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Entropy and the puzzle




What is your approach to solving a puzzle? I assume it starts with flipping over each cardboard-brown piece to make the patterns face up. We then transition to a narrowly focused mission to find the edges to visualize the frame, size, and scale. With a colorful array of harvested edge pieces to the jigsaw, you may find yourself with a momentary hyper-attention focus on pattern recognition and seeking the four corners. The properly sequenced edges have created the frame of your mission to validate Newton’s first law.

The law of inertia, also called Newton’s first law, postulates in physics that, if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at a constant speed unless it is acted upon by a force. - Britannica

The next tactic to solving the puzzle may differ depending on the person. Some people may peck for like colors and singularly piece patterns together while staring at the box cover. Others may first spend the time establishing siloed piles of like colors and then transition to the assembly phase. Not surprisingly, an engineer may break down these piles into convex and concave patterns dependent on the individual piece. Regardless of the strategy, the chaos that once existed in a box of a thousand optimally cut pieces begins to resemble the motif.


At this moment, friends and family may walk by your table and choose to join in. Those initially avoiding the first phase now want to contribute to the mission. In a thousand-piece puzzle, the frame is less than 13% of the entire puzzle. However, without a frame, the first follower may not have the courage to join.


However, with the frame established and the required courage to be the first follower, others will join. Piece-by-piece, the end seems near as more followers have their hands spinning, focusing, and plugging in each piece. Casual conversations accompany the paving of each piece, and short-lived wins finding an impossible piece creates the necessary motivation to seek the next problem piece. The rate of correctly placing each piece improves as fewer pieces dissolve the chaos within the edgeless pile. Finally, with a sign of relief, the last piece is inserted. Accomplishment achieved.


The law of entropy states that the more chaotic a condition is or the more something is in disorder, the more entropic we would consider it to have. To counter the disorder, one must initially establish order. It is from the order that entropy improves, and we see the rate of improvement increasing with an exponential curve due to less resistance creating the chaotic state.


Motivating someone to start a puzzle with you may not be the easiest thing to do. The entropy is at its peak within this moment, and the bystander may see the chaos as intimidating and not warranted. Yet as the entropy reduces to a level that breeds participation in the mission, a little less disorder created by a leader can motivate the first follower.


The term for this is “goal gradient” motivation and has origins in a behaviorist named C.L.Hull. He saw acceleration patterns in rat maze navigation with the proximity to an end goal. As the initial disorder is removed and inertia has begun, the goal is recognized by the bystander. It is from the recognition that the rate necessary to achieve the goal is increasing.

This pattern of increased effort in proximity to goals has been termed “goal gradient” motivation, a phenomenon originally described in the 1930s by the behaviorist Hull when observing patterns of acceleration in rat maze navigation. Hull, 1934

As leaders, we must take the first steps to remove the chaos and establish the foundations of order. We have to find the corner pieces, and not detract from the mission when others walk by not wanting to assist. With the borders and the frame established, the “why” is now understood as we are nearing an accomplishment. We have overcome established inertia to get to a level of entropy that encourages the followers. A team harmonizes the collaborative cognition to the mission. And as a team, the last piece of the puzzle is placed.



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