Orthogonal

Orthogonal, or orthogonally, is a technical word used to mean "not diagonally". It's shorthand for "East-West or North-South" or (for 2 dimensions) "up or down or left or right".

   Diagram 1:

    xox
    oCo
    xox

• The center tile, C, is orthogonal to the four o tiles.
  
• Each o tile is orthogonal to the center C tile, plus two x tiles.
  
• The x tiles are all orthogonal to two o tiles.
  
• No o tiles are orthogonal to each other, nor are any x tiles orthogonal to each other or the C tile.

In the domain of Dwarf Fortress, this concept is crucial in many aspects of construction, fluid pressure, and other areas. Especially in above-ground construction, where a tile not connected orthogonally to something either cannot be built, or will collapse.

These █'s are all connected orthogonally to at least 1 other █. If this was constructed walls or flooring, it would hold up:

  ██████   ███
    ██     █
     ███████

These █'s are not all connected orthogonally to another █ - some connections are only diagonal. If this was constructed walls or flooring, some parts would collapse, or not be legal to construct:

  ███ ██    ██
    ██     █
      ██████