VIEW FROM THE VOID
“Cosmic Nothing,” by Michael D. Lemonick, describes large empty areas of the universe called voids. It includes a quote from astronomer Gregory Scott Aldering concerning a void in the constellation Boötes: “If the Milky Way had been in the centerof the Boötes void, we wouldn’t have known there were other galaxies [in the universe] until the 1960s.” What technology came into play at that time that would have allowed us to see and identify galaxies for the first time?
RICK FRANEY BELLINGHAM, WASH.
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In the same manner as the scenario with the Milky Way and the Boötes void, I would imagine that if our present universe were in a huge void with a radius of more than 14 billion light-years, we would not know of other universes outside it. What are the possibilities of that?
HIROYUKI UCHIDA TOKYO
LEMONICK REPLIES: Regarding Franey’s question: Aldering may well have been referring to electronic detectors that replaced photographic plates used for recording the light gatheredby our biggest telescopes. These detectors were invented in the late 1960s, although they weren’t used in earnest in astronomy until a few years afterward.
To answer Uchida: It’s interesting to speculate about what things would look like if our entire universe were inside a gigantic void, but we know of no way such a void could be created. The voids I discuss in the article were formed mostly by the effects of dark matter and dark energy in an expanding universe. Something else would be necessary to create a void more than 28 billion light-years across.
SUPPLEMENTAL DAMAGE
As a physician who embraces critical thinking, I appreciated “The Rise and Fall of Vitamin D,” by Christie Aschwanden. The article focused on how worries about widespread vitamin D deficiencies are overblown. There are also dangers of vitamin D excess, which can cause hypervitaminosis D. This condition involves acute toxicity caused by high levels of calcium in the blood and can include confusion, vomiting and muscle weakness.
Vitamin D is fat-soluble, and as Aschwanden points out, it is stored in body fat and the liver. Chronic consumption of “megadoses” can lead to chronic intoxication, which may lead to kidney stones, bone demineralization and ectopic calcification. People can avoid toxicity when they get vitamin D from biosynthesis through exposure to sunlight.
There are many who think more and more consumption of vitamins must be beneficial. Taking megadoses of water-soluble vitamins and minerals just produces expensive urine and something to brag about at cocktail parties.
RALPH M. JONES CHILLIWACK, BRITISH COLUMBIA
WILD TILE
In “The Missing Piece,” Craig S. Kaplan describes the discovery of the first aperiodic monotile, a shape that can cover an infinite surface without repeating a pattern. It seems to me an inelegant loophole that mathematicians permit that tile (“the hat”) or the subsequently found shape called the turtle to be considered a monotile. Both must be reflected, which, in my mind, makes each two different tiles! The family of shapes called spectres repeat without flipping and were given arbitrary wavy edges to avoid reflections. But in physical reality, tiles generally have a definite front and back and can’t be just flipped, so there is no need for such edges in real life.
KEN WOOD NEWPORT, WALES
The pentagonal metatiles in the “Metatiles” and “Substitution (Metatiles)” diagrams are made up of slightly different shapes! I also notice that in the “Metatiles” illustration, the pentagonal metatile and the parallelogram-shaped metatile have the exact same underlying pair of hat tiles, which looks rather suspicious.
PHILIP KRAUSHAR VIA E-MAIL
At the beginning of the article there’s an illustration showing that regular pentagons don’t tile. I wonder, though, if the black kites in that illustration could be considered a second tile element and if the pentagons and kites together would be capable of an infinite tiling. If so, would that tiling be nonperiodic or aperiodic?
PETER FARSON EUGENE, ORE.
KAPLAN REPLIES: In response to Wood: Reflecting a shape indeed makes it behave quite differently in the real world (think of shoes, for example). We can see as far back as Euclid’s time, however, that a shape and its reflection are regarded as “the same” in geometry. To me, that legitimizes the hat as a true aperiodic monotile, although spectres are still interesting for their ability to avoid reflections.
Kraushar has done great detective work! At every level in our substitution process, the metatiles all flex slightly (except the equilateral triangle, of course). For that reason, we describe the rules as “nonrigid.” But they still work in that the analogousmetatiles at each generation combine to form supertiles using the same rules. The “Substitution (Metatiles)” diagram shows the theoretical limit of this flexing process: idealized shapes that truly are rigid. Needless to say, this was too much to explain in my article.As scientists are fond of saying, “see the paper for full details.”
To answer Farson: It’s definitely possible to create tilings with regular pentagons and 36-degree rhombuses (the black shapes in that diagram). German artist Albrecht Dürer even studied such tilings in the early 16th century. They’re quite beautiful, but they don’t form an aperiodic set: you can construct periodic tilings from these two shapes.
AGING AND BMI
“Stepping Off the BMI Scale” [The Science of Health], Lydia Denworth’s column on body mass index, did not mention changes in height as we age. At 83, I have lost about nine centimeters (3.5 inches) from scoliosis and kyphosis. My weight has not changed, but my BMI has gone up as my height has gone down. This is yet another reason to discount the BMI’s medical importance.
LAWRENCE GETTLEMAN VIA E-MAIL
ERRATA
“Quick Hits,” by Lori Youmshajekian [Advances], should have described niobium as a rare transition metal, not a rare-earth metal, in the entry about China.
“Not Your Father’s DNA,” by Sneha Khedkar, should have said that mitochondria power almost every type of human cell, not almost every human cell.
“The Era of Monster Telescopes,” by Phil Plait [The Universe; March], should have said that the area of a telescope’s mirror is proportional to the square of its radius, not that a telescope mirror’s area is the square of its diameter.
In “Last Stand,” by Alexis Marie Adams [April], the map of the Yaak River watershed incorrectly described Unit 72 as a 300-acre parcel. As noted in the main text, this area is 192 acres.