There is an ancient story in a 2d world named Myrandia of a great battle that was fought over an island called Yulomar that separated two oceans between the land of the Washtaks and the land of the Bicks. On any 2d planet, a land mass in a body of water separates the body of water completely in two. This particular island was of great strategic importance because it was halfway between the two main continents that the two countries inhabited.
The Washtaks were from the west, and the Bicks were from the east. The Washtaks caught wind of the Bicks' plan to take over the island and create a fortress there. They had to act fast. Their leader, a tyrannical type in the likes of Saddam Hussein, ordered a large number of boats to be constructed. He had each household in the city that was closest to the sea construct one boat. The thing you must understand is that since the surface of a 2d planet is linear, to pass anything while traveling, you have to go either over it or under it. To store in one place the number of boats that was needed would have required an extremely deep hole. Deep holes are problematic in 2d because of numerous reasons. Air pockets can form extremely easily, easily suffocating anyone trapped inside. Corkscrew drilling is impossible (3 dimensions are required). Limitations in 2d make extracting dirt from the deep quite difficult. The best way to store things is to spread them out across the surface.
The residents of the city slaved away for weeks, constructing the boats in the least time possible. Numerous skipped meals and lost hours of sleep later, the army's water transportation had been completed. The leader ordered the advance to begin. The residents of the city descended into their underground homes as the army lumbered overhead. The leading regiment of the army hopped into its boat and pushed into the water; subsequently, one boat after another was carried to the shore, tossed in, and the regiment hopped in to follow the boat in front of it. Once in the water, the boats were not able to change their order.
Traveling in a boat in 2d isn't on any top ten lists for exciting multidimensional tourist activities. It consists of staring at the back of the head of the person in front of you for the duration of the trip. Many great philosophical realizations have occurred during boat trips, because that's about the only to do with yourself. After the army hit ground on the shore of Yulomar, the Washtaks charged across the land in an attempt to secure the island before the Bicks arrived. Unfortunately, the Bicks had also arrived on the opposite shore just before them. Like the Washtaks, they sprinted across the terrain, trampling plants and small animals in a desperate attempt to claim as much land as possible. In 2d, the single soldier at the front of the army is the only person that can fight. The battle consists of the two front line soldiers battling it out until one is taken out, then the next person steps up and goes at it. The battle proceeds until one of the armies has been annihilated.
So, the forces clashed head on near the middle of the island and the battle began. If traveling in a boat in 2d is the most boring thing to do, waiting in the middle of an army while the two people on the front lines fight it out is the most nerve-wreaking. It would be like standing in a tight ditch so thin you had to walk through it sideways, with the sun's rays pounding on your skin. All you can do is stare at the back of the head of the soldier in front of you, study every bump and imperfection for several hours as your legs became sorer and sorer. Sweat drips into your eyes and stings like salt on an open wound. You know that as soon as your comrade falls, you are next in line, and that you have to kill an *entire* army just to survive. Here on earth we at least get the comfort of the possibility of survival. In 2d, the only warning you get is your buffer man dropping in a bloody mess in front of you with an ugly face staring at you from the other side as he jabs his sword at you. The average soldier has fought in approximately 0.0 battles. Soldiers are ordered to kill the person in front of them if they try to retreat. Pure havoc would result if this rule wasn't in effect.
Soldier after soldier in the Washtak army fell at the hands of the Bick army. The situation wasn't looking good for the Washtaks (even though they couldn't know given their viewpoint). The battle came to the last man surviving in the whole Washtak army, a young soldier named Dosha. He had waited in the far rear of the army for hours as the battle raged on, far away on the opposite side of the army. He considered ditching the battle since it was apparent that it would never come to him. But then he realized that if the rest of the army in front of him was killed, he'd be the only one protecting his country. Late afternoon, when his hunger had reduced him to considering passing insects as a source of food, the man in front of him suddenly dropped to the ground and an ugly Bick face stared at him from the other side.
After an intense duel with swords clanging and dirt flying, Dosha performed a quick feint and nailed his opponent hard. He proceeded to take out Bick after Bick as he fought on pure adrenaline. Feint, jab, feint, jab, he performed countless times, eating up the seemingly endless stream of them. One of them falls, another is waiting behind him to take his place. Just as twilight approached, he performed his trademark maneuver as usual on his opponent before him. But, the view he laid his eyes on was the most beautiful he had seen in his life. The sun was just flashing out of existence. He was the only man left, the last soldier standing. He was standing on top of the remains of hundreds of dead bodies, the remains of the two largest armies that had ever existed on Myrandia.
Battles in the 3rd dimension run quite differently than in the 2nd dimension. The meeting point of the two armies is a line instead of a point. Maneuvering, which was impossible in 2d, takes on a whole new importance. Lines can be flanked, a front line can retreat through the line behind it, rear lines can see through the front lines to launch stuff into the enemy, such as arrows, cannonballs, and other flaming objects. The element of surprise factors in a lot more. In 2d, you know your enemy is in front of you; in 3d, he can be in any direction, since he could have circled around to your rear. Soldier survival rate is a lot higher, but then there's hardly a possibility of a one-man army as is easily do-able in 2d. Overwhelming numbers, given other things equal, will win.
[ARMY MANEUVERING IN 3D]
If higher numbers help in the third dimension, they are even more of an advantage in 4d. A battle is fought on a "realm". A realm is the analog of the plane in 3d, line in 2d, and point in 1d. Our entire universe is an infinite realm, just as an entire 2d universe is an infinite plane. To picture a 4d battlefield, we use all of the x, y, and z coordinates. Maneuvering in a 4d ground battle would work the same as a space battle in 3d. The battle fronts of the armies are planes. An army with the amount of soldiers of a 3d ground army could all easily fit on the whole front of a 4d army. Individual targets can be destroyed much quicker because so much more firepower can simultaneously be focused on it. A much larger army is required to prevent passage; thus, it is much easier to circumvent or punch through enemy lines.
[ARMY MANEUVERING IN 3D]
[more to come]