camp boss informed me that comments were inadvertently closed on the previous lifelong learner post. i have updated it so commenting is back on, and can only assume wordpress is punishing me for my 5770-word verbosity. i have not reformed myself, in fact this post is split into parts because it got out of hand again. (another cup of tea is in order if you actually plan to read this one.)
the past few months have felt like a surge in quinn’s intellectual life, in the same way that the fall and winter months felt like a time of extreme vertical growth.
now he is flexing his mind muscles… hexaflexing them, that is.
if i had to point to a day when the current intellectual surge began to sweep us along in its current, i would say it was after seeing the movie a wrinkle in time. it was spring break, and since i was working, quinn was with me at work most of the week. on wednesday, we left work early and went to the afternoon matinee. his class had seen the movie the week before, but he had been at home with his dad nursing a cold, so he had missed the field trip. they had read the book in class and we had both re-read the book at home (it sat beside the bathtub for when either of us was soaking) in preparation for seeing the film. after the movie, it was incredibly fun to share our points of view on how the movie triumphed in ways that only movies can, and ways in which it failed to honor the book we hold very dear. we agreed point for point.
near the beginning of the movie (this would only constitute a mild spoiler, but just in case: spoiler warning), there is something not from the book, but which quinn and i both felt was a good visual representation of the feelings between meg and her parents. she holds a paper hexagon that folds into itself, and one of her parents says, “my love is there, even if you can’t feel it.” meg folds the paper, and a new design appears, having flipped inside-out, and one final fold surprisingly reveals yet a third image of a brightly colored rainbow heart galaxy (quinn’s description). meg murmurs, “not gone, just enfolded.”
when we got home from the movie, i wanted to show quinn what that paper hexagon was all about, so i looked on khan academy for a tutorial on hexaflexagons, and was not disappointed.
vi hart, the author of this, and 49 other awesome videos under the heading “math for fun and glory: doodling in math,” is now a hero to quinn. and between that day and this, he has watched all 50, most of them multiple times. our hexaflexagon journey began that very day, including both trihexaflexagons like meg’s, and hexahexaflexagons which can flip to 6 different faces. i highly encourage you to watch some of vi’s math for fun and glory videos, as they are both educational and witty. some of our favorites from the hexaflex section included her warnings in the safety video concerning possible ways in which hexaflexing can go awry, warning us against, amongst other things, the danger of hexaflexaperfectionism. we started asking each other to please pass the “interdimensional void” when we wanted the black marker. probably the most quoted line by quinn has been, “perfectly healthy snakes may turn into snake loops; or worse, become decapitated. either state is fatal for the snake, as having no head can lead to starvation.”
another favorite safety concern: “a change in chirality could be a sign that your flexagon has been flipped through four-dimensional space and is possibly a highly dangerous multi-dimensional portal.”
we made our own version of meg’s hexaflexagon, as well as a pile of others with rainbow colors, snakes, celtic knots, and mandalas, each enfolded with love, of course. enfolded isn’t just a collapsing of geometric shapes upon themselves… it’s a swaddling blanket surrounding a babe in a mama’s arms, a protective cocoon around the transformation of a youngling, a container underneath the overflowing emotions of a pre-teen whose gangly limbs can relax against the sides after that which needs to spill out has receded and what is left is love.
on quinn’s next foray into math for fun and glory, he tackled spirals, fibonacci, and being a plant, in which pinecones, and other things that begin with pine-, are examined to find that their spirals are arranged according to numbers in the fibonacci sequence. i’m kind of into spirals, but this is all new and magical math to me, so it’s been inspiring to learn about it alongside my kiddo.
i wore a spiral necklace for the last month of pregnancy, and on through quinn’s babyhood. i have a pair of silver spiral earrings i wear pretty much every day. i had a fancier pair of silver spirals made for my wedding day. my wedding ring is also a spiral of sorts, and i’ve explained the meaning behind that. i resonated with midwife ina may gaskin’s descriptive writing about how babies spiral into the world head first, facing down, then turning and facing up. each time i think of spirals, i think of birth and of beginning again, always having an opportunity to return to myself, return to a grounded place. the spirals quinn started drawing when he was barely 2 years old jumped off the page at me, but then having a child is a great way to rediscover everything you know and love about the world as they hand it back to you again and again. this verbose quote from one of the parenting books i read years ago with an emotional intelligence angle uses spiral imagery to describe the normal course of human development.
from: giving the love that heals a guide for parents
by harville hendrix and helen hunt
(quoting edward edinger ego and archetype): “the process of alternation between union and separation seems to occur repeatedly throughout the life of the individual, both in childhood and in maturity. indeed, this cycle (or better, spiral) formula seems to express the basic process of the psychological development from birth to death.”
hh and hh:
“there are two rhythms that move through the developing child at the same time: oscillation from the center that expands and then returns, and progression through stages of growth as the child moves through his preordained evolution toward adulthood. the interplay of these rhythms shapes the spiral pattern of healthy growth.
oscillation begins with attachment, expands into exploration and differentiation and then subsides back into attachment again. the baby internalizes this rhythm during the first years of his life and repeats it naturally as he progresses through the stages of growth. he is born emotionally connected to his mother, and as he feels that this connection is becoming secure, he cautiously moves out (still attached) to explore and connect with his nonmaternal environment, regularly returning to his mother’s presence for reassurance.
if this first and most basic rhythm is supported and allowed to follow its natural course without impediment, it will be repeated successfully later when the child falls in love with a romantic partner- or a job, a cause, an idea, or his own child, when he becomes a parent- and then learns to express his unique self within the context of a romantic relationship or other important life experience.
in fact, all of the primary tasks of childhood recur in coordinated rhythms throughout the individual’s life. the newborn child has within him all the impulses that will later flower at their appointed time. he falls in love with someone or something. he explores it and crafts a new aspect of his identity with it; he develops new skills; he manifests caring for others. he comes to know the rhythm very well and will repeat this cycle over and over again. the degree of his success depends on how well he has completed his basic evolution during the first eighteen to twenty years of his life.
perhaps you are aware of this rhythm in your own life. think for a moment about how it shows up in your experience as a parent. when your child was born, you fell in love with him. with this marvelous and mysterious creature in your life, you began to explore the world of parenting. that may be why you are reading this book. as you cared for your newborn and got used to your new role, you acquired a new layer of identity as a “parent.” with increasing experience, you learned to handle yourself more confidently as you expanded your competence. perhaps you also sought the support and guidance of others who shared your experience, your peers in parenting. and recognizing your participation in the preservation of the race, you became interested in the welfare of others and the quality of life in society. this expansion outward is a natural cycle in our lives.
the child’s growth depends also on the other rhythm that propels him forward, even as he comes back around to revisit previous tasks. this rhythm is not just an oscillation but also a progression through distinct developmental impulses. the seeds of them all are present at birth, but each blossoms in its own time in response to an inner impulse and the readiness of the environment. if his parents have nourished the first flower appropriately, the next bud will open. each time he responds to another developmental impulse that pushes him forward through the developmental stages, he returns to his primary connection with his caretaker for the emotional security to move to the next stage. each impulse solidifies and then dissolves, one into the other. it is as if the child were being blown unerringly toward the gates of maturity by the wise breath of nature. his life flows from one transformation into another and continues to do so even after he arrives at adulthood.”
~~~
“these two rhythms of oscillation and progression move together in a pattern that is both circular and progressive, suggesting, as edinger says, a spiral. think of a spiral staircase: each step is a progression upward in space and is also a revisiting of a particular point around the circumference of a circle. we spend our lives walking up our own spiral staircases. at each turn, we get the same view we had before at the same spot, but because we are higher up, the view is broader.
~~~
the beauty of the spiral is that we will always get another chance. encountering the step again at the same place on a higher level, we can learn to do it better the next time. we can become more surefooted as we get older.
so, having fibonacci spirals delight my eleven-year-old is not so out of left field, and serves to bring me back to myself yet again.
one of the delightful revelations of the fibonacci videos was that music notes also correspond to fibonacci numbers, and it is beyond me whether this is mere magical coincidence or something more tied to the rules of nature or mathematics. what was magical coincidence, was that quinn and i were exploring the piano keyboard at nearly the same time, as it relates to his percussion and musical training. while we watched rich’s son play his alumni basketball games, i taught quinn how to draw piano keys and he kept busy for many octaves. recalling the miles of piano key doodles of my own youth, i was yet again returned to myself, this time to the sound of basketballs dribbling down the court, sneakers squeaking on the polished floor, and the scratch of a pencil across a piece of graph paper.
when making math doodles, it’s hard to avoid sometimes making a don’t-dle, but i’m excited for quinn to be launching back into drawing, a form of creativity he has always ebbed and flowed with a bit, due in part to perfectionism. the math doodle genre seems to have really struck a chord with him, and he bounced from pascal’s triangle to sierpenski’s triangle and soon he was inventing quinn’s triangle.
the compass and protractor set he got for his birthday from his aunt and uncle have been handy during this math drawing phase. one of our new favorite math shapes is a cardioid. as vi explains, a cardioid is the inverse of a parabola. but i just learned from wikipedia that a cardioid is also an envelope of a pencil of circles (enfolding them!) and, get this, a cardioid is also part of a family of curves known as sinusoidal spirals!
starting to embrace nerd metaphors: parabola, because i cardioid you. (translation: smile, because i love you.)
after watching vi hart’s story about wind and mr ug, a tale woven along a mobius strip, quinn began to ponder the interesting form of a mobius strip in a more abstract sense – he postulated that the shape of the universe might be a mobius strip, and that there is always an alternate reality for every reality we experience.
another most-frequently-watched candidate was how-to-snakes! (one greeted him in his car seat at pick up time, cradling a fibonacci pinecone… more were hiding in his room when he got home. that way he could make an oroborus; snake knuckles; baby snakelets, supersnake; borromian ring snakes; snake spirals; and a many-headed hydra snake! of course, all of this led to graph paper drawings of many different configurations of snakes.
if you peruse the list of videos, it is easy to see how a guy like quinn got sucked in, given such titles as “doodling in math: dragon dungeons” and “infinity elephants” and “are shakespeare’s plays encoded within pi?” i was finding phi angle-a-trons tucked into his homework folder that he had ostensibly constructed during class time, and he spent the duration of his parent teacher conference drawing this:
quinn even watched every episode of thanksgiving math multiple times, learning about such culinary wonders as green bean matherole, borromian onion rings, apple pi and pumpkin tau, and turduckenen-duckenen.
speaking of food, quinn has helped me immensely in the kitchen recently, cheerfully offering help or asking if he can be involved in meal preparation on a pretty regular basis… some things he has been up to: prepping and making pancakes; making broccoli soup (operating the blender); meatball/sauce prep (can opener, garlic press). he became a certified muffin baking technician, because after he got past being “not good at eggs,” he decided, “i’m going to do all of the steps in the process myself,” right down to putting in and taking out of the oven. the filling of cups with batter got frustrating, and he was getting increasingly agitated, but i made jokes. he said you could smell the frustration in the air, and i said, no, that’s just the fish frying you smell – our neighbor had given us a lingcod fillet, and we were having fish and chips for dinner. i said, “it’s confusing because they sound alike. fish frying, frustrating…” and then i’d purposely use the wrong word in every sentence thereafter. he giggled, worked through the fish fry, got a cup of water to put the rubber spatula in after each cup was filled so the batter wouldn’t be sticking to the spatula so much. problem-solving in action.
vi warned us about hexaflex-mexican-food-cravings…
quinn had bought a goose egg for $1 at farmer’s market, and he had requested that we use it for something very special involving lemon (that was after i broke the news that he could not incubate this egg and hope for it to hatch, that these were for eating.) on a saturday morning i told him my idea was to use it to make lemon filling, which we would roll up into crepes and top with whipped cream.
“ooh, can i help?”
this was after his muffin adventure of the previous evening, so i was pleasantly surprised that he was ready so soon for another kitchen marathon.
he got to work, beginning with zesting an entire lemon, about which he was extremely thorough (the recipe only called for half, but we like it zesty). then he measured all of the lemon filling ingredients into the saucepan. while he stirred, i whipped up the heavy cream, and by then the filling was simmering. i took over stirring it while it thickened, and quinn measured crepe ingredients into the blender. he sliced strawberries and then arranged them on our plates while i sliced oranges and flipped crepes. then we worked together to enfold lemon filling into each crepe, top them with whipped cream (and a sprinkle of sugar, he settled on as a final touch) and he arranged everything on plates to serve.
later that afternoon, quinn’s 5’1” frame was enfolded into my lap, curled into a ball. he pulled the fuzzy owl blanket up over his head, and said, “you find an egg.” i laughed… and said how surprised i was to have found an egg, i had only ever found one billion other eggs since giving birth to quinn. “you find an egg” is the beginning of one of the most-frequently-played pretend scenario games of the boy named quinn, a boy who has played a higher than average number of pretend scenarios in his time on earth. i never know what creature may hatch out of the egg i find, and the main narrative arc of the game revolves around my suspense and anticipation of the secret that awaits me curled inside the egg. it could be a puffin, a penguin, or an owl. it could be a dragon or a dinosaur. it could even be a pokemon character, as it was today, once we finally got back on track after my teasing about always finding eggs i’m not even looking for. that day he was spheal, and i hope my teasing did nothing to discourage him from going on having me find an egg one billion more times, even though he can’t sit on my lap curled in a ball anymore without inflicting some small amount of pain.
the following day was sunday, so i made pancakes, which we topped with strawberry rhubarb sauce and maple syrup. quinn’s weekend consisted of studying math for fun and glory and computer programming on khan academy, adding turrets and reinforced walls to his minecraft fortress (i love finding the page in the book open to portcullises), making math doodles, dabbling with his robotics kit, planning out how he is going to make a bb-8 and a lin-v8k droid after i showed him a make magazine video of a homemade bb-8 using many cheap hacks (like old speaker magnets and cut off tops of roll-on deodorants for parts of the mechanisms; making the body out of paper mache using a dollar store beach ball). he couldn’t fall asleep by bedtime. he is just in one of those spongey phases, absorbing absolutely everything and asking for more and blowing me away with how much he already knows.
quinn: tau is bigger than pi! it’s 2 pi! it’s approximately 6.28!
me: um, ok, if you say so…
quinn: mo-ommmm, you didn’t know that?!?!
continued in part 2
