Learning to calculate

Tactics are NOT calculation. They're certainly part of it, and I dutifully sharpen my tactical blades by doing chess puzzles just about every day (I compose some too!). But calculation is a whole discipline of doing dozens of ply of analysis in multiple lines without moving the pieces and taking into consideration both tic-tic-tok forcing sequences AND all of the resulting strategic furniture.

It's something I can see myself working at in an embryonic way, but there's a huge amount of raw data floating on those squares, and it's hard to know what to calculate how far and how much to trust my own thoughts on the subject (I've been wrong before!).....are there good puzzles/exercises that can help develop calculation/visualization? I can win material, I can checkmate, I can take 2 bishops, promote pawns, and pick on bad structures. But I want to learn how to look not just further but better.

Immediately after every move by your opponent, you should answer the following two questions:

• What are your opponents threats?
  1. A mate threat, or other attacks against the King.
  2. A gain in material.
  3. Gaining a very good position for a piece.
  4. Gaining control of an important square, file, or diagonal.
  5. Any tactical. Or strategic advantage the opponent can gain on the next move.

            Evaluate which threats are real.  Only real threats should be taken into consideration.  For  example, if your opponent is threatening to gain the Bishop pair, you should evaluate the position to determine if this is really a negative. 

• What are the consequences of your opponents last move?

Almost every move has pluses, and minuses to them.  For example, you advance a Pawn to gain control of some squares, but you also lose control of squares.  You move a Bishop to gain control of a diagonal, but you may also lose control of an important square, or Pawn.  And any of the following:

1. Opening a file, or diagonal.
2. Blocking a piece with another.
3. Weakening a square, or Pawn structure.
4. Leaving a piece undefended.
5. And many others things you will learn about.

Some of the most important elements are:

1. The most important consequences are given by Pawn moves because they cannot move back. With every Pawn move, you gain, an lose control of squares. Pawn moves generally open files, ranks, and diagonals.  Therefore, any Pawn move must be well evaluated.
2. All moves have one common, and important consequence: Time. This is why all moves should bring you closer to your objective (Game Plan)
3. The side of the board you castle on is an important consequence. Opposite side castling tends to lead to more aggressive play, while castling on the same side may lead to less aggressive play.  
4. When moving a piece, it is important to understand that some squares become defended, or attacked, while others become unprotected. This is the cause of many blunders, and or oversights during games!  By remembering this, and understanding this, you can cut down on many of your mistakes, and benefit from those mistakes made by your opponent. 

This is a great set of ideas. A lot to digest, and - therefore - a lot to work on. Thanks, Bacon. 

Glad to help

Great advice from @IMBacon. In addition, I suggest two books by Andrew Soltis that address exactly what you are looking for: How to Choose a Chess Move, and The Inner Game of Chess. Both books are about how to think efficiently at the board. The former is a more general view of an effective thought process, while the latter is entirely about calculation.

Try to practice the stepping stone calculation technique.

http://www.braillechess.com/rreid.html

Try to solve white or black to mate in 5 moves(or more) problems.

More or less.

When talking about secret chess, aka what is the best move, aka right-brain, is just kibitzing and right-brain ego. The objective of an OTB game is to play 100-200 elo better and not WWCD(what would Carlsen do).