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Toilet paper rant
I’ve been here at HCSSiM for almost exactly a week now, and I’ve been exclusively blogging about what mathematics we’ve been teaching this year’s brilliant crop of high school kids. Considering the fact that I usually have lots of opinions on important subjects such as financial reform, data science, and the incorrigible misuse of statistics, you might think I’m dying to also post about such things now that it’s Sunday and I’ve finally had time to catch up on some sleep.
You’d be wrong.
What I really need to vent about this afternoon is toilet paper dispensers. You see, I’ve been using lots of bathrooms with stalls and with those new-fangled huge toilet paper dispensers.
Do you remember in the olden days when a toilet paper dispensing system was relatively easy to understand? There’d be room for at most two rolls, the normal smallish kind, and if that wasn’t enough there’d be extra rolls somewhere for you to use. Granted, sometimes there weren’t, and sometimes there were but they got wet or dirty rolling on the floor.
Nowadays there are they enormous plastic cases which contain about 4 huge rolls of toilet paper, and I guess it’s a good thing in terms of how often toilet paper runs out, although it’s not an excellent idea in terms of the overall cleanliness of the bathroom, since you can mostly fill those fuckers up and leave for vacation.
But I’m not here to complain about dirty bathrooms. What I’d like to complain about is that these huge toilet paper dispensers, which are now about 3 feet in diameter, are for some reason always placed at the same level, at their center, as their older counterparts which contained two small rolls and opened up in the front.
The old dispenser would allow you to get toilet paper at approximately shoulder level. It was a pretty good system.
But these new ones dispense out at the bottom, so now we’re immediately talking about having to bend down to even find a corner of paper, usually blind. God forbid if it’s a new roll.
And once you catch hold of the ephemeral toilet paper corner, you have to then pull out some paper, which sounds easy, but your natural inclination is to pull on the paper by pulling towards yourself. This causes your tiny little corner of toilet paper to be immediately cut off by the serrated edge of the dispenser mouth.
So what you need to do, unless you are satisfied with one square inch of toilet paper (which I am not, in general), is you need to devise a two-handed system of pulling where one hand acts as a soft corner, almost like a ball bearing pulley, directly below the dispenser mouth, and the other hand pulls on it, at first straight down and then around the other hand and up.
A metaphorical second hand when desperately grasping for toilet paper
But mind you, you’re already stooping over to get the paper. So at this point you are basically on hands and knees trying to get more than one square inch of goddamned toilet paper.
People. People. People who install bathrooms, I’m talking to you right now.
Don’t you ever go to the bathroom yourself? Can’t you modify your installation procedure now that these big toilet roll dispensers have been around now for 10 years? Can we get them to dispense at shoulder level some time in the near future? Is this some way of keeping people from using too much toilet paper? If so, it’s not working. I always take too much because I always figure, “what the hell, now that I’ve constructed a pulley system I might as well see what she can do. I’ma gonna let her rip.”
HCSSiM Workshop day 6
A continuation of this, where I take notes on my workshop at HCSSiM.
What is a group
We talked about sets with addition laws and what that really means. We noted that associativity seems to be a common condition and that some weird operations aren’t associative. Example: define 
We decided those things would make them crappy generalized addition operators. We ended up by defining what a group is, although we call it a “Karafiol” so that when our final senior staff member P.J. Karafiol arrives in a couple of weeks he will already be famous.
We showed that 
Graphs
We had already talked about graphs (“Visual Representations”) as defined by vertices and edges. Today we talked about being able to put vertices in different groups depending on how the edges go between groups, so we ended up talking about bipartite and tripartite graphs. We ended up being convinced that the complete bipartite graph on 6 vertices (so 3 on each side) is not planar. But we haven’t proven it yet.
Special Lecture
Saturday morning we have only two hours of normal class, instead of 4, and we have a special event for the late morning. Yesterday Johan was visiting so he talked to them about the projective plane over a finite field, and how every line has the same number of points. He talked to them a bit about his REU at Columbia and his Stacks Project and the graph of theorems t-shirt that he wore to the talk. I think it’s cool to show the students this kind of thing because they are the next generation of mathematicians and it’s great to get them into online collaborative math as soon as possible. They were impressed that the Stack Project is more than 3000 pages.
HCSSiM Workshop day 5
A continuation of this, where I take notes on my workshop at HCSSiM.
Modular arithmetic
We examined finite sets with addition laws and asked whether they were the “same”, which for now meant their addition table looked the same except for relabeling. Of course we’d need the two sets to have the same size, so we compared 
We essentially finished by proving the base case of the Chinese Remainder Theorem for two moduli, which for some ridiculous reason we are calling the Llama Remainder Theorem. Actually the reason is that one of the junior staff (Josh Vekhter) declared my lecture to be insufficiently silly (he designated himself the “Chief Silliness Officer”) and he came up with a story about a llama herder named Lou who kept track of his llamas by putting them first in groups of n and then in groups of m and in both cases only keeping track of the remaining left-over llamas. And then he died and his sons were in a fight over whether someone stole some llamas and someone had to be called in to arbitrate. Plus the answer is only well-defined up to a multiple of mn, but we decided that someone in town would have noticed if an extra mn llamas had been stolen.
Cardinality
After briefly discussing finite sets and their sizes, we defined two sets to have the same cardinality if there’s a bijection from one to the other. We showed this condition is reflexive, symmetric, and transitive.
Then we stopped over at the Hilbert Hotel, where a rather silly and grumpy hotel manager at first refused to let us into his hotel even though he had infinitely many rooms, because he said all his rooms were full. At first when we wanted to just add us, so a finite number of people, we simply told people to move down a few times and all was well. Then it got more complicated, when we had an infinite bus of people wanting to get into the hotel, but we solved that as well by forcing everyone to move to the hotel room number which was double their first. Then finally we figured out how to accommodate an infinite number of infinite buses.
We decided we’d proved that 
We ended by asking whether the real numbers is lodgeable.
Complex Geometry
Here’s a motivating problem: you have an irregular hexagon inside a circle, where the alternate sides are the length of the radius. Prove the midpoints of those sides forms an equilateral triangle.
It will turn out that the circle is irrelevant, and that it’s easier to prove this if you actually Circle is entirely prove something harder.
We then explored the idea of size in the complex plane, and the operation of conjugation as reflection through the real line. Using this incredibly simple idea, plus the triangle inequality, we can prove that the polynomial
has no roots inside the unit circle.
Going back to the motivating problem. Take three arbitrary points A, B, C on the complex plane (i.e. three complex numbers), and a fourth point we will assume is at the origin. Now rotate those three points 60 degrees counterclockwise with respect to the origin – this is equivalent to multiplying the original complex numbers by 
HCSSiM Workshop day 4
A continuation of this, where I take notes on my workshop at HCSSiM.
As usual, we started with the students showing us solutions to their problem sets. Today one of them showed a sharp lower bound on the Fibonacci numbers, although he hadn’t proved it was sharp.
Arithmetic modulo n
Then we talked more about how we can talk about addition, and now also multiplication, with a finite set of symbols 
Finally, we wrote down the subsets of 
Posets and graphs
We went back to the idea of a partial ordering, and came up with a bunch of examples (including the set of integers under “divides evenly into”). We talked for a while about how to represent partial orderings, and finally settled on a graph. We talked a bit about poset chains and antichains, and then we formally defined a graph (we voted and decided to call it a “visual representation”).
The complex plane
The founder and director of the program is David Kelly. The program has been going for 40 years now and for maybe the first time ever Kelly himself isn’t teaching a workshop, so I’ve invited him to do some guest lectures in my workshop on complex geometry. It’s always a treat to watch him teach.
Kelly came in and built on the idea of “modding out by an integer” by definine ![\mathbb{R}[x]/(x^2 +1),](https://s0.wp.com/latex.php?latex=%5Cmathbb%7BR%7D%5Bx%5D%2F%28x%5E2+%2B1%29%2C&bg=ffffff&fg=555555&s=0&c=20201002)
We then defined 
We heard a funny story Kelly told us about taking a test to get his pilot’s license. He was given 30 minutes and lots of suggestions once to compute a heading which involved a calculation in polar coordinates. Since he was a mathematician he was too proud to accept the props they offered him, and finished with 29 minutes to spare. Once aloft though he quickly realized his calculation simply couldn’t be correct, but fudged the test by eyeballing it and following a highway. Turns out that pilots use due north as the axis along which the angle is zero, and then they go clockwise from there. I’m not sure what the moral of the story is, but it’s something like, “don’t be arrogant unless it’s a clear day and you have a backup plan.”
Nim
Yesterday I gave a “Prime Time” talk here at HCSSiM, which is an hour long talk to the entire program. I talked about the game of Nim.
Nim is an old game (that’s the kind of in-depth historical information you’re gonna get from me) where you have a certain number of piles and each pile has a certain number of stones in it. There are two players and you take turns removing as many stones from any one pile as you want. The last person to remove a stone wins. Or, to anticipate my confusion later on, the person who gives back an empty game to their opponent wins.
You can play Nim online here with 3 or more piles and where the stones are matchsticks.
A bunch of the kids had never played so I got them to come to the board to play 2- and 3-pile Nim. Eventually it was discovered that, as long as you start out with uneven piles with 2-pile Nim, you have a winning strategy by making them even. But it wasn’t clear how to win with 3-pile Nim, so we put that question in our back pocket for later.
I then changed it up a bit and put a rook on a chessboard, and said the point was to land on the top left corner, and you could only go up and to the left. They quickly realized it was just two-pile Nim again and the winning strategy was to get the rook on the diagonal. Then I switched it up further and made it be a queen, not a rook, and allowed the piece to move up, left, and diagonally up and left. This was harder.
We then decided that, when you have a game like Nim which is two-player, and the players share the same pieces (so not chess) and moves, and when the game gets smaller every time someone makes a move, then every position can be considered either “winning” or “losing”, by growing the game up from smaller games. If you can only get to winning positions, then you’re at a losing position. If there’s an option to get to a losing position, then you’re at a winning position. A consequence of this way of thinking of things is that a “game” can be described by the options you have when given a chance to play (along with the rules that define the options).
We then discussed adding two games A and B, which just means you get to play from either A or B but not both. We decided that 2-pile Nim is already of the form A + A, where A is 1-pile Nim. And furthermore, 1-pile Nim is pretty dumb – the winning strategy is always to just take away all the stones. But in spite of this, 5 stones is not the same as 6 stones for 1-pile Nim, since you can get to 5 stones from 6 but not vice versa.
Then I defined A ~ B if for all other (impartial) games H, A + H always has the same winner as B + H. It’s easy to see ~ is an equivalence relation, and that G + G is always winning (again, by mimicking your opponent’s moves). It’s also pretty easy to see that if A is winning, then A + G ~ G for all G.
But it’s a bad definition of ~ in that it seems to take an infinite amount of work to decide if A ~ B, since you’d have to check something for all possible H. We decided to improve this by proving that G ~ G’ if and only if G + G’ is winning. It is pretty easy to do this.
Then it was time for action, namely to prove the Sprague-Grundy Theorem which states that:
Every impartial game G has G ~ [N] for some N, where [N] denotes 1-pile Nim with N stones.
We prove this by showing recursively on the size of the game that N above (also called the “Nimber” of the position) is just the “mex” function, which is the minimum excluded non-negative integer. In other words, we designate the winning position as having N = 0, and then we grow the game up from there. If a given position can get to a “0” position, then its Nimber is at least 0 – in fact it’s the minimum number that it can’t reach in one move.
In particular, if you are at a position with Nim number non-zero, you can get to a zero position (i.e. a winning position), as well as any smaller Nim position, and if you are at a position with Nim number zero, you can only get to non-zero positions. This is similar to the losing-winning dichotomy except slightly more nuanced.
We then drew a Nimber addition table, which is the same as the chessboard problem with a rook. We used this to reduce 3-pile Nim to 2-pile Nim and worked out a winning strategy for the 3-pile Nim game (2, 5, 3).
Next we drew a Nimber table for the queen on a chessboard problem. We decided we knew how to play that game plus a 3-pile Nim game.
I was running out of time by this time but I ended with showing them a fast way to find the Nimber of the sum of a bunch of games whose Nimbers you already know, namely the bitwise XOR function. I didn’t have time to prove it (it’s not hard to see with induction on the number of games you’re adding up) but it’s easy to see this recovers our “mimicking” strategy with two games.
HCSSiM Workshop day 3
A continuation of this, where I take notes on my workshop at HCSSiM.
Equivalence Relations and Partial Orderings
After going over many proofs of the geometry problem from last night’s problem set, I corrected the mistake in the “antisymmetric” property and we went through plenty of examples of equivalence relations and partial orderings. We ended with linear orderings, the real numbers, and the less than or equal relation.
Adding modulo n
Next we went back to the idea of maps 
![[n] = \{1, 2, 3, \dots, n\}](https://s0.wp.com/latex.php?latex=%5Bn%5D+%3D+%5C%7B1%2C+2%2C+3%2C+%5Cdots%2C+n%5C%7D&bg=ffffff&fg=555555&s=0&c=20201002)
![[n]](https://s0.wp.com/latex.php?latex=%5Bn%5D&bg=ffffff&fg=555555&s=0&c=20201002)
Pigs-in-hole Principle
We introduced the pigeonhole principle (but since our camp mascot is a yellow, pig, we call it pigs-in-hole). We actually defined the slightly more general idea that, if you have 
Greatest Common Divisor
We asked the kids what the greatest common divisor of 
Eventually we thought of a trick to reduce the problem, namely the division algorithm. Actually Edwin thought of the trick, and it eventually became the Edwinian Algorithm (not like it’s usually called, namely the Euclidean Algorithm). Edwin observed that 
Once we had the Edwinian Algorithm, we realized we could go backwards and express 
So it turns out I’m not going to be able to make the homeworks public, but we had an awesome problem set with lots of pigeon hole problems and Edwinian Algorithm problems. We asked them to decide which approach to calculating 
HCSSiM Workshop day 2
A continuation of this, where I take notes on my workshop at HCSSiM.
The watermelon cutting problem revisited
We prove that the maximum number of pieces of watermelon you can cut with 
First we proved it with a combinatorial argument, then with induction. I decided the first one is better because you figure out the answer as you go, whereas the induction route requires that you already know the formula. They both require you to use the recursion relation we talked about yesterday, and the first one involved writing a 2-d chart and showing how to unpack the value of 
All pigs are yellow
Next we proved, using induction, that all pigs are the same color, and then we exhibited a yellow pig so a corollary was that all pigs are yellow. The base case is that a single pig is the same color as itself, and then assuming we have n pigs of the same color, we get to the statement that n+1 pigs are all the same color by first putting one pig in the barn, and then some other pig in the barn, and the leftover pigs are the same color as each of those so they’re all the same color.
This argument, of course, doesn’t work when you’re moving from “1 pig” to “2 pigs” and exhibits how careful you have to be with working through enough base cases so that your inductive step actually applies.
Strong Induction
We then went to using the Principle of Strong Induction (after showing that there’s no Principle of Induction over the real numbers). We proved that all numbers can be written as the sum of powers of 2, that the Fibonacci numbers grow exponentially, that every positive integer at least 2 is divisible by a prime, and that every planar polygon can be diagonalized using strong induction.
Notation
Incidentally, instead of “Strong Induction” the students voted to call it “Thor Induction”, and instead of the standard end-of-proof symbol, which is a box with an “x” inside, we voted to use the symbol “(see next page)”. They had lots of fun with that one. As a corollary, they decided that if they wanted someone to actually see the next page, they’d use the “Q.E.D.” symbol.
Cross product of Sets
Finally, we talked about the notation 
HCSSiM workshop day 1
So I’ve decided to try to explain what we’re doing in class here at mathcamp. This is both for your benefit and mine, since this way I won’t have to find my notes next time I do this.
Notetakers
We started the math, after intros, by assigning note-takers. In one row we wrote down the students’ names (14 of them), and in the other we wrote down the numbers 1 through 14. We drew lines from names down to numbers. These were the assigments for the days they’d take notes.
But to make it more interesting, we added pipes between different vertical lines. The pipes can be curly (my favorite ones were loopedy-loop) but have to start at one vertical line and end at another at “T” crosses.
Then the algorithm to get from a name to a number was this: start at the name, go down the vertical line til you hit a “T”, follow the “T” pipe til you hit another vertical line, and then go down.
This ends up matching people with numbers in a one-to-one fashion, but why? We promised to prove this by the end of the workshop.
Map of Math
We next had the kids talk about what “math” is. We had them throw up terms and we drew a collage on the board with everything they said. We circled the topics and connected them with lines if we could make the case they were related fields. We drew lines from the terms to the topics that used that a lot – like the symbol 
Cutting Watermelons
Next, we asked the kids how many pieces you can cut a watermelon into with 17 cuts. Imagine the watermelon plays nice and stays the shape of a watermelon as you continue cuts, and you can’t rearrange the watermelon’s pieces either.
If you do a few cuts it quickly gets hard to imagine.
So go down to a 2-dimensional watermelon, which could be called a pizza or a flattermelon. We called it a flattermelon. In this case you’re trying to see how many pieces you can achieve with 17 cuts. But also you may notice that a single slice of a 3-d watermelon looks, to the knife’s edge, like you are spanning a flattermelon.
Similarly, you may notice that a cut of the flattermelon looks like a 1-dimensional watermelon, otherwise known as a flatterermelon. And there the problem is easy: if you have a one dimensional watermelon, i.e. a line, then n cuts gives you maximum n+1 pieces. But going back to a pizza a.k.a. flattermelon, any cut looks from the point of view of the knife like a 1-d watermelon, which is to say it is cutting n+1 regions into half assuming the lines are in general position. So we get a recursion. If we denote by 
Since we know 
Notation
Next, I went on at length about the utility and frustration of notation. Namely, notation is only useful if everyone agrees on what it means. I like standard notation because it’s more, well, useful, but Hampshire is a place where kids absolutely adore making up their own notation. As long as we are consistent it’s ok with me, and I like the fact that they own it. So instead of the standard notation for “n choose k” we are using a pacman symbol with n inside the pacman and k being eaten by the pacman. We call it “n chews k”.
Combinatorial Argument
We talked about putting balls in baskets, and defined that pacman figure to be the number of ways we can do it. Then we proved the pascal’s triangle recursion relation using the argument where you isolate one basket and talk about the two cases, one where there’s a ball inside it and the other when there’s not. Then we identified Pascal’s triangle as being equivalent to this concept of counting. I described this as an example of a combinatorial argument, which I like because it doesn’t involve formulas and I’m lazy.
Induction
Finally, I introduced Mathematical Induction and did the standard first proof, namely to show the sum of the first n positive integers is
How much of data science is busy work?
I’m at math camp, about to start the first day (4 hours of teaching a day, 3 hours of problem session) with my three junior staff (last year I only had one!). I expect I’ll be blogging quite a bit in the next few days about math camp stuff but today I wanted to respond to this blog post, entitled “The Fallacy of the Data Scientist Shortage”. I found this on Data Science Central which I had never known about but looks to be a good resource.
The author, Neil Radan, makes the point that, although we seem to have a shortage of data scientists, mostly what they do can be done by non-specialists. Just as you waste your time during a plane trip on things like security, waiting to board, and taxiing, the average data scientist spends most of her time cleaning data and moving it around.
If I understand this post correctly, they are saying that, because data scientists don’t spend that much time doing creative stuff, they can be replaced by someone who is good with data.
Hmm… let’s first go back to the idea that data scientists spend most of their time cleaning and moving data. This is true, but what do we conclude from it? It’s something like saying concert cellists spend most of their time practicing scales and rosining their bows, and don’t do all that much actual performing. Or, you could compare it to math professors who spend most of their time meeting (or avoiding) students and not much time proving new theorems.
My point is that this fact of time management is maybe a universal rule. Or even better, it may be a universal rule for creative endeavors. If you’re a truck driver then you can fairly said you worked the whole time you drove across the country, at a pretty consistent pace. But if you’re doing something that requires thought and puzzling then the nature of things is that it isn’t an 8-hour-a-day activity.
It’s more like, as a data scientist, you work hard to see the data in a certain way, which takes lots of time depending on how much data you have, then you make a decision based on what you’ve seen, then you set up the next test.
And I don’t think this can be done by someone who is strictly good at moving around data but isn’t trained as a modeler or statistician or the like. Because the hard part isn’t the data munging, it’s the part where you decide what test to perform that will give you the maximum information, and also the part where you look at the results and decipher them – decide whether they are what you expected, and if not, what could explain what you’re seeing.
I do think that data scientists can and should be paired with people who are experts at data moving and cleaning, because then the whole process is more efficient. Maybe data scientists can be brought in as 2-hour-per-day consultants or something, and the rest of the time there can be some engineers working on their tests. That might work.
Mixing colors: pigment vs. light
Today we will address another topic in a list of “things I’m kind of ashamed I don’t understand considering I am a professional scientist of sorts” (please make suggestions!).
Why is it that when you mix light blue (cyan) and yellow paint you get green paint, but when you mix cyan and yellow light you get white light?
Unlike with yesterday’s analemma post, where I couldn’t find a satisfactory write-up on another blog, today’s blog is actually pretty nicely explained and beautifully illustrated here. I will crib their illustrations and summarize the explanations but it’s really out-and-out plagiarism for the moment.
First, you’ve got the so-called “hue wheel” (which sounds more sophisticated than “color wheel”, don’t you agree?):
This is illustrating the following. There are three basic pigments: yellow, cyan and magenta. There are three basic colors of light, namely green, blue, and red. And if you mix the fundamental pigments pair-wise (as in, you get paints and mix them) you get the fundamental colors of lights.
And vice versa as well, although this time you’re mixing as in splicing them together but keeping them separate, like we use pixels on our screen. This means, specifically, that you can combine green and red to get yellow. That’s majorly unbelievable until you see this miraculous picture, also from this webpage:
See how that works? I just can’t get over this picture. The little piece of yellow on the left is just stripes of green and red. Really incredible. The purple I get because it’s blue and red just like it’s supposed to be.
So, why?
The first thing to understand is that this isn’t just a relationship between us and the object we are looking at. It is instead a three-part relationship between us (or more specifically, our eyes), the object, and the sun (or some other source of light, but it’s more traditional in explanations like this to use fundamental, macho objects of nature like the sun).
Nothing can happen without a source of light. Which begs the question, what is light anyway? Again a picture stolen from here:
The prism separates the white light into various wavelengths, where red is at 700 nanometers and violet at 400 nanometers. More on the visible spectrum here. Note that the hidden difficulty here is why a prism does this, which is explained here.
So when an apple looks red to us, we have to imagine white light from the sun hitting that apple, and the key is that the skin of the apple is absorbing everything except the red light:
That thing on top is the sun, and the thing on bottom is your eyeball. The point is the red part of the light is reflected off the apple skin into your eye. And even though white light from the sun is the whole spectrum, we are denoting it when just the fundamental three colors of light because other colors can be made from those. And this can be corroborated by looking at your computer screen with a magnifying glass, where you will see that the white background is actually made up of little pixels of green, red, and blue.
By the way, we are again sidestepping the actual hard part here, namely why some surfaces such as apple skins reflect some colors like red. I have no idea. But I don’t feel as guilty about not understanding that.
Finally, back to the first question, of why cyan and yellow paint make green whereas cyan and yellow light make white. Turns out the light one is actually easier, since our second picture above shows us that yellow light is actually a mix of red and green, and when you add cyan, you now have all three fundamental colors of light, which gives us white light.
If you have cyan paint, then it is reflecting blue and green light, so absorbing red light. If you have yellow paint then that’s a material which is reflecting both green and red, so absorbing blue. For some weird reason (a third moment of stuffing things under the rug), the mixture of the paint is additive on absorbing things, so absorbs both blue and red, leaving only green reflected.
In the end we get a kind of mini De Morgan’s Law for color.
I’ve convinced myself that, modulo the following three questions I understand this explanation:
- How does a prism separate white light into the colors really?
- How do different surfaces decide which lights to reflect and which to absorb? And a related question from Aaron, why do colors fade when they’ve been in the sun?
- Why is “absorbing light” an additive procedure when you mix materials? I feel like if I understood 2 then I’d get 3 for free.
Analemma
Today is a day of new things, since I finished my last day at my job yesterday and I’m going to math camp tomorrow. It’s exciting, and I’m going to kick off this first day of new things with a silly but fun thing I recently learned about the earth and the sun.
Some people know this already, but some people don’t, so sorry in advance if I bore you, but it’s super interesting the first time you think about it.
Namely, have you ever noticed, on your globe, a weird figure eight looking thing?
Nobody could be blamed for their curiosity, because there are so many important looking notches and then of course there’s the phrase “Equation of Time” next to it looking both pompous and intriguing. What is that thing??
After a few moments of contemplation, you’ve probably noticed there are months indicated, and since it’s a closed loop it’s probably describing something that is periodic with a one year period. Plus there are two axes, the vertical axis looks to be measured in degrees and the horizontal is called the “scale of time”.
Whenever I see north/south degrees I think of the earth’s tilt, and when I see something about time, it makes me think about how we measure time, which is vague to me, but probably has something to do with the sun, and orbiting around the sun, and spinning while we do it, again at a tilt. And if I want to be expansive at a time like this I’ll remember that the (pretty much circular) orbit of the earth lies on some plane where the sun also lives.
Now as soon as I get to this point I get nervous. What is time, anyway? How do we know what time it is? What with time zones, and daylight savings time, we’ve definitely corrupted the idea of it being noon when the sun is at its highest in the sky or anything as definitive as that.
So let’s imagine there are no time zones, that you are just in some specific place on the earth. You never move from that spot, because you’re afraid of switching time zones or what have you, and you’re’r wondering what time it is. If someone comes by and tells you it’s daylight savings time and to reset your clock, you tell them to go to hell because you’re thinking.
From this vantage point it’s definitely hard to know when it’s midnight, but you can for sure detect three things: sunrise, high noon, and sunset. I say “high noon” to mean as high as it gets, because obviously if you’re way north or way south of the equator the sun will never be totally overhead, as I noticed from living in the northeast my whole life.
But wait, even if you’re at the equator, the sun won’t be directly overhead most of the time. This goes back to the tilt of the earth, and if you imagine your left fist is the sun and your right fist is an enormous earth, and you tilt your right fist and stick your finger out and make it move around the sun (with your finger staying stuck out in the same direction because the tilt of the earth doesn’t change). As you imagine the earth spinning, you realize a point on the equator is only going to be directly in line to see the sun straight overhead about twice a year, and even then only if things line up perfectly.
Similarly you can see that, for any point between the equator and some limit latitude, you see the sun straight overhead twice a year – at the limit it’s once.
Going back to the point of view of a single person looking for high noon at a single place, we can see the height of the sun when it reaches its apex, from her perspective, is going to move around every day, possibly passing overhead depending on her latitude.
This is starting to sound like a periodic loop with a one-year period – and it makes me think we understand the x-axis. But what’s with the y-axis, the so-called “scale of time”?
Turns out it’s a definition thing, namely about what time noon is. Sometimes it takes the earth less time to spin around once than other times, and so the definition of “noon” can either be what we’ve said, namely “high noon,” or when the sun is at its highest in the sky, or you could use a clock, which has, by construction, averaged out all the days of the years so they all have the same length (pretty boring!). The difference between high noon and clock noon is called the equation of time.
By the way, back when we used sundials, we just let different days have different lengths. And when they first made clocks, they adjusted the clocks to the equation of time to agree with sundials (see this). It was only after people got picky about all their days having the same length that we moved away from sundial time. So it’s really just a cultural choice.
But why are some days shorter than others in terms of high noon? There are actually two reasons.
The first one, quaintly named “The Effect of Obliquity,” is again about the tilt. Imagine yourself sitting at the equator, looking up at the sun. It might be better to think of your position as fixed and the sun as going around the earth. And for that matter, we will assume the orbit of the earth around the sun is a perfect circle for this part.
Then what is being held constant is the spin of the tilted earth, or in other words the speed of the sun in the sky from the point of view of an observer on earth (this point is actually not obvious, but I do think it’s true because we’ve assumed a fixed tilt and a perfectly circular orbit. I will leave this to another post).
You can decompose this motion, this velocity vector, at a given moment, into two perpendicular parts: the part going in the direction of the equator (so the direction of some ideal sun if there were no tilt to the earth) and the part going up or down, i.e. in a right angle to the equator. Since we already know the sun doesn’t stay the same height all year, we know there has to be some non-zero part to the second part of this vector.
But since we also know the total vector has constant length, that means that the first vector, in the direction of the equator, is also not constant. Which means the length of the days actually varies throughout the year. The extent to which it does vary is approximated by a sin curve (see here)
The second reason for a varying length of a day, also beautifully named “The Effect of Orbital Eccentricity,” is that we don’t actually have a circular orbit around the sun- it’s an ellipse, and the sun is one of the two foci of the ellipse.
The thing about the earth being on an elliptical orbit is that it goes faster when it’s near the focus, which also causes it to spin more, due to the Conservation of Angular Momentum, which also makes an ice skater spin faster when her legs and arms are close to her body. Update (thanks Aaron!): no, it doesn’t cause it to spin more, although that somehow made sense to me. It turns out it just traverses a larger amount of angle with respect to the sun that we would “expect” because it’s moving faster. Since it turns as it moves faster, the day is shorter than you’d expect (this only works because of the way the earth spins – it’s counterclockwise if you’re looking down at the plane on which the earth is orbiting the sun clockwise). We therefore have faster days when we are closer to the sun.
When you add up these two effect, both approximated by sin curves, you get a weird function.
This is the “x-axis” of the analemma.
You can take a picture of the analemma by shooting a picture of the sun every day at noon, like these guys in the Ukraine did.
And by the way, you can use stuff about the analemma to figure out when sunrise and sunset will be, and why on the longest day of the year it’s not necessarily the day of the earliest sunrise and latest sunset.
And also by the way, there are lots of old things written about this stuff (see here for example) and there’s an awesome CassioPeia Project video (here uploaded on YouTube) explaining how all of this stuff varies over long periods of time.
Is a $100,000 pension outrageous?
There are lots of stories coming out recently about how public workers, typically police or firefighters, are retiring with “outrageous” pensions of $100,000. Here’s one from the Atlantic. From the article:
That doesn’t frustrate Maviglio, who insists that “people who put their lives on the line every day deserve a secure retirement.” But do they “deserve” more than twice the US median income? Do they “deserve” the sum the average California teacher makes, plus $32,000? Do they “deserve” pensions far higher than the highway workers whose jobs are much more dangerous? These aren’t idle questions, given the public safety worker retirements we can expect in the near future.
Okay, let’s go there. If the median income in the country is 38,000, then $100,000 is a lot. But the median income in the communities where these retired firefighters live is sometimes much higher. For example, in Orange County, where the pension system is getting lots of flak, the median incomes can be seen here. In only one community out of is it below $50,000, and in 8 it’s above $100,000. So if you look at it that way then it doesn’t seem so outrageous.
And maybe we should be paying our teachers and our highway workers more, for that matter.
Point #1: California is a rich state, and it costs a lot of money to live there.
Now let’s move on to articles like this, which frame the issue in a very specific way. The title:
Police and Firefighter Pensions Threaten Government Solvency
How about all the other things that have contributed? Why are we blaming these guys, who have worked all their lives to protect their community? Why aren’t we blaming the mafia behind the muni bond deals, or sometimes even the local politicians as well?
Point #2: This is all a political blame game, trying to manipulate you from thinking about who are the actual crooks behind the scenes here.
My momma always said double down, and this is the ultimate double-down opportunity. Instead of looking for where the money went, or why it was handled so badly, we are going to blame the guys on taking the boring public servant job, and doing it for their adult lives, and trying to retire. Basically, we are blaming them for being right, for making the better choice between public and private.
Point #3: They made the right choice and we can’t swallow it because we thought our whole lives they were suckers for working in public service instead of in finance.
And what about that? Why do we compare $100,000 pensions to median incomes but not to golden parachute retirement packages of failing CEOs? Where’s the real outrage? Here’s another list of some seriously outrageous golden parachutes.
Maybe it’s because we feel like private pay is not our business, as taxpayers. It’s a different arena, and we have no right to judge. Let me remind you then that we taxpayers paid for bonuses at too-big-to-fail banks:
Point #4: These pensions don’t look very big when you compare them to what happens in the private sector.
And yes, I’m talking about the extreme cases, but so does everyone else when they talk about “outrageous pensions”, so it’s extreme-case apples to extreme-case apples.
Free online classes: the next thing
I love the idea of learning stuff online, especially if it’s free.
So there’s this place called Code Academy. They teach you how to code, online, for free. They crowdsource both the content and the students. So far they focus on stuff to build websites, so javascript, html, and css.
I just found out about Udacity (hat tip Jacques Richer), which also seems pretty cool. They offer various classes online, also free unless you want an official certificate saying you finished the class. And they have 11 courses so far, including this one on basic statistics with Professor Thrun.
Then there’s Coursera, which is starting to have quite a few different options for free online classes. The thing I’d like to bitch about with this is that Andrew Ng’s Machine Learning class, which I took when it came out last year, is not being offered currently, which makes me confused. Why does it need scheduling if it’s already been made?
I also just discovered openculture, which lists lots of free online courses. When you search for “statistics,” it returns the Udacity course I already mentioned as well as a Berkeley stats course on YouTube, among others.
I know this stuff is the future, so I’m hoping there continues to be lots of competition from various small start-ups. We are bound to profit from such competition as a culture. What I’m worried about is that the model goes from “free” to “fee” if it gets crowded by large players who, say, pay their instructors a lot for the content.
Which is not to say the instructors shouldn’t get paid at all, but I hope the revenue can continue to come from advertising or through job matching.
The basic unit is risk
Today I’m going to gush over two excellent blog posts I read recently written over at Interfluidity. But first I’m going to state a pet theory of mine about what units we talk in.
In a mathematical sense, units make no difference. If I give you measurements in inches rather than feet, all I’m doing is multiplying by 12. If I say something in French rather than German, all I need is a translation and we’re talking about equivalent information.
But in a psychological sense, a choice of units can make an enormous different. Things sound bigger in inches, and sometimes you barely understand French and can make bad guesses.
I’d argue that speaking in terms of wealth is a mistake. We should instead speak in terms of risk. It’s a different unit, and it’s harder to quantify, but I think risk is what we actually care about. I claim it’s more basic than money.
For example, why are we afraid of not having money? It’s because we run the risk of not having resources to eat, sleep, or get medicine or treatment when we’re sick. If we didn’t have fears about this stuff then people would have a very different relationship to money. The underlying issue is the risk, not the money.
Financial markets putatively push around money, but I’d argue that why they exist and how they actually function is as a way to spread around risk. That’s why the futures market was developed, for farmers to have less risk, and that’s why the credit default swap market was created, to put a price on risk and sell it to people who think they can handle it.
It also kind of explains, to me at least, the weirdness of super rich people- people who have more money than they can ever use. Why do they continue to collect money so aggressively when they already have so much? My guess is that they are confused about their units- they think all their problems can be solved by money, but their remaining actual problems are problems of risk that can’t be controlled by money. Things like the fact that we all get old and die. Things like that people don’t like you if you’re an asshole or that your wife may leave you. These are risks that most people never get to the point of trying to solve through money, because they’re still stuck in a different part of reality where inflation could screw their retirement plans. But for super rich weirdos, we have the Singularity University where you get to learn how to transcend humanity and live forever.
I’m not making a deep statement here. I’m just suggesting that, next time you hear of a plan by politicians or regulators or Wall Street bankers, think not about where the money is flowing but where the risk is flowing.
A perfect example is when you hear bankers say they “paid back all the bailout”; perhaps, but note that the risk went to the taxpayers and is firmly fixed here with us. We haven’t given the risk back to the banks, and there doesn’t seem to be a plan afoot to do so.
Which gets me to Interfluidity’s first plan, namely to have the government protect up to $200,000 of an individual’s savings from inflation.
Now, on the face of it, this plan is not all that protective of the 99%, because it’s definitely benefiting people who have savings, where we know that the lowest 25% or so of the population is in net debt. Only people with savings to protect can actually benefit.
But if you think about it more, it is good for people like my parents, whose retirement from a state school does not rise with inflation, or more generally for people who have a fixed savings put aside for retirement. And it isn’t at all good for very rich people, who would see a benefit only on a small percentage of their savings (assuming it is possible, as Interfludity says it is, to outlaw the bundling of these inflation-protected accounts like some people now bundle life insurance policies).
Most economic policies in this country are made to benefit rich people, and are defended by saying we need to protect middle-class people nearing retirement with a modest nest-egg. As Interfluidity said, those middle guys are used as “human shields”. Very few policies go into to the weeks sufficiently to figure out how to protect that group without having outsized benefits at the top.
Said in terms of risk, this plan is pushing inflation risk to people who can handle it, and removing it from people who are extremely vulnerable to it.
Which brings me to the second post I want to rave about, namely this one in which Interfluidity dissects the lack of political will in the face of the current depression. From the post:
We are in a depression, but not because we don’t know how to remedy the problem. We are in a depression because it is our revealed preference, as a polity, not to remedy the problem. We are choosing continued depression because we prefer it to the alternatives.
The reason? Because no matter how much someone might say that we care about the middle class, the truth is we are protecting rich people from the risk of getting poor. We have, as he says, a population with individual power roughly weighted in proportion to their wealth (or, to be consistent with my theme, inversely proportional to their risk), and when you take a vote with those weightings, we get a “weighted consensus view,” manifested among the macroeconomists in charge of this stuff, that we should avoid inflation at all costs (ironic that the people with the least risk are also the people with the most influence).
In order to remedy this situation, we’d need to implement something like the inflation-protected bank accounts up to $200,000 for the individual. Then the weighted consensus may change – we might instead actually pull for a policy that would have some risk for inflation and would also possible create jobs.
But of course, in order to implement such a policy, we’d need to have the political will to change the risk profile, which goes back to the weighted consensus thing. Keeping in mind that this policy would push the risk to rich people, I’m guessing they wouldn’t vote for it.
On the other hand, smallish savers would. So it’s not a mathematical impossibility, because there may be enough people in favor of the inflation-protection plan to make it happen, and then the second question, of how to get us out of the current depression, would be easier to address. I’m definitely in favor of trying.
Why are pharmaceutical companies allowed to do their own trials?
A recent New York Times article clearly addressed the problem with big pharma being in charge of its own trials. In this case it was Pfizer doing a trial for Celebrex, but I previously wrote about Merck doing corrupt trials for Vioxx (see How Big Pharma Cooks Data: The Case of Vioxx and Heart Disease). In the article, it has the following damning evidence that this practice is ludicrous:
- Research Director Dr. Samuel Zwillich, in an email after a medical conference discussing Celebrex, stated: “They swallowed our story, hook, line and sinker.”
- Executives considered attacking the trial’s design before they even knew the results. “Worse case: we have to attack the trial design if we do not see the results we want,” a memo read. It went on: “If other endpoints do not deliver, we will also need to strategize on how we provide the data.” This simply can’t happen. There should be an outside third-party firm in charge of trial design, and there needs to be sign-off on the design in advance so no monkey business like this takes place.
- Executives disregarded the advice of an employee and an outside consultant who had argued the companies should disclose the fact that they were using incomplete data – they were using only half. This kind of statistical dishonesty is the easiest way to get numbers you want.
- In another email, associate medical director Dr. Emilio Arbe from Pharmacia (which was later bought by Pfizer) disparaged the way the study was being presented as “data massage,” for “no other reason than it happens to look better.” Mind you, this statement was made in September 2000, so in other words the side effects of Celebrex have been known for over a decade.
- Medical Director Dr. Mona Wahba described it as “cherry-picking” the data. In May 2001.
Why is this happening? It’s all about money:
It is one of the company’s best-selling drugs, racking up more than $2.5 billion in sales, and was prescribed to 2.4 million patients in the United States last year alone.
How much are you in doubt that the people in charge are being pressured not to be honest? Dr. Samuel Zwillich claims the hook, line and sinker statement was probably about something else. The cherry-picking Dr. Mona Wahba now can’t remember what she meant.
This is bullshit, people. Statistics is getting a bad name, and people are suffering and dying from bad medicine, not to mention paying way too much for fancy meds that don’t actually help them more than aspirin.
What we need here is some basic integrity. And it’s not just a few bad eggs either – stay tuned for a post on Prof. David Madigan’s recent research on the robustness of medical trials and research in general.
Coding is like being in a band
I asked my friend Nikolai last week what I should learn if I want to be a really awesome data scientist (since I’m an alpha female I’m sure I phrased it more like, how can I be even more awesome than I already am?).
Being a engineer, Nik gave me the most obvious advice possible: become an engineer.
So this past weekend I’ve looked in to learning Scala, which is the language he and I agreed on as the most useful for large-scale machine learning, both because it’s designed to be scalable and because the guys at Twitter are open sourcing tons of new stuff all the time.
That begs the question, though, to what extent can I become an engineer by reading books about languages in my spare time? According to Nik, real coding is an experience you can’t do alone. It’s more like joining a band. So I need to read my books, and I need to practice on my computer, but I won’t really qualify as an engineer until I’ve coded within a group of engineers working on a product.
Similarly, a person can get really good at an instrument by themselves, they can learn to play the electric guitar, they can perfect the solos of Jimi Hendrix, but when it comes down to it they have to do it in conjunction with other people. This typically means adding lots of process they wouldn’t normally have to think about or care about, like making sure the key is agreed upon, as well as the tempo, as well as deciding who gets to solo when (i.e. sharing the show-offy parts). Not to mention the song list. Oh, and then there’s tuning up at the beginning, choosing a band name, and getting gigs.
It’s a similar thing for coders, and I’ve seen it working with development teams. When they bring in someone new, they have to merge their existing culture with the ideas and habits of the new person. This means explaining how unit tests and code reviews are done, how work gets divided and played, how people work together, and of course how success gets rewarded. Moreover, like musicians, coders tend to have reputations and egos corresponding to their skills and talents which, like a good band, a development team wants to nurture, without letting itself become a pure vehicle to it.
Which means that when you hire a superstar coder (and yes the word seems to be superstar- great coders can do the job of multiple mediocre coders), you tend to listen more carefully to their ideas on how to do things, and that includes how to change the system entirely and try something new, or switch languages etc. I imagine that bands who get to work with Eric Clapton would be the same way.
I’ve been in bands, usually playing banjo, as well as in chamber music groups back when I played piano, so this analogy works great for me. And it makes me more interested in the engineering thing rather than less: my experience was that, although my individual contribution was slightly less in a band setting, the product of the group was something I was always very proud of, and was impossible to accomplish alone.
Now I don’t want you to think I’ve done no coding at all. As a quant, I learned python, which I used extensively at D.E. Shaw and ever since, and some Matlab, as well as SQL and Pig more recently. But the stuff I’ve done is essentially prototyping models. That is, I work alone, playing with data through a script, until I’m happy with the overall model. Since I’m alone I don’t have to follow any process at all, and trust me you can tell by looking at my scripts. Actually I wrote some unit tests for the first time in python, and it was fun. Kind of like solving a Sudoku puzzle.
The part I don’t think works about the coding/ band analogy is that I don’t think coders have quite as good a time as bands. Where are the back-stage groupies? Where are the first two parts of sex, drugs, and rock ‘n’ roll? I think coding groups have their work cut out for them if they really want to play on that analogy.
Is science a girl thing?
One of the reasons I chose to call this blog “mathbabe” is that when I searched that term, I found a website, now defunct (woohoo!), where semi-naked women were adorning math.
This pissed me off, because I want math babes to be doing math.
If you get that (what’s not to get?) then you might see why the European Commission’s latest effort to inspire girls to do science is truly repugnant (hat tip Debbie Berebichez, a.k.a. Science Babe).
It’s a commercial where you see a standard male scientist (in a white lab coat no less) being surprised, and, we assume, aroused, when three girly models come in, giggle, dance, and generally adorn the commercial.
At the end they put on lab goggles in the style of an ironic accessory. They’re all wearing high heels and there’s even lipstick in a few shots for some unexplained reason (are we supposed to infer that wearing lipstick makes you more scientific-alicious?).
And although there are a couple of shots of an actual female writing what could be actual formulas on a hyped-up whiteboard, that’s more than balanced by some other shots of the models with unmistakable come-hither looks, gestures and blown kisses.
People. At the European Commission. Do you have no advisors!? Do you have no common sense? Who vetted this garbage video?!?
I’d like to see us get to the point where our slogan is more along the lines of:
Science, it’s for really smart women
And our video consists of cool, funky women giving actual talks and lectures or actually working on experiments. Maybe they’re wearing heels, but for sure they’re not acting like complete fucking idiots. How’s that?
I personally could suggest about 40 people for such a video. Not hard to do.
Saturday morning reading
I’m feeling deliciously lazy today, with one more week left of my current job and one more week of hazy New York weather before I head up to math camp for three weeks (woohoo!). I’m trying to figure out what to do with my life after that, and suggestions are very welcome! Bonus for ideas on how to use modeling techniques to help people rather than to exploit them.
In the meantime, please join me in some light reading:
1) Read this (hat tip Kurt Schrader). Seriously, it’s incredibly snarky and funny and right on – a gawker’s view on the New York Times Style Section and its systematic approach of torturing its readers. My favorite line:
I want to take this sentence, drag it out into the backyard, and beat it to death with a shovel.
2) How are bee hives like too-big-to-fail banks? Turns out, in fewer ways than you think. Read more to understand a beekeeper’s perspective on risk (hat tip Eugene Stern). A nugget:
Take, for example, their approach toward the “too-big-to-fail” risk our financial sector famously took on. Honeybees have a failsafe preventive for that. It’s: “Don’t get too big.” Hives grow through successive divestures or spin-offs: They swarm. When a colony gets too large, it becomes operationally unwieldy and grossly inefficient and the hive splits. Eventually, risk is spread across many hives and revenue sources in contrast to relying on one big, vulnerable “super-hive” for sustenance.
3) As we already knew, people with bad credit scores don’t really have access to all this amazing lending at amazing rates, as the Fed now admits and as I suggested in this post, “A low Fed rate: what does it means for the 99%?”. I think the next step is a data dive into credit scoring histograms (say, aggregate FICO scores for all Americans) over the past 20 years, compared to corresponding credit card offers – I want to see what kind of deals average people can expect to get on loans. If you know how to get this data, please tell me!
4) One of my readers was kind enough to leave a link to this article on why incompetent people think they’re awesome. I’m sharing it with you guys but I reserve the right to write a post on this as well. Specifically, I’m thinking of writing a meta-piece about why, when people read about incompetent people thinking they’re awesome, they somehow always smugly conclude that those pathetic fools should get a clue and realize this article is about them.
Quants, Models, and the Blame Game
This is crossposted from Naked Capitalism.
Recently a paper came out written by Donald MacKensie and Taylor Spears. It’s about the role of the Gaussian Copula model in the credit crisis, and it’s partly in reaction to Felix Salmon’s article in Wired from February 2009. Both Felix Salmon and Lisa Pollack have written responses to this paper, and they’re quite entertaining and worth a read.
Without going into too many details about the underlying models, which I might do in another post, I wanted to spend some time appreciating this paper for bringing up two issues that I believe far too few people give notice to:
- The politics of being a quant. The pressures on a quant inside an investment bank, a ratings agency, on a trading desk, or for that matter in a risk group are real and need to be understood.
- The narrative of blame. Who gets blamed when a model fails? For that matter, who is responsible for making sure it works at all?
Politics
In the paper, they discuss the concept of a “model dope,” which is a rhetorical device helping you imagine an idiot who ‘unthinkingly believes in the output of the model’. The paper explains that, as far as they could tell, there were no such actual people, that the quants they interviewed all knew the model was and is flawed and overly simplistic.
I completely believe this, and I think it wouldn’t surprise any quant who’s worked in the industry. Quants are the guys who get metaphorically paraded out in front of the bank, with their Ph.D. hanging out as a kind of badge, but when they get back to work are put back in the mines. It’s a trader’s world, or a salesman’s world, and nobody asks the quants for their nuanced opinion on the validity of basing billions of dollars in transactions on these models if the P&L looks good.
Let me say it this way: how many places employing quants to create risk or hedging models have their quants actually in charge of stuff? Very, very few is the answer. The quants are not in charge, they rarely have real power, and as soon as they produce something semi-functional and useful, they no longer own that thing – it’s been taken away from them and is owned by the real power brokers.
Which is not to say the guys in power don’t kind of understand the stuff- they do, they’re smart, but they’re not typically wedded to the idea of intellectual integrity. They typically understand it well enough to see how it can be gamed.
So I don’t think it was the quants that were promoting the wide use of the Gaussian Copula model. In the paper, they explain that it happened for essentially political reasons:
First, it was easy to talk about, since an entire correlation matrix of default was boiled down to one number, “base correlation”:
“If traders in one bank … had to ‘talk using a model’ to traders in a different bank that used a different copula, the Gaussian copula was the most convenient Esperanto: the common denominator that made communication easy.”
Next, it allowed traders to book P&L on the same day they made a trade:
“The most important role of a correlation model, another quant told the first author in January 2007, is as ‘a device for being able to book P&L’,”
Next, once it was widely used, it had staying power just because it was difficult to explain something else, not to mention difficult to admit the current model’s flaws:
“Here, the fact that the Gaussian copula base correlation model was a market standard provided a considerable incentive to keep using it, because it avoided having to persuade accountants and auditors within the bank and auditors outside it of the virtues of a different approach.”
Putting that stuff together, we can see that the mere, lowly quant’s objection, if there was one, that the model sucked was the least of the considerations of the powers-that-were:
“From the viewpoint of both communication and remuneration, therefore, the Gaussian copula was hard to discard.”
Blame
As to the question of blame, that’s also all about power. Just because the objections of quants were likely ignored doesn’t mean we can’t blame them after the fact – that’s another useful thing about quants, since they even admit the models were overly simplistic. Easy fall guys.
By the way, I’m not saying that quants rebelled against the misuse of their models, that they tried their best to warn the public of the known flaws of the Gaussian Copula or any other model for that matter. In fact I don’t know of many quants who did stand up to these assholes, partly because they were paid really well not to, and partly because they were not the alpha males in the place.
I’m just trying to point out that blame can get kind of murky. If a quant comes up with a model and says up front, hey this is just a sketch of something, it’s not totally realistic, but it’s better than nothing, and then the investment bank ignored the quant’s misgivings and bets the house on the model, who is responsible for the resulting risk?
In other words, I’d love the quants to grow some balls, but it’s going to take a major revolution in the power structure for that to be enough.
A Question
The two issues of politics and blame raise for me a larger question in reference to modeling. Namely, why and how to models develop?
[This is a cultural question, and separate from the standard (and interesting) questions you usually hear people ask of a model:
- What does the model claims to do?
- How well it works with real data?, and
- If it is widely employed, how the model affects the market itself?]
- To simplify a businessman’s day. Instead of reading out results from 5 trading desks, we want to dumb it down to one single number, so we employ a modeler to come in and do their best to summarize with one P&L number and one risk number. In other words, it’s the modeler’s job to turn a report into a sound bite. Of course the problem with that model genesis is that it doesn’t necessarily make sense to combine a bunch of numbers into one number. Sometimes the world is actually complex and needs to be understood with a nuanced view. Sometimes a sound bite isn’t enough.
- To sound incredibly smart – in other words, pure spin doctoring. I encounter this more in tech than in finance, where there are enough model-savvy people that you can’t be quite as blithe about hiding bullshit in a model. But this is real in finance too, and I think is used to confuse regulators all the time.
- To dissect, or attempt to dissect, various kinds of ‘unintentional risk’ from ‘intentional positions’. This is the single most dangerous kind of model, because on paper it can look so good, and can seem to work for so long. Credit default swaps can be thought of as manifestation of this goal – an attempt to separate default risk from holding-a-bond risk. The problem we face is that our models are never really that good, or even testable, and there are unintended consequences of these new-fangled contracts that sometimes cause catastrophic events.
- Of course, in quant shops like D.E. Shaw or RenTech or Citadel, there are also quants who try to predict the market or trade superfast on currencies, which is different from the stuff I’ve been talking about which mostly deals with hedging and risk, with different kinds of corresponding risks.
Please don’t have any kids
I recently read this New York Times article about choosing to have kids, called “Think Before You Breed”.
It describes the pressure childless people have from breeders to have kids. I believe they feel that pressure, and I want to explain it a bit, from the point of view of a person with three kids.
First of all, if you feel pressure coming from me, it’s entirely unintentional. In fact, I consider having children a deeply irrational thing to do – any kind of cost/benefit analysis focusing on material costs and such would steer me very wide of the practice of sacrificing my health, my time, and enormous amounts of resources to these little economic leeches that likely won’t even talk to me after they leave for college, which I will be paying for if I can afford it.
And not only is having kids a stupid idea in terms of economics – it’s also a hugely dangerous proposition, because it’s so much easier to screw up your kids than it is to raise healthy, well-adjusted people. There are pitfalls in every direction, and when it comes to it I think there should be a 4-year college, with forced enrollment of people who are embarking on the parenting thing, before it happens. That nothing like this happens, that kids themselves can have kids without any planning or training, is actually crazy considering how much maturity is required to do a half-decent job of it.
The only defense I really have of bearing three children is that my instincts told me to do it, and they, my instincts, didn’t play fair. In fact until I turned 23 I didn’t want kids, and I had a completely rational view of how much of a pain they’d be, and how much they’d take over my life, etc.. But somehow when I turned 23, there was something deep in my gut that kicked in and made me start missing my as-yet-unborn kids, as if I’d forgotten to kiss them goodnight and they were whimpering upstairs in their rooms. I know, I know, it’s over the top, but there you have it, instincts take no prisoners.
In summation: I don’t want you to have kids unless you absolutely have to. It’s bad for the planet, it’s bad for you, and it’s likely bad for your kids. The only thing I’d be checking if I ask you whether you plan to have kids is whether you have caught the same disease I did when I turned 23 – it’s not a request! It’s a sanity check!
Now I don’t think I’m completely normal in my view. I do think that lots of people get so intoxicated with the breeding thing that they literally think other people are insane if they don’t want to join the club. That’s super annoying and I don’t think there’s much you can actually do about these people. If it helps, when I’m listening in on that conversation I’ll be happy to interject and suggest that nobody in their right mind would ever breed. But rational arguments such as lack of resources, time, and attention would probably not sway these people, because they are true believers and need to think that it’s the only reasonable thing to do. They are married to convention.
They are also usually convinced their kids will never hate them, never move across the country for college and refuse to write, so the argument that they’ll be lonely when they’re old also doesn’t seem to help – they will tell you that, as a non-breeder, it will be you who is lonely when you’re old. It’s ironic, this line of argument, especially because you’re often talking to someone who hasn’t invested themselves in hobbies; they’re obsessed with the progress of their kids’ violin lessons and robotics teams but don’t have a true independent interest outside their children. Do they really think their kids will still let them into their lives 24 hours a day when they’re 25?
I firmly believe that, without kids, I could be establishing a far richer network of (probably childless) friends that will still be around to hang out with and talk politics when I get old. I’m still trying to do this now, by the way, but most nights I need to get home by 5:45 to make plain pasta and steamed broccoli, the only two things I’ve eaten in the past 12 years.
Look, everyone tries to convince themselves and people around them that the life choices they’ve made are the right ones. It’s uncomfortable to constantly feel like an idiot about this kind of thing, believe me. For myself, in spite of how irrational I have been, I can truly say I’ve managed to convince myself on a daily basis that I don’t mind the sacrifice because at least I get to hear my kids say insulting, sarcastic things that seem new to me (“ooh, I hadn’t heard that one! It’s goooood!”). It all makes it worth it. Plus I love them to bits, and they happen to be really cool people that might just contribute positively to the world whilst having a raucous amount of mischievous fun. At least that’s what I’ll imagine is happening when I’m old and lonely.
mathbabe 
