Previously: Playing a Note of a Certain Frequency

So now that we have a pitch, how do we know how long a sound will be?  One second of audio generated in Flash requires 44,100 pieces of sample data.  So if we’re writing 8192 samples each time we call our function, we would have to call our function at least six times.  However, if we call our function six times, we end up with 49,152 samples – which is more than one second of audio.  So we have a problem.

Some of you might be saying, well why don’t we call our function 6 times, but drop the number of samples we write each time to 7350 – that way we have the perfect number of samples to make 44,100.  Your thinking is correct for this example, but there is at least one problem with that scenario.  What if you want to produce a quarter-second sound?  A half-second sound would work just fine, we would call our function three times instead of six.  But it is impossible to call a function one and one half times.  So what can we do?

My suggestion is to keep the sample size at 8192 and clip the audio where you need it.  If we know one second is 44,100 samples, we also know 11,025 is a quarter second (44,100 / 4 = 11,025).  In audio, a sound with an amplitude or volume set at 0 is silent.  So to play a quarter-second sound I would call my function twice which will produce 16,384 samples.  I only want to play 11,025 samples of real audio though, so I’ll let the sine wave write the first 11,025 samples, then I’ll fill the rest of the sample data with 0s.  Those 0s will be represented as silence and I’ll get a note that is only a quarter second long.

For example, consider the code:

1. var mySoundLength:int = 11025;
2. var mySound:Sound = new Sound();
3. function sineWaveGenerator(event:SampleDataEvent):void {
4. var frequency:Number = 440;
5. for ( var c:int=0; c<8192; c++ ) {
6. if(c+event.position < mySoundLength) {
7. event.data.writeFloat( Math.sin( Number(c+event.position) * (frequency * 2 * Math.PI) / 44100) * 0.25 );
8. event.data.writeFloat( Math.sin( Number(c+event.position) * (frequency * 2 * Math.PI) / 44100) * 0.25 );
9. } else {
10. event.data.writeFloat(0);
11. event.data.writeFloat(0);
12. }
13. }
14. }
15. mySound.addEventListener(SampleDataEvent.SAMPLE_DATA,sineWaveGenerator);
16. mySound.play();

In line 1 we set the length of the sound we want to play.  In line 6 we’re checking to make sure our current position within our audio is less than our sound length.  If it is, we’re writing our audio as normal.  If we’re past the length of the note we want to play, write 0 volume to our SampleDataEvent.

Next up: Playing a Note Without the Hideous Popping or Clipping

Previously: Overview of Generative Audio in Flash CS4

To play a normal sine wave of a specific note (or frequency) is pretty straight forward, but it’s different from what Adobe would tell you. Building on Adobe’s version, take a look at this:

1. var mySound:Sound = new Sound();
2. function sineWaveGenerator(event:SampleDataEvent):void {
3. var frequency:Number = 440;
4. for ( var c:int=0; c<8192; c++ ) {
5. event.data.writeFloat( Math.sin( Number(c+event.position) * (frequency * 2 * Math.PI) / 44100) * 0.25 );
6. event.data.writeFloat( Math.sin( Number(c+event.position) * (frequency * 2 * Math.PI) / 44100) * 0.25 );
7. }
8. }
9. mySound.addEventListener(SampleDataEvent.SAMPLE_DATA,sineWaveGenerator);
10. mySound.play();

In line 3 we are now setting our frequency or the note we want to play. 440 hz is middle A. On lines 5 and 6 we are taking that frequency and multiplying it by 2 PI. We then take the result, multiply that by our current position in the sample then divide all of that by 44100 – which is our samples per second. The rest you should recognize from the previous example.

So to play any note, you would just change the frequency to what you’re looking for. Wikipedia has a good quick reference of piano key frequencies (http://en.wikipedia.org/wiki/Piano_key_frequencies). Middle C for instance, is 261.626 hz – so that’s what you would put in your frequency variable.

Next up: Playing a Note of a Certain Length

Adobe Flash CS4 (Flash player 10) introduced the ability to generate audio in real time.  The ability, however, is a little confusing and there has not been much good information released on the subject.  There are the basics like “this is how you produce a tone” or “this is how you link the tone to your mouse x/y position”, but not much has been written on how to produce actual notes, on key, with a given length -so I’m hoping to break that down a bit.

Audio generation in Flash currently centers on the SampleDataEvent.  If you want to play a sound generated dynamically, Adobe’s help suggests something like the following:

1. var mySound:Sound = new Sound();
2. function sineWaveGenerator(event:SampleDataEvent):void {
3.   for ( var c:int=0; c<8192; c++ ) {
4.     event.data.writeFloat(Math.sin((Number(c+event.position)/Math.PI/2))*0.25);
5.     event.data.writeFloat(Math.sin((Number(c+event.position)/Math.PI/2))*0.25);
6.   }
7. }
8. mySound.addEventListener(SampleDataEvent.SAMPLE_DATA,sineWaveGenerator);
9. mySound.play();

Line by line, here’s what’s going on:

1. Create a new sound object and store it in a variable of the data type Sound with the name mySound.

2. Create a function named sineWaveGenerator. The function will take one argument, the SampleDataEvent that will be stored in a variable named event.  The function will not return any values so we declare it’s return type as void.

3. Set up a for loop.  Initialize a variable named c of the type integer with the value of 0.  Each time we loop we’re going to make sure c is less than 8192 (which means we’ll loop a total of 8192 times since we’re starting at 0 and going up to 8191).  Each time we’re finished with our loop we need to increment c which will add 1 to whatever the value of c is at the time.  The reason we loop for 8192, is that’s the maximum amount of data that can be written to a sound at one time.

4. Take our SampleDataEvent, get the data, and write a floating point decimal to that data.  The data we’re going to write  over time will be a sine wave.  The sine wave will be generated by taking the position in our audio sample and adding our variable c to that position, then calculating the sine.  Multiplying by .25 reduces the volume or amplitude of our audio sample to ¼ what it was.  If we don’t do this, Flash will produce a very loud tone.  All of this in line 4 is done for the right channel.

5. Do the same as line 4, except for the left channel.

8. Take our sound object, stored in the variable mySound and add an event listener to it.  Listen for a SampleDataEvent.SAMPLE_DATA and when we hear that event, run sineWaveGenerator once.  The event will be triggered when we try to play our sound – each time we need more data to play (if our sound keeps playing), we dip back into our function and get more audio data.

9. Tell the sound object, stored in the variable mySound to play.  When it tries to play there will be no sound data.  It will then trigger our event listener, which will call our function, which will write data to our sound object, which will then be played until it runs out of data, then the process will be repeated.

Adobe’s version above works, but it’s limited and they don’t give you a good explanation of what’s happening.  Even with the explanation I’ve given above, you would not know how to create a specific note, or how to tell the sound to last a certain amount of time.

Next up: Playing a Note of a Certain Frequency

Andres Serrano, The Morgue (Knifed to Death II), 1992, cibachrome, silicone, plexi-glass, wood frame, 49 1/2” x 60”.

I chose to review The Morgue by Andres Serrano.  The Morgue is a series of photographs Serrano took in 1992.  The specific work I’ve chosen to look at is The Morgue (Death by Drowning II).

Death by Drowning II is a dead body photographed, cropped from just below the nose to the top of the chest, lying on its back with the head turned toward the camera.  There are no clothes or sheets shown other than the black canvas backdrop in the background.  There is no other content besides the body and backdrop.

The work is very textured and rich in color.  The body is tinted red and purple as a result of the drowning and looks to have some dirt here and there.  The lights create a shimmer on the lips, chin and neck of the body producing a stark contrast with the black background.  The extreme cropping along with the open mouth and turned head create a sense of yearning mixed with sadness.  The skin is deeply textured and discolored with vines of dark dividing the lighter skin of the diseased.  The focal length of the shot blurs the neck and chest leaving the viewer focused on the details in the face and shoulder.

There was a time that death was everywhere, but America has moved to a point that death is no longer seen explicitly, rather death is something to be handled by professionals.  No longer does the common man or woman deal with death on a daily basis.  So for this work to be interesting or shocking beyond formal qualities, the culture surrounding the work must have been sensitive to viewing the dead.  These works tell us that our culture does not normally deal with death in any sort of routine manor.

The time of the work in the United States was such that the artist and the subject would be shown, not hidden.  Additionally, the work was photographed on film and printed in color, which tells us there is a certain level of technology involved.  Serrano has created quite a stir with each progressive subject he tackles.  This series and work did more of the same.

Works Cited

http://bombsite.com/issues/43/articles/1631

http://www.artnet.com/usernet/awc/awc_thumbnail.asp?aid=424202827&gid=424202827&cid=118026&works_of_art=1

James Turrell, Roden Crater. Flagstaff, Arizona, 1979-Present, extinct volcano.

James Turrell has been working on the Roden Crater since 1979, when he purchased the land to create his huge art installation.  The Roden Crater is an extinct volcanic crater just outside Flagstaff, Arizona. Turrell’s creation is site specific land art – no other site and no other medium would have quite the same effect as his volcanic crater.  He is moving massive amounts of earth, digging “viewing chambers” and tunnels into the land in order to create points and perspectives from which to view the sky, and certain celestial events.

Turrell emphasizes the action and experience of the site, taking in the views and walking through the tunnels as essential to the work itself.  He seems to say, if only indirectly, and his work of art is nothing unless experienced.  Even the journey to the site is important.   His perspective is certainly Post-Modern in nature.

Contextually, this great work fits within Turrell’s focus over his lifetime as an artist – viewing and experiencing light.   It is likely his inspiration for his works come, at least in part, from his lifelong experience and perspective as a Quaker.  The meditative nature of his work seems to correlate with the Quaker faith.  Perhaps the most impressive piece of the Roden Crater story is the fact that the work is still actively in progress 30 years after it began.

The Microsoft Surface was officially announced on May 29, 2007 at the D5 (All Things Digital) Conference.  The Surface announcement came 5 months after the iPhone was officially announced and around a year and a half after Jeff Han released his “Multi-Tough Interaction Experiments” demo reel.  Surface is not the first multi-touch device, nor is it the best.  However, the Surface does represent a general belief in and backing of multi-touch technology by the computer giant Microsoft.  Further, Microsoft established the Surface as a viable point-of-sale business tool, which was unheard of at the time.  Microsoft’s tag line for the Surface is “Experience Computing Together.”

Technologically the Surface is not extremely advanced.   The physical device is simply a sheet of acrylic held up by a steel frame in a table form factor.  A combination of backlighting the acrylic sheet with 850nm infrared light along with a series of motion cameras enable the perception of touch sensitivity.  Meanwhile a DLP projector mounted in the bottom of the table shines the imaging onto a diffusion surface attached to the bottom of the acrylic.  The whole setup is brought together by a motherboard running an Intel Core 2 Duo 2.13 Ghz chip with 2gb of RAM and a 250gb hard drive.  The Surface runs a modified version of Windows Vista as it’s operating system.

Of the technologies used to create the Surface, only the modified version of Windows Vista is really unique to Microsoft. The imaging mechanics of the Surface are no different than that of rear projection televisions, which has been around since the 1970s.   The system of cameras and infrared light is known to the multi-touch world as Rear Diffused Illumination.  Rear DI is now generally regarded as somewhat of a sub-standard technology in the multi-touch community. Frustrated Total Internal Reflection (FTIR), which is the technology Jeff Han introduced in 2005, seems to be building momentum as the hardware solution of choice among developers.

So if the Surface does not represent new, novel technology, what good is it to modern computing? Multi-touch computing is not new; rather it has been in the works for a number of years.  However, multi-touch computing has mostly been evident in fiction.  Hollywood has depicted multi-touch computing numerous times in film and television.   But the Surface is extremely important because of the stir and general awareness of multi-touch computing that it created.  In effect, by releasing the Surface, Microsoft made fiction fact, commercially and publicly.  In addition, Microsoft became a champion of a new way of interacting with the computer – a movement known as Natural User Interface (NUI).

Microsoft Surface represents a fundamental change in the way we interact with digital content. With Surface, we can actually grab data with our hands, and move information between objects with natural gestures and touch. Surface features a unique 30-inch tabletop display whose unique abilities allow for several people to work independently or simultaneously. All without using a mouse or keyboard. (Multimedia Information and Technology 2007)

When Microsoft released the Surface they showed their belief in the Rear DI hardware solution.  Until that time, the Rear DI setup had been viewed as a home-brewed or academic.  However, with the adoption of the Diffused Illumination technology, Microsoft stated that the technology was stable and viable at a business level. That step of taking the hardware technology to a business platform has opened up a whole new industry for multi-touch developers.

The Surface is certainly not perfect.  It would seem that Microsoft pushed the Surface as the new face of computing, but took its foot off the pedal shortly afterward. Among the Surface’s drawbacks are its continued limited availability and $12,500-15,000 price tag.  Development is reserved for those who are able to obtain a developers version of the Surface and have the knowledge to write programs in Microsoft’s Windows Presentation Foundation or XNA.  But even with all of the drawbacks, the Surface has been an important asset to the field of multi-touch computing.  Without Microsoft’s release of the Surface the interest surrounding table-based multi-touch computing would not be what it is today.

Works Cited

McClearn, Matt. “Touching the future.” Canadian Business 81.11 (2008): 41. OmniFile Full Text Select. Web. 15 Feb. 2010.

O’Leary, Noreen. “The Power of Touch.” Adweek 49.17 (2008): 20-1. OmniFile Full Text Select. Web. 15 Feb. 2010.

Han, Jefferson. “Multi-Touch Interaction Research.” Multi-Touch Interaction Research. N.p., n.d. Web. 15 Feb. 2010. <http://cs.nyu.edu/~jhan/ftirtouch/>.

Hein, Kenneth. “When Tables Become Ads: Meet Microsoft Surface.” Brandweek 48.39 (2007): 12. OmniFile Full Text Select. Web. 15 Feb. 2010.

Costa, Dan. “Touch Screens Done Right.” PC Magazine 26.16 (2007): 50. OmniFile Full Text Select. Web. 15 Feb. 2010.

“Microsoft’s Multitouch Table Computer.” PC World 25.8 (2007): 26. OmniFile Full Text Select. Web. 15 Feb. 2010.

“Microsoft Surface – Tabletop Computing.” Multimedia Information and Technology 33.3 (2007): 81. OmniFile Full Text Select. Web. 15 Feb. 2010.

Wikipedia contributors. “IPhone.” Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 15 Feb. 2010. Web. 15 Feb. 2010.

Wikipedia contributors. “Microsoft Surface.” Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 28 Jan. 2010. Web. 15 Feb. 2010.

The Magnavox Odyssey retailed for $100 in May of 1972 and is considered the first video game console for home use.  The Odyssey was the brainchild of Ralph Baer.

In 1966 Ralph Baer, an engineer at Sanders Associates at the time, started working on an idea for a game system that could be played using a television.  He began working with some colleagues and after two years of development ended up with a prototype video game system and 12 games.  They called the system the “Brown Box” after it’s housing and sought out licensing.

Baer took his Brown Box system to various Cable TV system operators and TV manufacturers around the United States.  There was moderate interest but a licensing agreement was not reached at the time.  It wasn’t until July 17^th of 1968 that Gerry Martin, the VP of marketing for Magnavox, saw an opportunity in Baer’s creation.  In 1971 Magnavox and Sanders Associates signed an agreement that left Magnavox with all the data and design specifications to create what would become known as the Magnavox Odyssey.  By the fall of 1971 Magnavox and a group of engineers led by George Kent had a final design, an “OK” from the FCC, and the Odyssey went into production.

Magnavox, despite very poor marketing efforts, went on to sell 130,000 units of the Odyssey in 1972.  Over the next two and a half years Magnavox sold a total of 330,00+ units of the original system before replacing it with an updated model named the Odyssey 100.  In addition to the original console and games, a rifle pack could be purchased for around $25 that added more functionality for four “shooting gallery” games.  The rifle pack sold around 80,000 units in total.

Baer’s Odyssey was not extremely complex, but was more of a unique idea.  The console worked by using “discrete transistors and diodes” – 40 of each to be exact – that functioned as the brain of the machine.  His setup was similar to the IBM 1401’s Diode-transistor logic circuits.  Each game was in a cartridge form, but was simply a “series of jumpers between pins of the card connector.”  The games themselves contained no other components, rather as the games were inserted into the console, the jumpers connected to the logic board and dictated the game play and output.  The inputs were two hand-held controllers and the output consisted of a simple rf connector that sent information to a television for display.

The Odyssey was capable of outputting a series of simple white dots on a black screen.  Depending on the game, and what was happening in the game, the dots would turn on or off.  To supplement the simple graphics, Magnavox shipped the system with a series of screen overlays.  The screen overlays were printed in color and came in two different “small” or “large” sizes – a screen overlay for each of the 12 games.

Baer’s creation was an important pioneer in the video game industry.  Before Baer, digital or “video” games were restricted to computers – which were not always accessible for that purpose.  The idea of taking a smaller, simpler version of the computer and using it for game play in conjunction with a television was a novel idea that started a whole industry.

On May the 24^th of 1972 Nolan Bushnell attended a demonstration of the console put on by Magnavox.  Mr. Bushnell then proceeded to found Atari on June 27 of the same year.  He then went on the produce a prototype and final version of their first arcade game “Pong” which he put into a local bar.  Pong began the Arcade game industry, as we know it now.  In 1974 Magnavox filed a lawsuit against Atari, which resulted in Atari’s licensing of the table tennis game that originally shipped with the Odyssey. Since then countless other videogames and game systems have spun off of, or been directly influenced by Baer’s Odyssey gaming system.

A couple interesting notes: The Odyssey did not have any “memory” thus it did not keep track of scores.  The system did respond to the user’s interaction and was made to be played by two people, but the original device did not have the capability to save any information.  As I mentioned earlier, Magnavox fumbled in their marketing of the Odyssey.  The original marketing made it sound as if the Odyssey would only work on Magnavox televisions, which, in addition to the high price-tag at the time, turned off a good number of potential consumers.

Of the final Magnavox version of the Odyssey, Baer is quoted as saying “We were happy with Magnavox’s design.  The only thing we didn’t like was the price.  It was that high partly because they spent a lot of money on plastic.” Baer has since been recognized with a Legend award by G4 at their video game award show G-Phoria.  In 2006 Baer received a National Medal of Technology, presented by President G.W. Bush, in honor of his “groundbreaking and pioneering creation, development and commercialization of interactive video games.” Baer has received numerous other awards over the years and is widely considered the “father of videogames.”

Works Cited

Slater, Derek, and Joe Sullivan “Good Idea, Bad Timing” CIO 15 Aug. 2001: 129-130

Wikipedia contributors. “Magnavox Odyssey.” Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 8 Jan. 2010. Web. 11 Jan. 2010.

Wikipedia contributors. “Ralph H. Baer.” Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 10 Jan. 2010. Web. 11 Jan. 2010.

Winter, David. “Magnavox Odyssey.” Magnavox Odyssey. 3 July 2009. Web. 11 Jan. 2010. <http:// magnavox-odyssey.com>.

Winter, David. “Pong-Story:Magnavox Odyssey, the first video game system” Pong-Story. 2010. Web. 11 Jan 2010. <http://www.pong-story.com/odyssey.htm>.

“Remembering the Magnavox Odyssey.” The News & Record (Piedmont Triad, NC) (Sept 29, 1997): D1. InfoTrac Newspapers. Gale. Lewisville Public Library System. 11 Jan. 2010 http://find.galegroup.com/gtx/start.do?prodId=SPN.SP00&userGroupName=txshrpub100226.

“The Untold Story of the History of Interactive Entertainment, From Mainframes to Mainstream.” Computer Gaming World 200 (2001): 59. MasterFILE Premier. EBSCO. Web. 11 Jan. 2010.

“Video Game Odyssey.” Technology Review 105.2 (2002): 96. MasterFILE Premier. EBSCO. Web. 11 Jan. 2010.

Julian Voss-Andreae's Quantum Man

Julian Voss-Andreae’s Quantum Man stands ten and one half feet tall at the center of the Bravern shopping center in Bellevue, Washington.  Quantum Man is one of the artist’s many quantum themed sculptures.  Voss-Andreae is an artist turned scientist turned artist once again.  He grew up around art, specifically painting, and began his artistic career as a realistic painter.  When painting ceased to be interesting in 1993, the artist turned to science and worked for the next seven years to eventually complete Physikdiplom in Europe – essentially a Master’s of Science in Physics.  While attending university Voss-Andreae participated in research regarding quantum physics.  That research in physics inspired the scientist to return to his artistic roots, moving to Portland, Oregon and completing a BFA in Sculpture at Pacific Northwest College of Art.  Julian Voss-Andreae now spends his energy sculpting physical representations of quantum objects and other science related phenomena.

Quantum Man, 2009, is the latest sculpture in the artist’s quantum figure series.  Viewed from the front or back, the sculpture appears to be a massive hunk of metal cut to the shape of a man walking forward.  But from the side that same man is nearly invisible.  The effect comes from the layering of more than 100 sheets of stainless steel, separated by metal rods, layered from front to back, vertically.  Voss-Andreae states that his aim, specifically through this sculpture, is to “increase the audience’s capacity to intuit the unfathomable deeper nature of reality.” [1] That reality is quantum mechanics.

Quantum mechanics is a mathematical theory that describes the behavior of microscopic particles.[2] Quantum mechanics allows for the observation of the qualities and possible movements of electrons, hydrogen atoms, and the like.  The historic problem with quantum mechanics, and science in general, is that even if there are unknowns, people will always want to visualize how an object might look.  As Voss-Andreae points out in his paper Quantum Sculpture: Art Inspired by the Deeper Nature of Reality:

The problem [with representing quantum objects visually] is the very notion that a hydrogen atom, or any quantum “object” for that matter, is an object and has a particular appearance or properties independent of the means used to observe it. Consequently, it seems impossible to assign a “quantum object” any objective existence at all. (…) Using images in science or philosophy to illustrate states of affair is generally a two-edged sword because it is essential that the audience knows the limits of a picture and uses it with discrimination and intelligence. With that caution, I believe that art, having shed the requirement to visually represent reality accurately, is uniquely capable of instilling an intuition for the deeper aspects of reality that are hidden to the naked eye. [3]

For Voss-Andreae, quantum mechanics is a source of inspiration and a springboard rather than a tether.  Inspired by a conversation in graduate school, Voss-Andreae set out to create an artistic rendering of a man walking through space-time.  The parallel vertical steel plates in Quantum Man are representative of the wave fronts a person might create as they stride forward in time.  Each plate is positioned with constant spacing, though the connecting rods are irregularly positioned vertically and horizontally to represent Richard Feynman’s 1948 method of path integral formulation for calculating quantum mechanical probabilities.  Voss-Andreae seems to be pointing to a duality between the reality we experience directly and the true nature underneath.  Any person at any moment appears to be a static figure – one person now and the same the second later.  Quantum mechanics would instead describe the same person as multiple objects over multiple instances of space-time. In essence, a person moves in waves, though those waves are rarely perceived.  Quantum Man most excellently illustrates this duality.  Voss-Andreae is not trying to be technically accurate in his sculpture; rather he is attempting to show mankind the alternate reality Quantum Mechanics describes.

In addition to quantum mechanics, Voss-Andreae also works with protein molecules and other underlying structures essential for human life.  In 2005 Voss-Andreae was commissioned to create a sculpture for the entrance of The Scripps Research Institute in Florida based on the molecular structure of the human antibody.  Angel of the West is a 1500-pound sculpture with a twelve-foot circular diameter and a four-foot depth.  The piece is made up of 1336 pieces of rectangular stainless steel tubing, assembled into ninety ‘beta strands.’[4] The beta strands were then assembled to mirror Da Vinci’s The Vitruvian Man.  Many of Voss-Andreae’s sculptures are created from metal pieces welded together, but Angel of the West required more technology than simple welding equipment.

To execute the piece, Voss-Andreae employed computer technology in the form of a custom program he wrote to envision how the beta strands might fit together.  Once the artist found the configuration he was looking for, he wrote another program to calculate the various mitre cuts that would need to be made, then executed those cuts on a laser-cutting machine.  Together, the programming took Voss-Andreae six months to write – but without the aid of the computer, the sculpture would be an impossibility.  Once the programs were written and the pieces cut to size, nearly two years were required to assemble all 1336 pieces inside the twelve-foot diameter stainless steel ring.

Angel of the West is impressive to behold.  The name of the sculpture is derived from Voss-Andreae’s belief that “Human antibodies are like an army of angels”[5] and also openly references the Angel of the North sculpture in England by artist Antony Gormley.  The sculpture itself is a tribute to both the research and science of Scripps Research Institute and the importance and significance of the antibody in human life.  As with any Voss-Andreae sculpture, the visualization of the science is truer in spirit than in function, but the final piece communicates exactly what it needs to: scientific research and the human antibody are immensely important to life.

[2] http://msc.phys.rug.nl

[3] http://www.julianvossandreae.com

[4] http://www.opb.org

[5] http://www.opb.org

Rattlesnake, opus 539

Robert Lang began his foray in origami when he was six years old.  His teacher gave him a book detailing several fold designs.  Lang, at that time, viewed origami as both a mental challenge and a world of endless possibilities.  The reality, as little Robert Lang saw it, was that any free sheet of paper he could obtain was a potential toy in the making.  As Lang got older he never grew out of what he thought might be a childhood obsession.  Instead, he began to create his own folded figures and always had origami on the back burner as he went through the rest of his life.

In 1987 Robert Lang and his wife Diane moved to Ludwigsburg, Germany where he was executing his post-doctoral work in Applied Physics as part of a program with the California Institute of Technology.  While in Germany the couple made a stop in Black Forest, original home of the cuckoo clock.  After seeing the intricately carved clocks, Lang was inspired to fold his own version of a Black Forest clock from paper.  On the artist’s website, he freely admits that his “first cuckoo clock was fairly plain”[1] but that his second was better.  By the third version he had a novel design, very intricately folded.  Black Forest Cuckoo Clock, opus 182 was Lang’s first real smash hit in the origami world.

The design is folded from a single one foot by ten-foot rectangle of Zanders “elefantenhaut” paper down to a fifteen-inch high version of a Black Forest Cuckoo Clock.  Lang’s masterpiece is complete with a pendulum and pinecones at the bottom, leaves along the sides, and a stags head at the top of the clock.  The final design was so involved it took Lang three months to complete the folding instructions and another six hours to actually complete the folds.  But the work paid off.  Lang was flown to Japan to demonstrate his design on television and was beginning to be recognized as an international origami master. 1987 was pre computational origami for Lang, but the Black Forest Cuckoo Clock was still one of the most complex origami figures produced to date.

Though Lang was receiving international acclaim for his origami designs in the late 1980s and throughout the 1990s, he kept pursuing physics as a full time career.  After his doctoral studies, Lang went on to work for NASA’s Jet Propulsion Lab in 1988, then spent more than nine years at Spectra Diode Labs and eventually ended his full-time pursuit of physics at JDS Uniphase in 2001.  In that time Lang was credited with more than forty patents, most revolving around laser physics, and produced more than eighty technical papers.  To this day Lang holds technical positions in the field of physics, including Editor in Chief for the Journal of Quantum Electronics.

In the early 1990s Lang and another origami master Toshiyuki Meguro both independently recognized that origami was fundamentally a circle-packing problem.  In other words, mathematics was the key to complex origami design because each flap or appendage of an origami figure must originate from a circular section of paper.  The more circles one can fit on a page, the more intricate the figure can be.  Lang wrote a program named TreeMaker in the early nineties that was designed to formulate a “non-trivial origami figure based on a description of the number, lengths, and connectedness of the flaps.” [2] Within a number of months Lang had written the first version and by 1998 he had released TreeMaker 4.0, which could solve origami problems that Lang could not solve with traditional pen and paper.

ReferenceFinder is another program Lang wrote in the 1990s, meant to accompany TreeMaker.  Where TreeMaker works to solve the problem of the placement of circles on a page, ReferenceFinder works with the problem of folding an object once the crease pattern is mapped out.  Before ReferenceFinder origami artists were left with a trial-and-error approach to folding.  Even if they could map out the creases, they then had to figure out in what order to make the folds to create the intended figure.  ReferenceFinder uses seven folding operations to calculate the best possible folding sequence for a given figure.  Those seven folding operations are known as the Huzita-Hatori Axioms.  The Huzita-Hatori Axioms come from the discoveries of the first six axioms in 1989 by Humiaki Huzita, and the last one by Koshiro Hatori in 2001.  The axioms are essentially a set of mathematic rules that define how paper may be folded.  Because the axioms are expressible in equation form, Lang recognized the ability to create a computer program based on those formulas.  By 2003, and the third version of ReferenceFinder, all seven axioms had been integrated and could generate the folding sequence for virtually any set of crease patterns.

With TreeMaker and ReferenceFinder now in hand, and the use of a commercial precision laser cutter to score paper, Lang is able to create works of art that would not be otherwise possible.  One such work is Rattlesnake, opus 539, a private commission in 2008 that features a snake coiled in a defensive posture, tail up as if to shake its rattle as warning before it strikes.  The tail itself contains ten beads and the body features approximately one thousand scales.  The head contains nostril indentations and an open mouth.  The snake is folded from one uncut rectangle of brown Thai unryu paper[3] and at completion is approximately 8″ in size.  The incredible precision of the folds and the intricacy of the hundreds of scales and rattle make the piece incredible and nearly unbelievable under the standard constraints of origami.

Lang’s complex origami is often referred to as computational origami because of his use of mathematics and the computer.   Without the mathematic discoveries of the Huzita-Hatori Axioms, the development of the computer as a tool for complex calculations, and without the laser cutter to aid in folds, Lang’s artwork would not be possible.  Lang is an example of a brilliant scientist porting his knowledge over to another field.  For that ability Jan Polish of Origami USA calls Lang the “renaissance man of origami.” [4]

[2] http://www.langorigami.com

[3] http://www.langorigami.com

[4] http://www.smithsonianmag.com

I would strongly recommend teachers and students not use the XanEdu service.  After not providing the correct materials in the first place, I requested the issue be corrected.  They told me the materials would be corrected “soon” but did not update me when they were corrected.  Rather, I was left to check and see when they would be updated.

Well, I checked the materials at the end of the semester, after the applicable period had passed and they had updated the materials – but they had scanned everything sideways.  When I emailed to ask for a refund, they cited the terms of service and told me no refund would be given.  They claim they fixed the error the day after I notified them.  I do not know if this is true.

My experience is that XanEdu is not interested in keeping their customers happy.  The other scans I received were poor quality and not worth the price paid – some were nearly illegible.  As a teacher I will not use them, and as a student I won’t bother purchasing anymore course packets from them.  XanEdu is not a company I trust.