The Laws of Physics in an Animation Universe

___Percy Jackson and the Olympians: The Lightning Thief is a retelling of Greek mythology set in modern times. In this story, Percy Jackson finds his whole reality turned on its head when he learns that he is not an ordinary human, but rather a demi-god, the son of Poseidon, god of the sea. All manner of wonderful and terrifying things begin happening to him. He is hunted by monsters, his friends and teachers transform into mythical creatures before his eyes, and he is propelled against his will into a quest to recover the stolen Bolt of Zeus, with the life of his mother and the fate of the world hanging in the balance. During his adventures he discovers some of the benefits of being half god. He finds he is stronger and faster than normal humans, abilities which he has in common with all other demi-gods, and best of all he discovers that what he previously thought were physical disabilities or oddities are really his greatest strengths. Many of his adventures with his friends defy reason and common laws of physics, and sometimes require the viewer to suspend belief as they make use of magical weaponry and equipment, give and receive severe beatings, and fly through the air with the greatest of ease.

(see blog post "Video Clip 1 - P.J. trailer 6")

___One of the most striking contradictions of natural physics in the reality of Percy Jackson and his fellow demi-gods is their apparent supernatural durability and resiliency. Percy gets propelled through the air against the trunk of a large tree after being struck a blow by the arm of a minotaur. Assuming a frame rate of 12 frames per second, the creature’s arm appears to strike him at a speed of at least 36 feet per second, which is close to 25 miles per hour. Getting tackled, wearing no pads, by a high school football player would do hurt a lot. Professional football players run the 40-yard dash in 4.5 seconds or less. This is a little more than 18 miles per hour. Being struck by a muscular arm of similar mass and density to a professional football player at 25 miles per hour would break bones and damage internal organs. The force of impact increases when the time of impact, or the duration of the impact, decreases. A mass colliding with a mass of greater density will have a significantly decreased time of impact and therefore the force of the impact will be much greater. It can be observed that an egg hurled violently at a draped bed sheet will not break on impact because the sheet lengthens the time of impact, whereas an egg hurled against a hard wall will be utterly crushed. If a human being collides with a large, dense, and unyielding pillar of wood, such as a large tree trunk, at between 18 and 25 miles per hour, they will likewise be crushed. The damage inflicted on the body can be fatal, as many automobile accidents verify. Yet Percy Jackson survives both the blow from the minotaur and the collision with the tree, and gets up, behaving as if he had only suffered a tackle in neighborhood game of football. He must have stronger bones and more durable muscles and internal organs. But then, there should have been damage done to the bark of the tree, and there was none.

___Another instance of this inexplicable great strength and durability occurs when Percy is combating a five-headed hydra. Each of the hydra’s heads is the size of a prize-winning pig­ (more than 800 pounds) and is covered with broad, hard scales. When each hydra head in turn lunges to strike at Percy, he blocks the attack with his shield. In fact, he easily deflects them with his shield. The heads recoil from the shield as though their mass and the strength of their necks was less than the head and neck of a common goat.

Since force is equal to mass multiplied by acceleration, in order to successfully deflect a hydra head Percy would have to either have the same mass and acceleration of striking as the hydra, or he would have to have a tremendous striking speed to compensate for the difference in mass between he and the head. Since there is no indication of Percy having gained the extra mass, not increasing in size or apparent density, he would have to strike the hydra with an acceleration of 55 miles per hour in one second, if he was able to put his entire mass behind it. If only considering the combined mass of shield and arm, with their combined weight at twenty-four pounds (arm: 4 lbs., shield: 20 lbs.), Percy would have to swing at the monster with an acceleration of 500 feet per second. That’s from zero to 340.9 miles per hour in one second. This could not have happened because he would have moved faster than the eye could detect. He was, in fact, easily seen courageously repelling the vicious and apparently light-headed hydra. On other occasions various demi-gods play capture the flag with real swords and cut each other to ribbons with no explanation as to why this would be of no mortal threat to them. Only Percy is shown to have the ability to supernaturally heal himself with water. (see blog post "Video Clip 2 - Hydra Battle")

___Before setting out on his quest Percy receives a pair of winged shoes, from a new friend, a fellow demi-god, a son of the messenger god, Hermes. One peculiar thing about these shoes is that they seem to serve not only as a means of propulsion, but also to free the wearer’s entire body from the usual effects of gravity, and even inertia. Luke, another demi-god, tries to intercept Percy on his way to Mount Olympus. With his own pair of winged shoes on he lunges at Percy and misses, flying past him. Traveling no more than one body length beyond Percy, he checks his forward progress, and flips horizontally around a vertical axis in order to kick Percy in the face. The law of inertia describes the tendency of an object to remain in whatever state of motion it was previously in. An object at rest will tend to stay at rest, and an object moving in a certain speed and direction will tend to continue in that same speed and direction. While it is conceivable to flip around like this by shifting the body’s center of mass by swinging one’s arms, it is not conceivable to cease forward momentum through the air without exerting force in the opposite direction. Luke therefore must either be able to turn off or on the forces of inertia and gravity or bend them according to his will, or he must be employing some kind of invisible forces of attraction and repulsion, such as Willy Wonka’s “sky hooks” in Roald Dahl’s The Great Glass Elevator. (Or, his motion is being guided by ropes attached to a body harness.) In another instance Percy flies horizontally at a very slow speed. It is not too much of a stretch to believe that a winged shoe flier might fly almost horizontally at a high velocity, being supported by aerodynamic lift. However, traveling at a slower speed, there is no conceivable means of support. The shoes must therefore make the wearer lighter than air, thus enabling them to float. Without the aid of supernatural intervention or manipulation, it is not very likely for wings, two on a shoe, to be able to generate enough lift even to cause the wearer to levitate, let alone fly like Superman.

___In addition to his winged shoes Percy receives or obtains a shield, which secretly contains the famed Bolt of Zeus, and a bronze pen, which somehow, between magic and mechanism, transforms into a 3-foot long sword when clicked. The discovery and use of the Bolt is the turning point of the whole movie. Once Percy discovers it he has only to escape from Hades and return the bolt to Mount Olympus. The Bolt is first used by Persephone, the wife of Hades, in order to help the adventurers escape. When Persephone discharges it at her deranged husband, what appears to be bolts of electricity shoot towards the target connecting with a concussive blast which knocks the Titan senseless. Later, when discharged at Percy and his companions by Luke, the bolt recoils in his hands. This should not happen unless the substance discharged has considerable mass (Force = mass x acceleration). There would very little, if any, force of recoil felt by the bearer of the Bolt because electrons have such negligible mass in this instance. Perhaps this lightning of the gods is specially equipped with enough mass to exert a force on a body. That would explain why Percy was able to deflect the bolts from the one Bolt with his pen sword when Luke attacks him a few sequences later. When the bolt of energy or electricity contacts the concrete wall of the Empire State building, the wall explodes violently. Trees have been known to explode when struck by lightning. This is due to the electrical current heating the moisture in the flesh of the tree beneath the bark to boiling. The steam generated causes the bark to burst asunder. It is conceivable for a wall to explode if it was porous enough and had absorbed enough water. The steam is the agent that causes the explosion. In the case of the wall of the Empire State building this seems unlikely.

(see blog post "Video Clip 3 - Percy vs. Luke")

___Many of the events in the story do require the suspending of belief. When the hero survives catastrophes due to miraculous circumstances the viewer may scoff. Lightning does not behave like a missile launcher. The ankles are possibly the worst place on a person to have a flight propulsion system. And alas! No person could ever be so impervious to damage as the characters in this story. The viewer may however, thrill with delight as they let themselves be deceived. But it is a strange deception when the viewer is fully aware of what is false and submits to it anyway. It is the delight of a child-like imagination, which fuels creativity and hope. Internationally acclaimed director of animated films, Hayao Miyazaki has said, “Realism in the service of imagination. Imagination in the service of living real life.”