Well, today is the day. A week ago, Urlesque blog dared the Interweb to ban posts about cats.

Well, that ain't right - so us Neatorama folks decided to stage a counter protest. To restore the cosmic balance caused by the lack of posts about cats today, we will post about cats, cats, and more cats!

Here are a few from the archives of the blog to kick start the whole thing:

The Original Keyboard Cats - $9.95

Neatorama's counter protest to A Day Without Cats deserve its own commemorative T-shirt, and what better design than this: from 1650, here's the Katzenklavier, a crazy musical instrument designed by Athanasius Kircher, a 17th century German Jesuit scholar:

The piano was designed to raise the spirits of an Italian prince who was too stressed out. The musician would select cats whose voices were at different pitches then arrange them in the pens accordingly. The piano delivered sharp pokes into the tails of the cats. (Source)

Link to T-Shirt (also available in sweatshirts & hoodies) | More Funny T-Shirts

Previously on Neatorama : Cat Piano (2006)

David Israel of mental_floss blog likes to ponder some of life's, shall we say weightier questions. Like, do fire stations ever catch on fire?

Apparently so:

More recently, Pennsylvania had a lulu of its own. On July 7th, the Strattanville Volunteer Fire Department was alerted to a roof fire at its own station. The cause? Arson! When the two guys who started the fire were caught and brought into the police station, one of them said he lit his boxer shorts on fire and then threw them onto the roof of the fire station, adding that he “thought it would be funny” if the fire station caught fire.

Of course, there’s nothing funny about any of these fires, but it does make you think.

A fire station catching on fire? What could be more ironic than that? Perhaps a police station getting robbed ... Link

It's like a modern day version of Captain Ahab's quest for the white whale Moby Dick. But ickier. A whole lot ickier and much more intriguing.

Sam Miller, BBC's former South Asia correspondent, has been obsessed with finding a man "whose dexterity and gall [he] admires beyond reason," ... the New Delhi Poo Squirter:

I was in Connaught Place, in the heart of New Delhi, and as I emerged from an underpass a shoe-shine man came up to me, and whispered into my ear.

He then pointed at my right shoe on which sat, to my amazement, a small worm of brownish goo. He offered to wipe it off, but I knew that something was, well, afoot, and cleaned my shoe with a few leaves.

Some months later it happened again and I had a minor altercation with the shoe-shine man. Then one day, I decided I would take a photograph of the person who squirted my shoe. But I was daydreaming as I wandered through the underpass and was squirted again.

Link - via Cabinet of Wonders

Photo: Cho Woong

I've always been impressed with some people's ability to collect things - stamps, soda cans, comic books, what have you. My amazement over Cho Woong's extensive collection of Star Wars figures is compounded by his ability to keep everything ... so organized and neat! I betcha there's a good amount of OCD (I'm kidding!) involved in this: Link [in Korean] - via Cribcandy

Al Fischer, an 75-year-old New York man has reached a very commendable milestone: he has donated 40 gallons of blood over 58 years!

The print shop operator from Massapequa, affectionately known as Albee, has been donating blood every year since 1951, when Harry S. Truman was in the White House - 11 presidents ago.

So far, Fischer has given 319 pints of blood and he will do it again Tuesday in Woodbury, bringing his lifetime donation to a total of 40 gallons.

"I'm too cheap to give money, so I give blood," Fischer, 75, said jokingly.

Fischer is estimated to have helped almost 1,000 people who needed blood transfusion. Newsday has the story: Link (Photo: Howard Schnapp)

This has got to be one of the most poignant things I've ever read. When 7-year-old Asa Hill died after a car accident, his parents honored the young boy's lifelong wish that they get married. And married they did, right after their child's funeral:

The Rev. Joel Miller of The Unitarian Universalist Church of Elmwood, where the service was held, was unsure at first when the idea of a wedding was proposed by the couple and their family.

"I asked twice, 'We're doing a wedding?' This was new for me. I never did a funeral service and a wedding ceremony at the same time, and normally wouldn't, but they have known each other since they were teens," Miller said. "And they had been providing for Asa, and they made a home together for all of Asa's life. ... It was clear they were following through on something they had been talking about for some time."

Hill and Ghirmatzion have been best friends since they were 15 and have been together for almost half of their lives. After Asa was born, marriage had always been something that they considered but, according to Hill, both felt that a wedding was "superficial and not necessary."

Asa, however, was insistent that they make their union official. "Asa really wanted us to do it, and every time he would ask us
we would say, 'Yes, we'll get married,' " said Hill. But the couple never did get around to figuring out the logistics for a ceremony.

While holding his lifeless son in his arms at the hospital, Hill was moved to finally officially propose to his lifelong partner. "Rahwa was overwhelmed at that moment and just looked at me. When the family sat down to plan the funeral service, she said 'Let's get married.' And everyone broke down at the table," he said.

Jean Shin of CNN has the moving story: Link

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We've featured a number of light graffiti or light painting before on Neatorama, but Jan Wöllert and Jörg Miedza of Light Art Performance Photography took the concept to a whole 'nother level.

Behold their spectacular artwork here: Link

Out of a job? If you live in the Great State of California, you're in good company: two out of five working-age Californians do not have a job!

“The current recession stands apart from prior downturns for both the depth and breadth of destruction in the job market,” the report says. “California has lost more jobs at a faster rate in the past two years than during any prior recession for which data are available, and employment has fallen in nearly every major sector of the economy.”

Because of the decline in the number of jobs coupled with growth in the labor force, the report finds that the percentage of working-age Californians who hold jobs has fallen to its lowest level in 32 years. Citing U.S. Bureau of Labor statistics, the report says just 57.5 percent of California adults are working.

The last time the percentage was that low was in 1977, a time when many women voluntarily chose not to work outside their homes. The percentage of employed adults peaked in 1989 at 64.9 percent.

Timm Herdt of Ventura County Star has the grim news: http://www.venturacountystar.com/news/2009/sep/06/jobless-rate-4th-highest-in-us/ | California Budget Project Press Release [PDF]

Stop and think about this for a second: how does a zooplankton eat in such a vast ocean? Turns out, it's not a trivial task: copepods, a type of zooplankton, filter a volume of water approximately 1 million times their own body volume to survive every day ... and at their scale, water has the consistency of syrup.

Scientists discovered a particularly interesting "ambush feeding" technique dubbed the Lucky Luke effect:

“So far, we know of four ways in which zooplankters tackle the engineering feat of finding food in water which appears as thick as syrup. Our contribution has been to describe the mechanism at work for the last of these: How some copepods perform spectacularly precise and rapid surprise attacks on their single-cell prey after first having registered the prey by means of hydrodynamic signals,” explains Professor Thomas Kiørboe, DTU Aqua.

The solution for the ambush-feeding copepods builds on what Thomas Kiørboe calls the Lucky Luke effect:

“Our recordings show that the sub-mm copepods accelerate to a speed of 100 mm per second in a few milliseconds, while at the same time rotating perhaps 180 degrees. Like Lucky Luke who is faster than his shadow, the copepods jump forward so rapidly and with such precision that they, so to speak, shake the viscous boundary layer off, in that way getting close enough to their prey to capture it with their feeding limbs.”

The viscous boundary layer is the layer of water which the copepods pull with them when moving their bodies through the syrupy water. The larger the animals are and the faster they swim, the thinner it seems.

Link

Oh, Snap! Mousetrap Cheese Board and Slicer

Somebody finally built a "cheddar" mousetrap! Here's the perfect "bait" to entice people to come to your next party: a giant 9" x 5" beechwood cheeseboard with a stainless steel cheese slicer shaped like a giant mousetrap. Available for $17.95 at the Neatorama Shop: http://shop.neatorama.com/product-info.php?oh-snap-cheese-board-slicer-mousetrap-pid481.html

Stony Brook University primatologist Diane Doran-Sheehy discovered something intriguing about the sneaky mating behavior of female gorillas that may explain human monogamy: how female gorillas use strategic sex to her advantage!

Female gorillas use sex as a tactic to thwart their rivals, new research suggests. Pregnant apes court their silverback male to stop other females conceiving.

"It seems to us that mating is another tactic that females use to compete with each other – in this case to gain favour with another male," says Diane Doran-Sheehy, a primatologist at Stony Brook University in New York.

Her team chronicled the sex lives of five female western lowland gorillas and one silverback almost every day for more than three years. "We wondered if, basically, [pregnant] females can mimic [ovulating] females and dupe the male into mating with them and distract him from what those other girls are doing," Doran-Sheehy says.

This kind of competitive behaviour may even help explain how humans evolved into a mostly monogamous species, she says.

Ewen Callaway of New Scientists has more: Link

Previously on Neatorama: 30 Strangest Animal Mating Habits

I love math (though it's debatable whether math loves me back, I suspect not) so it's a pleasure to read Cliff Pickover's newest creation, The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics.

Don't let the title fool you - The Math Book is a thoroughly enjoyable "walk" through the history of mathematics with each milestone narrated by Pickover in a short and sweet fashion (and surprisingly, with very little equations) that even non-mathemagicians like myself can enjoy. If you've ever heard the terms Bessel functions, Transcendental numbers, and Riemann hypothesis, and want to know more, then this is the book for you.

Below is an excerpt from the book (selecting which ones to show was a hard thing to do - there were just so many interesting articles!):

Cicada-Generated Prime Numbers

Cicadas are winged insects that evolved around 1.8 million years ago during the Pleistocene epoch, when glaciers advanced and retreated across North America. Cicadas of the genus Magicicada spend most of their lives below the ground, feeding on the juices of plant roots, and then emerge, mate, and die quickly. These creatures display a startling behavior: Their emergence is synchronized with periods of years that are usually the prime numbers 13 and 17. (A prime number is an integer such as 11, 13, and 17 that has only two integer divisors: 1 and itself.) During the spring of their 13th or 17th year, these periodical cicadas construct an exit tunnel. Sometimes more than 1.5 million individuals emerge in a single acre; this abundance of bodies may have survival value as they overwhelm predators such as birds that cannot possibly eat them all at once. (Photo: Joelmills [Wikipedia])

Some researchers have speculated that the evolution of prime-number life cycles occurred so that the creatures increased their chances of evading shorter-lived predators and parasites. For example, if these cicadas had 12-year life cycles, all predators with life cycles of 2, 3, 4, or 6 years might more easily find the insects. Mario Markus of the Max Planck Institute for Molecular Physiology in Dortmund, Germany, and his coworkers discovered that these kinds of prime-number cycles arise naturally from evolutionary mathematical models of interactions between predator and prey. In order to experiment, they first assigned random life-cycle durations to their computer-simulated populations. After some time, a sequence of mutations always locked the synthetic cicadas into a stable prime-number cycle.

Of course, this research is still in its infancy and many questions remain. What is special about 13 and 17? What predators or parasites have actually existed to drive the cicadas to these periods? Also, a mystery remain as to why, of the 1,500 cicada species worldwide, only a small number of the genus Magicicada are known to be periodical.

Borromean Rings

(L) Borromean Rings; (M) Valknut, or three interlocked triangles, on the Stora Hammar Stone; (R) Molecular Borromean Rings by J. Fraser SToddart

Peter Guthrie Tait (1831 - 1901) - A simple yet intriguing set of interlocking objects of interest to mathematicians and chemists is formed by Borromean rings - three mutually interlocked rings named after the Italian Renaissance family who used them on its coat of arms in the fifteenth century. (Image: Theon [Wikipedia])

Notice that Borromean rings have no two rings that are linked, so if we cut any one of the rings, all three rings come apart. Some historians speculate that the ancient ring configurations once represented the three families of Visconti, Sforza, and Borromeo, who formed a tenuous union through intermarriages. The rings also appear in 1467 in the Church of San Pancrazio in Florence. Even older, triangular versions were used by the Vikings, one famous example of which was found on a bedpost of a prominent woman who died in 834.

The rings appear in mathematical context in the 1876 paper on knots by Scottish mathematical physicist Peter Tait. Because two choices (over or under) are possible for each ring crossing, 2⁶ = 64 possible interlaced patterns exist. If we take symmetry into account, only 10 of these patterns are geometrically distinct.

Mathematicians now know that we cannot actually construct a true set of Borromean rings with flat circles, and in fact, you can see this for yourself if you try to create the interlocked rings out of wire, which requires some deformation or kinks in the wires. In 1987, Michael Freedman and Richard Skora proved the theorem stating that Borromean rings are impossible to construct with flat circles.

In 2004, UCLA chemists created a molecular Borromean ring compound that was 2.5 nanometers across and that included six metal ions. Researchers are currently contemplating ways in which they may use molecular Borromean rings in such diverse fields as spintronics (a technology that exploits electron spin and charge) and medical imaging.

Golden Ratio

Fra Luca Bartolomeo de Pacioli (1445 - 1517) - In 1509, Italian mathematician Luca Pacioli, a close friend of Leonardo da Vinci, published Divina Proportione, a treatise on a number that is now widely known as the "Golden Ratio." This ratio, symbolized by , appears with amazing frequency in mathematics and nature. We can understand the proportion most easily by dividing a line into two segments so that the ratio of the whole segment to the longest part is the same as the ratio of the longer part to the shorter part, or (a+b)/b = b/a = 1.61803 ...

If the lengths of the sides of a rectangle are in the golden ratio, then the rectangle is a "golden rectangle." It's possible to divide a golden rectangle into a square and a golden rectangle. Next, we can cut the smaller golden rectangle into a smaller square and golden rectangle. We may continue this process indefinitely, producing smaller and smaller golden rectangles.

If we draw a diagonal from the top right of the original rectangle to the bottom left, then from the bottom right of the baby (that is, the next smaller) golden rectangle to the top left, the intersection point shows the point to which all the baby golden rectangles converge. Moreover, the lengths of the diagonals are in golden ratio to each other. The point to which all the golden rectangles converge is sometimes called the "Eye of God."

The golden rectangle is the only rectangle from which a square can be cut so that the remaining rectangle will always be similar to the original rectangle. If we connect the vertices in the diagram, we approximate a logarithmic spiral that "envelops" the Eye of God. Logarithmic spirals are everywhere - seashells, animal horns, the cochlea of the ear - anywhere that nature needs to fill space economically and regularly. A spiral is strong and uses a minimum of materials. While expanding, it alters its size but never its shape.

Benford's Law

Simon Newcomb (1835 - 1909), Frank Benford (1883 - 1948) - Benford's Law, also called the first-digit law or leading-digit phenomenon, asserts that in various number lists, the digit 1 tends to occur in the leftmost position with probability of roughly 30 percent, much greater than the expected 11.1 percent that would result if each digit occurred with a 1 to 9 probability. Benford's law can be observed, for instance, in tables that list populations, death rates, stock prices, baseball statistics, and the area of rivers and lakes. Explanations for this phenomenon are very recent. (Photo from Mark J. Nigrini)

Benford's law is named after Dr. Frank Benford, a physicist at the General Electric Company who publicized his work in 1938, although it had been previously discovered by mathematician and astronomer Simon Newcomb in 1881. Pages of logarithms, with numbers starting with the numerals 1 are said to be dirtier and more worn by other pages, because the number 1 occurs as the first digit about 30 percent more often than any other. In numerous kinds of data, Benford determined that the probability of any number n from 1 through 0 being the first digit is log₁₀ (1 + 1/n). Even the Fibonacci sequence - 1, 1, 2, 3, 5, 8, 13 - follows Benford's law. Fibonacci numbers are far more likely to start with "1" than any other digit. It appears that Benford's law applies to any data that follows a "power law." For example, large lakes are rare, medium-size lakes are more common, and small lakes are even more common. Similarly, 11 Fibonacci numbers exist in the range 1 - 100, but only one in the next three ranges of 100 (101 - 200, 201- 300, 301- 400)

Benford's law has often been used to detect fraud. For example, accounting consultants can sometimes use the law to detect fraudulent tax returns in which the occurrence of digits does not follow what would be expected according to Benford's law.

Menger Sponge

Menger Sponge by Jeannine Mosely, at the Institute for Figuring. Photo: Ravi Apte

Karl Menger (1902 - 1985) - The Menger sponge is a fractal object with an infinite number of cavities - a nightmarish object for any dentist to contemplate. The object was first described by Austrian mathematician Karl Menger in 1926. To construct the sponge, we begin with a "mother cube" and subdivide it into 27 identical smaller cubes. Next, we remove the cube in the center and the six cubes that share faces with it. This leaves behind 20 cubes. We continue to repeat the process forever. The number of cubes increases by 20ⁿ, where n is the number of iterations performed on the mother cube. The second iteration gives us 400 cubes, and by the time we get to the sixth iteration, we have 64,000,000 cubes.

Each face of the Menger sponge is called a Sierpinski carpet. Fractal antennae based on the Sierpinski carpet are sometimes used as efficient receivers of electromagnetic signals. Both the carpets and the entire cube have fascinating geometrical properties. For example, the sponge has an infinite surface area while enclosing zero volume.

According to the Institute for Figuring, with each iteration, the Sierpinski carpet face "dissolves into a foam whose final structure has no area whatever yet possesses a perimeter that is infinitely long. Like the skeleton of a beast whose flesh has vanished, the concluding form is without substance - it occupies a planar surface, but no longer fills it." This porous remnant hovers between a line and a plane. Whereas a line is one-dimensional and a plane two-dimensional, the Sierpinski carpet has a "fractional" dimension of 1.89. The Menger sponge has a fractional dimension (technically referred to as the Hausdorff Dimension) between a plane and a solid, approximately 2.73, and it has been used to visualize certain models of a foam-like space-time. Dr. Jeannine Mosely has constructed a Menger sponge model from more than 65,000 business cards that weights about 150 pounds (70 kilograms).

The Quest for Lie Group E₈

E8 graph as a 2-dimensional projection, by Peter McMullen
(image by Claudio Rocchini [wikipedia])

Marius Sophus Lie (1842 - 1899), Wilhelm Karl Joseph Killing (1847 - 1923) - For more than a century, mathematicians have sought to understand a vast, 248-dimensional entity, known to them only as E₈. Finally, in 2007, an international team of mathematicians and computer scientists made use of a supercomputer to tame the intricate beast.

As background, consider the Mysterium Cosmographicum (The Sacred Mystery of the Cosmos) of Johannes Kepler (1571 - 1630), who was so enthralled with symmetry that he suggested the entire solar system and planetary orbits could be modeled by Platonic Solids, such as the cube and dodecahedron, nestled in each other forming layers as if in a gigantic crystalline onion. These kinds of Keplerian symmetries were limited in scope and number; however, symmetries that Kepler could have hardly imagined may indeed rule the universe.

In the late nineteenth century, the Norwegian mathematician Sophus Lie (pronounced "Lee") studied objects with smooth rotational symmetries, like the sphere or doughnut in our ordinary three-dimensional space. In three and higher dimensions, these kinds of symmetries are expressed by Lie groups. The German mathematician Wilhelm Killing suggested the existence of the E₈ group in 1887. Simpler Lie groups control the shape of electron orbital and symmetries of subatomic quarks. Larger groups, like E₈, may someday hold the key to a unified theory of physics and help scientist understand string theory and gravity.

Fokko du Cloux, a Dutch mathematician and computer scientist who was one of the E₈ team members, wrote the software for the supercomputer and pondered the ramifications of E₈ while he was dying of amyotrophic lateral sclerosis and breathing with a respirator. He died in November 2006, never living to see the end of the quest for E₈.

On January 8, 2007, a supercomputer computed the last entry in the table for E₈, which describes the symmetries of a 57-dimensional object that can be imagined as rotating in 248 ways without changing its appearance. The work is significant as an advance in mathematical knowledge and in the use of large-scale computing to solve profound mathematical problems.

Mathematical Universe Hypothesis

Max Tegmark (b. 1967) - In this book, we have encountered various geometries that have been thought to hold the keys to the universe. Johannes Kepler modeled the solar system with Platonic Solids such as the dodecahedron. Large Lie groups, like E₈, may someday help us create a unified theory of physics. Even Galileo in the seventeenth century suggested that "nature's great book is written in mathematical symbols." In the 1960s, physicist Eugene Wigner was impressed with the "unreasonable effectiveness of mathematics in the natural sciences." (Photo: MIT Physics Faculty website)

In 2007, Swedish-American cosmologist Max Tegmark published scientific and popular articles on the Mathematical Universe Hypothesis (MUH) that states that our physical reality is a mathematical structure and that our universe is not just described by mathematics - it is mathematics. Tegmark is a professor of physics at the Massachusetts Institute of Technology and scientific director of the Foundational Questions Institute. He notes that when we consider equations like 1 + 1 = 2, the notations for the numbers are relatively unimportant when compared to the relationship that are being described. He believes that "we don't invent mathematical structures - we discover them, and invent only the notation for describing them."

Tegmark's hypothesis implies that "we all live in a gigantic mathematical object - one that is more elaborate than a dodecahedron, and probably also more complex than objects with intimidating names like Calabi-Yau manifolds, tensor bundles, and Hilbert spaces, which appear in today's most advanced theories. Everything in our world is purely mathematical - including you." If this idea seems counterintuitive, this shouldn't be surprising, because many modern theories, like quantum theory and relativity, can defy intuition. As mathematician Ronald Graham once said, "Our brain have evolved to get us out of the rain, find where the berries are, and keep us from getting killed. Our brains did not evolve to help us grasp really large numbers or to look at things in a hundred thousand dimensions."

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Cliff Pickover is a prolific author, having published more than 40 books, translated into over a dozen languages, on topics ranging from science and mathematics to religion, art, history, computers and creativity, human intelligence, higher dimensions, time travel, and science fiction. He received his Ph.D. from Yale University's Department of Molecular Biophysics and Biochemistry, holds over 50 U.S. patents, and is an associate editor for several scientific journals. His computer graphics have appeared on the cover of numerous magazines, and his research has received considerable attention from media outlets ranging from CNN and WIRED to The New York Times. His website, pickover.com, receives millions of visits.

Links: The Math Book website | The Math Book on Amazon | Cliff Pickover's Reality Carnival

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Previously on Neatorama: 5 Scientific Laws and the Scientists Behind Them

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