A Valentine's Day Card

Giving something meaningful each Valentine's Day has become a sort of tradition between Katherine and myself.

This year, Katherine has truly outdone herself. Her handmade card quotes Carl Sagan's Demon-Haunted World, showcasing a principle that has guided my life ever since I first became a skeptic some twenty odd years ago. It's a principle that I've held close to my being and that has been at the heart of many conversations Katherine and I have about so many different things. She writes that the balance between openness to new ideas and ruthless skepticism is a dance where each of us often switch sides in our cooperative search for truth. Alongside the quote, she has made literal pinpricks of light, referencing the lone lights in the darkness that rational thinking helps us to uncover. These represent the deep truths that lie within the deep nonsense — the very same deep truths that we slowly aim to uncover as we dig through the arguments about the problems of our time.

Upon opening the card, we see that there is yet another layer to the quote on the cover. She says that I brighten her life, implying that, at a different level, the darkness of the card itself also represents our lives, separated, and the lights we have managed to uncover are the shining moments we have made in the course of our relationship. All of this is said within the confines of a Sierpinski triangle, a fractal shape of crystalline regularity that reveals yet another layer of meaning: here, the balance is in the construction of the shape, with its open spaces throughout (literally it has an area of 0) and the numerous lights that we nevertheless uncover via the application of strict logical rules within the triangle itself. It is a saga that shows us the things we can count on even within a field where nothing can be counted on. Here, she implies, is where our love resides.

On yet another layer of interpretation, we see that the lights themselves overwhelm the structure of the sierpinski triangle. The triangle itself is drawn in a dark color that is difficult to see on the black background even with the lights turned off — once they are turned on, it becomes impossible to see the logical order belying them. Only the front of the card, written in reflective ink, remains visible to the human eye when the lights wash out the scene on the dark void itself. Yet even then it is a difficult thing to make out: you must struggle to see the path before you. Ironically, it is the brightness of the lights, not the darkness of the background, that makes this so difficult. This, again, is in reference to our relationship: so many of our brightest moments sometimes overshadow our typical moments in life, and make it that much more difficult to see the structure beneath it all when we reside day by day.

I am completely taken aback at the various layers of meaning weaved into a single card. So many of our conversations over the past years point back to many of the points made on the card itself. I am sure that, to any other person, this must look just like a black card with lights embedded within. But, to me, I see the threads of our relationship here: the discussions and presented arguments, the successes within a background of seeming impossibility, and the simple joys that overwhelm even the lowest of lows in a relationship of this magnitude.

I don't know how I can top this, but I will have to up my game next year.

See also the Puzzle Portraiture she made for me, the screen print of The Tuft of Flowers, & her drawing of Jasper and the Amiibo. You can see more of her work at KatherineHess.com.

Cubic Star Number

Katherine's latest art project involves looking at the number of covid cases in our county every other day and making something that has to do with that number. On Monday of this week, there were 2140 cases per 100,000 residents in Montgomery County (averaged over the previous seven days). Katherine discovered that this was a "cubic star number", which she felt had an interesting name, but for which there was not a good explanation online. (Seriously, try looking it up yourself. No one seems to have ever written about it much at all (other than the A051673 OEIS sequence), and there certainly aren't any pictures of what the accompanying shape would look like.)

While making a three dimensional sculpture out of 2140 elements would be a little much for a series where she makes a new piece of art every other day, it did seem reasonable to make a much smaller cubic star number shape out of 120 marbles. So she did.

What you're seeing here is (as far as I can tell) the first picture of a cubic star number searchable on the internet. While diagrams of these may exist in yet-to-be-indexed books, I could not find such a picture in anything that refers to cubic star numbers (such as Gulliver's 2002 article Sequences from Arrays of Integers).

Star numbers are relatively well known. They're centered figurate numbers: you take one dot, then surround it with more dots in a certain shape, then surround that with dots, and so on, until you have a big shape of dots with a central dot in the middle. Gamers might recognize that a Chinese checkers board uses a star number shape of 121 spaces.

The star number polygon shown here consists of a hexagon with triangles on each side (i.e., a hexagram). But you don't have to use a hexagon on the inside. You could just as easily use a square, with four triangles on each side of that square. This square star number might not look as pleasing as the hexagram does, but it has interesting properties all on its own.

But I think things get even more interesting once you move into the third dimension. Instead of a square, you can use a cube; and, rather than making a stellated shape where a pyramid exists on every face of the square, you can merely place the pyramids on four of the sides, so that the front and back of the cube remain flat. In this way, you're extrapolating out what a two dimensional star number might look like if you literally pulled it out into a new dimension, but turned the triangles into pyramids while allowing the square to fill out a cube.

Almost no one talks about cubic star numbers. The closest I could find was a blogger referencing house numbers, which, to be fair, has a more distinctive shape to them. House numbers are closely related to cubic star numbers; rather than four pyramids, they exhibit just one. But it's easy to see how you can get to a cubic star number from the corresponding house number: just add three more pyramids and stick 'em on the sides.

Katherine chose to use the fourth cubic star number, 120. It consists of a 4x4x4 cube with four pyramids that each have a 3x3 base. This small cubic star number was created entirely out of marbles, using liquid silicone to connect them. It stands as a symbol of the much larger tenth cubic star number, 2140, which consists of a 10x10x10 cube with four pyramids that each have a 9x9 base.

I'm fascinated by Katherine's choices in what to display in this regular art series. COVID-19 has gotten pretty bad here in Montgomery County, Maryland, since the Omicron strain took over. We reached highs of 300 cases on this graph back in 2020, and that was scary because anything above 100 was considered high and worthy of shutting down schools. Now we hover in the ~2k range and people are demanding that schools remain open. She's dealing with the strain via creating art — I have to admit that that's better than my current method of shutting down nearly entirely.

I'm looking forward to seeing what else Katherine comes up with. I was fascinated by her prime factorization series, and this current series on the integers of covid cases seems just as good. I just wish we didn't have to keep spreading covid in order to generate these depressing numbers and associated fascinating art.

Cubic Star Number

Exploring the Integer of Seven Day Average Covid Cases per 100,000 People in my County Series. On Monday, January 10,...

Posted by Katherine Hess on Wednesday, January 12, 2022

Puzzle Portraiture

Made by Katherine Hess.

In May of 2018, Katherine sent me a photo of a piece she was working on. "It's a puzzle portrait," she explained. "Do you think you can solve it?"

I was fascinated by the small photo she sent me. It was a portrait of me, all in orange (my favorite color), using Futhark and Greek characters. I don't speak any languages other than English very well, but I did spend two years in college learning koine Greek, and I know enough to be able to muddle through a Loeb Classical Library-style text, so long as it has the English translation on the opposite page. And in middle school I transliterated Futhark characters whenever writing in my personal journal; to this day, I am still more comfortable writing freehand in Futhark transliteration than in actual English, because whenever I write for others, it is on a keyboard; when I write in freehand, it is always in my journal, which uses no English characters whatsoever.

If you're interested in attempting to solve this puzzle yourself, it may help you to at least know a few more things about me, since the puzzle was created specifically with me in mind. I'm an amateur mathematician and I adore mathematical games, such as the ones that Martin Gardner used to post in his old Scientific American column. Katherine is a lover of art, and the combination of art and mathematics is a common theme that comes up in gifts that she gives to me. Books like Gödel, Escher, Bach are prominent due to that combination of themes.

You now have enough information to solve the puzzle. I encourage you to give it a try before reading on, as the solution will be spoiled below. Don't look at nor use anything below this line of text when solving the puzzle. Open the above image in a new tab if it helps.

At the time I received the above photo, Katherine was still working on the actual drawing. You can see that only some of the boxes are shaded. She was working on it in her studio, which means I couldn't see her work on it. Instead, I had only the above photo to go on. She said she would finish soon and bring it home to me, so I set to work on solving the puzzle immediately. I wanted to see if I could find the solution before she made her finishing touches and brought home the piece.

It took a while to notice the pattern. At first, it seemed like a jumble of Futhark and Greek characters. Writing them out provided a few clues, but nothing too substantial. I found myself writing things like "ITJPEKS", "SOFZ", "ZDTHATL", and "KSJUZDTT". Most of these didn't make much sense to me. But a few stood out: "NLURKS" looked a bit like "lurks". "TORDERS" looked kind of like "orders". It didn't fit with all of the words, but I decided to separate out the first character from the remainder, to see if anything might happen. That's when I realized that all the initial letters were Greek.

Once I hit on this pattern, I realized that also all of the ending letters are Greek. It wasn't obvious at first because there are some characters which look extremely similar in both Futhark and Greek. It wasn't clear whether "I" was a Futhark "I" or a Greek "I". But I made a hypothesis: what if all internal letters are supposed to be interpreted as Futhark? This would change a number of my initial transliterations. Suddenly, I started seeing several words in the banners.

The words came quickly: "tjpe", "of", "that", "turnz", "can", "just", "of", "a", "lurk", "bejond", "an" "kaoz", "out", "order", "it", "fakade". Some of these weren't quite correct, but it was easy to replace "z" with "s" and "j" with "y", especially after remembering that scene in Indiana Jones and the Last Crusade where it is remarked that "j" is just "i", which also is just "y". Suddenly, I recognized the quote. It's from Douglas Hoftstadter's Metamagical Themas: "It turns out that an eerie type of chaos can lurk just beyond a facade of order."

But the word "eerie" is nowhere to be found in the puzzle. Nevertheless, this is clearly what was intended. I love Hofstadter's work, and I'm certain that Katherine chose this quote specifically because it would mean something to me. (The full quote is slightly different: "It turns out that an eerie type of chaos can lurk just behind a facade of order -- and yet, deep inside the chaos lurks an even eerier type of order.") 

Looking back at the initial Greek letters, I realize that they are now in alphabetical order. Gamma corresponds to "it"; delta corresponds to "turns". And the ending Greek characters are in reverse order. Interestingly, the missing word "eerie" ("ΘᛖᛖᚱᛁᛖΝ") would correspond to theta and nu, and theta is missing in the initial Greek characters, while nu is missing in the ending Greek characters.

This is it, I think. I'm onto the solution. Hurriedly, I texted Katherine: "ΘΝ".

While I waited for her reply, I tried to figure out what these letters mean. It can't just be two random characters as the solution to the puzzle. So I thought deeper.

Immediately, I am struck: written in Greek like this, I am reminded of Θέων ὁ Ἀλεξανδρεύς (Theon of Alexandria), a mathematician who edited and arranged Euclid's Elements. This fits! (ν is a lowercase Ν, so "ΘΝ" corresponds to "Θν", which consists solely of the consonants of "Θέων".) Theon was a great lover of order (which is why he edited the Elements), yet his additions to the text introduced new errors that persisted for thousands of years, before someone finally found a copy of Euclid's Elements from before Theon messed with them. This fits perfectly with the quote. It's natural to think of Theon, given that he was Greek, like the characters from the puzzle; he was a mathematician, which matched Douglas Hofstadter, the originator of the quote; and he was responsible for both the order and chaos inherent in Euclid's Elements, just like the quote suggests.

The answer, then, is Θέων, or perhaps Euclid's Elements. Or, perhaps, as my mind raced, the answer is Hypatia. She was Theon's daughter, a talented mathematician and philosopher in her own right. She lived an orderly life, working with astrolabes and hydrometers, and yet is most well known for her martyrdom, when chaos took hold and a mob of Christians murdered her. The 2009 film Agora portrays Hypatia as "the only woman who stands between civilization and chaos".

Here, I felt, we have finally found the true answer to the puzzle. I was certain that Hypatia was clearly the correct answer.

And then I received a response from Katherine. She was confused by me texting her "ΘΝ" a while earlier. I stopped in my tracks, realizing that something in my line of reasoning must have gone astray. She calls, and I speak with her.

It turns out that the omission of the "ΘᛖᛖᚱᛁᛖΝ" clue was an error. I had already solved the entire intended puzzle just by getting the Hofstadter quote. She said she would draw the missing clue before giving me the finished piece.

The final version.

I was flabbergasted. I had felt so sure, which, obviously, I should not have felt. But I had thought that everything made sense, and I asked her if she might not want to add in the final clue, so that its absence could be a clue in itself, as I had originally thought it to be. But she declined, and she finished the drawing.

I re-learned several valuable lessons that day:

• It's irresponsible to just assume that things have intended meanings beyond the first link in a chain. Each successive link in a chain of reasoning depends on all previous links, and so each has to be discounted proportionately.

• Even when someone makes something specifically for you, it is inappropriate to assume that it will have more than a half dozen properties that are intended to speak to you. Continuing to find more in each detail is nothing more than pareidolia.

• It's insufficient to just make a claim; one must also consider one's credence in that claim. And you should be properly calibrated to ensure that you're not putting more confidence in a low probability situation than it warrants.

Nevertheless, I adored the piece. It touched on many aspects of me, including my favorite color; the transliterated Futhark I've used all my life in journals; the Greek that I learned so long ago so that I could better appreciate Plato in the original; a quote by Hofstadter, who wrote so much that I enjoyed over the years, and which was about a topic I cared about deeply in mathematics; and a likeness of me that shows what I look like when I am uncombed, working my way through a puzzle just like this.

The framed drawing currently sits in our gathering room. It's one of my favorite pieces that she's done for me.

Post 5: nominate 10-day! I was nominated by the incredible found object sculptor and art education master Linda Popp and...

Posted by Katherine Hess on Thursday, April 22, 2021

The Tuft of Flowers

Screen print by Katherine Hess.

From Robert Frost's The Tuft of Flowers:

I went to turn the grass once after one
Who mowed it in the dew before the sun.

 

The dew was gone that made his blade so keen
Before I came to view the levelled scene.

 

I looked for him behind an isle of trees;
I listened for his whetstone on the breeze.

 

But he had gone his way, the grass all mown,
And I must be, as he had been,—alone,

 

‘As all must be,’ I said within my heart,
‘Whether they work together or apart.’.

 

John Donne wrote that no man is an island. He was arguing for the normative claim that we should expand our moral circle to include all of humanity, but I've heard the phrase used several times since to refer instead to the descriptive claim that social connections are a core human need. I personally feel that descriptive claim most strongly when I read Frost's The Tuft of Flowers.

The protagonist is "turning the grass", meaning that he is taking recently cut hay and turning it over so that it will dry and can be gathered later on. A man before him has cut the grass that he is turning. They both are working to make hay, but they do not see each other at all as they work. The first man has already left for the day by the time the second one has started.

Our protagonist feels alone as he works. Not just lonely, but deeply, depressingly lonely. "As all must be, … whether they work together or apart." When I was young, long before I ever read any poetry at all, really, I felt this way often, and I continued to feel this way into my early thirties. I worked in an office, but I never socialized. I'd attend birthday celebrations for the slice of cake, and I'd be personable enough to respond when others talked with me, but I think it's safe to say that I was always the quietest person in the office, even when I worked in offices with hundreds of people. My workplace was always where I went to earn money, not where I wanted to meet friends or maintain relationships.

I wasn't a complete loner, of course. I interacted with a few select friends and courted numerous relationships outside of work plenty of times. But work, for me, was a solitary procession. Each step I made in the workplace, whether it was coding later in life or being on the phones earlier in life, would just be a successive step to run out the hours until it was time for me to leave the office. Work was a way to earn money; nothing more.

The Veteran in a New Field by Winslow Homer.

But as I said it, swift there passed me by
On noiseless wing a ‘wildered butterfly,

 

Seeking with memories grown dim o’er night
Some resting flower of yesterday’s delight.

 

And once I marked his flight go round and round,
As where some flower lay withering on the ground.

 

And then he flew as far as eye could see,
And then on tremulous wing came back to me.

 

I thought of questions that have no reply,
And would have turned to toss the grass to dry;

 

But he turned first, and led my eye to look
At a tall tuft of flowers beside a brook,

 

A leaping tongue of bloom the scythe had spared
Beside a reedy brook the scythe had bared.

 

I left my place to know them by their name,
Finding them butterfly weed when I came.

 

At first, the butterfly is a momentary distraction. It's maybe a little sad to know that all the flowers the butterfly enjoyed were cut this morning, "withering on the ground". Our protagonist would have returned to his work of tossing the wet grass, but then the butterfly showed him that a small tuft of flowers still lived by the reeds in the water. He's intrigued enough to actually leave his work to go see them close up.

To thirteen-year-old me, this reedy brook was the internet, and the various fora I found there were those same tufts of flora.

I've always tended to be shy, both when I was young and even later, even outside of my workplace. Being IRL ("in real life") was never really a smooth type of interaction for me. I much preferred going online.

When I was 13, I took the moniker MG377 on America OnLine and pretended that I was an adult. I'd go to forums and debate all kinds of things. I made friends with a young Anthony Bourdain back when he was writing his first book. You could often find me in the Book Nook chatroom. (Interestingly, I could find only a single reference to the now defunct Book Nook in a 1997 interview with Diana Gabaldon. I'm not sure why I searched so long for this link. I think I just wanted the post the old Book Nook chatroom logo, but it is now inaccessible.) I lied a fair amount if anyone asked who I was or what I did; but when the topics were about things other than me, I always tried to be myself. It was invigorating. The internet allowed me to interact with people in ways that I never could IRL. Even if I rarely told the truth about my physical personal details, like my age, being on the internet allowed me to truly be myself and connect to real other human beings.

Tuft of Flowers by Ken Fiery.

The mower in the dew had loved them thus,
By leaving them to flourish, not for us,

 

Nor yet to draw one thought of ours to him.
But from sheer morning gladness at the brim.

 

The butterfly and I had lit upon,
Nevertheless, a message from the dawn,

 

That made me hear the wakening birds around,
And hear his long scythe whispering to the ground,

 

And feel a spirit kindred to my own;
So that henceforth I worked no more alone;

 

But glad with him, I worked as with his aid,
And weary, sought at noon with him the shade;

 

And dreaming, as it were, held brotherly speech
With one whose thought I had not hoped to reach.

 

‘Men work together,’ I told him from the heart,
‘Whether they work together or apart.’

 

Work is no longer something I do just for money. Internet memes are no longer just something funny to chuckle at. Being isolated during the pandemic year is not so bad as it may have one day been to me.

I don't know you, dear reader, nor do you know me; yet as you read my words here I hope that you feel as I do: working together, whether together or apart.

Card

Katherine Hess is the 2020 Maryland Art Educator of the Year!

The NAEA Awards are for every state in the US.

Congratulations to Katherine Hess for earning the Maryland Art Educator of the Year award!

It feels like déjà vu because this seemingly keeps happening every year. But in fact Katherine has continually won more and more prestigious awards each year for her excellent work as an art educator. In 2017, she was presented with the Montgomery County Secondary Art Educator of the Year award, showcasing her high school work at the county level. Then, in 2019, she won the Maryland Secondary Art Educator of the Year award, which is presented to high school art teachers at the state level. But this year, on March 4–7 at the virtual 2021 NAEA National Convention, the National Art Education Association will award Katherine the 2020 Maryland Art Educator of the Year award, the highest award that an art educator of any kind can receive in the state of Maryland.

MAEA is the Maryland division of the NAEA.

Previous awards she's won have been high school based and more local. But the Maryland Art Educator of the Year award is available not only to educators at the elementary, middle, and secondary levels, but also those in higher education, museums, preservice, emeritus, or any other level. This is a big step up from her previously won awards!

Learn more about the IB.

I'm extremely proud of just how much she has done to promote art education in the state of Maryland. Katherine serves as the Department Chair for the Art Department at Seneca Valley High School (2014–present) and the Vice President of Communications for the Maryland Art Education Association (2018–present). She's done quite a bit to help art education both nationally and internationally, including as an International Baccalaureate Visual Arts Examiner in the Eastern and Southeastern Regions of the United States and as an International Extended Essays Examiner for the International Baccalaureate Organization throughout the world (including students from over a dozen countries!). In Maryland, she's headed the Academy of Commercial and Fine Art, developed Secondary Visual Arts Curricula for Montgomery County Public Schools, and helped to develop the first IB Middle Years Programme in Maryland.

Katherine and the always fluffy Jasper.

Katherine has been especially active during the pandemic, focusing on running social media accounts on Twitter, Facebook, and Instagram that help art educators in Maryland succeed, as well as publishing the MAEA Gazette, the MAEA Year in Review, and the Black Lives Matter statement for the Maryland Art Education Association. I am constantly amazed that she has enough energy to do all of this while still providing a positive learning environment in her virtual classroom. (The only lack this past year was in not being able to present her artwork in public anywhere because of the pandemic. A shame, really, as her work has been displayed across five states and won multiple awards in themselves.)

I can think of no better art educator in the state of Maryland than her for this award. Congratulations, Katherine!

(You can send her your congratulations directly on her facebook wall.)

Influenced

Today, I participated in an art project which will be housed at the Brooklyn Art Library. I submitted a small amount of text to an artist who then drew the scene, bringing it to life. The piece is a book containing quotes, notes, and other such things by various people, each of which the artist, Katherine Hess, interpreted and illustrated within the confines of the sketchbook.

What follows is the text that I submitted to this art project:

Thirty years ago, my uncle rescued two people from a burning building. He’s not a firefighter, but he was in the right place at the right time. 

He became a hero that day. Although we don’t bring it up at family events, we know what he did, and we think better of him for it. He’s a hero because when he was put in a position to help, he did. I’d like to think that I would do the same. 

So when I learned about the effective altruism movement, that giving to the most effective charities could save a life just as real and just as important as those that my uncle saved, I decided to start giving a percentage of my income to effective altruism causes. 

For seven years, I’ve saved lives again and again. I don’t bring it up at family events, but I know what I do, and I think better of myself for it. I feel like a superhero, and it feels good. 

You, too, can feel this way. If you live in the developed world, you earn more than enough to donate and save lives every year. Visit effectivealtruism.org to learn more. 

Believe me: it’s worth the expense.

This and other sketchbooks by Katherine Hess are available at The Sketchbook Project. 

Jasper and the Amiibo

I just want to share one of my birthday gifts from Katherine this year:

The Silver Screen Survey

Yes, I know that surveys are silly. But well-written surveys can truly tell a lot about a person in only a few mere lines.

Feel free to copy this survey to your own journal, should you feel the desire to (or else if you're just really bored).

Thanks in advance to my best friend Robin for creating the survey. (c;


The Silver Screen Survey, all about movies:

Favorite movie of all time: Cool Hand Luke
Favorite musical: Grease
Favorite comedy: Princess Bride
Favorite satire: La Vita e Bella
Favorite romance: Escaflowne
Favorite drama: Shawshank Redemption
Favorite epic: The Godfather & Sequels
Favorite dramedy: Being John Malkovich
Favorite "indie": Pulp Fiction
Favorite big studio: Raiders of the Lost Ark
Favorite trilogy: The Back To The Future Trilogy
Favorite dualgie (with one sequel): The Predator Movies
Favorite quadrie (with three sequels): The Alien Series
Favorite horror: Evil Dead
Favorite action: Star Wars
Favorite genre-defying: Citizen Kane
Favorite teen flick: Grease
Favorite Sci-Fi: The Day The Earth Stood Still
Favorite period piece: Star Trek
Favorite dance-themed movie: Mary Poppins
Favorite John Travolta movie: Grease
Favorite made-for-tv: Babylon 5
Favorite foreign film: Escaflowne
Favorite documentary: Bowling For Columbine
Favorite book adaptation: Animal Farm
Favorite play adaptation: Sweeny Todd, the Demon Barber of Fleet Street
Favorite love scene in film: Mary Poppins, where the whole movie is about the best kind of love there is!
Favorite film adapted from a tv show: Cowboy Bebop
Favorite filmmaker: Robin Raven
Favorite film actor: Hmm...
Favorite film actress: Robin Raven
Favorite movie soundtrack: Cowboy Bebop
Favorite format (theater, dvd, etc.): *.VOB files
Favorite genre: Anything Thought-Provoking
Favorite actress to play you in a movie: Robin Raven
Favorite actor to play you in a movie: Me. (c;
(both of the above apply to both sexes)
Favorite thing about movies: The music!