Mathematicians as Birds and Frogs

Some mathematicians are birds, others are frogs. Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. They delight in concepts that unify our thinking and bring together diverse problems from different parts of the landscape. Frogs live in the mud below and see only the flowers that grow nearby. They delight in the details of particular objects, and they solve problems one at a time. I happen to be a frog, but many of my best frien...

 Letting Go of Dreams

Our culture lionises grit and perseverance, but the ability to be adaptable and flexible, and pivot to new opportunities, is just as important. The common phenomenon of ‘goal shielding’ puts us at risk of persevering for too long with unobtainable dreams, though there is no surefire way to make the right decision on this. To assuage the pain of letting go of a dream, be realistic about what you’re giving up – even if you succeeded, it was unlikely to be the romanticised version you pi...

 Convergence and Divergence of Focus

At any moment, we are either in a divergent phase of life, or in a convergent phase. During a divergent period, we’re usually focused on broadening our inputs. We go to school, take on internships, travel, try a career switch, and so on, exploring new paths. During a convergent time, we take what we’ve learned thus far to double down on just a handful of goals on which we can spend our energy – we become more focused. We grow fastest not by converging constantly onto some single point s...

 Attention, Flow, and Concentration

Chess thinking provides a rich metacognitive context that leads me to believe that we should tease apart three notions that are related but often conflated – attention, flow and concentration. Attention is fundamentally grounded in perception (how we attend), flow is fundamentally grounded in experience (how we feel), and concentration is grounded in praxis (how we purposively coalesce). We ask too much of attention and not enough of concentration. The recent cultural emphasis on attention...

 Chess as Recursive Evaluative Hunting

In chess, concentration usually unfolds in quick succession through perceiving, desiring and searching. But it’s recursive, so I often find something I didn’t expect in a way that leads me to see my position differently and want something else from it. My perception is pre-patterned through years of experience, so I don’t see one square or piece at a time. Instead, I see the whole position as a situation featuring relationships between pieces in familiar strategic contexts; a castled ki...

 Esports Workout Regimen

Eating right, sleeping right, exercising, cleaning up for sponsors — these ideas have undergirded traditional sports for generations. In e-sports, they are regarded as almost radical. “They don’t look at themselves as physical human beings,” said Hvidt, who won the European handball championship with Denmark in 2008. “It’s common sense, in a way. But with them it was not.” Rfrsh has a validating narrative under its belt. The company’s other team, Astralis, which competes in...

 A Quantum Game

Bell came up with “nonlocal” games, which require players to be at a distance from each other with no way to communicate. Each player answers a question. The players win or lose based on the compatibility of their answers. One such game is the magic square game. There are two players, Alice and Bob, each with a 3-by-3 grid. A referee tells Alice to fill out one particular row in the grid — say the second row — by putting either a 1 or a 0 in each box, such that the sum of the number...

 Darwin, Bach, and Professional Decline

What’s the difference between Bach and Darwin? Both were preternaturally gifted and widely known early in life. Both attained permanent fame posthumously. Where they differed was in their approach to the midlife fade. When Darwin fell behind as an innovator, he became despondent and depressed; his life ended in sad inactivity. When Bach fell behind, he reinvented himself as a master instructor. He died beloved, fulfilled, and—though less famous than he once had been—respected. The less...

 Variable Ratio Schedule for Getting Kids Addicted to Boar...

In light of the above, here’s a solid Variable Ratio Schedule for playing board games with your kid: the first time you play a particular game, let the kid win. thereafter, let the kid win some of the time. 60% of the time is good to start (you can dial it down slowly as the kid improves if you want). make the sequence of wins and losses as random as possible. critically, make the outcome as close as you can every time, especially when the kid loses. She should always feel like she bare...

 Words are More Powerful than Pictures

This “algebraic” flexibility of a word encapsulates the essence of something while leaving unnecessary concretes out. A photo doesn’t and can’t. Further, a word offers enormous flexibility in terms of input/output. It can be spoken, thought, gestured (as in sign language), written, grammatically combined with other words, or stored with very little memory. A photo can’t. Words are altered by syntax and grammatical endings. A photo can’t be modified in this way, other than the temp...