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03 Study Notes / Mental Models

86 von Neumann Thinking

A complex problem can be broken down into small details, and those small details can be recombined into a larger problem with certain meaning or specific properties. He summarized this from studying computer architecture: breaking an instruction down into 0s and 1s, and combining 0s and 1s into text, images, audio, and video — that's exactly what this means.

To refine further, it consists of two steps: decomposition and combination. They may look simple, but they can help us solve many problems—many problems are not as complex, vast, or difficult as we think. All of them can be reduced in scale through decomposition. If a problem is complex, decomposition can make it simple. If a problem is vast, decomposition can make it small. If a problem is difficult, decomposition can make it easy. How do you decompose? Mount Tai looks so tall, but isn't it climbed one step at a time? Reaching the summit is hard, but walking the steps is easy. Note, however, that decomposition must lead to solution: I can climb the steps, so decomposing to that level is enough; if my ability falls short, decompose further, down to a level you can solve. Decomposition is the means, but decomposition alone is of course not enough—you must also recombine to get the answer to the problem. If you can decompose, you can combine. But remember, the key to combination is connecting the decomposed parts. Walking the steps isn't just walking—you also need strategies like resting, drinking water, and shedding weight. The key to combination is not the 'union' of aggregation, but the 'organizing' in the word. Another important meaning of combination is that it lets you go from solving one problem to solving a whole class of problems—as long as that class of problems shares the same type of decomposed parts. If someone is good at stand-up comedy, they won't be bad at public speaking. The steps on a mountain climb can give us the courage to take on seemingly unscalable heights—as long as I can map out the steps of a matter, no difficulty is insurmountable. Behind many great things lie countless ordinary, simple things, repeated until greatness is achieved. A forest is the repetition of trees; a leaf is a combination of cells; clothing is the repetition of fabric, and fabric is a combination of threads. A life is the repetition of days, and each day is a combination of minutes and seconds—this second is that second, yet not that second; this thing resembles that thing, yet is not that thing. This is the fundamental reason why we can keep using decomposition to find answers in this world, and keep using combination to create.