Projection

Giridhar Madras on his blog commented on this report. To be perfectly honest, I did not read the entire original report, for two reasons: (i) I don't like artificial boxes, and (ii) I don't like artificial boxes whose labels and contents are not consistent. As soon as I realized this "study" suffered from both these afflictions, I figured I had better things to do.

Let me take reason (ii) first. Teaching load alone is a terrible metric to measure anything other than teaching load, and even there it is an uneven measure. It is harder to teach engineering design to a small class than an introductory class to a large freshman class. In the same way, research dollars are a pathetically inadequate way to sniff out true "pioneers".

Not everything that can be measured is of value, and not everything of value can be measured.

I seriously shudder at the prospect of such studies being taken seriously.

I have never been a big fan of such simple-minded measures. I gather this fascination has something to do with out inability to grope with multidimensional complexity. We try to project a complex high-dimensional space onto a simple scalar. We like scalars because we can intuitively compare two scalars. We can order them, plot them on graphs, and run statistics on them with ease.

Unfortunately, the rules of projection are often arbitrary (like this study), and the resulting scalar is of marginal value. The trouble is that they get taken seriously.

This disease is everywhere.

Using academic rankings to choose a university, using IQ to measure intelligence, using impact factor to measure journals etc.

Links:

1. Khan Academy: Wired has an article on the implications of Khan academy for the traditional classroom.

Initially, Thordarson thought Khan Academy would merely be a helpful supplement to her normal instruction. But it quickly become far more than that. She’s now on her way to “flipping” the way her class works. This involves replacing some of her lectures with Khan’s videos, which students can watch at home. Then, in class, they focus on working problem sets. The idea is to invert the normal rhythms of school, so that lectures are viewed on the kids’ own time and homework is done at school. It sounds weird, Thordarson admits, but this flipping makes sense when you think about it. It’s when they’re doing homework that students are really grappling with a subject and are most likely to need someone to talk to.

2. The Engineer Guy: What Khan academy tries to do with high-school topics, this site tries to do with engineering/technology topics.

Is higher education a bad value proposition?

Two recent "finance/econ" type articles seem to take opposite sides in this debate. On the one hand Vikram Manasharmani argues that higher education exhibits all the tell-tale signs of a classic bubble (it is useful to keep the recent US housing crisis looming in the background).

These include, among others (a) an unquestioning faith in the "assets" value, (b)  availability of easy credit to buy the asset, and (c) increasing participation of value-insensitive buyers.

The net result has been that the price of higher education has outstripped inflation in recent years by more than 5% at public institutions. The total student loan debt is apparently on track to beat the total credit card debt this year.

The other side of the debate comes from unemployment statistics. Saj Karsan presents a chart which breaks down unemployment numbers by education level.

It is nearly 15% for people without a high-school diploma, and about 4.4% for people with bachelors degree. As he notes:

Note that the overall unemployment rate in 2007, when the American economy was booming, was 4.6%, which is higher than the current unemployment rate of 4.4% for those with Bachelor's degrees. This data suggests (although it does not prove) that there is a shortage of educated workers in the US.

Printing Webpages

Many websites offer printer-friendly versions of documents (Google Maps for instance). When they don't, printing can be a messy affair, with blank pages, useless ads, and corrupted formatting. Recently, I found two nice browser-based utilities that make life a little easier.

1. PrintFriendly: This is simple tool, without many bells and whistles. You simply enter the web address, and it returns a simplified, printer friendly version. You can then save it as a pdf or directly print it. It allows you to make minimal changes, such as deleting some items, before you choose to save or print it.

2. Printwhatyoulike: This site supposedly offers you more control over which items you choose to display. There is also a utility which lets you "zip-pages" (combine long articles which require you to press "next" 10 times) into a single document. I tried to use this a little, but my results weren't all that great.

Orthogonal Polynomials: Mathematica

Orthogonal polynomials are everywhere.

The following Mathematica program takes in a weight function (as a function of x), the domain (a and b), and spits out the first "n" corresponding orthonormal polynomials.

OrthoPoly[w_, a_, b_, n_] := Module[{monoBasis, T},
  monoBasis = Table[{x^i}, {i, 0, n - 1}];
  oP = monoBasis;
  oP[[1]] = oP[[1]]/Sqrt[Integrate[w*oP[[1]]*oP[[1]], {x, a, b}]];
  For[i = 2, i <= n, i = i + 1,
   For[T = 0; j = 1, j < i, j = j + 1,
    T = T + Integrate[w*oP[[i]]*oP[[j]], {x, a, b}]*oP[[j]];
    ];
   oP[[i]] = oP[[i]] - T;
   oP[[i]] =
    oP[[i]]/Sqrt[Integrate[w*oP[[i]]*oP[[i]], {x, a, b}]] //
     Simplify;
   ] ;
  oP
  ]

Here's a screenshot, for the first four Chebyshev and Legendre polynomials (click to enlarge). Note that these polynomials are unique up to a multiplicative constant. Orthonormality freezes that constant.

Gary Taubes: Why we get fat

In this YouTube video, Gary Taubes of the "Why we get fat" fame, delivers a hour and half long lecture on Google's campus. Somewhere in the first five minutes, Gary Taubes says that this talk is a Cliff Notes version of the book (which apparently is a Cliff Notes version of his more fully fleshed book "Good Calories, Bad Calories").

As if all this was not enough, here's a Cliff Notes version of the talk:

Taubes compiles historical data, and argues that casting fat/weight reduction into a "Eat less, Exercise more" regimen, misses the point. I like the example, where he says that, that is exactly what you would do, if you had to work up an appetite. The primary claims of Taubes' critics seems to be that (i) he edits conversations with experts (many of his interviewees seem to have "recanted"), and (ii) he commits a crime of omission by not engaging the large body of research which contradicts his claims.

Essentially he upsets the implied causal connection between weight loss and negative energy balance, as implied by "accumulation = input - output", by suggesting that the "=" does not tell us what causes what.

The culprit is apparently insulin, which is released when carbohydrates are consumed. Insulin encourages fat cells to store fat. Mice that are injected with insulin, and then underfed, tend to become obese. The message is therefore to avoid carbohydrates, and actually consume fat (like Atkins diet).

It is a compelling point of view, but apparently still quite controversial. Here is a story countering Taubes' initial article in NYT. Here is Taubes' response. Here is the response to the response.

Links: July 4th edition

1. James Altucher on how we can get rid of Congress, and replace the republic with a true democracy. Beneath the cloak of irreverence are a few potentially interesting ideas.

2. BugMeNot: The subtitle "Bypass Compulsory Registration" says it all. Essentially allows you to find or share login/passwords for sites that force you to register before reading on (via Simple Dollar).

3. A portrait of the irresistible Jon Stewart of "The Daily Show"

Why we have college.

Louis Menand in the New Yorker examines the issue.

Soon after I started teaching there (a public school), someone raised his hand and asked, about a text I had assigned, “Why did we have to buy this book?

I got the question in that form only once, but I heard it a number of times in the unmonetized form of “Why did we have to read this book?” I could see that this was not only a perfectly legitimate question; it was a very interesting question. The students were asking me to justify the return on investment in a college education. I just had never been called upon to think about this before. It wasn’t part of my training. We took the value of the business we were in for granted.

Is the role of higher education to sort students according to intelligence, skill or merit, or is it to ensure that everyone has access to knowledge and the goodies that accompany it? As he argues:

A lot of confusion is caused by the fact that since 1945 American higher education has been committed to both theories. The system is designed to be both meritocratic (Theory 1) and democratic (Theory 2). Professional schools and employers depend on colleges to sort out each cohort as it passes into the workforce, and elected officials talk about the importance of college for everyone. We want higher education to be available to all Americans, but we also want people to deserve the grades they receive.

And one of the many facts that I did not know

In 1940, the acceptance rate at Harvard was eighty-five per cent. By 1970, it was twenty per cent. Last year, thirty-five thousand students applied to Harvard, and the acceptance rate was six per cent. ... Columbia, Yale, and Stanford admitted less than eight per cent of their applicants. This degree of selectivity is radical. To put it in some perspective: the acceptance rate at Cambridge is twenty-one per cent, and at Oxford eighteen per cent.

It is an interesting read.