Shape thoughts book notes

“God is a circle, whose center is everywhere and whose circumference is nowhere.” - The Book of the 24 Philosophers

My husband, James, used to work as a geometric artist, so he was frequently thinking in the back of his mind about questions like whether you could make a nice tiling pattern using both pentagons and hexagons.* Often these thoughts would boil over right before bedtime.

“Oh no,” he would say, “I’m having shape thoughts again.” Then he would get up and spend half the night turning his surprise solution into a stunning piece of art. For a while, after the tiling patterns, the shape thoughts were mostly about the fourth dimension, fifth dimension, and so on. These ideas were more challenging and more abstract, harder to turn directly into something flat. Iit was during this time, though, that I started to discover the power of Shape Thoughts for myself.

I’m a writer with a complicated set of interests, and getting those interests to line up neatly together is often about as difficult as combining pentagons and hexagons. Imagine, for example, that there are four things you want to write about: visual art, spirituality, holistic health, and the history of science. There are lots of potential connections between all of those subjects, and a lot of writing advice tells you that in order to write nonfiction you should start with a mind map. Draw some circles on a piece of paper so you can see what’s central for you right now, what’s connected to that, and how you could start to make a path through it.

If the mind map gets too complicated, though, you can run into some problems pretty quickly. If you have three subjects in mind, for example, you can link them all neatly in a triangle pattern. [diagram] When you add a fourth subject, though, you have to make a choice. You can arrange all four more or less in a square (which strongly implies that two of the subjects are less closely connected than the others),[diagram] or you can make one subject the most central, with the obvious complications there. [diagram].

If you imagine a three-dimensional mind-map, this problem is much easier to solve. Suddenly you’re able to create a tetrahedron, a shape with four equally connected points. [diagram] This is a bit harder to represent on paper, but solves the problem fairly elegantly on an organizational level. What if you want to make connections between for or more subjects [add more examples], though?

On a two-dimensional piece of paper, you can perfectly fit six circles around the edges of a seventh circle. [diagram] In three dimensional space, you can pack exactly twelve spheres around a thirteenth sphere. [diagram] According to James, in four dimensions you can fit an infinite amount of whatever passes for a sphere in 4-D space around another one of the same. What does that mean? I don’t have the faintest idea how to draw a picture of it, but the organizational implications are staggering. The problem, then, is in compressing the actual unimaginable shape of a thought like that into a three-dimensional imaginal space, then a two-dimensional paper space, and, finally, a one-dimensional sequence of words.

This is what keeps me up at night.

One thing that inspires me as a writer, on the other hand, is the Sufi tradition of storytelling. This often involves a lot of short pieces on seemingly distinct topics, sometimes described as the scatter method. Your subsconscious mind has to piece the details together, which can give you a better sense of that impossible extra-dimensional geometry. It’s one way, at least, to deal with the fact that a narrative doesn’t always want to fit in a continuous line.

You’ve probably heard the old story about the elephant and the blind men, for example, or as Rumi tells it in the Masnavi, the elephant in a dark room. Several men who have never seen an elephant examine it with their hands. One touches the elephant’s ear and says the animal is like a fan, another touches the tail and says it’s like a rope, etc. They disagree because, like the rest of us, they’ve been forced to experience the same reality from mutually exclusive perspectives.

Rumi describes the situation like this: “The eye of outward sense is as the palm of a hand; the whole of the object is not grasped in the palm.” He also suggests that someone could have brought a candle. Given the nature of the opportunity, though, you can hardly fault the men in the dark for attempting to figure out whatever they could. Another thing they could have tried, sans candle, is rotating around the elephant, taking turns examining different parts. This wouldn’t have provided a total picture, but it might have given them a more complete sense of the invisible living thing in the center of the room—which we, the omniscient readers, can easily see is of central importance.

There are two major Shape Thoughts that I’ve been feeling around the edges of as I lie awake in bed recently: The first is like a three-dimensional cluster of points, a little like the shape I described above for information mapping. The dots connect to each other, but possibly in a flexible or fluid way. This shape is important to me for many reasons; it reminds me of dynamic systems like the words in a language, the cards in a tarot deck, or maybe a swarm of bees. Most importantly, though, it seems to be my mental model of a mental model [diagram]. I think a lot about mental models, or, as I will eventually explain at length, metaphors, and so I spend a lot of time turning shapes like this over in my mind.

The second shape is pretty boring on a geometric level, but pretty huge in terms of human experience. It’s a line that goes more or less in one direction (an arrow, you could say) though its trajectory may wiggle a bit, loop around or even get tied in knots. For me, this shape is mostly about the sequential way that we move through space, communicate verbally, and even do life in general. We keep moving “forward” regardless of our preferences, but our choices control the direction of that movement. So, how do you decide the shape of your life, and how do you navigate from inside it?

Both of these formal ideas have been making increasing demands on my time and energy, and I’ve had the sense that each might make an interesting book in its own right. Models and metaphors, or direction and desire? For a while I got deeply stuck at that point–stuck straight through the time that I set aside an entire week to get started on one of them and didn’t write a word until the sixth day, when I finally sketched out a mind map and noticed something interesting: These two shapes fit together visually. [diagram] What’s more, the combined shape reminds me of some more very interesting concepts, from form and essence in Greek philosophy to matter and energy in systems biology. Complex shapes that have that kind of historical longevity tend to hold a lot of meaning. But how does that meaning fit together now?

I had no idea at the time, but the next day I was finally excited to start writing. The really interesting thing about the Shape Thoughts is how many complicated problems can be solved on that imaginary level. When the ideas I’m pondering work out geometrically I’ve come to trust that, if I follow that wiggly line, the shape of the model I’m navigating will eventually click into place.

“The greatest thing by far is to have a command of metaphor. This alone cannot be imparted by another; it is the mark of genius, for to make good metaphors implies an eye for resemblances.” - Aristotle

The Shape Thoughts, as I’ve said, started as a vague sense of the way ideas can begin to connect outside of conscious mind-space. Since I noticed that pattern, though, I’ve been studying hard to figure out what ’s actually going on here. Why do people have Shape Thoughts at all? Who else has wondered about this question, and what did they discover? Maybe most importantly, what are they actually good for?

On a basic level, what we’re talking about is metaphor–specifically, spatial metaphor. Thinking with metaphor is something we’re all familiar with on an intuitive level. It’s like the way that you can approach a decision between two possibilities (for example, two jobs you might like to have some day) by imagining that there are two paths in front of you and you need to decide which one you want to take.

We use this kind of reasoning all the time. It’s never perfect, because two things (e.g. a job and a path in the woods) are never exactly the same. It’s still an extremely powerful way to think, though, often carrying lots of weight in surprising ways. For example, when you think about the two different career paths, here are some thing your subconscious mind may be noticing about paths:

  • You may not know exactly what either path looks like before you follow it, how long it will take to reach your destination, how difficult it will be, or even whether you will successfully reach that destination. You probably understand that you will see more of either path as you move along it.
  • You may be able to get some more information about the possibilities ahead of time by talking to people who have traveled the same paths already, or by using some kind of guide book or map.
  • You will encounter different things along the way depending on which path your choose. These things may be surprising or unsurprising. You may change your mind and decide to go in a different direction once you encounter them.
  • You probably can’t follow both paths at once, though. In order to move forward at all, you will need to make some kind of decision.

Ideas like these are called entailments of this metaphor, meaning that they’re attached and implied when you think about an idea in these specific metaphorical terms. Entailments are often helpful and account for much of the computational power of metaphorical thinking, since they’re often processed subconsciously. Entailments can also be misleading, though. For example, if you pick up on an implication that traveling either career path may be more difficult during the winter, it’s possible that you’re perceiving a subtle dimension of reality, but there’s also a good chance that you’ve run into a limit of the similarity between career paths and paths in the woods.

You may or may not have thought about this type of mental process in such specific terms, but when you do it should feel very familiar. What’s a bit more surprising is the extent to which we use metaphorical thinking, which is: constantly.

For example, in the previous section here are a few relatively obvious spatial metaphors that I used by accident:

  • I said that entailments are “attached” to metaphorical thoughts, like objects can be attached to each other.
  • I said that entailments can be “misleading,” as though you might be going in a certain direction and they could lead you in a different one.
  • I said you might “perceive” a “dimension” of a situation, as though it were an object you were looking at.
  • I said you could “run into” a limit while thinking.

That’s a pretty average paragraph, and once you start to think about this kind of thing you will notice similar examples everywhere. It’s also, as I said, only the most obvious type of metaphorical language. The next thing you could look at is prepositions, which almost always suggest relationships based on spatial orientation: on, in, to, from, about, and so on.

All of these types of language are what are sometimes called living metaphors, meaning that when you think about the words, you can easily imagine the spatial basis of each concept. Language is also composed of a lot of dead metaphors, meaning figures of speech that used to be metaphorical even though we no longer understand the physical situations they were originally based on. For example, there’s the phrase “beat around the bush.” English speakers know exactly what this phrase means, colloquially, and we can easily see that it’s some kind of spatial metaphor—but why? In the past, beating around a bush was probably an activity that people could relate to in a different way (the internet suggests, as a means of flushing small game out while hunting). That living knowledge is long gone, for most of us, but the shell of it is now part of the structure of the English language. Complete phrases like this aren’t extremely common in everyday speech, but if you start to look into the etymology of individual words they’re absolutely everywhere. Words in this paragraph that are secretly spatial metaphors include:

  • extremely (outermost, farthest)
  • individual (unable to be divided)
  • origin (rising, like the sun)
  • absolutely (unable to be loosened or dissolved)
  • metaphor (from meta pherein, to carry across)

When you consider the obviously metaphorical, the subtly metaphorical, probable dead metaphors and metaphorical etymology, so much of speech (besides speech describing concrete physical situations we can directly see and feel, which are the basis of all those metaphors in the first place), you get close enough to all speech that it would be pretty reasonable to assume that we’ve just lost track of the origins of the rest and it’s actually all metaphors all the way down.

But why?

For now, let’s put that model and its attendant questions down, and look at this other one. This one, the general shape of a human life, feels much more subjective, and it’s tempting, in the spirit of “show, don’t tell,” to write a long-winded description of how I’ve come to have some of these weird ideas. Having just read through a draft of that story, though, I think it’s better for everybody if we keep the biographical sketch simple.

I wasn’t a badly behaved kid, but I’ve always had a strong feeling about doing my own thing If the rules don’t make sense. For example, my early report cards often mention that I insist on sitting on the floor. Why shouldn’t I? I have, I guess, always been attracted to paths that feel a bit unusual and expand my sense of what could be possible, and my strong existing commitment to doing whatever I want was further cemented as I discovered witchcraft as a teenager, anarchism in college, and unschooling (the idea that kids don’t need to be formally educated) by the time I had young kids of my own.

Since then, I’ve been pretty convinced that doing whatever you want is not just convenient, it’s also morally right, politically desirable, and a good example for children. Most importantly, maybe, I will argue that it’s what you’re doing and will continue to do whether you like it or not, so you might as well acknowledge and enjoy it. In short, I think of this shape as not just the shape of a life but also any other kind of process, and especially of desire.

If you’ll permit me a metaphorical flight of fancy, what I’d really like to show is that this is also more or less the shape of a snake. In fact, I’d like to propose that we think of this shape as a snake from now on, for several reasons:

  • A snake, unlike an arrow, Is a self-motivated and conscious individual moving through time as well as space
  • It is shedding its skin, transforming as it goes. In a way, the shape and the motion are the part that continues

I am an enthusiastic but relatively late adopter of this kind of complicated philosophy. I have always had a strong sense that I was driving toward //something// of personal significance, but it took many years to get a good sense of what that something actually was. For a long time, it was much easier to see what it was not.

I was not, I don’t think, a very mean-spirited kid, and I mostly followed the rules because they mostly made sense. I do get the sense, though, that I was kind of a difficult kid because there were still plenty of things that didn’t make sense to me, and those things were not easy for me to ignore. For example, my early report cards repeatedly mention the way I would insist on sitting on the floor to do my work, because why not? I also remember trying to talk my parents into experiments like shutting off the electricity for a week just to see how that would be, learning to read an alphabet I created, going vegan, or letting me drop out of high school even though–seating preferences aside–I had always been a pretty good student. I have, I guess, always been attracted to paths that feel a bit unusual and expand my sense of what could be possible.

My first really significant encounter with something outside myself that had that kind of expansiveness was as a when I discovered witchcraft as a teenager. At that time, most people who were interested in anything witchy were calling it Wicca, and it was mostly a Goddess-based nature religion that promised a surprisingly no-frills approach to magical power–like a different way of praying, I was told. Also, somewhat mind-blowingly coming from a Christian perspective, this religion had nothing to do with rules. The Wiccan rede, as the guiding principle of Wicca is called, says “an’ it harm none, do what ye will.” So, technically, one rule–but given my background and sense of natural good will toward others, a general intention to avoid harm felt like a ridiculously low bar. For me, this casual way of approaching life answered some big questions in a fairly permanent way, but also opened up many others, most importantly: What do I actually want?

I don’t mean to imply that wanting things, or even getting them, was new to me. I always had access to a significant number of things that I wanted, and I certainly did any number of things just because I wanted to. My creativity was encouraged and my weird ideas and habits were, at least, generally tolerated. Like most young people, I also thought about the question of what I wanted to do as an adult. I had never taken any of that very seriously, though. When I started to think about desire through a Wiccan lens, that slowly started to change. I had definitely understood, prior to that point, that there was a way (or possibly several ways) to be a good person, and that thinking about how to do that was important. So, as much as I welcomed the newfound sense of freedom and integrity between how I was and how I wanted to be, these new ideas required some unpacking.

There is actually a significant amount of thinking on this topic, and I’ll get into more of the details later. A lot of it boils down to the idea that people usually want constructive and pro-social things, though, especially once their basic needs are met (and if someone’s basic needs aren’t being met, then it’s going to be hard to sell them a rigorous ethical code, anyway). While this isn’t a philosophy that many people are willing to go to bat for, it’s a significant cultural undercurrent that we would do well, I think, to at least consider seriously.

For example, while I doubt if most therapists would come out and say they think that people should do whatever they want, a lot of modern psychological theory and practice is based some version of Abraham Maslow’s pyramid of needs, which illustrates a similar idea. According to Maslow, once people’s basic needs for things like safety and food are met, we naturally tend to move on to pursuing loftier-sounding goals like group belonging and self-expression. In other words, doing what you want and getting what you want often leads, eventually, to becoming more pleasant and helpful to others.

In Wiccan and other magical circles, there’s also some emphasis on the idea that if you practice going after what you want, you will learn pretty quickly about which kinds of results are really fulfilling and which aren’t. There’s the concept of true will, which means the things you really deeply desire rather than the things you just have to have because culture and advertising are shoving them down your throat, and these deep desires very often tend to be things that would look right near the top of that pyramid of needs–for example the desire for love, or to do fulfilling work. Crucially, though, none of that counts as your true will if you skip over the messy stuff you would rather not think about to get to it. If what you really want is the burger but you order the salad because you think you’re being virtuous, you are not going to be satisfied. In other words, desire is a skill that requires practice, and as a newly independent young adult, I suddenly had a lot of opportunity to practice it.

In college I also encountered my next unpopular and liberating idea: anarchism. If you’re not familiar with this political philosophy, you may associate the word with chaos, which is not entirely unfounded but definitely not the point, either. Politically, anarchism is just the idea that nobody, including the government, has a fundamental right to decide how people should behave and particularly to enforce punishments on others. Real life anarchists are not, as a rule, interested in being free to exploit or abuse others. In fact, anarchist organizations (yes, it sounds like a joke, but they definitely exist) spend a lot of time discussing how to make decisions consensually, create networks of mutual support, and solve problems of injustice.

The arguments for this philosophy are in many ways similar to those of Wicca, for example: People are generally well-meaning and enjoy having friends and social relationships. Would we all make slightly different choices if there were no laws? There would probably be quite a bit more speeding, I guess, but ask yourself if you really think you would start murdering people or walking into random houses to take TVs. Of course, nobody really thinks that they would be the person who would become a criminal, we are mostly just worried about other people–and, to the extent that other people are desperate to meet their basic needs, this might be a legitimate worry. There’s plenty of evidence, though, that punishment (legitimate or not) doesn’t really work to reduce crime, harsher punishment definitely doesn’t work better, and if we’re really concerned about the problem of other people and their violent potential, making a reasonable attempt to provide for everybody’s basic needs would be a pretty good place to start.

I would have said, at that point, that I was already pretty sold on the centrality of desire–but several years later my first child was born, and I somehow learned even more about how that works out. Questions that had been pretty abstract for me suddenly led to much more practical decisions. As an anarchist or a witch without a compulsion to teach morality, how do you think about raising a child? I discovered the idea of unconditional parenting, promoted by psychologist Alfie Kohn, during my pregnancy. It basically boils down to the idea that punishment (on pretty much any scale) doesn’t really improve behavior outcomes, and children naturally learn to imitate the adult role models in their lives as they mature. I appreciated this philosophy more and more as I started to put it into practice, since I would have felt like a big hypocrite if I punished my daughter for trying to do whatever she wanted.

I kept reading about this kind of theory and also became increasingly interested in unschooling after a few years had passed and my second child had been born. The idea of unschooling is that much like it’s unnecessary to punish kids in order to teach them to behave, it’s also unnecessary to deliberately educate them in order for them to grow into fully functioning members of society. Just as babies learn to walk and talk without instruction in infancy, we continue to be internally motivated to continue expanding our capabilities–and while few children would set up an educational program that looks much like school for themselves, most or all will practice culturally normal activities through repeated exposure and eventually decide which kinds of skills to focus on based on naturally evolving personal goals.

So, my two children were unschooled from birth (though both eventually chose to attend a Sudbury school, which allows for a similar level of freedom and self-direction in a kid-centered community), and watching this process evolve has been an amazing demonstration of the guiding power of desire. We’re no more perfect than any other family and both kids love computer-based activities (which some parents worry about with this kind of philosophy), but both can also read and write well, have plenty of friends, hobbies, and general knowledge of the world, care about social justice issues, and my older daughter even taught herself enough digital animation to get her first job at the age of thirteen. They are both unique individuals who share some of my interests, reject others and come up with plenty of their own, and it’s amazing to watch those interests guide them toward the kind of futures they will fit well inside.

As all these things were happening, It wasn’t always easy to see that they were part of a larger pattern. Looking back, though, while there were plenty of twists and turns, all these discoveries seem to have been trending in a certain desire-centric direction. These days I identify as a hermetic polytheist rather than a Wiccan, as well as a normative hedonist and anarchist (meaning that I think of these states–the way that people make decisions based on what they want and the way that government has no legitimacy–mainly as realities to be acknowledged rather than options to promote). Still, I feel that desire is a major key to creative problem solving as well as to building a meaningful life, and in reality I am probably not going to stop pushing that on people.

Some useful quotes:

“What then is truth? A movable host of metaphors […]which, after long usage, seem to a people to be fixed […] Truths are illusions which we have forgotten are illusions—they are metaphors that have become worn out and have been drained of sensuous force.” -Nietzsche

“In sum, in the binary operation between religion and science, superstition/magic functions as the third term in a Derridean sense. “Magic” is the point where the system does not close. Like all of these terms, it has a dynamic function. Its role emerges from a position as the negation of the negation; and therefore, looked at from on eperspective, it is the conjunction from which the system emerges.” - Jason Josephson-Storm, The Myth of Disenchantment

What if magic is precisely the awareness that there are multiple incomplete/paradoxical models for everything, and the skill of navigating between those models with the understanding that there can’t possibly be a complete map for that system of navigation?

When we are denied a story, a light goes off. I am asking you to study the dark. - Anne Carson

To ask for a map is to say “tell me a story.” - writers as cartographers book (also thinking about the difference between maps and stories)

More ideas:

  • doing what you want is probably either building environmental supports or getting into flow. and is flow metaphor? not necessarily
  • figure and ground reversal in geometry, metaphor
  • analogies and the history of scientific understanding
  • form and essence in aristotle, matter and energy in contemporary biology
  • look up twitter thread about metaphoric duals
  • reference back to how the elephant applies to metaphors
  • stephen buhner: magic words shape of what you write shibboleth - luckily, writing secretly isn’t just a straight line; it can contain metaphors.
  • metaphor is also a magic word, all language metaphorical
  • feeling of sensing the shape of a piece of writing before fitting the concepts together
  • story of DNA dream
  • story of Descartes dream
  • einstein quote about thinking with images
  • aristotle thoughts on metaphor?
  • stephen buhner: you get a sense of metaphor from any activity, but writers are the most self-aware
  • I don’t fully understand the math, but I understand enough to use it metaphorically
  • stephen buhner writing exercise, crocodile example
  • Platonism and the power of books
  • analogy in meditations on the tarot
  • self-referential stuff is hypnotic, is the shape of the universe self-referential? Is that why hypnosis is powerful?
  • bringing the two thematic parts, model and path, closer together until the orientation flips
  • importance of figure and ground thoughts in general, subject and environment
  • maybe reread plant intelligence

I am also a bit of a thief. I mean, when I was younger, that I would walk out of stores with things that I needed or, to be honest, just kind of wanted. Immediately there are all kinds of qualifications that I want to make–that I was broke, that these were big box stores, that I would never want to steal from an individual or small business, etc. But the fact is this: When I was a kid, I discovered that I could open the flap of a vending machine, stick my arm up into it and take candy out, and more importantly I discovered that doing that felt a lot like solving a puzzle and very little like stealing. As an anarchist with certain political beliefs about private property, capitalist enterprise and excess wealth, it was equally easy to justify other kinds of theft, though of course there are also arguments against it. Logical justification, though, is always secondary. I know this because I could recognize the feeling of stealing something that doesn’t feel like stealing.

Thinking back, my feelings are mixed. I’m not sure if my arms fit into vending machines like that anymore, and I can’t remember the last time I walked out of a store with anything because that slowly started to feel a lot more like stealing. These days, I’m pretty cautious when I notice that slippery feeling of justification because it feels a bit avoidant and I prefer to keep my reality intact. I haven’t yet quit pirating TV, and my advice to TV companies is that if they really don’t want people to do that they need to find a way to make it feel a lot more like stealing and a lot less like clicking videos on Youtube.

The trolley problem is an old philosophical saw about a similar concept. The first question is, if a trolley were headed down a track toward five people and you had the option to pull a lever and switch it to a track with only one person, would you do it? If you’re like a vast majority of people, you would (and I suspect that if you wouldn’t, you’re more concerned about your own feeling of guilt than you are about actual morality). That changes, though, with the second question. If you were standing on a bridge above the track watching the trolley speeding toward five people, would you throw one innocent bystander down onto the track if you thought that would stop the trolley? Ridiculous, yes, but there are real-world corollaries. What if a surgeon killed one healthy person to save five others with his organs? The effect is almost the same as the first problem, but we all agree that it feels different, and I would argue that that feeling is important. It’s hard to make a logical argument that one is right and the other is wrong, but it’s easy to agree that we don’t want to live in a world where organ piracy is a thing.

The nature of this note situation is that some of the notes will always be extremely unfinished.
Questions? Comments? Write to me at (or @me).