We often think of color in a Roy G. Biv sort of way; young kids are taught about the basic primary colors of blue, red, and yellow, and eventually they graduate to the “color wheel” that you may remember from school. The wheel actually has quite a history: it was Isaac Newton himself who invented it, in 1704. Newton also assigned a musical note to each color; meaning in theory you could take any array of colors - like those in a painting or photograph - and derive a musical composition from them.
A later version the wheel that strongly influenced the way color is taught in schools was invented by Milton Maycock-Bradley (the guy, not the toy company that later bore his name); it turns out Mr. Bradley was extremely worried that kids weren’t learning enough about colors in school.
But more than just learning the names of different hues, it’s the way we perceive color that’s important. As Michael mentioned in his classic video, Is Your Red the Same As My Red?, color does not, in a sense, exist out there independently in the world; it’s a function of the human visual system, a sensation constructed by our brains as they perceive visual input. What we see as color is the way our grey matter interprets varying frequencies of electromagnetic waves that are experienced by the eyes. So a red ball isn’t really red, it’s made of a material that exists in the world in a way that humans perceive it as red - as it reflects red wavelengths of light back into our eyes.
And because of the way our eyes are receiving that red light, the ball is, in a weird way, everything except red, since it’s absorbing the light that’s in every other color of the spectrum but reflecting the red light back at us. So an argument could be made that the ball is actually every other color; you could even consider it “anti-red”! Interestingly, if you want to figure out what colors of light something is absorbing versus reflecting, you go back to that color wheel: an object is absorbing the color that you see on the opposite side of the wheel from which it appears to be; so a blue object is absorbing orange light, a yellow one is absorbing purple, etc.).
While we’re talking about this: what does it mean when you hear people say something “absorbs” some of the colors of light? How does an object absorb colors? It’s really just a way of discussing where the energy in the light goes: when light hits the atoms in the object, the energy is transferred to those atoms, and causes electrons to jump about a bit; so the energy is “absorbed” into the material in the sense that it is transformed into another form of energy and not seen again as light.
For your cube, though, because it’s transparent, most of that light isn’t absorbed, it’s transmitted through. For details on how this affects the colors you see and their wavelengths, check out Michael’s short video on the cube, below. In general, light hitting an object can do three things: 1) be transmitted, 2) be absorbed, or 3) be reflected. This leads to two different ways that things out in the world can be colored (or appear colored to our brains), which are known as additive and subtractive color.
Additive color mixing is, to some degree, the color of light. It’s the colors you see on a computer monitor or phone screen, and is generally made up of red, green, and blue (RGB color), which are combined in various amounts so your brain puts them together to perceive an array of different colors. With additive color, the color you see is created by combining lights of different wavelengths.
Subtractive color mixing involves the opposite - filtering out different wavelengths to get specific colors. Generally it uses a white background and then, like in your cube, the colors are created by mixing different amounts of cyan, magenta, and yellow (called the “subtractive color primaries” - CMY color). Typically, it’s the type of color mixing you get with pigments: printed photos and graphics are created with subtractive color, for example. One of the unusual things about your cube is that it’s an example of subtractive color using white light, rather than pigments.
Now, you might imagine that using additive versus subtractive colors wouldn’t make a lot of difference, but in practice, because of the way each uses different wavelengths of light to create colors, you get some strange results when you compare additive and subtractive mixing. For example, with additive, pink is made up of a mixture of red and purple light; in subtractive, it’s a mix of red and white pigment.
Another strange thing about colors is that because it’s really the interactions between wavelengths that create them, an object’s color doesn’t just depend on what color it “actually” is, but what type of light you’re seeing it in. We usually talk about objects by the color they would appear to be in regular, white light - like the red ball from a few paragraphs ago. In white light, that ball looks red, because the light has all the other colors in it: the ball is reflecting red light back, and absorbing the blue, green, and other colors. If you shine a red light on the ball, it’ll still look red (because there is red light present to be reflected). But what if you shine a blue light on it? It can’t look red, because there’s no red light to reflect back; and it won’t look blue because it’s absorbing the blue light - so it will just sort of look black.
That’s similar to what happens when you view human blood underwater. Blood is red; as you see below, a spectral analysis of its color reflectance shows that. But you’ll also see that it’s a tiny bit green.
graph by Christopher Baird
Now, blood is always a little bit green, but it’s so red that in normal light we don’t notice that, only the familiar bright crimson. But in light that doesn’t have much red - like the bluish light at the bottom of the ocean - the green would show up, but the red would not, and boom - green blood.
Chromatics - the science of color - is a fascinating field, and this is just a taste of the surprising things it’s discovered. It turns out that color really is in the eye of the beholder, and we hope you enjoy beholding your new CMY cube, and all of the many colors you’ll find dancing within.
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Autonomous Underwater Vehicles (AUV’s) are used for deep sea exploration, underwater surveillance, and marine biology research. Because AUVs are so useful, scientists and engineers are always looking for more efficient ways to power them. In 2006, two French engineers proposed a unique AUV engine called the Magnetic Coupling Thruster; it’s a motor that uses commercially available rattlesnake eggs - just like yours - to transmit torque. The new engine could lead to vehicles with longer operational lives, able to explore deeper and farther under our oceans.
And that’s not the only experimental futuretech using the eggs! Robotic hands that can properly mimic the manual dexterity of the human original are complex and difficult to build. But just last year, two engineers at the University of Tulsa created a biomimetic human thumb using rattlesnake eggs - an important step towards engineering functional and efficient mechanical hands that can act like human ones.
Your rattlesnake eggs can also be used to make a rudimentary compass! It’s long been known that if you float a magnet in a bowl of water, it will point towards the magnetic north pole. The first known floating compass dates to China around the year 1050; and they were in use by European sailors in the 1100s. How does it work? The magnetic field of your rattlesnake egg will attempt to align itself with the magnetic field of the Earth; and when floating in water it’s able to move freely enough to do that; the north-south magnetic field in your magnet will line up with the north-south magnetic field produced by the Earth, and voila - a compass! Don’t forget, the magnetic north pole actually moves (around 45 kilometers/28 miles each year) but it’s close enough to true north for general navigation.
For your compass to work, all you need to do is get that magnet to float; but unless you’ve got a tiny, ellipsoidal-magnet-shaped boat handy, that can be an obstacle. We’ve found an easy solution: get a small paper, piece of cork, or light plastic bowl, tape the magnet to the center, then float the small bowl in a larger container of water. You’ll find that the rattlesnake egg will turn to align itself along a north-south direction. Congratulations, you’ve made one of the most important navigational aids in human history! Important note: the north-south magnetic poles in the rattlesnake eggs are not along the long axis of the magnets, but through the short, middle one. So the “pointy” ends of the rattlesnake egg will actually be pointing to the east and west.
Even if you’re not using the eggs to create an advanced propulsion system, a futuristic cyborg hand, or a survival compass, we hope you enjoy the simple, satisfying feel of the rattlesnake eggs in your hand, and the fun sound they make when tossed in the air. Enjoy!
]]>You (or your parents) may remember the original color-changing shirts; they were first marketed in 1991, and were extremely popular; the company that made them sold $50 million in just three months! Your shirt is the modern descendent of those first color-changing pioneers, and can handle washing and daily treatment like they never could.
How do the shirts work? It’s a fascinating combination of chemistry and textile engineering. The first secret is that there are actually two separate dyes in the shirt - a “base” dye (in this case, yellow) and a heat-sensitive leuco dye (in this case, blue). The heat-sensitive dye is contained in tiny microcapsules, along with a weak acid and a salt that’s dissolved in a fatty alcohol called 1-Dodecanol. When exposed to heat, the fatty alcohol dissolves, releasing the salt, which reacts with the dyes and causes them to change color.
Leuco dyes can either start clear and change to a color when warmed, or start as a color and change to clear. For your shirt, when it’s cooler the dye is blue, combining with the yellow base dye to make a green shirt. As the shirt heats up, the blue dye turns clear, showing the yellow base dye underneath. The change generally occurs at around 29ºC (84ºF).
Studies have shown that using thermochromic paints based on that same technology could save billions of dollars every year. How? Through energy conservation, using paint that turns dark in the winter (absorbing light) and light in the summer (reflecting it), in order to increase the efficiency of heating and cooling. Scientists have found it’s possible to save almost 51% of heating and cooling costs by painting a building with thermochromic paints; doing so made the buildings 11ºC (20ºF) cooler in summer and 2.7ºC (5ºF) warmer in the winter! And more than just paint, researchers are studying how to make the entire building - the concrete, the windows, even the asphalt on the road outside - similarly color-changing, for even more savings. We may one day live in cities that look different depending on whether it’s warm or cold outside.
Thermocromic tech could also save more than 3,000 lives annually in the US alone! Each year, spoiled food causes 3,000 deaths, 78 million illnesses, and $6.5 billion in medical expenses. So the US Department of Agriculture has sponsored promising research into “smart packaging” - thermochromic labels that would show people if the food they buy had ever been heated to the point where bacteria or other pathogens might be present, alerting customers that the perishables inside could make them sick.
Thermochromism can also be found in nature, including among that most desired of gemstones: the diamond. “Chameleon diamonds” are an extremely rare form of carbon that changes color when exposed to heat - around 150°C (302°F). And just like your shirt, chameleon diamonds change from green to yellow. Because of their rarity, chameleons are also extremely expensive, roughly twice the price per carat of a beautiful “normal” diamond, routinely fetching $20,000 USD or more for just .2 grams of stone.
We can’t promise that your shirt is worth twice its weight in diamonds, but we can say it’s a lot of fun, and the shifting designs are always intriguing. So get out there and let your colors shine! And shift.
]]>One of the many interesting things about Lucas’ Tower is that there is an equation that will tell you the minimum number of steps you can take to complete the puzzle - the optimal solution. Since you can make a Lucas’ tower with any number of disks (in theory), that number is determined by an explicit equation: 2^n-1, with n being the number of disks. In your case, with eight disks, that means the fewest number of moves possible to complete the puzzle is 2^8-1, or 255.
That formula is actually what ties the Tower to the legendary Hitchhiker’s Guide to the Galaxy. It has to do with the number 42, which as anyone who’s read, seen, or listened to an adaptation of the Guide knows, is the answer to the Ultimate Question of Life, The Universe, And Everything!
We’ve found that eight disks make for a satisfying but solvable puzzle, but do you remember the number in the mythical temple of the tower’s origin story? (just so you don’t have to go back and look that up, it’s 64). Now, as computer scientist Ian Parberry discovered, if you plug 64 disks into the solution equation, you find that according to that story, the puzzle that will bring about the end of the world when solved will take the monks 2^64−1 moves to complete. If they move a disk once per second (they’re monks who have spent their lives moving the disks, so they’re probably pretty good at it), that will take them 5.85x1011 (585 billion) years. While the precise age of the universe isn’t known, cosmologists believe it’s around 13.77 billion years old. And if you divide 585 billion by 13.77 billion you’re in the ballpark of - you guessed it! - 42. Maybe Douglas Adams was onto something after all.
How about the strange death of Édouard Lucas, inventor of the puzzle? Lucas was a renowned French mathematician, known for his work on number theory; among other things, he coined the term “Fibonacci sequence.” But poor Édouard died in what’s been called an “absurd accident,” all because he picked the wrong place to eat dinner.
One night in 1891, Lucas was enjoying a fancy banquet at the French Society for the Advancement of Science, when a passing waiter dropped an armful of plates. As the crockery shattered, a fragment rocketed up and scratched Édouard Lucas on the cheek. A minor cut, no problem, right? A few days later, the scratch became infected, and one of the greatest mathematical minds of the 19th century passed away, from what is now an easily curable case of erysipelas.
Poor Édouard is gone, but his legacy lives on! Our Lucas’ Tower is a classic, compelling puzzle, with a clever but achievable solution. We hope you enjoy it.
]]>We’re very excited about this set of stereoviews: things you would never be able to see in 3D without this technology (or at all!) because they are lost to us forever. Extinct animals, demolished buildings, natural wonders destroyed by time, or vanished into the depths of space: this is a reel of things we are truly privileged to see.
Slide 1: Quagga; went extinct in 1883
This may look like a weirdly striped zebra, and essentially, that’s what it is: the quagga was a subspecies of the plains zebra that had an unusual coat pattern - their stripes slowly faded below the neck, totally disappearing by the hindquarters (the rear was also more of a tan than the white color of a standard zebra). Extensively hunted for meat and hides, quaggas became extinct in the wild by 1878. The individual in your stereoview - the last living member of the subspecies - died in an Amsterdam zoo in 1883.
But luckily, before they went extinct, some quaggas bred with the regular zebra population, and the genes for the distinct stripe pattern still exist in the zebra gene pool. In 1987, the Quagga Project, a selective breeding program, began to re-breed the quagga stripe pattern back; and they’ve had some success. After four generations, the project has bred “new” quaggas! Though not genetically identical to the last true quagga that you see on the slide, they sure do look alike. So in a sense, the “quagga” may be back.
Slide 2: Thylacine, or “Tasmanian tiger”; went extinct by 1936...or did it?
The Thylacine, also known as the “Tasmanian tiger” and “Tasmanian wolf,” wasn’t really related to tigers or wolves at all: it was the largest known predatory marsupial, and the apex predator of its environment. That's right, it’s basically the T-rex version of a kangaroo!
The size of a medium dog, originally the thylacine lived all across Australia and New Zealand, but by the time of European contact, the only thylacines remaining were on the island of Tasmania, where they were hunted to extinction. In 1936, just two months after a law had been passed to protect the species - too little, too late - the last living animal, named Benjamin, died in a Tasmanian zoo.
...or did it? For decades after the “official” extinction of the thylacine in 1936, people reported seeing them in the wild. And not just a few people - over a thousand. Between 1910 (the supposed date of wild extinction) and 2020, 698 members of the public, and 429 experts, claimed to have spotted thylacines. Based on the range and frequency of the sightings, a group of biologists recently reset the extinction window, claiming that it probably happened sometime in the late 1990s or early 2000s!
Their study, if you’re curious, can be found here.
Slide 3: Old Man of the Mountain, New Hampshire; collapsed in 2003
One of the most famous rock formations in the United States, the Old Man of the Mountain watched over Franconia, New Hampshire for more than 10,000 years before collapsing on May 3rd, 2003.
The indigenous Abenaki called the formation Stone Face, and long before Euro-Americans discovered the Grand Canyon or the Yellowstone basin, the Old Man was seen as one of the predominant natural wonders of the newly-formed United States of America. He was a huge tourist attraction in the mid-1800s; Nathaniel Hawthrone wrote about the Old Man in his famous story, “The Great Stone Face,” in which a local prophecy says that a child would be born in the town beneath it, who would become "the greatest and noblest personage of his time.” Daniel Webster wrote “up in the Mountains of New Hampshire, God Almighty has hung out a sign to show that there He makes men.”
But the face was actually a delicately-balanced geological feature, and was always in danger of collapse. Attempts to affix it to the mountain with metal ties and other contraptions were made in 1916, 1936, and 1958. In 2003, it fell due to two natural processes: kaolinization, a metamorphosis where stone chemically turns into clay, and the geological freeze-thaw cycle you’d expect of a New England winter. Sadly, all that remains today is a bare mountain cliff.
Slide 4: Pink Terraces, New Zealand; destroyed by volcano in 1886
Once known as the Eighth Wonder of the World, the dazzling Pink Terraces, called Te Otukapuarangi in Maori, were located on the shores of Lake Rotomahana in New Zealand. Formed by silica-rich water from a group of geothermal mineral springs tumbling down a hillside, the Pink and neighboring White Terraces drew visitors from thousands of kilometers away, who traveled for weeks, and even months, to see what you’re seeing right now.
Though other sinter terrace formations can still be found in Yellowstone National Park (US), Pamukkale (Turkey), and a few other places, the Pink and White Terraces were the largest formations of this type ever known to exist; they took between 500 and 1,000 years to form.
But being part of a volcanic geothermal system means that area was a ticking time bomb. On June 10th, 1886, Mount Tarawera erupted in what is considered the worst natural disaster in New Zealand history. It cost 150 lives, destroyed the Maori village of Te Wairoa, and radically altered the local landscape. The amazing Pink and White Terraces were completely obliterated.
...or were they? For over 100 years, people have pored over old maps and 19th century compass readings, looking for their remains. In 2011, scientists using underwater imaging equipment claimed to have found the remains of the terraces, about 60 meters below the lake’s surface. But another group of geologists challenged those claims, saying the first group had misread the original location of the terraces, and that they were actually buried by ash on the shore of the lake. The two groups have been going back and forth for years, publishing increasingly snarky articles in scholarly journals saying the other group doesn’t know what they’re talking about, the most recent in 2020.
We may never know if anything remains of these beloved natural wonders. But we know nobody will ever be lucky enough to see them again, as you do on this slide.
Slide 5: Comet Morehouse; will not return after single 1908 visit
Comet Morehouse - official designation C/1908 R1, was a non-periodic comet discovered in 1908 by astronomer Daniel Morehouse, who got to name it. Non-periodic means that the comet’s one and only visit to the Sun was in 1908, and it will never be seen (by human eyes) again.
Morehouse was known for the remarkable and unusual variation in its tail; sometimes it would be short, sometimes long, occasionally wavy, and sometimes it looked like the comet had seven different tails. Astronomers at the time suspected that bits of the comet’s nucleus split off and followed behind it, creating the extra mini-tails.
Morehouse was also one of the earliest comets to have its spectra studied, allowing scientists to determine its composition: in this case, a lot of carbon monoxide.
Slide 6: The Crystal Palace, London; burned to the ground in 1938
The Crystal Palace was a giant, glass-and-iron building, built for the 1851 Great Exhibition of the Works of Industry of All Nations, the first world’s fair, held in London and organized by Prince Albert, husband of Queen Victoria.
The Palace was enormous: 1,848 feet long, 460 feet long wide, and 108 feet tall. When completed, it held over 100,000 exhibits (including pianos, perfumes, hydraulic presses, and other wonders of the Victorian age), laid out on eight miles of display tables, and included a small forest of 90 foot tall trees. Millions of people passed through the glass doors, and the exhibition was one of the defining cultural moments of the 19th century.
The Palace was initially built in Hyde Park, just two years after the fair, they moved the entire building - including all 294,000 panes of glass - to a park in a different area of London. That park also became famous for the Crystal Palace Dinosaurs, the first attempt ever to recreate dinosaurs life-sized.
But in November 1938, a small fire in the palace (possibly in the workshop of John Logie Baird, the inventor of television) became a roaring inferno. More than 80 fire engines responded to save one of the treasures of London, but it burned to the ground. Winston Churchill called it “the end of an era.”
Today, the Palace lives on in the Crystal Palace Football club, the oldest football/soccer club in the world, and the park surrounding the site. Of the Palace itself, only parts remain - mostly decapitated statues and a few stone sphinxes. But here you can see it in its heyday, as one of the most magnificent buildings of it’s time.
Slide 7: Frank Lloyd Wright’s Imperial Hotel, Tokyo, demolished in 1967
Frank Lloyd Wright is arguably the most famous architect in the world; certainly of the 20th century. But despite that, many of his remarkable buildings have been destroyed; and the Imperial Hotel in Tokyo was among the most majestic. Wright had a deep affinity for Japan and it’s art, and it was the only country outside of the US where he ever lived and worked.
Designed by Wright in a Mayan Revival style (though he’d probably have denied this), the hotel took four years to build, 1919-1923. Wright was on the cutting edge of construction methods in that era, and the hotel is built of uniquely designed patterned concrete blocks, reinforced poured concrete, and Ōya stone.
It opened on September 1, 1923 - by horrible coincidence, the same day as the Great Tokyo Earthquake, a 7.9 Richter temblor that demolished almost all the buildings nearby, leaving the Hotel standing amidst a pile of rubble. It’s survival was credited to Wright’s unusual construction technique and several earthquake resistant features he’d built into the design. But nothing could save the Hotel from progress, and in 1968, it fell to the wrecking ball, where a newer, taller Imperial Hotel replaced it.
A small part remains: the central lobby and reflecting pool were saved, and are now at the Meiji-mura museum, in Inuyama, Japan.
This is a reel of truly historic photographs: the very first 3D images ever taken of these subjects. Prior to the ease of modern travel and proliferation of printed photos, most people never got a chance to see distant sights or attend legendary events. Imagine the wonder people experienced the first time they ever saw things like the pyramids of Egypt, an exhibition of ancient treasures they’d never otherwise visit, and the first wedding photos ever taken!
As you look at the dates on these photos, remember that photography had literally just been invented. The first glass (daguerrotype) photos were taken in 1838; and the first collodion print - which many of these photos are - in 1851. Because of their age, very little is known about most of these photographs.
Slide 1: First 3D image of a museum, 1854
This image is from the first series of stereoviews ever taken of a museum, and shows the Egyptian Hall at the British Museum. It was taken by Peter Fenton, who was inspired to become a photographer after seeing early photos at the Great Exposition at the Crystal Palace (Slide 6 of the Things That Are Lost reel).
Fenton was asked to photograph the museum by Charles Wheatstone, the inventor of stereoscopic photography, and became the museum’s first official photographer in 1853.
Slide 2: First 3D image of the moon, 1858-1859
This is actually a “trick” steroeoview! Photographing the Moon can be difficult even today - and it was really hard in the earliest days of photography. Due to exposure times and other limitations of the first cameras, instead of actually taking two simultaneous stereo images of the moon, this is really two individual photos taken 15 months apart, when the moon looked similar enough to make a stereo image.
The technique was invented by the man who took the photos, William de La Rue, one of the earliest astrophotographers. To do it, he not only had to figure out how far apart (in time) to take the pictures, but also develop his own clockwork mechanism to move the telescope and track the moon as the image slowly developed. De la Rue was a member of the wealthy De la Rue family, whose company (DeLaRue) still exists, literally printing money for countries around the world.
Slide 3: Michael Faraday, first 3D image of a scientist, 1848
This very early photograph (1848!) is of Michal Faraday, one of the preeminent minds of the mid 19th-century. Faraday’s discoveries revolutionized science, and led to a tremendous amount of the technology in our daily lives.
Faraday discovered electromagnetic induction, which creates an electrical current; and from that he invented the machines that are the foundation of much of modern society: the electric motor, transformer, and generator. He also discovered benzene, coined the terms “electrode,” “cathode,” and “ion,” and invented the Faraday Cage, which you'll find, among other places, in the window of many microwave ovens.
Slide 4: First 3D image of a woman, 1850
This stereograph of an unknown female model was taken by Alexis Gaudin in 1850. Gaudin was one of the earliest stereo photographers, and the only one to exhibit stereo images at the 1851 London Exposition; so it was probably his photos that inspired Peter Fenton, who took the British Museum photo in slide #1, as well as the interest of Queen Victoria, below. He also founded the magazine La Lumière, one of the very first publications dedicated to photography.
The identity of the woman in the image is, alas, lost to time.
Slide 5: Queen Victoria, first 3D image of a head of state
Queen Victoria is, without doubt, one of the most famous and influential monarchs in history, and oversaw the British Empire at its height. She was also fascinated by photography, first becoming entranced by stereographs at the 1851 London Exposition (you may be starting to sense a trend here).
In 1854, she summoned photographer Antoine Claudet to Buckingham Palace, and had him make four stereo images. They are the first known 3D photos of a head of state; Victoria was just 35 years old at the time.
Photographs of that era were, of course, in black and white, but many of these slides were hand-colored to show Victoria’s blue dress and sash.
Slide 6: Wedding of Tom thumb, first 3D wedding photo
The so-called “Fairy Wedding” of Charles Stratton, aka General Tom Thumb, was one of the biggest social events of the 19th century: it literally made international headlines, and bumped coverage of the Civil War off the front page of the New York Times for three straight days! It was also the first known wedding to be photographed.
Stratton was a little person, and one of the most popular performers managed by P.T. Barnum. And flawless promoter that he was, Barnum turned the wedding into the event of the mid-century. The bride and groom arrived at the church in a carriage made by Tiffany & Co.; Barnum charged people $75 each to attend the reception (about $1,600 in today’s money); and after the wedding, the Strattons were invited to the White House by Abraham Lincoln. Barnum then arranged for the wedding to be re-created in the studio of early photographer Matthew Brady, who created the photo on your stereo reel.
One of the strangest things to come out of the event was the proliferation of “Tom Thumb Weddings”: ceremonies where people would have two children dress up like grown-ups and pretend to get married, largely for entertainment purposes (sometimes, they argued, to teach the kids about manners). These were a huge deal in the 19th century, and amazingly still happen! About a dozen Tom Thumb Weddings occur each year in the United States.
Slide 7: Giza, Egypt, from the first set of 3D images taken outside Europe, 1856
Frances Frith wasn’t the first person to take photographs outside of Europe; several series of photos of Egypt were published before he made his famous trip there 1856. But he was, so far as we can determine, the first to take a stereo camera there, and produce 3D images for people to see these legendary locations.
Frith’s photo expeditions were complex affairs: he carried three cameras, and they each took photos on glass plates that had to be kept both intact and wet; no mean feat when you’re talking about carrying 16x20-inch glass plates over desert dunes on a camel.
This photograph shows the Great Pyramid of Khufu and the Great Sphinx. The Great Pyramid was the tallest man-made structure in the world for over 4,000 years, and at 4,500 years, the Great Sphinx is considered to be the oldest monolithic statue in the world. The photo was taken when most of the sphinx was still buried in the desert sand, with only the neck and head exposed. The statue wouldn’t be completely excavated until 70 years later, in the mid 1920s!
“I consider Hein’s invention, like many puzzles, to be a work of art...I created my own version of it long before I even imagined making the [Rubik’s] Cube.”
- Erno Rubik
In Cubed, Erno Rubik’s 2020 book about his life and work, the creator of the best-selling puzzle of all time spends several pages writing about the Soma Cube. He details his own attempts to make one from scratch, and how it was one of two inspirations for the shape of his own iconic puzzle (the other, if you’re curious: MacMahon’s Cubes).
Rubik wasn’t the only person inspired by the Soma; when it was first released in the early 1930s, it became a hit in Hein’s native Denmark; but it wasn’t internationally well known until 1958, when Curiosity Box favorite Martin Gardener wrote about the Soma in his famous Scientific American column. Suddenly, the cube exploded in popularity; fans created hundreds of new shapes that could be made with Soma pieces, and Parker Brothers, who released a version of the cube in 1969, even published a magazine called “Soma Addict.” (if you’d like to find more shapes and figures to create with your cube pieces, the magazine is full of them, and you can read past issues here.)
For decades, the story behind the Soma Cube was that Hein came up with the idea for it when his mind wandered during a dense 1936 lecture on quantum mechanics by Werner Heisenberg, Nobel Prize winner and namesake of the famous Uncertainty Principle. As Heisenberg started to talk about space being sliced into cubes, Hein’s mind wandered, and he thought about ways to put a bunch of shapes together to form a cube.
It’s a great story, involves two great thinkers, and shows the value of daydreaming. But... here's the thing: recent scholarship has found that Hein’s first patent was issued in Denmark on December 2, 1933 - three years before the alleged lecture. Further research shows that Heisenberg did actually give his famous Nobel lecture on quantum mechanics in 1933 - but on December 11, nine days after the patent was issued. This is why your box says that’s how the cube was “legendarily” created. That said, it’s possible that Hein came up with the idea during a lecture that wasn’t by Heisenberg, or that it was an early lecture by Heisenberg on a different subject, so we can’t completely discount it; Hein never corrected the story, probably because it was good press. As, for example, was the other legendary story about the cube: it’s name.
Many places - including Wikipedia - repeat the story that the cube is named after “Soma,” the recreational drug from Aldous Huxley’s famous 1932 science fiction novel Brave New World. In the book, Soma is a drug given to the populace to keep them happy and in line; it smooths out feelings and emotions, and in larger doses lets people go on a soma holiday, where they completely tune-out. The idea is that the cube is so addictive, it’s like taking a drug.
But it’s not clear where that story came from. Hein himself, on the original Soma package, claimed that “SOMA is the ancient Indian symbol for life's diversity and the universe's hidden connection.” Of course, that doesn’t seem to be the case, either. Its a Sanskrit word, but for a juice or drink made from the sap of the Cynanchum viminale plant, which was used ritually and medicinally in India. Hein presumably liked the word for it’s exotic and mysterious connotations, as did Huxley.
In fact, hidden meanings and cyphers were at the core of Hein’s part in the anti-Nazi resistance during WWII. After the Germans occupied Denmark, Hein said he had two options: flee to Sweden or join the resistance. He stayed, and became famous for a series of poems he called Grooks, which he wrote under a pseudonym that translates to “tombstone” and published in the newspaper Politiken. The grooks were really coded messages of resistance and hope for his fellow Danes; their subtlety allowed them to escape the Nazi censors. Hein’s most famous grook may this one, titled Consolation; it translates into English as:
“A person who loses one glove,
is fortunate compared to the person
who loses one, throws away the second,
and then finds the first one again.”
The message is that once you’ve lost one glove - your freedom under the occupation - don’t lose the second by becoming a collaborator. Especially if the war ends and people find out (i.e. finding the first glove again).
Hein survived the occupation, and went on to an extremely successful career as a furniture designer, puzzle creator, and artist. Today, the cube is still popular - enough to have it’s own Guinness World Record category, “Fastest Time to Complete a Soma Cube”! This isn’t a dusty old record: the newest one was set just a few weeks ago, on October 22, 2021! It’s held by Ye Jiaxi of China, who was able to solve the cube in an astonishing 1.4 seconds; beating the previous record holder, Lim Kai Yi of Malaysia, who solved the cube in 2.4 seconds last April. You can see the latest world record here.
Our unique take on this legendary puzzle celebrates seven of our favorite hues of blue, matching nicely with the book Blue, In Search of Nature’s Rarest Color. We’ve provided the perfect tool - now can you break the new world record?
]]>Curiosity Box: Kai, in this book, you travel around the world. What’s an amazing, surprising, or funny story from your journeys?
Kai Kupferschmidt: One thing that has really stuck with me was visiting Yoshikazu Tanaka in his laboratory outside Kyoto. Tanaka had worked on creating a blue rose for more than a decade, before he finally succeeded in breeding a rose that produced blue pigment. I asked him what his first thought was when he saw that flower for the first time and was expecting him to describe his joy and exhilaration.
He said: “Could be bluer.”
Incidentally, Tanaka works for Suntory, a beverage company famous for its whisky (it features heavily in “Lost in Translation”). So while I was in Kyoto I did go on a tour of the brewery including a whisky tasting. I was probably the only person on that tour who really doesn’t like whisky.
CB: What’s a place you’d really like to go back to? One you haven’t been able to visit yet?
KK: I hope I’ll have a chance to visit Crater Lake in Oregon again some day, which is famous for its blue water. When I was there the smoke from wildfires was hanging in the air and it was not very sunny. It’s a beautiful place in any weather, but I could tell how stunning it must be in sunny conditions. So I hope to see that some day.
Crater Lake, Oregon
There are also many places I still want to see. I have a whole list of “blue” places I want to visit when I have the chance. I would love to see hyacinth macaws in the wild, for instance, and there is a species of frog whose males for a brief period each year change their skin color to blue. I really want to go and see this too.
CB: One thing we love about this book is that the reader isn’t just learning about the color blue; to explain and explore it, they also learn about the physics of visible light, and x-ray crystallography, and cellular biology and a vast array of other scientific principles and processes. Which was the hardest thing to explain? The easiest?
KK: Yes, this was one of the challenges in writing this book. You can only explain things really well that you have understood really well yourself. I studied molecular biomedicine, and so explaining things like the evolution of color vision or plant pigments was much easier for me than, say, the physics of what makes lapis lazuli appear blue. But the nice thing about being a science journalist is that you can just call experts and ask them to explain these things until you understand them well enough to explain them to others.
CB: What’s something you wish you knew when you started writing the book?
KK: Sometimes it helps not to know a lot at the outset. I started this book with a lot of questions and knowing very little about what I might find in terms of answers. There are much more efficient ways to write a book I think, but it made for an exhilarating experience and I really enjoyed it.
CB: So...what’s your second favorite color? What intrigues you about it?
KK: I've never really thought about that! It’s probably green. I just find it very soothing and it is amazing to think that chlorophyll, which colors leaves green, is likely the most abundant pigment on earth.
Come to think of it, it’s also fitting for green to be my second favorite color given that many languages do not have separate words for green and blue.
CB: Do you have a favorite hue of the color blue? One that instantly grabs you?
KK: The one that most stands out to me is International Klein Blue. That’s the hue “created” by the artist Yves Klein. (It’s really the combination of synthetic ultramarine and a specific binding agent called Rhodopas M60A that does the trick.) At one point when I was writing the book I went to Paris to see some of Yves Klein’s works at the Centre Pompidou. I remember standing in front of this large, entirely blue canvas there and just having this very visceral reaction to it. The color really packs a punch in a way that I have rarely experienced. It’s almost as if the blue is so intense that it just overwhelms your senses, as if you cannot put any distance between yourself and the color.
Another blue that comes close is YInMn blue, which I got to produce myself in Mas Subramanian’s lab at Oregon State University in Corvallis.
Feeling Blue: 7 unique shades, including Klein Blue, chosen by Vsauce for their re-imagination of the famous Soma Cube puzzle in the Fall Curiosity Box
CB: What’s something that you really wanted to put in the book, but just didn’t quite fit in somehow? Something that got edited out?
KK: There is so much. The color blue is endlessly fascinating, and there is no way to include everything there is to say about it in one book. I really had to force myself to just focus on some things and the structure of the book helped with that.
One thing I would have loved to talk about but that did not fit well into the structure is the story of Paul Ehrlich and methylene blue. Ehrlich was a famous researcher (he won a Nobel prize in 1909), and he discovered that a blue dye called methylene blue was good at staining bacteria or the malaria parasite but not human cells for instance. It gave him the idea that the compound might actually work as a drug against these pathogens, and that was really the birth of chemotherapy, and has led to the modern era of antibiotics and other drugs.
CB: You originally wrote this book in German; is the English edition different in any way? How is it experiencing your book in another language?
KK: This is something I really struggled with. These days I write mostly in English (I work as a journalist for Science Magazine). But I carried the idea for this book around with me for a long time and it became very personal. So when I started writing it, I wanted to make sure I found a voice that felt like it was truly me, that sounded like me. And I just felt more comfortable doing that in my mother tongue, German.
The translator did a fantastic job, but invariably there is something about the sound that is just hard to convey in a different language. And of course there is a whole chapter in the book about language that is an absolute nightmare to translate! It is all about the meanings of “blue” and has a lot of wordplays. On the other hand, the English version is a special case, because I do speak the language, and I did go over the translation and made changes where I felt I could convey a better sense of what I meant. That is a luxury I do not have with the other translations of this book, for instance the Korean version that came out recently, or the Italian one which is coming soon.
CB: What was something that really surprised you when you were researching the book?
KK: I was really surprised how much history is associated with some of the blue compounds I researched, and how easily stories went from beauty and joy to horror and darkness. Take Prussian Blue, which alchemists discovered by accident in Berlin at the start of the 18th century. It quickly became a pigment beloved by artists. Van Gogh used it in his "Starry Night,” Hokusai in his famous print “Under the Wave Off Kanagawa.” But researchers trying to understand its chemical composition then discovered a deadly poison, prussic acid or cyanide. This became the basis for Zyklon B, the poison the Nazis used to carry out mass murder in their concentration camps. Today, Prussian Blue in yet another twist is an important medicine to treat certain types of poisoning.
CB: What’s your next project?
KK: For the last one and a half years I have been completely immersed in covering the COVID-19 pandemic for Science Magazine. I hope for all of our sakes that I can get back to writing about other things again soon but I feel that it is still too early to make any such plans.
CB: Finally, this book is still new, so it may be too soon to ask this, but: are there any updates on some of the research you mention in the book? It looks like some Spix’s Macaws were born in the wild a month or so ago. Has David Dobson managed to stabilize ringwoodite, for example? Did Suntory breed a bluer rose?
KK: I have no updates from Dobson or Suntory yet. Mas Subramanian’s YInMn blue finally hit the shelves as a color for artists this year, and he has pushed forward on developing another class of blue pigments. Since the book has come out there have also been quite a few interesting scientific developments: I recently wrote about a research paper that found a new way to produce a blue food colorant from red cabbage, for instance!
We’d like to thank Kai for sitting down and taking the time to answer our questions, and hope you enjoy Blue: In Search of the World’s Rarest Color!
]]>Slide 1: Solar flare and spicule
The first two images are from NASA’s Solar TErrestrial RElations Observatory (STEREO) mission, a unique solar observatory that consists of two identical spacecraft that provide the proper binocular disparity to create 3D solar images. The STEREO-A spacecraft is located ahead of the Earth, leading it in orbit around the Sun; and provides the “right eye” perspective. STEREO-B is located behind the Earth, following the Earth in orbit and providing the “left eye” perspective (the “A” stands for “ahead” and the “B” for “behind”).
This image from STEREO’s Extreme Ultraviolet Imaging Telescope was taken on March 17, 2007; the green is a false-color added for clarity, showing the area of the Sun’s atmosphere that is at 1.5 million℃. The feathery structure you see is a “spicule” - a burst of gas that explodes off the Sun’s surface - that stretches up to 10,000 km, then collapses. As many as 10 million of them are erupting at any given time!
Slide 2: Solar prominence
Your second image taken by the STEREO mission, this slide shows a solar prominence erupting from the left limb of the Sun’s north pole on March 20, 2007.
Prominences are eruptions of plasma from the Sun’s surface that extend into it’s corona; they flow along a twisted structure of magnetic fields that are generated in the Sun’s interior. A typical solar prominence reaches a height of 100,000 km, almost ten times the diameter of the Earth! The red false color shows the features of the Sun that appear around 80,000℃.
Slide 3: Ares Vallis floodplain, Mars
This photo taken by the Mars Pathfinder spacecraft shows its landing site on the Ares Vallis floodplain, including the airbags and solar petal of the craft itself. Ares Vallis is an outflood site, carved by rivers of liquid (probably water) during a warmer period in Mars’ past.
The airbags are part of Pathfinder’s amazing landing system: it involved supersonic parachutes and a cocoon of airbags that blew open and enveloped the craft about ⅓ km (1,000 feet) above the surface. Upon impact, the airbags caused Pathfinder to bounce 15 meters (50 feet) back into the air like a superball! It bounced about 15 more times before settling on the landing site.
Slide 4: Pooh Bear rock and Mermaid Dune, Mars
This photo was taken by the Pathfinder mission’s Sojourner Rover on the Ares Vallis floodplain. The large rock on the left is called Pooh Bear, and the smooth area stretching across the top of the image is the Mermaid Dune. Many of the rocks at the Pathfinder landing site are named after cartoon characters: in addition to Pooh Bear, other formations are Piglet, Scooby Doo, Stimpy, and Yogi!
Slide 5: Comet 67p dust jet eruption
Here’s some good news: you may get to see this comet live, in just a month! The downside: you’ll need at least an 8-inch telescope to do it, so check with your local astronomy club. Comet 67p, also known as Churyumov-Gerasimenko, has an orbit of 6.45 years, and it’s next closest approach to Earth will be on November 12, 2021. 69p is the first comet humans ever landed on: in 2014, the ESA’s Philae robot lander dropped from the Rosetta spacecraft and touched down on its surface.
This image shows typical (and dramatic!) cometary behavior: as they near the sun, comets start to melt, causing them to blast gas and dust off into space. How much do they melt? Comet 69p loses about 1 meter of thickness with each orbit. The smaller lobe has a diameter of over 2 km, and will completely evaporate in a few thousand years.
Churyumov-Gerasimenko is a “Jupiter Family” comet, and its orbit loops around the Sun, crossing the orbits of Jupiter and Mars; but it doesn’t cross Earth’s orbit - right now. Its orbit has shifted significantly over the last few centuries. Before 1840, the closest it got to the sun was 4 AU, which wasn’t close enough to melt any of its ice - meaning the comet had no tail, and wasn’t visible from Earth. Passing by Jupiter in 1840 altered its orbit enough to bring it even closer to the sun, at 3 AU. Further orbits brought it ever closer, and by 1959, it was orbiting at just 1.3 AU from the sun. In 2220, it will cross Earth’s orbit, at just .8 AU.
Why does it have two names? 67p means it was the 67th periodic comet to be discovered, and the people who discovered it were Soviet astronomers Klim Churyumov and Svetlana Gerasimenko.
Slide 6: Pluto
The largest of the Trans-Neptunian Objects, Pluto was once thought to be a bland, featureless world; but NASA’s New Horizons spacecraft showed it had mountains, craters, glaciers...and red snow. This image was taken by New Horizons in 2015.
The scarlet plain you see on the bottom left is the Cthulhu Macula, an area covered by reddish tholins that fall from the sky like snow (and yes, named after H.P. Lovecraft’s Cthulhu). On the right, you’ve got the heart-shaped Tombaugh Regio; the left half of the heart is a giant glacier of frozen nitrogen.
Slide 7: Arrokoth
The end of our tour leads to distant Arrokoth, the farthest object yet visited by a human spacecraft: NASA’s New Horizons flew past it in 2019, four years after encountering Pluto. Arrokoth is the word for “sky” in the Powhatan/Algonquian language; prior to its official naming, the object was known as Ultima Thule. The minor planet is about 36 kilometers long.
Arrokoth is extremely distant: 6.6 billion kilometers from Earth (and 1.6 billion kilometers past Pluto). It orbits the sun once every 293 Earth years and has an unusual shape from being a “contact binary” - meaning that it was once two objects until gravity pulled them ever closer, finally smooshing them together.
Slides 1 & 2: Impossible colors
The first two slides are “impossible colors.” These are colors that don’t in a sense really exist, because your brain can’t normally process them. Why not? What we perceive as colors are wavelengths of light received by the cone cells in your eyes. The brain then combines the millions of signals from your cones and creates a composite image of the color you’re seeing. So in a sense colors don’t exist, only the perception of them that our brains put together.
But here’s the weird part: the neural cells that register those signals can only process one color at a time; some of them are blue or yellow, and some of them process red or green. When you look at a green image, the green portion of that neuron is stimulated and the red portion inhibited. So your brain literally can’t normally register a color that is equally red and green, or equally blue and yellow (there’s also a good explanation of this on pages 75-76 of your new Blue: In Search of Nature’s Rarest Color book). But experiments in the early 1980s showed that if you can show each eye, completely separately, the opposing colors, the brain combines them into the so-called “impossible” colors.
To make these slides work, stare at the cross in the center of each one; your brain will produce the impossible color. One important note for best results: the colors entering each eye should be the same luminance, so try and use a stable light source that shines equally brightly into both eyepieces.
Slides 3, 4, & 5: Binocular Rivalry
The third, fourth, and fifth slides on this reel explore the phenomenon of “binocular rivalry.” Normally, each of your eyes sees a very similar, but slightly different image, and the brain puts them together into one single picture. Binocular rivalry happens when the eyes present the brain with two images that are so different from each other that it can’t merge them into one image. Instead, your perceptual experience will alternate between the images. For example, in slide 3, you’ll start off seeing a person’s face, then after a few seconds, it will switch and you’ll be looking at a building. The time between switches changes randomly, but it’s generally every 3-4 seconds.
Neuroscientists use binocular rivalry experiments to investigate perceptual conundrums, including:
Slides 6 & 7: 3D afterimage
For this illusion, we’ve presented a negatively inverted 3D image of the Earth. By staring at the dot in the middle for about 30 seconds, and then clicking to the next slide (the blank one), you should see a regular, positive color 3D afterimage of our home planet.
Afterimages occur because when light enters your eye, it produces chemical changes in the photosensitive cells called rods and cones. If you stare at the same thing for too long, the chemicals can get temporarily “exhausted,” desensitizing the cells to the color they’ve just been staring at. When looking at a neutral background, the other, fresher cells nearby send a nice bright input, while the exhausted ones send only a weak signal, and you see the reverse of the image you’ve been staring at - the afterimage.
Focusing on that dot in the middle of the image is important to making those photoreceptors tired. That’s because your eyes normally have tiny little jittery movements called “saccades,” to prevent them from becoming fatigued when staring at the same place for too long. Focusing on the dot in the center reduces the saccades, allowing those photoreceptors to get tired, and the afterimage to appear!
That’s why so many optical illusions have focus points in the center; your eye is pretty good at avoiding the types of tricks that cause these illusions, and the saccades are a big part of that.
]]>Now that you’ve performed the experiment and see some colonies nurtured in the agar of your petri dishes, you’re probably wondering: what’s in there? What am I actually looking at? Here are some broad guidelines for figuring out what you’ve grown in each petri dish (we’ll have some specific ideas in a bit):
Figuring out the specific species you’ve got growing can be a little tougher, though. There are over 3,500 different genera of bacteria, with more than 20,700 specifically known and named species. And that’s just the tip of the iceberg: scientists think there are probably over 200,000 total species! To identify them, microbiologists consult Bergey's Manual of Determinative Bacteriology, a 750 page book that lists the colony characteristics, then cross-reference that with the much longer (!) 4-volume Bergey's Manual of Systematic Bacteriology. For preliminary identification, scientists rely on four characteristics: the color (pretty obvious), the form (shape of the colony), elevation (what it would look like in cross-section), and the margin (the shape of the colony’s edges). Here’s a general guide:
While it’s possible to identify the type of growth just by looking at the colonies, determining the specific species usually requires more specialized equipment: particularly a microscope for identifying the shape of an individual microorganism in the colony. And since there are over 150 species of bacteria on your hands alone, we unfortunately can’t give you a rundown of everything that might be growing on your petri dishes. But a few good possibilities of what you might be looking at, and their characteristics, are right here:
So, how many bacteria are in each colony you’re growing? Of course that depends on the species of bacteria present in the colony (they come in many different sizes) and how large the colony dot on your petri dish is. In general, common bacteria are often around 2 microns wide and 10 microns long; so in a round area about 1 centimeter in diameter, you’d find (very) roughly 3,920,000 individual bacteria.
And that’s nothing! A teaspoon of soil has around 1,000,000,000 (a billion) bacteria, and there are about 1,000,000,000,000 (1 trillion) living in your digestive system! Current estimates suggest that there are 5,000,000,000,000,000,000,000,000,000,000 (5 million trillion trillion) bacteria living in the Earth’s ecosystems (including) us; that’s 2,500,000,000,000,000,000,000 times the number of stars in the entire Milky Way!
As with any science experiment, please remember to stay safe: wash your hands after handling any of the dishes, keep food and drinks away from them, and dispose of everything in a ziploc bag when your experiment is done.
We hope you enjoy this incredible opportunity to transform the microscopic into the macroscopic, and explore the wonders that are all around (and inside of) you!
P.S. You might be wondering about the agar in your kit, which is used as the medium for growing the bacteria: agar is a gelatinous compound derived from red algae seaweed! It was first discovered in Japan in 1658 and is now used around the world for food (often sugary treats). Agar began to be used as a basis for lab-grown bacteria in the early 1980s. Scientists use different types of agar to grow bacteria, with some better at hosting specific species than others: for example, chocolate agar (named for its color, which comes from sheep blood used to make it) is good for Haemophilus and Neisseria, and tissue grade agar is used for growing plants. We’ve given you nutrient agar, which is a great medium for growing a broad range of common bacteria and fungi.
]]>We’ll begin with the seemingly oxymoronically named circular triangle. These are triangles that have arcs (curves) for sides, instead of straight lines. They can be constructed in a few different ways: among the more common are convex circular triangles, called Reuleaux triangles, and concave ones, called arbeloses. The arbelos was first discovered (or written about, anyway) by Archimedes; he named it after the Greek word for a shoemaker’s knife. The arbelos also has a closely related shape called the salinon, but that’s not quite a triangle, so we’ll skip that and move on to….
...the Schwarz triangle! The Schwarz is a spherical triangle tesselation tile. That means it’s essentially a 3D circular triangle that’s made from a space along the outside of a sphere, and if you have enough identical Schwarz triangles and fit them together (the process of tesselation), they’ll completely cover the entire outside of the sphere, with no gaps.
On the subject of unusual triangles that reference their surfaces, we also run into the hyperbolic triangle, which as you’d guess, is a triangle made up of three points connected by hyperbolic line segments that lie on a hyperbolic plane (that’s a surface where the space curves away from itself at every point). Or perhaps a hyperbolic triangle can also be one that tells a lot of wildly exaggerated stories? But that’s linguistics, not geometry.
There are also some “standard” Euclidean three-sided straight triangles with unique properties. Remember the circumscribed circle on your shirt? You can circumscribe other spaces inside a triangle, too - like a square; that is, find the largest square you can fit inside a given triangle. In most regular triangles, the square can be placed inside only one way, but in a Calabi triangle, that square will fit in three different ways:
Finally, we’ve got a triangle filled with other triangles: the Sierpiński! A Sierpiński triangle is a triangular fractal pattern; a triangle composed of triangles, that are composed of smaller triangles, that are composed of smaller triangles, etc., in a recursive pattern. A three-dimensional version also exists, the Sierpiński pyramid.
Hopefully we’ve sated your curiosity for fantastic triangles! But we encourage you to go out and look for more. As the poet Isidore Lucien Ducasse wrote: “Grandiose trinity! Luminous triangle! Whoever has not known you is a fool!”*
*original: “Trinité grandiose! Triangle lumineux! Celui qui ne vous a pas connues est un insensé!”
]]>It’s an old trope: the mad scientist. Drs. Frankenstein, Doom, and Evil, of course, but also Dr. Jekyl, Dr. Octopus, Dr. Moreau, Dr. Frank N. Furter...it’s enough to think that graduate school turns you evil (maybe it’s the student loans). Like Dr. Frankenstein, for centuries, scientists have been portrayed as brilliant, but unstable and dangerous. And it’s something about scientists as an occupation - there’s no Mad Architect trope, or Mad Violinist. Luckily for the profession, we occasionally get a good one too, like Doc Brown or Bunsen Honeydew
But traditionally, fictional scientists have been bad. One study showed that scientists on TV were more likely to be villainous than members of any other profession: 1 out of 5 scientists were bad seeds, as opposed to 1 out of every 19 doctors, or 1 out of every 40 law-enforcement agents. Scientists were also more likely to kill than members of any other profession (5% as opposed to the mere 3.7% of military characters) and die: 10% of the scientists in the sample were killed, while only 2.8% of military characters died. When scientists in feature films tried to do something, those actions had harmful consequences twice as often as good ones.
Historians of science have traced modern movie, book, and comic portrayal of mad scientists to medieval and renaissance images of alchemists, astrologers and sorcerers: figures viewed as mysterious and aloof, with access to supernatural or even forbidden knowledge and powers. When the literary novel started to become the most popular form of fiction in the 19th century, chemistry was the primary form of experimental science people were hearing about. Literary chemists - like Jekyll and Frankenstein - begin to be the pop culture face of science, starting the trend towards scientists being seen as misguided at best, insanely mad at worst.
Interestingly, these scientists are not always portrayed as being evil per se; but they exhibit a desire to know and understand the universe that is not constrained by the moral standards of their day. They come across as evil because they don’t follow the rules of what their society thinks is proper (and in academic terms, they probably didn’t pass an ethical review board). Since those norms change over decades, how evil they seem may also change over time.
Which leads to possibly the most important thing about mad scientists: they’re a mirror on society, showing us what people think and fear about contemporary science, just like in the days of Jekyll and Frankenstein. In the 1950s and 60s, as worries over nuclear weapons became a primary avenue for people’s fears, there were a slew of movies where mad scientists created fearsome weapons and more importantly, fearsome creatures, with radiation: like the giant ants in the movie Them, or Beginning of the End’s hilariously terrifying giant grasshoppers. In those days, it seemed everyone with a “Dr.” in their name and a relation to nuclear energy was portrayed as mad, even in James Bond movies (Dr. No) and satirical comedies (Dr. Strangelove). As fears of nuclear science were replaced by worries over DNA manipulation and other biological sciences in the 1990s and early 2000s, that changed a bit; cinematic mad scientists in particular began to mess with organisms they didn’t seem to understand, like in the Jurassic Park and Resident Evil franchises.
But things are improving! Those studies showing evil scientists dying and killing are over two decades old, and it’s rare to find a movie or TV show today that exclusively has evil scientists. In many popular movies, you routinely see heroic scientists - often literal superheroes - saving the day. Organizations like the National Academy of Science’s Science & Entertainment Exchange and the Alfred P. Sloan foundation are also specifically working to improve the image of scientists in TV and movies, making science consultants and experts available to screenwriters, directors, and studios, and encouraging more nuanced portrayals of science and scientists.
In any case, we know you won’t go mad from the 90+ experiments in this book - unless it’s “mad with curiosity” or “mad with fun.” Enjoy!
P.S. one more interesting note: it seems that the idea of mad scientists didn’t come out of nowhere, and may have originated with historical scientists who came up with farfetched ideas, or seemed to have eccentricities or quirks that people associated with their brilliance. Isaac Newton was known to be paranoid. Pythagoras thought beans came from the same place as humans and believed eating them was like cannibalism. When he was 20 years old, Tycho Brahe lost his nose in a duel - he wore an artificial brass nose glued to his face for most of the rest of his life. And it’s hard to mention mad scientists without talking about Johann Dippel, who was literally born in Castle Frankenstein, and created a potion he claimed could extend life and cure any diseases. But everybody has some quirks, so it seems unfair to single out long-gone scientists for this. Other than the dueling, perhaps.
]]>The putty in your kit - and the original Silly Putty - are silicone polymers. The substance was created during World War II, when the war made natural rubber supplies largely unavailable to the Allies. Chemists worked hard to find an artificial rubber substitute, and voila! – silicone polymer putty was born. Of course, it turned out putty wasn’t very useful for making tires, boot soles, and other wartime supplies, so the formula largely fell by the wayside. Years later it was rebranded as Silly Putty, becoming instantly popular and selling millions and millions of putty-filled plastic eggs.
Your magnetic putty is considered a “viscoelastic non-Newtonian fluid”; viscoelastic means it has both elastic (stretchy) and viscous (thickening) properties when it’s deformed by stretching, pulling, or pushing. Viscoelastic things are actually pretty commonly found - they include nylon, human tissue, wood, rubber, clay and lava (okay, maybe lava isn’t super common). What makes this putty unusual is that it’s more highly elastic, and has a lower viscosity, than most other viscoelastic solids.
But “non-Newtonian”? What’s it got against Isaac Newton? Really, the putty loves him as much as the rest of us, it’s called non-Newtonian because it doesn’t follow Newton’s Laws of Viscosity. In Newtonian fluids, the thickness remains the same no matter how hard you pull or push it (think of water, for example). This putty is specifically a dilatant non-Newtonian fluid, meaning that viscosity increases when shear force is applied. That’s why it does seemingly odd or counterintuitive things, like snapping when yanked suddenly vs. stretching when pulled slowly, or bouncing when it hits something. Ketchup is a Casson plastic non-Newtonian fluid, which is close to the opposite - the more force applied, the less viscous it becomes. That’s why to get it out of the bottle, you apply force by shaking it up and smacking the bottle. That makes the ketchup less viscous, and it flows right onto your hamburger.
Non-Newtonian fluids are a lot of fun to play with, and it’s easy to make one yourself at home! The stuff is called “oobleck” after the crazy substance in Dr. Seuss’ 1949 book “Bartholomew and the Oobleck.” The recipe is simple:
Mix the ingredients together thoroughly (you can do this by hand), then it’s time to play! Smack your hand down on the oobleck and it instantly solidifies; but push it with your finger (or whole hand) and they goes right through, like a liquid. Try dropping a ball on it! If you have enough water, cornstarch, and space, you could even put it in a bathtub and try to walk on it. And to see the incredible result when you blast oobleck with sound waves, check out the new Vsauce3 video Could You Survive A Quiet Place!
And of course, what makes this putty extra special is its magnetic properties; even though the iron particles make up only 3.3% of the putty, they have a powerful effect. We’ve provided you with a robust neodymium magnet, but you can boost the fun by adding more! Gather a couple of magnets together, split the putty in two with long tentacles, and have them “race” to each of the magnetic “goals.” See how the putty reacts to the magnet rocks from your zen garden. If you've got a stack of magnets, lay the putty on top - we’ve found that it will shape itself to the magnetic field of the stack.
It stretches like an amoeba, laughs in the face of Newton’s laws (of viscosity, at least), and it’s a lot of fun. We hope you enjoy hours of experimentation with your magnetic putty!
P.S. if you’re wondering what’s in it, the putty is about 65% polydimethylsiloxane, 17% crystalline quartz (that’s where the silica comes from), 9% thixatrol ST (castor oil), 3.3% magnetic iron particles, and a few percentages of other chemical compounds, including 1% titanium dioxide!
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Okay, so what's a metagrobologist? If you’re a Curiosity Box subscriber, especially one who reads these newsletters about the conundrums that arrive in your box, then you are: a metagrobologist is a person who studies and ruminates about puzzles! Even though it sounds like a word cobbled together from latin roots like "meta” and the “graboid” monsters from the sci-fi cinematic classic Tremors, the term was actually created as a joke in the 17th century by french satirist François Rabelais; he invented it as a verb (métagaboulizer) meaning “to puzzle or mystify." Later English-speaking puzzlers turned it into a noun.
So what can we learn about your new puzzles? To start with, far from just a simple set of blocks tied together with a string, snake puzzles model fascinating and complex mathematical concepts, and inspire cutting-edge biological research. And of course, they’ve also got a link to Hamilton - not Alexander, of Broadway (and constitutional) fame, but William Rowan Hamilton, the 19th century mathematician and Royal Astronomer of Ireland, who gives his name to the concept of the Hamiltonian Path.
Hamilton invented a puzzle called the Icosian Game: given an icosahedron, the player needed to find a path around the outer edges which visited each vertex once, and then returned to the start. It’s a brain-challenging mathematical game and led Hamilton to lend his name to the solution: the Hamiltonian Path. An HP is a route through a graph that visits each vertex exactly once; and when solved, that describes your snake puzzle! A properly folded snake puzzle shows a path through a 3 x 3 cubic grid graph that visits each space in the square one time.
This puts the snake puzzle in the category of graphing puzzles, which includes other famous mathematical puzzles that make use of graph theory. Some of the most famous of these, the Five Room Puzzle and the Seven Bridges of Königsberg, eventually were found to be unsolvable. Luckily, your snake puzzle definitely is - it’ll just tax your spatial reasoning and problem solving abilities to their utmost.
It’s also possible to mathematically calculate the possible number of different snake puzzles that can be made; in this case, it turns out that there are 11,487 possible ways to make a snake cube puzzle, each with the blocks attached a different way. And one of the interesting things is that they have different numbers of solutions: some of these snake cubes can be solved in only one way, others have multiple possible solutions - up to 142.
Of those 11,487 possible types, there are six common organizations of the snake puzzle; and they’re often color coded. You can see those iterations on this excellent website. Based on the configurations shown, can you figure out which type you have? Hint: it’s not necessarily related to the green color of your puzzle.
But metagrobology isn’t just about puzzles, it’s sometimes about what else you can learn from them: biologists use the snake cube puzzle to model mechanisms of protein folding. By doing so, they have theorized that the final 3-dimensional structure of some amino acids may in fact be determined by the pattern in which they fold; it’s like saying the snake form of your puzzle was back engineered because they needed a shape that could be folded into that 3 x 3 cube (which is sort of true). You can read one such study here.
The burr puzzle is quite different from the snake, but just as interesting! Burr puzzles have been around for literally hundreds of years, and possibly thousands: there are theories they evolved from Chinese woodworking techniques first developed in the 4th century BCE, and the first one shown in print turns up in the 1698 book Cyclopædia: or, An Universal Dictionary of Arts and Sciences. They became especially popular after metagrobologist Edwin Wyatt included them in his famous 1928 book on wooden puzzles. Wyatt called them "burr puzzles" because the shape reminded him of the burr seeds that sometimes get caught on your clothes when you go hiking.
In the 1970s, Bill Cutler and Arthur Cross started analyzing burr puzzles, calculating how many different ways the pieces could be shaped, and the number of burr puzzles you could create from those pieces. Your burr is what they call a “classic” 6-piece burr, which has 26 possible piece shapes that can be assembled into a puzzle in one of 314 different ways (though each puzzle has only one solution). They even figured out a way to make a puzzle called a Holey 6 Piece Burr, featuring “blind alley, internal space” pieces, whose shapes can be formed into a total of 35,657,131,235 different puzzles! They calculated this out in 1990; at that time the standard computing speed was 8 mhz, at which rate it would have taken 62.5 years of computer time to crunch the numbers. Cutler and Cross were able to cut that down by using the fastest computers of the day, including a Cray-1, one of the first supercomputers.
The Snake and Burr puzzles are mathematical conundrums, engaging problem solving games, and inspirations for scientific discovery, and we hope you enjoy solving them as much as we do!
]]>In maze-solving terms, an algorithm is essentially just a plan, or a set of instructions for executing a plan. Do you really need an algorithm to solve a maze? Can’t you just draw a line, or walk it, until you find the end? Of course you can – and in fact, doing that is its own kind of algorithm, known as the Random Mouse algorithm. Which is just one of dozens (at least!) known maze-solving algorithms.
When you’re looking at a maze and selecting an algorithm, it’s important to know that there are two different types, depending on your perspective. One is good for solving mazes if you’re on the ground, walking them, the other if you can see the whole maze at once; essentially, if you’re a person staring down at it, or a maze-solving computer program. Since there’s an (admittedly slim) chance you’re reading this while lost in a maze, let’s start with the ones for travelers who are on the inside.
Probably the best known of these is the Wall Following algorithm, also known as the right- or left-hand rule (it doesn’t matter which hand you use). The basic idea is simple: you just put one hand on a wall and then keep walking, with the hand always in contact with that wall. Eventually, you’ll get out, because you’re effectively stretching the maze into one really long wall and just following that to the exit.
The Wall Following algorithm is simple to remember and remarkably effective, but there are some drawbacks. Among other things, it only works if you’re trying to get through a maze from one exterior wall to another, not if the start or finish is in the center. It also only works if the maze is “simply connected” - that is, all the walls inside are connected somehow to the outer wall; it doesn’t necessarily work if there are islands in the maze, or shortcuts like tunnels or bridges over some walls, both of which are found in modern hedge and corn mazes.
So we need a better solution. Enter Trémaux’s Algorithm, which works in all mazes! It involves marking the decision points of the maze as you walk through it, essentially letting you block off places you’ve been before. Now, this does mean you need some way to mark where you been - a magic marker, a pebble, or a snapped branch, but it’s only got four rules, so if you can remember these, you’re good:
Eventually, you’ll exhaust all possibilities and find your way out of the maze!
Trémaux Algorithm simulation from Grj23 CC BY-SA 4.0
There are also a lot of maze-solving algorithms that work extremely well, but can’t be performed by somebody inside the maze. However, if you’re looking down from above (like with a paper maze, or more importantly, the one on your shirt), or are a computer solving a maze problem, they’re very effective. These involve solutions that are impossible to do on the ground, or can’t be done realistically in the real world at all.
The Dead End Filling algorithm, for example, is simple and effective. You just scan the maze, find a dead end, and then start filling it in backwards until you reach an intersection. After you’ve filled them all in, the remaining path will be the solution, or solutions if there is more than one. Dead End Filling isn’t useful if you’re inside a maze, because you have to KNOW where the dead ends are in order to start; but it’s great if you’re looking down from above.
Similarly, the Flood Filler and Collision Solver algorithms work on computers. They operate by “filling” the maze with imaginary water, then analyzing how the water flows through the maze. In the Collision Solver algorithm, for example, every time the water in two flooded paths collides, the computer creates a wall where they meet; this continues over and over, until all the dead ends are sealed, and it finds the shortest solution to the maze.
But whether you’re solving the maze from inside or outside, know that you’re giving your neurons a great workout, because mazes activate a LOT of your brain. Neuroscientists using functional magnetic resonance imaging (fMRI) have shown that when solving a maze, huge portions of the brain are stimulated. In one study, brains that were solving mazes had 20 separate areas activated at the same time
Parts managing complex thoughts, like the prefrontal cortex, are activated, but even stranger, so are the cortical and subcortical motor areas, which are responsible for voluntary muscle movement. These are activated even if you’re not actually moving, which indicates that when you’re solving a maze just by looking at it, your brain imagines that you’re walking through it!
And of course, you’ll really get that motor cortex going if you get up and walk around in your new maze shirt, so we hope you’ll enjoy wearing it as much as solving it!
]]>Congratulations on harnessing one of the fundamental forces of the cosmos, right on your table! The universe functions because of four forces: the strong nuclear force, weak nuclear force, gravity, and of course the electromagnetic force, which is what makes your homopolar motor spin. In this instance, it’s known as the Lorentz force, and it’s created when electric charges flow inside a magnetic field. In your motor, the battery provides the charge, the wire provides the path for it to flow, and the magnet, of course, provides that all-important magnetic field.
One of the amazing and fun things about homopolar motors is that because those three basic elements are all you need to generate the Lorentz force, as long as they’re all present, you can arrange them in essentially any configuration: that’s why the “wing” and “spiral” builds both work, as well as the hearts, flowers, and other creative wire designs you’ve come up with, and the bonus build, below.
It also means you can experiment with the motor by changing the current and/or the magnetic field. Current can by increased with different battery sizes, or more effectively by stacking batteries in series. A magnetic field can also be increased by stacking magnets together; this trick works up to the point where the stack is as long as the diameter of the magnets (so the four magnets we’ve provided are already at maximum power when used together; but you could try magnets with a larger diameter).
With that in mind, here are a few more things to explore:
And here are a few tips to help with your builds:
We’ve also got a bonus build that you can make with the elements we’ve included in your kit, plus two safety pins, and some tape.
Directions:
And finally, railguns! These futuristic weapons often show up in sci-fi franchises: you may have seen them in the Transformers movies, video games like Halo and Mass Effect, or The Expanse. A railgun is constructed so that an electrical current and magnetic field produce a perpendicular force that shoots the projectile out at a tremendous speed – the exact same Lorentz force that spins the wire of your homopolar motor! And that force makes the projectiles go fast. How fast? Current (ha!) railguns can fire a projectile at Mach 6 (7,400 kmh/5,400 mph). That would take you from LA to New York in less than an hour, or New York to Paris in about 67 minutes.
It won’t fly you across the ocean, but we hope you find this homopolar motor kit provides hours of curiosity-satisfying experimentation!
]]>Two balls that look and generally feel the same, but when you bounce one it springs up like it drank two cups of coffee and an energy drink, while the other thuds to the ground as if exhausted. The balls are a trick favored by stage magicians, who switch them out to amuse and astound audience members; but you’ll know better. To uncover what’s happening, we’ll take a look at why rubber balls bounce, and how a few extra atoms in each molecule cause these two to bounce differently from each other.
When a dropped ball hits the ground, the force of the impact causes it to slightly deform; a moment later the material of the ball snaps back, at which point it exerts a restoring force on the ground as it springs back into its equilibrium shape. That force acts in the opposite direction of the way the ball was deformed, pushing back down and causing the ball to spring up into the air.
How high the ball springs up depends on how much the material absorbs kinetic energy, and how fast the material returns to its original shape after the deformation. Famously, steel balls will bounce higher than rubber ones, because the steel springs back to its original shape much more quickly than the rubber. “Elasticity” is the measure of how much something can return to its original shape during the collision, and the process of it occurring is called “elastic deformation” (“plastic deformation” is when something changes shape but doesn’t change back).
But you’ll notice that even the springiest superball doesn’t 100% bounce back up to the height from which it was dropped. Why not? When a ball (or anything else) falls, it converts gravitational potential energy into kinetic energy. After it hits the ground and the ball is deformed, that kinetic energy is mostly turned into elastic potential energy, and when the ball springs back up, the potential energy is converted back into kinetic energy.
But some of that kinetic energy is also absorbed in the deformation and gets lost, so it isn’t available to spring the ball up to its original height. Where does it go?When the rubber is deformed, most of the “lost” energy is transferred to the molecules of the ball and dissipated by internal friction, causing heating. So each time you drop a ball, you’re actually heating it up a bit, though generally not enough that you can feel the difference.
So a key part in why balls bounce has to do with that deformation. And the reason the two rubber balls act so differently is because of the way rubber reacts when it hits the ground and gets deformed. Rubber is a polymer which, generally speaking, means its molecules are arranged in long chains. Those chains can rotate around the chemical bonds that link them together, allowing them to change shape, at least for a moment. The key, as you probably guessed, is that each of the balls are made of a different kind of rubber. To see why one of your balls springs back up and the other doesn’t, take a look at the molecules:
The “bounce ball” is made of natural rubber in the top image, and the “no bounce” of butyl rubber, in the bottom image. The key difference is those bulky CH3 sections, called methyl groups, which make it harder for the molecule to change shape. You’ll see that the natural rubber molecule has just one methyl group, but the butyl rubber molecule has three. That means the natural rubber will deform and spring back much more easily, as the molecule rotates smoothly around its chemical bonds. But because it doesn’t move as freely, the butyl rubber ball absorbs much more of that kinetic energy, and won’t bounce as high. It also technically gets much warmer than the bouncing ball.
The bounce/no-bounce ball set is great for illustrating how small molecular differences can have big effects in the macroscopic world, for demonstrating kinetic and potential energy – and for just having fun!
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That list is a who’s who of curious minds: along with Sagan and Dali, his fans included W. H. Auden, Arthur C. Clarke, Isaac Asimov, Vladimir Nabokov, and Stephen Jay Gould. Neil deGrasse Tyson called him “the last of the polymaths,” and Pulitzer prize winning science writer Douglas Hofstradter said Gardner was "a major shaping force in my life.”
Gardner’s fame among scientists and mathematicians is so great that there is an annual “Gathering 4 Gardner” convention, where experts in mathematics, puzzles, and more gather to discuss the many, many subjects that he loved. Both Michael and Kevin had been slated to attend the 2020 gathering before it was postponed, and are looking forward going in the future.
Interactive exhibit from the last Gathering 4 Gardner event.
But Gardner’s contributions to science didn’t just come from inspiring others: his groundbreaking 1957 book Fads and Fallacies in the Name of Science debunked pseudoscientific beliefs in everything from the Flat Earth to ESP and quack medical treatments. In 1976, Gardner, Sagan, and Asimov helped form the Committee for the Scientific Investigation of Claims of the Paranormal, in order to increase scientific literacy and prevent people from being conned, hoaxed, and manipulated by false paranormal and pseudoscientific claims. He’s regarded as the father of the modern rational skeptic movement.
Martin Gardner
Though a famous debunker of the paranormal, stage magic was one of Gardner’s lifelong passions (which you may have guessed from the two books in your box), and he was named one of the most influential magicians of the 20th century. He also loved classic fantastical literature: Gardner was a renowned expert on the works of Lewis Carroll, particularly famous for his annotated edition of Alice in Wonderland. He was such a fan of The Wizard of Oz that he wrote a sequel called Visitors From Oz, in which Dorothy and the gang are transported to Earth in the year 1998. You could think of it as an early form of fan fiction.
Despite decades of public writing and opening himself up to the public, Gardner still held some surprises:
We hope you enjoy your new Gardner books; we’re very happy to have added him to the list of Curiosity Box authors. Gardner was a huge proponent of the power of curiosity to make our lives better, and we’ll leave you with some of his thoughts about it:
When you place the tentacle in your hand, something strange happens: it might curl up, or flip end over end, or the edges may twist in towards each other. What’s happening? The tentacle reacts that way because it’s made of a special polymer that absorbs water, and it’s reacting to the moisture on your skin.
That polymer is sodium polyacrylate, a hygroscopic material that really likes to absorb water. How much? It can absorb up to 800 times its weight in water, assuming that water is pure; for H2O with other dissolved minerals (like tap water), it absorbs around 300 times its weight. Sodium polyacrylate is more common than you might think: it’s the same substance used in disposable diapers, an application where you really want to make sure you’re absorbing as much moisture as possible. It's also used in wound dressings, and for entertainment as artificial snow – and fortune-telling tentacles, of course.
The water absorption is happening through osmosis: sodium polyacrylate, as you can probably guess from the name, has a lot of sodium atoms it. Water molecules are drawn to the sodium ions, and end up being absorbed by the polymer. But here’s the thing: it only absorbs those molecules when it’s in directly contact with the water. As you hold the tentacle, the molecules on the palm side absorb moisture from your skin and start to expand, but those on the side facing the air don’t; that causes the tentacle to change shape.
What’s amazing is that this trick seems to have been used for centuries, long before the discovery of chemical compounds like sodium polyacrylate. In fact, the first known appearance of this kind of magic trick is in 1786, where it’s mentioned in the Testament de Jérome Sharp, a book by early modern magician and teacher Henri Descremps, in which he exposed other magicians who claimed to have paranormal powers. Your box contains books by one of his modern descendants, Martin Gardner, who both loved magic tricks and was famous for debunking claims of pseudoscience in the 20th century.
Descramps wrote about a trick where a magician would take a small piece of paper with a picture of a baby, and give it to two women. When it wiggled in the hands of one of them, that “proved” that she had given birth before (you’d think this would be easy to prove or disprove, but apparently people bought the trick). So what did they use three centuries before the discovery of modern hydrophilic polymers? It’s unclear, but it appear the “paper” in this case was probably onionskin.
It may have started with babies in the 18th century, but your Mind Reading Miracle Tentacle is one of a long line of fortune telling shapes used in the trick; over the years there have been fortune-telling mermaids, soldiers, leaves, Santa Clauses, and Yogi Bears. The best known is probably the Fortune Telling Fish, which seems to date to the 1920s. Hundreds of thousands – possibly even millions – of these fish have been made; a restaurant in New York City used to give one out with every order, and a mind-reading fish was included with physical copies of Leonard Cohen’s 2010 album “Songs For the Road.”
So does it work? Well, the tentacle material reacts to water, and the moisture of your skin does change. The way scientists measure it is through your skin conductance response (SCR); basically a test of how well your skin conducts electricity, which primarily happens because of more or less moisture. Studies show that your SCR changes with both positive and negative emotional stimuli, as well as visual cues that evoke those stimuli. So in a way, an object that reacts to that moisture can in fact say something about what going on in your head.
We won’t make any claims that the tentacle is actually reading anybody’s mind, or truly displaying your emotional state, but it’s interesting to see how the idea of reading minds through skin moisture has some basis in real neuroscience. Truly mind reading or not, we hope it helps amaze your friends!
]]>Believe it or not, “wettability” is actually a scientific term. It describes the ability of a liquid to adhere to or spread on a solid surface: in other words, how wet it makes whatever it lands on. Wettability is usually measured by the surface angle at which a drop of liquid sits on a surface: a high angle means the liquid has formed a spherical bead and things stay relatively dry, a low angle means it’s spread out, and the surface has become wet.
Water likes to form spherical beads because of something you’re probably familiar with: surface tension. H2O has a high surface tension because its molecules are strongly attracted to each other via a web of hydrogen bonds; because the molecules on the outer edge of the droplet don’t have any water molecules above them to cling to, they form a stronger bond with the molecules next to them – thus surface tension. That’s why water forms drops as it falls through the air. But when that drop lands on something, surface tension isn’t quite strong enough to keep the water in that spherical shape, and it spreads out, making the surface wet.
But there are ways around this! The interior of your maze is coated with a “nanoparticle superhydrophobic surface.” This surface increases the contact angle of the drop, basically turning it into a complete sphere. Compared to the flattened bubble of a low-angle drop, a sphere only touches the surface with a tiny area, so it rolls around super easily! When the drop is like this, the water is said to be in a “Cassie-Baxter State,” named after the equation that governs contact between liquids and surfaces.
What’s amazing is that the key to making that kind of superhydrophobic effect isn’t to make the surface smoother, but rougher. The secret is that the coating covers the surface in tiny bumps. And we mean really tiny: each one is around 100 nm tall; that’s about the size of a virus (a human hair is around 90,000 nanometers wide). The bumps affect the way the water rests on the surface, changing that all-important contact angle. They also leave space for some air, called a gaseous plastron, to be trapped between the water droplet and the surface, which causes that silvery sheen you see beneath the drop.
The development of these incredible coatings was inspired by two examples found in nature: the lotus leaf and the Stenocara gracilipes, also know as the Namib Sternocara Desert beetle. The self-cleaning hydrophobic qualities of the lotus leaf have been known for almost 2,000 years; as it says in the Bhagavad Gita, “just as a lotus leaf is untouched by water.” In fact, the rolling action of droplets on a superhydrophobic surface is often called “the lotus effect.”
Water on Lotus leaf
The Stenocara gracilipes beetle lives in one of most arid regions on Earth, and has evolved superhydrophobic channels on its back to channel tiny amounts of moisture that it harvests from fog into its mouth. Scientists designed superhydrophobic coatings by mimicking the pattern found in electron microscope scans of the beetle’s’ carapace.
Check out the superhydrophobic channels the Stenocara Gracilipes beetle uses to drink.
Full of paths to be discovered and dead ends avoided, rough when it looks like it should be smooth, and inspired by nature: the hydrophobic maze is a labyrinth of wonders!
]]>This incredible shirt says one thing when read by somebody standing next to you, but something else when they’re just a few meters away. Is it an illusion? Magic? Neither, really: it’s actually a special type of “hybrid image” that takes advantage of different spatial frequencies to work its wonder. Images are composed of elements that are viewed in different “spatial frequencies.” What’s the distinction? In general,
Low spatial frequencies:
High spatial frequencies:
It’s all part of visual perception, that strange realm where the input from your eyes meets the functioning of your brain. The specific perceptual phenomenon at work here is known as “visuospatial resonance”: because your brain is trying to make sense of what it sees as quickly as possible, it takes the less-detailed information you see at a distance (low spatial frequency) and starts trying to fit those patterns into information stored in your memory. As you get closer and more of the high spatial frequency details emerge, the brain adds those to give you a fuller picture of what you’re seeing.
For example, when you see a person from farther away, you can identify their general shape, height, maybe even tell if the person is male or female, based on the low spatial frequency parts. As you get closer, the high frequency details emerge and you can tell if the person is smiling or frowning, and if they’re familiar, exactly who it is. By processing the visual data this way, your brain gives you a clue as to what you’re seeing as soon as possible, a process with a pretty obvious evolutionary benefit.
Up close, you'll see famous physicist Albert Einstein, but from afar Marilyn Monroe's face will begin to appear.
The hybrid image on your shirt works because most of the time your brain is good at putting all these pieces together so you see a complete image, but a hybrid image tricks the brain by pairing the low spatial frequency parts of one picture, with the high spatial frequency parts of another (in our case, two words).
Hybrid images were invented in their modern form in 1994, but the phenomenon has been known – at least to some people – for centuries. One example is Leonardo da Vinci, who used it in what is arguably the most famous painting in the world: the Mona Lisa!
The Livingstone Lab at Harvard separated out the different spacial frequencies of Mona Lisa's smile.
The Mona Lisa’s smile is famous because of how it seems to change depending on how you’re looking at it. For centuries, people have marveled that from a distance or to the side, the lady is smiling at you, but if you stand right in front of her the smile seems to disappear and she has a more neutral expression. Sound familiar? We now know that with his skills as one of the greatest painters of the Renaissance, Leonardo was able to imbue her with a smile based on different spatial frequencies. So the tip to seeing the Mona Lisa’s smile is to stand far away, or focus on her hands or the background so her mouth is in your peripheral vision. Then she’ll smile at you with the warmth of the Renaissance sun.
If you’d like to learn more about the world of hybrid images, there are a number of places to create them online (you can try this one), as well as continuing research to follow, like this study to see if you can put three images into a single picture using this technique. Let your curiosity be your guide!
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Geometrically, a spiral is a smooth curve that winds about a central point or axis while also receding from it. Spirals form some of the most graceful and powerful forms in nature, and you see them in places big and small: from the double helix of DNA and the butterfly’s tongue to the swooping dive of a peregrine falcon. Spirals can be found in the curl of a fern tendril, the shape of an octopus’ retracted arm, a mountain goat’s horns, the curving shell of the nautilus (one of Inq’s cephalopod relatives!), fossilized ammonites, the horns of the kudu antelope, the arrangement of seeds in a sunflower, the scale of a pinecone, the curl of a chameleon’s tail, and the pattern of buds on a pussy willow stem. Martin Gardner pointed out that the Eperia spider spins a web that is a logarithmic spiral.
And of course, about a third of the known galaxies in our universe are spiral shaped, including our own Milky Way. The question of why the spiral shape is so common in duodecillion-ton masses of stars is still a subject of research and debate. The basic cause is that galaxies rotate; the problem is they often rotate faster at the core than the edges, and eventually that would destroy the spiral pattern. What seems to keep the spiral arms intact – somehow – are “density waves,” which are pileups of stars that happen when a lot of them are in motion: think of it like how cars sometimes bunch up on a freeway. The movement of stars in these waves keep the arms from bunching up, and boom – you get a cool-looking galaxy.
What’s this about radar? In the electromagnetic spectrum, every frequency has a wavelength – the distance between the top of one wave and the next. The lower the frequency, the larger the wave: radio waves can be the size of buildings, x-rays the size of a water molecule. The size of the wavelength of your spiral is about 2.5 cm (1 inch), which turns out to be roughly 11 gigahertz (GHz). 11 GHz is the wavelength of radar, specifically the “X-band” used for military and space-borne radar systems. Circular polarized EM waves propagate in a spiral, so when you hold your Mephisto spiral, you’re looking at a model of a circularly-polarized 11 GHz wave.
And finally: who is Mephisto? The name might sound familiar; there’s a Marvel comics supervillain with that name, and if you’re into classical music, Franz Liszt wrote his the “Mephisto Waltzes” between 1859 and 1885 (as well as one Mephisto Polka, no joke). Etymologically, Mephisto is another name used for Mephistopheles, the devil of the famous Faust legend, the classic folktale where a Renaissance scientist sells his soul to the devil in exchange for knowledge. In this case, it may refer to the devilishly puzzling way the spiral seems to unwind forever. But we promise there are no real devils involved – just a fun and interesting optical illusion. So enjoy!
]]>Your new book about the lifetime works of M.C. Escher comes to you at a special time - almost exactly 50 years from his passing, on March 27th, 1972. The introduction is a rare chance to read Escher’s own words about his art and life.
It won’t surprise you to hear that Escher was deeply engaged with mathematics in his work. He routinely corresponded with mathematicians, some of whom were inspired by his inquiries to try their own hand at art, including Nobel Prize winner Roger Penrose. After viewing Escher’s work while attending a mathematics conference in 1954, he was inspired to create the famous Penrose Triangle illusion - which Escher himself then used in his famous Waterfall illustration, the very last image in your book on page 95.
You can see how the Penrose Triangle and other famous illusions work on Vsauce3 in Jake's video: Impossible Objects.
For a number of years, Escher conducted his own mathematical research, most of which (as you’d guess) focused on geometry, and how to fit shapes into each other. He even discovered two unique mathematical theorems: one was about congruent lines in a triangle, the other about diagonals in hexagonal patterns. A number of subjects that Escher investigated were later topics of formal investigation by scientists and mathematicians, but only decades after Escher had already incorporated them in his work. For a full list, we encourage you to read this article.
Interestingly, Escher never considered himself an artist, instead always referring to himself as a designer. He also insisted that his prints didn’t have any hidden meanings, and were just illustrations of mathematical concepts, though art historians have noted how they are often rooted in his life experiences, including the loss of his close friend and mentor to the Nazis, along with personal issues in his marriage and relationships. While the works in this book cover the entire breadth of his career, they particularly focus on two subjects that have a geometric, mathematical connection: tessellations and knots. Escher himself called tessellations “the richest source of inspiration I have ever struck.”
Tessellations are repeating geometric patterns that cover a surface with no gaps or overlaps. They’re also called “tilings,” because that’s where they came from; the original tessellations were Roman floors covered in ceramic tiles. In honor of that origin, the shapes in a tessellation are still technically called tiles. There are several ways to manipulate each tile to fit them together and form a tessellation:
You can see some of these manipulations at work in the tessellations in your book; for example, Circle Limit III (page 42) is an example of rotation and Horseman (page 27) is an example of glide reflection. There are a total of 17 types of symmetrical tessellation patterns that can be created by combining these four manipulations together
It’s fun - and surprisingly easy - to make your own tessellation! With a piece of paper, or in your favorite computer illustration program, just follow these simple steps:
1. Take a square or rectangle, and draw a line through it
2. Cut and separate the shape along the line:
3. Take the left side of your divided shape, move it to the right side of the shape, then reconnect them along the flat edges:
4. You’ve now created a tessellation tile! You can copy this shape over and over and create your own tessellated surface:
M.C. Escher is just one of many artists who influenced, and were influenced by, mathematical concepts; if you’re interested, check out works by Robert Fathauer, Ada Dietz, and Simon Beck. Escher’s illustrations are engrossing, thought-provoking, and fun. We hope you enjoy this fantastic book, and it encourages your own artistic journeys!
]]>Slip on your new t-shirt, and feel the warm embrace of Earth’s only natural satellite. But which part? Let’s start with the big stuff: while wearing the shirt, your tummy contains the entire Mare Nectarus (Sea of Nectar). The Moon’s mares – Latin for “sea” – are giant plains of volcanic basalt that generally appear darker than the rest of the lunar surface. Mare Nectarus is the smallest of these basalt seas, but has some interesting features, including a gigantic, 3.2 km (2 mile) high cliff on its southwestern edge. Nectarus was actually formed when a giant asteroid slammed into the moon 3.9 billion years ago, and the basin later filled in with lava.
On the lower right edge of Mare Nectarus, that big crater with the mountain in the middle is Theophilus. It may just look like a little dot, but that central mountain is 1,400 meters (9/10ths of a mile) high! Theophilus is joined with the crater Cyrillus, and if you keep moving along to your left (when you're wearing the shirt) is the crater Catharina. The large, dark crater on the left side that merges into the Mare Nectarus is Fracastorius.
Your right arm is bathed in the Mare Fecunditatis, the "Sea of Fecundity" or "Sea of Fertility,” depending on how you translate the Latin. Among other things, it’s notable for the presence of a number of “ghost craters”: craters formed by meteorites that were later filled in with lava during the Moon’s volcanically active period. It’s also one of the first features to appear when the moon begins waxing. Sitting on the edge of the Mare Fecunditatis, near your collar, the large bright white patch is the crater Langrenus. It’s named after Flemish astrocartogapher Michael Florent van Langren, who in 1645 made the first known map of the moon’s surface that labelled features - including this crater, which yes, he named after himself.
The bright white lines on your left arm are rays of material ejected from the Furnerius A crater. Furnerius is just 11 km (7 miles) wide, but the rays created when it was blasted into the moon’s surface stretch an incredible 1930 km (1200 miles)!
If you see tiny astronauts walking on your shirt, that’s because the Apollo 16 landing site is near the bottom right hand side, on your hip. Apollo 16 was one of the three lunar missions specifically dedicated to science and exploration; it was the first mission to land in the moon’s highlands, and the first to use the moon as an astronomical observatory. The astronauts actually brought back moon rocks which were formed from the impact that created Theophilus.
Right nearby the Apollo 16 site, on the bottom of your shirt, is the very edge of the Sinus Asperitatis (Bay of Roughness), where it meets the lunar highlands of the Rupes Altai mountain range. The mountains were formed by shock waves from the asteroid impact that first hollowed out the Mare Nectarus basin. Your left hip is in a flat plain area, which also approaches the Rupes Altai (the mountains curve around the bottom of Nectarus) near the crater Piccolomini, which is named after the 16th century Italian archbishop and astronomer Alessandro Piccolomini.
Those are the highlights; you’ll also see innumerable smaller craters, and hundreds of square kilos of moon dust. We hope you’ve enjoyed this little tour of your own personal portion of the moon. Curiosity Box shirts: comfortable, fashionable, AND educational!
]]>Your parents always said that eating right would give you a boost of energy, but they probably didn’t expect you to be literally generating electricity from your food! So how does the potato clock work? The key lies in two simple things: the chemical environment inside the potato, and the elements in the two probes you put into it.
Despite what it looks like, the power isn’t really coming from the potato, it’s generated by chemical reactions in the metals of the two electrodes you’re plugging into the spud. But without the potato’s delicious interior, the reaction wouldn’t work. To start with, potatoes are mildly acidic (and we mean very mildly, with a pH between 5.4 and 5.9; even maple syrup can be more acidic). As a reminder, a pH of 7 is neutral, 1 is extremely acidic, and 14 is extremely basic.
The moment you insert the zinc strip, it starts reacting with phosphoric acid inside the potato; the important part for us is that the zinc loses some of its electrons in that reaction. The copper strip is also reacting with the acid, but it’s looking to pick up those spare elections, so they flow up the wire from the zinc strip to the copper one. A flow of charged particles (like electrons) is literally the definition of an electrical current, so voila! Your clock is powered.
That’s the basics, but let’s step it up a notch. If the electricity is generated by a reaction between the environment of the potato and the metals in the electrodes, can you increase the power by changing either of those things? The answer: yes! In fact, both of them. And depending on what you’ve got around the house, these may even be things you can try at home.
Let’s start with the potato. A few years ago, researchers at the University of Jerusalem discovered that if you boil potatoes for eight minutes, you can boost the electrical production by up to TEN TIMES. They think that it works by rupturing the tissue membranes inside the potato, lowering their resistance and making the reaction more efficient. Using this method, they used a potato to power an LED light for 40 days.
You can also increase the amount of power by changing the materials the electrodes are made out of. Your kit uses zinc and copper because they’re readily available, and work well in the reaction. But more exotic materials can increase the electricity generated: for example, with electrodes of magnesium and gold, you get more than three times the power out of your potato! You can calculate how much electricity is produced by looking at a table of the standard reduction potential of different materials.
On the chart here, for example, you can see that copper has a potential of 0.34 volts, and zinc -0.76 volts. From the difference, you can calculate that the amount of power generated in their reaction is 1.1 volts. From this, you can see that with gold (1.5) and magnesium (-2.37), you can generate a whopping 3.87 volts!
ELEMENT | POTENTIAL |
Gold (Au) | 1.50 |
Silver (Ag) | 0.80 |
Copper (Cu) | 0.34 |
Lead (Pb) | -0.13 |
Nickel (Ni) | -0.26 |
Zinc (Zn) | -0.76 |
Magnesium (Mg) | -2.37 |
Lithium (Li) | -3.04 |
You can also hook up a bunch of potatoes together to generate more power. Your setup uses two because 1.1 volts isn’t quite enough to power the clock, but by connecting the two potatoes in a serial circuit, you add their power together, so you’ve got 2.2 volts. And in fact, you can go farther than that! Three potato batteries hooked up together are usually enough to power an LED light, and one team of scientists linked four together to run their scientific calculators. If you’ve got an entire field of potatoes and some time on your hands, we’ve seen setups that link hundreds of potato batteries together. And according to some calculations, if you had about 300,000 potatoes you could replace a car battery!
Finally, one of the really fun things to do with your clock is find different foods (and drinks!) to use as power cells. Anything with an acidic environment should work, and you might be surprised at some of the foods that fit that criterion: lemons and cola of course, but also eggplants, strawberries, and cheese! Have some fun experimenting with the foods in your kitchen, and if you want to spark some ideas, here’s a chart of foods with their associated pH levels (remember, lower levels mean more acidic).
You can even get really creative, and try to can come up with entire meals that activate the clock. Breakfast, for example: will it work with pancake batter, maple syrup, and milk? With so many ways to continue experimenting with your potato clock, we hope it engages your curiosity – and helps keep you on schedule - for a long time!
Lenticular sheets are amazing; covered in hundreds of tiny lenticular lenses, they can grant partial invisibility, create 3D pictures, and animate still images. That’s a lot of heavy lifting for lenses just half a millimeter thick. What’s the secret? The power of refraction: the ability of the lenses to bend light. But it works a little differently in each case; let’s investigate how.
We’ll start with the 3D effect, which is sometimes called “autostereoscopic display,” because it doesn’t require 3D glasses or outside elements to make it work. So what’s going on? Just as with other printed 3D effects (like the stereoviewer from your Fall 2021 box!), lenticular 3D operates by presenting each eye with a slightly different image. While most 3D systems show the images side by slide, or slightly overlapping, for lenticular 3D, the image is interlaced: the picture is sliced into strips that alternate next to each other. When the lenticular sheet is put on top, the lenses adjust the view of each little sliver of the image so that it enters one eye. Your brain adds the slivers together and delivers two complete, slightly different, images that take advantage of the stereoscopic effect to appear 3D.
Each R and L is a tiny slice of the right-eye and left-eye images. Illustration by The Electronic Visualization Lab at the University of Chicago.
Lenticular animation works the same way, but instead of two stereo images, the interlaced picture is essentially of two animation cells - the same picture, each slightly changed to show motion. So lenticular animation is essentially combining two (or more) pages of a flipbook into one image, then letting the lenses show you a different “page” as you change your viewing angle.
An illustration how lenticular animation works, courtesy of The Smithsonian
Lenticular 3D and animation have been around for years, but it’s a newer application that’s extra fascinating: lenticular invisibility. Recently, people have become aware of this cool invisibility effect, which you’ll sometimes see referred to with the grandiose phrase “quantum stealth technology.” If you’ve played around with the sheet, you’ll note that it can turn things - especially straight lines or relatively long, thin objects - invisible. And unlike with the 3D effect, the invisibility doesn’t change if you move your head up, down, or sideways. But it only works in one direction - either horizontal objects are invisible, or if you rotate the sheet 90 degrees, vertical ones. How does it work?
As mentioned above, the effect is due to refraction. Hundreds of rows of tiny lenticular lenses refract (bend) the light that runs parallel to the orientation of the sheet’s lenses. In effect, when you look directly at the sheet, the lenticular lenses are bending the light so that you’re seeing around it: so instead of looking directly at an object, you’re actually seeing the background on the other side of it (that’s why the effect works best against a uniform background).
Try experimenting with your sheet around the house, playing with different household items and locations to test the invisibility. The sheet works best when the item you’re making invisible has strong lines, and is oriented in the opposite direction of nearby objects. For example, you can hold a pen or pencil in your hand, and see it disappear while your fingers remain visible; make the stems of wine glasses disappear, while the bowl stays intact, hovering in mid-air.
The directional orientation of the invisibility - why the pencil in your hand disappears but your fingers remain visible (then vanish in the other direction when you rotate the sheet 90 degrees) is because of the structure of the lenticular lenses, which affects the direction in which they refract the background light. Basically, things become invisible when they’re lined up in the same direction as the tiny lenses that make up the sheet. In a sense, the sheet is only an invisibility-producing refractive lens perpendicular to the direction of the bumps.
You can see a large-scale version of how the lenticular invisibility works - as a lenticular invisibility shield! - in the Harry Potter episode of Jake’s Emmy- and Streamy-award winning series Could You Survive the Movies?
3D without glasses, animation without cels, and directional invisibility: we’re continually amazed at the flexibility (no pun intended) of lenticular sheets. Try the sheet on shapes, objects, and text around your house. Amaze your friends, surprise yourself - and have fun!
]]>We hope you’ve found a cool place to set up your Solarcan, and can’t wait to see the solargraphs you create - post and tag ‘em with #SeenOnSolarcan!
To start with, some frequently asked questions:
Pinhole cameras like your Solarcan seem like incredibly simple devices, and they are. But believe it or not, the 2,500 year old technology offers some advantages over traditional, and much more complex, lens-based cameras! In a photographic sense, a pinhole camera can capture an unlimited depth-of-field; so essentially, the entire image is in focus, every time. And because they don’t have lenses that bend light, pinhole cameras often have much less optical distortion than traditional cameras. Pinholes also have an advantage in size; because they don’t require a lens, they can be absolutely tiny, and are easily disguised in other objects - for use in pens, glasses frames, and other James Bond-like gadgets.
Because of those advantages, pinhole cameras lend themselves to some very high-tech scientific endeavours: they’re used inside of tokamak plasma reactors on the bleeding edge of nuclear fusion research, and a few years ago astronomers proposed the New Worlds Imager, a two-spacecraft pinhole camera sitting out in deep space in order to see distant exoplanets.
The New Worlds Imager solves the problem that planets are, of course, much fainter than the stars they orbit, so they’re very hard to see - from a few light years away, the Earth is 10 billion times fainter than the Sun, for example. By putting a “starshade” spacecraft - a giant pinhole camera, with the hole 10 meters across - in front of an existing space telescope, astronomers could block out the parent stars and see thousands of exoplanets directly for the first time.
And what about OUR star? When you look at your solarcan image, what do you see? We’ve provided a helpful guide to interpreting your solargraph below! As an example, let’s start with this picture from a Solarcan mounted right in front of Vsauce HQ:
This photo comes from a Solarcan that was up for a month, starting right around the time of the autumnal equinox. It shows a couple of things you might expect to see on your solargraph image:
Here are a few other things you might experience, courtesy of Sam Cornwell, inventor of the Solarcan:
Every Solarcan creates a wholly unique image: latitude, weather, and other factors lead to endless possibilities. We’ve shown you our solargraph - now we’re excited to see YOURS! #SeenOnSolarcan
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Decorative gift wrap as we know it was invented in 1917 at the Hall Brothers stationary store in Kansas City, Missouri! (before that, people used plain brown or tissue paper). It was such a hit that in ten years, it became their primary source of business, and the brothers renamed the company – to Hallmark. Today, people spend more than $3.2 billion on wrapping paper every year.
In the annals of scientific research, there are some interesting scientific studies on gift giving. In case you’re curious as you do your holiday shopping, researchers have discovered that expensive gifts are not more appreciated that cheaper ones, and sentimental gifts are appreciated more than ones keyed to the recipient’s hobbies. But we’re more interested in the science of gift wrapping – and there’s some neat stuff there, too.
The first thing to know is that people prefer wrapped gifts; if you give someone a present that’s wrapped, they have a more favorable attitude towards whatever’s inside the box. Scientists speculate that by activating happy birthday and holiday memories, wrapping paper elevates the mood of the person getting the gift.
And incredibly, how well you wrap the gift can influence how much somebody enjoys it, but not the way you might expect! In one study, people enjoyed sloppily wrapped gifts about 8% more than neatly wrapped ones (the scientists used the same gift both times). It’s all because of a psychological concept called “expectation disconfirmation”: the gap between what you’re expecting and what you get. A neatly wrapped gift raises the preconceived expectation of what’s inside, and the sloppily wrapped one lowers it. So once the present is unwrapped, the sloppy one seems cooler.
But that’s not always the case. The one time when neatness counts? If you don’t know the person all that well. Studies show that if you’re just an acquaintances with someone, the way a present is wrapped is interpreted as reflecting how you feel about them: if it’s neatly wrapped, they believe you think the relationship is important, if it’s a sloppy mess, then not so much. With close friends, your bond is already strong, so how nicely you wrap the gift doesn’t seem to affect people’s attitudes towards the relationship. These two studies were conducted by the same team, and provide the best answer that science could give you about wrapping a gift: if you barely know someone, make sure those edges are sharp, but with good friends, a sloppy wrapping job is better. So don’t worry about the perfect bow for your bestie, it’s what’s inside that counts!
And finally, if you’ve wondered about the most efficient way to wrap presents, British mathematician Sara Santos has calculated some formulas that use simple measurements to calculate the least amount of wrapping paper needed to cover each gift.
In practice, that means
Not only do you need the least amount of paper, you’ll only use one piece of tape!
Now that you’re armed with all the best science and math on the wrapping of gifts, we hope both you and the people you give gifts to enjoy this optical illusion paper – and the holiday season!
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Knots are all around you; when you tie your shoes, untangle your computer cables, or at this time of year, perhaps when putting bows on presents or putting out some holidays lights. In fact, in 2007 the National Academy of Sciences published a popular study on why knots form in things like computer cables and strings of holiday lights. But those are just regular knots, not mathematical knots.
Defined as a closed curved form, mathematical knots are interesting shapes; think of them like regular knots, but with the ends attached to each other. It’s the fact that the ends are attached that makes them special: because there are no loose ends, there’s no tying or untying a mathematical knot, but you can twist and untwist them. The branch of mathematics that deals with understanding them is called Knot Theory.
Knot theory is complex and fascinating, and one of the interesting things about it is that it evolved out of a completely discredited branch of Victorian science! See, many of the top minds of the 1800s believed in the existence of “æther,” a substance that at the time was thought to pervade all of outer space. In these theories, atoms were thought to be tiny knots in the æther, so studying knots was the equivalent of subatomic physics.
Though belief in the æther fell out of favor by the 20th century, people became interested in knot theory again in the 1980s, when it was discovered that DNA is essentially a mathematical knot, and understanding how tangles work was an important key to molecular genetics. Even more recently, knot theory has been tied up (pun intended) with the creation of advanced quantum computers: researchers have theorized about creating a “topological quantum computer” by dragging particles around each other to form space–time knots.
But what about your torus knot? It’s made of eight and a half meters (28 feet) of steel wire, and when it springs up, it’s 13 times taller than when stored as a flat ring. If you could do that to a human, the average person would stand around 21 meters (70 feet) high! You’ve probably spent some time playing with it already, and found out how engrossing this kinetic sculpture can be. As you discover all the things your torus knot can do, here are a few more fun things to try:
Engaging your curiosity by playing with a tactile kinetic sculpture like the torus knot engages your mental and physical creativity. We find it hard to put down, and hope you enjoy it as much as we do!
]]>Each season, the Curiosity Box founders put their brains together to bring our members a mind-tingling mix of viral physics toys, custom puzzles and intelligent showpieces designed to feed your brain. We spend over a year researching and developing our exclusive pieces, adding in thoughtful new elements to reimagine science and math classics. If you're ready to see all the brain boosting activities we packed into the fall box, then keep reading. But if you prefer a surprise, subscribe today and we'll ship it all right to your door!
No drivers license required for this car powered by a star! The build-it-yourself solar powered car kit will keep your hands and brain busy. Once you build it and get a hang of the steering, then you can dive into the science of solar power in our monthly newsletter.
Get your best ideas down on paper with everyone's favorite graphite-filled writing utensil: the pencil! But these pencils aren't just for writing, you can measure with them too – in inches and centimeters, of course! We even included a sharpener modeled after INQ's tentacles to keep them just as sharp as your mind.
Ever wish you had an extra set of hands... how about 8? Octopuses are known for being some of the most curious creatures on the planet, so who better to keep your desk tidy than a ceramic bust of our lovable mascot, Inq?
We decided to make this T-shirt as useful as possible, with all the information you’re likely to need and the precision you require. If people are staring, it's because you already got all the information they need to know – like the gravitational constant and the speed of light in a vacuum!
Reading is an essential part of exploring your curiosity, that's why we include a book in every box. 50 visionary artists, thinkers, activists, and entertainers contributed to this illustrated hardcover explaining how the use of observation and inquiry can change how you see the world.
Explore your imagination with this downloadable brain game where you'll design, build, and operate a functioning mechanical creation of your own. The open-ended format lets you build endless creations for hours of entertainment!
This classic puzzle sounds easy at first: just get the cylindrical center piece out of the wooden block, easy! Except, you can't use your hands... now what? Well, you'll have to use your brain – it's an exercise in lateral thinking.
]]>George Loewenstein literally wrote the (academic) book on the science of curiosity, and categorized it as “a cognitive induced deprivation that arises from the perception of a gap in knowledge and understanding.” In other words, curiosity is a “drive state” that motivates learning in the exact same way as the hunger drive motivates eating, and the thirst drive motivates drinking. And that’s not just a metaphor: psychologists believe that once you’ve learned enough to satisfy your temporary curious state, you feel sated, the same as when you’ve had a full meal.
Interestingly, studies show the hunger for curiosity is greater in people who know just a little bit about a subject. For example, subjects shown trivia questions have a u-shaped graph of their curiosity based on how sure they are of the answer: if they’re absolutely certain they’re wrong or certain they’re right, they have little curiosity about the real answer. But if they’re kinda sure? Then people really want to know. Related studies also show that curiosity helps to optimize your learning, making you want to focus on filling the gaps in your existing knowledge.
Using functional Magnetic Resonance Imaging (fMRI), which highlights oxygen use in the brain, scientists have also recently figured out where in your brain curiosity originates: a region called the posterior cingulate cortex, deep inside the cerebrum. Those experiments also show that once you’ve satisfied your curiosity, the reward sections of the brain activate, creating a powerful incentive to learn. FMRI studies also show not only that you learn better when you’re curious about something, but that the more curios you are, the more you learn! When they were really curious about an answer (as opposed to just slightly curious), people were 15% more likely to remember the answer.
Curiosity may also have significant effects on creativity: in a 2019 study, neuroscientists who prepped participants to be curious about a famous Harry Houdini trick came up with creative ideas about how it was performed 60% of the time, while “uncurious” people in the control condition imagined creative solutions only 36% of the time. That’s a serious bump.
Finally, curiosity is a lifetime pursuit: not surprisingly, research shows that infants and small children benefit from increased curiosity. Among other things, children prefer to play with toys that they don’t understand the workings of; psychologists speculate that trying to understand how the toys function gives kids a curiosity reward which makes play more enjoyable. Studies have also shown the importance of curiosity to older adults, with proven benefits in maintaining cognitive function and both mental and physical health. So stay sharp, stay well, and stay curious!
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