Pixar's 2008 animated short Presto is a comical short story about a magician attempting to perform a show with his rather uncooperative rabbit. Filled with gags, Presto can be seen as an homage to classic cartoons such Tom and Jerry and Looney Tunes and was nominated for an Annie Award and Academy Award. Although the story takes place in a world modeled after our own, there are subtle disparities for comedic emphasis and entertainment value. Throughout the film we see evidence of real world characteristics such as gravity acting upon falling objects. An element of magic is present as well however. We soon realize that Presto's hat is no ordinary hat, but appears to act as a portal or wormhole linked to the wizard's hat worn by Alec the rabbit. A seemingly incredible object, the wizard's hat does not exist (sadly) in the reality in which we live. Presto is, after all, full of magic, and magic bends the confines of reality to the extreme.
First off we shall investigate the presence (or lack thereof) of gravity. Gravitational force is a natural phenomenon by which objects with mass attract one another. Gravity as we know it refers more specifically to the force exerted by the Earth on objects in its vicinity. This gravitational force can depend on a number of factors, including mass and rotation. Gravity acts upon all objects in our world, from the smallest particle to the largest mountain.
The force of gravity can be calculated by the equation F = mg, where F is the force of gravity, m is the mass of an object, and g is the acceleration due to gravity. Gravitational acceleration on Earth is also known as standard gravity and defines how fast an object accelerates while falling at sea level. Although the actual strength of gravity on Earth varies according to location and altitude, standard gravity for calculation purposes is defined as 9.81 m/s2. Using this definition allows us to calculate all sorts of variables within our world, or in the scope of this paper, within the world that Presto and Alec inhabit
As the short opens, we meet one of our primary characters, Alec the rabbit. He is in distress, locked in a cage, hungry, with a wonderfully savory looking carrot sitting just out of reach. This carrot is to become a central focus of the story, as well as our calculations. Most of the action takes place during Presto's performance. After becoming frustrated with Alec, Presto tosses an egg into the hat in an attempt to strike back at the poor rabbit. Now Alec is a reasonably small rabbit. His height can be approximated by using a familiar object as reference, in this case the carrot he desires so much. This lovely vegetable turns out to conveniently be the same height as Alec. The average length of a carrot root (the carrot itself) is approximately 20 centimeters, or nearly 8 inches. Double that to get the length of the carrot with its leafy green top and you have Alec standing around 1 foot 3 inches in height.
Now as the egg reaches its peak, it begins to free fall back into the hat. Using the formula distance = ½ gravity*time2, the distance the egg should fall from rest in a certain amount of time can be calculated. Rearranging this equation yields time = √(2*d/g). The egg falls from its peak at the top of Alec's head in the animated sequence, or 0.381 meters (15 inches) high from the surface of the table on which Alec stands. Plugging this into the time formula along with the standard coefficient of gravity on Earth (9.81 m/s2), the time it should take for the egg to fall 0.381 meters comes out to be 0.28 seconds. In watching the film carefully the egg actually takes 11 frames to drop from its peak and disappear into the hat. At 11 frames at 24 frames per second we can figure out that on screen the egg actually takes 0.46 seconds to fall, almost twice the amount of time it should take in reality.
As the egg exits the hat to smash back into Presto's face, it travels a distance of approximately twice Alec's height (30 inches or 0.762 meters) in blazingly fast 5 frames, or 0.21 seconds. In order to travel that distance in that amount of time, the acceleration acting upon the egg due to gravity would have to exceed 30 m/s2, a gravitation force larger than if the egg was falling on Jupiter rather than Earth. Now this egg has just traveled through a wormhole of sorts, perhaps that is the reason for its extreme acceleration but we'll touch on that later.
The climax of the short sees Presto dangling upside down high above the stage floor, a rope wrapped tightly (or not to tightly it turns out) around his ankle serving as the only link between life and death. At the pinnacle of the shot Presto is seven stories above the stage (conveniently placed box seat balconies along the right side of the stage makes this an easy calculation of approximately 70 feet). It takes Presto 19 frames to fall 10 feet from rest, or the height of a single box seat balcony. 19 frames / 24 frames per second = approximately 0.8 seconds. Plugging this into the formulas we used previously we can solve for the variable g (gravity due to acceleration) and this yields 9.54 m/s2 , quite close to realistic gravity here on Earth. It appears in this shot the animators were able to create a fairly accurate representation of poor Presto plummeting towards his death awaiting him seven stories below on the hard wooden stage floor. Thankfully Alec is there to save the day with the trusty (and magical) wizard's hat. Falling objects are all well and good however, it is the magical link between Presto's hat and the wizard's hat that forms the true entertainment and focus of the story.
This mysterious portal between hats appears to act as a sort of wormhole or teleportation device, something that has long existed in the genre of science fiction. But could it actually exist? Spacetime is a mathematical model combining space and time into a single continuum, visualized as a two dimensional plane. By hypothetically bending or folding spacetime back upon itself a shortcut through space and time can develop in what is known as a wormhole, or wormhole bridge, with two mouths connected by a tube or throat. If a wormhole is traversable it is possible (theoretically) for a physical object composed of matter to travel from one open mouth to the other by passing through the throat. While there is obviously no observational evidence pointing towards the existence of wormholes, spacetimes containing wormholes are known to be valid solutions in general relativity. I may not be Stephen Hawking, but I can appreciate the fact that modern physics does seem to point to the existence of wormholes in our own world.
What exactly happens within a wormhole might be the next logical step in deconstructing the magic of Presto's two hats, yet is far too complex to even attempt to unravel within the scope of this paper. In short, Lorentzian traversable wormholes theoretically allow travel through points in space seemingly instantaneously, or travel between different universes. In theory wormholes allow velocities exceeding the speed of light and also time travel, while the objects that are actually traveling through the wormhole bridge maintain velocities that are lower than the speed of light. The analogy of a simple bridge comes to mind. If you were to race someone from one side of San Francisco Bay to the other, obviously the bridge would provide the fastest means of travel. However, your opponent might maintain maxim speed around the bay during travel, yet you can beat him to the other side by traveling a much slower speed. The only difference is that the distance of travel is so much shorter. This is in essence what happens when spacetime is folded and a wormhole tunnel is formed. Matter traveling through the tunnel can reach the other side faster much faster (but at slower speed of travel) than matter traveling around the spacetime plane to the other side at a much higher speed of travel, or the speed of light.
So were the animators up in Emeryville thinking about all of this while working away furiously away on their next magficient new animated short? Most likely not. Is Presto's hat actually the mouth of a wormhole bridge linked to another one within the wizard's hat? No, probably not, but it does behave like one. The simple fact is the animators were aiming to create a story, one that entertained, brought laughs, and had a magical element to it. In the end I feel they succeeded greatly. Animation requires one to adhere to the laws of physics in order to create the illusion of life. This believability is what draws into the story and world of the characters who we love so much. When animators choose to break the rules of physics it is usually for a good cause; to create a dramatic effect that leaves us hanging on the edge of our seat, to draw emphasis or significance to an object or action, or to create a comedic flourish that leaves us thoroughly entertained and smiling with joy. In short, animation should always follow the laws of physics, except when it is more entertaining to do otherwise.
