Left out: Indian scientist Satyendranath Bose is a “forgotten hero” in the celebrations over the discovery of the Higgs boson “God particle”, the Indian government has said. Picture: AP AP

While much of the world was celebrating the international cooperation that led to last week’s breakthrough in identifying the existence of the Higgs boson particle, some in India were smarting over what they saw as a slight against one of their greatest scientists.

Media covering the story gave lots of credit to British physicist Peter Higgs for theorising the elusive subatomic “God particle,” but little was said about Bose.

The scientist in question, Satyendra Nath Bose, worked with Albert Einstein in the 1920s and made discoveries that led to a kind of particle being named for him.

It was Peter Higgs, a British physicist, who in the 1960s made advances in the field, resulting in the naming of  Higgs boson.

Indian newspapers have been unhappy that their star scientist’s name has somehow been forgotten in all of this.

For a start, only the “H” in Higgs boson is capitalized in most cases. In many cases, it’s referred to as the Higgs particle, erasing all allusion to the Indian scientist.

Despite the fact that Bose had little direct involvement in theorising the Higgs boson itself, in India the lack of attention given to one of their own was seen as an insult too big to ignore.

“He is a forgotten hero,” the government lamented in a lengthy statement, noting that Bose was never awarded a Nobel Prize though “at least 10 scientists have been awarded the Nobel” in the same field.

The annoyance marks yet another case in the ever-growing list of perceived global snubs Indians feel they suffer, from the US airport searches of Bollywood star Shah Rukh Khan to the naming of a superbug after New Delhi, where it was found.

“Indians are touchy about this. All post-colonial societies are touchy about this,” said political psychologist Ashis Nandy of the Delhi-based think tank Centre for the Study of Developing Societies.

“The sooner we get out of that, the better.”

Mr Nandy, who interviewed Bose before his death in 1974, said the scientist himself was “least concerned about rankings and prizes.”

The Times of India opined: “Unfortunately, no one seems to care about, at least conveniently forgets, Satyendra Nath Bose, the late Indian physicist whose last name bears the mark of a set of particles including the elusive Higgs boson.”

The boson is named in honour of the Kolkata-born scientist’s work in the 1920s with Albert Einstein in defining one of two basic classes of subatomic particles.

The work describes how photons can be considered particles as well as waves – such as in a laser beam. All particles that follow such behaviour, including the Higgs boson, are called bosons.

Higgs, the English physicist, and others proposed the Higgs boson’s existence in 1964 to explain what might give shape and size to all matter. Laymen and the media sometimes call it the “God particle” because it existence is key to understanding the early evolution of the universe.

By then, Bose was living in his Indian city of Kolkata after 25 years running the physics department at Dacca University, in what is now Bangladesh. Bose died aged 80 in 1974. The Nobel is not awarded posthumously.

Indian newspapers decried the fact that Bose was mostly ignored last week when scientists announced the Higgs boson breakthrough, made using a giant atom smasher at the European Organisation for Nuclear Research in Switzerland.

Bose “remains unmentioned in most news stories about this discovery,” read an opinion piece in the Hindustan Times written by Yale University professor Priyamvada Natarajan, who says Western scientists often gain credit for major discoveries.

“It is harder for scientists to be recognised if they are seen as outliers and if their gender, race or work do not let them belong,” she said.

The Sunday Times of India noted other eminent Indian scientists who “never got their due,” including physicist G.N. Ramachandran who died in 2001 after making biological discoveries like collagen’s triple-helix structure and 3-D imaging used in studying the human body.

Was Satyendranath Bose Merely Lucky to Have the Bosons Named After Him?

Do you know who discovered oxygen? Even though you know oxygen is all around you and that you will die without it, you probably would have died without ever knowing who discovered it. That’s because no one bothered to name the gas ‘Scheelgen’ after the Swedish pharmacist Scheele, who is widely credited with its discovery. (The credit is usually shared between the Swedish pharmacist Carl Wilhelm Scheele, and the British clergyman Joseph Priestly.)
However, with a week which passed by, in which the world media was inflated with Higg’s Boson, you are more likely to know the Scottish professor who predicted the existence of the ‘God particle’ which was named after him and that Boson itself is named after Satyendranath Bose of India, who predicted, nearly a century back, the existence of a group of sub atomic particles called Bosons.

While much of the media focus itself was on the ‘God particle,’ very little has been mentioned about the work of Satyendranath Bose, which had far reaching implications on the advancement of particle physics which has lead up to the investigation to find the Higg’s Boson. If Bose hadn’t postulated on this group of sub atomic particles, we might have been, in all possibility still a long way from finding the God particle.

Was Satyendranath Bose Merely Lucky to Have the Bosons Named After Him?

Though India and the Indian government had recognized his greatness by awarding him various honours and positions while he was alive when the Nobel committee itself had failed to acknowledge it, Bose remained a forgotten name, unknown to the new generation Indians and to the world at large, until the discovery of the God particle, announced last week.

In fact, after his death in 1974, the Indians and most of the world outside scientific community weren’t aware of his contribution or achievement. A couple of generations have never heard of him. This was mainly due to the very esoteric nature of his work and contributions to science, which not everyone can understand.

It took a genius like Albert Einstein to recognize the genius in Bose and eventually jointly produce scientific contributions like Bose-Einstein condensate in particle physics. Perhaps the most important of all work of Satyendranath Bose is his short paper with statistical postulations on Max Planck’s quantum mechanics, which Einstein recognized as explaining a gaping hole in the theory and which predicted the existence of sub atomic particles called Bosons, later named after him, in recognition.

Respected Sir, I have ventured to send you the accompanying article for your perusal and opinion. You will see that I have tried to deduce the coefficient … in Planck’s law independent of classical electrodynamics.

What makes Satyendranath Bose the greatest scientist India has produced is his mathematical prowess, a record not broken in the University of Kolkota where he did most of his work, which he applied to postulate his theories about the nature of a set of sub atomic particles, no one had ever seen, until after several years. His greatness, like that of Einstein and many other eminent scientists of the past, lies in the fact that most of his work was done in his own god given faculties, in a world which had no computers, software or internet, and in a country far away from Europe, where the mainstream scientific advancement was taking place.

Part of the reasons, other than the implicit difficulty to explain his work to the people, why Bose was not universally recognized or given a Nobel Prize might have been his nationality, like in the case of Mahatma Gandhi, who was never awarded the prestigious price.

Not that Satyendranath Bose and his work would have gone in to oblivion even if the Bosons weren’t named after him or no one really would have searched and found the God particle. His work was undoubtedly a corner stone of modern physics and one way or the other, if not now sometime in the future would have revealed and shown itself as future scientists would have strived for answers to the secrets of the universe.

Now that God particle has reinvented his greatness for the world, it has become all the more important that a modern and emerging India do everything to unearth the greatness and increase the awareness of its immortal scientist to instil ambition and purpose in its youth and future generations. That only can atone a grate scientist who had the misfortune of being born an the wrong place at the wrong time.

A thousand years from now, like oxygen, Bosons will still be around reminding everyone about Satyendranath Bose and his contribution to science, while Professor Higgs, credited with the prediction of Higg’s Boson itself, the God particle everyone went gaga about, might be forgotten as it will be broken down, dissected and analyzed, extending the frontiers of human knowledge.

But that is not why Bose will be remembered. His name will stand out because, if greatness is to be judged by the contribution to the advancement of scientific knowledge, Satyendranath Bose is undoubtedly, the greatest scientists India has produced in recent times.

Scientists have found that when albatrosses forage for food, their flight path looks like a mathematical pattern called a fractal. Credit: Coedekoven/SWFSC/NOAA

People may say that math is for the birds. A new study shows this may be true, at least for a giant seabird called an albatross.

A team of scientists in Europe recently studied the flights of these large birds as they hunted for food. The scientists did not observe the birds adding, subtracting, multiplying or dividing. But when the researchers looked at the shapes traced by the birds’ flights, the formations looked familiar.

The twists and turns of the flight path looked a lot like a fractal, a mathematical design. Fractals are curves or shapes that look almost the same no matter how far you zoom in or how far you zoom out. (Mathematicians call this feature “self-similarity.”) The shape of a country’s coastline, for example, looks like a fractal. Observed from a faraway satellite, the coastline looks like a squiggle. If you fly over the coast closer, in a helicopter, you’ll see that the squiggles have their own, smaller squiggles (like large jutting rocks or cliffs). And if you walk along the coast on your own two feet, you’ll see even smaller squiggles where the tide laps against the land.

The scientists who studied the albatrosses found self-similarity in the birds’ flights. They attached GPS devices to 88 birds. Each GPS device recorded the position of the bird it was attached to either every second or every 10 seconds. Using this method, scientists could trace the path of the bird on a map. The team found that the birds often flew long distances in a straight line and then made lots of turns and shorter flights as they hunted for food over a new section of the ocean.

“Think about searching for your car keys,” team member David Sims told Science News. “You intensively search in one area, but if you don’t find them there, you jump to someplace else and search there.” Sims is a behavioral ecologist at the Marine Biological Association of the United Kingdom in Plymouth, England. Behavior ecologists study how where an animal lives influences its behavior.

This kind of fractal-like pattern is called Lévy flight. Like a fractal, the shape of the birds’ flight path looked similar when viewed from far away or close-up. However, the birds’ path wasn’t a true fractal: The pattern disappeared at extreme distances. But within a certain range, the pattern was self-similar.

Scientists suspect that many animals, including sharks, jellyfish and penguins, follow a Lévy flight path when hunting for food. This approach — a long trip, followed by a short and choppy hopscotch around an area — may help them find more food faster.

Not every scientist believes the giant seabirds use math to hunt, however. Simon Benhamou, an ecologist at the National Center for Scientific Research in Montpellier, France, told Science News that he’s not convinced. He said he thinks the new study is interesting but limited. Scientists can get a truer view of hungry birds’ flights, he said, by looking for even more complicated patterns.

POWER WORDS

fractal A curve or geometric figure, each part of which has the same basic character as the whole. Fractals are useful in modeling structures (such as eroded coastlines or snowflakes) in which similar patterns recur at progressively smaller scales.

GPS, or global positioning system An accurate worldwide navigational and surveying facility based on the reception of signals from an array of orbiting satellites.

behavior ecology The study of how animal behaviors help them survive in their environments.

albatross A very large oceanic bird with long, narrow wings. Some species have wingspans greater than 10 feet.

No, you don't need a degree in structural engineering to win at Jenga, but it sure seems that way sometimes, doesn't it? Jeffrey Coolidge/Getty Images

The child’s intuitive logic is the same that inspired the Mycenaean architects of the 13th century B.C.E. to construct the famous Lion Gate out of two stone columns and a slightly arched beam. It’s the same structural savvy that told the ancient Egyptians that if you want to build something tall out of stone, you need to start wide at the base. And it’s that same natural-born engineer in all of us that says, “Dude, if you want to win at Jenga, don’t leave a single support at the bottom of the tower!”

Jenga is one of the most popular games in the world, third only to Monopoly and Scrabble in the number of units sold [source: Little]. The object of the game is simple: You start with a stack of 54 blocks — three blocks across, 18 levels high. Each level of blocks should be perpendicular to the level below it. Each player must remove a block from near the bottom of the tower and place it on the top using only one hand at a time. Eventually the tower becomes dangerously unstable. If you’re the one who finally knocks it over, you lose.

Jenga was invented by Leslie Scott, a British citizen born and raised in Kenya and Tanzania. (Jenga means “build” in Swahili.) Scott played the game with her family in Africa for years; she eventually left a job with Intel to launch Jenga at a 1983 toy fair, where it became an instant gaming phenomenon [source: Little].

Part of Jenga’s charm is its simplicity; nothing but wooden blocks and gravity. But even this simple game can teach us a lot about the more complex world of structural engineering. Buildings, after all, are vulnerable to the same forces that can topple a Jenga tower — forces like loads, tension, compression, torsion and more. An accidental bump of the game table is an excellent scale version of a catastrophic earthquake.

1: Loads

One of the most important principles of structural engineering is loading. Have you heard of a load-bearing wall? It’s usually an internal wall (like the one that divides your kitchen and living room) that also serves as a column that holds up the second floor or the roof. If you remove a load-bearing wall, the structure might not be able to support its own weight — and that spells trouble.

In Jenga, no two wooden blocks are cut to exactly the same dimensions, which means that the blocks rest on each other unevenly [source: Smith]. One of the main tricks of Jenga is locating the “loose” pieces, which are easier to remove without disturbing the integrity of the tower. If a piece is loose, then you know it can’t be load-bearing.

So what does this teach us about structural engineering? When designing a building, engineers need to consider the load path from the top of the building to the foundation. Each level of the structure needs to support the forces applied downward from the levels above. There are three kinds of loads that occur in a building:

• Dead loads — The forces applied by all of the static components of the structure, like beams, columns, rivets, concrete and dry wall.
• Live loads — The forces applied by all of the “moving” elements that can affect a structure, including people, furniture, cars, and normal weather events like rain, snow and wind.
• Dynamic loads — Dynamic loads are live loads that occur suddenly with great force. Examples are earthquakes, tornados, hurricanes and airplane crashes [source: Yes Mag].

Engineers need to do careful calculations to ensure that load-bearing walls, ceilings and roofs can support dead, live and even dynamic loads, particularly when building in seismically active zones.

2: Foundations

Just as you need to find the perfect surface on which to play Jenga, structural engineers need to consider the surfaces upon which they choose to build. Richard Elliott/Getty Images

Every family has their favorite surface on which to play Jenga. The flimsy card table is out of the question because the slightest bump from an errant elbow will send your tower tumbling. The sturdy kitchen table is a solid choice, because it doesn’t rumble around as easily as the card table, but nothing beats a good hardwood floor. You can’t knock it sideways, it’s pretty darn flat and the only threat to stability is the occasional crawling baby or pet.

Structural engineers must also consider the surface onto which they’re building their structure. If you plop a 15-story building onto loose soil, the structure might settle unevenly, causing cracks in the walls or even a collapse. Even if a building is constructed atop solid rock, an earthquake could jostle it sideways, causing it to slide down the street a few feet, crushing anything in its path. That’s why all modern buildings, small and tall alike, are built upon foundations.

A foundation serves a couple of key purposes. Firstly, it transfers the load of the structure into the ground. (We talked about loads on the last page.) The taller and heavier a building, the more load is driven downward. If the building sits flat on the surface, then the lowest elements in the structure would have to bear the combined load of everything above them. But with a properly engineered foundation, the load of the entire structure passes through the lowest elements and is dispersed into the earth below.

Foundations also serve the purpose of physically anchoring the structure to the ground. This is a crucial role in very tall buildings. Imagine trying to balance a yard stick on one end. You might be able to pull it off on an extremely flat surface, but even an exhale would topple it over. But what happens if you take the yard stick out back and jam one end into the ground a few inches? Now you can tap it, or even kick it, and it won’t tip over. A foundation buries a portion of the building in the ground, giving it increased stability against dynamic load changes.

For tall buildings built on loose soils or sand, engineers drive steel piles deep into the earth until they reach bedrock. Then they build a reinforced concrete foundation around the steel piles to create a firm anchor on which to build.

3: Tension and Compression

In structural engineering, there are two basic forces at work in any structural element: compression and tension. Compression is the force applied when two objects are pushed together. Think of a stack of heavy stones. The force crushing down on the bottom stone is compression. Tension is the force applied when an object is pulled or stretched. A good example is the surface of a trampoline. When someone jumps down on the trampoline, the material stretches.

Engineers talk about the tensile strength of materials. This is the maximum force that can be applied to a material without pulling it apart. Bundles of steel cables have an incredibly high tensile strength, which is why they’re used in the world’s longest and heaviest suspension bridges. Even a single steel cable only 1 centimeter in diameter can hold the weight of two full-grown elephants [source: Yes Mag].

Now let’s think about a typical structure in Jenga. If you remove the center piece in a row, then you create two simple beam-and-column structures on either side of the tower. A beam laid across two columns experiences both compression and tension at the same time. The weight bearing down on the top of the beam compresses it inward toward the center of the beam. And even though you can’t see it with your naked eye, the underside of the beam is being stretched outward.

Imagine if the beam was made of rubber. The weight would stretch it into a “U” shape. That’s why rubber makes such a lousy construction material. Structural engineers choose (and sometimes design) materials with the best compression and tension characteristics for the job. Stone is excellent under compression, but remarkably easy to pull apart. That’s why a stone arch lasts a lot longer than a stone beam. Reinforced concrete is an ideal building material, because the concrete gives it compression strength and the embedded steel rods give it tensile strength.

Jenga towers don’t get tall enough or heavy enough to apply serious compression or tension on the wooden pieces, so there’s very little concern of splitting a beam. But in real construction projects, engineers need to carefully consider each element’s strengths and weaknesses.

4: Rotational Force

Experienced Jenga players know that the quickest way to a falling tower is to pull away the two outside pieces of the bottom row, leaving the whole structure balancing on a single narrow wooden block. With only one support at the bottom, every bump and nudge of the tower is magnified, causing it to sway precariously from side to side. But what exactly are the forces that act upon a structure with such a narrow support? And what makes them so dangerous?

Keeping this teetering tower upright involves a lot more than mere luck. Staff/Getty Images

Structural engineers don’t talk about keeping a building “balanced.” They talk about maintaining rotational equilibrium. Imagine a tall building as a long lever arm with the majority of the arm above ground and a smaller section (the foundation) below ground. The point where the building meets the ground is the fulcrum of the lever. Now picture the building tipping slightly to the right or the left. Instead of merely falling over, you can think of it as rotating around the fulcrum. Engineers and physicists have two names for this rotational force: the moment or torque.

A basic tenet of structural engineering is that the longer your lever arm (or the further it is away from the fulcrum), the greater the moment. To decrease the moment of a very tall building, you need to build wide supports. The wider the supports, the lower the moment. To understand this, try standing with your feet spread wide apart and have a friend try to push you over sideways. It requires a lot of force. Put your heels together and try the same thing. Your friend barely has to touch you and you tip right over. A structure with a nice wide base is inherently more stable that a building with a narrow base.

5: Earthquake Forces

The tallest Jenga tower on record was 40 levels, reached using the original Jenga set designed by Leslie Scott herself [source: Museum of Childhood]. Most players are lucky if they can get more than 30 levels before the whole thing comes crashing down. The reason the tower becomes increasingly unstable as is grows is due to uneven weight distribution. When too much weight is located at the top of the structure, it begins to act like a reverse pendulum, swaying back and forth on its narrow connection to the earth [source: FEMA]. In Jenga, the result is a two-minute cleanup. In real life, you’d have a catastrophe.

When structural engineers choose to build in a seismically active region, they need to consider the effects of lateral vibrations on their building. When seismic waves ripple through the earth, they jostle buildings both up and down and back and forth. The up and down bumps aren’t as dangerous as the lateral movements, which are more likely to lead to collapse [source: Association of Bay Area Governments].

These side-to-side vibrations are experienced differently at different distances from the ground. The higher you travel up a building, the more pronounced the vibrations. When you throw weight into the equation, the effects can be disastrous. According to the seminal text, “Why Buildings Fall Down,” earthquake forces grow in proportion to the weight of the structure and the square of its height [source: Levy].

A top-heavy structure vibrates with a much longer period — the time it takes to cycle through one complete vibration — than a bottom-heavy building. A longer period also means a larger physical displacement. Take the example of a two-story building. When an earthquake strikes, the building sways 2 inches (51 millimeters) off center. When you add weight to the top of the same building (even if it’s something simple like a heavy tiled roof), the sway increases to 3 inches (76 millimeters) off center [source: Association of Bay Area Governments].

You can find eco-friendly, sustainable and locally-made and grown products on shelves in almost every store these days. So perhaps it’s no surprise that some people want to make the buildings themselves more in tune with the environment, too. Or it could simply be that people just really like the idea of living inside giant soccer balls, which is what geodesic domes look like. In short, geodesic domes are structures that look like half spheres made up of many triangle supports.

Geodesic domes (and the homes based on those designs) are extremely efficient and inexpensive. Those traits, when considered in the context of today’s economic and environmental issues, mean domes are enjoying the kind of popularity not seen since their heyday in the late 1960s and early 1970s. Many communities throughout the world boast geodesic domes, either as homes or as commercial structures, and you can’t miss them — they’re so futuristic-looking that they make it seem like an alien mothership has landed and begun a planetary takeover.

And if fans of geodesic design have their way, that’s exactly what these domes eventually will do. As the push for sustainable living continues and our population burgeons, domes may offer affordable and smart ways to house humans. Or, they could simply cause a lot of complications. As you’ll soon see, there are plenty of arguments about how useful these domes really are (or not).

But there are some inarguable points regarding geodesic domes. The first is that they are eye-catching. Maybe because these shapes are so rare in architecture, it’s hard not to let your eyes be drawn to these domes.

Another concrete fact about the domes is that they come from geodesic designs, which are based on a polyhedron. A polyhedron is a three-dimensional solid that’s made up of many flat faces. Both pyramids and prisms are examples of polyhedrons.

One of the most common polyhedrons used for geodesic dome designs is called an icosahedron, which is a solid shape composed of 20 flat faces. Each face is an identical equilateral (all sides are equal) triangle. Rotate the edges of those triangles slowly towards an imaginary center and eventually you wind up with a rough version of a sphere, called a geodesic sphere. Cut that sphere in half and you have an approximation of a geodesic dome.

And here’s a bit more basic geometry. You probably already know that a line is the shortest distance between two points. The word geodesic refers to the shortest distance between two points on a curved surface, and it comes from a Latin word that means “earth dividing.”

Read on to find out more about the history of geodesic domes — and how some people thought they might mean housing salvation for humankind.

Origin and Uses of Geodesic Domes

The Long Island Green Dome, in New York, has the same kind of ultrastrong roof found in all geodesic domes. In addition, it sports a unique green roof on which various kinds of plants can grow. Image courtesy Kevin Shea

In 1926, the world’s first geodesic dome opened in Jena, Germany, as a planetarium funded by legendary optics manufacturer Zeiss. It features an exterior diameter of 82 feet (25 meters) and is the oldest planetarium on Earth.

The planetarium’s construction was the brainchild of Zeiss engineer Walter Bauersfeld, who realized that the building had to be extremely lightweight — as it was to be placed on the roof of a Zeiss factory — yet big enough to accommodate a large audience, strong enough to withstand storms and rounded enough to feature a nice projection surface for the planetarium’s stars and planets.

To those ends, Bauersfeld decided on a geodesic design. In terms of their interior space, geodesic domes enclose the largest volume of space using the least amount of construction material. In turn, because they require so little with regards to material, they’re also extremely lightweight. Finally, the geometric dimensions of the domes also lend them great strength.

The novel Jena building sparked worldwide interest in planetarium construction, and domes became more common. But in the 1950s United States, only a guy nicknamed Bucky could’ve popularized something as futuristic as geodesic domes.

“Bucky” was Buckminster Fuller, an American engineer who helped spread and commercialize polyhedral constructions throughout the country. It was Fuller who stuck these buildings with the term “geodesic,” and he was awarded a U.S. patent for his dome in 1954, even though Bauersfeld unveiled his designs decades earlier.

Fuller took his dome design inspiration from nature. He marveled at the structural uniformity of things like snowflakes, seed pods, flowers and crystals and resolved that humans should emulate those simple, strong, and noticeably spherical arrangements [source: The Futurist]. Thus, he began working in earnest on geodesic domes, which he saw as an economical, efficient way to address the post-World War II housing shortage.

He began construction on his first dome in 1948. That dome immediately failed due to the weak and thin Venetian-blind slats he used. Subsequent (and much more successful) models featured strong, lightweight materials such as aluminum aircraft tubing.

They worked in part thanks to a structural principle that Fuller coined – tensegrity. Tensegrity is a word made of two others — tensional and integrity — and refers to to the relationship and balance between tension (tightness or tautness) and compression (a force shortens or squeezes something) in a structure. Although these structures had relatively little mass, their shape allowed them substantial rigidity that supported great weight.

The low quantity of materials necessary for geodesic domes, matched with their durability and good looks, means they’ve found their way into places all over the world. In Antarctica they’ve stood for decades and resisted winds of around 200 miles per hour (322 kilometers per hour). Domes have also withstood hurricanes, earthquakes, and fires better than rectangle-based structures.

They’ve been used for military radar systems, churches, auditoriums and also for all sorts of special events in which temporary, inexpensive and strong shelters are needed. Read on to see why the special construction of these domes makes them so useful.

Geodesic Geometry

The triangular windows of this home serve as a reminder of the geometric shape that helps make this dome structure so strong. Image courtesy Timberline Geodesics

People have been building domes for centuries. Ancient peoples such as the Romans applied their masonry skills — and their knowledge of the arch — to create massive domes. But those domes needed equally large supporting walls keep the entire structure from crashing to the ground. In short, huge old domes were heavy and bound to fail at some point.

Geodesic domes are different. Not only do they incorporate the strength of a strong arch shape, but they’re also made up of many triangles. Pair domes with triangles, and you have one extremely durable structure. Triangles are the strongest shape because they have fixed angles.

Much of that durability results from the characteristics of triangles, which are the superheroes of shapes. Triangles are the strongest shape because they have fixed angles and don’t distort very easily.

Michael Busnick, owner of American Ingenuity, which sells dome homes, says triangles are key to making domes strong. “(Domes) are three-dimensional structures using stable triangles approximating spheres to create multiple load carrying paths from point of load to point of support. The triangle is the only arrangement of structural members that is stable within itself without requiring additional connections at the intersection points to prevent warping of the geometry.”

In other words, apply pressure to one edge of a triangle, and that force is evenly distributed to the other two sides, which then transmit pressure to adjacent triangles. That cascading distribution of pressure is how geodesic domes efficiently distribute stress along the entire structure, much like the shell of an egg.

The pattern of those triangles is critical to the structure of geodesic domes. To understand why, consider first a basic four-sided square. If you lay many squares perpendicular (at right angles) to each other, they can lay neatly into a flat plane.

The same isn’t true of pentagons or hexagons. Try to lay these shapes flat in the same manner as the square and it won’t work. But tilt these shapes inward into a ball or sphere shape and the sides match up nicely as tessellations, which are simply patterns that can be repeated to create another shape without overlapping or spaces between the shapes. And it just so happens that pentagons and hexagons can be neatly divided into triangles, the foundation of geodesic domes, so they’re also exceedingly strong.

Different tessellations result in varying designs for dome buildings. Read more about how designs make it easier — or much harder — to assemble domes.

The Lowdown on Geodesic Dome Construction

Dome homes may have nontraditional designs, but they can still incorporate traditional construction materials, such as wood beams and concrete. Image courtesy American Ingenuity

Not all geodesic domes are alike. The most basic and common dome is based on the aforementioned icosahedron with its 20 faces made up of equilateral triangles. You can make ever larger domes by dividing the face of each triangle into smaller and smaller triangles.

As you view a geodesic dome, you may notice that the lengths of support struts (the individual rods or bars) making up the dome’s frame usually aren’t identical. In the most basic kind of dome design, there are many different lengths of struts necessary to complete an unbroken sphere.

A one-frequency dome employs struts of one similar length. Likewise, a two-frequency dome uses two distinct strut lengths. Lower frequency domes (those with fewer parts) are easier to put together, but those with greater frequency can be built to bigger sizes. When assembled into triangles, struts are called trusses. The joint where the straight ends of the struts meet is called a node.

Struts must be measured and cut precisely in order for the dome to take proper shape. So for anyone who has to deal with the challenges of the dome’s actual physical construction, fewer lines make for fewer struts and much easier assembly.

So although software might be able to calculate enormously intricate domes, in reality, only a few basic designs usually wind up in the real world. More complex plans – that is, those with great frequency — require struts of many varying lengths, and as such they are more difficult to put together.

Once a dome design is ready to go, builders select the desired materials. Dome struts may be high-strength metal alloys, or more traditional wood members. The nodes, or hubs, that connect struts are often steel.

After the framework is complete, it must be covered. The triangle panels are generally made of plywood, plastics or concrete. The interior of the dome is often lined with insulation and finished with triangular sections of drywall or wood.

With a smart dome plan, there’s no limit as to how high those triangles will go. Keep reading to find out more about how domes are built and how Fuller’s geodesic creations took on gigantic proportions — and then went up in flames.

Fuller’s Fantastic (and Sometimes Flaming) Domes

Dome "daddy" Bucky Fuller liked to think outside the box -- literally. Nancy R. Schiff/Hulton Archive/Getty Images

Logical, thoroughly planned domes can accomplish feats that other construction techniques cannot. As evidence, there’s the mammoth dome that helped hurtle geodesic domes to celebrity status.

In 1953, the Ford Motor Company hired Bucky Fuller to create a dome that would enclose a central courtyard at the company’s headquarters. The gap over the courtyard was 93 feet (28 meters) across, and traditional building techniques would make a gigantically heavy dome that would crush its supporting walls.

Enter Fuller and his geodesic designs. He convinced the Fords that his plan would weigh less than 10 tons (9 metric tons) and cost much less than an old-fashioned dome. Within months, Fuller had disproved all of his doubters by finishing the project ahead of schedule, covering the opening above the courtyard as planned. Engineers around the world were amazed, and Fuller became famed for his expertise.

A few years later, a leak was spotted in the dome, and a team was sent to fix it. Unfortunately, they accidentally set the dome on fire and it was destroyed. No matter — Fuller’s idea had already taken hold.

He was later hired to create what would become one of his most famous domes, this time for the 1967 International and Universal Exposition in Montreal. This 250-foot (76-meter) dome was nearly 200 feet (62 meters) tall and served as an architectural centerpiece to the fair.

Fuller liked to think big. After his success at Ford, he even speculated that a huge dome could cover part of Manhattan Island. The dome would moderate temperatures, and equipped with air filters, could keep people healthier by lowering germ and virus counts. What’s more, Fuller thought the dome would pay for itself by eliminating the cost of snow removal. His audacious idea never quite caught on, though.

Not all domes are built with immensity or grandeur in mind. Some are very practical.  Read more about how some imaginative homeowners trade blocky, rectangular houses for domes, sweet domes, as homes.

The Bucky Dome Home

Carbondale, Ill., is home to a prototype dome built by Bucky Fuller. It was the only dome he ever lived in — and it’s also falling apart due to storm damage and neglect. A restoration fund drive is currently under way to save the building.

Dome Sweet Dome Home

In the 1960s and 1970s, counterculture was all the rage, and newfangled geodesic domes fit that anti-mainstream vibe. Many people viewed strong, eco-friendly, inexpensive domes as the homes of the future, and they were ready to ditch traditional right-angled, squared construction for triangle-based houses.

The Long Island Green Dome has a high ceiling interlaced with wooden struts that add to its aesthetics. Image courtesy Kevin Shea

The benefits seemed obvious. Spheres enclose a maximum of space with a minimum of materials, and they don’t require interior supports. Their aesthetic appeal for many people is undeniable; the high ceilings and open feeling can make them attractive, and it’s easy to build lofts inside for partial second-floor space.

The spherical design results in highly efficient and effective air circulation in both summer and winter. Less surface area makes these buildings less susceptible to temperature changes, and thus, inexpensive to heat and cool as compared to rectangular homes. The aerodynamic exterior means cold and warm air flows around the structure instead of forcing its way into the interior.

They are so easy to assemble from kits that do-it-yourself types without construction experience can assemble color-coded kits in just a day or two with the help of friends. These kits may include wooden struts or metal alloy parts, but either way, the components are lightweight and don’t require cranes or other high-powered equipment.

Yet some of the advantages of dome homes also translate into disadvantages. The same shape that makes for efficient airflow means sounds and smell travel throughout the home, too, meaning there’s very little privacy and a lot of potential for annoying, amplified echoes. Similarly, light bounces around domes, meaning a single small light can wake up everyone in the house.

Interior curved walls are major challenges when it comes to construction contractors. Everything from insulation, to plumbing, and electrical conduits must be carefully reconsidered in a round home, and because standard construction materials are made for rectangular homes, dome components are generally more expensive. What’s more, some contractors refuse to even work on domes because the frustrations and costs are too high, and profits too low.

Even furnishings can be problematic. Couches, tables and beds are all made to sit flush against flat walls. Put them in a sphere and not only do they look out of place, but they also waste much of the wonderful extra space that spheres impart.

Waterproofing is another hurdle. Flat roofs are easy to shingle so that they shed rain. But the many triangles and seams in a dome home are another matter altogether. Water intrusion has spelled the end of many a rounded home.

These days, dome kits are still popular with hobbyists and the sustainability-minded. Many companies, such as American Ingenuity, Pacific Domes, Timberline Geodesic Domes, Oregon Domes and Natural Spaces Domes all sell dome homes and plans. The complications and drawbacks of domes, however, may prevent them from reaching the kind of popularity of years past.

Ultimate Dome-inations

Epcot's famous silver golf ball, Spaceship Earth. Man, check out all those triangles! Matt Stroshane/News/Getty Images

There’s no sure count of how many geodesic domes exist in the world, but the big ones are easy to spot.

The world’s largest dome resides in Fukuoka, Japan and is aptly named the Fukuoka Dome. This huge dome serves primarily as a baseball stadium and seats more than 30,000 people.

It also has a unique retractable roof. The roof comprises three steel-framed titanium panels that have a surface area of around 59,795 square yards (50,000 square meters). Altogether, the struts and panels of the roof weigh about 12,000 tons (10,886 metric tons) [source: Web Japan], yet it takes only about 20 minutes for the panels to retract, exposing spectators to the skies above the city.

Tacoma, Wash., is home to the world’s largest wooden dome: the Tacoma Dome. This structure has enough room to seat more than 17,000 fans for basketball games, thanks to its 530-foot (160-meter) diameter and 152-foot (46-meter) height. Although the arena was primarily constructed as a home for the former professional Seattle Supersonics basketball club, it’s big enough to be used for the 100-yard long fields of football games, although this significantly reduces seating capacity [source: Tacoma Dome].

The Eden Project, located in Cornwall in the United Kingdom, is another dome masterpiece. The project includes two huge domes that are climate controlled to emulate different regions from around the world. One dome, for example, encloses a very warm and humid tropical environment that keeps the equatorial plants inside flourishing.

The tropical dome (called the Tropical Biome) covers nearly 4 acres and uses a steel frame to reach a height of 180 feet (55 meters) and width of 328 feet (100 meters). The adjacent Mediterranean Biome is comparatively small, at 115 feet (35 meters) high and 213 feet (65 meters) wide. Because the plants below need ample sunlight, a thin, transparent plastic film that’s durable enough to withstand local weather [source: Eden Project].

One of the most iconic geodesic dome designs in the world is actually a complete sphere. It’s Spaceship Earth, an 18-foot (54.9-meter) tall, silver geosphere at the center of Epcot theme park , which is part of the Walt Disney World Resort in Orlando, Fla. Epcot is an acronym for Experimental Prototype Community of Tomorrow, which was Walt Disney’s idea for an experimental, utopian community.

Unlike most domes, this one doesn’t even try to repel the rain with any sort of shingles or panels. Instead, the panels are arranged with 1-inch gaps between them. Water flows into these spaces and to the bottom of the building, where it’s used in one of the park’s lagoons.

There’s a ride inside the sphere that’s also called Spaceship Earth. Riders move briskly through scenes of humankind’s development, from prehistoric cave dwellers to a modern, technology-driven society. For that reason, maybe the Epcot sphere is a good symbol for geodesic domes as a whole.

These rounded structures represent our capacity for imaginative thinking and building, as well as our ability to create concrete, useful items from abstract ideas and theories. Although geodesic domes may never be as popular as Bucky Fuller and his acolytes hoped, these half-spheres are a testament to the inventiveness and persistence of people everywhere.

Review of Steven G. Krantz’s Mathematical Apocrypha Redux

Mathematicians perform their labours in an abstract space. However, when they do return to planet earth for rest, recuperation and, more often than not, to grab a cup of coffee, their encounters with fellow homo sapiens (colleagues, students, friends and family, and, last but by no means the least, officialdom) are wholly unpredictable and often funny. Mathematical Apocrypha Redux, by Steven Krantz, tells how.

Steven Krantz, a well-known mathematician and author of an earlier volume, Mathematical Apocrypha, is from the University of Washington, St. Louis, U.S. The book is in anecdotal form, with each anecdote running from a few lines to a page at the most. Brevity may be the soul of wit but that alone, perhaps, would not suffice to hold a good story together, let alone a whole book of them — a good tale lies in the telling. In reality, one suspects that each story has been written with considerable care, based on some non-trivial research, and then honed to perfection over a period of time. They have the quality of a collection of pictures in prose. The result is a compelling read — but perhaps only for mathematicians. Many of the stories relate what happens when mathematical genius alights on terra firma…. For non-mathematicians, the strange and unconventional ways of mathematicians, related in some of the stories (see p.96-97, but you can take your pick) may be quite incomprehensible. A degree of social alienation is perhaps the price mathematicians pay for our esoteric endeavours.

It is not uncommon in academia to identify knowledge with the skill and virtuosity of its most successful practitioners, a practice that effectively masks their personal attributes. In the forest of mathematical research, it is easy to miss the trees. The book provides that missing dimension that brings to life and colour the personalities of some of our most famous and best-known mathematicians. The maximum number of stories relate to Paul Erdos, with Nobert Wiener and von Neumann tying for the second place. For Indian readers there is Srinivasa Ramanujan (p.254), Raghavan Narasimhan (p.133), P.R. Masani (p.134), the ‘Tata Institute’ (p.92), and the ‘Statistical Institute’ (p.227) based in Kolkata. The book is not only about famous personalities. The author has spread his net far and wide — the result is a 275-page panoramic, ground-eye view of mathematicians at work and out of it. It brings out the breadth and depth of mathematical research in the Anglo-Saxon-European world, peopled as it is by a diverse array of nationalities.

The book, published by the Mathematical Association of America, is a celebration of a system of creating knowledge — a world-class system of research — that drives the search for knowledge in its own country and influences that search in much of the rest of the world.

A minor quibble relates to the chapter headings — they did not seem to quite connect with the contents. Many of the stories are set in the academic institutions of the U.S. Some of the stories that invoke ‘local colour’ may leave us nonplussed (example ‘Beavis and Butthead,’ p. 67).

But into the mouth of this particular gift horse, we shall no further look! And whichever part of the world you may be doing your mathematics in, this is a delightful book, whose stories, we are sure, will be told and retold in meetings around the world, when the day’s work is done, and mathematicians gather around the food and drinks, and remember the legends of their fields.

(B. Rajeev is with the Indian Statistical Institute in Bangalore)

Broadcom MASTERS, Robert Heckman, Justin Barber, Adriana Monzon, Alicia D’Souza, and Valerie Ding, finalists work together on a team challenge. Credit: Broadcom Foundation

Guests checking into the posh Palomar Hotel in Washington, D.C., recently, might have been surprised to hear pounding footsteps, shrieks and laughter pouring out of a conference room late one evening. And they would have been even more surprised to see what was behind those doors: 30 of the nation’s top middle school science students, flushed and sweaty, playing dodgeball, riding piggyback on their parents and squirting one another with water bottles.

The students were finalists in the first Broadcom Math, Applied Science, Technology and Engineering for Rising Stars — or MASTERS — challenge. The three-day competition kicked off with an evening of icebreaking and team-building activities meant to help these students from throughout the United States and Puerto Rico get to know each other.

It may have looked like all fun and games. But the purpose of these activities was to get students comfortable working in teams to solve problems creatively and to accomplish a shared goal.

“We know these kids are smart, but getting together with others and innovating is another skill set entirely,” says Paula Golden, executive director of the Broadcom Foundation, in Irvine, Calif., which cosponsored the MASTERS program with Society for Science & the Public, in Washington, D.C., publisher of Science News for Kids. “One of our goals is to integrate that team approach. It takes a village to innovate, and science isn’t done in a vacuum,” she explains.

To qualify, students took part in a science fair affiliated with Society for Science & the Public last spring. Teachers and fair organizers then nominated promising students to apply for one of the prestigious slots as a Broadcom MASTERS finalist.

What sets this new program apart from a traditional science fair is its emphasis on teamwork. Finalists were judged not only on their individual science fair projects but also on how they demonstrated leadership and creative problem-solving while working as part of a team during a series of group challenges.

“You tend to get very siloed in a science fair competition,” Golden says. “A science fair is all about you. Our goal is to give these kids insight to broader fields and to learn how to tap their colleagues for ideas.”

This focus on group activity mirrors the way science is done in the real world, competition organizers say.

“No scientist works alone anymore,” observes Bill Wallace, a science teacher at Georgetown Day School in Washington, D.C. A former biologist at the National Institutes of Health, he served as a judge for the team challenges.

“We think learning to work as part of a team will be very important as students move ahead.”

Finalist Maria Elena Grimmett, 12, of Jupiter, Fla., agrees. “If we learn to work well as a group, it’ll help us to work together as a community in the future.”

Perhaps even more important than practicing how science works, says Golden, is introducing students to teamwork at the age when they are first beginning to form their own identities and to choose those students who will become their friends. Adolescence, she says, is a time when students actively seek out a “tribe,” or group of like-minded people to belong to.

“By teaching kids the benefit and joy of collaboration at a time when finding common ground is so critical, we may help them identify groups of young people with common vision and potential,” she argues.

Of course, teamwork comes with more concrete benefits as well. It empowers students to tackle a project that would overwhelm an individual. In groups, students can pool their strengths. That proved a plus when the young researchers were charged with projects that ranged from building a suspension bridge and wiring a model house to designing and building a Rube Goldberg machine, a device that’s deliberately overengineered to complete a simple task.

When Ria Chhabra, 14, of Plano, Texas, came to the competition’s Science Relay — a set of six different experiments to be completed in 90 minutes or less — she was initially intimidated.

Broadcom MASTERS finalists, from left, Ria Chhabra, Mahita Tovinkere, and Kyle Davis, work together on an experiment. Credit: Broadcom Foundation

“When I first saw the challenges, I thought, there’s no way,” she recalls. “But when you start to do them together, you realize there’s more you could do than you thought. We really pushed ourselves more than we could have imagined.”

Teammate Mahita Tovinkere, 12, of Portland, Ore., agrees. “When we first came in, I didn’t think I knew how to do any of them and I thought I’d just follow the others. But when I actually took part in it, it was fun. And it was easier because I was confident.”

“If we split up and do our parts, then everyone can contribute and we’ll get it all done,” Anirudh Jain, 13, of Portland, Ore., told his teammates during their challenge to develop a campaign to persuade politicians about the benefits of alternative energy.

It’s a point that the competition judges didn’t miss.

“The most successful teams are the ones that came up with a plan and then divided up the work,” says judge Amy Kruse, executive director of the neuroscience division at the software company Intific. “Because of the time constraints behind all the group challenges, everybody can’t work on the whole thing at once. They need to break it down.”

But many students acknowledged it’s not always easy to collaborate, especially when people with strong opinions must interact.

“In science class, working in groups, one kid usually stands out as the leader,” says Katherine Landoni, 14, of Sequim, Wash. “But here, we are all leaders,” so the trick becomes how to decide whose ideas to use and how to figure out which team members should implement them, she says.

Indeed, explains Stephanie Lemnios, who manages the competition for Society for Science & the Public, “Being a good team member is not just about sharing your ideas, but respecting other peoples’ perspectives and working together. For some students, this is a very new concept,” she says. Those who may be used to always being the smart kid in class may not have felt compelled to listen carefully to their peers. But listening to and respecting the suggestions of others —“that’s an important part of teamwork.”

During some team projects, judges intervened to make sure one student wasn’t dominating his or her group, and to ensure that the ideas of quieter team members were heard and considered.

Sometimes judges also stepped into the role of coaches, offering suggestions to teams that found collaboration a struggle, notes Meagan Bethel, 14, of Tucson. “Our team wasn’t working well together on one of the challenges,” she says. Then a judge provided some hints on how they might cooperate more effectively.   “We tried really hard to follow his advice to not be too controlling and to let other people say things,” she says. “And our challenges after that went better.”

Carolyn Jons, 13, of Eden Prairie, Minn., learned about the importance of trusting in her group members’ abilities. “We’ve all heard 500 times about how we need to be able to work together so we can do our best — but these activities really showed it,” she says.

A side benefit to all of this sharing and collaboration: Most students went home with a new group of friends. And that can be empowering.

“Students who are deeply immersed in something, especially at a young age, can feel isolated socially, because it can separate them from their peers,” says Elizabeth Marincola, president of Society for Science & the Public and publisher of Science News for Kids.

“The intellectual aspects [of science] are just as important as the social aspects of finding each other,” she maintains.

It’s a sentiment many finalists shared.

“This competition is motivating, but it’s really nice to meet new people,” says Jordan Kamimura, 14, of Hilo, Hawaii.

Mahita Tovinkere found that the students she worked with were so nice that “I don’t feel like we’re in a competition.” To her, they became simply colleagues.

The MASTERS program also met another important need for many science and engineering students: interacting with kids who share their interests and who did not criticize them for being smart.

“Science is usually classified as nerdy,” maintains Benjamin Hylak, 14, of West Grove, Pa., who placed second overall in the competition. “But here, there are no stereotypes. Everybody is used to being the smart kid who does all the work,” he continues. “So to have real teammates and people backing you up is amazing.”

Indeed, adds Daniel Feeney, 15, of Woodside, Calif., during the Washington program “we were really allowed to just be ourselves. We could all let out our inner nerds.”

“This is the beginning of the rest of your life,” Golden told the students. “The beginning of friendships you’ll have for the rest of your life — they will define you, they will support you, and you will very likely cross paths again in your professional careers.”

That observation certainly resonates with first place winner Feeney, who says, “Some of the friends I made here I’ll keep forever.”

The Broadcom MASTERS competition is cosponsored by Society for Science & the Public, publisher of Science News for Kids.

People as far back as the Greek philosopher Democritus believed that things were built up from irreducible pieces. Isaac Newton himself thought that light was not a wave, but rather a collection of tiny “corpuscules.” Physicists have only recently acquired tools with sufficient resolution to see nature’s inherent graininess.

Here’s a quick tour of the quantum underbelly of the things around us.

Matter

If you split a banana, and then split it again, and again, and again… you eventually get down to cells, molecules, atoms. Each atom has a nucleus of protons and neutrons, with tiny electrons buzzing around. Both protons and neutrons contain three quarks.

But the dissection stops there: electrons and quarks are the smallest pieces of ordinary matter.

How small are they? The electron is sometimes said be a few femtometers across (about a trillionth of a hair’s width), but this is misleading. Electrons and quarks are more like puffy clouds than rigid balls.

This puffiness is the result of unavoidable quantum uncertainty: You can’t precisely know a particle’s motion and position at the same time. If you try to hold a quark still, you would have almost no idea where it is.

Such slipperiness makes exact size measurements meaningless.

Light

If we turn our scalpel on light, we find that its seemingly continuous glow is actually composed of little bundles of energy, called photons. Don’t bother squinting your eyes to see them, though: a 100 Watt bulb emits a billion trillion photons per second.

So was Newton right? Light is a particle, not a wave? The answer is yes and no.

Light acts like a wave when you do an experiment looking for a wave property (like scattering through a pinhole). It behaves like a particle if you test for a particle property (like colliding with electrons).

“You get what you ask for” is a common refrain in quantum physics.

Rotation

Particle properties can be “quantized” as well. Probably the weirdest example is particle rotation (what is called spin) which, by the way, is nothing like how a planet or a top moves.

First of all, particles have only one rotation speed—they can’t speed up or slow down.

And second, the axis of rotation depends on how you look at it. In an experiment, one detector might report a particle’s spin points North, while another detector might say East. And they’d both be right!

Gravity

The force of gravity has largely resisted this quantum tomfoolery. But some physicists believe that Newton’s apple fell from its tree thanks to gravitons—photon-like particles that carry the gravitational attraction.

Falling apples would not generate a lot of gravitons, but colliding black holes would. Detectors are currently looking for signals from these distant collisions, but it may be many years before any evidence for gravitons is found.

Vacuum

Even nothing acts strange at the smallest levels. The vacuum is presumably not really empty, but instead filled with “virtual” particles that constantly blink in and out of existence.

This virtual reality follows from a quantum rule that says probable events influence real outcomes. More specifically, it is possible (though highly unlikely) for particles and anti-particles to pop out of nowhere and then quickly annihilate. Nobody ever sees this happen, but the sum of all this quantum probability is a real energy.

Space and time

The above vacuum energy is not constant: it seethes and fizzles with bubbles the size of the Planck length. This foam warps the fabric of space-time, blurring the answers to when and where.

Essentially, the underlying geometry of the world is not smooth. Instead, there are “pixels” that cannot be further resolved. Particles do not move continuously, but instead make little quantum leaps from one pixel to the next.

Such quantized space-time, though not yet observed, is the endpoint of smallness, as well as the end of this tour.

Garibaldi, a rock climber in his spare time, did the math to disprove the theory, which involves a mysterious structure known as E8. The resulting paper, co-authored by physicist Jacques Distler of the University of Texas, will appear in an upcoming issue of Communications in Mathematical Physics.

In November of 2007, physicist Garret Lisi published an online paper entitled “An Exceptionally Simple Theory of Everything.” Lisi spent much of his time surfing in Hawaii, adding an alluring bit of color to the story surrounding the theory. Although his paper was not peer-reviewed, and Lisi himself told the Daily Telegraph that the theory was still in development and he gave a “low” likelihood to the prediction, the idea was widely reported in the media, under attention-grabbing headlines like “Surfer dude stuns physicists with theory of everything.”

Garibaldi was among the skeptics when the theory hit the news. So was Distler, a particle physicist, who wrote about problems he saw with Lisi’s idea on his blog. Distler’s posting inspired Garibaldi to think about the issue more, eventually leading to their collaboration.

Lisi’s paper centered on the elegant mathematical structure known as E8, which also appears in string theory. First identified in 1887, E8 has 248 dimensions and cannot be seen, or even drawn, in its complete form.

The enigmatic E8 is the largest and most complicated of the five exceptional Lie groups, and contains four subgroups that are related to the four fundamental forces of nature: the electromagnetic force; the strong force (which binds quarks); the weak force (which controls radioactive decay); and the gravitational force.

In a nutshell, Lisi proposed that E8 is the unifying force for all the forces of the universe.

“That would be great if it were true, because I love E8,” Garibaldi says. “But the problem is, it doesn’t work as he described it in his paper.”

As a leading expert on several of the exceptional Lie groups, Garibaldi felt an obligation to help set the record straight.

Using linear algebra and proving theorems to translate the physics into math, Garibaldi and Distler not only showed that the formulas proposed in Lisi’s paper do not work, they also demonstrated the flaws in a whole class of related theories.

“You can think of E8 as a room, and the four subgroups related to the four fundamental forces of nature as furniture, let’s say chairs,” Garibaldi explains. “It’s pretty easy to see that the room is big enough that you can put all four of the chairs inside it. The problem with ‘the theory of everything’ is that the way it arranges the chairs in the room makes them non-functional.”

He gives the example of one chair inverted and stacked atop another chair.

“I’m tired of answering questions about the ‘theory of everything,’” Garibaldi says. “I’m glad that I will now be able to point to a peer-reviewed scientific article that clearly rebuts this theory. I feel that there are so many great stories in science, there’s no reason to puff up something that doesn’t work.”

Researchers at the University of Illinois are helping shape the futures of children with visual disabilities by creating innovative teaching tools that are expected to help the children learn mathematics more easily — and perhaps multiply their career opportunities when they reach adulthood.

Nearly 5 million — or one in 20 — preschool-aged children and about 12.1 million children ages 6-17 have visual impairments, according to the Braille Institute.

Sheila Schneider, who is a senior and the first student who is legally blind to major in sculpture in the School of Art+Design within the College of Fine and Applied Arts at Illinois, is creating a series of small sculptures with mathematical equations imprinted on them in Braille that will be used to help children with visual impairments learn mathematics. The equations will be written in Nemeth Code, a form of Braille used for mathematical and scientific symbols.

“The sculptures are organic forms that are designed to be hand-held by children around the ages of 7-10,” said Deana McDonagh, a professor of industrial design and the lead investigator on the project. “They’re designed from the viewpoint of a younger child.”

“They’re very engaging, fun educational tools, and when the children run their hands over them, they’ll realize that there are Braille equations embedded within the forms,” McDonagh said. “We’re hoping that they’ll become mainstream educational tools.”

Traditionally, children with visual disabilities are taught to solve mathematical problems using abacuses, tools that may seem antiquated in today’s world and foster stigmatization, Schneider said.

“We’re trying to bring the education of visually impaired children more up to date, rather than relying on staid methods of doing things,” Schneider said. “We’re hoping to eliminate this idea that blind children have to learn math with an abacus because they can’t see to write on a piece of paper. We’re trying to eliminate the stigma and provide them with a method of engaging in and with math.

“We’re hoping that as they grow older, they’ll become more interested in careers in science, technology, engineering and mathematics fields.”

Schneider sculpted six models, each a few inches in diameter, from cubes of balsa foam. The models are being translated into three-dimensional computer images to finalize the shapes and position the equations before the sculptures are cast from bronze, a durable material that can withstand extensive handling and occasionally being dropped.

“Where you and I might place the Braille equations is of no consequence,” McDonagh said. “When children with visual impairments are handling the sculptures, and reading them with their fingertips, it’s got to make sense to them where we place the Braille in three-dimensional space.”

Once the sculptures have been cast, the next step will be to have children with visual impairments and their teachers use them in math instruction to assess the sculptures’ efficacy as teaching tools.

“The number of people with disabilities is on the increase, and our population and its needs are changing,” said McDonagh, whose research and teaching focuses on empathic product design, assistive technologies and disability issues.”

“We’re trying to use people’s different life experiences and respect that there are different ways of doing things,” McDonagh said. “It’s an opportunity to bridge the gulf between the lived experience and science, mathematics and technology through sculpture.”

The study, part historical journey but mostly mathematical proof, was conducted by Philip T. Gressman and Robert M. Strain of Penn’s Department of Mathematics. The solution of the Boltzmann equation problem was published in the Proceedings of the National Academy of Sciences. Solutions of this equation, beyond current computational capabilities, describe the location of gas molecules probabilistically and predict the likelihood that a molecule will reside at any particular location and have a particular momentum at any given time in the future.

During the late 1860s and 1870s, physicists James Clerk Maxwell and Ludwig Boltzmann developed this equation to predict how gaseous material distributes itself in space and how it responds to changes in things like temperature, pressure or velocity.

The equation maintains a significant place in history because it modeled gaseous behavior well, and the predictions it led to were backed up by experimentation. Despite its notable leap of faith — the assumption that gases are made of molecules, a theory yet to achieve public acceptance at the time — it was fully adopted. It provided important predictions, the most fundamental and intuitively natural of which was that gasses naturally settle to an equilibrium state when they are not subject to any sort of external influence. One of the most important physical insights of the equation is that even when a gas appears to be macroscopically at rest, there is a frenzy of molecular activity in the form of collisions. While these collisions cannot be observed, they account for gas temperature.

Gressman and Strain were intrigued by this mysterious equation that illustrated the behavior of the physical world, yet for which its discoverers could only find solutions for gasses in perfect equilibrium.

Using modern mathematical techniques from the fields of partial differential equations and harmonic analysis — many of which were developed during the last five to 50 years, and thus relatively new to mathematics — the Penn mathematicians proved the global existence of classical solutions and rapid time decay to equilibrium for the Boltzmann equation with long-range interactions. Global existence and rapid decay imply that the equation correctly predicts that the solutions will continue to fit the system’s behavior and not undergo any mathematical catastrophes such as a breakdown of the equation’s integrity caused by a minor change within the equation. Rapid decay to equilibrium means that the effect of an initial small disturbance in the gas is short-lived and quickly becomes unnoticeable.

“Even if one assumes that the equation has solutions, it is possible that the solutions lead to a catastrophe, like how it’s theoretically possible to balance a needle on its tip, but in practice even infinitesimal imperfections cause it to fall over,” Gressman said.

The study also provides a new understanding of the effects due to grazing collisions, when neighboring molecules just glance off one another rather than collide head on. These glancing collisions turn out to be dominant type of collision for the full Boltzmann equation with long-range interactions.

“We consider it remarkable that this equation, derived by Boltzmann and Maxwell in 1867 and 1872, grants a fundamental example where a range of geometric fractional derivatives occur in a physical model of the natural world,” Strain said. “The mathematical techniques needed to study such phenomena were only developed in the modern era.”

The study was funded by the National Science Foundation.