Duchampian Multimedia

Paul Mellon 21th Century Exhibition and Study Room

We envision an innovative installation of Marcel Duchamp.s works which would include hands-on participation and new, amazing (but friendly) computer technology all of which will not only enhance the museum visitors. understanding of modern art by making it fun, but also, at the same time, break the artificial boundaries between art and science, and actually accomplish some much needed education of the public in science.

We believe that end result of such an entertaining, informative, and unusual exhibition will be a new, wider audience for an art museum, popularity with the press, interest from new funding sources, as well as new enthusiasm from sources in government and education, arising from our demonstrated links of art with science.

Computer Technology: An Advantage In Art Research And Display

Our Duchamp exhibition will demonstrate to the museum visitor the strength and marvel of new computer technology both as a research tool and for innovative art display. Our exhibition involves the best of what computers can do in visualization and measuring. Duchamp.s .lost readymades., and several of his machines (where he only left us a few photographs, paintings or drawings), are presently being constructed into three dimensional models in computer space as part of Shearer.s research. Visitors will be able to rotate Duchamp.s objects on a monitor, and turn and view them from all sides, from top down at various angles, and likewise from bottom up with only a few pushes of several buttons.

This particular three dimensional modeling technique was used in Shearer.s research on readymades and became a pivotal part in her recognizing that the readymades are not unchanged, store bought objects. In addition, the perspective in Duchamp.s photographs, paintings and drawings can be easily and accurately checked without laborious, and often inaccurate, hand-drawn geometries. These colorful and attractive computer results from the analysis of Duchamp.s perspective in drawings, paintings and photographs will be exhibited on monitors along with his original objects to illustrate the perspective tricks that Duchamp used, and that fooled even art historians. trained eyes and that of artists studying recreations of Duchamp.s perspective.

Specific examples of how the computer will be used for particular works will be provided in the following sections, including details about how these three-dimensional computer models will also be animated.in other words, in the case of Duchamp.s Chocolate Grinder, Water Wheel, or Bicycle Wheel, these reconstructions will all be able to move as if they were real machines in three-dimensional space! This computer feature is especially important for Duchamp.s machines, for it is only when we see them move in three-dimensional space that we can really see their unexpected, irregular shapes and construction with the greatest impact. For example his tilting Bicycle Wheel, or his oval shaped Water Wheel leaning at an angle, or his irregularly shaped Chocolate Grinder Wheels, cannot possibly operate as we had assumed!.that is, as real machines, readymade. We never would notice these facts without using our minds to analyze the perspective.

In order to assist older museum visitors unfamiliar with computers, as well as younger people unfamiliar with this new technology, we will have .computer-friendly human helpers. continually circulating with the exhibition, and wearing easily recognizable shirts. These .helpers. will assist visitors and demonstrate computer displays.

Finally, a very new technology which produces an animated three-dimensional .hologram. called .volumetric displays systems,. will also be integrated and used in various ways in display sites throughout the exhibition. This technique produces holograms which float in a room in such a way that visitors can put their hands or walk through the hovering , 3-D image.

All the 3-D computer models and animations of Duchamp.s works, with the exception of the holograms, can be brought home by visitors, and used on their own computers in the form of a CD ROM which will be placed at the back of each exhibition catalogue. Journals and books have begun including CD ROM.s in their publications. This Duchamp Exhibition, as far as we know, will be the first major museum catalogue to include a computer disk.

Exhibition Concept

We envision the exhibition as divided into four parts:

  • The Readymade: Brain Teasers, Not Humble Store Bought Objects!
  • Optical Experiments: Machines And Illusions To Move The Mind
  • Chaos And Chance Systems: The Creativity Machines Of Nature
  • Duchamp.s Creativity Game: His Poetic Creation Of The Process

I. The Readymade: Brain Teasers, Not Humble Store Bought Objects
We envision the exhibition tour for the museum visitor as beginning with a three-dimensional recreation of the two photographs of Duchamp.s famous 1917 Fountain urinal, using two three-dimensional urinal reproductions in simultaneous comparison with the two original photographs. Duchamp claims, as for so many other of his original readymades, that he lost the original urinal. His claim has always been suspicious since (a) Duchamp kept a detailed and careful chart to keep track of the locations of his works on title cards, as a general would keep track of military moves in a war room. Moreover, Duchamp kept every scrap of paper and maniacally reproduced them right down to seeking out the exact inks, papers .from all over Paris. and even recreating every torn edge of paper. (b) No one has been able to find identical examples of his allegedly .readymade,. found everyday, store-bought items. None has ever been found in either manufacturing or sales catalogues of the period or in antique collections despite, researchers. extensive and thorough efforts.

A scholar.s approach to art and the mysteries of its history has traditionally been done with art historical techniques, such as interpretation. In Duchamp.s case, it is scientific techniques that reveal a surprise! Almost everyone is familiar with such techniques from popular brain teasers, brain riddle or puzzle books. We can learn by these techniques that the readymades aren.t humble store bought items, but have been carefully and cleverly altered by Duchamp in such a way that only our minds, with mental effort, can see!

The museum visitor will then follow through the story of each of the readymades displayed, and be creatively led to use for themselves three basic scientific techniques, and to discover directly how these approaches used by scientists allow them to see nature and art in a new way. Using science, and their own puzzle solving capacities of basic, commonsense logic, museum visitors can see that Duchamp .hid. what he was doing in plain sight, and continued to fool art historians and scholars for more than fifty years! These three scientific techniques are:

  • Identify Similarity and Difference
  • Check The Perspective
  • Move Objects From Two Dimensions To Three, Or Three Dimensions To Two

Popular brain teaser or puzzle books will often give two similar pictures of objects, where the mental task and game is to identify the subtle difference between the two images (technique 1). Another brain teaser task involves checking the perspective in a line drawing, such as a house with a roof, door and windows, and identifying the difference between the correct perspective lines in a two-dimensional drawing (technique 2). Finally, brain game and I.Q. game books invariably show three-dimensional objects in their two-dimensional form — like a cube with a pattern on three of its faces with a selection of unfolded cubes in their two-dimensional state — and one then has to match the pattern from the cube.s three-dimensional state to its matching equivalent in two-dimensions (technique 3).

Two Examples Of Readymades Displays: The Hat Rack And The Bicycle Wheel

In our playful, scientific, participatory display of Duchamp.s readymades, we will use all three of the above techniques employed by Duchamp himself. For example, we will show the two photographs of his lost .Hat Rack.. On a computer monitor, these two-dimensional photos will be transformed into a three dimensional object that can be easily manipulated by a museum viewer. A visitor with a push of a button will be able to rotate this three-dimensional hat rack form on a two-dimensional computer screen. When the visitor checks the perspective of this 3-D Hat Rack and compares it to the various images of what Duchamp claims to be his Hat Rack, the visitor can readily discern that they are not dealing with the same object in all cases. (Duchamp only gives us two other images of his .lost. Hat Rack — two shadow projections, one in a photograph and the other in a painting. Visitors will be able to try to match Duchamp.s shadows on the computer screen.)

When visitors rotate these two-dimensional images of his hat rack on the computer as three dimensional objects, they suddenly see that each hat rack, although similar to the others, is quite different and that the main view presented by Duchamp as his .readymade. hat rack is actually missing a hook! (either created by his having retouched the photo or by having physically sawn off the hat rack hook before photographing it.) Scholars were fooled by Duchamp.s Hat Rack because (a) he manipulated the position of the hat rack as he photographed it to allow only the most limited and ambiguous information to be communicated; and, moreover, (b) he later authorized, helped to develop, and signed .readymade. reproductions of his Hat Rack (and other objects) which were completely different from what, by his own photographs and drawings, Duchamp indicated that he used at first as the .original.. Whoever heard of an authorized, signed reproduction consciously not based upon the original object, but supposedly serving as an accurate copy?!

In addition to displaying Duchamp.s .official. hat rack non-reproduction (made by Arturo Schwarz) we will also display the original Thornet Bentwood hat rack (that Duchamp must have used to create his original, retouched photographs) as well as a model of Duchamp.s Schwarz reproduction made so that museum visitors can experiment by attempting to hang hats on the downward, bending hooks and see the hats fall off! Duchamp said that he wanted to make .playful physics..

As a second example of our interactive readymade displays, we will present Duchamp.s Bicycle Wheel. Again, Duchamp gives us only four photographs of his first reproduction of the original Bicycle Wheel by Duchamp (which he claims to have lost as well) — thus making two lost bicycle wheels in total. When we use technique 1.looking for similarities and differences among the four images.we immediately see that, (A) we are either dealing with four different bicycle wheels; (B) or the same bicycle wheel physically changed or retouched in the photographs, four different ways. When we check the perspective (technique 2) in the four photographs, we can see, especially when we move the object from a two-dimensional photograph to a three-dimensional model on the computer monitor, that the legs of the stool and position of the wheel and bicycle fork are not regular in shape, and, like the Hat Rack, are also not functional. In fact, when we spin the wheel we can predict with absolute certainty.as in all probabalistic systems of chance.that the stool will fall, and will do so by chance in the computer animation to demonstrate this principle to visitors. Like any particular number in roulette or heads on a coin, we just won.t be able to say exactly when a predictable chance event will occur. The computer model of the Bicycle Wheel and stool will be manipulated by museum visitors on a computer monitor as well as via a .hologramic. life-size projection, in a three-dimensional moving animation, that will show the bicycle wheel on the stool spinning and eventually falling down. When Shearer looked for Duchamp.s original bicycle wheel with a straight fork in late 19th and early 20th century catalogues, examples of this modern type of wheel and spokes never had straight, but only curved forks.a structural and mechanical feature invented to increase stability in bicycle motion and reduction of oscillations or vibrations. Even the spokes that Duchamp used in his original .lost bicycle wheel. seem to be altered and not the type that would have been .readymade. from a store in 1913 or earlier. Images from late 19th and early 20th century manufacturers. catalogues will illustrate for visitors that straight forked bicycle wheels never looked like the one used by Duchamp. Like the Hat Rack, we can only conclude that the bicycle wheel was not an unchanged, store bought object.

The display of the Bicycle Wheel will include one of the Schwarz reproductions as well as our own model, recreating the original photograph with both the missing rungs, and unstable, leaning wheel and stool. This will be displayed in such a way that museum visitors can spin the wheel and change the pegs in the different legs to experiment safely with the amusing instability of the stool that Duchamp hid in plain sight within his photographs.

In an important Green Box note, Duchamp depicted himself as like the person who creates the brain quiz puzzles. He instructs himself to .lose the difference between two similar objects. like .two similar hats. etcetera. This note and other biographical information will be integrated into signage and will illustrate, in a simple way, Duchamp.s conscious intent to create the .beauty of grey matter,. instead of .retinal art..

II. Optical Experiments: Machines And Illusions To Move The Mind
We envision the next section of the exhibition as divided into three parts:

  1. 19th century photographic tricks
  2. Duchamp.s original inventions and impossible objects
  3. Rotating from two to three dimensions or three to two dimensions moves the mind to be creative

1. 19th Century Photographic Tricks
Duchamp .lost. many of his readymades and then .retouched. their photographs, never saying why. This retouching is comical when observed with critical thinking. For example, Duchamp retouched the only photograph of the .original. Coat Rack by redrawing lines and adding colors to the point where its original reality is not enhanced, but rather given to us in such a cartoon form that it becomes analogous to someone handing us a picture of Bugs Bunny while telling us that it is a retouched photo of his lost pet rabbit!

Upon further examination of his works and the photographs related to them, we see that Duchamp used a whole set of trick photography techniques that were very popular in the late 19th and early 20th century. These include: (a) Spirit photography – phantom images of Duchamp himself as a ghostly apparition are juxtaposed into photographs of his studio which also include his works; (b) Multiple imagesphotography – a photograph shows Duchamp sitting at a table in five different rotations around the same table, an effect created by a hinged mirror; (c) Composite photography – in the composite technique, two or more faces were juxtaposed into one composite face for various purposes, including scientific averaging (allegedly to understand racial or other social differences by creating a summary or averaging among individual differences) as well as for entertainment and fun. Initial analysis of Duchamp.s famous .Mona Lisa. indicates that he not only put a moustache and beard into the Mona Lisa.s face but also made a photographic composite by adding a photo of himself to La Gioconda.s face. When we critically examine Duchamp.s Mona Lisa, looking for similarities and differences (technique 1).we find Duchamp himself!

For the exhibition, 19th century techniques would be explained and illustrated simply alongside examples of Duchamp.s work utilizing these techniques. In addition, all three techniques.spirit, multiple-images, and composite photography.would be set up into a demonstration participant area, where museum visitors could try out each technique and thus see themselves in three different computer monitors as Duchamp saw himself.(a) as a spirit image in Duchamp.s studio; (b) multiplied by five when sitting at a table; and (c) with their faces joined in a composite with the Mona Lisa. [Perhaps a corporate sponsor would contribute so that visitors could have a computer print of themselves capturing the images of themselves in these three 19th century photographic situations!]

2. Duchamp.s Original Inventions
Amazingly, Duchamp.s contributions include several innovative developments in optical effects.only one of which was previously recognized by scholars. Our exhibition would display Duchamp.s original inventions, and also have demonstration models for viewer participation and experimentation. Some examples include:

(A) Impossible objects.Duchamp was the first person to formally develop what is now known as .impossible objects..where an object depicted in two-dimensions, although appearing correct, could never exist in three-dimensional space. Duchamp.s experiments in .impossible figures. began in 1916, whereas Escher did his famous experiments much later, in the 1950’s!

As part of the display we will use Duchamp.s original .Chess Poster. with a three-dimensional recreation of the falling cubes that he depicted. The poster and 3-D recreation will illustrate not only the impossibility of Duchamp.s cube shapes in real three-dimensional space, but will also include a bendable light source, where visitors can move the direction of light and resulting shadows on the cubes in various ways and yet never be able to duplicate the lighting and shadow that Duchamp illustrated in the Chess poster. The lighting that Duchamp used is impossible as well! Duchamp said that he simply .photographed cubes falling out of a bag. and later used this photograph to create his poster. When we examine the poster, we realize that he presents us with an impossible story.

We will also exhibit many other impossible objects of Duchamp.s that also fooled scholars for 50 years by perspective tricks. These amusing and entertaining examples include the famous Coffee Mill painting, where Duchamp explained that .the arrow showed the direction of the movement of the handle. and was .very important.. Yet when we examine the painting, it is impossible that the handle could move in the vertical direction following the arrow but, in fact, must be restricted to a horizontal movement. Throughout his work Duchamp used perspective to fool our eyes into thinking his machines were possible. Two other .impossible machines. that Duchamp created are his Water Wheel and Chocolate Grinder. Computer animations, both as 3-dimensional volumetric displays (.holograms.) or on monitors manipulable by visitors, will animate these various machines.

(B) A new stereoscopic illusion.Since the 19th century, certain .ambiguous figures. were discovered by psychologists, such as the .Necker cube,. which can look both three-dimensional or flat in the same drawing. Shearer discovered that Duchamp had invented a previously unrecognized, ambiguous figure with a quadruple optical effect, unequaled by other inventions. (The famous Necker cube displays only two states: either it looks 3-D or 2-D.) Visitors can see the original Duchamp stereoscopic slide, and can also enjoy looking through a replica of a 19th century stereoscopic viewer at Duchamp.s stereoscopic slides. Signage will illustrate the 19th century craze for the stereoscopic images and machines, mostly forgotten today, and will encourage museum visitors to examine the two slides closely. One is for the right eye and the other is for the left, note the subtle difference between them. The two figures may appear identical at first glance but they are actually two distinct images.just like in a brain puzzle! Most people don.t realize that the two stereoscopic images are different, and that the brain always merges right and left eye information into one coherent image.

(C) The Rotoreliefs.the effect of a two-dimensional disk suddenly appearing three-dimensional when moving was created by two scientists shortly before Duchamp. But Duchamp.s third historic attempt was by far the most sophisticated, and pushed this optical invention to a new level of complexity. Most Duchamp scholars, not to mention museum visitors, have never seen the magical effect of spinning Duchamp.s 12 Rotorelief disk designs. We will have original machines on display, and in addition, will have models that people can operate themselves to make experiments with the different optical effects created by various viewing distances and lengths of viewing time.

3. Rotating From Two To Three Dimensions Or Three To Two Dimensions Moves The Mind To Be Creative
Duchamp.s machines include the Rotary Glass Disks, at Yale which, famously, almost decapitated Man Ray when he and Duchamp turned it on to photograph the effect in Duchamp.s studio. Analogous in form to a set of five separate airplane propellers, gradually increasing in size, these forms appear as one entire circle in motion, when spinning in a row. The Rotary Glass Disks are opposite to the Rotoreliefs, for they demonstrate that a three-dimensional object can not only be moved to appear like a two-dimensional one (whereas the Rotorelief made a 2-D disk appear 3-D) but that, with a change in our perspective, we can experience a new object. In other words, what we see as .true. depends on our perspective and the geometries and dimensions presented. A model of this machine is presently being made by a Yale student and we hope to borrow this machine and have it displayed so that it can be operated by visitors with a switch (while safely contained in a cage) along with Yale.s original machine and various photographs made by Duchamp and Man Ray in Duchamp.s studio.

III. Chaos And Chance Systems: The Creativity Machines Of Nature
Chance. systems were the major component of Duchamp.s life.s work. Yet because of both scholars and the general public.s misunderstanding of the concepts of .luck,. probability and randomness, Duchamp.s interest in chance has never been clearly understood. Museum visitors will be reminded that they observe or participate in chance systems every day as these situations exist everywhere around us.from a coin toss to begin a game, to deciding whether or not to buy insurance.

This section of the exhibition will begin with a roulette wheel, for Duchamp was very interested in roulette. He even created a work.Monte Carlo Bonds.when he spent months in a casino, after obtaining investors, to work on his gambling system. Curator Walter Hopp.s voice will be heard by visitors upon entering this room. He will describe his experience of being with Duchamp at a casino, and the technique Duchamp used to guide his moves during roulette.

Visitors can try the roulette wheel for themselves.spinning it to observe the irregular jumping of the ball and the randomly resulting numbers. Signage will explain that when we consider chance, we tend to get trapped between total ignorance and total knowledge. In other words, we know that the number 18 will eventually win with absolute certainty.which shows absolute knowledge. Yet, at the same time, we can never predict exactly when 18 will occur as an event.showing our total ignorance of certain knowledge.

With a press of a button, a computer volumetric display will create a dramatic three-dimensional visual experience for visitors, which will quickly and clearly illustrate this concept of chance systems. Visitors will see .hologramic. numbers leap from the wheel, circling and colliding in the space of the room and randomly returning in their indeterminent appearances to the spinning wheel.

Visitors will be told how all systems of chance.probabalistic systems that, in recent times, have been called part of chaos science, and including roulette, pendulums, the weather, gaseous molecules, dust in fluid or the Milky Way.all work in the same basic way. (These specific examples were all used by Duchamp in his body of work.)

The smallest changes (muscle strength, air currents and vibrations from a distant truck turning a corner as example) affect the spin and result of the roulette wheel in these chance systems, just as chaos theory claims that the flap of a butterfly.s wing can affect the weather on the other side of the earth three months later. Duchamp learned the basics of what is now called chaos theory, as a result of his ardent study and application of Henri Poincaré .the father of chaos science..

The exhibition will display Duchamp.s notes and his resulting works and experiments in chance. Duchamp.s creative efforts were organized like roulette.for just as the wheel with limited numbers and a bouncing ball generates millions of combinations of occurrences in time, Duchamp.s work begins with notes (1911-1915) from which he generated his works for the rest of his life, which ended in 1968.

The Three Standard Stoppages

One famous example of Duchamp.s experiments in chance is his Three Standard Stoppages. A note published in 1914 describes how Duchamp dropped three meter length threads from a one meter height three times to create a measuring system based not on the metric system, but on the averaging of similarity and differences among the three dropped thread events.

Visitors can study the results of what Duchamp actually did by looking at the original Three Standard Stoppages in the display, as well as by trying the experiment for themselves. They will find out, as Kirk Varnedoe and other scholars have observed, that it is impossible to attain the smooth curves that Duchamp presents us in this work. Not only can we not replicate Duchamp.s experiment with the method he describes.three meter threads dropped and attached to a surface with drops of glue.but we cannot do so with any method! Even carefully arranging the threads by hand doesn.t work, for thread, by its physical nature, is elastic and therefore curves irregularly when one tries to shape it. In fact, we can.t even figure out (to our frustration) how Duchamp created what appears to be a simple experiment!

With observing and directly experiencing this work, Duchamp amuses and challenges visitors to think about the idealization of science and systems of measure as approximate at best, and urges us not to blindly accept scientific or artistic authority however simple the appearance may seem!

Visitors will learn by experience that art scholarship and enjoyment of modern art and science aren.t just based on esoteric interpretations and theories, but also can be thought provoking fun!

IV. Duchamp.s Creativity Game: His Poetic Creation Of The Process
Duchamp.s masterwork, The Large Glass, will be the focus for this last section of the exhibition. After learning about chance systems in the previous rooms, visitors will immediately recognize the aspects of chance or chaotic systems that Duchamp included in his Large Glass machine. Duchamp, in fact, uses all of Poincaréexamples of chance systems: pendulums, the weather, gaseous molecules, dust in fluid, the Milky Way.

Visitors will be encouraged to see Duchamp.s Large Glass machine as a slice of all chance machines in nature, but also including a new aspect of chance not yet discussed, and now featured in this section of the exhibit.namely human creativity. Duchamp, throughout his life, stated that we can define .no progress. as art and science changes every .fifty years.. He describes creativity, and the life of an artist, as being similar to a gambler in a casino.that is, you can know certain aspects of how an artist and their works become famous. However, even the greatest geniuses are subject to the cruel slings and arrows of randomness and chance. Duchamp stated that if he had invented a .Newton theory, an Einstein would come along and replace it.. Duchamp wanted his role in art to be more like the insurance company that deals with chance by making a profit, than like the lottery ticket buyer. Instead of making creative products as his final goal, Duchamp would make the machinery of the process as his art.

Duchamp.s Large Glass will be an entertaining, dramatic and educational presentation in the last room of the exhibition.a visitor will experience a volumatic display similar to roulette, but far more visually rich and complex. Duchamp.s notes will appear literally put together with his Large Glass as Duchamp always said we should do. Next, this animated .hologramic. computer display, will illustrate numerous trajectories and their orbital returns to the Glass.thus visualizing Duchamp.s entire lifetime of work as a system similar to roulette.where a small quantity of numbers began on the wheel, sail off into space, and eventually return to the wheel in a series of events through time, as the ball lands on its red or black numbered location. For example, Duchamp.s last hidden work, discovered at his death in 1968, and entitled Given. 1. The Waterfall, 2. The Illuminating Gass, began as a note in 1912, made appearances in various forms throughout his life as smaller works and finally returned in 1968 after Duchamp.s death as the final event in this series.analogous to a roulette number emerging and disappearing from its source for a fifty-eight year period.

The volumetric display will illustrate, in the three-dimensional space of the room, orbits of Duchamp.s single works or themes in their series through time.first like planets circling the sun, as schematic dots, and then as switching by sudden appearance to a series of related real objects. Duchamp himself represented his work, and all chance events throughout nature, as a field of dots. Duchamp stated that he could .say whatever he wanted to say. with .conventional schematics … like a dot.. Gaseous molecules, dust in fluid, or Milky Way stars or Duchamp.s works.all chance systems appear to similarly operate in space when their movements are plotted into dots in a diagram or schematic.

The Large Glass display in the exhibition room will first show a field of orbiting dots. Visitors will learn from experience that size is relative and that the orbiting dots that are swirling around them could be stars or molecules. (A point Duchamp had intended to convey and often illustrated). Visitors will be able to physically explore this .constellation. as the orbits of dots or stars in their schematic form collide, and dynamically and randomly move about the room like a cosmic or microcosmic vent. The orbiting dots will then shift into a series of readymades or other works in series created by Duchamp beginning in 1911 and ending in 1968, thus illustrating the relationship of his individual works to the Large Glass machine as an entire body or system nested within various sizes or scales of similar chance systems throughout the whole of nature. A visitor.s experience will be so effective that they feel like they have to .duck. as Duchamp.s urinals, Chocolate Grinders and Hatracks in their various incarnations randomly float and careen around the spacious room.

Computer monitors will be available for visitors to manipulate animated views of the Large Glass, thus visualizing what is happening in the room, but at smaller scale. Lively animations of the movement of Large Glass machine parts will begin when various buttons are pushed, and visitors will be able to rotate their view around the Large Glass as a three-dimensional model.including bottom up to top down views and close-ups never possible with real objects. All of the Large Glass animation and computer displays experienced by visitors (on the monitors only) throughout the exhibit, will be available on a CD-ROM at the back of the exhibition catalogue. This innovative and lively exhibition will thus include a life that visitors can bring home, and educators can use as an important and interesting technology not only to show art and science as linked but also as a means to make learning the abstractions of art and science both more understandable and fun.