For the love of fractals

Fractals are awesome.  Fractals are EVERYWHERE in your life - but what the eff IS a fractal?  I decided to consult the all-knowing Wikipedia and a fractal is defined as a

mathematical set that has a fractal dimension that usually exceeds its topological dimension[1] and may fall between the integers.[2] Fractals are typically self-similar patterns, where self-similar means they are "the same from near as from far"[3] Fractals may be exactly the same at every scale [or] they may be nearly the same at different scales.

That’s all fine and good, but what does that mean?  What does a fractal look like?  Why do fractals matter?

What does a fractal look like?

Imagine a tree.  Starting with the base of the trunk you have a thick stick coming out of the ground.  This ‘stick’ then splits into smaller branches - 

branches that look very very similar to the original ‘stick.’  From there, each smaller branch splits into even smaller, very similar branches and so forth to form the complete tree. This is a ‘natural’ fractal - one that appears in nature EVERYWHERE on earth.

You also have the example of river deltas and other flowing bodies for liquid, where each new path the liquid takes creates an nearly identical and to scale replica of the larger formation itself:

There are also fractals that can be simulated using computers and mathematical formulas, of which I have no understanding in even the most basic aspect.  The images they create, however are incredibly beautiful, with a strange almost ghostly implied symmetry as you change the scale (zoom in or out infinitely, theoretically).  The most famous, and iconic of these simulated fractals is the Mandelbrot Set, discovered and described by French-American mathematician, Benoit Mandelbrot (1924-2010).

Starting at the x1 magnification and increasing up to x2000, the patterns are self similar, the patterns are the same near or far!


Why do fractals matter?

While fractals were first described as early of the 17th Century, the first real practical use and description was provided by the previously mentioned Mandelbrot.  His usage?  Measuring the length of Great Britain’s coastline!  I know it seems like a piece of information we should have had for awhile, it was discussed in the 1967 paper by Mandelbrot titled “How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension.”  

The main issue with measuring the coast line is what had been known as the coastline paradox.  This paradox explains that as you measure a coastline, the total length of the coastline increases without limit as the too used to measure the distance get’s smaller.  In English:  if you measured a coastline with a yard stick and then a stand 12-inch ruler, the ruler would return a LARGER length of coastline than the yard stick.

By using smaller and smaller measuring devices, you are able to measure finer and finer number of natural curves in the coastline itself.

Using a yardstick may result in this type of measurement:

Using the ruler may (not to scale, of course) result in something more like this:

What the exploitation of fractals allowed was a calculation of the dimensionality of the curving coastline, to calculate the actual length.  Again, much of this goes over my head, but from what I understand a coastline can be measured using any number between (or including) 1 or 2.  The West Coast of Britain, as an example has a calculated dimension of 1.25 (and that's a jagged coast).  While I couldn’t find if the measurement was ever made, the wonder of fractals made it a possibility.

Further reading and sources:
http://en.wikipedia.org/wiki/Fractal

http://en.wikipedia.org/wiki/How_Long_Is_the_Coast_of_Britain%3F_Statistical_Self-Similarity_and_Fractional_Dimension

http://www.glyphs.com/art/fractals/what_is.html

Pretty Picture of fractals:
http://www.enchgallery.com/fractals/fracthumbs.htm

http://sprott.physics.wisc.edu/fractals.htm

Farewell, Lonesome George and the La Pinta giant tortoise subspecies

Lonesome George, the last known survivor of the La Pinta giant tortoise subspecies, has died.  His kind is no more.  Extinct.  We've lent hand to the annihilation of another type of living being - giant Galapagos tortoises were often used as a reliable food source on ships, due to their ability to live without food or water for up to a year. 

First, we wiped out the females, because they were easier to catch due to the mating habits.  Slowly but surely, we wiped them out by 1906. 

Then, we got lucky - 66 years after the last giant tortoise was spotted, George was discovered (possibly again) by an invertebrate expert studying snails.  He smartly snapped a photo, and shortly thereafter, Lonesome George became the most famous reptile in the world.  The exhaustive search to find him a mate ensued and ultimately failed.  We were unable to correct the mistakes of our forefathers.  

Will we keep making those mistakes?  Conservation isn't a fad, or political opinion: it's vital for the survival of the human species.  This blue world is all we have.  

Roger Waters presents The Wall, in Nashville - a Review

My wife and I had to park about half a mile from the venue (Bridgestone Arena) itself, since all of these close parking was either sold out or over $10.  The night was pleasant, in the high 80s (F) with low humidity (for Nashville) and a slight breeze from the Cumberland River.  Entering the place was simple enough - they don’t give a sh*t about regular digital cameras anymore, so it was basically a look over to see if we had a bomb strapped on.  I guess a rock show attended by a bunch of hippies - young and old - and performed by a pacifist wasn’t pegged as a ‘high security’ situation.

The obligatory flying pig

We decided to hit the merch table before finding our seats, and after about 20 minutes in line I was able to nab the last “Trust Us” camo tshirt in size large.  The selection of merch was honestly disappointing.  Roger’s ‘Dark Side’ tour had some fantastic and original shirts, like the one with Roger from the 70s, but The Wall merch mostly seemed rehashed shirt designs with the 2012 update and “Roger Waters” everywhere “Pink Floyd” had been.  Let’s be honest - who goes to Roger Waters for the merch?

Finally winding our way upstairs and grabbing a soda, we started the sojourn around the outer track of the building to get to our seats in section 333 (top tier in the VERY back of the arena).  As we rounded a ‘corner’ a well dressed gentleman stopped us and said he worked for the arena, and that they were trying to get rid of some lower-level tickets, much closer to the stage.  He then handed us two tickets to section 107, stage left.  

The mighty Wall!

The seats were ‘limited view,’ but we only missed the flower sex, and given the very nature of the live show The Wall, it wasn’t a big deal in the slightest.  Free seat upgrade.  

This is how close we were

Win.

The show did not start promptly at 8pm, despite the clear indication printed on the ticket - not that this was unexpected.  There was no opening act, no encore.  For nearly three hours, there was only The Wall.

As the lights dimmed the announcer warned us to turn the flash function in our cameras off - the flash of light would wash out the projections on the MASSIVE white ‘brick’ wall that served as both projector screen and visual centerpiece.  A lone spotlight appears on the stage, and the ending to the movie “Spartacus” begins playing over the speakers, as two officials carry the ‘Pink’ puppet on on the stage to say “I am Spartacus” before being dropped to the ground.
A lone trumpet plays the lonely melody from “Outside the Wall” in the darkness before the audience is caught off-guard by the sudden first chords of “In the Flesh?”  Balls of fire and spark shoot from the base of the The Wall portion of the stage followed by that old codger himself, strolling out all badass like.

We did our hammer salutes and mad screaming as he patrolled to each side of the stage, his enjoyment clear on his face.  He might be getting older but compared to when he first performed these shows in the early 80s, he is at the top of his game and loving every second of it.  All of the pyrotechnics were used in the first song of the evening, including an airplane that flew over our heads to crash behind the Wall in a fireball, and the rest of the show focussed on the gorgeous visuals Roger and Co. projected onto Mr. Screen and the Wall itself.  If there wasn’t action being projected on the bricks, then a stone-brick texture was projected, making the otherwise whitewashed wall far more realistic and menacing. 


“The Thin Ice” gave us our first taste of our ‘not David Gilmour’ of the evening, Mr. Robbie Wyckoff.  While I was expecting the worst after enduring the  awful job that Doyle Bramhall II did in the 2000 tour, “In the Flesh,” Wyckoff didn’t sound like a dying basset hound.  He was competent, if a bit unassuming - but this IS Roger’s show.  The ‘screen’ that as the Wall itself as well as Mr. Screen began to show us the name, birth and death of people killed in the name of some authority, starting with Roger’s father and including people like the Persian ‘angel,’ Neda Agha-Soltan.

The Schoolmaster

The trio of Another Brick 1, Happiest Days and Another Brick 2 were pretty damn true to the source material.  Dave Kilminster’s performance of Gilmour’s ABITW2 solo was spot-on.  Add in a little Snowy White goodness at the end and you have one worked up crowd.  For the children’s chorus, a group of Nashville’s school-aged kids got on stage and performed a simple rhythmic dance while singing and gesturing to the Schoolmaster puppet that had descended on our side of the stage.

Between “Another Brick in the Wall Part 2” and “Mother,” something of a new song was played.  The best way I can describe it is to call it “Another Folk in the Wall.”  It had the same hook as the other three “Brick” songs, but was acoustic and had a funkier rhythm.  It broke up the proceedings nicely, and helped to keep the audience on its toes.  From here, Roger broke with the 1980s script and talked with the audience a bit, mainly about Brazilian Jean Charles de Menezes who was shot eight times by London authorities, because they erroneously ‘suspected’ him of terrorism.

While the show has always had some anti-authoritarian themes, they were nothing like what was on display tonight.  Roger pulled no punches, and it felt damn good to see someone do this - be unapologetically bleeding heart.  No excuses: every rocket launched is a theft from someone that is in need (to terribly paraphrase Ike).

“Mother” was straightforward with two notable exceptions;  a black and white (not gray-scale, true black and white) projection of Roger performing the same song back in 1980 at Earls Court and after Roger sings “Mother should I trust the government?” three words appeared in bold red on the Wall in rhythm with the song: “NO FUCKING WAY.”  The synch of the projection with the performance was remarkable.  This is one polished show.

While one of my favorite songs on the album and sequences in the movie, “Goodbye Blue Skies” was a fantastic rendition - but something felt missing without the terror that the song invoked in the movie.  That said, the harmonies were crisp and the visuals (bombers dropping symbols like the dollar sign, the star of David, the cross, the logo for Shell gasoline and many others).

By the time “Empty Spaces/What Shall We Do Now” started, we could no longer see Mr. Screen at all, as it had become completely obstructed by the continual construction of the Wall itself.  We were treated, however, to the new ‘root’ animation to go with the flowers.  The roots writhed and pulsed as the music and flowers danced until the climax which saw the portion from the movie being projected on the Wall.   “What Shall We Do Now” was probably the second most ‘pumped’ song of the evening for me, since I hear it so rarely.  The only song that ‘rocked’ harder for my money was “Run Like Hell,” but more on that later.

I tried to get a nipple shot, but this was the best I could do, bell button and camel toe;)

T&A was the order of the day for “Young Lust,” as it should and there were many a pair of young breasts and smooth bellies projected across the Wall as the band rocked out and the stage crew slowly enclosed the band in their stage-tomb.  I can’t be sure, but I thought I may have caught Wyckoff doing some scat vocals ala’ Gilmour during the Young Lust solo (he was not playing guitar, however), but I can’t be certain.

For “One of my Turns” and “Don’t Leave Me Now,” Roger was in front of the Wall, while his band backed him up from behind the Wall.  He roamed the stage while singing the former and sat dejected for the latter.  As always, the projections on the Wall were incredible, but this is the slowest part of the show so nothing really stuck with me.

The beginning of Another Brick Part 3

“Another Brick in the Wall Part 3” took the projections to a level last seen on LOST when the ‘others’ are seen brainwashing people with a strange, jumbled movie.  It’s something you really just have to see for yourself.

“Last Few Bricks” was fairly uneventful, as the extra medley through the set so far gave the stagehands time to finish constructing all but on brick of the Wall.  Finally, we see Roger in a lone beam of light shining through the last crack in the Wall.  “Goodbye Cruel World.”  The last brick is placed and the Wall’s construction is complete.

The completed Wall during "Hey You"

After a pleasantly punctual intermission (25 minutes on the nose), the melancholy beauty of “Hey You” filled the arena.  The songs presentation was plain.  No fancy lights or fire and no projections aside from the static “stone-brick” texture.  There is also no visible band.  The entire band is performing, unseen, behind a thirty foot tall ‘brick’ wall.  The concept is so simple when you read it, but ‘seeing’ it in action is absolutely surreal.  No mistake about it, Roger’s “Wall” concert concept is completely brilliant.  The man makes you cheer to what is, for all intents and purposes, as singing brick wall.

"Is There Anybody Out There"

Two bricks were then removed stage left for “Is There Anybody Out There” to reveal two guitarists (Dave and Snowy, I believe) on nylon-strung classical guitars for the gorgeous tune.

"One of my Turns"

As the song ended, a drawbridge type panel began to lower itself from a section of the Wall on stage right.  The panel lowered until it was perpendicular to the Wall and had a tidy living room set-up - a chair, lamp and LCD TV.  His performance from his ‘living room’ is projected on the stage left side of the wall, in crisp color and detail.  The projection gave us an awesome look at just how animate Roger is these days - often miming lines like “all down the front of my favorite satin shirt.  The Pink Floyd song written in a night during The Wall recording sections still sounds like an original, intended piece and is all the more gorgeous for it.

The Wall projection for "One of my Turns"

"Comfortably Numb"

“Vera” and “Bring the Boys Back Home” were incredibly moving - the former featured video of families (especially children) welcoming home their parents from their tours of duty, often streaming tears.  The latter of the two displayed the entire Dwight Eisenhower quote I referenced above, juxtaposed with video and pictures of children in poor conditions, tastefully.

I won’t be very surprised if “Comfortably Numb” was on top of the audiences list of best performances, and for once, Roger pulled it off without Gilmour.  Dave’s solo was INCREDIBLY faithful and Wyckoff delivered quite well also, though nobody can sing the part quite like Gilmour does. Both were positioned at the TOP of the complete 30 foot wall, with spotlights shining from behind them, casting their shadows across the audience. 

Wyckoff's shadow

Roger was fantastic as well - and nobody can sing his portion of that song as well as he does.  A few bars into the second and final solo, Roger ‘pounds’ a spot on the Wall, which triggers a GORGEOUS shattering animation from the point of contact across the entire Wall.  The gray mass of brick and gloom exploded temporarily into a bright cascade of primary colors mimicking a sunset. 

The shattering

 As the solo nears its end, several trap doors on the stage in front of the Wall open and elevators appear carrying guitars, a drum set and a keyboard set-up, all for the “surrogate band” to use for the remainder of the show.  Unfortunately, I didn’t see any of the old-school masks.

A full, two verse version of “The Show Must Go On” brought us screaming back into the more militant “In the Flesh.”  Roger marched to the mic with his black leather trench coat and aviators and began the reprise full of gusto.  As a finale for the song, following “I’d have all of you shot,”

Roger, having all of us shot

Roger pulls a tommy-gun from his jacket and begins ‘shooting’ the audience.  While the ‘gun’ he was ‘shooting’ only had a blue LED light in the tip, on the Wall projection, his exact image was doing the same thing, only this time bullets and shell casings were flying about madly.  While the video of Roger was very well synched with the live act, it did appear to be pre-recorded and amazingly choreographed for the live experience.

“Are there any paranoids in the audience tonight?” Roger teases darkly from behind his sunglasses.  That’s how faithful this show was to the original run, in terms of musical direction.  Well done Mr. Gilmour.  “Run Like Hell” was a very energetic performance for the crowd - there were hands rhythm clapping and fists pumping.  As the song ends, Roger gets the crowd worked up by ‘thanking’ them quite loudly, sending us into another cheering frenzy.  As “Waiting for the Worms” began, the tension in the air was growing thick - that Wall had to come down soon.  

“Stop” sees the brief return of the ‘Pink’ puppet, as he is seen sitting atop the Wall before plummeting to the floor for climax of “The Trial.”  As the first orchestra begins this next to last song, the ‘Surrogate Band’ set up sink beneath the front stage again, and the animations from the movie are projected to go along with Roger’s lone performance. After being sure to sing “go on judge, shit on him,” Roger soon disappears from the stage and the loud speakers and audience begin deafeningly chanting “TEAR DOWN THE WALL!  TEAR DOWN THE WALL!”

Then, as if it were the Biblical Jerhico, the Wall began tumbling and crashing to the ground, falling just short of the front row (a yard from their feet, maybe).

As the ‘rubble’ cleared, the entire band (including Roger’s son, Harry and the incredible Jon Carin) appeared on stage, with Roger holding a trumpet and others holding various guitars, banjos and such.  The delicate “Outside the Wall” finally swooned us away after an amazing night of music.

The band took its bows and Roger gave us his deepest thanks, and the night was over. As we left the arena, I saw people in tears.  I understand that feeling: I was born WAY too late to have been able to see the original shows, so this was a big deal in terms of my musical consumption.  Since 1996 (when i discovered Floyd in HS) I had been dying to see The Wall live - it was so worth the wait!

Episodic Music: The Great Red Eye Part VI

The Great Pendulum

Track Available for Purchase Here!

The Great Pendulum was originally commissioned by the United Authority of the Earth, Luna and Europa in the year 2935 as a means to test 'scooping' gas out of the Terrible Titan Jupiter to fuel long term space voyages. Using the Jovian gravity to pull the pendulum down and out of it's grasp would save energy and ensure better monitoring capabilities from the Lagrangian pivot point set impossible far away - but physically tethered to the Pendulum itself.

By 2940, exploits in quantum gravity discoveries helped to lead, laterally, to the discovery of the dark energy drive - allowing enclosed vehicles to bypass the speed of light by riding the wave of expanding space, pulling and pushing them to their interstellar destinations at a mind bending pace. The Great Pendulum was now going to be a one-off, exploration mission. It didn't take long for the main Pendulum to be re-engineered from the 'ground' up to include one pilot. Man was going to visit Jupiter's Great Red Eye in person in 2953.

The main cockpit, officially called the Science Module, was set 100 meters from the front of the vessel, with layers of water shielding and a nuclear centrifuge (to power the G-Suppressor, which was designed to divert some of the g-forces away from the pilot) and 100 meters of precisely cut CarbonCompress to allow for clear, crisp view through the front and rear should any exterior cameras fail.

As the great lattice pressure cage encloses the Science Module, Cosmonaut Shem Aglig completes his third and final round of system checks before the countdown to release commences, and he becomes to second man to ever breach the Jovian atmosphere.

Episodic Music: The Great Red Eye Part V

Earthshine

Track Available for Purchase Here!

December 15, 2950 was officially declared Interplanetary Earthshine Day in remembrance of the first sight to inspire man to reach for the stars: the ever changing face of the moon.  Even when in it's finest crescent, the majestic surface cast in shadow is faintly set alight by the shine of the mother Earth herself.  This image emblazoned every spacecraft mankind built, and finally was placed upon the flag of the Interplanetary Alliance as a symbol of mankind's roots - and an inspiration to keep growing.