The title of the single-topic issue “Beyond the Limits of Science” left me scratching my head. To my eyes, the issue was packed with accounts of topics firmly within the limits of science. Science does have its limits, but I cannot understand why Scientific American would portray indisputably scientific endeavors as being beyond them.

Zachary Miller
Fleetwood, Pa.


In “Beyond the Quantum Horizon,” David Deutsch and Artur Ekert describe how a π/2-pulse—a pulse of light with the same frequency but half the duration or amplitude of a π-pulse that would change the state of an atom's electron from 0 to 1, or vice versa—works in the computation for finding the square root of NOT (a logic gate in which inputting 0 or 1 results in the opposite figure). The authors state that if you “start with an electron in state 0, send in a π/2 pulse, then send a second π/2 pulse,” the electron will be in state 1. Yet how is this possible unless the superposition state retains a “memory” of where it came from? Wouldn't the second π/2 pulse have equal probability of bumping the superimposed state into either sharp state?

Robert Friefeld
Long Beach, Calif.

EKERT REPLIES: Two consecutive applications of the square root of NOT convert 0 to 1, or 1 to 0, but the intermediate superpositions of 0 and 1 are not the same in the two cases. Although both superpositions contain the same proportion of 0 and 1, they differ in the relative phase between the two. Thus, the superposition state indeed retains a “memory” of where it came from. The square root of NOT would be impossible if there were only one equally weighted superposition of the states representing 0 and 1.


“Machines of the Infinite,” by John Pavlus, states that the “universe itself is beholden to the computational limits imposed by P versus NP,” the question of whether tough problems whose solutions can be quickly verified can also be quickly solved.

This is a common misunderstanding. Nothing in the real world (whatever that is) is constrained in any way by our mathematics, physical laws or anything else we invented. Mathematics is merely a useful tool created to describe the universe. When we find something that we can't calculate or describe with our math, it may be that we've found a limit or constraint on the universe; it could also be that we've found a limit or constraint to our mathematics.

Ted Grinthal
Berkeley Heights, N.J.


“Can We Keep Getting Smarter?” by Tim Folger, referred to researchers having attributed the Flynn effect, the fact that IQ scores have been steadily rising since the start of the 20th century, to the world perhaps becoming increasingly representational rather than actual. Yet that doesn't necessarily make us smarter. If an IQ test asked something like “How are fire and deer similar?” a modern person might answer that both words have four letters or one syllable. Most hunter-gatherers, however, would know about the concept of using fire to manage deer habitats. And even in the fairly recent past, people off the street knew how to make soap or to shoe a horse.

Because modern people interact with computers in a graphical user interface and have grown up playing video games, it is natural for us to quickly respond to simple geometric shapes. But a modern person in an unfamiliar environment can't respond to three-dimensional shapes in the same way.

“Smart” is a relative term. Our ancestors would marvel at how stupid we are that we can't even skin a rabbit or operate a printing press.

Tom Whitley

I question using the abstract-reasoning sections of the Wechsler Intelligence Scale for Children (WISC) as proof of rising intelligence. Folger points out the paradox of these supposedly “culture-free components of intelligence” seeming to be altered by culture, but he doesn't mention that the tests themselves have altered the culture. After the tests were used, their concepts were everywhere, such as in books of puzzles and popular magazines. It is no wonder that each new class of children knew more correct answers.

Richard S. Blake
East Falmouth, Mass.


“How We All Will Live to Be 100,” by Katherine Harmon, reports on different strategies proposed to further increase human life span beyond what appears to be an approaching limit.

A 2005 paper by S. Jay Olshanksy and his colleagues in the New England Journal of Medicine has argued, however, that the U.S. might face a decline in life expectancy this century because of an increase in obesity, diabetes, hypertension and accompanying comorbidities. Considering such factors, a separation of wealthy and less privileged countries might represent more in-formative projections.

Harmon also writes that advances in sanitation might continue to extend our life expectancy. If the hygiene hypothesis is true, above a certain threshold, however, increased sanitation might have an opposite effect by increasing the rate of autoimmune diseases.

Thomas Boehm
Medical University of Vienna


“Questions for the Next Million Years,” by Davide Castelvecchi, explores environmental questions such as seismologist Thorne Lay's thoughts on the future commonness of large earthquakes, but several really big issues on the subject are overlooked. For instance, the biggest earthquake might topple every building in Los Angeles, but the atmospheric pollution generated by an eruption of the volcano in Yellowstone National Park would endanger everyone on the planet. How often do such supervolcano eruptions occur? The last was about 75,000 years ago, but Paleolithic scientists never published their observations.

Gerald Davidson
Red Lodge, Mont.


“The Winters of Our Discontent,” by Charles H. Greene [December 2012], referred to the National Climatic Data Center forecasting a mild 2010–2011 winter for the eastern U.S.; that forecast originally came from the National Oceanic and Atmospheric Administration's Climate Prediction Center. The article also described La Niña as bringing warmer, mild winters and El Niño bringing colder, harsher ones; La Niña should have been described as bringing drier, mild winters and El Niño as bringing wetter ones.

Further, the article stated that by early March 2012, a strong and persistent atmospheric high-pressure system developed in the eastern Pacific; it should have said that the already existing high-pressure system in that region strengthened. The article also indicated that in certain circumstances El Niño and La Niña steer the trajectory of the jet stream; they do not steer it but are associated with climate conditions that can affect the jet stream's path.