“The First Starlight,” by Michael D. Lemonick, discusses the formation of the first stars and galaxies in the universe.

Slight mention was made in the article of the role dark matter may have played in the process. Because dark matter will also have been drawn into the gravitational collapse that formed the first stars, these stars may have been bloated with this nonfusible dark matter, delaying star formation until the masses became enormous. Perhaps million-solar-mass black holes could have been formed directly from dark matter without a star phase at all, and these black holes became the seeds of the earliest galaxies.

Martin Urban
Silver Spring, Md.

Dark matter doesn't interact much, if at all, with normal matter and radiation. Would not black holes continue to gorge themselves on dark matter regardless of the intensity of the surrounding radiation field? Maybe the combination of black holes and dark matter has something to teach us about both.

Peter J. Turchi
Santa Fe, N.M.

LEMONICK REPLIES: Several readers have pointed out that dark matter must have had some role in the formation of the first stars and galaxies. Indeed, it did. Because dark matter doesn't interact with electromagnetic radiation, it was free to begin collapsing under gravity even before matter and energy were decoupled from each other about 400,000 years after the big bang. When that happened, there were already “halos” of dark matter whose gravity sucked in the ordinary matter that ultimately formed into the first stars.

Because it can't cool by radiating energy, dark matter can't collapse the way ordinary matter can, so it is hard to imagine how it could form a black hole. It is also likely that the amount within reach of even a supermassive black hole would be relatively small. Not much to gorge on.

In “The Great Net Debate” [TechnoFiles], David Pogue discusses net neutrality, the principle that Internet providers should not be able to charge varying amounts for different data or to discriminate against particular data by blocking them or slowing them down.

The way such providers currently charge their customers is perverse and needs to change. They charge a flat fee per month for unlimited high-speed Internet usage. The elderly widow who checks her e-mail twice a week pays the same as the twentysomething dude who downloads two Blu-ray movies every day.

Internet providers can adjust their fee schedule to make exactly the same amount of money as they do now. The only difference is that low-volume users will no longer be subsidizing high-volume ones.

Frank Weigert
Wilmington, Del.

In “False Hope,” Michael E. Mann explains that the slight easing of the rate of global warming during the past decade was not a “pause,” because temperatures still rose, and even if it proves to be more persistent than expected, that would give us only until 2046, rather than 2036, before our current emissions cause enough warming to harm human civilization.

I think there is an easy way to explain that this recent slowdown isn't a pause and that it's still leading to disaster. Consider a bullet speeding toward your head. It slows down, but it's still heading toward you. You have a little more time to duck, but if you continue to stand there, you're dead. We have a little more time to reduce or eliminate use of fossil fuels. If we continue with what we're doing, we'll have a catastrophe.

Ted Grinthal
Berkeley Heights, N.J.

In “The Secret Spiritual History of Calculus,” Amir Alexander argues that Jesuit mathematicians did not accept 17th-century Italian mathematician Bonaventura Cavalieri's “method of indivisibles,” in which every plane is made of an infinite number of lines and every solid is made of an infinite number of planes.

But Flemish Jesuit mathematician Gregory of Saint-Vincent developed a method that was essentially the same as Cavalieri's indivisible calculus in the 1620s, before Cavalieri.

Gregory hoped to use his ductus plani in planum method of summing infinitely thin rectangles to find a volume to solve the problem of squaring the circle. But his superiors in Rome refused to grant him permission to publish his work on the grounds that the method lacked a solid logical basis.

Ad Meskens
Artesis Plantijn University College Antwerp, Belgium

Alexander translates the Latin title of Italian mathematician Bonaventura Cavalieri's “In Guldinum”—his response to criticism from Swiss mathematician Paul Guldin—as “On Guldin.”

If Cavalieri had wished to say “On Guldin,” he would have written “In Guldino,” with the ablative case. The preposition “in,” with the accusative case, means against a person, as in “Against Guldin,” which was, plainly enough, the point of the response.

John Traill
Professor Emeritus, Department of Classics University of Toronto

ALEXANDER REPLIES: In addition to Meskens's account of the suppression of Gregory of Saint Vincent's ductus method in the 1620s, I would add the story of another Flemish mathematician, Jesuit André Tacquet, who showed an interest in indivisibles three decades later. Tacquet insisted that indivisibles were mere heuristic devices and denounced them for “destroying” geometry, but this did not mollify the Jesuit authorities. Superior-General Goswin Nickel ordered him to desist from original mathematical research, and he spent the rest of his days writing textbooks for Jesuit schools.

“Against Guldin” is indeed the right translation and more appropriate to the context.

In “Antibiotic Overkill” [Advances], Dina Fine Maron reports on a study finding that physicians who had signed a pledge to avoid unnecessarily prescribing antibiotics reduced such overprescription.

When I feel “cornered” into writing an “unnecessary” prescription, I write one but also explain why the antibiotic may not be necessary. And I give patients an option to wait for more specific signs of treatable infection and to call me if they choose to start treatment. I find that many prescriptions then go unfilled, with no harm.

I do not have numbers to show how effective this patient empowerment/education approach is, but I hope this letter, by itself, will reduce some overkill.

Janivara P. Umesh
Lakeland, Fla.

“Journey to the Bottom of the Sea,” by Mark Schrope, incorrectly referred to the epicenter of the 2011 Tohoku earthquake occurring below the seafloor. An epicenter is the surface directly above the place where an earthquake starts. The correct term is hypocenter.