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“The problem of writing: in order to designate something exactly, anexact expressions are utterly unavoidable. Not at all because it is a necessary step, or because one can only advance by approximations: anexactitude is in no way an approximation; on the contrary, it is the exact passage of that which is under way.”—
Deleuze and Guattari, A Thousand Plateaus
A072398/A072399 - Best approximations to Pi
A072398 - Numerator of best approximation to Pi with denominator <= 10^n.
A072399 - Denominator of best approximation to Pi with denominator <= 10^n.
3/1, 22/7, 22/7, 355/113, 355/113, 312689/99532, 1146408/364913,…
You could fill an entire blog with posts about pi (π). As the ratio between a circle’s circumference and its diameter, it’s remarkably useful. It helps you calculate the area and volume of circles and spheres and cylinders and cones. It’s central to trigonometry. It is part of a normal distribution. It describes the shape of rivers. It’s infinite, and it never repeats (trascendental), and all digits are probably distributed evenly throughout it (normal).
Four thousand years ago, Babylonian mathematicians were using the value of 25/8 for π. In the 9th century BC, the Indian astronomer Yajnavalkya was using 339⁄108. In 263 AD, the Chinese mathematician Liu Hui obtained 3927⁄1250 by inscribing a circle with polygons. Today, we know more than a trillion digits of π.
But how exact does π need to be? If you were calculating the circumference of a circle the size of the entire universe (r = 46.6 x 106 light years = 4.409 x 1026 m), and wanted to be certain that your answer was accurate to the size of a Hydrogen atom (1.2 angstroms = 1.2 x 10-10 m). You’d only need 36 or so digits.
Although π is a very useful — and nearly ubiquitous — number, there’s been a lot of discussion in recreational mathematics circles (although not anything serious in academia) that it should be replaced by a number equal to 2π. This number is sometimes called a “turn”, but more recently has been dubbed tau (τ).
Words I Will Miss
Sutton learns new words every day.
Considering where we started, his vocabulary is fairly enormous.
And his intelligibility (pronunciation and clearness of his words) is improving as well.
Although Sutton has plenty of mispronunciations to work out, he has several early words that he’s left behind.
I’m thrilled by his progress.
It is somewhat bittersweet however that as Sutton’s language develops, he is outgrowing those first attempts at words that have filled our ears for months.
I have vivid memories of his first word attempts, approximations of words that emerged one at a time, shedding slow, steady light on his thoughts, needs, ideas, and questions about the world.
All parents have stories of those early words - toddler pronunciations captured in baby books, saved for future conversations about “when you were little.”
Sutton’s early words not only came later than most children, but his were marked by factors that can’t be captured in a list in his baby book.
Sutton’s early words brought promise. Promise that he would be capable of sending the words filling his brain through his tongue, jaw, and lips, so we could hear them too.
Sutton’s early words brought hope. Hope that Sutton would find his voice. Hope that communication with the rest of the world was possible.
Sutton’s early words showed strength and courage, creativity, & cleverness. Sutton used his limited vocabulary, a mere17 words at just over two years old, to say countless things.
In many ways, Sutton was defined by those early words. They set him apart.
They made him special. Sweet. Vulnerable. Unique.
I have no intention of holding Sutton back.
His “big boy” words are just as beautiful as his early words.
Regardless there are words I will miss:
pape (cape) - Just recently Sutton worked out the /c/ sound in cape. He no longer has to be a paped crusader.
Nana (dad) - Sutton called his dad Nana for the better part of a year. What seemed a little silly and misplaced initially, became symbolic of a unique bond between Sutton and his daddy.
ober dere (over there) - Sutton was almost three before he started using phrases. This one was a favorite.
Lala (Lila) - Sutton has been able to say Lila’s name for some time. He actually shifted from Lila to Lala in the early months of therapy. Lila requires more motor planning, and was replaced by Lala for ease. He still slips every once in a while.
an eyon (Buzz Lightyear) & ah ha (Woody)- Sutton found early and clever ways to communicate his needs and interests long before finding words. Around his second birthday, Toy Story became his favorite movie. Woody, Jessie, and Buzz took a front seat in his make believe world. It’s not surprising that their names were among the first words Sutton uttered.
ah man (Spiderman) - When Sutton began to take an interest in superheroes, he used his tone and facial expression to talk about them. It was unmistakable when he was referring to his web slinging hero.
gaga (water) - Sutton referred to water as gaga for a long time. Water, cereal, and cheese were three of the few items that Sutton could ask for with an approximation. It took many months of therapy for him to add edible items to his vocabulary.
awi (sorry) - Recently Sutton’s version of sorry turned from awi to sawi.
lub (love) - This isn’t the first time I’ve written about Sutton’s ability to show love. His love was palpable long before he had words for it. But here is nothing quite like the first time your child says they love you, even when it ends with a /b/.
And the final three words have yet to move from their original pronunciations, but if history repeats itself, they will disappear soon enough:
fwee (three) - I’ve written about Sutton’s counting words before too. He used to make fun of himself instead of attempting to count out loud. One of his first words was oo (two), spoken shortly after his second birthday. He hasn’t quite moved from fwee to three yet, but that day will come soon enough.
fanks (thanks) - Similar to three, Sutton doesn’t have exactly the motor control to produce the /th/ sound in thank(s). He can often be heard declaring, Fanks, mommy. Fanks.
fawkit (chocolate) - And finally, there’s chocolate. Sutton loves chocolate ice cream. He loves any kind of chocolate, really. His pronunciation of chocolate turns some heads. At least for the moment anyway.
Little boy, big words