Archive
Weekend Reading
FogOfWar and I have compiled a short list of weekend reading for you that you may enjoy:
- What’s the right way to think about China’s economy?
- Is Japan’s “lost decades” a media myth?
- Can I hear a FUCK YEAH for Elizabeth Warren? I feel a follow-up post coming on how much she rocks.
- Get ready to be depressed by how few natural resources there really are.
- This essay really pins Robert Rubin to the wall in a totally awesome way. I will add more in another post.
- The Republicans are holding the entire nation for ransom over the possibility of default. Is it all political posturing? Or is it for the sake of the insanely shitty idea of a tax repatriation holiday? Here’s another article about this crappy idea; when Bloomberg makes you out as a selfish bastard then you know you’re a truly selfish bastard. I’m convinced that the politicians (and union leaders) arguing for this are just counting on the average person not understanding the actual issues well enough to know how evil it is (and how much kickback they must be getting). Another example of asymmetric information that really gets my goat.
- I think it’s fair to say we all need a little more of this in our lives.
Adding-up rules and Hockey Sticks
So I’m at the math program HCSSiM, teaching for three weeks in a “workshop,” which means I am responsible for teaching 12 teenagers the basic language and techniques of math- things like induction, proof by contradiction, the pigeon-hole principle, and how to correctly use phrases like “without loss of generality we can assume…” and “the following is a well-defined function…”, as well as familiarity with basic group theory, graph theory, number theory, cardinality, and fun things like Pascal’s triangle.
It’s really beautiful, classical math, and the students are eager and fantastically bright. They are my temporary brood, and I adore them and feed them chocolate at evening problem sets.
It’s also a fine opportunity to do some silly math doodling just for fun, the only rules being you can’t use a computer to look anything up until you’re done, and you can only use the stuff your kids at the program already learned. I’m going to describe what my mom and I, and then a junior (Amber Verser) and senior (Benji Fisher) staff member at the math program, figured out in the last couple of days. It’s super cool and turns out is at least 400 years old.
One of the most common examples of proof by induction is the formula for the sum of the counting numbers up to n:
1 + 2 + 3 + … + n = n(n+1)/2
And then, once you figure that out, you move on to the next case:
1^2 + 2^2 + 3^2 + … + n^2 = n(n+1)(2n+1)/6.
If you’re really into it, you can put the next case on the problem set:
1^3 + 2^3 + 3^3 + … + n^3 = (n(n+1)/2)^2.
Two obvious patterns are emerging when you add up successive dth powers up to n.
- It’s a polynomial of degree d+1, and
- The roots of the polynomial are symmetric about -1/2 (mom noticed this!).
How do you prove those two facts?
If you think it’s totally easy, stop reading now and give it a shot. There are about a million things you could try and none of them seem to work. I’ll wait.
…okay, let’s say you gave up, or already know, or don’t care. (Why are you reading still if you don’t care?!)
First let’s generalize the question to, if we add up values of some degree d polynomial for values i=0, 1, 2, …, n, then we want to prove the result is a degree d+1 polynomial in n. That this is equivalent to the first statement above is pretty easy to see by just re-arranging the terms of the double sum over i and over the terms of the polynomial in question. But it still seems like you need to know at least the answer to the question of what is a formula for 0^d + 1^d + 2^d + … + n^d, which is of course where we started.
But that’s where Pascal’s triangle comes in! We can generate Pascal’s triangle by the familiar “add up two consecutive numbers and put the answer below,” but we also can think of the element on the nth row and kth (tilted) column of Pascal’s triangle as the number of ways to choose k things from n things, which is referred to as “n choose k”, and where we start both the row and column counts at 0, not at 1. That definition satisfies the addition law because, if we have n things, we can label one as “special,” and then the choice of size k subsets of the n things divide into two categories: the size k subsets that contain the special guy and the ones that don’t. If they do, then we need only find k-1 other things in the remaining n-1 size set, and the number of ways to do that is given by the element on row n-1 and column k-1. If they don’t contain the special guy, we need to find k things in the remaining n-1 size set, and the number of ways to do that is given by the element on row n-1 and column k.
On the other hand, we also know a formula for the numbers in Pascal’s triangle: the guy on the nth row and kth column is given by a degree k polynomial in n, namely n!/k!(n-k)!. (This is because we can label all of the guys 1 through n, and just take the first k guys, and there are n! ways to label n things, but we don’t actually care about the order among the first k or among the last n-k.)
For example, in the second column, where we are looking at “n choose 2” for various n, we have the equation n(n-1)/2. This is a LOT like n^2 but has extra terms sticking on the end of lower order. When you’re looking at the third column, you’re working with the formula n(n-1)(n-2)/6, which is like the basic polynomial n^3 with extra stuff. In other words, the formula for “n choose k” is a degree k polynomial in n which we can think of as being a stand-in for n^k. Awesome.
The last ingredient is something called the “Hockey Stick Theorem,” which you gotta love just because of the name. It states that if we add up the values along a column, from the top of the rows down to the nth row, then the sum will be the number just below and to the right, and the entire picture will resemble a hockey stick.
The proof of the Hockey Stick Theorem is trivial- the answer is of course the sum of the two above it, and we have one in the sum already, but the other isn’t… but that other is the sum of the two above it, one of which is again already in the sum but the other isn’t… and you keep going until you get to the top edge of Pascal’s triangle, where the missing number is just 0.
Why does the Hockey Stick Theorem give us what we want? Going back to our generalized statement, we want to show the sum of values on a (any) degree d polynomial for i = 0, 1, 2, …, n is a degree d+1 polynomial. Well, use the dth column and make a hockey stick from the top to row n. Then the sum is on the (n+1)st row, in the (d+1)st column, which we know is a degree d+1 polynomial in n. Woohoo!
One way of looking at this is that we were actually asking the wrong question: instead of asking what the sum of the dth powers is we should have perhaps been asking what the sum of the dth column of Pascal’s triangle is; in other words, there is a better basis for the vector space of polynomials than x^d, namely “x choose d”. In fact, if there were an agreement in the world that actually the “x choose d” polynomials should be the standard basis, (by the way, these basis polynomials would be called “Pascalinomials”!) then the hockey stick theorem would be the last word on how do those things add up. As it stands, to figure out the actual formula for the sum of the dth powers for i=0, 1, 2, …, n, we need to write the first row of the change-of-basis matrix from one basis to the other.
As for the second question, we simply need to extend the definition of the sum F(n) of dth powers from 0 to n to the case where n is negative, by iteratively using the relation:
F(n) = F(n-1) + n^d, or
F(n-1) = F(n) – n^d.
Then we have F(0) = 0, F(-1) = 0, F(-2) = (-1)^(d+1), F(-3) = (-1)^(d+1) – (-2)^d = (-1)^(d+1)(1^d + 2^d) …, and it’s easy to prove that, for any n,
F(n) = (-1)^(d+1)F(-n-1).
This means that if we have a root at -1/2 + a, we also have a root at -1/2 – a = -(-1/2 +a) -1.
Does an academic job in math really suck?
My cousin recently sent me a link to this article about women in science. Actually it’s really about jobs in science, and how much they suck, and how women are too practical to want them. It’s definitely interesting- and pretty widely read, as well, although I’d never seen it. It makes a few excellent points, especially about the crappy amount of money and feedback one gets as an academic, two issues which were definitely part of my personal decision to leave my academic career.
I think his overall argument, though, is simultaneously too practical-minded and not practical-minded enough. And although his essay is about science, I’ll concentrate on how it relates to math.
It’s too practical in that it doesn’t really understand the attraction- the nearly carnal desire- people have to math. It essentially assumes that after some amount of time, maybe 20 years, people will lose interest in their subject, perhaps because they are getting poorly paid.
Is this really true? Maybe for some people this is true, but the nerds I know are nerds for life – they don’t wake up one day thinking math isn’t cool after all. And from what I know about people, they acclimate pretty thoroughly to their standard of living by the time they are 40.
It’s not practical enough, though, because it doesn’t get at one of the most important reasons women leave math, namely because they are married and maybe have kids and they simply can’t be that person who moves across the country for a visiting semester in Berkeley because their husband has a job already and it’s not in Berkeley.
[As a side note, if someone wants to actually encourage women in math, and they are loaded, I would encourage them to set up a fund that would pay costs for quality childcare and airplane tickets for kids when woman go to math conferences. You don’t even need to help organize the babysitting, just pay for it. It would help out a lot of young women and free them up to go to way more conferences, evening the playing field with young men.]
In fact there are plenty of women who are super nerdy and would love to go do math across the country, but when it comes to choosing between that lifestyle and having a family life, they will choose the family life more times than not. Really it’s the “nomadic monk” system itself that is crappy for women at that moment, even if they are theoretically happy to be a poor nerd for the rest of their lives.
I have another complaint (which will make it sound like I don’t like the essay but actually I do). It says that people in science don’t have the ability to switch careers, essentially because they don’t have the money. But that’s really not true, at least in math, and I’m a testament to the possibility of switching careers. One thing a nerd is really good at is learning new things quickly.
I also thought that there was something missing about the alternative jobs he mentions, in industry or otherwise, which is that, yes you do get paid better outside of academics, but on the other hand pretty much any nonacademic job requires you to have a boss, which can be really fine or really horrible, and restricts your vacation time to 3 or 4 weeks. By contrast the quality of life as an academic is, if not luxurious, at least much more under one’s control.
Glucose Prediction Model: absorption curves and dirty data
In this post I started visualizing some blood glucose data using python, and in this post my friend Daniel Krasner kindly rewrote my initial plots in R.
I am attempting to show how to follow the modeling techniques I discussed here in order to try to predict blood glucose levels. Although I listed a bunch of steps, I’m not going to be following them in exactly the order I wrote there, even though I tried to make them in more or less the order we should at least consider them.
For example, it says first to clean the data. However, until you decide a bit about what your model will be attempting to do, you don’t even know what dirty data really means or how to clean it. On the other hand, you don’t want to wait too long to figure something out about cleaning data. It’s kind of a craft rather than a science. I’m hoping that by explaining the steps the craft will become apparent. I’ll talk more about cleaning the data below.
Next, I suggested you choose in-sample and out-of-sample data sets. In this case I will use all of my data for my in-sample data since I happen to know it’s from last year (actually last spring) so I can always ask my friend to send me more recent data when my model is ready for testing. In general it’s a good idea to use at most two thirds of your data as in-sample; otherwise your out-of-sample test is not sufficiently meaningful (assuming you don’t have that much data, which always seems to be the case).
Next, I want to choose my predictive variables. First, we should try to see how much mileage we can get out of predicting future blood glucose levels with past glucose levels. Keeping in mind that the previous post had us using log levels instead of actual glucose levels, since then the distribution of levels is more normal, we will actually be trying to predict log glucose levels (log levels) knowing past log glucose levels.
One good stare at the data will tell us there’s probably more than one past data point that will be needed, since we see that there is pretty consistent moves upwards and downwards. In other words, there is autocorrelation in the log levels, which is to be expected, but we will want to look at the derivative of the log levels in the near past to predict the future log levels. The derivative can be computed by taking the difference of the most recent log level and the previous one to that.
Once we have the best model we can with just knowing past log levels, we will want to add reasonable other signals. The most obvious candidates are the insulin intakes and the carb intakes. These are presented as integer values with certain timestamps. Focusing on the insulin for now, if we know when the insulin is taken and how much, we should be able to model how much insulin has been absorbed into the blood stream at any given time, if we know what the insulin absorption curve looks like.
This leads to the question of, what does the insulin (rate of) absorption curve look like? I’ve heard that it’s pretty much bell-shaped, with a maximum at 1.5 hours from the time of intake; so it looks more or less like a normal distribution’s probability density function. It remains to guess what the maximum height should be, but it very likely depends linearly on the amount of insulin that was taken. We also need to guess at the standard deviation, although we have a pretty good head start knowing the 1.5 hours clue.
Next, the carb intakes will be similar to the insulin intake but trickier, since there is more than one type of carb and different types get absorbed at different rates, but are all absorbed by the bloodstream in a vaguely similar way, which is to say like a bell curve. We will have to be pretty careful to add the carb intake model, since probably the overall model will depend dramatically on our choices.
I’m getting ahead of myself, which is actually kind of good, because we want to make sure our hopeful path is somewhat clear and not too congested with unknowns. But let’s get back to the first step of modeling, which is just using past log glucose levels to predict the next glucose level (we will later try to expand the horizon of the model to predict glucose levels an hour from now).
Looking back at the data, we see gaps and we see crazy values sometimes. Moreover, we see crazy values more often near the gaps. This is probably due to the monitor crapping out near the end of its life and also near the beginning. Actually the weird values at the beginning are easy to take care of- since we are going to work causally, we will know there had been a gap and the data just restarted, so we we will know to ignore the values for a while (we will determine how long shortly) until we can trust the numbers. But it’s much trickier to deal with crazy values near the end of the monitor’s life, since, working causally, we won’t be able to look into the future and see that the monitor will die soon. This is a pretty serious dirty data problem, and the regression we plan to run may be overly affected by the crazy crapping-out monitor problems if we don’t figure out how to weed them out.
There are two things that may help. First, the monitor also has a data feed which is trying to measure the health of the monitor itself. If this monitor monitor is good, it may be exactly what we need to decide, “uh-oh the monitor is dying, stop trusting the data.” The second possible saving grace is that my friend also measured his blood glucose levels manually and inputted those numbers into the machine, which means we have a way to check the two sets of numbers against each other. Unfortunately he didn’t do this every five minutes (well actually that’s a good thing for him), and in particular during the night there were long gaps of time when we don’t have any manual measurements.
A final thought on modeling. We’ve mentioned three sources of signals, namely past blood glucose levels, insulin absorption forecasts, and carbohydrate absorption forecasts. There are a couple of other variables that are known to effect the blood glucose levels. Namely, the time of day and the amount of exercise that the person is doing. We won’t have access to exercise, but we do have access to timestamps. So it’s possible we can incorporate that data into the model as well, once we have some idea of how the glucose is effected by the time of day.
Cookies
About three months ago I started working at an internet company which hosts advertising platforms. It’s a great place to work, with a bunch of fantastically optimistic, smart people who care about their quality of life. I’m on the tech team along with the team of developers which is led by this super smart, cool guy who looks like Keanu Reeves from the Matrix.
I’ve learned a few things about how the internet works and how information is collected about people who are surfing the web, and the bottom line is I clear my cookies now after every session of browsing. Now that I know the ways information travels the risks of retaining cookies seem to outweigh the benefits. First I’ll explain how the system works and then I’ll try to make a case for why it’s creepy, and finally, why you may not care at all.
Basically you should think of yourself, when you surf the web, as analogous to someone on the subway coming home from Macy’s with those enormous red and white shopping bags. You are a walking advertisement for your past, your consumer tastes, and your style, not to mention your willingness to purchase. Moreover, beyond that, you are also carrying around information about your political beliefs, religious beliefs, and temperament. The longer you browse between cookie cleanings, the more precise a picture you’ve painted of yourself for the sites you visit and for third parties (explained below) who get their hands on your information.
Just to give you a flavor of what I’m talking about, you probably are already aware that when you go to a site like, say, Amazon, the site assigns you a cookie to recognize you as a guest; when you return a week later it knows you and says, “Hi, Catherine!”. That’s on the low end of creepy since you have an account with Amazon and it’s convenient for the site to not ask you who you are every time you visit.
However, you may not be aware that Amazon can also see and parce the cookies that other sites, like Google (correction: a reader has pointed out to me that Google doesn’t let this happen, sorry. I was getting confused between the cookie and the “referring url”, which tells a site where the user has come from when they first get to the site. That does contain Google search terms), places on your web signature. In other words Amazon, or any other site that knows how to look, can figure out what other sites’ label of you says. Some cookies are encrypted but not all of them, and I think the general rule is to not encrypt- after all, the people who have the tools to read the cookies all benefit from that information being easy to read. From the perspective of Google, moreover, this information is helping improve your user experience. It should be added that Google and many other companies give you the option of opting out of receiving cookies, but to do so you have to figure out it’s happening and then how to opt out (which isn’t hard).
One last layer of cookie collection is this: there are other companies which lurk on websites (like Amazon, although I’m not an expert on exactly when and where this happens) which can also see your cookies and tag you with additional cookies, or even change your existing cookies (this is considered rude but not prevented). This is where, for me, the creep factor gets going. Those third parties certainly have less riding on their brand, since of course you don’t even see them, so they have less motivation to act honorably with the information they collect about you. For the most part, though, they are just looking to see what kind of advertisement you may be weak for and, once they figure it out, they show you exactly that model of showerhead that you searched for three weeks ago but decided was too expensive to buy. If you want to stop seeing that freaking showerhead popping up everywhere, clear thy cookies.
Here’s why I don’t like this; it’s not about the ubiquitous showerhead, which is just annoying. Think about rich people and how they experience their lives. I touched on this in a previous post about working at D.E. Shaw, but to summarize, rich people think they are always right, and that’s a pretty universal rule, which is to say anyone who becomes rich will probably succumb to that pretty quickly. Why, though? My guess is that everyone around them is aware of their money and is always trying to make them happy in the hope that they at some point could have some of that money. So they effectively live in a cocoon of rightness, which after a while seems perfectly logical and normal.
How that concept manifests itself in this conversation about cookies is that, in a small but meaningful way, that’s exactly what happens to the user when he or she is browsing the web with lots of cookies. Every time Joe encounters a site, the site and all third-party advertisers have the ability to see that Joe is a Republican gun-owner, and the ads shown to Joe will be absolutely in line with that part of the world. Similarly the cookies could expose Dan as a liberal vegetarian and he sees ads that never shake his foundations. It’s like we are funneled into a smaller and smaller world and we see less and less that could challenge our assumptions. This is an isolating thought, and it’s really happening.
At the same time, people sometimes want to be coddled, and I’m one of those people. Sometimes I enjoy it when my favorite yarn store advertises absolutely gorgeous silk-cashmere blends at me, or shows me to a rant against greedy bankers, and no I’d rather not replace them with Viagra ads. So it’s also a question of how much does this matter. For me it matters, but I also like New York City because it is dirty and gritty and all these people from all over the world live there and sweat on each other on the subway and it makes me feel like part of a larger community- I like to mix it up and have it mixed up.
I’d also like to mention another kind of reason you may want to clear your cookies: you get better deals. A general rule of internet advertising is that you don’t need to show good deals to loyalists. So if you don’t have cookies proving you have an account on Netflix, you may get an advertisement offering you three free months of membership. Or if you want to get more free articles on the New York Times website, clear your cookies and the site will have no idea who you are. There are many such examples like this.
Lastly, I’d like to point out that you probably don’t need to worry about this. After all, many browsers will clear your cookies but also clear your usernames and passwords, and you may never be able to get some of those back. And maybe you don’t mind being coddled while online. Maybe it’s the one place where you get to feel understood. Why question that?
Fair Foods
This post will only be indirectly quantitative, and not a rant, so I guess that means I will have to either apologize or change my mission statement. Sorry. Oh and by the way I do have lots of ideas for quantitative blogs coming up, topics to include:
- clear your cookies! how internet companies track your every click
- update on the diabetes model
- is being a mathematician just a crappy job?
- shout-outs to other nerd bloggers who are sending me readers
So yesterday I loaded up the (rental) car to the brim, with my mom, my two older sons, a guitar (for me) and an air conditioning unit (for my mom), and drove out to Amherst for the math program I’m teaching in for three weeks.
Before I left I visited my friend Nancy at Fair Foods in Dorchester.
I drove to her house early, getting there at maybe 8:30am. She wasn’t home- she had me meet her at a church near Codman Square, where she was making a drop. When I got there I helped her unload a van full of maybe 40 or so boxes of vegetables and fruit, with a few 50-pound bags of carrots and potatoes. She got on the van and handed me the boxes and I carried them over to a sidewalk, while the woman, Marie, who was accepting the drop, carried some smaller boxes into the basement. Nancy introduced me to Marie as her daughter, and introduced Marie to me as the beautiful, wise Haitian woman who was a professional cook and would turn all of these vegetables into a delicious feast for her congregation. Nancy and Marie talked about the church, and the fact that it was shared between two different congregations, one Haitian immigrant and one African-American, and how the church was run.
After a while it didn’t seem like Marie was going to get the help she was expecting to carry the larger boxes into the basement, so Nancy and I moved all of the boxes down there, temporarily rigging a window to be a de facto dumb waiter to avoid three corners and some stairs. There were tomatoes, white potatoes, red potatoes, carrots, ugli fruit, limes, lettuce, string beans, wax beans, and others I can’t remember. Almost all of these were in great condition, but some needed sorting before going into the feast. Marie asked for corn for the 4th of July- since the food that is collected is surplus, a given request may be hard to fill, especially around a holiday, which Nancy explained. But then she said that if we got corn we would call Marie right away.
After we finished unloading the van I was soaked in sweat; it reminded me of how incredibly strong I’d gotten working one summer for Nancy, unloading trucks all day (as well as loading them at the Chelsea Produce Market every morning at 7) and driving around the city in the big yellow truck making drops to churches, senior centers, and youth centers, and holding dollar-a-bag sites in vacant parking lots and sidestreets. That was in 1992; and Nancy, who was born in 1950, has been doing the program ever since, with various peoples’ help.
Nancy mentioned that before I’d gotten there she had gone into the church and listened to the singing and the praying of the Haitian congregation, and that it had been seriously beautiful. Marie insisted on us coming inside. We sat in the pews as the woman leading the small prayer group of about 8 people, mostly women, was talking to one woman who was clearly in distress. Perhaps she was in mourning. They were speaking in Creole, which I don’t understand (although I know some French so every now and then I can pick up a word or two), but it was viscerally moving how kindly the leader was speaking to the sad woman seated in front of her. After she allowed that woman to finish, she looked up and welcomed us in English and asked us our names. Marie explained in Creole something about us, probably that we had just brought in the food for the July 4th meal, and we were instantly welcomed by the entire group. After that they told us they were wrapping up their prayer session and would stand and have a group prayer.
Everyone stood, except for the mourning woman who was holding her head in her hands. And at once everyone started praying, but the interesting thing was they were all saying different prayers, and it was fascinating to watch and listen to how they could be both praying together and praying individually. I could make out a few words from Marie’s prayer, which near the beginning was quiet and included lots of words like “please” and “hope”, but which, like everyone else’s, became louder and more fervent and contained more words like “thank you” and “hallelujah”. It ended by everyone holding their hands up to the front of them and giving thanks. Everyone ended at exactly the same time.
After the prayer group ended, there were lots of hugs and hand shaking. Many of the women wanted to talk to Nancy and she probably ended up hugging and being hugged by everyone there. There was a deep human connection inside that little church, which is pretty different from my normal assumptions about piousness and rules-based religions. Connection and empathy.
After we left the church we went to a playground and sat and had coffee together, and Nancy laid something down that was pretty thick. She talked about her disillusionment with her generation- the hippy generation- how they made all these promises but then didn’t follow through- the words she uses is didn’t apply themselves. She talked about having faith in her generation up to the “We Are the World” moment, and then waiting, and seeing nothing come out of it, and how bitter that had made her feel, how disappointed. She said it took her years to get over that, and now she feels like those years of her life, until recently in fact, are in some sense unaccounted for, both because she’s been sick and because she was somewhat paralyzed with anger.
She went on to say that she’s in a new phase now, she’s accepted the lazy fact of life that the people she was counting on, if anything, have made the world a worse place, not a better one, but that she’s decided to love them and love the world anyway, and to continue to make human connections with individuals, because it makes her have faith in a different way, a more diffuse but a stronger faith that won’t be disappointed.
It’s interesting to me that Nancy would ever describe her life as unaccounted for or her feelings as bitter. When I met her in 1989, she had been diagnosed with MS and lived in a huge old house with very little working anything (and what was working she’d installed herself- wired the electricity and installed plumbing). She had a great Dane and a broken-down donated truck, and when I came to her we spent the whole night cleaning out and reorganizing the truck. Whenever the truck’s insurance was due, or the phone was about to be cut off, we’d get a check for $50 and it would be a miracle, and I always felt like if I was ever going to believe in something it would be because of her.
I fell in love with her and with her approach to problem solving- namely, do the right thing, and go figure how to with bare knuckles and sweat. Over the years she’s been better or worse off with her health, but she’s never given up and, to be honest, I never sensed bitterness from her. Maybe these are relative notions, that bitterness from her is like frustration from someone else. Unaccountability from the woman who moves tons of food a week, that will otherwise be thrown away, into the homes of impoverished, mostly immigrant households, who know her and appreciate her act of kindness and take part in that act, would mean… what? to other people. Hard to say.
Did you have a happy childhood?
For whatever reason, I’ve been thinking about my childhood recently. Partly it’s the post I wrote about why I chose to call myself “mathbabe”, partly it’s an old essay of Jonathan Franzen’s that got me all riled up (in a good way). Plus I’m traveling to the math camp of my youth to teach, and stopping on the way in Harvard Square at my parents’ house; that’s enough to make you reconsider your memories in short order.
I have never understood what people mean when they talk about carefree, happy childhoods. I think I’ve always assumed this to be some kind of ironic joke, or maybe a plastered-over memory, a convenient approach to pain management. While it’s true that children have fewer responsibilities than grown-ups, it’s really not the responsibilities of adulthood that weigh me down (says the woman with three kids), or ever did. For me it was the constant awareness of my helplessness and impotence, my inability to decide my own fate, my feeling of having to wait forever for freedom, that got to me. I was also teased, but not relentlessly, and I did have friends, and moreover I wasn’t thought of (I don’t think) as a worrying child. From the outside people may have imagined me as a normal albeit nerdy kid. However, I always identified with the oppressed, and I had a keen sense of fairness which was constantly being challenged by reality. When we studied the “Manifest Destiny” in third grade, it killed me to think of the white man’s assumptions. When I saw a kid getting bullied at school, it tore me up that I didn’t know how to put an end to it and no teachers bothered. The list goes on, you get the idea. Also, I had an internal standard that was painfully high- I wanted to become a musician, a pianist, but never thought I’d be good enough, and I questioned my creativity, since what I really wanted to do was compose. When I decided to become a mathematician I started worrying about my thesis (I was 16). By the way, lest people get the wrong impression, my parents never put pressure on me to play music (in fact they openly discouraged me since it was expensive) and thought my worrying about my thesis was downright amusing. This was all internally generated. In short, I was a struggler, at best of times a striver, but never ever carefree and happy.
I have always been attracted to other people who struggle and strive; for the most part my closest friends are, like me, in constant flux with respect to their identities and their goals and even the interpretation of the most basic cultural assumptions like toenail polish and the role of the FDIC.
This brings me to the Franzen essay, where he talks about being isolated in childhood as a reader, and spending the rest of your life trying to find and form a community with other isolated readers. As an aside, Franzen makes a distinction in this essay between isolated readers and isolated math or technology nerds. He basically said that math nerds are isolated because they are autistic, incapable of social interaction, whereas readers are isolated because they feel more deeply and can’t relate to artificiality. I’m not sure whether to argue that math nerds aren’t all autistic or just count myself as both a reader and a math nerd and be proud of out-isolating Franzen, no easy task. Basically, I agree with Franzen. From my perspective upon meeting someone I am always looking for that inner torture, the hallmark of an examined life. It doesn’t make you happy, perhaps, but it makes you real, and moreover interesting.
But here’s the thing, I was blindsided this week by the discovery that my husband, of all people, had a happy childhood. He insists on this, even when I ask him if perhaps he’s misremembering his inner turmoil– he claims no. He moreover avers that, at the age of 12, he decided to become a mathematician and has never looked back, never once questioned that decision. Is this possible? That I’m married to a man who had a happy childhood? For all I know, it is true and moreover it may be exactly why I have a happy marriage. Maybe strugglers need to be married to non-strugglers to maintain some kind of balance. I don’t know, I’m still thinking about it. It does explain something that I’ve always been confused by, though- when my husband comes across an ethical or moral decision, he does so painlessly and makes a decision instantaneously. I now think this is because he just doesn’t think about things like that in between those moments, and so he’s got a clarity of consciousness which allows him to make snap decisions. When I come across such dilemmas, I am much more confused and ambivalent. I usually decide it’s a matter of opinion. I’m wondering if it’s this element of our differences that makes our marriage work.
Asymmetrical Information
From my experience, there are only a few basic kinds of trading models encountered on Wall Street. These are:
- chasing dumb money, which I’ve described already,
- asymmetrical information, which I want to talk about today,
- market-making,
- providing “insurance”,
- seasonality, which I’ve touched on, and
- taking advantage of macroeconomic misalignment (think Soros’s pound trade)
The concept of asymmetrical information is incredibly simple: I know more than you so I can make a more informed assessment of the value of some underlying contract. This could mean I know inside information about a company and trade before the announcement (illegal but common), or that I know the likelihood of bankruptcy for a company is higher than the market seems to think, or that the underlying mortgages of a packaged security are likely to default.
I could go on, and probably will in another post, but I’d like to make a very basic point, which is this: a lot of money is made every day via asymmetrical information, and in particular there’s a major motivation to obfuscate data in order to create asymmetry. One of the missions of this blog is to uncover and expose major, unreasonable examples of obfuscated information that I know about.
At this point it’s critical to differentiate between two things which typically get confused by non-nerds. Namely, the difference between a technical but thorough explanation and true information obfuscation. A technical explanation, if thorough, can be worked through eventually by someone with enough expertise, or someone who is motivated enough to get that expertise, whereas true information obfuscation just doesn’t provide enough details to really know anything.
The worst is when you are given pretty specific technical information, but which only explains half of the story. This leads to an imprecise false sense of security, which I suspect underlies most of the very large mistakes we’ve seen in finance in the last few years.
For example, let’s talk about the bank stress tests in the United States in 2009. They were conducted in two distinct phases. In the first, a bunch of economists were asked to write down two scenarios. The first was kind of a prediction of how 2009 and 2010 would play out, and the second was a more negative scenario. Okay so far, even though economists aren’t all that pessimistic as people (more on this on another post). The scenarios were averaged in some way and then publicly posted. The good news is, if you thought the scenarios were unrealistic, you’d at least know how to complain about them. The bad news is that they are pretty vague, only really specifying the GDP growth and the unemployment rate.
In the second phase, the banks were allowed to predict the impact of those two scenarios on their portfolios using their own internal models, which were not made public. Here’s the white paper if you don’t believe me. So, in the name of asymmetrical information, why is this a problem? Here are a few reasons:
- Banks had bad internal risk models
- Banks had clear motivation to mark their portfolios to their advantage
- The fact that their methods weren’t made public gives them ample cover to do whatever they wanted
There are two reasons I say that banks had bad internal risk models. The first reason is the one you know about already- they evidently bought a whole bunch of toxic securities leading up to 2008 and seemed to have no idea about the risks. But moreover, my personal experience working in the risk field is that banks used external risk modeling companies as a rubber stamp, essentially to placate those worrywarts who insisted on obsessing about risks. To be more precise without getting anyone into trouble, it was commonplace for banks to not notice when a model at a risk software company had very basic problems and would spit out nonsensical numbers. It was almost as if you couldn’t trust the banks to look at their risk numbers at all. This isn’t true of every bank at all times, but as a general rule when models had major problems it was hedge funds, not banks, who would bring attention to those problems. Moreover, the banks did not seem to have internal risk modeling across their desks. In other words, a trading desk which trades a certain kind of instrument may have some risk monitoring in place (mostly to bound the amount of trading of that type), but when it comes to understanding systemic risk across instrument types, the external risk companies were the source.
It is obvious that banks were motivated to mark their portfolios to their advantage. The ultimate result of bank stress tests were possible additional capital requirements, which they clearly wanted to avoid. This temptation meant it would benefit them to make every assumption of their risk model liberal to their cause.
Finally, they didn’t expose their methods- not even to explain in general terms how they dealt with, say, interest rate risks across instrument types. This meant that only the Fed people involved got to decide how honest the banks were. This is the opposite of what is needed in this situation. There is no reasonable need to keep these methodologies secret from the general public, since it is we who are on the hook if their methods are flawed, as we have seen.
Here’s where I admit that it’s actually really hard to come up with good methodologies to measure impact of vague GDP growth and unemployment estimates. But that admission is only going to add to my rant, because my overall point is that the instruments themselves have been created to make that hard. They are examples, especially tranched mortgage-backed securities but others as well, of intentional obfuscation for the sake of creating asymmetrical information. Instead of living in a world where banks who own things like this are allowed to measure them at their whim, and benefit from that obfuscation, we need to create a system where they are penalized for having illiquid or complex instruments.
And here’s where I admit that I’m not an expert on all of these instruments – some would say I don’t have the right to talk about how they should be assessed. Yet again, I choose to use that fact to add to my rant: if, after working for four years in finance as a quant at a hedge fund and then a researcher and account manager at a risk company, I can’t have an opinion about how to assess risk, then the system is too freaking complicated.
mathbabe 
