user21643: An acquaintance whose family was from Turkey, told me that the pieces move the way do based on ideas about Persian warfare.  Moving in a rank or file was considered earthly, and moving diagonal was heavenly.  
The king and advisor (queen) are combination of earthly and heavenly power. They are both equal in power, but the king can only move one space at a time, because he is burdened with the weight of command.  
The pawns must move in an earthly way, but can only capture with the help of god (so the capture is diagonal like the bishop).  
Everything else is fuzzy: There was something about why the pawn's first move could be one or two spaces.  I can't remember anything about the knights.  There was a reason rooks where earthly.  There was also a bit about why castling goes the way it does, and why pawns can be promoted.
Does this ring a bell with anyone?  It was a cool story, and I'd like to hear the whole thing again.

user19877: Your acquaintance is right, and wrong to some degree, since before chess went to Persia, its precursor is considered to have been invented in India. It was based on troop movements there, so they had already been established by then, even if they were later modified.
This is taken from Wikipedia here:

Precursors to chess originated in India during the Gupta Empire.
  There, its early form in the 6th century was known as chaturaṅga,
  which translates as "four divisions (of the military)": infantry,
  cavalry, elephantry, and chariotry. These forms are represented by the
  pieces that would evolve into the modern pawn, knight, bishop, and
  rook, respectively."


21643: <p>An acquaintance whose family was from Turkey, told me that the pieces move the way do based on ideas about Persian warfare.  Moving in a rank or file was considered earthly, and moving diagonal was heavenly.  </p>

<p>The king and advisor (queen) are combination of earthly and heavenly power. They are both equal in power, but the king can only move one space at a time, because he is burdened with the weight of command.  </p>

<p>The pawns must move in an earthly way, but can only capture with the help of god (so the capture is diagonal like the bishop).  </p>

<p>Everything else is fuzzy: There was something about why the pawn's first move could be one or two spaces.  I can't remember anything about the knights.  There was a reason rooks where earthly.  There was also a bit about why castling goes the way it does, and why pawns can be promoted.</p>

<p>Does this ring a bell with anyone?  It was a cool story, and I'd like to hear the whole thing again.</p>
 19877: <p>Your acquaintance is right, and wrong to some degree, since before chess went to Persia, its precursor is considered to have been invented in India. It was based on troop movements there, so they had already been established by then, even if they were later modified.</p>

<p>This is taken from Wikipedia <a href="https://en.wikipedia.org/wiki/History_of_chess#Origin" rel="nofollow noreferrer">here</a>:</p>

<blockquote>
  <p>Precursors to chess originated in India during the Gupta Empire.
  There, its early form in the 6th century was known as chaturaṅga,
  which translates as "four divisions (of the military)": infantry,
  cavalry, elephantry, and chariotry. These forms are represented by the
  pieces that would evolve into the modern pawn, knight, bishop, and
  rook, respectively."</p>
</blockquote>
