Today, I'm going to address the answer titled "You Think, Therefore I Am", from which I'll quote the first few paragraphs (but be sure to go to the Edge.com link above to see this and the rest of the answers):

"I think, therefore I am." Cogito ergo sum. Remember this elegant and deep idea from René Descartes' Principles of Philosophy? The fact that a person is contemplating whether she exists, Descartes argued, is proof that she, indeed, actually does exist. With this single statement, Descartes knit together two central ideas of Western philosophy: 1) thinking is powerful, and 2) individuals play a big role in creating their own I's—that is, their psyches, minds, souls, or selves.

Most of us learn "the cogito" at some point during our formal education. Yet far fewer of us study an equally deep and elegant idea from social psychology: Other people's thinking likewise powerfully shapes the I's that we are. Indeed, in many situations, other people's thinking has a bigger impact on our own thoughts, feelings, and actions than do the thoughts we conjure while philosophizing alone.

In other words, much of the time, "You think, therefore I am." For better and for worse.

An everyday instance of how your thinking affects other people's being is the Pygmalion effect. Psychologists Robert Rosenthal and Lenore Jacobson captured this effect in a classic 1963 study. After giving an IQ test to elementary school students, the researchers told the teachers which students would be "academic spurters" because of their allegedly high IQs. In reality, these students' IQs were no higher than those of the "normal" students. At the end of the school year, the researchers found that the "spurters'" had attained better grades and higher IQs than the "normals." The reason? Teachers had expected more from the spurters, and thus given them more time, attention, and care. And the conclusion? Expect more from students, and get better results.

*all*of the students were promising, one might ask, wouldn't all of the students have done well?

The answer is: maybe. But the Rosenthal study has a more intuitive interpretation in keeping with the assumption that humans are (at least boundedly) rational thinkers (at least sometimes). This explanation, as we'll see, suggests there's no magical stuff going on here. The Pygmalion effect results from teachers acting rationally given the information they obtain about their students's diverse abilities.

It goes like this. Suppose teachers want students to be successful. Suppose also that teachers have limited energy to spend focusing on any particular students. Suppose also that the laws of thermodynamics apply, so that teachers cannot invest energy in two things at the same time. Suppose also that investing energy in a student produces diminishing marginal returns because eventually the student cannot absorb further information. The relationship between the amount a student learns and the energy expended on that student might look something like this:

Now suppose that we have two students. One is intelligent and motivated: the model student. The other is not so intelligent or motivated. The model student can absorb more information; so the benefit of investing energy in that student doesn't diminish as quickly as for the other student. Suppose that the model student is three times better than the other student. Comparing the learning functions for these students might look like this:

Suppose the teacher wants to maximize the average success of these two students (actually, you can suppose the teacher wants to maximize the total success of the students; the results won't change). How much more time should the teacher spend on the model student? It turns out that the the teacher should spend on the model student an amount of time triple that of the other student, which is exactly how many times better the model student is than the other student. That's classic expected utility theory for you (some would call it the expected utility hypothesis, because human behavior appears to deviate in some contexts from that predicted by the expected value logic).

Thanks for everything, von Neumann and Morgenstern!

So what does this result mean for the Pygmalion effect? It means that we should have expected the teachers to invest more in what they believe is a better investment. The Pygmalion effect doesn't prove anything about self-fulfilling prophecies or any other such mysticism. It's just basic thermodynamics and classical economics. It also demonstrates a harsh reality of teaching: If teachers aim to maximize the average success of their students, they're going to focus less on the students who need the most help.

(Interestingly, if there weren't diminishing marginal returns to the teacher's investments, you'd expect the teachers to flip the bird to everyone but the best students.)

When it comes to my own research on migrants' decisions about how much money they spend on their family and friends back home versus themselves, diminishing returns is a crucial assumption. Whether migrants remit because they have altruistic inclinations toward their close kin, or they're maintaining relationships for self-interested reasons, they wouldn't send anything if there were linear or increasing returns to the dollars they kept in their own pockets. Since migrants from developing countries send more money to developing countries than official development aid organizations, we should be thankful for the existence of diminishing marginal returns.

For my own part, whatever the reason I care enough about my own family to send something home every month, I'm also thankful for diminishing returns. In fact, if there were no diminishing returns to anything at all, neither of us would have gotten out of bed this morning. Chew on that.