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Nice my parents have owned a timeshare in Cocoa Beach just south of Canaveral and for the first time this year in the 20+ years they have had the place we got to see a launch. Got to see 2 infact. Crew 3 and Starlink
Conversations at the International Meeting on Origami in Science, Mathematics and Education often pause for a hand to dart into a pocket, emerge with a square of plain paper and fluently fold it up to make a point—both geometrically and rhetorically. The tables at the meeting, which was held in Oxford last September, are strewn with paper constructions that must have taken weeks to make and which participants are nevertheless welcome to handle. But the meeting is not just, or even mostly, about folded paper. It is about the folds themselves: how to design them; how to think about them; how to use them. It is about making creases in everything from steel to sheets of carbon mere atoms thick. It is about differential geometry and elastic moduli. It is about adult nappies and satellite antennae. The more ways are found to fold things up, it seems, the more wide open the field becomes.
People have folded things up since there were things for them to fold. In Europe, for many centuries, the things folded were mostly cloth; in Japan and China, paper. The uniting of these traditions within a single systematised craft is largely a 20th-century phenomenon, as is its description as “origami” (ori, the Japanese for fold, kami for paper); in Japan the practice was previously known as tatogami.
Friedrich Froebel, the man who invented the kindergarten, was the first person to suggest the systematic use of folding as a way of teaching geometry. Educators steeped in “Froebelian” methods—whose number, intriguingly, included the mother of Frank Lloyd Wright, a revered architect—spread folding for learning and fun as far as kindergarten itself. Some mathematicians took note. In “Geometric Exercises in Paper Folding”, published in 1893, T. Sundara Row took on with folded paper various problems geometers had tackled with compass and straight-edge since the days of Euclid: finding exactly half of the angle between two creases, say, or constructing a figure of three or nine or 15 perfectly equal sides. It could be applied to algebra, too. Mark a spot on the midline of a piece of paper, and fold the paper in as many ways as you can that touch its bottom edge to that spot; the folds will inscribe a parabola, as described by quadratic functions such as y=x2.
Good clean educational fun. But nothing could be folded that could not be equally well done with Euclid’s tools—until, in 1936, Margherita Beloch, an Italian mathematician, developed a form of folding that produced the curves of cubic functions (y=x3). Mastery of such functions lets you “double the cube”—calculate from the length of the side of one cube what the length of the sides of a cube with twice its volume would be. It is a problem that cannot be solved with just edge and compass, and had stumped the ancients. Folding was more than just drawing lines without a pencil.
A few mathematicians took these ideas further (though for the most part they abandoned paper for idealised folds more suited to mental manipulation). They moved from everyday algebra to differential algebra and, in so doing, from flat sheets to curved ones, and even to non-Euclidean geometries like that with which the theory of relativity describes spacetime.
While the maths of folding raised its ambitions, so did the craft side. In 1958 Lillian Oppenheimer founded the Origami Centre, which in turn led to the current organisation, Origamiusa. It did much to bring together traditions from East and West and also opened up, on a personal level, the art’s link to science. Acknowledged “masters” of Origamiusahave included Michael LaFosse, a marine biologist, and John Montroll, an electrical engineer. It was surely not a coincidence that one of Oppenheimer’s highly mathematical children, Martin Kruskal, spent time studying the folding-up of spacetime inside black holes.
In 1989 a few such enthusiasts convened a meeting to explore what origami could contribute to science and engineering. Robert Lang, a former laser physicist, says that meeting in Ferrara, Italy, “played an outsized role in the triggering of the explosive growth that we’re now in the middle of, because it brought together isolated individuals and fields.”
He should know. Since hanging up his lab coat and taking origami on full time, Dr Lang has had a hand in a mind-bending array of pursuits both academic and artistic, penning 21 origami how-to books along the way. At the sixth sequel to the meeting in Ferrara, the one in Oxford, he is treated like a rock star.
It works on paper
Dr Lang’s greatest hits have been in formalising and building enthusiasm for the mathematics behind origami with systematic, quantitative studies on how to achieve a particular shape starting from a single flat, square, uncut sheet. He developed software that can compute the folds and their order for almost any beast imaginable. The patterns that the program spits out for, say, deer with multiply-branching antlers, are staggering to behold, both in their flat and folded forms. The mathematical operations through which the former becomes the latter, one can only imagine, represents a peculiarly elegant trajectory through a vast and bewildering space of possibilities.
The flashiest early example of origami solving a scientific problem was when Koryo Miura and Masamori Sakamaki, astrophysicists at Tokyo University’s space-science department, devised a new approach to the unfolding and refolding of a satellite’s solar panels, first put into practice in 1995. The obvious approach is to fold them as one does a map. But anyone who has tried to return a good-sized map to its folded state knows the damage it can inflict on the paper. The scientists’ insight was not to fold the panel at right angles, which produces rectangles between folds, but at a slightly skewed angle, producing parallelograms. This creates a panel that can be completely unfolded just by tugging two of its opposed corners out, and refolded by pushing them in.
To have a fold named after you is a rarefied honour in the origami world, but “Miura-ori” has since earned that distinction. Simon Guest, who works on structural mechanics at the University of Cambridge, calls it the “crucial link between origami and science”, and vividly recalls the first time he saw it. Dr Lang says the fold connects “hundreds of moving parts that move in different directions in a synchronised way”—which is just what builders of exotic experiments are often aiming for. “There are so many connections that it shouldn’t be possible for it to move,” he says. “That’s really powerful, and those properties come almost naturally from patterns that arise in the world of origami.”
In the wake of the Miura fold, more scientists and engineers took an interest, and more applications began to crop up in the scientific literature. In 2012 America’s National Science Foundation decided that this sporadic enthusiasm could do with some institutional legitimacy, and set up a programme called Origami Design for Integration of Self-assembling Systems for Engineering Innovation, or odissei; it offered grants to scientists interested in trying an origami-based approach to a problem, on the condition that they collaborate with origami artists. It was, in the rather non-paper-friendly words of Larry Howell, a mechanical engineer at Brigham Young University, in Utah, “like throwing gasoline on a match”. The still-spreading flames lit up the Oxford meeting.
Though origami is at the centre of this applications boom, many of the devices displayed and discussed in Oxford represent a kind of goal reversal. For a recreational folder, the purpose is to finish with a given shape, such as a tato, the traditional paper purse that accessorises a kimono; for many applications, it is the unfolded version of an object that is the useful one.
Quite a few such applications are medical; the human body, like outer space, is best entered with small packages that can be spread out once you reach your destination. There are stents for arteries, retinal implants for the eye, forceps that scrunch up to pass through a tiny incision before getting to work within the body. Not all the bodily uses are interior, though. Dr Howell’s group is developing new designs for nappies, folding away the structures within them to better control the wicking of liquid and to fit to a wider range of body shapes.
Some are for lab use. One group has built a flat, origami-inspired contraption which is folded up by the growth and movement of the cells living on it. Another group is showing off sheets of carbon atoms—graphene—that bend into shape when their environment changes—for example, when it becomes more acid. It is at such scales that self-assembling systems—the ss of odissei—come into their own, beyond the reach of fingers or tweezers.
Back in the visible world there is shape-shifting furniture based on a puzzle called a Yoshimoto cube that folds into a wide array of squishy seating options, to the delight of its child users. A three-metre-tall architectural arch made from fibreglass folds flat for transport. A fairing for locomotives is designed to reduce aerodynamic drag but to fold away when the engines are parked, or used in the middle of a train; it could, its makers say, save millions of dollars a year in fuel. “Origami tubes”—imagine a Miura-folded sheet further folded into an extensible prism—are unusually stiff in some directions. Architects and car designers have taken notice. Thanks to Dr Lang and many others, there is a general, mathematical folding theory underlying all these applications.
“Rigid origami” needs new maths; it also offers new abilities
As a result the mathematics of origami has moved beyond early efforts to show how much higher maths could be recapitulated in folds (answer: a surprising amount). The folders are now providing the mathematicians with interesting new challenges, which can elicit intriguing mathematical proofs. For example, Erik Demaine, a computer scientist at mit, has proved that any straight-sided figure—an octagon, a cityscape silhouette or a blocky Bart Simpson—can be extracted with exactly one straight cut if you fold the paper up the right way first (you can make a just-one-cut Christmas tree, and your own Miura fold, at economist.com/origami). This is just the kind of thing Dr Lang relishes: “gaining an understanding of a phenomenon that we see in the world of folding but don’t yet have a mathematical description for”.
The need for such approaches becomes acute when you move to materials other than paper—materials which cannot be treated by assuming that they are infinitely thin and stress-free. Bend a sheet of steel and it will not lie flat. It may also be under considerable strain at and far from the fold. Such “rigid origami” needs new maths; it also offers new abilities. The non-local strains in non-paper materials can be used to generate forces which will make things fold, or unfold, seemingly spontaneously. To make the most of such wonders, though, you need a much richer theory. Dr Demaine, whose particular interest is in curved folds, another frontier with even more demanding analytical requirements, says that work is under way toward a unified theory of rigid origami as good as that now available for paper.
Such a theory, he cautions, may not exist. But he and his colleagues will have a lot of fun looking for it.
Correction (December 20th 2018): An earlier version of this article suggested that OrigamiUSA descended directly from the Origami Centre. Its original incarnation was in fact set up as a non-profit, separate from the Origami Centre. The piece also suggested that Robert Lang’s folding software created a design for one origami praying mantis eating another; in fact that design was done by hand. Sorry.
A black hole's outflow is contributing to star formation in a dwarf galaxy
Universe is fucking nuts.
On Christmas morning of 2021, astronomers watched their new, greatest tool successfully blast off into space. Now the James Webb Space Telescope (JWST) is fully deployed and has arrived at its deep-space destination, a quiet locale 1.5 million kilometers beyond Earth.
Massimo Stiavelli heads the JWST Mission Office at the institute that allocates research time on the telescope. According to Stiavelli, “every area of science is covered” in the proposals his group has approved, from the search for potentially habitable exoplanets to studies of the earliest stars. Yet he is particularly hopeful that JWST could help settle one of the biggest controversies in modern astronomy: the dispute about the expansion rate of the universe.
“If you try to measure the current expansion rate, well, there’s a variety of techniques that people use, and they tend to get a certain number,” says Tommaso Treu, an astrophysicist at the University of California, Los Angeles. “And it turns out that those numbers don’t match.”
Measurements of the universe’s expansion rate, known as the Hubble constant, currently cluster around two figures: 67 and 73. Each number is an expression of the same thing—the kilometers-per-second rate of cosmic expansion per every megaparsec (roughly 3.26 million light-years) of space. Although seemingly slight, the difference between these figures is enormous in comparison with the high-precision agreement that exists for other cosmological measurements. Simply put, something is not adding up.
Researchers are not sure how to account for this discrepancy, which they call the Hubble tension. It may just be an error resulting from the different ways the Hubble constant is being measured. Otherwise, the tension could spell trouble for our current understanding of physics, forcing theorists to revisit (and perhaps even discard) some of their most cherished models.
“The quest to measure the expansion rate goes back around 100 years,” says Adam Riess, an astrophysicist at Johns Hopkins University. Scientists taking part in that quest fall into two main camps.
The first camp gathers data from the very early universe. These researchers rely on the cosmic microwave background, a residual glow of radiation from roughly 400,000 years after the big bang. By taking measurements from the cosmic microwave background and extrapolating them into the present using our best physical models, astronomers in this camp can reach an estimate for the expansion rate of the universe today. Their calculations indicate that the Hubble constant is around 67.
But Riess adds that JWST will not improve measurements of this kind. Microwaves from the early universe have wavelengths that are too long for JWST—which focuses on infrared light—to detect. Instead JWST has the potential to improve results from the other camp (of which Riess is a prominent member): local measurements.
“Local” is a relative term. Here, it refers to measurements of the Hubble constant that hinge on calculating the distances to stars and galaxies, which may be “only” millions of light-years away. “Measuring distances is what you need to measure the Hubble constant because the Hubble constant is how distances change over time,” Treu says.
Astronomers have found a few ways to gauge such celestial distances. Most of them rely on “standard candles,” astronomical objects of known brightness. By comparing such an object’s actual, intrinsic brightness with its apparent brightness through a telescope, observers can reliably determine its distance from Earth.
Wendy Freedman, an astronomer at the University of Chicago, uses a certain class of red giant stars as her preferred standard candle. “The physics [of these stars] leads to this standard luminosity,” which makes them perfect distance indicators, Freedman explains. Using the Hubble Space Telescope to observe these red giants, Freedman’s team arrived at an estimate for the Hubble constant in 2019: roughly 70.
That is on the low end of local estimates. (In fact, it is vexingly midway between the standard values embraced by each camp.) According to Riess, whose standard-candle work uses supernovae and Cepheid variable stars instead of red giants, most local studies have produced somewhat higher values for the Hubble constant—some as high as 75, with an average around 73.
This is a much bigger range than the measurements out of the early-universe camp. Likewise, local studies tend to have greater “error bars” (or uncertainties) than studies that use early-universe data.
That is where JWST can help. By observing in the infrared spectrum, it will be able to look straight through pesky clouds of space dust that all too often interfere with local astronomers’ measurements. The Hubble Space Telescope—the previous tool of choice for local astronomers—has far more modest infrared capabilities; its infrared measurements come at the expense of lower image quality. As Riess explains, JWST can do both: observe in infrared and maintain high-resolution imaging.
Crisper, dust-free images: that’s the JWST promise.
JWST is such a technological improvement that, rather than altering their methods, many astronomers are planning to carefully replicate their prior research in order to see if the results change. Both Riess and Freedman have been granted research time on JWST to do just that.
Whether or not their results will change is uncertain. It is possible that data from JWST could lead local studies to cluster around an estimate for the Hubble constant as low as the one from the early-universe camp. But that seems very unlikely: Riess points out that virtually no local study has produced a result so low, just as no early-universe study has produced a result as high as 73.
So what would it mean if local studies again cluster around 73 but this time with even greater precision? According to Treu, that would imply the Hubble tension is a real discrepancy and not just the result of study error.
If so, Treu adds, that would probably point to something fundamentally absent in our understanding of physics. Because early universe studies rely on physical models to extrapolate their primordial data into the present, missing physics could be the reason those studies are producing a figure as low as 67.
What sort of missing physics? “It could be another neutrino,” Riess says. “It could be an early episode of dark energy. It could be decaying dark matter. It could be primordial magnetic fields. All of these have been suggested as things that would help mitigate or explain this.” But Riess points out that none of these have “a strong second line of evidence” besides the fact that they could help explain the Hubble tension.
Likewise, Freedman notes that most of these ideas wind up “wrecking” other, agreed on parts of physics somewhere along the line. “This turns out to be really difficult to solve—which is not to say somebody’s not going to come up with a brilliant idea at some point,” Freedman says.
There may be a hole in physics. There is no guarantee that JWST will help us figure out how to fill it. But by giving greater insight into the Hubble tension, JWST can at least help confirm that the hole is really there.
A powerful solar flare from over the weekend will make its way to Earth Wednesday as a "moderate" geomagnetic storm, the National Oceanic and Atmospheric Administration said, making the northern lights visible throughout the northern part of the United States.
On Saturday evening, a solar flare released a coronal mass ejection from a sunspot called AR2936, which had been rapidly increasing in size in a two-day span, according to SpaceWeather.com. The spot had gotten so big it could "swallow our planet five times over."
The phenomenon was classified as an M-class flare, meaning its initial shock would be enough to cause some radio blackouts in Earth's polar regions. (X-class flares could cause planet-wide blackouts.)
BREAKING : Last night a sunspot region produced an M1.1 (medium-sized) solar flare
Expected to safely impact Earth in a few days, creating spectacular auroras pic.twitter.com/FZDvZef41u
— Latest in space (@latestinspace) January 30, 2022
By the time the solar flare went off, the spot was facing the direction of Earth. As a result of its direct course, the flare is expected to produce a geomagnetic storm on our planet.
Storms are rated from G1 to G5, with G1 storms resulting in the possibility of weak power grid functions, whereas G5s are extreme storms that can cause widespread collapse or blackouts of power grids, according to the NOAA.
On Monday, the agency said that a G2 storm watch was in effect for Wednesday, meaning the storm could result in some polar power systems to experience voltage alarms.
SpaceWeather.com reported the coronal mass ejection hit Earth's magnetic field Tuesday night but did not produce a geomagnetic storm. However, the storm is still expected to hit as Earth moves through the waves.
If that's the case, people in Canada and states like New York, Minnesota and Washington will be able to spot the northern lights on Wednesday night. A plus is also the storm isn't expected to be strong enough to disrupt power grids or satellites, as it is an "auroras only" event.
The northern lights, also known as the aurora borealis, form when the ejection's particles interact with Earth's magnetic field, and the planet's atmospheric gases cause the glowing red and green colors that many people recognize.
The NOAA said the storm is expected to weaken to a G1 level storm by Thursday.
In november last year Russia blew up a defunct satellite, creating shrapnel that will orbit the Earth for decades. The “direct ascent” missile test was a first for Russia and echoed a similar weapons test carried out by China in 2007, which also created an enduring cloud of debris. India and America have shot at inoperative satellites, too, although fortunately without creating as much associated long-lasting space junk.
All this target-practice concerns American defence chiefs, who would struggle to fight a war if critical satellites were knocked out. The Pentagon, therefore, wants its next generation of satellites to have enough power to be capable of evading attacks. It thinks the answer lies with nuclear-powered propulsion.
Two initiatives will investigate the concept. The first, led by the Defence Advanced Research Projects Agency (darpa), will test a technology known as “nuclear thermal propulsion”. Working with American firms, including Blue Origin, General Atomics and Lockheed Martin, darpa spacecraft will carry a small nuclear reactor. Inside, uranium atoms will be split to generate tremendous heat. That heat will be absorbed by liquid hydrogen sucked from a tank on board the spacecraft. The hydrogen, which will start at a storage temperature colder than -253°C, will rapidly expand as it warms. As that hot gas shoots out of a nozzle at the back of the spacecraft, it will produce thrust.
Such a spacecraft could climb to a geostationary orbit above the Earth, nearly 36,000km up, in mere hours. Satellites that burn normal rocket fuel need several days for the same trip. Nuclear-powered satellites with abundant power would also be hard to destroy—their trajectories could be changed often enough to become unpredictable. darpa wants to test its spacecraft, dubbed draco (Demonstration Rocket for Agile Cislunar Operations), in orbit in 2025. This is an ambitious timetable, given that nuclear thermal propulsion has never been tried out in space.
The Pentagon’s Defence Innovation Unit (diu) runs the second nuclear initiative. In September 2021 it solicited proposals for nuclear systems for satellite propulsion or, alternatively, to power onboard electronics. Companies pitching ideas need to meet a few conditions: they should steer clear of the nuclear-thermal-propulsion technology that darpa is already working on; they should be able to build a prototype within three to five years; and they need a credible plan for testing in space. Out of the dozens of proposals received by the diu, the first two winners are set to be announced later this month.
Beyond the dragon
Ryan Weed, a captain in the United States Air Force (usaf) who leads the diuprogramme, says the submitted proposals fall into distinct categories. Some incorporate nuclear reactors, but not to heat liquid hydrogen. Instead, the heat will be used to generate electricity that will then be applied to a propellant gas such as xenon. This will ionise the gas which, thanks to an electric or magnetic field, will zip out of a nozzle to produce thrust.
Ion thrusters are not a new idea but a nuclear reactor could produce far more electricity to power them than even a large solar array. Satellites without solar panels would, usefully for military purposes, also be harder for enemies to track and disable.
Many of the designs for nuclear electric propulsion call for the same process of splitting atoms used in terrestrial nuclear-power plants. The kit for space would weigh at least a tonne, so it would only power big satellites.
Other proposals are for radioisotope thermoelectric generators (rtgs). These kinds of “nuclear batteries” have long been used to power probes sent into deep space, where solar power is especially feeble. Instead of building a nuclear reactor, an rtg uses devices called thermocouples to produce a modest wattage from heat released by the decay of radioactive isotopes. Plutonium-238, which is a by-product of weapons development, has been used by nasa to power both the Voyager probes, launched in the 1970s and still functioning, as well as the Curiosityrover currently trundling around Mars.
Plutonium-238, however, is heavily regulated and in short supply. And with a half-life of 87.7 years, the heat it produces from radioactive decay is spread over a long time. The diu is therefore looking for alternatives with a shorter half-life and a “much higher thermal power density”, says Captain Weed. Cobalt-60, with a half-life of 5.3 years, is a promising alternative and available commercially. He would like rtgs to provide electricity for thrust and also the onboard electronics for satellites that are the size of a washing machine.
First, do no harm
How safe is it, however, to send nuclear devices, especially reactors, into space? Nathan Greiner, a major in the usaf who leads darpa’s programme, says that one concern he often hears is about the potential explosion of a draco spacecraft on the launchpad. He says that such an event would not present any more danger than the explosion of a conventional spacecraft—because the reactor would not have been switched on at that point, its uranium fuel would pose no radiological hazard.
A bigger problem would be if the nuclear reactor crashed into the sea. Water can encourage the start of a nuclear chain reaction in which uranium atoms split and release neutrons that can go on to split further uranium atoms. If uncontrolled, this chain reaction can lead to a meltdown. draco is therefore configured so that even if submerged in water, “poison wires” made from boron will remain in place. Boron is used in nuclear reactors to moderate—or even stop—nuclear fission.
Another danger is accidental atmospheric re-entry. The Soviet Union flew at least 33 spy satellites with nuclear reactors for onboard power (but not propulsion). In one accident, the reactor in a satellite named Kosmos 954 failed to ascend into a high-enough “disposal orbit” at the end of its mission. In 1978 it ended up spraying radioactive debris over a swathe of Canada’s Northwest Territories. To avoid a similar accident, darpa’s nuclear reactor will not be flown in low orbits, says Tabitha Dodson, draco’s top engineer.
The recent swell in interest in nuclear power for space can be directly traced to improvements in engineers’ ability to use computers to model their reactor designs. For a long time, scientists believed that, for a nuclear reactor to be able to fit on a rocket, it would need to run on fuel that was highly enriched with uranium-235, an isotope of uranium that easily splits apart. The fuel for the Soviet Kosmos 954, for example, was 90% uranium-235, similar to the material used in the atom bomb detonated over Hiroshima in 1945.
Given the fuel’s worrying potential for dual use, therefore, scientists have had to deal with thick bureaucracy, long delays and huge costs when building nuclear reactors. And, even if all went well, “a lot of guards and guns”, says Michael Eades, head of engineering for usnc Advanced Technologies, a Seattle subcontractor involved in draco. But better computer modelling has, in recent years, allowed scientists to design reactors in which the fuel is enriched to less than 20% uranium-235. That is below weapons grade, so government restrictions will be less onerous.
Want to reach Mars faster? First, split some atoms
America is not alone in its nuclear quest. China and Russia are also developing nuclear power for space. China’s wish list includes a fleet of nuclear-powered space shuttles. Russia is designing an electric-propulsion cargo spacecraft called Zeus, which will be powered by a nuclear reactor. Roscosmos, Russia’s space agency, hopes to launch it in 2030.
The prospect of more capable satellites will, no doubt, raise suspicions among spacefaring nations. Nuclear spacecraft with abundant electrical energy could be used to jam satellite communications. Documents from kb Arsenal, a St Petersburg firm at work on Zeus and, reportedly, another nuclear spacecraft called Ekipazh, refer to the possibility of using large antennae to flood an area with lots of electromagnetic radiation—this could overwhelm the relatively weak radio signals normally sent and received by communications satellites. Such stirrings may have focused minds. In 2019 the then president, Donald Trump, issued a memorandum declaring that nuclear-powered space systems were “vital” to America’s dominance in space. In that and subsequent presidential actions, Mr Trump simplified regulations. His successor, Joe Biden, has not changed course, fuelling subsequent research and development in both government and the private sector.
To boldly go
And not all of the interest in nuclear power comes from the armed forces. nasa, keen to put astronauts on Mars one day, is studying reactor-powered electric propulsion and is also working on a project to develop nuclear thermal propulsion. The second system is named padme—Power-Adjusted Demonstration Mars Engine—and its prototype is slated for testing in 2026.
padme will weigh about 3.5 tonnes and, once in orbit, will be able to accelerate a large spacecraft to 12km a second in around 15 minutes. Such a craft could reach Mars in under six months, three less than with chemical propulsion. nasawants to test it on a possible cargo mission to Mars in the 2030s. By the end of this decade, nasa also wants a nuclear plant to power a base on the Moon. Proposals for a ten kilowatt “fission surface power” facility are due in to the space agency by the middle of February. All this means that one way or another, space is entering its nuclear age. ■