I developed a small program which allows visualization of the potentiometric surface of a confined aquifer subject to pumping using Processing. This particular example uses aquifer and pumping parameters from a Geo-Slope whitepaper.

The source code may be downloaded here. All values including aquifer, pumping, visualization, and numerical parameters may be varied to apply to a wide variety of situations. The exponential integral (or “well function”) is calculated using a numerical approximation accurate to at least 1 part in 10,000,000 .

Interestingly enough the points do not simply fall in from arbitrary directions like a gravity field, but display structure by instead swirling along a clear path up the z axis.

You can see fights clumped into UFC (top) and Pride (bottom) organizations, with a subset of fighters acting as ambassadors between both.

A brain teaser goes as follows: a farmer is returning from market, where he has bought a wolf, a goat, and a cabbage. On his way home he must cross a river by boat, but the boat is only large enough to carry the farmer and one additional item. The farmer realizes he must shuttle the items across one by one. He must be careful however, as the wolf cannot be left alone on the same side of the river as the goat (since the goat will be eaten), and the goat cannot be left alone on the same side of the river as the cabbage (since the goat will eat the cabbage).

How can the farmer arrange his trips to move the wolf, the goat, and the cabbage across the river while ensuring that no one eats the other while he’s away? The problem usually yields to an analysis by trial and error, where one of the possible solutions is found by iterating and checking the possible decisions of the farmer.

But is there a more rigorous approach that will allow us to easily find all possible solutions without having to resort to guessing and checking?

A Discrete State Space

Let’s create a three-dimensional vector that represents the state of the system. The components of this vector will be 0 or 1 depending on which side of the river the wolf, the goat, and the cabbage are. Let’s list off all possible combinations without worrying about whether something is going to get eaten – we’ll get to that later.

Now a giant list like this isn’t much help. We’ve listed off all possible states, but we can structure this in a more sensible manner which will make solving the problem much easier. Let’s allow the vectors to represent the corners of a cube, with the edges of the cube representing trips across the river. Movement along the x axis represents the wolf moving, movement along the y axis represents the goat moving, and movement along the z axis represents the cabbage moving.

Alright, that seems a bit better. What we need to do now is find an allowable path along the edges of the cube from (0,0,0) to (1,1,1), and this will represent the solution to our puzzle. First we need to remove the edges where something gets eaten.

Our allowable state space now looks like this.

The problem has simplified itself drastically. We want to go from (0,0,0) to (1,1,1) by travelling along the black (allowable) edges of this cube. We can see that if we ignore solutions where the farmer loops pointlessly, there are two allowable solutions to this puzzle.

Move goat to other side. Move cabbage to other side. Move goat back. Move wolf to other side. Move goat to other side.	Move goat to other side. Move wolf to other side. Move goat back. Move cabbage to other side. Move goat to other side.

This is a beautiful example of the simple structures that underly many of these classic riddles.

Alright, 30 seconds to think, don’t panic… the first few second sound like some random trumpets, but that drum beat in the middle – you know that beat! You’ve heard it everywhere, hundreds of times. That “dum-dum-tish” break has driven itself into your brain, but you’ll be damned if you can remember where it’s originally from.

	Is it “Straight Outta Compton” by NWA?
	You can definitely hear part of it in the Powerpuff Girls theme song.
	It sounds like it’s in the beat of Slipknot’s “Eyeless“.

But it’s originally from none of those. Not David Bowie’s “Little Wonder“, not Oasis’ “D’You Know What I Mean“, not Maestro Fresh Wes’ “Bring it On“, not Orbital’s “Satan“, nor Nas’ “Hip Hop is Dead” – but instead the song “Amen Brother” from funk and soul outfit The Winstons recorded in 1969.

Hip Hop and Sampling

The song “Amen Brother” was initially recorded in 1969, but it took until the late 1980s and early 1990s for it to be begin to be revived as an integral part of pop culture. This was the time when samplers, machines which allowed short bits of music to be recorded and played back at will, finally became affordable to the hip hop artists of the streets. Short bit of drum beats that could be stored in a sampler were called “break beats”, or simply “breaks”. No one is certain who was the first to sample the Amen Break, but its use became ubiquitous in early nineties hip hop. Eventually the beat became overplayed, and the Amen Break seemed to be a flash in the plan, something brought up for nostalgic value if anything on new tracks.

Jumping the Pond

But as “Straight out of Compton” was selling millions in the US, the rave scene was exploding in the UK. This was a scene with little money, little social support, and was a subculture by any definition. But it was growing rapidly, and it demanded new music. The Amen Break was adopted as a foreign son, and the very basis for an entire genre and hundreds of songs. The break was sliced up into tiny pieces, each high hat, each snare, each bass drum hit cut into a tiny piece of audio. These pieces could be saved in a sampler, and played back in any permutation or combination. At first the variations were homages, but quickly the variation and volume spread. A sampler was cheap, the breaks were freely passed along, and flimsy acetate records of your new track could be written in the morning and played at the rave in the evening. This organic creativity caught the attention of the art scene, and effectively undanceable constructions were born, a fusion of the fundamentalism of the Amen Break homage and the polymeter and highbrow musical structure of the new creators who now went to art school. A prime example of this new wave was Tom Jenkinson, known as Squarepusher, who created multiple albums worth of songs all based on chopping and mixing the Amen Break.

The Rewards of Sampling

But what of the Winstons, the creators of the oft-sampled beat now so widespead that Fortune 500 companies use it in their ads? Did they blow the royalties on the fleeting rewards of fame, or have they hidden themselves and their fortune away? The staggering fact is that despite a recent Supreme Court ruling that even three notes can be considered a sample and subject to royalties, the Winstons haven’t received a single cent. Instead of property, the Amen Break now appears to be a part of the popular collective unconscious, ever-present and unownable.

For more detail, check out this great video by Nate Harrison from 2004.

The fact that we’ve never seen any evidence of its presence is a big deal. The Standard Model is a shining jewel of modern physics, a mathematical model describing the most basic facets of the world using a symmetry group. The predictions of this model have been confirmed so many times and in so many different ways that it’s almost become more exciting to think of what it would mean if the theory were broken by some strange event than to rejoice at yet another correct prediction.

So this is why the missing Higgs boson fascinates so many. But why is it missing at all? The answer comes from the Standard model itself and its mathematical foundations. Like the sides of a many-faceted jewel, a symmetry group has many parts, all reflecting some basic property of an underlying structure. Every single observation so far indicates a jewel of a certain shape, and we’ve seen every face except for one. There seems to be no other possible structure that would fit the observations and create a complete crystal to speak, so we’re left inevitably with the conclusion that one face remains in the dark.

Broken Silence

But now something very interesting has happened. Evidence of the Higgs boson may have been found! Not at the new and fancy Large Hadron Collider, but the good old Tevatron, home of Fermilab. Apparently a rather prominent physicist passed some rumours going around the physics world to a blogger.

On a completely different issue, I’ve heard that there’s a rumor going around Aspen that the Tevatron will be announcing discovery of gluon + b → b + Higgs, which would then require large tan(beta), which would fit the MSSM. I guess we’ll find out in a couple of weeks.

This is big news – the observations indicate a “light” Higgs boson, which is why the older Tevatron was able to find it when everyone thought the higher power Large Hadron Collider would be required. What does a light Higgs boson mean? Something very inspiring – that particle physics isn’t quite done figuring out the world quite yet.

…a light Higgs boson pretty much proves that there has to be new physics beyond the Standard Model well below the Planck scale. The new particles should be bosons and the only natural reasons why the Higgs, or the new bosons, should stay light is supersymmetry.

The best fits based on this assumption imply that the squarks and slepton masses – and more generally, other superpartner masses – should be close to 500 GeV or so and they should be observable by the LHC, possibly by the end of 2011.

But what does Fermilab, the apparent source of this grand discovery have to say about it?

I find it interesting that there is not an explicit denial, but a statement that these rumblings in the physics community are “just rumours”. Rumours can’t be published in scientific journals – so I suppose we’ll have to wait and see just what this all means.

Live in STEREO

One of the largest solar flares in recent history was captured last week by STEREO, a pair of satellites staggered along Earth’s orbit to obtain a constant clear view. The flare was about half the width of the sun, or 800,000 km at its largest. Here’s another view from the Solar Dynamics Observatory.

Brother Sharp

A homeless man with piercing looks and an oddly consistent sense of fashion was dubbed “The Ultimate Gorgeous #1 Passerby Handsome Guy” by Chinese bloggers, or “Brother Sharp” when photos taken of him by a passerby appeared online. This led to a “人肉搜索 (Rénròu Sōusuǒ)”, or “human flesh search” as hundreds of people combed the streets to find him and his story. Unfortunately, it seems that Brother Sharp has some big issues and won’t be designing couture anytime soon. A local blogger spoke:

“Long ago in 2008 I encountered him. Most people who see him will avoid him, treating him as a beggar and the link, but actually this is not accurate. 乞丐 [qǐgài "beggar"] in our country’s ancient words first appeared as a monosyllabic word. The meaning of 乞 [qǐ] in the golden texts was “to beg”. But he does not beg, nor does he know how to beg, because he has psychological problems (in Ningbo they call it “great fog sickness”). They do not have an identity, they do not have family, they’ve even forgotten who they are. They are a group of people abandoned by society, and their final outcome is to die without anyone inquiring about them. They wander in the space between humans and animals. Help them a bit and they become humans, ignore them and they are animals.

He once said this to me: “Find a girl to love me.”

Bloops and Bleeps

The VENTS group has a collection of six unknown noises captured by undersea microphone arrays, including the infamous “Bloop” signal.

The “Bloop” signal was detected repeatedly by the Equatorial Pacific Ocean autonomous hydrophone array, which uses U.S. Navy equipment originally designed to detect Soviet submarines. The signal was traced to somewhere around 50° S 100° W, a remote point in the south Pacific Ocean west of the southern tip of South America.

The noise rises rapidly in frequency over about one minute and was of sufficient amplitude to be heard on multiple sensors, at a range of over 5,000 km. The system ruled out any known man-made origin such as a submarine or bomb, or familiar geological sounds such as volcanoes or earthquakes. While the audio profile of the bloop does resemble that of a living creature, the system identified it as unknown because it was far too loud for that to have been the case: it was several times louder than the loudest known biological sound. If it was biological, it would have to be produced by an animal far larger than any currently known to science.

This video shows 5000 fish swimming while the weightings of the three behavioural rules vary using sinusoidal functions. I love the “borders” created as large fish schools collide, and fish attempt to escape along the plane of intersection.

Triumph of the Golden Rule was also linked to as recommended reading for MIT course 6.033 Computer Systems Engineering – one of the best compliments I’ve received. Thanks Evan!

While the process of creation may not be quite as elegant as the cellular automata of the Conidae snail, it certainly is not lacking in effort. If you have any information on where this photo is from please leave a comment!