The Birth of Thought
Tool of Thought 3. Abstraction
Scientists, painters, and poets all work to find the essential meaning of a complex system by stripping away every variable 'except one.' Reality is a synthesis of every possible abstraction, and by recognizing this possibility we can understand reality better. In other words, true abstraction is the process of starting from reality and cutting away unnecessary parts to reveal the astonishing essence of a thing. So ultimately, what we must do is find the essence of abstraction itself.
You are looking but you are not seeing. Don't just look — think. Look for the astonishing quality hidden behind surface appearances. (Pablo Picasso)
What literature does is look at the species rather than the individual — attending to the traits that run through the whole and the dominant phenomena. (Samuel Johnson)
Picasso painted what he saw with his mind, not his eyes. Abstraction is simplification. The essence of abstraction is to catch a single characteristic. Even motion can be abstracted. The boundaries between fields dissolve through abstraction. Abstraction is the process of exposing the significant, surprising essence of things.
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Cummings: "I want to write a painting."
(An everyday calligrapher — the sound comes through, shapes pressed tight against each other)
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All abstraction is simplification. The brilliant abstract work done by people like Picasso, Wilson, and Cummings was the act of revealing, through simplification, qualities and relationships that had not been visible before — and the result was new, layered insight and meaning. Another truth these examples tell us is that the simplest abstractions are the hardest to grasp or devise, yet they hold the most important insights.
128 The essence of abstraction is to catch just one characteristic
Recognizing what it means to abstract and why it matters is only half of the problem. The other half is how to find the simple concepts hidden behind a complex phenomenon.
According to Picasso, to arrive at abstraction you must always start from concrete reality. Only by starting from something tangible can you later strip away the traces of the real. In that process you have to find the unerasable idea the object stands for.
Reality is the sum of every possible abstraction, and by recognizing that possibility we come to understand reality better.
Tool of Thought 4. Pattern Recognition
To recognize a pattern is to anticipate what will come next. From patterns we draw general principles for perception and action, and we use them as a foundation. Then we fit new observations and experiences into the frame of our expectations. When something happens that shakes that frame of observation and experience, we create another pattern, and new discovery happens in those moments.
The most important thing is not any one specific piece, but finding enough pieces — and the connections between them — to grasp the whole picture. (Nüsslein-Volhard)
Finding shapes in a complex pattern on a wall is like picking out names and words we know from a noisy clang of bells. (Leonardo da Vinci)
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Of all pattern recognition, the most important is knowing what to predict and how to compare things before the pattern has clearly appeared.
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Our pattern recognition is stuck in ruts. There are countless ways to approach a single object or concept, but most of us use only one.
Gauss famously used a pattern to solve the sum from 1 to 100 with minimal effort.
5. Tool of Thought: Pattern Forming
The more patterns we devise to represent, delineate, and define the world we experience, the more real knowledge we can hold.
Juxtaposing one element or operation with another using a consistent technique creates a synthetic pattern entirely different from the original ones. (Painter Emily Carr)
Even the most complex wave function arises from a combination of simpler functions. (Mathematician Joseph Fourier)
Beyond the puzzle game that began in China, the ability to build synthetic, visual patterns is called tangram.
6. Tool of Thought: Analogy
An analogy is the recognition of functional similarity or a matching internal relationship between two or more phenomena or complex phenomena. Many philosophers dismiss analogy as illogical and as something that distorts judgment, but the very inconvenience and imprecision of analogy is exactly what lets it bridge the known and the unknown.
I was able to find 'countless associations and similarities' between the things I couldn't see or hear and the things I knew through taste, smell, and touch. (Helen Keller)
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Before, I didn't know what impressions rose up from touch and smell, but now I began experimenting with one thing after another. I was astonished to find that these senses supplied me with countless 'concepts.' And they gave me clues to the world of sight and sound.
Keller, as a person with disabilities, was able to draw analogies because she could pull out 'countless associations and similarities' between what she couldn't see or hear and what she knew through taste, smell, and feeling.
Making similarities between what one can and cannot perceive became the main tool Keller used to access a vast range of information she couldn't reach directly.
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The important thing in this process is not to confuse analogy with resemblance. An analogy identifies a functionally similar or matching internal relationship between two or more phenomena.
In practice we reserve the term 'analogy' for comparison. Resemblance, on the other hand, refers to similarities between things based on observation — like color or shape.
The philosopher A. E. Heath argues that analogy is the cornerstone of the scientific method. He says that criticizing analogy is precisely what renders useless the attempt to explain the 'unknown' through the 'known.'
Stanislaw Ulam likewise said that a great mathematician is someone who finds similarities between things, and a greater mathematician is someone who finds similarities between similarities.
If you want to build a world of your own — or help children realize the other possibilities, uses, and purposes that materials have —
when you look at an object, focus not on 'what it is' but on 'what it could become,' and only then can we put things to entirely new uses.
Anyone who wants to explain something has to compare the unknown to something well known so that people can follow. Without analogy, explanation is impossible.
When, through analogy, we find the hidden reality of function and purpose, we come to realize the meaning of the world and the self 'step by step.' And then, in a single moment, we understand everything.
