twelve is sublime!

twelve is a sublime number, a number that has a perfect number of divisors, and the sum of its divisors is also a perfect number. there are six divisors of twelve (1,2,3,4,6,12) and 6 is perfect; adding 1+2+3+4+6+12 = 28, which is another perfect number; this double perfectionism defines twelve as a sublime number.

something about two scoops of perfectionism feels familiar, almost like i’ve written about it in the context of quinn before.

sublime also means “of such excellence, grandeur, or beauty as to inspire great admiration or awe.” i think that may turn out to be true of twelve as well. i may be a biased observer, though!

1+2+3+6. i have found the months leading up to 12 to be rather intense. the list of divisors adding up to 12 and making it therefore a semiperfect number all happen to be ages i can look back on and say were also ages where i noticed intensity. it remains to be seen what level of intensity is in store for this new year of quinn.

there are only two known sublime numbers, 12 and (2¹²⁶)(2⁶¹ − 1)(2³¹ − 1)(2¹⁹ − 1)(2⁷ − 1)(2⁵ − 1)(2³ − 1). The second of these has 76 digits:

6086555670238378989670371734243169622657830773351885970528324860512791691264, so it’ll be a little while before he celebrates another sublime number birthday. i believe he is excited for next year, however, since it’ll be a fibonacci birthday! his first since becoming aware of the existence of fibonacci birthdays, so it’ll be big, aside from other reasons why people blow 13 out of proportion (eek! a teenager!).

he climbs into the front seat of the car to ride home from school now, so nearly adult-sized (he has surpassed several of my good friends in height, in fact) that he is safe up front. the same kid whose outgrown car seat (with 5-point harness) i had to gently remove while he was at his dad’s, because he was quite attached, not even 3 years ago. i pull away from the curb, and he immediately starts rocking back and forth, the sign that he needs a bathroom badly and hasn’t gone all day. we chat about strategies for actually using the multiple bathrooms provided by his institution of learning, i have him picture them, decide which ones he likes most, picture where they are in relation to each classroom, and then have him mentally walk through his daily schedule to try to find the most likely mid-day opportunity to fit in the use of his preferred one en route between classes. he decides on the way to or from band will work best, since he passes a good one, band takes place just before lunch, and he is only carrying sticks and music books, as opposed to his gigantic binder and computer.

later that same day, he is finishing his math homework with some reluctance, when he notices that the last problem is about the great pyramid of egypt, and forges ahead so he can get to that one. when he does, he reads that he is to calculate the lateral surface area of the pyramid, which (the math text claims) originally had dimensions of 754 feet slant height and 610 feet along each side of the base.

q: oh! 610 is a fibonacci number!

me: um, is it?

q: i remember, because 144 is a fibonacci number, and 610 is the one that breaks the pattern of double numbers… 144, 233, 377, then bam, 610.

me: huh.

q: maybe the ancient egyptians knew about fibonacci numbers! and phi! do you think they could have?!

he is cuckoo for irrational numbers, and phi is one of his faves. the asynchronous life of a poppy at twelve is struggling with bathroom planning, while being 100% set for a dissertation topic.

actually, it turns out he is not the first person who noticed something phi-ish about the pyramids at giza. he was thrilled to hear the google results, as he really didn’t much fancy the idea of writing a dissertation, but he does want to go visit the pyramids one day, and is glad they may reflect a number sequence near and dear to his heart.

although i have gotten away from enumerating quinn’s life in months, he can appreciate that he is now 144 months old! 12 squared! 144 being a member of the fibonacci sequence, to make it extra awesome.

other than being sublime, 12 makes an uncanny number of important appearances in mathematics. i read in a paper on the occurrence of 12 as the solution to lattice polygons that the various methods of proving this fact suggests connections among seemingly unrelated branches of math. which reminds me of another math research paper we came across recently. we were tackling a logic puzzle together, and quinn had wanted to try the most difficult one. after two nights of post-dinner work, we were getting close to finishing, but the final steps were dependent on a single clue we weren’t entirely sure how to interpret. we did trial runs of the results based on two different interpretations to see if either one came up with a valid solution, or hit a dead end. if we decided to read the clue as “neither x nor y is z” implying that x is also not y, then we could complete the grid without conflicting results; but if we decided that “neither x nor y is z” leaves the possibility that x could be y, we could not complete it, but also did not end up with conflict, we simply lacked enough information. quinn felt we couldn’t be sure, and said, “i have to google something,” pulled out his computer and typed in, “if neither x nor y is z, does that imply that x is not equal to y?” and google gave him one result. both of us reacted with, “that’s never happened before,” and laughed about that one time quinn broke google. the one result was for a 51-page dissertation on math logic which mentioned david hilbert on the first page, with whom quinn was familiar because vi hart talks about him. not a lot of other 11-year olds would say, “ooh, hilbert!” but now he is no longer eleven, he is twelve.

one of the biggest deals in math relates to 12, in that a function in number theory, the riemann zeta function, is considered to be of great significance, in fact it is considered the most important unsolved problem in pure mathematics, and its solution promises a million dollar reward, as one of the millenium prize problems established in the year 2000. hilbert, that guy who quinn and vi hart keep mentioning, had declared the importance of the problem exactly 100 years before that in a celebrated speech at a 1900 international conference. the function relates to the distribution of prime numbers, and where 12 comes in is that the value of the zeta function at −1 i.e. ζ(−1) = −1/12

-1/12 is the theoretical sum of the harmonics of all the primes. the zeta function not only relates to prime numbers, it also describes the music they make, which, if the riemann zeta hypothesis is true, turns out to be beautifully harmonious, and if it is false, dissonantly ugly. the hypothesis has yet to be proven, but this has not stopped its provisional use in a towering pile of proofs of other theorems on the assumption of its being one day proven true. if not, the pile will collapse like an epic game of jenga. euclid, euler, gauss, have all worked on this problem of the primes; riemann took it to imaginary number land, wrote a ten-page paper, and cracked the mystery. with how tickled quinn is by irrational numbers, i think imaginary numbers will be right up his alley when he gets there.

twelve is symbolic for quinn in other non-math venues. he is of course an avid fan of greek mythology, and the twelve olympians and the twelve labors of hercules are just two of many examples of the appearance of twelve therein. in norse mythology, another of quinn’s interests, odin has twelve sons. quinn was born a fire pig in the chinese zodiac, a fact of which he is fond, and we have now come full circle to a new year of the pig. so anyone born this year is a pig like quinn (can we think of any newborns? yes we can! though this year’s babies are earth piglets! and speaking of people with twelve sons, one of our new babes is named for a couple of the sons of jacob!)

uncle quinn holding new pancake w

there are twelve lunar cycles in a year, so each time quinn travels once around the sun, the moon goes from kayak moon to boat moon to fender moon and back again a dozen times! many other aspects of timekeeping (a skill around which i hope to see much great development during his year of twelve) involve twelve, of course.

it’s the number of noon, of midnight. of magnesium and cranial nerves. of a hurricane wind on the beaufort scale. of humans who have walked on the moon. of the seats filled around king arthur’s round table. of notes on the chromatic scale (see also twelve tones by our favorite mathemusician.)

speaking of music notes, i just learned from my twelve-year-old that his synesthesia extends to them. i finally thought to ask if he saw music notes in colors like he does letters and numbers. “eighth notes are orange,” he told me. “quarter notes are blue. whole notes are green. they used to all be orange and yellow, but now they’re different colors.”

“what about half notes?” i asked.

“i think those are white. sixteenth notes are red.”

“and rests and other symbols?”

“rests are black. they’re devoid of color because they’re devoid of sound. i think.”

i had wondered about it, thinking maybe he saw the color corresponding to the letter name of the note (A orange, B red, C gray, D black, E white, F brown, G red), rather than colors designating each type of note, and when i brought that up, he said that yes, he does also have those letters still associated with the same colors when they are naming a note, but the note itself has the note color, not the letter color (reference chart here – and he still names the same colors for the same letters, 3 years later).

things about quinn at twelve:

he knows how to self-soothe with graph paper.

he is a nonlinear learner. giving him harder version of problems helps him articulate the procedures laypeople might use to solve them, when he just *knows the answers without knowing how he knows.

he still wants to be a paleontologist. for a presentation on occupations that he had to give to his spanish teacher, he included a slide about it. he was nearly undone by the dreaded literal interpretation nemesis, given that he was supposed to write 10 sentences about future occupations, and technically, he did. he wrote 5 questions and 5 answers for his 10 sentences, however, his “sentences” for the answers were “no,” and “si.” i spent a few days convincing him that wasn’t what his teacher had in mind, and he finally agreed, added 5 more slides and questions to his presentation, and scored 100% instead of 50%.

as he cruises past 5’3”, he still manages to tuck himself into position to tell me, “you find an egg.” being his mama, i feel even more sublimely lucky than if i found a dozen eggs! happy dozen years to my mighty quinn!