The Coalition of the Stubborn:
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Prime Number Spiral

August 25, 2007

This is a neat complex visualization for how numbers relate.
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Number spirals are very simple. To make one, we just write the non-negative integers on a ribbon and roll it up with zero at the center.

The trick is to arrange the spiral so all the perfect squares (1, 4, 9, 16, etc.) line up in a row on the right side:

Number wheel, figure 1

Numbers on the marked curve are of the form
the famous prime-generating formula discovered by Euler in 1772.

If we continue winding for a while and zoom out a bit, the result looks like this:

Number wheel, figure 1

If we zoom out even further and remove everything except the dots that indicate the locations of integers, we get the next illustration. It shows 2026 dots:

Number wheel, figure 2

Let’s try making the primes darker than the non-primes:

Number wheel, figure 2

The primes seem to cluster along certain curves. Let’s zoom out even further to get a better look. The following number spiral shows all the primes that occur within the first 46,656 non-negative integers. (For clarity, non-primes have been left out.)

Number wheel, figure 2
It looks as though primes tend to concentrate in certain curves
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These are so awesome, I wish I could have been there to take the pictures myself!
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Hubble telescope’s top ten greatest space photographs

The Sombrero Galaxy – 28 million light years from Earth

The Ant Nebula, a cloud of dust and gas whose technical name is Mz3, resembles

In third place is Nebula NGC 2392, called Eskimo because it looks like a face
face surrounded by a furry hood.

At four is the Cat’s Eye Nebula

The Hourglass Nebula, 8,000 light years away

In sixth place is the Cone Nebula. The part pictured here is 2.5 light years in
years in length (the equivalent of 23 million return trips to the Moon)

The Perfect Storm, a small region in the Swan Nebula, 5,500 light years away

Starry Night, so named because it reminded astronomers of the Van Gogh painting.

The glowering eyes from 114 million light years away are the swirling cores of two merging galaxies called NGC 2207

The Trifid Nebula. A ’stellar nursery’, 9,000 light years from here, it is where new stars are being born.
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It helps in other ways. The worst case is if Jupiter were the size of Saturn. It would basically be big enough to increase the bad effects but not quite big enough to contribute the good.
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Earth experienced an especially heavy bombardment of asteroids and comets early in the solar system's history (Illustration: Julian Baum)
Earth experienced an especially heavy bombardment of asteroids and comets early in the solar system’s history

Contrary to prevailing wisdom, Jupiter does not protect Earth from comet strikes. In fact, Earth would suffer fewer impacts without the influence of Jupiter’s gravity, a new study says. It could have implications for determining which solar systems are most hospitable to life.

A 1994 study showed that replacing Jupiter with a much smaller planet like Uranus or Neptune would lead to 1000 times as many long-period comets hitting Earth. This led to speculation that complex life would have a hard time developing in solar systems without a Jupiter-like planet because of more intense bombardment by comets.

But a new study by Jonathan Horner and Barrie Jones of Open University in Milton Keynes, UK, shows that if there were no planet at all in Jupiter’s orbit, Earth would actually be safer from impacts.

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Can you smell the teen spirit?

A tip o’the hat to Newser for pointing to me to this article.

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<img src=”; alt=”Spencer Elden on the cover of Nirvana’s Nevermind, 1991″ />

Some of the most vivid album covers in history featured young kids — where are they now? MTV News tracked down some of our favorites to see what they’ve been up to since finding their ways into our CD collections — and to find out how being on some of rock’s most iconic album covers has affected their lives.

Spencer Elden
Famous For: His appearance on the cover of Nirvana’s breakthrough 1991 LP, Nevermind

When Spencer Elden’s parents agreed to let their friend, photographer Kirk Weddle, snap a whole roll of film of their infant son swimming underwater in a crystal-clear swimming pool, they couldn’t have known that, eventually, more than 9 million people would own a picture of their naked son.

“Yeah, it’s kind of creepy that that many people have seen me naked,” Elden said. “I feel like I’m the world’s biggest porn star.”

Spencer hasn’t seen any royalties from the record’s sales; his parents were paid just $200
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I get that sensation when I fall asleep on my arm and my hand twitches too close to my face. One night, I thought a rat was attacking me.
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By deliberately scrambling a person’s visual and tactile senses, it is now possible to give them an “out-of-body” experience.

Two procedures – which are the first to imitate an out-of-body experience artificially – use cameras to fool people into thinking they are standing or sitting somewhere else in a room. They provide the strongest proof yet that people only imagine floating out of their bodies during surgery or near-death experiences.

To trick his subjects, Ehrsson gave had them wear a head-mounted display that showed them footage of themselves filmed from behind, while preventing them from seeing anything else.

He says the work is important because it de-stigmatises reports of out-of-body experiences by people who are on drugs, or ill with conditions such as migraine or epilepsy. “They don’t have to be mad to experience these things,” he says.

Both researchers say their experiments reinforce the idea that the “self” is closely tied to a “within-body” position
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Peyton is all about the details.
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Peyton Manning

Manning demonstrates the proper form to use while holding the clipboard with one hand and using the headset during third-quarter second-and-long situations.

Indianapolis Colts quarterback Peyton Manning interrupted an intrasquad scrimmage Tuesday for approximately 45 minutes in order to show backup quarterback Jim Sorgi how to properly hold his clipboard.
“He’s got to learn consistency if he’s going to be the backup on this team, and that starts with the little things, like holding the clipboard with two hands,” Manning told reporters following the practice.
Manning claimed to have mentioned several previous clipboard-mishandling incidents to Sorgi prior to the on-field confrontation, including times when Sorgi held only the bottom-left corner of the clipboard “as if he didn’t care if he dropped it”; when he caught Sorgi gripping the clipboard with two hands, but loosely and “as if he was just going through the motions”
“We’re only as strong as our weakest link,” Manning added
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