23 April, 2021

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

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