Voyagers to the Stars,” Tim Folger’s article on the history and the status of the Voyager spacecraft. But I was puzzled when he mentioned that Voyager 1 and 2 will continue their journey and pass the nearest neighboring star, Proxima Centauri, in 16,700 and 20,300 years, respectively.

NASA’s website says that the Voyagers won’t reach the halfway point to Proxima Centauri for 40,000 years and will travel two light-years to do so. If I use the speeds given at NASA’s Voyager mission status web page and assume 365.25 days in a year, I get approximately 70,000 years for Voyager 1 and 78,000 years for Voyager 2 to travel four light-years.

JOHN CARY Sacramento, Calif.

The graphic in the box “The Longest Voyage” shows both Voyager spacecraft making abrupt course deviations from the plane of the solar system. What was the cause of these course changes? Were they the result of programmed flight changes or some aspect of leaving the solar system?


FOLGER REPLIES: To answer Cary: In 40,000 years the Voyagers will reach the outer edge of the Oort cloud, which is indeed about halfway to Proxima Centauri. But tens of thousands of years before that time, Voyager 1 and 2 will make their closest encounter with that star, coming within about 3.5 and 2.9 light-years of it, respectively. That’s not very close: the sun is currently about 4.2 light-years away from Proxima Centauri. On a cosmic scale, the sun and the Voyager spacecraft are essentially the same distance from our nearest stellar neighbor. But because the spacecraft are moving away from the sun, and Proxima Centauri is moving toward it, the Voyagers’ closest approach to our neighboring star will occur in 16,700 and 20,300 years.

Regarding Schonrock’s question: Voyager 1’s trajectory was designed to take it as close as possible to Saturn’s moon Titan. That trajectory eventually took Voyager 1 “north” and out of the ecliptic—the plane of the solar system. Voyager 2’s path was designed to take it beyond Saturn, to Uranus and Neptune. That path sent Voyager 2 “south” of the ecliptic. These weren’t course corrections. Rather the spacecraft were just following the paths that would give scientists the best views of the outer planets.


In “Climate Miseducation,” Katie Worth reports on the shockingly disproportionate influence that the fossil-fuel industry has in setting science education standards in Texas, which consequently influence much of the textbook content throughout the U.S. As a science educator and school sustainability leader at an international school in Italy, I found the process in Texas of setting standards based on volunteer committees and decision-making by members of the State Board of Education extremely worrying. But I do not entirely disagree with their push to include a “cost-benefit analysis” of energy resources. While there is little doubt this is an attempt to divert attention from the need for climate action, I also see an opportunity.

Too often human impact on the environment is reduced to a “mea culpa” description, with little analysis of decision-making mechanisms that often have led to even further devastation of the environment. Students must acknowledge and demonstrate an understanding of how and why environmentally poor decisions are made to realistically and authentically offer alternatives. By allowing them to analyze the costs and benefits associated with fossil-fuel usage—and who pays—they will certainly come to the same conclusion as any other rational scientist: Although the start-up costs are great, converting our society to renewable energy will save us from the dramatically greater health, social, economic and environmental costs associated with continuing on the current path. And no, it won’t be a perfect solution.



Adam Fishbein’s fascinating article “How Birds Hear Birdsong” [May] made me wonder about some issues that I encounter in my own research on popular music singing. It was no surprise to me that the “melodies” birds sing are more of a vehicle for what they are actually communicating through sonic “fine structure.” I found the article was based on a very Western way to think about language and music by focusing on abstractions rather than actual sounds. But in Fishbein’s defense, this is widely the case in the field.

First, the idea of limiting the conception of music to mere notes (what I call “abstract parameters”), which has been shared by many “traditional” musicologists and music theorists, is now being strongly questioned. Indeed, recent research suggests that popular music listeners, while of course sensitive to pitches (melody), also especially react to aspects of sound production related to timbre. In popular music singing, paralanguage (the surrounding sounds we emit when speaking that are often wrongly considered mere noises) is used systematically to convey rather specific emotional content. Melodies, though essential, act as vehicles to such paralinguistic production.

What about tonal languages such as Mandarin Chinese, for example? Studies show that Chinese speakers have a much better ability to identify pitch by ear, or “perfect pitch.” While most people recognize a given melody when it is sung in a different pitch despite its new key, there is a large proportion of the population that can hear the shift. For many musicians, each tonality culturally conveys its own emotional signature.

In the research conducted by my colleagues and me—as well as by many other musicologists around the globe—we study microvariations in timbre that are very similar to the fine structures described in the article using the very same tools (waveforms and spectrograms). Many researchers are interested in such finer structures in music precisely because humans are very sensitive to microvariations in timbre (perhaps even more than they are to melodic structures), as well as to those in rhythm. In fact, we came to realize that the lack of study on humans’ ability to precisely perceive these finer structures was based on millennial-long Western ideology favoring the abstract over the concrete.

I believe that topics such as birdsong would be a perfect terrain for true interdisciplinary research. We, as musicologists of microvariations, are absolutely ready to contribute (well, at least, I am!).

SERGE LACASSE Full Professor of musicology, Laval University, Quebec

FISHBEIN REPLIES: Lacasse makes excellent points about the importance of microvariations in music and language. I wholeheartedly agree that this topic is a ripe terrain for interdisciplinary research. Birdsong studies often attempt to draw parallels to syntax and other more abstract parameters of language and music, but I think humans and birds are more similar when it comes to extracting emotional content from subtle changes in sounds. Still, it is the case that songbirds, at least the species studied so far, do appear to be much better than humans at hearing changes in fine structure. This may be because of fundamental anatomical differences in the structure of the inner ear. And although melodic structures in music differ across cultures, the ability to hear melody is universal in humans. Songbirds simply appear to not hear strings of sounds as melodies like we do.

This article was originally published with the title “Letters” in Scientific American 327, 5, 6-9 (November 2022)


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