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Persuasive Games: Puzzling the Sublime


December 23, 2009 Article Start Previous Page 2 of 3 Next
 

The Mathematical Sublime

In his eighteenth century tome on aesthetics, the philosopher Immanuel Kant distinguishes between the beautiful and the sublime. He relates beauty to non-logical, subjective aesthetic judgments about the form of things. He describes the sublime in terms of a relationship between the faculties of imagination and reason.

Kant characterizes two kinds of sublimity. The mathematical sublime is a feeling of boundlessness or vastness, as caused by reflections on the infinitely large. A pyramid is an example of such a structure, one that cannot be wholly taken in in a single gaze.

The dynamical sublime describes the feeling of being overpowered. This latter sense often comes from natural objects such as the face of a cliff over the sea, or of an enormous thunderhead. Sensations of the mathematical sublime arise from largeness; sensations of the dynamical sublime arise from fear.

I submit that the meaning of games like Drop7 and Orbital are best understood in relation to the sublime, and particularly to the mathematical sublime.

Drop7 asks the player to drop discs emblazoned with a number from one to seven down the columns of a 7x7 grid. Gravity carries them until they reach bottom or stack atop other discs. If a disc's number matches the quantity of discs in a row or column (no matter their numbers), the matching disc disappears.

Grey discs cannot disappear, until they are unlocked to reveal a number. This is done by causing a numbered disc to disappear adjacent to the grey disc two times. Points are scored for each disappearing disc, with bonuses awarded for chains and board clears.

Much is left to chance in Drop7. The board starts with some discs already in place, and each disc the player must place is drawn randomly. In some cases, a convenient number appears, allowing the player to execute a planned chain or avoid a dangerous situation. In other cases, an undesirable disc forces the player to change plans. Furthermore, when grey discs appear, their contents remain unknown to the player until surrounding discs reveal them.

All together, these mechanics require the player to reassess the state of the board each turn. Grey discs can be taken as uncertainties, but doing so is unwise. It's much smarter to assume the worst of hidden numbers and plan accordingly.

Yet, even then, each turn requires a total reassessment of the state of the board based on the last turn's results and the present disc. While emergent consequences exist in chess and go, Drop7 makes the long-term impact of a single move visible even to the amateur player.

The experience of playing Drop7 is thus one of planning present moves against a series of contingent future ones, given a set of slowly changing uncertainties. The vastness of possible moves is calculable for a moment, until it is disrupted by the randomness of new information. This is where the player finds the game's mathematical sublimity.

Mastery of the game is always temporary, as each move collapses the innumerable possibilities that exist before a disc drops into the fixity of a new situation just after. Yet, unlike the constantly changing dynamics of a chess or go board, each move in Drop7 reveals something more about itself later on, as previously unknowable impacts begin to exert torsion on the present.

In Orbital, the player fires orbs from a rotating gun at the bottom of the playfield. These orbs ricochet off walls and one another, until inertia stops them. Once stopped, the orbs grow until they touch a playfield wall or another ball.

The player's goal is to break the orbs by striking them three times with new ones (a large counter on each ball shows the current hit count), scoring a point. However, should an orb bounce such that it passes a white line just above the player's gun, the game is over. Following its cosmic theme, the orbs in play create gravitational fields that alter the path of subsequent ones.

Like Drop7, players of Orbital suffer under an environment dependent on the increasing contingency of aggregate moves. One tactic for play involves estimating the trajectories of orbs based on the friction and gravity of the environment. One can, for example, attempt to lodge a cluster of small orbs in the corners, increasing the likelihood of destroying many with a single shot.

Yet, as each orb settles, it alters the gravity well of a part of the playfield, effectively erasing whatever understanding the player had developed about the earlier topology. Notably, this same disorientation occurs even when the player succeeds, since an exploded orb alters local gravity too.

In Drop7, the mathematical sublime enters the game primarily through chance: the random generation of discs under the grey coverings and in the player's hand. In Orbital, there is no chance whatsoever. Every move in the game is calculable. Yet, the vastness of the ever-changing universe makes such planning impossible for the human player, who must win out over both timing and physics to carry out a shot intentionally, whether or not it was well-planned in the first place.

Orbital is less forgiving. While Drop7 slowly winnows down choice until the player is overcome by failure, Orbital puts failure on the screen, a thin, fragile line subject to even the lightest graze.

To play Drop7 or Orbital is to practice string theory, to assess the unknown branches of infinite futures. Whether one plays effectively or not, these games force players to reflect upon the mathematical boundlessness of the systems that drive them, systems that alter themselves with every move.


Article Start Previous Page 2 of 3 Next

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