~a month in the life of a lifelong learner~ favorite college professor

Posted on March 10, 2021 by marybethrew

~June 23 to July 23, 2020~

Dinosaur Discoveries virtual camp

Since camp was during the day, we moved our noon video call to 6 pm for camp week. He was animated! I wasn’t sure if it was the time of day or due to camp, but he was ON FIRE in his nerdy mind. I got on the call on the first night to him frantically spinning his cube into an alternating colors pattern and he held up the blue-and-green side to the camera and said, “this is like a nerve check for me because I have to do the opposite of what I’ve trained myself to do,” and then babbled for the whole hour about phylogenies and homologies.

That day they made a tik tok, a google slideshow, did an interactive (video game) learning module, read and discussed a scientific publication. They talked about how paleontology, biology and geology relate to each other. They used starburst candy to illustrate the rock cycle (melted by microwave onto cardboard: igneous.) Two of his buddies from camp last year were in attendance, and he added seven new teens and two new instructors to his paleontology community.

The theme for day two was “geologic context of the Mesozoic,” because isn’t that what we all think of in our summer camp memories? They did a Pangaea puzzle, read about and discussed some contemporary dino fossil discoveries, met with a real paleontologist, sifted a bag of sand to find a whole bunch of fossils (24 sea snails, 17 amber pieces, no trilobites, 3 squids, gastropods, ray teeth, shark teeth – some of them not yet counted).

Day 3: biologic context of the Mesozoic. Mass extinctions, why birds are the only living dinosaurs, why Triassic animals were just the weirdest, a handy paleontology database. This was a dress-up day and Quinn chose to wear his “brambleproof” long-sleeved shirt, his Indiana Jones hat, and a rock pick. He worked on his dino diorama, which they made in the box that the camp supplies were shipped in.

Day 4: Reading the fossil record! Quinn finished up counting his sifted fossils and had 32 pieces of amber, 25 Sahara gastropods and 3 fragments (so at least 28 individuals), and he mentioned both Devonian squid and a Devonian fish called Dunkleosteus, but I’m not sure if they were included among his fossils. His knowledge on this subject has far exceeded mine and I can no longer keep up! He discovered he did have half of a Trilobite. On this day he was set the task of writing a scientific report of one of his fossil finds, and he came up with this:

“A new genus named a Trilobita was discovered to have lived about 520 million years ago and though not all measurements are available the specimen is certainly unique. The front half of this almost crab-like creature has been preserved in its 3-D structure representing a very small creature living in the Upper Cambrian Lodore formation.”

“I made up the part about the formation that it was found in, and I approximated on the million of years ago. Also I’m not sure if I’m pronouncing Trilobita correctly. Trilobita?” (Think: kilometer/kilometer.)

Quinn has a theory on Trilobites; that they were the first sentient organisms, and that they traveled in groups. I let him talk that night and recorded some audio after he introduced his Trilobite theory. These are just some segments I gleaned from a twenty minute treatise:

“To me it looked like in our fossil record, all of the things in that time period look practically the same almost, like really really similar, so it makes me think there was one kind of first species that evolved and then that evolved into a whole myriad of other things that evolved into a multitude of different things. Each species branching as it goes. To me the length of a species is determined by when it branched off the thing behind it to when it branched into multiple different things itself. That’s how I think of how long a species lived… when did it come into being from the thing that branched to BE it? That’s the start of it. and then the end is when it branched into multiple things itself. And everything kind of looks really similar that we have from back then. So it kind of looks like everything is one thing. And then that thing splits into several similar things. I mean a bird doesn’t look anything like a whale. But if you trace the two back far enough, then like a chickadee and a humpback whale, were once the same species. It might be somewhere back in the Mesozoic or before the Mesozoic, it might have been different things already when the dinosaurs were alive but if you trace them back far enough, everything has a common ancestor with everything else. So my thing is I’m thinking of like the ultimate common ancestor. I think of a trilobite.”

“Like someone looks at a rock on Beverly beach and is like, “there’s a clam shell imprint here,” but you can only see this little imprint for a bacteria if you’re looking at it micro microscopic. Attach several microscopes to your eye and walk around Beverly beach.”

“Soft parts still fossilize is my thing. If you think about it, it’s not the meteor strike that wiped everything out. It incinerates everything in one small area. Back then we happen to know that there was pretty much one continent with several large islands around it, maybe? And even when that was the case, that all the water that had life in it, was all one thing. You can swim from any point in it to any other point that has life in it. and so the biodiversity wouldn’t have been the greatest…”

“A meteor hits. let’s just say at the time trilobites are alive a meteor hits and we don’t know about it- it doesn’t deposit what it usually does or whatever. Let’s say that’s what wiped out the species then except for what evolved into what we have today… If there were bacteria I think they would have fossilized, because in the water, their soft forms would slip between molecules… If you’re willing to actually be really careful and chip them out of the rock, I think that you would have ended up with (and this is all under a microscope that’s under a microscope that under possibly another microscope.)”

“Even so I think that then that would have been like I don’t know like thinking… I think that that would have been like … I think that that would have fossilized” (I’m including this verbatim to illustrate his words trying to keep up with his brain.)

“If a meteor had struck, pretty much the whole earth is covered in possibly a mile thick cloud of ash just hovering above the earth or like encasing the earth. If you think about the Cretaceous-Paleogene extinction, the story goes: meteor hits earth. Ash cloud for several million years, meaning all the plants couldn’t get sun because of the ash cloud so all the plants died meaning all the herbivores died meaning all the carnivores died. Mammals survived because back then we were scavengers right? We were able to eat survive in pretty much any climate. So we were able to just eat dead stuff which there would be plenty of, so we survived.”

“The producers are subsisting off of sun, like just subsisting off of some non-living thing, like eating rocks, or filtering sand through itself, photosynthesis, like it’s always there. And if you use it, it’s not like you use it and some of it goes away. You’re done using it, and you get the energy from it, but it still has just as much energy on itself to give as when you picked it up and used it to give yourself energy. So what the meteors do when they hit is they take away that thing in some way or another. So meteors take away the producers source of energy.”

Day 5: Dinosaurs in pop culture and media! They met with another real life paleontologist, this time one who works on prehistoric penguins, and specifically the plumage – the colors of fossil feathers! Fossils can tell us about the evolution of the shape and color of penguin feathers! And other dinosaur plumage – they learned about a Jurassic bird that had iridescent feathers. The camp kit included (modern) feathers that they had looked at in preparation for this segment. Maybe not all the mamas have gathered piles of feathers for their kids.

This day’s topic on pop culture and media and dinosaurs (and misconceptions about them) was fascinating for Quinn. There were lots of links and resources provided, which were fun things like Jurassic Park and Disney’s Dinosaur.

Here is our conversation about the 1914 animation of Gertie the dinosaur:

“A sauropod eats a boulder and the top of the tree, sees a sea serpent in the lake next to them, starts dancing, eats the other half of the tree, tosses a mammoth into said lake, the mammoth swims back over and blasts the sauropod with water, and then swims away, a mammoth can swim, then the sauropod picks up a boulder and hits the mammoth, and then the sauropod takes a drink and drains the whole lake…”

“When were mammoths and when were sauropods?” His scientist/writer mom replied, modeling her grasp of both science and grammar.

“Sauropods were in the Jurassic period. Mammoths weren’t around until after the Cretaceous.”

“Are you saying it would be anachronistic for a sauropod to toss a mammoth in a lake then? And throw boulders at it?”

“I’m saying that a sauropod wouldn’t have lived at the same time as a mammoth. I’m saying that sauropods can’t toss mammoths by the tail…”

“Even if they didn’t have to time travel in order to do it?”

“If they didn’t have to time travel in order to do it, and they were capable of doing that time travel, and they could actually get a mammoth, they still physically could not pick up a mammoth by the tail and throw it five miles into a lake, and then accurately hit it at that range with a boulder.

“Are you sure? Aren’t you being kind of a party pooper?”

The two camp instructors and both guest visitors were women. I love that this camp group makes a strong effort towards inclusion and is working hard for fair representation for all in a science that has historically been exclusive to white men. I like that my white man-to-be is surrounded by all other types of people in these camps.

Q and I watched an episode of PBS prehistoric road trip together that night.

Day 6 was the final day of Dino camp, and they presented their Dioramas and played games.

On his diorama presentation, Quinn was complimented that he must have done a lot of research because of how his time period aligned with the species of dinosaurs and plant life represented. Here is his spiel:

“This is my museum diorama of the K-Pg extinction which is extremely late cretaceous. So the meteor is still in the sky yet it has already struck, so all of the grass has been burned off, and the rocks are bleached because of the immense heat. there is a river running through here, and there is a velociraptor pack here attacking this herd of triceratops, and all that’s left of these trees are small shrubs, which the triceratops herd is taking cover in trying to save themselves, however the raptor pack has expertly sent in an ambusher from behind. there are also a pair of tyrannosaurs attacking these two ankylosaurs, because big predators like tyrannosaurs assuming they were predators and not scavengers, would probably hunt in pairs or trios rather than full packs. there’s a quetzalcoatlus up in the sky looking for food, and there’s a volcano that’s erupting.”

He told me that night:

“For our final meeting they gave us like traditional class clown, most likely to become a rock star awards. Except they were specific to us regardless of the traditional ones. Frizzie got most likely to lead a paleontology expedition while wearing fancy clothing. Lead got most likely to draw the most scientifically accurate drawing of a T. rex. I got most likely to become everybody’s favorite college professor which I think is extremely accurate.”

Extremely!

(slightly modified by mama)

In which I realize why this post incubated a while…

I revisited my educational priorities for Quinn during this month. This was motivated by looking ahead to the 2020-2021 school year and grappling with which path to choose: hybrid online/in person public school, fully online Edmentum public school, or fully homeschool. Because I am writing this as we approach the end of 8^th grade, I know what was chosen and how the story turned out to not be about what I would choose at all. It’s weird to have been thinking about things like scaffolding removal and then realize – oh we’re done with scaffolding. Now he’s taking charge of his own path. He chose Edmentum, and has handled his schooling. It turns out the scaffolding was even more temporary than I realized, and I was slow to take out the final pieces despite my awareness that removal was the goal.

Since I’m writing this later, I have control over leaving out the awkward and tense discussions of pros and cons, of offers on my part to advocate, which he kept gently but firmly turning down. I can see now that he was telling me he’s got this. If we had homeschooled, it would have been something he was doing to please me. (I cannot ensure that he did not choose his path out of wanting to please his father but that is out of my control. )Yes, I know it would have been odd to homeschool remotely – him at his dad’s but with me facilitating learning. But that would have worked, in fact I’m confident we would have slam dunked it, if it had been what he wanted and needed. It’s just that it wasn’t. It’s just that it was hard for me to hear that at first.

When I wrote the priorities, consent took up more of the bandwidth than it had in the past, though I could see it was there all along when I wrote the original mamafesto when he was six. It just wasn’t named quite as directly – it was emergent curriculum, choice, opting in. Looking through a 2020 teen parenting lens, consent rose to the surface. As I rewrote, I was thinking about how he needed to have autonomy in body and mind in the learning context. Keep those outside influences at bay and let him decide for himself, follow his own compass. But I was still a little bit holding onto some need for control over his learning in that way we have as parents of operating from a blind spot. The cliché about practicing what we preach. The cliché about 2020 and hindsight. Again.

So I’m leaving the awkward, tense conversations in my private journal, with this mile marker placed here from my somewhat expanded perspective of months. A reminder, an honest reckoning with yet another thing that was tough about the past year.

Quotable Quotes of Q:

“Flight was not why things evolved feathers… feathers were why things evolved flight.”

“When overwhelmed thinking about covid, I distract myself. Like, I think about how to write pi in binary.”

“An Illithids mindflayer is like a dementor possessing Davy Jones, but purple.”

Literature

We spent time in Rohan this month, and by the time we ended the month were reading the Appendices.

Q read the Monkey Wrench Gang this month.

We discussed the pronunciation of pronunciation.

One evening I just sat for a while, listening to the sound of popcorn popping upstairs, and the pages of Calvin and Hobbes turning on the other end of the video call.

Math

“Volume of a warbler” and “how many warblers on earth?” Oh, the things you google. These were inquiries during Quinn’s quest to remix Vi Hart’s binary tree of birds – her turducken-en-ducken-en…. but with 13 birds nested inside each other bird, in a long list of types of birds.

Which brought him to the question, “How many birds in the world?” So he could compare to how many in this thirteen-to the eighteen factorial power bird stuffing scheme. The 200 billion birds in the world seems like a big number, however, >121 quintillion is way bigger!

He took this ridiculously high numbers of birds even higher and google calculator eventually returned the result, “Infinity,” and he was laughing so hard at breaking google again.

Honorable mention to, “how many square feet is New York City?” and an ensuing discussion of area codes.

Nature

He was visited by a grouse in the pile of firewood he has been using a splitting maul to help create. He also used the hatchet to strip small branches off limbs, and off one cedar sapling they used to make a railing. He helped replace deck boards and build a deck addition. The seeds from Sam’s garden box were beginning to sprout – he described the sunflowers “busting out” of their seeds, and the pea “vines” that were starting to lengthen and reach out curling tendrils. He saw the comet on a few different nights, explaining to me the best time to see it at sunset and how the remaining light on one side of the sky made it shine brighter against its darker corner of the sky.

More dinos

This is Q’s giddy anticipation the night he unveiled his plans for what we would do after we finished reading the appendices.

He recreated the dinosaur game he made up on graph paper where I had to build my own Jurassic park role-play style, in a google sheets version for us to play together remotely!

Another memorable quote for the month came a few days later, “oh my god, oh my god, I’m so excited about this dinosaur game.” And we did start in before the end of this month, by the end of which I had collected three different ceratopsians and some stegosauruses.

Oh, the dinos you’ll know!

tides

Posted on January 10, 2020 by marybethrew

I have always been fascinated with the tides. For me, the place at the edge of the ocean, where the earth, air and water converge, is where the magic and bioluminescence are found. When I was in college, a few of my courses contained lessons on what drives the tides, and while most of the learning from the courses of that time period has ebbed away from the shores of my mind, I tucked those particular sets of notes away in a folder to one day revisit, so that I could stitch together the fragments I had learned into a more cohesive understanding.

Twenty years after college graduation, the time has arrived! I saturated my brain with this topic over the first weekend of 2020, autodidacting my way through a weekend graduate course in tides. The second chapter of my book (now that one chapter is written I’m daring myself to say out loud that I’m writing one) contains a tidepooling scene, and in my quest to represent factually both my level of understanding of our local tides at the time, as well as to avoid putting any dubious information out into the world, it felt like an auspicious moment to take this deep dive. A big part of my quest is to take on the challenge of writing about such subjects without wringing all the life out of them, but instead retaining as much of the magic and bioluminescence they naturally contain as I possibly can, to write descriptively and with metaphor about topics that often get handled, instead, with stuffy textbook sterility.

It took immersing myself in this coastal reality with a tide chart in my pocket to be able to holistically appreciate the factoids I had memorized in school. With theory and experience tucked under each arm, I waded in.

In disentangling the enigmatic cycle of the tides and putting it into words, I’ve noticed that my notes from each of my undergraduate courses contain only incomplete segments of the information, and that online resources, even from my beloved NOAA dot gov, are likewise incomplete and occasionally provide some misleading or conflicting information. I gleaned useful clues where I could and sorted through inconsistencies to integrate the theory with my lived experience to support the scene in chapter two.

Then I ended up with 700% more brainiac thoughts on the matter than the chapter requires, so the overflow is resulting in this blog post. This way when I forget what I learned, I can come refer back to this synthesis.

In my notes from Dr. Serafy’s Field Bio taken in the Spring of 1997 was a list of three types of tides that came closest to being understandable and seeming accurate, but it was missing one level, and some further nuance. His hierarchy of tides spanned daily, monthly and what he called yearly categories. I would compile a new list with four levels including daily, monthly, I would change his third category to monthly-yearly, and add a fourth level yearly:

Daily aka Diurnal tides: twice a day high, twice a day low, at least where I live. We can visualize the earth rotating through a bulge of water created by the gravitational forces on the earth’s oceans of the moon (primarily) and the sun (secondarily). When our geographic location on earth rotates through this bulge, we experience high tide, and as it rotates through the skinny part of the bulge, we experience low tide. On the far side of the earth away from the moon is a similar bulge, the result of centrifugal force – so we get one more high and one more low before we return to the point of origin on our rotation. Though the earth takes only 24 hours to rotate once on its axis with respect to the sun, it actually takes 24 hours and 50 minutes for the earth to return to the same relationship to the moon because the moon has also been moving during the 24 hour period and it takes 50 extra minutes for the earth to catch up.

Monthly aka Lunar tides: The pulling of sun and moon in synchrony or at odds with one another result in spring and neap tides. Full moon and new moon are created under conditions of syzygy, you’re welcome for this awesome new word in your life with its three sometimes vowels, which means the tidal forces of moon and sun act to reinforce each other, and cause the diurnal tides to be spring tides (higher highs, lower lows). Closer to half moons, the lunar and solar forces run perpendicular to and therefore counteract each other, causing more moderate neap tides which see the smallest change between high and low tide (higher lows and lower highs).

Monthly-yearly aka Perigee tides (Dr. Serafy called perigee tides simply “yearly”): Each trip of the earth around the sun (we call this a year) contains about 13 lunar cycles of 27 1/3 days. During each of these thirteen trips of the moon and earth around each other, the moon is closer to the earth at one point each month. This state is called perigee and is a consequence of the moon’s orbit being elliptical; apogee is when the moon is farthest from earth. Perigee produces even higher/lower spring tides. Twice-ish per year, the timing of this close approach of the moon to the earth coincides with the lunar spring tide on the new moon or full moon, and the effects are additive, resulting in spring tides of even greater magnitude. We can call this perigee syzygy, okay?

The internet will tell you that perigean spring tides occur “about three or four times per year, in spring and fall” but I took some time and dissected what this meant, and what it means is that in spring and fall, the syzygy-perigee phenomena are most likely to overlap each other in time, so the best bets are around March and October. Like blue moons, sometimes we can get an extra one or two of these perigee-syzygies happening in, say, April, or September. This year, in March, a full moon (syzygy) will take place on the 9th, while perigee will occur on the 10^th! A nice block of negative low tides (6^th through 11^th) coincides with this lunar magic. In October, we’ll have new moon perigee syzygy, both occurring on the 16^th, with several days of negative tides once again.

A September 17^th-18^th new moon perigee, and a full moon perigee on April 7^th seem like they bring us to four perigee syzygies for this year! It seems that we probably have perigee-syzygy a minimum of twice per year, and could have it up to four times, with two of them having possibly slightly decreased magnitude based on how well synchronized the perigees and syzygies are.

Finally, Yearly aka Perihelion tides would be level four on my list: The sun is closest to earth (a condition called perihelion) on January 2, and farthest (aphelion) on July 2. (Aside: I know that sounds backwards, trust me it’s not, we have summer in the northern hemisphere because of the tilt of the earth on its axis, and that tilt being oriented sunwards in summer; summer is not a condition of the earth’s distance from the sun.) When perihelion and perigee coincide, the result is what in the past decade I started hearing referred to as “king” tides. If we picked ONE king tide of the year, it would be the high tide associated with the perigee-syzygy situated closest to that January 2^nd perihelion: in 2020, the closest perigee is January 13, and the closest full moon is January 10 (hey, that’s today! First full moon of 2020!). The absolute highest high tide for the year, then, is predicted to occur on January 11, according to my tide table. Oh hey, that’s tomorrow!

last full moon of 2019

Sea level matters… so, the January king tide will have a nice negative low tide corresponding to it, but the lowest of low tides for the year will not occur until June. Sea level will be at its lowest in summer, which is one factor contributing to this being the case (but not the only one).

The folks in charge of king tides have named quite a few dates as king tides, not just ONE regal tide reigning for the year. Still, these dates do cluster around the perihelion, corresponding to when the perigee-syzygies occur.

Winter 2019-20 king tide Dates:

November 25-27, 2019

December 24-26, 2019

January 10-12, 2020

February 8-10, 2020

I looked at them closely, and I believe they can be summarized as occurring around perihelion, around perigee UPON (some of) the new/full moons between November and February. Let’s call them perihelion perigee syzygy tides instead of king tides, alrighty? The syzygies of interest in November and December happen to be new moons, while the ones in January and February happen to be full moons. This isn’t coincidence, it has to do with the stuff I said before about “more nuance” that I was missing from my notes from college (keep reading).

After I had tackled this much of the tide cycle picture, I still didn’t understand why the “clamming” negative tides always take place in the morning during summer time, and in the evening during winter time. I took it as a clue that these big tides are close to solstices, and another clue that the “switch” from the high magnitude tidal variations from morning to evening occurs very close to spring and fall equinoxes – you can see this in very abrupt jumps from the AM column to the PM column of the shaded “negative tide” segments of the months if you thumb through your pocket tide table. Okay, so this is something seasonal, which means, it relates at least in part to the sun.

Seasons happen, as I mentioned earlier in an aside, because the earth is tilted on its axis, and as it revolves around the sun, the angle of the relationship between our equator and the sun changes. Let’s be geocentric for a second, and we’ll talk in terms of declination, which is the angle of a celestial body above our earth’s equator. Declination is a term I learned during celestial navigation, because if I knew the angle of the sun above the horizon wherever I was in time and space on a schooner, leaning against the rail measuring said angle with my sextant, right at exactly noon, this translated very accurately (through some complicated mathematical gymnastics) into my latitude. Which is good to know! At dawn or dusk, when a few stars and the horizon could be seen through the sextant, triangulating the latitudes indicated by the declinations of several of these navigational stars could be used for another accurate latitude estimate. We can talk about the declination of any celestial body – stars, sun, planets, moon, even though we realize they’re not all revolving around us.

From our earth’s equator, the declination of the sun can range from 0 degrees (at both equinoxes) to 23.5 degrees north latitude, (on ~June 21 or Northern hemisphere summer solstice) or to 23.5 degrees south latitude (on ~Dec 22 or Northern hemisphere winter solstice). When the sun’s declination is 23.5° North, it is the closest it is going to get to our latitude of roughly 45° north, giving us our longest, warmest days we fondly refer to as summer.

Guess what! The moon also has a declination! The moon’s orbit is at about a 5 degree angle to the earth’s orbit around the sun (confusing, I know, but we’re juggling three balls here) and so when considering all three orbs, we arrive at maximum north and south declinations for the moon of 28.6 degrees. The moon travels between its maximum extremes of declination north and south (and through zero declination relative to our equator) during each lunar cycle (aka month). Here in the north, it pulls on us hardest at its maximum northern declination. Any phase of the moon can correspond to any declination, but!!! There are times of year when the moon’s maximum northern declination (when it pulls on us most and makes our higher tides higher) coincides with syzygy (which is when our high tides are already higher because of full or new moon). These effects are additive as well, so when we have both conditions coinciding, we get extra big tides. As much as I read about this, it took drawing myself a diagram to fully grasp how this interaction of the moon’s phase and its declination indicated June low tides in the morning and December low tides in the evening.

When we are at the part of our trip around the sun where our axis is tilted towards the sun (and it’s summer solstice) and we are at the part of the moon’s cycle where it reaches its most extreme northern declination (it’s at 28.6 degrees just because that’s where it is in its orbit), AND we are in a state of syzygy (new moon in the case of summer solstice), we get the most extreme “diurnal inequality” of tides, in other words, our extreme low low razor clamming tides. In the case of summer, the highs will not be quite as high as the winter king tides, because sea level is lowest; the corresponding highs are maybe 9.5 ft instead of the 10 ft levels of king tides.) This June, we will have a very low tide on June 23 of -1.7 ft (perigee will occur June 30, syzygy/new moon will take place on June 20, and maximum moon declination will take place on June 22, with, of course, maximum sun declination on June 21). We will also have a -2.3 ft low tide (the most negative low tide predicted for the coming year) on June 6, with a perigee on June 3 and full moon on June 5. I think that the close correspondence of perigee and full moons in May, June and July are the reason the tides closest to full moon on these months will be the lower lows for those months.

In winter, the maximum northern declination of the moon (Dec 30) will instead correspond to a full moon (Dec 29) near winter solstice (Dec 22). Still with me?

Finally, to really get why the summer lows are in morning and the winter lows are in evening, we need to consider that the moon, when it is new, crosses overhead at noon in our geocentric paradigm. When the moon is full, it crosses overhead at midnight! (I have always felt that it is magic that the moon rises right at 6 pm whenever it is full, so we get to see it, and not be asleep for it.) The big low tides following syzygy occur about 18 hours after this passage of the moon overhead, at either time of year. Without getting too technical, the actions of gravity are not instantaneous because we are subject to laws of physics like friction; there is lag time. Summer solstice low tide associated with new moon, therefore, takes place 18 hours after noon, or the next morning around 6:00 a.m. Winter solstice low tide associated with full moon happens 18 hours after midnight, the following evening around 6:00 p.m.

Okay! That’s all there is!

Just kidding, that’s not it… there’s more! (But you might need to go make more tea.) Please…. Consider the following:

One of the most memorable and mind-blowing days of my undergraduate career was the day my physical oceanography professor had us perform a harmonic analysis and compile a tide chart from 11 different harmonic constituents of the local (Long Island) tide. Harmonic constituents are the things I was talking about above – the various forces acting in concert to produce the tidal cycle, mainly exerted by the moon and the sun, except summarized into coefficients, numbers that tell exactly the magnitude and frequency at which these forces are exerted.

Harmonic analysis is based on Fourier theorem which says that any repeating disturbance can be written as the sum of a series of sinusoidal waves. You can superimpose a collection of sine/cosine curves of different frequencies and amplitudes upon each other, adding and subtracting their contributing magnitudes at any point along the x axis of time to result in a function representing any “repeating disturbance,” say, a tidal cycle. I like that it is called harmonic, because that makes me think of music, and the harmony of all the different instruments and voices working together to produce one cohesive piece of music.

Here are two cosine curves with different magnitudes and frequencies.

Here I have marked them up to show how you can add them together. At any value on the x axis, you come up with a new y value that is the sum of the y values of the two separate curves. At certain points along the x axis, the effects of the two curves will reinforce each other, while at other points, they will counteract each other.

All you need to do is connect the dots and you have found the sum!

Here the sum of the two blue curves is shown superimposed in orange. You can see that in some places, the two original curves worked together to produce larger peaks, while in other places, they offset each other and resulted in a more moderate value.

The various cosine curves we add together each represent one component of the moon’s or sun’s influence on the tides, that when combined, will either reinforce one another and add up to bigger tides, or will cancel or counteract each other and neutralize the curve to result in smaller tides. If you visit the NOAA tidal prediction page, you can download a set of 37 harmonic constituents for each of a whole bunch of different geographic locations where we might care about the tides, and then generate the tide tables for that area. My professor had us do this with just 11 of the harmonic constituents, of course he chose 11 of the ones that play the largest role in formulating the tides. First, we plotted 11 different cosine curve time series as separate functions. Then we added them up.

Tidal predictions will not always equal tidal observations in real time, because the predictions are based only on the gravitational forces acting on the tides, while other factors such as onshore winds and storm surges can play an unpredictable role as well.

OK! Let’s do the same fun exercise for right here on the Oregon coast!

For South Beach I found the harmonic constituents, starting with M2: amplitude = 2.91, phase = 359.3, speed = 28.984104

For each constituent, we need to graph the function:

h(t) = R cos (at-φ)

Substituting in amplitude for R, speed for a, and phase for φ (that’s lowercase phi for the Greek fans in the live studio audience).

For our first constituent in South Beach, M2, we plug in our values and graph this equation:

h(t) = 2.91 cos (28.984104t-359.3)

And it looks like this:

M2 is the Principal lunar semidiurnal constituent, one of the many semidiurnal factors acting on the tides, semidiurnal meaning twice a day. Some constituents do their thing once a day, and others with more frequent (terdiurnal like meals!) or less frequent (fortnightly like fried chicken cravings! Annual like birthdays!)

Here is K1, the Lunar diurnal constituent. Compared to the twice a day constituent, you can see the difference in the wavelength, even if you don’t know the Greek symbol for that. This one does its thing just once a day.

Wait till you see the next one! Hold onto your teacup!

Looking at the same time frame for the SA Solar annual constituent, it looks like it’s not a repeating function at all… because we’re only looking at one day! It will take a whole year for this one to repeat itself.

See it now? I changed the scale of the x axis to show a whole year of the solar annual constituent, instead of just one day.

A whole bunch of constituents graphed as separate equations on the same grid

You can see how much each variable of the constituent matters as you graph each one, and what they do to the graph as they change. Large amplitudes will add more height to the tide… They will add it at greater frequency based on the speed, so that a new peak happens, say, every 27.3 days instead of every 365 days. The amount the whole curve is shifted along the x axis away from the origin is determined by the phase.

You can see how each of the constituents doing their own thing is a pretty graph, but not a tide table. Each curve repeats… well, repetitively, without the variation we’re used to in our tides, for example, here is what our January 2020 looks like:

We get to this by adding our separate curves together! Let’s start by adding just two components together. This is M2 + K1 or

h(t) = 2.91 cos (28.984104t-359.3)+ 1.42 cos (15.041069t-117.7)

showing this graph within the desmos interface where I made them all

Wow! It already looks more like a tide table! Each time we add in another constituent, the influences reinforce or counteract each other in such a way that the curve starts to approach what we are used to in our tide tables – now there are some higher highs and lower lows aka spring tides, and some more moderate neap tides, and they come and go in a wave of their own.

I made this!

For 730 hours (aka one month), behold an approximation of the tides in South Beach based on 8 tidal constituents namely:

M2 Principal lunar semidiurnal constituent

K1 Lunar diurnal constituent

O1 Lunar diurnal constituent (they’re fraternal twins, OK?)

S2 Principal solar semidiurnal constituent

N2 Larger lunar elliptic semidiurnal constituent

P1 Solar diurnal constituent

SA Solar annual constituent

K2 Lunisolar semidiurnal constituent

M2+K1+O1+S2+N2+P1+SA+K2

Which really looks like this in equation format:

h(t) = 2.91 cos (28.984104t-359.3) + 1.42 cos (15.041069t-117.7) + 0.86 cos (13.943035t-109.8) + 0.79 cos (30.0t-19.3) + 0.6 cos (28.43973t-339.9) + 0.44 cos (14.958931t-114.2) + 0.4 cos (0.0410686t-285.5) + 0.21 cos (30.082138t-9.9)

My understanding is that there are hundreds of harmonic constituents if not an infinite supply beyond the 37 reported by NOAA, if one wanted to measure the way each star in the galaxy exerts a (nearly negligible) gravitational tug at one’s shoreline. But we can achieve a functional tidal prediction based on just a handful of the ones that have the greatest influence. We don’t always have to include the Lunisolar Synodic Fortnightly Constituent to be able to predict our tides reasonably well. Nor the Lunar Terdiurnal Constituent. Not even the Shallow Water Overtides of Principal Lunar Constituent (aren’t you glad these names exist though?). But you can, if you choose, or if those constituents play a larger role in determining the tides in your local area.

Back on Long Island during undergrad, our tides were also semidiurnal, and we had two highs and two lows per day, but they were much more equal in height, unlike our Pacific Northwest unequal semidiurnal tide pattern. Plugging in the harmonic constituents for Montauk, NY (I picked this station of the available ones for Long Island because of the purple sand) paints a very different wavy line on our graph!

Some constituents exert a greater influence on tides in different geographic locations! There is still a lot more to learn! Yippee!

I could keep doing this for other locations! Maybe I will! We can try the Bay of Fundy! Or an exotic island someplace! If you want to check out this fun graphing interface I used called Desmos, click on the embedded graph below. I think it could be fun for youngsters taking algebra to play with and explore their equations in a more interactive, engaging, and artful way (hint hint camp boss I’m talking about Panda). Also, isn’t it fun to know those cosines are useful for something you care about in your real life?

Ok, thanks for sticking with me through the peaks and troughs of this learning adventure! I’m off to write more of chapter two!

one year of tides; math oceanography art fun

~a month in the life of a lifelong learner~ smuggle in a dinosaur

Posted on July 11, 2019 by marybethrew

~february 23 through march 23~

The day after quinn’s birthday, as soon as sleepover friends went home we set out for a visit to see/meet our new pancake w. rich had met her on the day she was born, but this would be quinn’s and my first time meeting this new little person, still very brand new at only two days old! Quinn has always liked babies, but i think he has a special even softer spot in his heart for his new niece, born the day before his birthday, and he wasted no time getting her into his arms.

triceratopses and tesseracts

There is a little pisces boy i know who just turned 3 who reminds me so much of quinn. he loves drumming and dinosaurs and is very articulate… when i see him he reminds me a lot of those days. His mom posted a video from his birthday of him opening a present. he gasped, “a triceratops!” then put his little hand out to the side how quinn used to do, “i love triceratopses!!!” studied it some more, found a slot with his finger, “it’s a triceratops so you can put pennies in it!” as his mom elaborated on that, he turned and looked up at the camera with this smile, “it’s for me!”

Quinn and i both watched it over and over. and then we did an anagram of the word “triceratopses” (plural) because, well duh. and i don’t know if it was because we had just re-watched a wrinkle in time that weekend, but one of the first words we found in “triceratopses” was “tesseract.”

he had some poetry homework to catch up on from missing several days of school one week. he was venting about how long the poetry unit had been and how he felt like it was making him hate poetry instead of like it. i told him he should reclaim poetry for his own, and whenever he was assigned to write a poem, smuggle in something he likes, regardless of the assigned topic. we got off on a tangent of smuggling dinosaurs into every poem. To test this idea, he would give me a topic such as “book” and i would say, “the small boy turned to the diplodocus page of his book,” and got him doing it too. all that week i’d ask “did you get a chance to smuggle in any dinos today?”

sand and sea lions

on a wednesday afternoon i picked up quinn from school and took him to the maritime museum. there were tibetan monks visiting, and they were creating a sand mandala all week. They had started creating the mandala on tuesday so by wednesday they had gotten a portion of the work done, and would keep working outward from the center until sunday when it would be swept… it is such a cool concept to me because of the celebration of impermanence, of putting time and effort and love into something in painstaking detail knowing it will all wash away… so much to reflect on there of course. a mystery and a paradox that is central to the human condition, really. i did not know quinn would be so captivated. when we went in, i gave him a tiny bit of background but not much. but he just instinctively knew it was a calm quiet space, he sat down and folded his hands and quietly watched. a woman came over to where we were sitting and watching and showed us where we could make a small mandala of our own and use the tools and get the feel of it… quinn loved making a sand mandala. he was so into it, saying, “we need to do more of this.” and then he was completely fine with brushing it all away at the end! that was the part i was most amazed about, i think. the metal tools for the sand sounded like such a happy sound, and reminded me of frogs. bayou frogs have been vocal the past week so it is starting to feel like spring, but when i said that both quinn and another little girl who was making a mandala thought i meant the wooden musical frogs (she apparently has some at her grandma’s house and quinn has one as well). the monks were all smiling and doing their work but when they’d take a break they were all on their smartphones and ipads. one of them came over to the table the kids were working at and played a video of the dissolution ceremony of the big mandala (another time they did it) to show them the idea of the whole thing, but it was just so funny (to me- the kids were not phased) to have him prop an ipad up and hit play.

something about the calm of those monks, the happy sounds of the metal tools they were using, the beauty and color of the sand, the sun glancing off the bay in through the windows. he didn’t want to leave.

on our way in he had said he wanted to visit the sea lion dock while we were on the bay front, so eventually after an hour went by i suggested a walk to the sea lions and he was ready. so we walked. he held my hand the whole walk to the sea lions, up and down the bayfront and back to the car. i know he doesn’t even really think about it but i just love that he wants to hold my hand.

at the sea lion dock we watched them for a while (there were lots, all sleeping and jockeying for sleeping positions on the floating docks) and we were commenting on their behaviors. one had a strap or collar around its neck looking like it needed to be removed and it didn’t look healthy, and quinn was moderately upset by that (“someone needs to DO something about that”). our other observations were more amusing. one huge sea lion we nicknamed grandpa was situated on the corner of the dock with his face hanging over the edge. he would lift his head enough to breathe but then let his head loll into the water. you could watch him exhaling bubbles into the water as he slept! there were other snorers above water level, whose cheeks/whiskers you could watch as they would shake or flap, and we’d point them out to each other. the way sea lions assert dominance by opening their mouth at each other… sometimes it gets much more heated with barks and bites, but a lot of times it’s, “i open my mouth in your general direction,” and that settles the dispute. we had fun doing behavioral ecology observations.

social studies homework on ancient civilizations

Also this month we played a game from christmas called tiny epic quest, that we hadn’t had a chance to play yet. It is roughly a board game d and d adventure with lots of little props and pieces and spells and quests and goblins. when he was going to school that friday morning i asked him what his best parts of the week were, and he chose making the sand mandala and playing the game.

he spent some time with his birthday present called turing tumble, a fun marble-programming gizmo with an anime workbook full of challenges that build on each otherr in story format. basically a toy made precisely for quinn.

with 2/3 of 6th grade behind him, he attended his 3rd dance (glow in the dark theme).

pie!!! lots of little blueberry pies. i dropped quinn off at the dojo on pi day (march 14^th) for jump tag and pi day pie fest.

a dear friend commented on quinn’s birthday post that he might like the book navigating early by clare vanderpool so i immediately requested the audio book from our library. he loved it, finished listening to it before i had gotten to the halfway point, so continued to listen again along with me as i caught up. It’s a book that takes place in maine in 1945 about 13 year old boys, friendship, mothers and sons, and brothers. There is hiking on the appalachian trail, boat building and rowing, and fly fishing. It is also a book about pi, which coincidentally made it a wonderful book to happen to be listening to on 3/14. One of the boys in the book knows pi in colors and textures and reads the digits of pi like a story. He is not only a synesthete, but has other quirks of sensory, intellectual, and emotional intensity that remind me of someone i know who also likes numbers. sock seams and shaking water out of his face; in a metaphor for his friend’s ability to be irrationally stuck on an idea, the narrator likens his brain to a lobster in a lobster trap; literal interpretations and sureness of being right; jelly bean sorting to organize his neurons in emotionally or intellectually puzzling situations. highly recommend.

executive function skills

he remembered at 7:15am on the last day of 6 week term, after completing 2 missing assignments (for days on end) and getting up to speed on how to do his upcoming math homework, that he also had an art project to finish and hand in first period that day. doh!

one day he was getting up to speed on graphing linear equations, y= b+ mx; he knew what all the variables meant and understood what recursive functions are and how to find the ordered pairs that solve this equation and how to graph ordered pairs and find the y intercept. and yet… was getting stuck on how to do it. He did not stay stuck for long. however I spent quite a bit of energy trying to convince him that graph paper would be a good thing to use for his homework this time since it is all graphing which is what graph paper was invented for. one feels one is stating the obvious sometimes. he finally came around. again, the culprit was stuckness. having used blank paper all year for math homework he was in a groove and reluctant to change, but in the end realized it’s ok to change your way and adapt to what is happening in real time. increasing flexibility one millimeter at a time!

i distinctly recall feeling thankful for spring break on the horizon!

make like a geek ~ game sliders and creative dice rolling

Posted on January 25, 2016 by marybethrew

a long time ago (2015), in a galaxy far, far away, there was a yoda snowflake.

yes, it all started with a yoda snowflake. that was what possessed me to buy another exact-o knife, even though somewhere in storage, there is already a perfectly serviceable exact-o knife in my possession. even for what could be considered essentials, it is hard to convince me to buy something that i already own a set of in storage. rich had to give me an assignment about long johns one day over christmas break, because thus far into the cold weather months, i had just been carrying on with a single pants layer; the pair of long johns i own are buried deep in a box with all the winter clothes, in a galaxy far, far away, called storage.

unconvinced by my reasoning, he told me i could find time in my busy day to buy myself a pair of long johns. “and get the good ones, not the cheap thin ones.” thank you, honey, for saving me from my frugal self.

i digress. because of storage, and because we had no ornaments, i collected fun free ornament-making ideas earlier in december, and i was excited about star wars snowflakes, and so i overcame my reluctance to buy a tool i already own and got the exact-o knife. i only managed to make the one snowflake, yoda. it was an arduous process, so i laminated that bad boy, and maybe next year i will attempt leia.

meanwhile, my son, game engineer (he named his game engineering firm qaz8quintillion just yesterday; no idea what qaz means, but it sounds like the first syllable in quasi) has taken his game engineering to such a new level that i have started having trouble holding all of the various numbers and quantities and damage points and health points and karma points in my admittedly deficient brain.

game master pajama

another aside: rich laughed and laughed, when my sister-in-law posted a retort about “rew memory” on my bro’s facebook post concerning a time capsule from 22 years ago that he had discovered in the junk drawer. none of us rews could remember anything about it, but apparently he had unearthed it, she said, maybe even within the past year. “good old rew memory” she teased us, for how the same discoveries are novel, over and over again. i think rich felt validated by this aspersion cast upon our collective brains as a family. there are many times he just shakes his head and laughs at my forgetfulness. but, i mean, we’re smart people, everyone forgets things now and then, right?

what was i saying?

oh yeah, so i was trying not to poke my eye out with the pencil while quinn was going back over which ninja weapons each ninja of various expertise could use depending on their belt rank status, and how many times they could attempt to roll the d20 any time they were on the attack, based on which weapon they chose, while i tried not to let static take over my brain as all the rules blurred together on me. (you feel me after reading that run-on sentence, i know you do.) while my son would have been perfectly content to play this game verbally, and hold all the growing and shrinking relevant variables in his considerable noggin, the only things growing and shrinking for me were my dread and my attention span, respectively. i needed a visually appealing, tactile way to keep track of it all.

and then it came to me: sliders.

for every geek attack, there is an equal and opposite geek attack reaction. at least, when i bring my a game to being a mama.

d20, the 20-sided die from d&d, comes in handy for lots of games!

it’s possible, as a mama, to not really actually desire to play ninja wars on graph paper for the entire 72 hours of long weekend, and yet also possible to surrender to the need for connection with my son (who i rarely get to hang out with for 72 consecutive hours anymore), and fully immerse in ninja wars on graph paper for the entire 72 hours. as for me personally, i just needed to put my own spin on it, and get a little crafty so that i could remain awake and static-free.

qaz8quintillion h.q.

i grabbed my exact-o knife, some card stock and a thin sharpie, and started by making a slider for keeping track of my ninja’s health points. (she has princess leia buns: see? my own spin.) something about keeping my hands busy while the game went on… and on… really enhanced my endurance. as usual, this is not a tutorial, i don’t really do tutorials, but i am hoping that the pictures give you a sense of how to make something similar, should the need arise in your household. it’s essentially a piece of paper sliding along another piece of paper, with some way of indicating the value it is keeping track of (in this case, a hole punched in the sliding piece of cardstock).

by the time i finished the first one, i had a sense that we were in this for a very long haul, so then i really let my geek out to run around. we ended up making sliders for keeping track of 4 different ninja’s hp’s, 8 opponents’ hp’s, each ninja and each opponents’ belt rank status, which boss we were fighting, the boss’s hp, karma points, level, and gold coin earnings.

belt color slider; she’s an orange belt!

opponent belt color and hp slider consoles

karma points, level, and gold coin sliders; for some sliding pieces i hole punched and cut 2 slices with the exact-o, and for others like the yin-yang symbol, i taped an additional strip of card stock to the back.

like a boss; a side note: this game is heavily inspired by ninja warz 2, a game i’ve never played and that quinn saw his friend playing online. quinn is not allowed to play this game online, as the site requires an account owner to be age 13 or older. we’re talking a lot these days about ethics and honesty and integrity in online choices.

it wasn’t until after i got fully involved that we worked out some actual rules and ways of making the game really a game that someone could walk up and play, even if they didn’t happen to be quinn. since he had already applied hp as a quantity to determine who would win each battle, we used the multi-sided dice from d & d and came up with a points system, also based on belt status, weapon choice, and so on. ultimately, we spent the whole weekend doing arithmetic and rounding out loud with each other: “14 plus 8, that’s 22, plus 7, that’s 29, plus 6 is 35, now roll the d10 mama, ok plus 4 is 39… that rounds up to 40 damage!”

we get a lot of mileage out of those dice, such as when quinn decided to bust out his oregon trail journal from last year at ols, and begin writing in it again. we made a list of 20 events that could happen on any given day that he has to incorporate into his story writing, just to add that element of chance that one would experience out on the trail. broken axles, backtracking, weather, health, and hunting bison. river crossings aren’t on the list, because he’s actually attempting to write over a realistic number of days, and traveling a realistic number of miles per day while following a map, so rivers will come along in the story according to geography. this is all just part of my plot to help quinn bloom as a writer, of course.

but maybe that’s the subject of another make like a geek moment. until next time… embrace your inner geek!

mb

magic & bioluminescence

Tag Archives: graph paper

tides

~a month in the life of a lifelong learner~ smuggle in a dinosaur

make like a geek ~ game sliders and creative dice rolling