Similitude between the progression in the world and puzzle mechanisms

The most basic rule of The Witness is that you have to find your way through the island (by walking) and through the puzzles (by tracing lines). And the two are often connected. More precisely, it is often possible to draw analogies between the design of an area and the design of the puzzles in that area.

Relation with other principles
The idea that there is a similitude between the way we progress in an area and the puzzle mechanisms relates to the opposition between symbolic and intimate knowledge: Navigation in the world usually only requires intimate knowledge, and so we use symbolic knowledge and analytical thinking only to solve puzzles. The whole idea of noticing the similitude between the progression in the world and the progression in the puzzle is to transfer our intimate knowledge gained by progressing in the world into a symbolic knowledge that can be used in the puzzles, and reciprocally.

Start Area
In the start area, you learn that after completing a puzzle a wire will light up and that you just have to follow the wire to find the next puzzle (similarly, in the puzzles, you light up a path). But you quickly learn that you cannot always do it that easily: in the environment as in the puzzles, there are obstacles, forks, multiple exits and multiple starting points.


 * Obstacles: in the start area, the wires pass above two walls, and you quickly understand that you cannot jump over them so you have to make a detour. Of course, the whole area is also enclosed by walls.


 * Forks: think about the puzzle in one of the tower, that also controls the opening of the coastal footpath, each possible exit opens a different path.


 * Multiple starting points: there are three wires connected to the exit door of the area, but you can only follow one wire at a time.

Actually, the only puzzle rule that has no correspondence in how you progress in the world is that you cannot cross your path.

Moving platforms
In the Marsh, the big yellow squares on the floor allow the transfer of knowledge between the environment and the puzzles, since they definitively look like the blocks in the polyominoes of the puzzles. The moving platforms make an explicit use of this correspondence (the second moving platform even uses non-yellow tiles), in which the lines you draw in the puzzles represent the frontier between platforms and water. In other words, the areas containing polyominoes represent platforms on which you can walk, and areas without polyominoes represent water.

For the moving platform puzzles, this representation is an exact mapping: each polyomino block maps to a well-identified platform in the world. The puzzle solutions and platform states are synchronized so that changing a puzzle solution will cause a displacement of the corresponding platform. The second moving platform even completes the analogy by using the same rotation direction (clockwise or anticlockwise) than the line drawn in the puzzle. The moving platforms in the red structure add a meaning to blue-outline polyominoes, making the cells removed from the yellow polyominoes represent platforms on the lower floor, in accordance with the correspondence between color mixing and vertical directions.

Todo: paragraph on white vs. yellow lines.

An interpretation that works for all puzzles
A similar representation can also be seen in other (static) puzzles, but it is then more symbolic. We should rather talk about an interpretation of the puzzles, but this interpretation can help understand some other aspects of the puzzles and of the Marsh area. In this interpretation, the areas containing polyominoes represent platforms above the water level on which you can walk, and areas without polyominoes represent water. In the solution paving, Yellow-filled polyominoes represent all walkable areas. Blue-outlined polyominoes represent underwater rooms. So the solution of the puzzle — once the Blue-outlined polyominoes have been subtracted from the Yellow-filled ones — represents the walkable areas that can be seen from above the water surface. This interpretation is once again in accordance with the correspondence between color mixing and vertical directions. Todo: rule for fully-cancelled yellow polyominoes.

An interpretation that matches the design of the Marsh
This interpretation allows to transfer rules or strategies used in the puzzle to the design of the environment. For instance, the last puzzle of Row 1 teaches the heuristic: in the solution paving, at least one of the polyominoes must touch the border of the puzzle. This constraint is also respected by the design of the platforms in the Marsh: no platform is an island, all platforms are connected to the firm ground on the border of the area. Similarly, puzzles in Row 3 requires to place the polyominoes so that they form a path covering all the polyomino cells, in a way that reminds how the metal platforms are used in the Marsh area to create paths between distant places separated by water.

The two states of shortcut doors
The two shortcut doors in the Marsh area have the unusual (but not unique) property of having two puzzles on them. Solving the two puzzles (left one first, then right one) will open the door. In these two pairs of puzzles, the left one represents the “closed” state of the door (before solving the puzzles) and the right one represents the “opened” state of the door (after solving both puzzle). This static representation of actions is by itself an use of the principle of a similitude between the progression in the world and puzzle mechanics. Here the possibility of a two-state interpretation relies on a similitude between the left and right puzzles, so that the two puzzles can themselves been understood as two variations on a same design: In the first shortcut door, the two puzzles use the same polyominoes in the same corners but differ in grid size; In the second shortcut door, the two puzzles have the same grid with the same L-shaped rotatable polyomino in the top-right corner, but it is Yellow-filled in the left puzzle and Blue-outlined in the right puzzle. (Note also how the start en end positions are the same for the puzzles of both doors, and how they both use polyominoes in the corner cells, including the ones next to the start and end positions).

The way each puzzle conveys the idea of its corresponding state also relies on the interpretation of puzzles that is specific to the Marsh: In both pairs of puzzles, the start point and end points of the left puzzle are in different areas and would be separated by water, but these two points are in a same walkable area in the puzzle on the right. This interpretation correspond to the establishment of a walkable path according to the principle of connecting distant or separated areas that is important in the Marsh and applies to doors.

Relation with other principles of the Marsh
Note also that the Marsh is one of the areas that introduce the principle of opposition between symbolic and intimate knowledge, which can be seen as a meta-principle for the one discussed here.

Symmetry Island
To do...

Jungle
To do... basically what has been said here (three vertical levels, and looking for your path using sound).

Monastery
To do...

Shady Trees
To do...

Confirmations
The existence of such analogies has been indirectly confirmed by game artist Luis Antonio saying “I (...) tried to define a navigation that would take into account the puzzle design.”

See also the Evidence for the existence of Design Principles