Dimensionality of Information

by Robert Simple on 02/18/13 10:23:00 am

The thoughts and opinions expressed are those of the writer and not Gamasutra or its parent company.

What does one think when they see the word dimensionality when considering games? I believe most of us would think about the game world, or more likely the game graphics, but both of these assumptions are not what I mean when I speak of dimensionality in this article. I’m not saying that 2D and 3D graphics are not dimensionality, but I am trying to describe context of understanding during game play. What if I were to tell you that information is also organized into dimensions? In order for a player to fully comprehend any game, they must understand the dimensions of information that the game expects and the dimensions of information the game will provide. Most games developed in the past and today exist in the realm of zero and one dimension of understanding. I believe a mathematical, logical, and relational definition and a few examples are needed in order to fully catch what I am talking about.

Let us begin with the mathematical definition, that I’m sure we’re all familiar with. Zero dimension objects are known as points, a singularity or individual spot in space. One dimension objects are something that exists along one direction. Two dimension objects are something that exists along two directions. Three dimension objects are something that exists along three directions. These are best described as a point, a line, a square, and a cube respectively. When describing a change that occurs on a zero dimension object, there is no definition, since a point without respect to any direction cannot move. When it comes to a one dimension object on the other hand, the point can move along one direction and every point along the direction is considered part of the same line. Similarly when it comes to two dimension objects, we can move the point along two directions simultaneously. With three dimension objects we are capable of moving the point along three directions simultaneously. So the real definition to be understood in mathematics is that the dimensionality is the understanding of how many directions can be observed and how many directions can be changed.

Let us move on to a logical definition of dimensionality of information. When I refer to a logical definition, I’m not talking about some physical description, but the level of deduction the player is required to perform. A zero dimension understanding means that the player has a simple deduction, where as a one dimension understanding means that a player must deduce a linear amount of information and similarly with increasing dimensions, but perhaps an illustration of the same process but increasing dimensions like mathematics is needed. So what is a simple game to have a zero dimension understanding and requires deduction by the player? The number guessing game; here is a game where the player is asked to guess a number between 1 and 100. At every point in the game, the player makes a guess as to what number the game is holding as the answer. The guess is correct, lower than the value, or higher than the value. It’s upon receiving a response from the game, that the player gains an understanding of information and deduces what their next guess should be. So what happens when we extend this same game into one dimension? We end up with another game, and like the number guessing game, it is considered simple. It’s mastermind, here is a game where the player makes a linear guess about colors involved in a password. The password is either correct or the player is given back a linear amount of information about how correct the guess is in relation to the actual password. The player uses the information given to deduce what their next guess should be. Now we extend the game once again into another dimension and once again we end up with another game, it’s Minesweeper. The player is asked to locate the mines, and unlike the input method of mastermind, the player can either make a single point guess or an area guess that is a two dimensional input method. The player is given a response that informs them of hitting a mine, or how many mines are nearby. Luckily the original designer was kind and felt it would be nice to say when a player clicks a square which is not a mine and has no mines around it, the game reveals all nearby squares as well.

Next is the relational dimension of understanding, which is similar to logic, except that instead of having deduced understanding, a player is given two sets of information and the player is required to understand what the relation between the two sets is and then enter an appropriate response based on the relation. This type of understanding is best represented by the classic Myst series and for my example I will use one of the puzzles from Myst II:Riven. If you have played this game and have not solved this puzzle, I am sorry for divulging the relation of the puzzle, for I know that the main purpose and enjoyment of the Myst series is for the player to gain understanding of relational information. In order for the player to gain access to the latter parts of the Riven world, the player must activate a set of machines which hold transportation books. In order to activate these machines the player must scour the Riven world and find a power plant mechanism which provides power for these machines to operate. The problem comes when the player finds the power plant; in order to activate it, the player must place 5 out of 6 colored marbles on 5 specific squares on a 25x25 grid. One can easily become overcome by the near limitless combinations to which these marbles can be placed and therefore a simple guess and check solution would consume way more effort than solving the puzzle. Being true to its design, the world of Riven has information scattered over it and the player is responsible for finding this information and putting it all together. The first part of the solution is determining what five squares are to be used. The second part of the solution is determining what color each of the five squares should be. The information that is relatable to the position of squares is found when the player finds themselves on an island that has a miniature grid and as the player stares at the terrain formation of the grid, they find that the grid is actually a compressed model of the world of Riven. As the player scans over the terrain features, they will notice 5 domes that stand out. This is the zero dimension understanding, no real relation, just recognition, five circular domes is five grid points, and they are placed on a miniature grid to make it more obvious to the player. The next piece of the puzzle is determining which colored marbles to place at these five locations on the grid. An observant player would notice that the domes that are placed in the world of Riven have symbols on them and these symbols are a variety of eye positions. These symbols alone have no meaning, until the player comes across an underwater viewing station. The station has several observation posts or cameras and they reveal some underwater construction. What is directly on the screen is not the clue, but sitting on the control console is a set of eye position symbols. Not only does pressing these eyes make the view screen shift between cameras but each camera is lit by a particular color. This gives us a one dimension set of information, a set of symbols that correspond to colors. Looking back at the domes, the player can see that one particular eye position symbol is highlighted and all others are dull or faded. By combining the linear information of symbols to colors with the highlighted symbols on the domes, the player can conclude that each dome has a specific color associated with it. Therefore a two dimension understanding for solving the grid power plant puzzle is for the player to relate the color information to symbols, and relates the symbols to domes. Combining the zero dimension information of the miniature grid locations with the two dimension understanding of color gives the solution to the puzzle, five colored marbles placed on a grid. I may make this solution sound simple, but trust me, anyone who has played a Myst series game struggles to put these relational ideas together.

Although from the context of intelligent design (and no, I’m not talking about God), we gain another understanding of the dimensions of information. Suppose we wanted to construct an intelligence system for determining the next guess in our logical examples, then it also becomes apparent about the dimensions of information. For instance, the number guessing game requires the intelligence system to hold two variables, the lower and upper bounds. Mastermind requires the intelligence system to hold onto the set of possible solutions and with each guess it removes all guesses that would not correspond to the given response. As for Minesweeper, this is unfortunately an NP-Complete problem (very interestingly), but nonetheless does have rules for inference to a point. When it comes to relational information we end up with the same idea of expanding our frame of reference and a programming language like prolog makes the best use of relational problem solving.

Uh-oh, I’m talking too much again for a single article, or am I? I know that my understanding of dimensions of information in this nature of mathematical, logical, and relational has made every game a simple understanding. Every game that I found challenging before is not so challenging afterwards, and all future games to be developed will most likely be just as simple to understand. I ask you, after reading this article, “are any of your games difficult to understand?” This is because most games exist in the realm of zero and one dimension understanding, whether it’s mathematical, logical, or relational. When will we finally be developing three dimensional games? I assure you, whoever does, will be considered a genius in design principles, but let it be known here, it’s already been defined by my simple game theory and three is not the end of dimensionality.

My final point is to say that I am entirely open to criticism and conflicting views, feel free to tell me anything about your own game theory ideas or comment on what I have been talking about here. I will be spacing out my articles to give people time to read, review, and respond to what I am writing. Also it will give me time to review what others are saying or asking and give an appropriate response. I look forward to any and all feedback.