Matchstick pattern analogy to thought

A system for classifying basic thought processes, proposed by Piers Anthony in On a Pale Horse, the first novel in Incarnations of Immortality.

Apologies for the awful ASCII diagrams, but the patterns are fairly straightforward.

The first pattern of matchsticks is a series:

  - - - - -

This represents linear thought, or chain logic. It is definitive and straightforward, although to use it, one must have all the correct facts, and be able to connect them in the right order. Additionally, a weakness of this pattern is that if the chain is in error at some point, the conclusion will be flawed and inaccurate.

The second pattern is in parallel:

     -
     =
     =

This represents many facts, all pointing towards the same conclusion. While not as far-reaching as the first pattern, it begets fewer errors. It is very powerful, yet tends not to advance thought far.

The third pattern is divergent:

     |
    - -
    / \

This is the creative formation. Thoughts go off in all directions, relating to the main idea. Useful for problem-solving where there is not a set procedure, its strength is new solutions. However, this pattern is only useful at the onset of a block. Continuing thought in this pattern will lead to an entirely different topic, tangential to the task at hand.

The fourth pattern is the schizoid formation:

   / \
   |_|

It symbolizes going around and around in a circle, trapped in one's own thoughts. While not necessarily productive to the outer world, internalizing can be useful to the inner development of the individual. When "coming to terms with an ugly necessity," contemplating one's circumstances, meditating on a desired goal, or simply enjoying oneself, this is a useful pattern.

The fifth pattern relates to intuition:

   -|||-

This is "a sudden jump to a conclusion," taking facts into consideration unconsciously. Not the most reliable method, it results in conclusions that are hard to justify. However, sometimes it is the only way past a block in understanding. After a conclusion is reached, one can then go back and fill in the missing parts by investigation or correllation with knowns.

These are only the most basic of basic processes, textbook examples, if you will. Actual human thought takes a combination of these, as well as wild leaps, daisy chains, random odd associations, and is constantly dealing with new data besides. However, I feel that these are a good guideline for when one happens to be stuck in an untenable situation. All text in quotes is Piers Anthony's original text from the book, as are the diagrams, appellations and very brief descriptions of the patterns. All past the concept is mine, pure common sense.

Another matchstick analogy illustrates a common flaw in our thinking, an inability for many to think different [ly] in order to solve novel problems. For example; try and think of a way you could make four equilateral triangles

                    
                   /  \
                  /    \
                 /      \
                /        \
               /          \
              /            \
             /              \
            /                \
           /                  \
          /                    \
         /                      \
        /                        \
       /                          \
      /                            \
     /                              \
    /                                \
   /                                  \
  /                                    \
 /                                      \
/                                        \

 ----------------------------------------

Kinda like this one here

Out of six of these matchstick type things (presented below by our very own lovely Vanna White)

 O   -------------------------------------- 
_|_/
 |
/ \ 

Hokay. Think about it for a bit before you scroll down to fulfill your instant gratification addiction.Visualize a bit. Bend around some of the paperclips on your desk. It's kinda hard. Most people give up with something like this:

                   
                  /  \
                 /    \
                /      \
               /        \
              /          \
             /            \
            /              \
           /                \
          /                  \
         /                    \
        /                      \
       /                        \
      /                          \
     /                            \
    /                              \
   /                                \
  /                                  \
 /                                    \
/                                      \

 --------------------------------------

 \                                    /
  \                                  /
   \                                /
    \                              /
     \                            /
      \                          /
       \                        /
        \                      /
         \                    /
          \                  /
           \                /
            \              /
             \            /
              \          /
               \        /
                \      /
                 \    /
                  \  /
                   

And they don't really know what to do with that extra one, becuase the only real thing you can do with it is stick it out at some funny place where it'll be all alone, and won't really do anything. But I insist, it can be done. The trick, is to think in 3D, like this;

                                                                                                                                                                                                        
                                                                                                                                                                                                        
                                                                                                                                                                                                        
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Psychologists refer to it as a fixed mental set - basically you get stuck thinking about a problem in a specfic context even if possible solutions exist within others. In this case, when people can't find a solution within a two dimensional context (which there is none), they jump to the conclusion that there is no solution, which is wrong - the matchstick problem can be solved, but only in three dimensions. Fixation within certain parameters prevents people from approaching problems from a different angle and finding novel solutions.