this job. I'm assisting in the PROMYS for Teachers program. The goal of the program is to give math teachers an experience similar to the way mathematicians do math.
We mathematicians approach math differently from the way anyone else does. Most people learn math by watching a teacher explain a concept and demonstrate some examples. Students then apply these concepts to some practice problems, and that's pretty much it.
Mathematicians are in the business of discovering new mathematics, not reproducing what is known. To do this, we do what all scientists do: we experiment. Except that for us, experimentation involves only a pencil and paper (computers are sometimes used, but not as much as you might think.) We take numbers or shapes or other mathematical objects and play around with them. This can be a frustrating and fruitless process, but eventually we hope to discover something interesting about the way these objects work.
The next step after discovery is to describe our discovery. This is harder than it sounds, because mathematical language is very precise. One's first few attempts to describe a discovery are often wrong in some way; perhaps an important qualifier has been left out. Sometimes we have to invent new language to describe a discovery.
Finally, we try to justify our discovery by proving it from first principles or from other established theorems. This process can range from easy (a few minutes of thinking) to moderately hard (a few weeks) to epic (a few centuries.) The most famous mathematical theorems come from discoveries that are simple to describe but surprisingly difficult to prove.
In the PROMYS for Teachers program, we try to give teachers a taste of this experience. We give them numerical problems that hint at deep mathematical patterns. We then ask them to describe these patterns precisely and prove them if possible. This is often frustrating for them, since they haven't been shown how to do the problems or proofs beforehand. But by making their own discoveries, they take ownership of the mathematics, and when the process works it is tremendously exciting.
This program is modelled on the Ross program at Ohio State University, which I attended as a high school student. That program basically made me into a mathematician, so it is very rewarding to me to be able to share this experience with teachers.
WSJ: Teach for America "proves" that teachers don't need pay
I know it’s my own fault for evening opening the Wall Street Journal to the editorial page. But somehting I found there last weekend irked me more than their usual “liberals are naive idiots” fare.
An editorial entitled "Amazing Teacher Facts" argued, using the example of Teach for America, that teachers don’t need to be paid any more than they currently are. If these bright young college grads are lining up to teach in inner-city schools at standard salaries, and doing a good job of it, then clearly money isn’t the issue in hiring quality teachers. The culprit must instead be the bureaucracy that requires teachers to take “education” courses (their quotes) to enter the profession the normal way.
This pinched my nerve because I did Teach for America, teaching for two years at Austin High School in Chicago. I was lost my first year and barely competent my second, but in a school with a large number of burnout teachers, this made me a valued member of the faculty.
So yes, TFA teachers do make a positive contribution to their schools. Some of them even become outstanding teachers. This despite being paid a salary that, while livable for 20somethings with no families to support, is far less than these Ivy League grads could be making on Wall Street.
But the WSJ editorial completely fails to ask the question of why, precisely, these Harvard and Yale types are flocking to teach in inner-city LA and rural Louisiana. In my opinion this is due to a phenomenal feat of marketing on the part of TFA. They managed to convince college seniors that teaching is A) a noble cause (which it always has been) and B) an attractive career move (which it never has been in the past.) Paradoxically, by admitting such a small percentage of applicants, TFA has made teaching an elite profession, at least when it is done through TFA. I can’t tell you how many conversations I’ve had that went:
“I’m a high school teacher”
“Oh.”
“...through Teach for America.”
“Oooooooooooooooooohhh!”
What the example of Teach for America proves is precisely what the Wall Street Journal was unwilling to admit: that to recruit quality teachers, you need to raise the status of the teaching profession. Our society usually equates status with money, so the most direct way to get qualified teachers is to pay them what they’re worth (six figures, at least!) TFA is bringing new respect to the teaching profession, but it will never be able to fill our massive teacher shortage while simultaneously maintaining its elite identity. Fixing public education will require a societal consensus that teaching is one of our most important professions, and they need to be paid accordingly.
An editorial entitled "Amazing Teacher Facts" argued, using the example of Teach for America, that teachers don’t need to be paid any more than they currently are. If these bright young college grads are lining up to teach in inner-city schools at standard salaries, and doing a good job of it, then clearly money isn’t the issue in hiring quality teachers. The culprit must instead be the bureaucracy that requires teachers to take “education” courses (their quotes) to enter the profession the normal way.
This pinched my nerve because I did Teach for America, teaching for two years at Austin High School in Chicago. I was lost my first year and barely competent my second, but in a school with a large number of burnout teachers, this made me a valued member of the faculty.
So yes, TFA teachers do make a positive contribution to their schools. Some of them even become outstanding teachers. This despite being paid a salary that, while livable for 20somethings with no families to support, is far less than these Ivy League grads could be making on Wall Street.
But the WSJ editorial completely fails to ask the question of why, precisely, these Harvard and Yale types are flocking to teach in inner-city LA and rural Louisiana. In my opinion this is due to a phenomenal feat of marketing on the part of TFA. They managed to convince college seniors that teaching is A) a noble cause (which it always has been) and B) an attractive career move (which it never has been in the past.) Paradoxically, by admitting such a small percentage of applicants, TFA has made teaching an elite profession, at least when it is done through TFA. I can’t tell you how many conversations I’ve had that went:
“I’m a high school teacher”
“Oh.”
“...through Teach for America.”
“Oooooooooooooooooohhh!”
What the example of Teach for America proves is precisely what the Wall Street Journal was unwilling to admit: that to recruit quality teachers, you need to raise the status of the teaching profession. Our society usually equates status with money, so the most direct way to get qualified teachers is to pay them what they’re worth (six figures, at least!) TFA is bringing new respect to the teaching profession, but it will never be able to fill our massive teacher shortage while simultaneously maintaining its elite identity. Fixing public education will require a societal consensus that teaching is one of our most important professions, and they need to be paid accordingly.
The Wire
I've been working my way through The Wire for the past semester or so. For those who don't know, the Wire is a TV drama exploring the drug trade in Baltimore and its intersection with all the different systems that function in the city. The first season centers on a drug organization and the police unit investigating them, and the series telescopes outward from there, adding the docks, city hall, the education system, and the print media to its focus in subsequent seasons. The creator, a former cop and public school teacher in Baltimore, has a deep understanding of how all these systems interact with each other, and in particular, how the organizational dynamics of a system can impede that system's objectives. Watching the series should be worth graduate credit in both sociology and complex systems theory. (In fact, one academic journal has issued a call for papers on the series. Deadline is September!)
There are many different jumping-off points I could use from the series, but I'll focus today on a recurring pattern: Drug sellers run a highly complex organization. They switch stash-houses frequently, speak in code, and never let the top guys get anywhere near the actual drugs. Some within the police department realize this, and set up sophisticated surveillance operations to gather information about the drug sellers. But every now and then one of the "top brass" in the police department gets wind of this operation, and wonders why so much time and money are being spent to investigate a bunch of "thugs." They send down a command to send a boatload of units down to the drug area and start locking people up.
Needless to say, this works about as well as attacking a swarm of gnats with a sledgehammer. They catch a couple low-level dealers, but ruin all the intelligence they had on anyone higher up. So the investigation must start all over again.
In theoretical terms, the mistake here is attempting a blunt, simple solution to a nimble, complex problem. When you look for it, you can see this mistake in many places, from our pre-Petraeus anti-insurgency strategy in Iraq, to our federal education policy that mandates standardized tests. To truly solve a complex problem requires an approach as subtle and multifaceted as the problem itself.
There are many different jumping-off points I could use from the series, but I'll focus today on a recurring pattern: Drug sellers run a highly complex organization. They switch stash-houses frequently, speak in code, and never let the top guys get anywhere near the actual drugs. Some within the police department realize this, and set up sophisticated surveillance operations to gather information about the drug sellers. But every now and then one of the "top brass" in the police department gets wind of this operation, and wonders why so much time and money are being spent to investigate a bunch of "thugs." They send down a command to send a boatload of units down to the drug area and start locking people up.
Needless to say, this works about as well as attacking a swarm of gnats with a sledgehammer. They catch a couple low-level dealers, but ruin all the intelligence they had on anyone higher up. So the investigation must start all over again.
In theoretical terms, the mistake here is attempting a blunt, simple solution to a nimble, complex problem. When you look for it, you can see this mistake in many places, from our pre-Petraeus anti-insurgency strategy in Iraq, to our federal education policy that mandates standardized tests. To truly solve a complex problem requires an approach as subtle and multifaceted as the problem itself.
Sub-Prime Mortgage Crisis Part II: Lessons for Complex Systems
Last time, we talked about what went wrong in the US mortgage market, based on the explanation given by NPR and This American Life. What does this debacle tell us in general about how complex systems can go wrong?
The main problem, in a theoretical sense, is that a feedback loop got too long and complex.
A feedback loop is the process by which an action leads to a consequence for the actor. Let's look at the old mortgage system:
Under this system, if the bank made a bad loan, they'd lose their money. So there was a very direct link between action and consequence. Banks have been dealing with this feedback loop for centuries and have gotten pretty good at making only loans that will get repaid.
But in the early 2000's, the system was replaced by this:
There's still a feedback loop here, but it's longer and more complex. Long, complex feedback loops are dangerous because they can fool people into thinking they're making good decisions, when really their bad decisions haven't caught up with them yet. The investors were pouring yet more money into the broken system, because their actions hadn't caught up with them yet, and they were too far removed from the homeowners to see what terrible shape they were in.
We moved essentially from
bad action ---> bad consequence
to
REALLY bad action --- (long time delay) ---> REALLY bad consequence
It's unlikely that investors will make this same mistake again, because they understand much better now how the mortgage market works. But the general mistake of stretching out a feedback loop, and assuming that you're doing well just because nothing's gone wrong so far, will probably be repeated many, many times.
The main problem, in a theoretical sense, is that a feedback loop got too long and complex.
A feedback loop is the process by which an action leads to a consequence for the actor. Let's look at the old mortgage system:
Under this system, if the bank made a bad loan, they'd lose their money. So there was a very direct link between action and consequence. Banks have been dealing with this feedback loop for centuries and have gotten pretty good at making only loans that will get repaid.
But in the early 2000's, the system was replaced by this:
There's still a feedback loop here, but it's longer and more complex. Long, complex feedback loops are dangerous because they can fool people into thinking they're making good decisions, when really their bad decisions haven't caught up with them yet. The investors were pouring yet more money into the broken system, because their actions hadn't caught up with them yet, and they were too far removed from the homeowners to see what terrible shape they were in.
We moved essentially from
bad action ---> bad consequence
to
REALLY bad action --- (long time delay) ---> REALLY bad consequence
It's unlikely that investors will make this same mistake again, because they understand much better now how the mortgage market works. But the general mistake of stretching out a feedback loop, and assuming that you're doing well just because nothing's gone wrong so far, will probably be repeated many, many times.
Sub-Prime Mortgage Crisis-Explained!
Recently, my favorite radio show teamed up with NPR news to do an in-depth collaboration on exactly what went wrong with the US sub-prime mortgage crisis. It turns out to be a perfect example of how a complex system can go wrong. So I thought I'd give a summary of what they found, and discuss how it relates to what we know about complex systems in general.
The whole thing started with what our radio hosts call "the global pool of money." In the early 2000's, there ended up being a whole lot of people around the globe with lots of money to invest. The amount of money looking to be invested had doubled in the past xxx years, due in part to growing economies in other countries.
The wealth holders of this money needed somewhere to invest this money, to keep it safe and growing. A large subset of them wanted safe investments, where the return on their money would be moderate but reliable. So they and their brokers looked around for safe investments to make.
While this was happening, Alan Greenspan was trying to help the US economy out of the post-internet bubble slump. He did this by setting interest rates extremely low: around 1%. This means that US treasury bonds, one of the safest investments historically, would be getting extremely low returns for a long time. So the pool of money had to look elsewhere.
The lack of traditional safe investment options meant that the brokers had to get creative. So they looked around and they saw this:
All over the country, retail banks (the kind of banks you and I use) were loaning money to homeowners, who were repaying the money with interest. These were safe investments on the banks' part because historically, very few homeowners default on their mortgages. The brokers wanted to get in on this action, but mortgages are too small and detailed to get involved with on an individual level. So they set up a system like this:
The retail banks would lend money to homeowners, and then sell these mortgages to investment banks. The investment banks would buy tons of these mortgages and organize them into "bundles" of hundreds at a time. These bundles would be sold to Wall Street firms, who would create "mortgage-backed securities" out of the bundles, and sell shares in these securites to the global pool of money.
This system worked fine for a while. But by 2003 or so, virtually every credit-worthy indvidual with a home had already taken a mortgage. There were no more mortgages to be bought. But the global pool of money had seen how effective these mortgage-backed securities were, and they demanded more. This sent an echoing voice all the way down the chain saying "GIVE US MORE MORTGAGES!"
To fill this incredible demand, the retail banks started relaxing the standards for who they loaned to. The radio show tells the fascinating story of how every week, one requirement after another was dropped, until they reached rock bottom: the NINA loan. NINA stands for "No Income, No Asset." It means you can get a loan without even claiming to have a job or any money in the bank whatsoever. In the words of one former mortgage banker "All you needed was a credit score, and a pulse."
In the old system, no bank would ever think of giving a loan without verifying the borrowers income and assets. This is because the bank had an interest in seeing that it got its money back. But under the new system, the banks would just sell the mortgage up the chain and wash their hands of it. If the borrower defaulted two months later, it would be someone else's problem.
Still, you would think that someone would realize that an investment system built on no income, no asset loans was bound to fail. And indeed, many people did realize it. But the money kept flowing in from the global pool, and everyone in the chain was getting rich in the process. Saying "no" to the system seemed like ignoring a pot of gold right in front of your face.
Two additional factors prevented reason from prevailing. First, the computer models used by the investment banks and Wall Street firms were telling them that everything was going fine. No one made the connection that the models were using data from pre-2003, when loans were made on the basis of actual assets. Second, housing prices in the US were going up. If a borrower defaulted, then the bank would own the house, which as long as prices were rising would be worth more than the bank loaned originally.
Of course, housing prices didn't keep going up. And the Wall Street firms noticed at some point that some of the mortgages they were investing in were defaulting on the very first payment. So they stopped buying these bundled mortgages. At that point, the middlemen in the system (the retail and investment banks) were left holding mortgages that no one up the chain wanted, and that would almost certainly be defaulted from the bottom of the chain. And they went bankrupt en masse.
That's enough writing for today. Next time we'll use this crisis as a case study for some general complex systems principles.
The whole thing started with what our radio hosts call "the global pool of money." In the early 2000's, there ended up being a whole lot of people around the globe with lots of money to invest. The amount of money looking to be invested had doubled in the past xxx years, due in part to growing economies in other countries.
The wealth holders of this money needed somewhere to invest this money, to keep it safe and growing. A large subset of them wanted safe investments, where the return on their money would be moderate but reliable. So they and their brokers looked around for safe investments to make.
While this was happening, Alan Greenspan was trying to help the US economy out of the post-internet bubble slump. He did this by setting interest rates extremely low: around 1%. This means that US treasury bonds, one of the safest investments historically, would be getting extremely low returns for a long time. So the pool of money had to look elsewhere.
The lack of traditional safe investment options meant that the brokers had to get creative. So they looked around and they saw this:
All over the country, retail banks (the kind of banks you and I use) were loaning money to homeowners, who were repaying the money with interest. These were safe investments on the banks' part because historically, very few homeowners default on their mortgages. The brokers wanted to get in on this action, but mortgages are too small and detailed to get involved with on an individual level. So they set up a system like this:
The retail banks would lend money to homeowners, and then sell these mortgages to investment banks. The investment banks would buy tons of these mortgages and organize them into "bundles" of hundreds at a time. These bundles would be sold to Wall Street firms, who would create "mortgage-backed securities" out of the bundles, and sell shares in these securites to the global pool of money.
This system worked fine for a while. But by 2003 or so, virtually every credit-worthy indvidual with a home had already taken a mortgage. There were no more mortgages to be bought. But the global pool of money had seen how effective these mortgage-backed securities were, and they demanded more. This sent an echoing voice all the way down the chain saying "GIVE US MORE MORTGAGES!"
To fill this incredible demand, the retail banks started relaxing the standards for who they loaned to. The radio show tells the fascinating story of how every week, one requirement after another was dropped, until they reached rock bottom: the NINA loan. NINA stands for "No Income, No Asset." It means you can get a loan without even claiming to have a job or any money in the bank whatsoever. In the words of one former mortgage banker "All you needed was a credit score, and a pulse."
In the old system, no bank would ever think of giving a loan without verifying the borrowers income and assets. This is because the bank had an interest in seeing that it got its money back. But under the new system, the banks would just sell the mortgage up the chain and wash their hands of it. If the borrower defaulted two months later, it would be someone else's problem.
Still, you would think that someone would realize that an investment system built on no income, no asset loans was bound to fail. And indeed, many people did realize it. But the money kept flowing in from the global pool, and everyone in the chain was getting rich in the process. Saying "no" to the system seemed like ignoring a pot of gold right in front of your face.
Two additional factors prevented reason from prevailing. First, the computer models used by the investment banks and Wall Street firms were telling them that everything was going fine. No one made the connection that the models were using data from pre-2003, when loans were made on the basis of actual assets. Second, housing prices in the US were going up. If a borrower defaulted, then the bank would own the house, which as long as prices were rising would be worth more than the bank loaned originally.
Of course, housing prices didn't keep going up. And the Wall Street firms noticed at some point that some of the mortgages they were investing in were defaulting on the very first payment. So they stopped buying these bundled mortgages. At that point, the middlemen in the system (the retail and investment banks) were left holding mortgages that no one up the chain wanted, and that would almost certainly be defaulted from the bottom of the chain. And they went bankrupt en masse.
That's enough writing for today. Next time we'll use this crisis as a case study for some general complex systems principles.
Pirates are even cooler than we thought!
So this is mostly a "I saw this and thought it was cool" kind of post: An article in Sunday's Boston Globe describes the research of Peter Leeson and Marcus Rediker claiming that pirates were practicing democracy aboard their ships in the 1600's, well before America or Europe ever got around to it.
Before each voyage, pirates voted on a captain and a quartermaster, whose main job was to be a check on the captain's power. Either officer could be "recalled" at any time. Ground rules were laid out in a written charter. They also had primitive forms of trial and workmen's compensation.
The researchers differ on the motivation for this democracy. Leeson sees it as a necessary organizational system for a cadre of criminals who have to work together without killing each other. Rediker sees it as a political reaction to despotic organization of commercial ships, wherein captains hold absolute power and floggings were routine and often deadly. Pirates, according to Rediker, tried to create a utopian alternative.
Inasmuch as there is a single motivation for anything, I'm inclined to agree with Leeson's point of view. The success of a pirate ship depends on the ability of its members to work together. There is a natural check on any one pirate's power in that any other pirate could pretty easily kill him in his sleep. Unlike the case of commercial ships, pirate society is not tied to any larger land-based social structures.
The question then becomes, what is the based way to maintain organization in a small self-contained society where no individual can dominate the others through force? I think the best and perhaps only workable answer in the long term is democracy, or something like it.
Before each voyage, pirates voted on a captain and a quartermaster, whose main job was to be a check on the captain's power. Either officer could be "recalled" at any time. Ground rules were laid out in a written charter. They also had primitive forms of trial and workmen's compensation.
The researchers differ on the motivation for this democracy. Leeson sees it as a necessary organizational system for a cadre of criminals who have to work together without killing each other. Rediker sees it as a political reaction to despotic organization of commercial ships, wherein captains hold absolute power and floggings were routine and often deadly. Pirates, according to Rediker, tried to create a utopian alternative.
Inasmuch as there is a single motivation for anything, I'm inclined to agree with Leeson's point of view. The success of a pirate ship depends on the ability of its members to work together. There is a natural check on any one pirate's power in that any other pirate could pretty easily kill him in his sleep. Unlike the case of commercial ships, pirate society is not tied to any larger land-based social structures.
The question then becomes, what is the based way to maintain organization in a small self-contained society where no individual can dominate the others through force? I think the best and perhaps only workable answer in the long term is democracy, or something like it.
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