fourteen ~ quasar

In recent years, I have been learning math concepts and obscure number facts for each birthday Quinn reaches, in keeping with his own fascination with math. It helps me grapple with things like the slippery acceleration of time, and learning how to accept that my baby is growing up. It brought comfort to me that 10 was an order of magnitude, 11 was indivisible, and 12 was sublime.

I wasn’t sure numbers would be consoling this year. On the day before Quinn’s fourteenth birthday, the United States surpassed 500,000 Covid19 deaths, so the flag today outside my work was flying at half-staff. Quinn has been living solely at his dad’s house since March 14, pi day, so we have now been separated for 346 days with only a few in-person social distance masked hikes infrequently taken. These are numbers from which I can derive no comfort on this birthing day.

That 14 is part of pi, however, is a pleasing aspect of Quinn turning 14. He was born at 3:14 PM, pi o’clock, a time that catches my eye on a digital clock occasionally and makes me smile. So I thought I’d find out if there was anything fun about 14 that might help me create some joyful meaning on a day when I am painfully aware of some numbers whose meanings are devoid of joy.

I asked Quinn during our video call last night whether he thinks 13 and 14 feel different and he said a definitive yes, though he did not articulate the difference. I wrote last year that, “Thirteen is cleaning his room independently, having a passport, opening a checking account, getting a debit card, taking ownership of his google account, having an A in Algebra, reminding me not to buy anything “too dorky” when I went to buy some paper party plates at the dollar store. It’s sitting here writing this blog post while some new teenagers sing Take on Me and fling themselves around the trampoline, then carry out a Dungeons and Dragons campaign, emptying bowls of snacks while one of them strums my guitar. Imagine thinking 13 is unlucky. In Italy, where Quinn is heading soon, fare tredici (translated literally, to do 13) is to hit the jackpot! Any way you calculate it, 13 feels incredibly lucky to this mama!”

At least, that’s what it seemed like thirteen was going to be. Instead, we found ourselves in a global pandemic, and so much of what we anticipated about lucky 13 was irrevocably changed. No trip to Italy, nor even to the bank to obtain the debit card, no more friends on the trampoline, not even emptying any bowls of snacks on my kitchen table.

So I hesitate to say what I think fourteen will bring, unsure if the trip to Italy or other much hoped-for events such as reunion with each other and with beloved family members will be occurring during the year he is fourteen.

But I’ll give it a shot anyway. I think fourteen is: taking charge of his own schooling in unprecedented ways. Being informed and opinionated about the wider world. Humor that grows deeper, darker, richer, funnier all the time. Empathy that grows long tendrils reaching ever outward. The first taste of cynicism, of disappointment in his fellow humans. Realism, but also relentless hope. A fervent belief in the long arc of the moral universe bending toward justice if we push on it right.

I’m going to forgive myself if my assessment of fourteen doesn’t sound as perky as some years. It’s taking courage to show up and write today at all, and I am cutting myself some huge slack if the light of my metaphors does not escape the event horizon of the black hole that has been sucking my motherly soul for nearly a year. I also took myself to the beach briefly, as the sun came out after days of rain on this day of celebrating my son. The first thing I saw in the sand was a fossil, of course.

Then I met Quinn in the lab parking lot and delivered him his “birthday garbage,” a big trash bag full of presents, and I took this one photo of him. Tonight I will watch him open presents over zoom, where they will be piled at the foot of his bed just like in Harry Potter.

And now for some other fun facts about fourteen…

Silicon has atomic number 14. Quinn is a big fan of the periodic table, especially as written by Theodore Gray in his book, Elements:

“Silicon based life forms have been the subject of speculation in science fiction ever since chemists pointed out that silicon, of all the elements, is most like its neighbor, carbon (6), in its ability to form complex molecular chains, in some ways not unlike the long-chain carbon molecules that are reading this text. (That means you.)

“About the only thing that doesn’t have a lot of silicon in it is you: while some sea sponges grow bones of silica glass, your bones, assuming you are not a sea sponge, are calcium phosphate, in the form of rigid hydroxyapatite foam with almost no silicon.”

An honorable mention goes to nitrogen, with its atomic weight of 14.0067 g/mol. As an indispensable component of fertilizer, we depend on it for food. In its liquid form, it cryo-preserves specimens to -196 degrees C, useful for, say, ensuring the integrity of a coronavirus vaccine, or preserving elephant cell lines into which you might want to splice woolly mammoth genes, or putting Han Solo into cryogenic stasis. (Oh wait, that was carbonite).

Quinn has been making an elaborate D and D scenario (character, map, script) for his dad to play, and said that on the province-level maps he makes, the side of one graph paper square is one mile. “Or, square root of two, going diagonally.” Just showing off his knowledge of right isosceles triangle geometry.

Speaking of Diagon Alley, we are closing in on the ending of the final book of Harry Potter, and Quinn was delighted to hear that I had spied someone wearing the sign of the deathly hallows printed on their face mask. I made Quinn some math equations to graph that turn into a message for him that I think will remind him of that symbol. But the message really says I cardioid U Q.

 

In other comfortingly familiar pop culture, 14 appears in Star Wars when Rey, in The Force Awakens, realizes she’s on the Millennium Falcon. “This is the ship that made the Kessel Run in 14 parsecs?” Han of course barks, “Twelve!”

But back to the square root of 2. Last year we were thrilled for Quinn to celebrate a Fibonacci birthday, but 14 also belongs to an infinite sequence of numbers called companion Pell numbers or Pell-Lucas numbers. The closest rational approximations of the square root of 2 in fractions follow a sequence

1/1, 3/2, 7/5, 17/12, 41/29…

The denominators of said fractions are the Pell numbers 1, 2, 5, 12, 29…

And if you double the numerators you get the companion Pell numbers 2, 6, 14, 34, 82…

14 is in that group!

Like the Fibonacci sequence, the Pell companion sequence grows exponentially, like other things that shall not be named, but in this case to powers of the silver ratio 1 + √2. Quinn would happily embrace this ratio, irrational though it may be. Like the golden ratio of Fibonacci, the silver ratio can be represented visually as a spiral. My forever favorite symbol for the passage of time as a mother.

Spiraling outward, we can look at the universe at large for more instances of 14, like Messier object M14, a globular cluster in the constellation Ophiuchus. Better yet, NGC 14, an irregular galaxy in the constellation Pegasus! Not as far away as GNZ11, maybe, but located in a winged horse from some of Quinn’s favorite mythology is good!

His birth story aside (let’s just say maybe his mother was a bit misunderstood), it is said that when Pegasus was born, he flew to where thunder and lightning are released. Everywhere he stepped on earth, springs of water sprouted (naturally, as his dad was Poseiden). My favorite detail: when Zeus rewarded him by transforming him into a constellation, a single feather fell to the earth.

He earned that reward for helping Perseus rescue Andromeda from the sea monster who was going to eat her as punishment for her mom bragging her beauty exceeded that of the sea nymphs. Perseus turned the monster to stone by showing it the decapitated head of Pegasus’s dear old mom Medusa, and they lived happily ever after. So Pegasus will forever shine in the night sky, as will Delphinus, the dolphin who comforted Andromeda while she was chained to a rock at sea.

Anyway, NGC 14 galaxy is irregular because it appears like it is separating apart. I feel that. Separation can feel pretty irregular. It’s not the only galaxy inside Pegasus – there’s a whole cluster. There’s a spiral galaxy in there, some 40 million light-years from Earth. A supernova exploded there in 2014 while astronomers watched. One of the stars in the Pegasus constellation is also the first star known to have a planet orbiting around it, also known as an exoplanet, about fifty light-years from Earth.

Then there’s the Einstein Cross, also located in Pegasus. It’s a quasar, which starts with Q, and is therefore awesome. This quasar is 8 billion light-years from Earth and does a nifty thing called gravitational lensing. Because it sits behind a galaxy from us, one that is 400 million light-years away, and because quasars are intensely luminous, the gravity of the galaxy bends this intense light to project four images of the quasar around the galaxy. And that is just rad.

just a beach picture that reminds me of galaxies

So this Q thing, with its extreme luminosity, gets its powerful energy from matter being sucked into a supermassive black hole at the center of a galaxy. It took a while to work this out. Around the time of the flu pandemic just over a century ago, astronomers were figuring out that some of the objects they were looking at in space were galaxies like our own. In the 1950s, some of the objects being detected out among the galaxies had properties that defied explanation. They were thought to have very small sizes, but to put out the amount of light they did, they either had to be enormously powerful for their size, or be traveling at a velocity beyond the speed of any known star. These astronomical puzzles were named quasars. In the 1960s, measurements and observations were made and their implications debated. Were unknown laws of nature invoked?

Though no mechanism could explain the enormous luminous power of quasars, some astronomers held this as the most likely scenario – that they were very small and very far away but packed a lot of punch – more than the energy conversion of nuclear fusion. In 1964 the currently accepted explanation was put forth but was rejected by many because black holes were still theoretical. Now we know that many galaxies, ours included, do have supermassive black holes at their center, but at the time this was unconfirmed.

Quasars played a big part in drawing together the fields of physics and astronomy. In this time of separation, I like to think of things that are instead drawing closer. Einstein’s general theory of relativity predicted the gravitational lensing of quasars, and in 1979 this was confirmed by astronomical observation.

In summary, quasars are found at the heart of galaxies; they are some of the most luminous Q-named objects in the universe, with an energy output greater than the hundreds of billions of stars of our Milky Way. The light from some of the most quasar-y quasars had to have left its source only a few hundred million years after the Big Bang in order to be reaching our eyes, that is how profoundly distant, and bright, quasars can be. And if light from such a corner of the universe can meet our eyes, there are far shorter distances we can hope to traverse in far shorter periods of time, even if the times are unknown for right now, and that is a nice thought. Distances larger than the distance light could travel in the 13.8 billion year history of the universe have been traveled by quasars, because space itself has also been expanding. Wrap your head around that.

And even those distances are smaller than the size of my love for another luminous being with a Q name: fourteen quintillion light-years traveled by the light of a quasar. To me, Quinn is out of this world. Happy Birthday Mighty Q!