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Puzzle Learning

An approach to learning new subjects.


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Jigsawing Towards Knowledge

I view knowledge gain as a jigsaw puzzle. The scope and final picture of the puzzle requires the box, whereas lack of box can make things more difficult:

Regardless, once the border is established, the inner pieces begin to fall in place, giving more and more information with every single successful connection. But ease of completion is superlinear with number of pieces remaining because the already-placed pieces provide significant information for the surrounding missing ones: shape and picture. This narrows the search immensely and makes it much easier to find the correct piece.


Finding the Missing Pieces

The border is the obvious starting point for most puzzles. It establishes the outer edge of the puzzle/knowledge arena, akin to the so-called foundation of certain real-life career fields. For example, traders at Jane Street must be proficient in basic probability and statistics before moving onto developing algorithms. But the important thing is that they know this. They know what they need to know (and sometimes not know) and how best to study it. Veteran traders can guide their paths to optimize time spent learning.

From there various patches of the puzzle are filled out based on a) obvious pictures from the box, or b) pictures that form while randomly trying pieces together. Bridges form between these small islands, linking two seemingly separate areas of knowledge together. The overall picture is made more obvious with each piece that is placed.

The knowledge puzzle is different from a standard puzzle in that pieces get smaller and smaller the further in one goes. The knowledge there is much more specific and harder to obtain. It takes trial and error of placing those pieces down, trying different configurations with many different pieces until it's finally nailed down.


Recipe

Enough with the analogies. The point has been made.

The recipe for knowledge gain is fairly straightforward.

First, define the areas of knowledge within the field in order of difficulty.

Second, learn the foundational topics well. This will make learning more advanced topics easier.

Third, begin choosing specific areas of interest or those that are easier. Attempt to make foundation-area or area-area connections.

Fourth, either a) continue filling in the unknown areas by adding on to the known areas, or b) directly venture to the more difficult areas with no known bridge. In the former, all areas will eventually be filled out by diffusion. In the latter, more distinct areas will be filled out, but the unfilled distance between them will be smaller, making connections easier.


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