Mathematics After The Fall

Archive for the ‘Statistics’ Category

Killing the White Swan

Finally, after almost two years, I’ve gotten around to reading the much talked about book The Black Swan, by Nassim Nicholas Taleb. The term Black Swan has entered financial vocabulary, so it’s good to evaluate the source. Overall, it’s a good term; a Black Swan event is a rare event, hard to predict, that has a large impact. For instance, until the 17th century Europeans thought all swans were white. They are, in Europe. In Australia, they’re not.

Overall, it’s a pretty good book. I’ll award it a 3 out of 5. However, it can be tough to read at times. Dr. Taleb is pompous. Very pompous. He seems to be basically alone in this world. Describing someone, he wants to “put a rat down his shirt.” While I don’t appreciate false humility, either, or too much self depreciation (as in the saddest hoopster), this book would have more power if it was more targeted. A statistician’s review says it well, so I’ll quote Robert Lund in the American Statistician: “reckless at times and subject to grandiose overstatements; the professional statistician will find the book ubiquitously naive.” As a professional statistician, I agree wholeheartedly.

Before I come back to why I agree, let me list what Dr. Taleb gets correct. He is right that many things in this world are not Gaussian or normal, and not subject to the bell shaped 95% cutpoints like the linked applet. There are many things in his Extremistan, particularly those that follow Mandlebrot power laws, and putting them into his Mediocristan is dangerous. Note that by choosing the word Mediocre for the other group, against the currently positive word Extreme, he induces stylistic bias. Who would ever want to be in Mediocristan? Well, except nature with height and growth processes and stuff. So he’s got a correct point, but overreaches.

Another clear point is about the Ludic Fallacy, which notes that real life does not have the same structured randomness of games. Though he had to invent a term for it, the author is correct. Too many introductory examples involve games of chance, cards and dice and roulette wheels. Equal probabilities and independent events are much rarer in reality than Moore and McCabe’s introductory text. In my classes, I make a point about independence, with several reminders of its importance, including the most important one, the test question.

In other words, I do my job as a professional statistician. That’s the big deal here. I know Dr. Taleb has had dealings with the professional statisticians since the publication of this book, since I quoted Dr. Lund from the American Statistician special August 2007 issue on the book. I suspect that he had very few dealings with my kind before. Unfortunately, what passes for “statistics” nowadays mostly comes from economists. Economists, well, are pretty nasty. A friend of mine once said that “Economists are just sociologists with Asperger’s Syndrome.” I replied that I’ve always thought of them as megalomaniac statisticians, or just plain bad ones. Even the so called revolution, this Freakonomics thing, is really just regression analysis, at the second course level. In some places, it’s not even a good second course level, as this blog post acknowledges a mistake and then tries to defend an abortion model with serious interaction problems. Do they not understand saturation or degrees of freedom? I recommend this critique; even though I might not like all the articles from Steve Sailer, he’s demolished Dr. Levitt on this one. It’s too bad he’s not cool enough to get a fancy book. And who knows – maybe I’ll venture into that perilous topic myself, soon.

On page 239 of my hardback edition, Dr. Taleb thinks that in comparison to what he calls dull statistics classes, “Clearly it would have been more beneficial, and certainly more entertaining, to have taken classes in the neurobiology of aesthetics or postcolonial African dance, and this is easy to see empirically.” I should be careful here. Particularly before computers became readily available, statistics courses focused heavily on computation. I’ve seen those books from before roughly 1990; they weren’t as good as the courses of today. Given his age, he likely had one of those older courses. Postcolonial African dance might well be better. I also wish that standard deviation had a name that didn’t imply standards, like how I prefer credible interval to confidence interval. That doesn’t affect the main point, that the true professionals know the problems, and that at least now we’re trying to get those across.

Precision, research, and greater balance could have taken this book from decent to great, so I look in a little frustration at Dr. Taleb’s work. I do have his other book, Fooled by Randomness, which might not show the problems of this one. It won’t be random, or a Black Swan, if I get around to reading that.

The homeless figures dilemma

I was visiting my parents in Pennsylvania, and I returned to an interesting request. A reporter from the New York Times had found the abstract of my talk on the age of homeless in America. The New York Coalition for the Homeless had received donated time for television advertisements. You can view the modified ads from this page.

Why do I call them modified ads? Well, they used to be different. The 90 second ad and the Facts ad used to include less quotes in the middle, and a different ending. It used to conclude “and by the way, the average age of a homeless person is nine.” As of early July, the original ad still appears on Youtube. I had heard this statement earlier, during the December 2007 Commencement at Bellarmine.

The article appears online at the Times’ City Room blog. Thus, I helped cause a change in the ads.

The full implications of this work startled me. There’s the boost to my professional career. Bellarmine also gets a mention in a big publication, helping the school. Of course, this means I now need to know a lot about the situation. This was originally just a teaching example, but now it’s not. Fortunately, I managed to find an assistant for the research; she and I will have something ready by Mathfest at the end of this month.

There’s a moral issue, as well. The Coalition was hurt by the negative exposure. That’s not a good thing, as homelessness is a large problem. Many people without permanent shelter are children, thousands in New York alone. Even if not half, they could use support. Weakening the groups that provide and advocate for support does not help. On the other hand, I have an academic responsibility to accurate statistics, as much as we can. An average age of 9 does not appear correct. In Catholic thought, even for the right ends, wrong means are inappropriate and sinful. This is a right end. Using a misleading (at best) figure is an inappropriate, potentially sinful way to do that. I should help. But it hurts a little. It’s funny how seemingly simple things, like 15 minute talks, can become moral dilemmas. I wish I had an answer here, or even better words to describe my feelings. Maybe later, I will.

Millennials, Part 2: Anthropology

Late in the semester, Bellarmine faculty literally packed the Fireplace Room for a talk about generations. Over one-quarter of the faculty showed. Half that count would be nice when my collaborator and I present in early February. The conversation focused on the differences between pre-Boomers, Baby Boomers, Generation X, and the current college Millenials. Each generation attempts to fix some flaws of the prior one. For instance, pre-Boomers had a large focus on community and sacrifice, with the Depression and Great War. Boomers maintained the outward idea of process, while privately revolting against stifling convention. My people, Generation X, fixed the grave contradiction between public and private, and can no longer believe in hypocritical institutions. We kept private focus and reduced hypocrisy, but destroyed the public process; we preferring to do separate things and interlink them. Wikipedia could only be a Gen X creation. The latest group, Millenials, maintained the suspicion of Gen X, but wanted some interconnectedness. Their groups became extremely tight and extremely compact, a short loop. With better communication, keeping in touch with close friends and family becomes paramount. My generation had abandoned kids; we offer helicopter parents to the millenials. If you look closely, you can see a pattern:

1. Wilderness, neither private nor public groups: Generation X.
2. Village, private but not public: Millenials.
3. City, private and public: pre-Boomers and likely post-Millenials.
4. Destruction, not private but public: Boomers.

One problem with education is that senior teachers are two generations removed from their students. There have been changes in the 15 years since I began college. Without my time at the Catholic center, I would be removed now. People 30 years away have to be distant. To examine the changes, people write books like My Freshman Year. It has a psuedonym of Rebekah Nathan from AnyU, though the author was revealed as anthropologist Cathy Small from Northern Arizona University. Northern Arizona is a fourth-tier large state school. The ACT quartile range is 20-25; Bellarmine’s is 22-27. There are differences between normal and elite institutions, and smaller and larger schools, thus I’m going to concentrate on the major points, particularly those that surprised me about American students. As Dr. Small notes, international students find the American system confusing, more outwardly affable yet more inwardly hollow.

What do students want? Friendly Fun in College Culture. “Friendly fun is associated with spontaneity, sociability, laughter, and behavior (including sexuality) that is unconstrained.” Formal rules come from outside, which need to be minimized or avoided. Several students called classes the “price one has to pay” for access to college culture. That stings. I never thought that. To be fair, I didn’t take enough advantage of Harvard’s culture, focusing instead on class learning and knowledge building. I enjoy academics. I savor the pursuit of knowledge, politics, and theology. Most of her students don’t; neither do most of mine. We professors need to remember that our students don’t look for consciousness; they seek interest and relevance.

How much do students study? Less than what professors work. For each in-class hour, I spend very close to two hours between preparation, grading, and reporting. Professors generally recommend that 2:1 ratio. At Harvard, I followed that 2:1 ratio; I allocated 8-10 hours weekly for most classes. Computer Science and Math took more.
Looking back, I followed the ratio because I was a motivated student in a challenging program at an elite institution. That’s a very small portion of the college population. In general, the quartiles of the study time distribution are much less. The median student studies less than ONE hour outside class for each hour of instruction. National surveys report that; Dr. Small reports that; the group from my class that surveyed study time reported that. None of the data points from my class reached 2:1.
Given this information, I’ve decided to go for 1:1. If my students did that, I’d be pleased. It hurts to reduce the goal, but one of my strengths as a statistician is the ability to follow the evidence, no matter how painful. I’ve done it before and need to do it again.

How do students organize themselves? As individuals, in compartments. Universities often cite a large amount of activities and events as evidence of the much-desired community, and large counts of minorities as diversity. That’s not true. Large counts with small attendance are the exact opposite of community. I call it Balkanization, but today’s students might not know Yugoslavia. As the author writes, “Community in the American university is paradoxically a private and an individual decision.” The shared group with general membership and goals has disappeared. I’ve seen the idea, but only the idea, thanks to Boomer corruption. We in Gen X couldn’t even provide the concept to the Millenials. Now, students have close friend groups of less than six. New dorms have individual bedrooms and bathrooms, larger private spaces at the expense of hall areas. 15 years ago, we used common rooms from time to time, and converted spaces into common rooms when necessary. Now, the Super Bowl is a good example. The hall big-screen TV attracted FIVE people. Instead, people had festivities inside individual rooms.

Individualism also applies to actions in class. Dr. Small’s work as a professor was very illuminating. In her anthropology class, she asks the lecture hall to identify the witch. Typically, students identify the best students from the professor’s eyes, those engaged and prepared. Aligning with the professor is suspicious, like witchcraft. As a student, she felt this push towards silence. I shouldn’t be surprised, because I spoke little in undergraduate classes. At my large elite school, though, lecture halls were normal and even small classes taught in lecture style. Recitations led by graduate students rarely served the intended purpose of discussion. Most became sequential statements of opinion. At least one TA checked off when we spoke, so I made sure to speak once per class, thoughtful or not. “Yes, but …” was the phrase to ensure the participation point, though it didn’t lead to coherence or flow.

On the other hand, my Bellarmine class is (barely) small enough to allow personal notice, and I include time for practice and questions. Like many professors, I consider students speaking a success. Perhaps I need to reconsider. My goal is not students speaking, it’s students learning. If quick answer questions don’t help and make students uncomfortable, I should rethink my approach.

Finally, how do students view school and us professors? As things to be managed. Student reports suggest a boss and worker relationship. Like schedules and workload, professors need to be managed. The workers must be publicly friendly, while private opinions may differ. That’s OK; I will be affable as well, but we won’t be friends. An evaluator can’t be a friend, anyway, since the intimacy of true equality can’t happen. Instead, we get strategies.

One management strategy suggests sitting in the area of the center T, the front row and the center aisle. Knowing this, I try hard to spread my time throughout the room; I might even underserve people directly in front of me.
Others relate to tone. I understand the students. We’re not in this together; they have substantially different goals than I. I don’t think the ideal of academic purity ever existed, but it certainly does not now. From a philosopher’s perspective, Economic Man has won. Every action balances cost and reward. If the students look at class as work, I’m willing to be the boss. I’m willing to learn about them.

Oh, as for the book, it’s nice. Not everyone needs to read it, and I wish she would think a little more about reasons behind reasons, and her effect. Despite that, I learned a lot. It gets a 3 out of 5.

Heading to the Grown-Up Table

It’s 1:15 PM, 23 June 2006, and I feel so old right now.
I’m at the formal luncheon of the MSMESB Conference, in the Winter Garden of the GSB. It’s mostly statisticians from business schools. It’s not that I’m physically old, at all. I’m one of the youngest; there are lots of balding white-hairs. Yet I belong here. I just finished lunch, where the conversation felt right. I’ve been treated as a junior colleague – people ask about my work, I ask about theirs, they look at my poster. We talk about projects, and they listen. Yes, it’s good work. Yes, it’s strange to be a colleague. I’m not just a student anymore. Yes, technically I’m still not done, but (God and Rob willing) I’ll be done in a couple months. Maybe I’ll become a lecturer, a bank worker, or a consulant. (At least one of those would only be temporary.) In any of those fields, I’m not getting my hand held any more. I love this conference. There are 4 afternoon concurrent sessions and I want to go to three! And I can contribute to them. Welcome to the Grown-up Table, Adam.

That was transcribed from my luncheon notes. I’ll add one other quote here. Steven Levitt received the Harry Roberts Statistical Advocate of the Year award, and gave about a half hour of remarks. He talked about the difference between statistics advocate and policy advocate. I had been seated at a table with Mark Berenson, a true policy advocate; his daughter Lori Berenson is a political prisoner in Peru. He was there last weekend, visiting. There’s one good quote from Professor Levitt. He had talked to a high class Chicago callgirl, who was charging $300 an hour. $200,000 yearly for ten hours a week is good, but she dreaded hearing the phone. He tried to convince her to raise her rates. Later, he invited the callgirl to speak to his class on the economics of crime. In response to a question, her rates were now $400 an hour. As she said, “Professor Levitt convinced me my services were far more valuable than $300.”

Mathematics After The Fall

There’s this undergraduate I know, Patrick. He’s a third year at the University of Chicago, occasionally posts to
his blog, prefers
traditionalist liturgy, and most importantly likes theoretical
mathematics. We actually took Math 207-208-209 together two years ago,
him as a freshman (my blog gets to use this term, as it is quite
appropriate) and myself as a second year doctoral student in Statistics.
We didn’t know each other, though, until we recognized each other around
Easter. Patrick sat in the front and was diligent; I sat in the back
and was lackluster, though a large part of that was due to health
reasons. At one point last school year, we got to talking in the lounge.
I wondered about his academic intentions. With the hubris of a
teenager, he touted the wonders of the mysterious field, group, and
topological space. I countered with the joy of searching the numbers of
applied statistics. Like most theoreticians, admittedly including me
when I was 17, he found the messiness unattractive. I think his actual
phrasing was like “statistics is mathematics without honor.” My
rejoinder translated an old political saying, “Statisticians are
Mathematicians Mugged by Reality.” (Substitute Republicans for Stats,
and Democrats for Maths.) Another quip from Patrick’s mouth is that “Statistics is Mathematics after original sin.” Unlike his first one – my strong sense of personal dignity really does not appreciate a challenge to honor – this one has potential. I like it. A lot.

For those of you not intimate with Genesis, let’s review original sin. To begin Chapter 3, Eve and Adam are just hanging out in the Garden of Eden, naked in a pleasure park. Earlier, the Lord told Adam not to eat from the tree of knowledge of good and evil, on pain of death, and Eve knows too. The cunning serpent stops by, just to chat. He mentions that if they eat the fruit, they will not die, rather “your eyes will be opened and you will be like God who knows what is good and what is bad.” Eve eats the fruit and gives some to the man, who also feasts. The serpent’s statement is true, and they realize a lot of things, including nudity, shame, and evil. When God next stops by, they hide, and God realizes what they’ve done. The man blames it on “the woman you put here with me”, and the woman claims trickery on the serpent’s part; neither gender comes out well. The Lord is kind enough to make them leather garments before booting them from Eden. The term original sin is used to apply to this act, the loss of trust in the Lord, the need to search for seeming wisdom. The consequences are dire, as Adam and Eve lose the state of original holiness, and fall into decay and death. The story is in some ways allegorical, but the fundamental fact of the search for individual glory is true. After all, a friend once noted that the only doctrine of faith that can be empirically proven is original sin.

How do we respond and organize our thought? I don’t recall much from my Catholic theology elective as an undergraduate, but I remember a discussion on “from Below” and “from Above”. The terms are applied to Christ and Church. The Catholic belief is that Jesus is both human and divine. Early church history contains many false beliefs and starts away from this path; most of the false paths denied one of Christ’s two natures. (The Arians with logos denied both, but this site is not designed to expand on Nicaea and Chalcedon.) If one looks only at divinity, one looks at Jesus from Above, and denial of divinity means looking from Below. It’s not that hard to extend the concepts of Above and Below to the world. Patrick’s preferred study, theoretical mathematics, is world from Above; he creates structures irrespective of what humans perceive, then assigns the world into those structures. My preferred study, model development, is world from Below; I examine the rhythms and patterns that humans perceive, then create structures that attempt to contain those data elements.
At extremes, both Above and Below are problematic. Mathematical theorists can receive doctorates without considering a set that exists on earth. That denies one of the two natures of the world. It presumes a pure divinity, one without decay, death, or uncertainty. Theologically, it’s Gnostic, wanting only the symbolic. On the other side, applied statisticians grab hip waders and jump into the streams of despair. This has its problems; focusing so much on collection and optimization can form no structure, and grasp no sense on the underlying unity. Model builders become fully human; theologically, it’s A-Gnostic, wanting none of the symbolic.

To break this impasse, I go back to Original Sin. In Eden, my namesake had no knowledge of good and bad; his world was clean. After the fall, humanity was booted into a world with good and evil, and more importantly the knowledge of such. Becoming like gods means that we perceive, interact, and change the world. That requires investment in the causes and actions of earth. Running away from that, as some mathematicians do, fails in our humanity. It also denies the God on earth, the Spirit promised and delivered. I can’t see how it can be ignored.

Thus, when Patrick calls me a “Mathematician After the Fall”, I take it as a compliment. We all should be. I’ve even thought about a new title for this site, “Mathematics in a Fallen Land”. Given my consulting on foster care systems this year, it feels even closer. The image is appealing; walking the country, a long black coat flapping in the breeze, saddlebag and laptop computer on my back. I come into town, find the problem, put together the model, take the payment, and ride out on the sunset. Maybe that’s why I like consulting; I even have the soundtrack.