The Laws of Physics in an Animation Universe

Ice Age 3: Dawn of the Dinosaurs is set on a distant world undergoing a prolonged, and uncharacteristically warm, ice age. Wooly mammoths and saber-toothed cats roam the snowy, and sometimes not so snowy, planes; while odd shaped and poorly bathed sloths make futile attempts to utilize their cognitive array. All is well; except maybe in the instance of the tiny Scrat, whose acorn woes know no bounds... I often wake in the depths of the night, covered in cold sweat, perused by nightmarish visions of acorns; for in my dreams I have peered in to the cold eyes of despair and touched the cackling hell that is acorn ownership.

Rather than subject oneself to that kind of adversity, one could alternatively invest in the geological sector. Say what you will but you probably won’t find yourself climbing a tree in a thunderstorm to save a plot of land, which inadvertently rolled away while you were on the phone with the in-laws.  In this world porous formations dominate the geological landscape which has a number of benefits. When thrown out of your high rise apartment by an angry wife one could fall with relative peace of mind, knowing that upon impact the small cells making up the terrain will collapse and absorb ones kinetic energy.

Timecode [00:03:10] shows our wayward hero meeting the floor of a canyon, face first, after a speedy plunge. He walks away unscathed but leaves a detailed extrusion in the topology. On the other hand a large force distributed over a large area results in stable support. Timecode [00:03:18] shows a wooly mammoth run by without making holes in the ground.

Timecode [01:25:42] shows the female Scrat push an acorn in to the ground. It goes in suddenly with force but quickly stops as the energy is dissipated by the crumpling lattice of the geological formation. When more force is applied the ground breaks up in wide spreading cracks, suggesting the lattice becomes denser with depth; when sufficient force is applied the lattice shears along the plane of weakest connections. This behavior is consistent with a porous structure.

Inertia seems to hold in this world. While falling from your high rise apartment, having aforementioned peace of mind, one does not have to worry about landing in the thorny bushes covering the perimeter of ones fine domicile. Knowing that your wife gave you an initial velocity in the horizontal direction one can be sure ones future does not include an awkward conversation with a doctor regarding extraction of things from other things.

Timecode [00:13:49] shows the sloth, while sliding down the mountain, let go of two eggs above his head prior to entering a hollow log. Upon exiting the log he finds them where he left them; above his head. Since no different forces acted in the negative X direction on the eggs they continued to travel horizontally at the same speed as the sloth. In the Y direction the forces acting on the sloth and the eggs are the same however, the eggs are in free fall while the sloth is sliding down a hill. Part of the force due to being in the gravitational field is converted in to horizontal motion for the sloth. However because the log was very short the fact that the eggs were accelerating downward at a faster rate than the sloth can be ignored as there is not enough time for them to drop a non-trivial amount.

As a corollary; momentum is conserved. Timecode [01:17:40] shows the tiger saving the sloth by knocking him out of harms way. Because the tiger has a large mass relative to the sloth, and because momentum is conserved, when the tiger hits the sloth he experiences a small acceleration and continues virtually unimpeded on his trajectory. The sloth on the other hand, having a smaller mass, is violently accelerated out of harms way.

This world also features exaggerated paths of action. When the wife reaches for a household appliance of significant mass and acceptable geometry to launch in your direction, one could exploit the fact that her hand will travel far back before beginning its inevitable motion forward. This could be critical in giving one a chance to successfully dodge the projectile by providing an early warning system.

Timecodes [01:25:24] and [00:47:09] show characters follow through with the motion of their limbs and facial muscles in a way that would indicate high inertial mass. The inertial mass isn’t necessarily equal to the gravitational mass in this world and could be very high for most elements. As a result it requires more time to slow a moving limb, resulting in it traveling on its original trajectory for a longer period of time. The same could apply to facial muscles. Once your bushy eyebrows and floppy ears are in motion it takes time to stop them.

On a few occasions this world does not conform to our laws of physics. Timecode [00:20:39] shows what I call the impossible soap bubble. The male Scrat tries to catch up to the female Scrat by jumping inside his soap bubble and hitting the top with his head to translate it vertically. This would not be possible in our universe because during the jump the Scrat would apply a force to the bubble in the negative Y direction; causing it to go down. His momentum upward would be equal to the momentum of the bubble downward. When his head would impact the top the momentums would cancel out; him and the bubble will return to accelerating downwards at “1g”. At best if there was no gravity he would break even but with it he won’t even get that.

Timecodes [00:36:40] and [01:25:45] show objects and creatures stretch greatly under relatively low forces. The Scrat fight scene and the Scrat goo scene show relatively weak molecular cohesion. The attractive forces between molecules are weak enough that one can stretch once own body. In addition these forces are not proportion to 1/r^2 like our universe; they stretch yet hold. I would say that while the forces are weak they are more proportional to 1/r^1 as they do not wane at a distance as quickly as in our universe.

Animators seem to hold on to the majority of probable physics to create an environment the average person can relate to. They alter specific scenes to bring comedy or emotion in to the work or to otherwise emphasize something. I think creating physics that are drastically different works well in abstract games but in majority of the films, shows and games a fair amount of our physics has to be present to make a connection with the audience. Much like one designs an audio amplifier to give the most accurate reproduction possible, then colors the sound with a specific harmonic distortion signature, animators create a realistic landscape and alter it in specific ways to communicate better with the viewer.