Today’s reading is “Prior Knowledge on the Illlumination Position” by Pascal Mamassian and Ross Goutcher of the University of Glasgow (Cognition, 2001 [PDF link]).

When we see an embossed seal such as a notary stamp, how do we know which parts are convex (bumps) and which are concave (dimples)? When we look at such a seal through a microscope (or even a toilet paper roll), so that we don’t know where the illumination is coming from, we can’t tell what’s up and what’s down. This effect was first recorded in 1744, and first accurately explained in 1786 by David Rittenhouse: we assume the light is coming from over our heads; if the light isn’t coming from where we expect, then we reverse the image. This makes sense: most of the time in the natural world, that’s where the light is coming from. This preference doesn’t appear to be learned: baby chicks raised with light coming only from below still behave as if the light source is above them.

Over the course of the twentieth century, some of the researchers investigating this problem noticed that the observers in their experiments not only preferred the light source to be above their heads; they expected it to be slightly to their left as well. This phenomenon made no sense: people don’t tend to orient themselves with the sun to their left. The scientists were so certain that this finding was in error that they simply discarded results from observers who favored light from the left.

Mamassian and Goutcher suspected that we may really have a preference for light sources on the left, so they devised an experiment to test it. Consider the following two objects:

If we imagine we are in a room with very low light, coming from above, and we’re looking at the objects head-on, they will look like this:

Notice that if you turn the image on the left upside down, you see that it’s actually the identical image. What Mamassian and Goutcher did is take this figure and rotate it in increments of 15 degrees. Then they asked observers whether it looked like the wide bars or the narrow bars were projecting out from the figure. In fact, observers were looking at the same image each time, so their responses would reflect only where they perceived the light source for the image to be.

They found that observers were most consistent in their responses when the light appeared to be coming from about 25 degrees to the left of vertical. It didn’t matter whether observers were left- or right-handed; all observers had the same preference.

Mamassian and Goutcher suggest that a possible explanation for this result might be a “visual field bias.” When recognizing at people’s faces, for example, we tend to pay more attention to the right-hand side than the left. If the light source is on the observer’s left, then the right side of the person they’re looking at is illuminated.

Brad DeLong is quoting a long explanation of the Bush Social Security plan by Matthew Yglesias

The White House says the average worker can expect a 4.6 percent real rate of return on his private account. Under explanation two, this makes borrowing the money at a 3 percent rate turn out to be a smart investment move. You get a 1.6 percent net return. Under explanation two, it’s a little hard to see why taking the private account is the right move, but the math comes out the same way, a 1.6 percent net return. Thus, having already implemented phases one and two, the private accounts are a good deal for workers. Phase two and — especially — phase one, however, are terrible deals for workers. The cuts undertaken in step two (and made necessary by phase one) are bigger than the gains you can make by starting your account.

Not that I’m in favor of the Bush plan (Anyone who’s read my earlier rants knows I’m not), but it seems to me that Yglesias is making a significant error. He’s comparing the 4.6 percent REAL return to the 3 percent interest rate. The real return takes inflation into account; the interest rate does not. If you’re going to compare these two figures, you need to either adjust the interest rate for inflation or look at the non-adjusted return on investment.

If the real return is 4.6 percent and the interest rate is 3 percent, the actual difference will be more than 1.6 percent. As many have pointed out, however, if the real return on stocks is 4.6 percent for the next 75 years, we’ll have experienced such amazing growth that the Social Security “problem” will have vanished whether we adopt the Bush plan or not.

The real problem is that Bush is advocating margin investment as a way to bring the lower income sectors into the stock market. Not a good idea. Another huge problem, which Yglesias hints at, is assuming the interest rate will remain stable at 3 percent. Not a very good assumption, given the huge increase in borrowing that will be necessary to pay for this program. Even if we do see such astonishing economic growth over the next three-quarters of a century, some people will come out in the hole. Some people will be hit with the double whammy of Bush’s Social Security cuts and the personal debt they owe to cover their private accounts. Instead of a social security program we’ll have a social lottery program.

Regardless of the state of the economy in 75 years, the Bush plan will never guarantee that everyone has a liveable benefit. Someone will lose out: in order for the average real return to be 4.6 percent, some people will have to earn much less. If, as seems likely, the economy does worse, then many more people will be left out in the cold, and the price we’ll all pay to undo the damage will be even greater.