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

03 April, 2021

The Reality of My Dreamscape

We should not fall prey to the typical mind fallacy. Our minds are not so similar as we at first think.

Robin Raven trying to protect the innocent.

My friend Robin became vegan very early on because she saw fellow consciousness everywhere. As a young child, she cried when a Halloween-carved pumpkin would be thrown away because she deeply felt that having a face was sufficient for a being to have feelings. This experience was not typical, and it took her until high school before she internally understood that other people didn't feel the same way.

Katherine is a supertaster. She didn't understand that this was a different way to be when she was younger. She was called a picky eater because she'd turn down certain foods that she didn't like the taste of. Those foods, if tasted, would linger for days, tainting all other meals. I've gone with her to fast food places and watched mesmerized as she could identify all the foods made previously on the same grill as the item she was eating. As a child, she wanted most of all to make others feel okay, so she would often sacrifice her own desires when others were arguing -- whether this was choosing who got to sit in the front seat, deciding who had to take "the high road" when friends or family got nasty, or even just "sucking it up" and eating what was given to her even though it tasted vile. Adults around her would say: "We all have to sometimes eat stuff we don't like", but they did not understand. For her, the taste lingered. It was significant and primary. Katherine was a supertaster, and this was a big deal. She describes with relish the day she first found out:

You can test if you're also a supertaster.

I was in Europe on vacation and every meal had fish. I abhor fish. I ate it anyway, because I didn't want to rock the boat. Days later, over a breakfast that I ordinarily would have loved, I mentioned to others how the fish was still so pungent to me that it was ruining what would have been an excellent breakfast. To me, this was commonplace; it happened all the time in my life whenever I'd give in and eat something disgusting. But the surprise on others faces clued me in on the reality: other people do not have this same internal experience of taste.


Bebeflapula explains different levels of phantasia.

For me, it is my dream world which differs from so many others. I have aphantasia, and so cannot visually imagine anything at all in my waking life. But when I dream, I have full access to visual imagination. I'm also a lucid dreamer: unlike most people I get to choose what happens in my dreams. Unexpected things do happen there, but I have at least the illusion that I get to choose how I react to things that happen in my dreams. The combination of aphantasta with vivid lucid dreams is that I grew up valuing my dream worlds much more than other people do.

To me, the worlds that I visit when I sleep are alive. They feel like real spaces that truly matter. They aren't fuzzy or indistinct, like I see them portrayed so often in movies or when others describe their dreams. Rather, they are much more solid and distinct than anything at all that I can imagine in my waking life, and since I wear glasses they also appear much less fuzzily and as though they have a strength of reality to them that the actual real world lacks. Combine this with the fact that I get to explore that world just as lucidly as I get to explore the waking world, and you get a hyperrealistic upside-down conception of existence where the waking world just feels inferior to the dreaming world. At a gut basis, naively, I just feel as though the two worlds are equally valid and valued. The waking world is more fuzzy and less distinct, but it has continuity between every day, which I value. And the dreaming world is more solid and feels more real, even though I only get to revisit places intermittently as I return to well-known old dreamscapes.

From the now defunct study-hack site.

Of course, I understand that that the dream world is not real. But it took many years for me to get to a point where I was actually acting that way. Getting glasses for the first time as a child was a surreal event: all of a sudden the waking world started looking like the dream world did when at a distance. Glasses made me start to value the waking world much more in a way that I don't think happens with many other people. Later in life, I would tolerate living situations that many people would not be able to stand, because in dream life things could be fixed so much more easily than in waking life. Yes, I'd have to tidy up in both worlds, but, in one, I could but make the intention to do so, and it would happen, just as a nose-twitching witch might; but, in the other, tidying up meant actually taking the time to do so. When both worlds felt (naively) equally valuable to me, you can imagine that this resulted in me prioritizing the effects that occurred in my dream life over those that I built in my waking life. Many times in my life I would accept squalid conditions in one if I had good conditions in the other, merely because, to me, both were real.

It wasn't until I understood that aphantasia was a thing in mid-2020 that I finally realized what was going on here, I had had the typical mind fallacy for so long that it just hadn't occurred to me that the reason I valued dream life so strongly was because there I could visualize, even though I couldn't anywhere else.

Today, I finally value the waking world more. But it is a thoughtful decision that I do so; it still feels naively as though they should be equally valid. I just realize that this is a wrong thing to think now.

Yesterday, I had a nightmare, Jasper's dead body had come home. We were mourning when suddenly his body moved, and I heard the smallest of sneezes. I rushed to him, horrified to realize that maybe the euthanasia had not worked, and when I got next to him, his head raised, looking at me with the most expressive face. It was a face of unbridled pain. He was suffering physically, but more than that, it was a look that showed he felt betrayed. Why had I not fought harder to help him to live? Didn't I love him? Why had I caused him to die, and to suffer these many days in pain away from his family?

I screamed, waking up both myself and my partner. I was sweating. I looked over to the box where Jasper's remains actually lay in the waking world. I cried. Katherine reminded me that Jasper lived a happy life, right up until the end. I had not betrayed him. Jasper loved me. Slowly, I calmed down.

Nightmares for me are thankfully rare. But when they happen, they are horrendous. I don't think I can successfully explain just how real they are to me other than to point out that my dream world naively feels more real than my waking world. It is only with intellect that I understand the waking world to be more real than my dream world. Nightmares, to me, are true horrors second only to the waking world horrors one learns of in rationality or effective altruism circles.

From Corey Mohler's Existential Comics.

When I speak to people in my life, I'm not likely to mention any nightmares I have. It doesn't come across well. Others have nightmares, too, but their nightmares don't seem to have that same feeling of reality that mine have. My nightmares linger. For others, a dream passes quickly from the mind. Mine do, too, in the specifics. But, unlike others, when I sleep again I go back to the same place, and the specifics come back to me. An area previously explored has some changes, but the layout is the same. The rules are the same. I get to talk to the different people that are there, and visit the areas I care about most as often as I want, even years later when I return to that same dreamscape. Over time, the memories of these repeated dreams linger in my waking world memories. Even now, I can tell you about a certain dream place that I have gone to dozens of times, even though I haven't visited in the past year or so, where certain people live, where the decor is a certain way, where a path leads from the back door through the woods, where the path diverges to different locales depending on where I want to visit.... I know this dream place well because I've gone there so often. It's real to me. And so even though I have only had this Jasper dream once, I feel fear. Because it has been 24 hours now and I still remember every detail. I remember Jasper's tortured face. I remember feeling that it was my fault. I remember not fighting for his life.

There are even more reasons to stay up for me now. I don't want to go to sleep.

01 April, 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.