Cubed: The Puzzle of Us All
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Read between February 5 - February 22, 2025
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As Albert Einstein said, “The true sign of intelligence is not knowledge but imagination.”
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Simple and complex. Moving and stable. Hidden and exposed. I believe contradictions are not opposites to be resolved, but counterpoints to be embraced. Rather than becoming frustrated by what seems irreconcilable in a contradiction, the better option is to appreciate that a contradiction helps us make connections we may never have considered.
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Q: Why did you invent the Cube? [For me this is the most irritating question.] A: I found a problem that captured my imagination and did not let me escape.
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For all its shortcomings, writing does offer a chance to explore some questions in order to gain a deeper understanding. So even though I may hate to write, I am always eager to try to understand things better, especially those things that we take for granted. What makes us tick? What makes us create? And how are people inspired to make something that has never been made before?
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creativity, symmetry, education, architecture, questions, playfulness, contradictions, beauty. But at its core, this book is about puzzles. It is about the puzzle of myself. It is about the puzzle of this strange object I discovered almost fifty years ago. And it is about the puzzle of us all.
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was not assigned these puzzles, was not graded on my performance, nor was anyone observing whether I solved them or not. If I failed or had trouble with one, I could start again on it the next day. This entertainment was solitary. Without an opponent, I was always the winner—not that I really thought that way. What
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Puzzles bring out important qualities in each of us: concentration, curiosity, a sense of play, the eagerness to discover a solution. These are the very same qualities that form the bedrock for all human creativity. Puzzles are not just entertainment or devices for killing time. For us, as for our ancestors, they help point the way to our creative potential. If you are curious, you will find the puzzles around you. If you are determined, you will solve them.
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You found the solution by discovering that not the individual pieces but the movements of the whole were important.
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In this early puzzle, I explored how cubes that are connected can be put together in a number of different ways. The visual capacity of the puzzle was beautiful.
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“solving problems that cannot be formulated before they have been solved. The shaping of the question is part of the answer.”
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MacMahon’s cube, which is also made up of cubes, much like a child’s colored building blocks, in which all the faces are different colors and none are repeated.
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When I think about the one aspect of my many identities that connects them, what I always come back to is that I am a playful man or, rather, a man who likes playing—what the Dutch scholar Johan Huizinga once called the Homo ludens.
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Children are masters of play. It is often described as their most important job, and a basic part of how they learn.
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By the time we are adults, the instinct for spontaneous play seems to have disappeared, and we seem eager to have rules constrain and define our actions.
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All the exciting, imaginative play from childhood is gradually replaced by the more structured and conventional “play” of board games and team sports, in which there are clear winners and losers.
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Too often as adults we seem to believe play is just a diversion, or another form of competition outside of the workplace. But play is one of the most serious things in the world. We often do things really well only when we do them playfully. We are more relaxed about them; the task becomes not a burden or a test, but an opportunity for free expression. We can engage without overthinking or feeling anxious about whether we did something correctly.
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Confucius teaching: “The man who asks a question is a fool for a minute, the man who does not ask is a fool for life.”
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grow older and become curious in a different way, our world becomes more defined by the “hows.”
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Our everyday curiosity is rooted in such “How?” or “What if?” questions.
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THERE ARE TWO WAYS to create change: Either find a new answer for an old question or find a new question that has never been asked before.
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and yet we never learn it in school.
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on’t you understand that we need to be childish in order to understand? Only a child sees things with perfect clarity, because it hasn’t developed all those filters which prevent us from seeing things that we don’t expect to see.”
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Learning is not about merely collecting knowledge; it’s a wholly different process. In a way, knowledge partly consists of data, while learning is a skill that you achieve after you practice it over and over again. Soon
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When one learns something, one collects both data and the skills to master that data, and the final product is knowledge.
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not just the facts but their relationships, their connect...
This highlight has been truncated due to consecutive passage length restrictions.
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You are capable of being online, but to find what you are looking for requires some skill, some ability to separate the useful information from the dross.
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remember both. Learning is a lifelong process, but it is most intense when we are children.
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would be if our ways of teaching were more sensitive to the best way of learning, which, once again, is playing!
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word meant a space for leisure and idleness,
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What I mean is that I would know more. My breadth of knowledge would be greater. Maybe I would be able to communicate in different ways. Maybe I would not hate to write because
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My school was not able to capture my attention. But it did provide me with plenty of time to draw during class, and I consider that self-education to have been very valuable.
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How can we encourage children to combine self-education with formal education? When we finish school, we typically don’t know who we are. We don’t really know what we know or what we are interested in or what we are capable of. Nor do we walk away with an understanding of how colorful the world is. Perhaps real education should hold a mirror up to children so that they can truly see themselves.
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ASTRONOMER CARL SAGAN called understanding “a kind of ecstasy,” and I think anyone who has had the experience of finally understanding something that once seemed difficult
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an IQ test. But this does not begin to consider some of the mysteries of real intelligence, which is fundamentally the capacity for making connections.
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“It’s the first thing she’s ever been able to do,” she wrote, “that so many normal children can’t.”
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it illustrates so beautifully what we may never fully understand about how intelligence might be expressed in unexpected ways.
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often we forget about the other crucial aspect of human intelligence: emotions.
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An object, its shape, its substance, its structure always has an emotional content.
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Of course, the Cube has an intellectual side as well, but his emotional appeal is essential.
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high achievers in school, but when they finally graduate, they do not have a clue about how to succeed in the real world.
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For me, the capacity to solve problems—creatively, confidently, and effectively—is the one important sign of true intelligence.
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Karl Popper in Realism and the Aim of Science:
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only one way to science—or to philosophy, for that matter: to meet a problem, to see its beauty and fall in love with it; to get married to it and to live with it happily, till death do ye part—
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the existence of a whole family of enchanting, though perhaps difficult, problem children for whose welfare you may work, with a purpose, to the end of your days.