While Not All Graphs Can Be Drawn In R2, Every Single Finite Graph Can Be Drawn In The 3 Dimensional

“We can read even a correct proof, and be completely convinced of the logical steps of the proof, but still not have any understanding of the whole. Like being led, step by step, through a dark forest, but having no idea of the overall route.”

Eugenia Cheng (via cofinaldestination)

Maybe this is why I have trouble reading math textbooks sometimes? I can understand why a step is valid, but I get caught up on, “Wait, where are we going? Where are you taking me?”

(via ryanandmath)

1. Allow yourself the uncomfortable luxury of changing your mind. Cultivate that capacity for “negative capability.” We live in a culture where one of the greatest social disgraces is not having an opinion, so we often form our “opinions” based on superficial impressions or the borrowed ideas of others, without investing the time and thought that cultivating true conviction necessitates. We then go around asserting these donned opinions and clinging to them as anchors to our own reality. It’s enormously disorienting to simply say, “I don’t know.” But it’s infinitely more rewarding to understand than to be right — even if that means changing your mind about a topic, an ideology, or, above all, yourself. 2. Do nothing for prestige or status or money or approval alone. As Paul Graham observed, “prestige is like a powerful magnet that warps even your beliefs about what you enjoy. It causes you to work not on what you like, but what you’d like to like.” Those extrinsic motivators are fine and can feel life-affirming in the moment, but they ultimately don’t make it thrilling to get up in the morning and gratifying to go to sleep at night — and, in fact, they can often distract and detract from the things that do offer those deeper rewards. 3. Be generous. Be generous with your time and your resources and with giving credit and, especially, with your words. It’s so much easier to be a critic than a celebrator. Always remember there is a human being on the other end of every exchange and behind every cultural artifact being critiqued. To understand and be understood, those are among life’s greatest gifts, and every interaction is an opportunity to exchange them. 4. Build pockets of stillness into your life. Meditate. Go for walks. Ride your bike going nowhere in particular. There is a creative purpose to daydreaming, even to boredom. The best ideas come to us when we stop actively trying to coax the muse into manifesting and let the fragments of experience float around our unconscious mind in order to click into new combinations. Without this essential stage of unconscious processing, the entire flow of the creative process is broken.   Most importantly, sleep. Besides being the greatest creative aphrodisiac, sleep also affects our every waking moment, dictates our social rhythm, and even mediates our negative moods. Be as religious and disciplined about your sleep as you are about your work. We tend to wear our ability to get by on little sleep as some sort of badge of honor that validates our work ethic. But what it really is is a profound failure of self-respect and of priorities. What could possibly be more important than your health and your sanity, from which all else springs? 5. When people tell you who they are, Maya Angelou famously advised, believe them. Just as importantly, however, when people try to tell you who you are, don’t believe them. You are the only custodian of your own integrity, and the assumptions made by those that misunderstand who you are and what you stand for reveal a great deal about them and absolutely nothing about you. 6. Presence is far more intricate and rewarding an art than productivity. Ours is a culture that measures our worth as human beings by our efficiency, our earnings, our ability to perform this or that. The cult of productivity has its place, but worshipping at its altar daily robs us of the very capacity for joy and wonder that makes life worth living — for, as Annie Dillard memorably put it, “how we spend our days is, of course, how we spend our lives.” 7. “Expect anything worthwhile to take a long time.” This is borrowed from the wise and wonderful Debbie Millman, for it’s hard to better capture something so fundamental yet so impatiently overlooked in our culture of immediacy. The myth of the overnight success is just that — a myth — as well as a reminder that our present definition of success needs serious retuning. As I’ve reflected elsewhere, the flower doesn’t go from bud to blossom in one spritely burst and yet, as a culture, we’re disinterested in the tedium of the blossoming. But that’s where all the real magic unfolds in the making of one’s character and destiny.

Maria Popova, “7 Lessons from 7 Years” at Brain Pickings (via universityandme)

When I think of how I see myself, it would have to be at age eleven. I know I’m thirty-two on the outside, but inside I’m eleven. I’m the girl in the picture with skinny arms and a crumpled skirt and crooked hair. I didn’t like school because all they saw was the outside me. School was lots of rules and sitting with your hands folded and being afraid all the time. I liked looking out the window and thinking. I liked staring at the girl across the way writing her name over and over again in red ink, or the boy in front of me who wore the same dim shirt every day. I imagined their lives and the houses they went home to each evening, wondering if their world was happy or sad.

Sandra Cisneros, from “Straw into Gold,” A House of My Own: Stories From My Life (via lifeinpoetry)

We don’t want to conquer space at all. We want to expand Earth endlessly. We don’t want other worlds; we want a mirror. We seek contact and will never achieve it. We are in the foolish position of a man striving for a goal he fears and doesn’t want. Man needs man!

Solaris (1972), Andrei Tarkovsky (via giveintosin)

“Infinity is just an 8 that has gone to sleep.”

Real analysis professor (via mathprofessorquotes)

fav japanese vine so far

DENDROMORPHIC

[adjective]

shaped like a tree.

Etymology: from Greek dendron, “tree” + morphē, “shape”.

[hoooook]

There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.

Nikolai Lobachevsky (via curiosamathematica)

This satellite, Explorer 24, was a 12-foot-diameter inflatable sphere developed by an engineering team at Langley. It provided information on complex solar radiation/air-density relationships in the upper atmosphere.  It was launched on November 21, 1964.