We are fond of saying things are symmetric, but what does that really mean? Intuitively we have a sense of symmetry as a kind of mirroring. Suppose we draw a vertical line through the middle of a square.

This line cuts the square into two equal parts, each of which is the mirror image of the other. This familiar example is called line symmetry. But there are other kinds of symmetry that have nothing to do with mirrors.

For example, the square also has rotational symmetry.

Here we see the process of rotating a square counterclockwise about its center point (the intersection of its diagonals). After it rotates 90 degrees (one quarter turn), it looks the same as before. It is this transformation of an object so that the result is indistinguishable from the original that defines a symmetry. The above rotation is one symmetry of the square, and our example of line symmetry can be thought of as another.

Let’s take a moment to define a few terms. We will call the original object the “pre-image” and the transformed object the “image,” and we will use the term “mapping” to refer to the process of transforming one object (a point, a segment, a square, etc.) into another. A symmetry requires that the transformation not alter the size or shape of the object. A transformation that meets this requirement is known as an “isometry,” or a rigid motion, and the fundamental isometries are reflection over a line, rotation about a point, and translation along a vector.

Now we can continue our analysis of the symmetries of a square. We know that one symmetry is “line reflection over the vertical line through the center”; another is “rotation about the center counterclockwise by 90 degrees.” Are there others? What are they, and how many are there? As is often the case in mathematics, planning ahead and good notation will make our analysis much easier.

First, suppose I told you that we had transformed the square via a symmetry and this was the result.

Which symmetry was applied? Was the square rotated? Was it reflected? Of course it’s impossible to tell, precisely because of the criteria for a symmetry. To help us identify specific symmetries, let’s start by labeling the vertices of the original square.

Further, let’s agree that whenever we picture the original square, we will always imagine it to be labeled like this: The top left corner is *A*, the top right is *B, *the bottom right is *C, *and the bottom left is *D*.

Now when we transform the square, we can watch where the labels go. For example, after reflection through the vertical line through the center, the image of the square looks like this:

Relative to the original labeling, *A *is now in the *B* position and *B* is now in the *A* position. Similarly, *C *and *D* have exchanged positions. Taking the original labeling as *ABCD*, we denote the new labeling resulting from this transformation as *BADC*. This communicates that, under this transformation, *A* is mapped to *B*, *B* is mapped to *A*, *C* is mapped to *D*, and *D* is mapped to *C*. We can visualize how the notation works in the following way:

We will always take the starting position to be *ABCD*, so the relative position in the list describes where each original vertex is mapped under the transformation. As another example, our rotation by 90 degrees counterclockwise would be denoted *DABC*, as *A *is mapped to *D*, *B *is mapped to *A*, and so on.

Technically, this only describes what happens to the corners under a transformation, but as it turns out, this is enough to describe what happens to the entire square. That’s because symmetries are isometries, which preserve the size and shape of the object. An isometry can’t flatten out a corner, or vertex, as that would change the object’s shape. This means the corners *A*, *B*, *C* and *D* all have to get mapped to corners. Similarly, the properties of isometries guarantee that line segments get mapped to line segments. And so, once we know where the corners of the square go, the sides come along for the ride. In other words, the image of a side of the square is determined by the image of the vertices that are its endpoints.

This means we can completely specify a symmetry of the square by some arrangement of the four letters *A*, *B*, *C* and *D*. This is remarkable in and of itself, but it also immediately implies an upper bound on the number of symmetries of the square: There are no more symmetries of the square than there are arrangements of those four letters. How many such arrangements are there?

Think about creating an arrangement of these letters*.* You can start with any of the four, but once you choose a letter to start with, you have only three choices for the second. Once you choose a second letter, you’ll have only two choices for the third, and finally there will be only one option for the fourth letter. An elementary counting argument tells us there are then

4 × 3 × 2 × 1 (= 4!) = 24

possible arrangements of the letters *A*, *B*, *C* and *D*. Thus, there are at most 24 symmetries of the square.

In fact, the square has far fewer than 24 symmetries, and one more simple argument will show us why. Let’s return to our original diagram. Suppose we know that a symmetry of the square maps *A* to *B*. Where can *C *go?

The answer is that *C* can only be mapped to *D*. *A* and *C* are endpoints of a diagonal of the square. Since isometries don’t alter size, the distance between *A* and *C* must be the same before and after the mapping. If *A *is mapped to *B*, there is only one point on the square that is a diagonal’s length away from where *A* is now, namely *D*. That is where *C* must go.

This greatly reduces the number of possible symmetries of a square. Suppose we construct a symmetry; how many possibilities are there for where point *A* ends up? Since vertices must go to vertices, there are only four possibilities for the image of *A*. And once we’ve chosen a destination for *A*, there is only one possibility for the destination of *C*: the vertex diagonal to the image of *A*. This leaves only two choices for *B*, and a similar argument shows there will be only one choice for *D*.

Ultimately, in determining a symmetry of the square, there are really only two things to decide: where *A* goes (four choices) and where *B* goes (two choices). That means there are only 4 × 2 = 8 possible symmetries of the square. Here’s a complete list, using our notation:

Now, we aren’t guaranteed that all eight possibilities are actual symmetries of the square. But it’s a small list, so we can check them and verify that, indeed, they all correspond to legitimate symmetries: the four on the left are rotations (by 0, 90, 180 and 270 degrees), and the four on the right are reflections (two by vertical and horizontal lines, two by diagonal lines).

So these eight transformations are all symmetries, and since we’ve established that a square has at most eight symmetries, apparently we’ve found them all. But can this really be all of them?

One concern arises when we notice a natural way to combine symmetries: We can simply apply them in succession (an operation on transformations called “composition”). Since applying a symmetry to the square gives us the same square again, you could apply another symmetry, which would produce the same square yet again. This means that if you apply multiple symmetries in succession, the composition of those symmetries is itself a symmetry of the square! We could potentially generate new symmetries of the square through various combinations of the above eight.

But something interesting happens when we try that. Suppose we rotate the square by 90 degrees counterclockwise and then reflect it over the vertical line through the center. What happens to the vertices? The rotation takes *A* to *D*, and then the reflection takes it to *C*, so ultimately *A* goes to *C*. *B* rotates to *A*, then gets reflected back to *B*, so *B* is mapped to *B*. *C* gets rotated to *B* then reflected to *A*, and *D* gets rotated to *C*, then reflected back to *D*. In our adopted notation, the composition of these two transformations can be described as

But this symmetry is already on our list! Rotation by 90 degrees counterclockwise followed by reflection over the vertical line through the center is actually reflection about the diagonal line *BD*. As it turns out, every combination of the eight symmetries above is itself one of the eight symmetries above.

Now we’ve exposed the underlying algebraic structure inherent in this set of symmetries. When we combine two symmetries through composition, we get another symmetry, in much the same way that we combine two numbers through addition to get another number. There is an identity symmetry (rotation by 0 degrees) that acts just as the number zero acts in our number system. And every symmetry can be undone, just as adding 3 can be undone by adding –3: For example, rotating the square by 90 degrees can be undone by rotating the square by another 270 degrees.

These are the essential algebraic properties of groups, and they endow groups, like the set of symmetries of the square, with a structure and a regularity akin to those of our familiar number systems. Yet groups of symmetries also exhibit their own complex and subtle characteristics. For example, our group of symmetries of the square contains only eight elements, a stark contrast to our infinite number systems. And while we can combine symmetries in a manner similar to the way we add numbers, the order in which we combine them makes a difference: 3 + 4 = 4 + 3, but reflection followed by rotation is not necessarily the same as rotation followed by reflection.

We’ve gotten a glimpse of the algebraic structure underlying the simple symmetries of the square. What will mathematicians and string theorists find lurking in the depths of the monster?

*Download the “Counting Symmetries” PDF worksheet and watch the following video about how symmetries shape nature’s laws.*

For the next two decades, Witkin sought to understand how and why these mutants had emerged. Her research led her to what is now known as the SOS response, a DNA repair mechanism that bacteria employ when their genomes are damaged, during which dozens of genes become active and the rate of mutation goes up. Those extra mutations are more often detrimental than beneficial, but they enable adaptations, such as the development of resistance to UV or antibiotics.

The question that has tormented some evolutionary biologists ever since is whether nature favored this arrangement. Is the upsurge in mutations merely a secondary consequence of a repair process inherently prone to error? Or, as some researchers claim, is the increase in the mutation rate itself an evolved adaptation, one that helps bacteria evolve advantageous traits more quickly in stressful environments?

The scientific challenge has not just been to demonstrate convincingly that harsh environments cause nonrandom mutations. It has also been to find a plausible mechanism consistent with the rest of molecular biology that could make lucky mutations more likely. Waves of studies in bacteria and more complex organisms have sought those answers for decades.

The latest and perhaps best answer — for explaining some kinds of mutations, anyway — has emerged from studies of yeast, as reported in June in *PLOS Biology. *A team led by Jonathan Houseley, a specialist in molecular biology and genetics at the Babraham Institute in Cambridge, proposed a mechanism that drives more mutation specifically in regions of the yeast genome where it could be most adaptive.

“It’s a totally new way that the environment can have an impact on the genome to allow adaptation in response to need. It is one of the most directed processes we’ve seen yet,” said Philip Hastings, professor of molecular and human genetics at Baylor College of Medicine, who was not involved in the Houseley group’s experiments. Other scientists contacted for this story also praised the work, though most cautioned that much about the controversial idea was still speculative and needed more support.

“Rather than asking very broad questions like ‘are mutations always random?’ I wanted to take a more mechanistic approach,” Houseley said. He and his colleagues directed their attention to a specific kind of mutation called copy number variation. DNA often contains multiple copies of extended sequences of base pairs or even whole genes. The exact number can vary among individuals because, when cells are duplicating their DNA before cell division, certain mistakes can insert or delete copies of gene sequences. In humans, for instance, 5 to 10 percent of the genome shows copy number variation from person to person — and some of these variations have been linked to cancer, diabetes, autism and a host of genetic disorders. Houseley suspected that in at least some cases, this variation in the number of gene copies might be a response to stresses or hazards in the environment.

In 2015, Houseley and his colleagues described a mechanism by which yeast cells seemed to be driving extra copy number variation in genes associated with ribosomes, the parts of a cell that synthesize proteins. However, they did not prove that this increase was a purposefully adaptive response to a change or constraint in the cellular environment. Nevertheless, to them it seemed that the yeast was making more copies of the ribosomal genes when nutrients were abundant and the demand for making protein might be higher.

Houseley therefore decided to test whether similar mechanisms might act on genes more directly activated by hazardous changes in the environment. In their 2017 paper, he and his team focused on *CUP1*, a gene that helps yeast resist the toxic effects of environmental copper. They found that when yeast was exposed to copper, the variation in the number of copies of *CUP1 *in the cells increased. On average, most cells had fewer copies of the gene, but the yeast cells that gained more copies — about 10 percent of the total population — became more resistant to copper and flourished. “The small number of cells that did the right thing,” Houseley said, “were at such an advantage that they were able to outcompete everything else.”

But that change did not in itself mean much: If the environmental copper was causing mutations, then the change in *CUP1* copy number variation might have been no more than a meaningless consequence of the higher mutation rate. To rule out that possibility, the researchers cleverly re-engineered the *CUP1* gene so that it would respond to a harmless, nonmutagenic sugar, galactose, instead of copper. When these altered yeast cells were exposed to galactose, the variation in their number of copies of the gene changed, too.

The cells seemed to be directing greater variation to the exact place in their genome where it would be useful. After more work, the researchers identified elements of the biological mechanism behind this phenomenon. It was already known that when cells replicate their DNA, the replication mechanism sometimes stalls. Usually the mechanism can restart and pick up where it left off. When it can’t, the cell can go back to the beginning of the replication process, but in doing so, it sometimes accidentally deletes a gene sequence or makes extra copies of it. That is what causes normal copy number variation. But Houseley and his team made the case that a combination of factors makes these copying errors especially likely to hit genes that are actively responding to environmental stresses, which means that they are more likely to show copy number variation.

The key point is that these effects center on genes responding to the environment, and that they could give natural selection extra opportunities to fine-tune which levels of gene expression might be optimal against certain challenges. The results seem to present experimental evidence that a challenging environment could galvanize cells into controlling those genetic changes that would best improve their fitness. They may also seem reminiscent of the outmoded, pre-Darwinian ideas of the French naturalist Jean-Baptiste Lamarck, who believed that organisms evolved by passing their environmentally acquired characteristics along to their offspring. Houseley maintains, however, that this similarity is only superficial.

“What we have defined is a mechanism that has arisen entirely through Darwinian selection of random mutations to give a process that stimulates nonrandom mutations at useful sites,” Houseley said. “It is not Lamarckian adaptation. It just achieves some of the same ends without the problems involved with Lamarckian adaptation.”

Ever since 1943, when the microbiologist Salvador Luria and the biophysicist Max Delbrück showed with Nobel prize-winning experiments that mutations in *E. coli *occur randomly, observations like the bacterial SOS response have made some biologists wonder whether there might be important loopholes to that rule. For example, in a controversial paper published in *Nature *in 1988, John Cairns of Harvard and his team found that when they placed bacteria that could not digest the milk sugar lactose in an environment where that sugar was the sole food source, the cells soon evolved the ability to convert the lactose into energy. Cairns argued that this result showed that cells had mechanisms to make certain mutations preferentially when they would be beneficial.

Experimental support for that specific idea eventually proved lacking, but some biologists were inspired to become proponents of a broader theory that has come to be known as adaptive mutation. They believe that even if cells can’t direct the precise mutation needed in a certain environment, they can adapt by elevating their mutation rate to promote genetic change.

The work of the Houseley team seems to bolster the case for that position. In the yeast mechanism “there’s not selection for a mechanism that actually says, ‘This is the gene I should mutate to solve the problem,’” said Patricia Foster, a biologist at Indiana University. “It shows that evolution can get speeded up.”

Hastings at Baylor agreed, and praised the fact that Houseley’s mechanism explains why the extra mutations don’t happen throughout the genome. “You need to be transcribing a gene for it to happen,” he said.

Adaptive mutation theory, however, finds little acceptance among most biologists, and many of them view the original experiments by Cairns and the new ones by Houseley skeptically. They argue that even if higher mutation rates yield adaptations to environmental stress, proving that the higher mutation rates are themselves an adaptation to stress remains difficult to demonstrate convincingly. “The interpretation is intuitively attractive,” said John Roth, a geneticist and microbiologist at the University of California, Davis, “but I don’t think it’s right. I don’t believe any of these examples of stress-induced mutagenesis are correct. There may be some other non-obvious explanation for the phenomenon.”

“I think is beautiful and relevant to the adaptive mutation debate,” said Paul Sniegowski, a biologist at the University of Pennsylvania. “But in the end, it still represents a hypothesis.” To validate it more certainly, he added, “they’d have to test it in the way an evolutionary biologist would” — by creating a theoretical model and determining whether this adaptive mutability could evolve within a reasonable period, and then by challenging populations of organisms in the lab to evolve a mechanism like this.

Notwithstanding the doubters, Houseley and his team are persevering with their research to understand its relevance to cancer and other biomedical problems. “The emergence of chemotherapy-resistant cancers is commonplace and forms a major barrier to curing the disease,” Houseley said. He thinks that chemotherapy drugs and other stresses on tumors may encourage malignant cells to mutate further, including mutations for resistance to the drugs. If that resistance is facilitated by the kind of mechanism he explored in his work on yeast, it could very well present a new drug target. Cancer patients might be treated both with normal courses of chemotherapy and with agents that would inhibit the biochemical modifications that make resistance mutations possible.

“We are actively working on that,” Houseley said, “but it’s still in the early days.”

]]>Mathematicians understand this as well as anyone. It’s barely an exaggeration to say that their main enterprise is sorting. The impulse goes back to at least the ancient Greeks, who established that while there may seem to be a never-ending variety of solid objects with identical faces (so-called “regular” polyhedra), only five exist: the tetrahedron, cube, octahedron, dodecahedron and icosahedron.

My newest article for Quanta, “New Shapes Solve Infinite Pool-Table Problem,” relates to an ambitious classification project that is just getting underway. The story is, in one sense, about the search for polygons that have so-called “optimal dynamics,” meaning it’s possible to analyze every path a rebounding billiard ball could take within them. Mathematicians recently discovered two quadrilaterals with that property — dartlike shapes with angle ratios of 1:1:1:9 and 1:1:2:8. They’re the first shapes found to have optimal dynamics in a decade.

The mathematicians identified these shapes by appeal to classification. As I explain in the article, one way to study a polygon is to transform it into a point in an abstract structure called moduli space. Once in moduli space, you can study the point’s behavior — specifically, what’s called the “orbit closure” of the point. For many reasons, most of which have nothing to do with billiard balls, mathematicians would like to classify all the different varieties of these orbit closures.

Yet until recently, no one knew if this could be done. You could imagine that orbit closures might be their own special snowflakes — truly random objects that would defy efforts to say any two are alike. But in the last decade, three mathematicians — Alex Eskin, Amir Mohammadi and the late Maryam Mirzakhani — proved that orbit closures are always manifolds, which implies that they are neat, orderly and amenable to classification.

At the time of the manifold work, mathematicians knew of at least two types of orbit closures: dense and closed. Many mathematicians, and especially Mirzakhani, suspected there weren’t many more. In the course of trying to prove that certain other kinds of orbit closures don’t exist, the mathematician Alex Wright (who was collaborating with Mirzakhani) stumbled across the first hints of the new quadrilaterals with optimal dynamics. One of those quadrilaterals, the 1:1:1:9 shape, ended up relating to a new kind of orbit closure, which the mathematicians describe with the term “totally geodesic.”

Now we know that at least three kinds of orbit closures exist: closed orbits, dense orbits and totally geodesic orbits. Whether there are more (or many more) is an open question, but this new discovery will almost certainly intensify the search, just as finding a single nugget of gold will lead people to scour an entire mountain.

“Classification is like a definitive study for all time, like writing the final book so nobody has to write another book,” Wright said.

Of course, all-time studies take time. One of the great achievements in 20th-century mathematics was the classification of what are called “finite simple groups.” That effort required more than 50 years to complete. By that standard, the classification of orbit closures has only barely begun.

]]>In order to bring out their exquisite flavor, the ribs have to be grilled evenly using a very fine wire that goes all the way around the middle of the rib. Without the wire, the rib cannot get properly cooked, but no metal should touch the snake at any point between two ribs. The chef achieves this by suspending the snake over coals in a long narrow trough using multiple rigid grilling frames, each of which is as long as the snake and consists of a long rod from which hang thin, evenly spaced wire rings that are a whole number of inches apart. In order to get perfect results, the chef insists, each grill must have evenly spaced rings any whole number of inches (except one) apart, with no missing rings. The chef is adamant that it must be so, though scientists are skeptical of these claims.

Several frames, each with differently spaced rings, are therefore carefully aligned, one on top of the other, and the snake is suspended so that it is encircled by the rings. All frames always start from the edge of the grilling pit, and the snake is always placed with its first rib 1 inch from the left edge. Thus, if a snake is suspended using three frames with wire rings spaced 2, 3 and 5 inches apart, out of the first 10 ribs, ribs 2, 3, 4, 5, 6, 8, 9 and 10 would be grilled properly but not ribs 1 or 7, as shown in the figure below.

Once the snake is cooked, it is divided into portions by cutting out all the improperly cooked ribs. This creates uneven-sized edible portions, the smallest of which have just one cooked rib. In the above three-frame example, you’ll obtain a five-rib portion which includes ribs 2 through 6, a three-rib portion extending from rib 8 through rib 10, a one-rib portion for rib 12 and so on. The most prized and expensive dish is the largest portion — the one that has the maximum number of contiguous perfectly cooked ribs. Obviously, the size of this largest portion depends on the number of grilling frames used and the gaps between their rings. Using two frames with rings that are 2 inches apart in one and 3 inches apart in the other, the largest portions that a snake of any possible length can produce are three ribs long. The first such portion starts at rib 2: ribs 2 and 4 are cooked with the 2-inch-spaced frame and rib 3 with the 3-inch-spaced one.

That completes the story of this how this unique dish is prepared and the intricate conditions that are thought to be required to achieve perfect results. I now have two sets of questions for you that are inverses of each other.

If you are free to use five grills with any spacing (except a 1 inch gap, of course), what is the largest sized well-cooked portion you could create, one that includes the maximum number of ribs possible? And what’s the shortest length of snake that can yield this maximum portion? Obviously, this question can be generalized to any number of grills. Ambitious readers can amuse themselves by calculating the answers for higher numbers of grills such as nine. Note that you can use brute force searches, but the length of snake required for larger numbers of grills soon becomes astronomical, requiring snakes as long as the constellation Serpens is wide. Such computations are known as models of high computation complexity. So some cleverness will surely be required.

What’s the smallest number of grills that can yield maximum portions of 50, 100 and (gasp!) 150 ribs? What are the smallest sized cosmic serpents that will be required for these? Note that the latter question for 100 and 150 are open problems, at least for me. Perhaps one of you will provide answers that can be proved to be the smallest. This may require heavy-duty mathematical tools but even they may not be able to give a provably correct answer. However, there is scope for cleverness and tinkering, and we may be able to find heuristic methods that generate some plausible candidates.

No doubt by now you will have seen the connection to prime numbers implicit in the details (and title) of this puzzle. Prime numbers are connected to an endless source of unsolved problems in number theory, such as the famous Riemann hypothesis, whose solution carries a prize of $1 million from the Clay Mathematics Institute, and which some physicists are attacking using quantum mechanics. Primes invoke in mathematicians a deep sense of awe and continue to inspire new generations of researchers, such as Kaisa Matomäki, who “dreams of primes.”

The above story is an attempt to come up with a physical situation that naturally mimics the Sieve of Eratosthenes. I’ve enjoyed this challenge, but let me now throw this out to readers. Can you come up with even remotely plausible situations in which the prime number sieve might occur naturally?

Happy puzzling, and I look forward to seeing your comments.

*Editor’s note: The reader who submits the most interesting, creative or insightful solution (as judged by the columnist) in the comments section will receive a** *Quanta Magazine* **T-shirt. And if you’d like to suggest a favorite puzzle for a future Insights column, submit it as a comment below, clearly marked “NEW PUZZLE SUGGESTION.” (It will not appear online, so solutions to the puzzle above should be submitted separately.)*

*Note that we may hold comments for the first day or two to allow for independent contributions by readers.*

Pasachoff, an astronomer at Williams College in Massachusetts, will view the event in Salem, Oregon, accompanied by a group of students and thousands of pounds of equipment. That’s because even in this age of space probes and orbiting telescopes, there’s still a good deal of science that can be done from the ground during those brief moments in the moon’s shadow — science that, in fact, can be done only during a total solar eclipse.

*Quanta* spoke with Pasachoff about life as an eclipse chaser and the observation opportunities that only a total eclipse can bring. An edited and condensed version of the conversation follows.

We professional astronomers take advantage of whatever special opportunities we have, to learn more about the sun and our universe. During an eclipse, we see parts of the sun that aren’t visible from Earth at other times and that are never visible from spacecraft. It’s only during an eclipse that we get a complete view of the sun, from the surface out through the corona — the sun’s tenuous outer atmosphere, which becomes visible during totality — and farther out, into what we call the heliosphere, the region of space dominated by the sun. So given that we only get a few minutes every 18 months or so, we astronomers certainly want to take advantage of this wonderful opportunity.

**Today we have more than one space-based telescope equipped with a ****coronagraph****,**** a kind of shield that blocks out the light from the photosphere, the bright disk of the sun. Don’t they accomplish the same thing as an eclipse?**

It depends how much money you have. If you give me $10 billion, then I might be able to simulate an eclipse, using a space-based coronagraph. That’s as good as the ones that we get on Earth. But that hasn’t happened. The best coronagraph that we have in space is now over 20 years old, on the Solar and Heliospheric Observatory . It has three nested coronagraphs. The inner one is now defunct; in fact, it never worked very well. The two that remain, known as C2 and C3, are what we call externally occulted coronagraphs, which means there’s a disk that blocks some of the sun’s light, but the disk is located close to the lens and is therefore at a different focus than the corona. So to make it all work, it has to block three-quarters of a solar radius around the sun. And that’s the region that we see best, during an eclipse. And the C3 has an even bigger blockage.

So there’s a whole region, from the surface of the sun out to three-quarters of a solar radius that we can see in white light only during an eclipse. Further, the C2 coronagraph has a resolution of only 23 arc-seconds, whereas during an eclipse, from the ground, we can achieve two or maybe one and a half arc-seconds. So there’s an overlap region that we see during an eclipse — overlapping with what we see using the C2 coronagraph — and we’re seeing everything over 10 times more clearly, from the ground, during an eclipse. So if we want to study the region where the solar wind is formed and where we have these wonderful magnetic field displays and these solar coronal streamers, near the sun’s equator, and the plumes from the sun’s polar regions — then we need the eclipse, which we only get every 18 months or so, somewhere on Earth.

**What kind of data, in particular, do you want to collect? Are we talking about images, or spectra, or something else?**

Yes, yes, and yes: Images, and spectra, and something else! I feel a big responsibility, now that we have this eclipse in our home territory, to make the most complete observations possible. We have the advantage of the shipping being less expensive, compared to taking 2,000 pounds of equipment to India, which I have done, for an eclipse. So I’ve gathered, with the support of the U.S. National Science Foundation and the Committee for Research and Exploration of the National Geographic Society, a crack team of astronomers and equipment, to study the sun with a variety of telescopes and spectrographs.

**What do you want to learn?**

Perhaps the most difficult and most complex experiment in our group of a dozen or so experimental setups is to try to determine observationally which of the competing models of coronal heating is correct — to understand how the corona is heated to a million degrees. We know that it’s related to the sun’s magnetic field, but the details of just how it’s related are still unclear and are much debated among the theoreticians.

**What are some of the ideas?**

There’s a whole set of competing theories that involves something called nanoflares — where nano of course means a billionth — and so, instead of a few big solar flares erupting from the sun, there could just be a lot of little flares, each a billionth of the intensity of the big flare, going off all the time, thousands of them going off all the time. So that could account for much of the heating of the corona. Another idea involves coronal loops, oscillating loops of ionized gas held in place by the sun’s magnetic field. So we want to see what we can measure and see if we can distinguish between the contributions of nanoflare heating and coronal-loop wave heating.

**How can you distinguish between the two?**

Different models predict different kinds of oscillations and vibrations in the loops of gas held in place by the coronal magnetic field, in the lower corona. Some theories say that there should be vibrations with periods of many seconds; one set of theories predicts sub-second vibrations — and if the nanoflare idea is correct, there may be no oscillations at all.

We have some very special filters, in what’s called the coronal green line and the coronal red line — emission lines associated with electrons in highly ionized iron atoms in the solar corona, as they jump between energy levels at temperatures of a million or over a million degrees, respectively. The special filters isolate the hot coronal gas from the background coronal light that we see with our eyes, which is largely the everyday surface of the sun — the solar photosphere — scattered by the electrons in the corona. But with these special filters, we can pick out the actual emission from the corona. And we’re looking for very rapid vibrations.

**Does that mean you need video or some way of capturing images at a very high frame rate?**

What we use is even better than video, in that each observation is more precise. We use a special kind of CCD — an electronic charge-coupled device — that’s actually two CCDs in one. One is off to the side , hidden behind a metal cover. We record images at a rate that can go up to 10 hertz — 10 times per second, or even more — and almost instantaneously the data is transferred to the CCD that’s hidden behind the metal shield, which can then be read out while the next image is being taken using the open one. The result of that is that there’s almost no dead time — we can take very high-precision observations without any gaps between the successive images.

We’ve been using this method very successfully for the last dozen years, on a series of occultations of stars by Pluto and other objects. We’ve had it at a transit of Venus, and we’ve had it at a previous eclipse, and we’re looking forward to using it at this eclipse.

**I understand that eclipse measurements can also be used to track Earth’s rotation rate?**

That’s right. Earth doesn’t rotate at a completely constant rate. That rate depends on the distribution of mass of Earth’s surface, which depends on such things as the amount of ice at the poles, and the distribution of glaciers and other flows around Earth’s surface. The difference may only be a fraction of a second per year, but that’s enough, if you go back 1,000 or 2,000 years, to have Earth not quite rotated as much as it is today — which means that an eclipse would take place at a slightly different place on Earth. Now eclipses are so dramatic that you can potentially read old chronicles from a couple of thousand years ago, especially if you know about ancient languages — especially Eastern languages, Asian languages — and interpret whether an eclipse was visible at a given location. And you can use that to track what Earth’s rotation has been since then.

**There’s ****a famous story**** about how astronomers used the solar eclipse of 1919 to test Albert Einstein’s theory of general relativity. But Einstein had a bit of luck in the years leading up to that event, didn’t he?**

Einstein had been corresponding with a young German astronomer, Erwin Finlay-Freundlich, who took some equipment to see the solar eclipse of August 1914, in Russia, to see if he could detect the deflection of starlight by the sun, which was predicted by Einstein’s theory. But the First World War broke out, and Finlay-Freundlich was interned by the Russians as an enemy alien, and his equipment was seized, so he was prevented from making the observations.

At that time, Einstein had only a preliminary version of his general theory of relativity. A couple of years later, in 1916, he came out with a more complete version, which turned out to predict twice the amount of deflection compared with the initial version of the theory. And this was the actual deflection that was found, when astronomers made their observations of the eclipse in 1919.

Now if Finlay-Freundlich had succeeded in making the measurements in 1914, he’d have found Einstein to be off by a factor of two — and when Einstein corrected his mistake, it would have seemed like a fudge. And as philosophers of science point out, you want to make a prediction and then verify the prediction; you don’t want to make a prediction and then figure out a way to make your theory fit the observations after the fact. So in fact Einstein — who of course became famous once the results of the 1919 observations were announced — was very lucky that astronomers weren’t able to view the 1914 eclipse.

**Aside from the science, what can you say about this August’s eclipse in terms of outreach?**

I think if we get millions or tens of millions of schoolchildren out watching the eclipse — it is so amazing to be out during totality, and it’s such a dazzling spectacle, that maybe they could be persuaded to pay more attention to their studies. Who knows, in the long term we may get more scientists out of this, more big discoveries.

Of course, not everyone will get on board. I remember viewing an eclipse in the winter of 1979 from a balcony in Brandon, Manitoba. I remember looking down and seeing that the cars kept driving, though they turned their headlights on for a couple of minutes, when it got dark. So we’re trying to get across to people just how wonderful it is to actually see an eclipse.

I’m trying to make the point that when even 1 percent of the sun is visible — a so-called 99 percent partial eclipse — the sky is still 10,000 times brighter than it is during totality because 100 percent coverage causes the sky to get darker by a factor of a million. So even if 1 percent of the sun is visible, you miss all of the exciting phenomena associated with totality. So we’re trying to persuade all 300 million Americans, plus all the Canadians and all the Mexicans and all people from Central America and from northern South America, to travel into the path of totality — OK, maybe not literally all of them — but for those who can make it, it will be a wonderful thing for them to see. A total eclipse is indescribably wonderful.

**During the two minutes of totality, you’ll be busy collecting data. Will you still have a chance to look up and enjoy the spectacle?**

I always steal a few seconds, at least! But these days, we have computer programs that can control the cameras; we can program all the cameras to snap away with bracketed exposures and to make all of the other exposures during the eclipse. As well, I’ll have my eight summer students helping out. So I hope I’ll be able to watch the two minutes of the eclipse, or most of it, and even look up with my binoculars and see the details of the polar plumes and the coronal loops and coronal streamers.

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