In the article on the caregiver's dilemma, Francine Russo offers research-based advice to help family members and friends maintain their own psychological well-being while tending to a loved one who is elderly or disabled. Some of our readers shared comments on Facebook. Shiby Sahadevan writes, “It takes umpteen hours of thoughtful service to keep up the spirits of those who need constant care. Finding your footing and recuperating are not easy unless you are surrounded by family.” Odessa-Nanette Fields notes, “The psychological health of caregivers is so important, especially with the growing numbers of aging baby boomers needing some form of assistance.” Elise Kathleen adds, “So glad you're tackling this issue!”


I enjoyed Sunny Sea Gold's article “How to Be a Better Forgiver” [Head Lines]. Having done a lot of forgiveness work myself, I found the ideas relevant and useful. I would like to see a longer article that goes into more depth and discusses the work of Robert Enright, a professor of educational psychology at the University of Wisconsin–Madison, who established the International Forgiveness Institute.

I took a seminar with Enright 20 years ago that turned my life around. I was reeling in the vortex of a very nasty divorce, and he showed me a way to take care of myself and stay on the high road. Since then, his teachings have helped me maintain my equanimity in other difficult situations.

I was disappointed to see that Gold didn't mention Enright or the institute. Please share with your readers the name of the organization. There's a wealth of great information that can help people struggling with feelings of resentment and guilt.

Thanks for a great magazine.

Dave Birren
Stoughton, Wis.


After reading Meredith Knight's story “Weight-Loss Surgery Alters the Brain” [Head Lines] and the hypothesized mechanism responsible for the sudden brain activity (the rapid, novel contact of undigested food hitting the stomach), I couldn't help but wonder how the transmission or activity of the satiety hormone leptin might be altered by bariatric surgery. Are greater levels of this hormone a response to the changes pursuant to the procedure?

Andrea Dasilva
Vancouver, B.C.

KNIGHT REPLIES: Leptin does appear to play a role in appetite changes after gastric bypass surgery, but the details are far from certain. For instance, some studies have found a decrease in blood levels of leptin after surgery, which is somewhat expected because leptin is generated by fat cells. But other studies showed no change in leptin levels after surgery and resulting weight loss. Intriguingly, genetically engineered mice with disabled leptin systems do not lose weight after bariatric surgery. But the system that regulates appetite is complex, and our knowledge of it is slim. Other substances also play a role for bariatric patients. GLP-1, another hunger-inhibiting gut hormone, is more directly affected. A wealth of studies have shown that its concentration increases after bypass surgery in both mice and humans.


Jo Boaler and Pablo Zoido's article “Why Math Education in the U.S. Doesn't Add Up” [Perspectives] itself does not add up. The resistance to “memorization” and “rote procedures” and the uncritical privileging of “open, visual, creative inquiry” do not accord with a good deal of research in cognitive and educational psychology. Psychologists have shown that students are at first novices with respect to academic skill and subject matter, but a structured and directional approach helps to build long-term memory and frees up working memory to more effectively tackle a given task or problem. Then as core skills, knowledge, fluency and automaticity develop, students can move on to (guided) open, visual and creative inquiry.

Andrew J. Martin
Professor of educational psychology
University of New South Wales

BOALER REPLIES: It is a well-known scientific fact that sometimes committing something to memory through automation frees up working memory to tackle problems. What is not established is the timing of such actions or their place in classrooms. Some studies support the belief that automation should precede understanding, but this order is not necessary and has led to unhelpful instruction in schools, in which teachers try to drill students with methods that they do not understand. This can lead to a misunderstanding and dislike of mathematics. Many studies show that when students are introduced to number sense and encouraged to understand numerical relations they can later commit methods to memory and become effective and engaged mathematics students. Mathematics education has suffered from an overemphasis on drill and repetition, and that is shown in the data from the Program for International Student Assessment; it is important to dial this back. The focus of mathematics teaching and learning should be on conceptual understanding, aided, when appropriate, with memorization of what is understood.


I would argue that the metaphors presented in “How We Make Sense of Time,” by Kensy Cooperrider and Rafael Núñez, are directional, not spatial, and that the metaphor “time is like space” introduces a false dichotomy. One of Einstein's great insights was that time and space are not separate. The big bang produced spacetime, not time and space. Scientists define a second as a certain number of complete oscillations of a cesium 133 atom. More generally, the definition of anything involving time (for instance, velocity, day) involves motion.

One of my takeaways from the authors' studies is that there is a universal understanding—without knowledge of modern physics or metrology—that time is perceived and actualized as motion. The examples presented provide culturally different views of the direction in which time moves. They are metaphors about the unified nature of time and space, not about time being like space.

Charles H. Jones
Eugene, Ore.


Matthew Hutson mentions the trolley or railway switch test of morality in “Why We Love Moral Rigidity” [Head Lines]. The test, as usually posed, involves the decision to push an overweight man off a footbridge to block a trolley from killing five rail workers. Psychologists really should devise a more realistic thought experiment to get meaningful results. Except for employees of the railway company, how could I ever be in a position to know enough to decide that changing a switch might save lives and then to actually do it in time? It is even more implausible that tossing a person onto the tracks will slow a train sufficiently to alter the amount of damage it will do. And are the five rail workers all totally deaf? Fast-moving trains are loud. If I do nothing, all I can be accused of is cowardice. I will accept that rather than risking life imprisonment for murder.

Martin J. Greenwood
Stirling, Australia

THE EDITORS REPLY: Ethicists have devised many thought experiments that call for even greater leaps of the imagination. The purpose of these thought experiments is not to represent a plausible scenario but rather, through metaphor, to illustrate a particular principle.