“[…] a reprehensible haven for heterodoxy. “
Babylonian thinking is a global perspective.
It’s really not that surprising that “Babylonian” is how Feynman described this mindset, method, what have you. When you do any kind of initial research, which is inherently going to be inquiry based, as all research is, the theorems that you come up with in math will be a mess of theorems that might not even appear to be related. Especially in constructing setups in graph theory, the facts about the nature of a type of graph seem wildly contingent, though they hold for a class of graph. As a result, I have developed this anxious feeling when thinking about math, the feeling that contingency and process reign supreme in mathematics, and that the organization of branches of math into an axiomatic setup is secondary, perhaps artificial. As it is, the further we delve into an area of mathematical research, we often have to revise our axiomatic setup.
Throughout my many years of attempting to learn complex concepts in a linear format, I have consistently run into this revision process. The inefficiency of having to re-sort is mentally taxing. Taking a top-down approach, or reverse-engineering the concepts, has always felt better for my brain.
accommodāre
verb
accommodated; accommodating:
to provide with something desired, needed, or suited
to make room for
to bring into agreement or concord : reconcile
to give consideration to : to allow for
to make fit, suitable, or congruous
to adapt oneself
to bring one thing into correspondence with another.
The whole of technology is essentially accommodation. Disability is a social framing.
I’ve spent years trying to figure out the best practices for accommodating the specific support needs that typically overlap ADHD and PDA. I studied school models around the world and educational practices late into the night, trying to determine what worked and what didn’t. Throughout this process, I came to recognize a central, underlying human need being overlooked in attempts to educate kids with disabilities: inclusion.
Schools that separate kids with high support needs require far more staff to accommodate students than a more typical school environment, and the school, which is essentially a microcosm of larger society begins to evolve away from its original intention: preparing children for the realities of the adult world. We are always learning to work with others. We are not grouped by our neurotypes in adulthood.
Attention is the beginning of devotion.
Play schema > sensory > we never truly outgrow this need
I read about a woman,
Who chose cleaning
As her path
To enlightenment.
Rather than beads,
A toilet brush and broom,
From door to door
And train station, too,
Like a servant
Who had been given an example.
What if…
Instead of sitting with “om”
In my inner-city monastery
I asked my neighbor’s permission
And cleaned the sidewalks
Each morning, raking
Leaves, sweeping litter.
Only one block…
One block at a time.
On Revival and Returns
I have a stack of unread books double paper bagged, sitting on the floor in the corner of my living room that have been in need of a ride back home to the local library for… oh my god, six months now. Since I’ve likely incurred well over one hundred dollars in fees/charges for essentially (though unintentionally) thieving library books, I figured I should probably read a few. The initial visit was intended for physics/physical science concepts that were already written simply because I was experiencing one of the most intense periods of burnout in my adult life and couldn’t write a damn thing. Recall has always been tough for me even when I’m presently immersed in a subject but typically once I get going, hyper-focus takes over and I recall far more than I remember learning. During burnout there are no functioning backup safety features to kick in when I struggle. There’s just a wide expanse of nothingness, and the void is telling me to watch Gilmore Girls until I can remember words again. But I have a child, so instead we watch Zoey 101 which is her burnout phase comfort show.

I found this book near the top of the bag. It’s one that my daughter picked out from some adult choices. I’ve mostly parented in a loosely regulated but intentionally communicative fashion. Sometimes it works well but sometimes it does not. When you parent with the intention of being openly approachable about any topic, it’s necessary to maintain a high level of trust and mutual respect. I have been failing to do this sufficiently for at least the amount of time those library books have been crashing in my living room. But as is typical in life, circumstances begin to shift and we become aware of the areas we have neglected to nurture in our relationships, and we work to restore the balance.
I flipped the book open to a random page to see what was going on. Turns out this is a Christian book which would typically not be my thing as a recovering Evangelical but Anne uses profanity so I trust her for now. In a chapter titled Snail Hymn, I found this:
People like to say that we cannot forgive others until we forgive ourselves. Isn’t that nice? People like to say all sorts of stupid bumper-sticker things that aren’t true and that in fact can be shaming, such as that God never gives us more than we can handle. What a crock. (My friend Mary says, in response, that you should never give God any idea of how much you might be able to bear. Lowball Him, like a trainer at the gym who thinks you might be able to lift heavier weight. Say that you injured your lower back doing that once. Hint at liability.)
I have forgiven most people who have hurt me or behaved atrociously to those I love, although there is one extended family member who (I’m positive) makes Jesus sick to His stomach. Yet from time to time, I forgive myself for being a bad forgiver. Forgiving ourselves is the advanced practice–it’s Senior Lifesaving.
It is tricky business. Comedian Cameron Esposito put it well: “I remember a close friend’s mom asking me if I really felt comfortable wearing a swimsuit next to her daughter’s much more slender body. I was eight. When you are a little kid, you can’t protect yourself from this shit. You think the shit is you.”
You thought the shit was you, all through the years, and droplets got trapped in various chambers of memory. Even with years of recovery or therapy–after making amends and working on self-acceptance and even experiencing patchy moments of transcendence, after having mostly forgiven ourselves for not caring, for ambition, materialism, wasting time, and gluttony–it can still be exacting. The fear of your defective nature resurfaces, the way chicken pox resurfaces as shingles. But at some point you realize that we all have dual citizenship here, perfect and neurotic. Ram Dass said you have to remember only two things: your Buddha nature and your Social Security number. And wonderfully, there is not enough memory to keep track of every old grievance. This is the grace of age. So one forgives as one is able, except for maybe those two or three special contenders and oneself.
Each full act of forgiveness and even each partial act is not only a miracle, but a prize of redemption, as with books of S&H Green Stamps. But instead of a toaster, you get a unit of peace. Each act of forgiveness gives us more awareness of the beauty that surrounds us and of the friendly light inside, the tiny usually ignored part that hasn’t been faked, cheapened, or exploited. It is an infinitesimally small point of light–like when our ancient TVs were turning off–and eternity, the world in a blade of grass.
[…] Forgiveness, I know now, is maturity. Mercy is maturity. It is slow release, like certain medicines. It’s incremental, like traveling along the spiral chambers of a nautilus.
I once brought my Sunday school kids a nautilus shell, because if you want to help kids fall in love with God, help them fall in love with nature. My friend Mark, who also teaches Sunday school, taught me that, and it is one of only a few great lessons I can teach.
He also showed me a way to help my kids with their terror of what we’ve done to the earth. “Ah!” he said, excitedly, when I asked for guidance, as if I had come to the right place. “First teach them how we live with sin.”
I nodded Hasidically. Then I asked, “How do we live with sin?”
I sinned so much in my twenties and early thirties, until I got sober, when I moved from moral turpitude to the simple cloth-coat sins of inertia, judgment, and morbid reflection. The woman who helped me get sober in the eighties, when I told them how bad my behavior had been, waved their hands dismissively and said, “Oh, me too.” This began to relieve me of my bottomless shame. They said, Leave it alone. Don’t pick at it. Let it heal. Don’t have any affairs today.
Sin is not just affairs, or porn shops, or drug cartels. It is also the ignorance and brokenness of the world, extreme self-centeredness, hoarding wealth, using others as objects, not caring.
Mark said that to teach the kids how we live with sin, take them to a beach. So I did. (Never disobey Sunday school teachers. They will fuck with you.)
The beach was cluttered and littered with plastic bottles and crap of every kind. We walked around and saw what we saw–damage to this gorgeous beach, what human behavior had wrought. I invited the kids to experience sorrow, disgust, and anger. I asked them how it made them feel.
It made them feel sad, scared, hopeless. So we cleaned up one part of the beach as much as we could. Mark had recommended that we bring back some of the garbage. Bring in the ugly and the sad, along with sand and shells. So we brought in some trash and some treasures. Then, this being Sunday school and not biology, we laid it all beneath the arms of the cross, because then it is held; it became part of the bigger story, the bigger reality. Not just the crud from one section of one ruined beach, but a variety of things from what was now a cleaner beach, a beach loved and held by caring people, kids who care. You admit that the ugly and repulsive and sad do exist, and they are happening, but we don’t have to believe it is us, and run away from it, from the cross, from the beach, from our own crooked hearts.
This is how we live with sin, sickness, and a world on fire.
Taking kids outside to love God in nature is just about the most Jesusy thing we can do. Jesus was nearly always outside with His disciples or alone with the stars. To take kids to a beach, even one that is littered, is to bring them to an altar, a big one, surrounded by the blue-gray ocean billowing outward like a skirt, flecked with sunlight, like foil or diamonds.
But the nautilus class was at the end of summer and was scheduled to be a short service, and it didn’t make sense to take the kids to the beach. Only one girl was in the Sunday school classroom that day. So I brought the beach to her, as a bag of shrimp chips, a Hawaiian Punch from the church pantry, and a few nautilus shells. Far be it from me to dive into such a New Age cliche, although even my bad attitude atheist friends have to admit that the nautilus is mathematically interesting and beautiful, the inside especially. But I could show the girl only the outside, and a photo of the inside.
Each of the nautilus shell chambers, starting at the very inside of the spiral, is incrementally bigger than the one before, until there is the outermost space where the mollusk lives. It’s the creature’s living quarters, its crib. The chambers hold gas extracted during respiration, for buoyancy and propulsion. The nautilus, protected in the final chamber, is both inside and yet connected to the outside, to water and food. Even my atheist friends admit, too, that this is a good metaphor for the safe space that’s in each of us, where there is relief from anxiety and self-consciousness, where there is room to breathe, to settle in, settle down, mull things over without anyone’s hot breath on our necks.
The girl handled the shell with due reverence. It was all curves and stripes, reminiscent of animal stripes, asymmetrical and good for camouflage. She traced the curve with her small fingers, as you might stroke a cat’s back. Nature seems to know that the curve is the best way to be, smooth and flowing, without any sharp edges. A shield is curved, our ribs are curved; there can be protection in a curve. You don’t get so easily smashed into by curves as you do by objects with sharp sides. And everything in the curve is balanced, which is so rare.
I was not going to teach the usual message of the spiral, that we can grow from the innermost kernel of understanding into expansion.
Well, maybe I would, just for a second, in passing.
A spiral is the ultimate statement of the harmonious. It does not grow in fits, starts, and back steps, but rather, in a flow. And chambers can be sacred, because they invite you in, even as they protect you, perhaps somewhat like your parents were supposed to, and possibly meant to.
The girl turned the shell over in her hand to study the opening. It was small, unlike a conch, but still she held it to her ear to hear the song of the universe, elegant and playful, like Bach with a girl-group backup, centered in harmonies.
We took some time to study the photograph of the shell’s inside chambers, the swirl of its expansion from barely visible to roomy. It has an exquisite, perpetually steady rhythm, like the ocean or our heartbeats.
The last detail I wanted to point out, before we had the sacrament of shrimp chips, was that when everything keeps expanding, there is still room in all of us for breath, which is what keeps us alive.
What is nature sharing with us? If something is allowed to grow the way it was designed to, it works. When we try to get it to conform to the supposedly more efficient image we have of it, we get grotesqueries, imbalances. When we try to get difficulties to conform to our way of thinking, we often push them toward being fancier, and thus absurd. We strip away the grace of what is real, and true, and maybe even lovely.
My Sunday school class and I had only ten minutes left, so we couldn’t get into the Fibonacci spiral, the mathematical sequence we find in pine cones, seed heads, and the nautilus. The outside of a pineapple or seeds in a sunflower, for instance, are arranged in uniform, efficient spirals so that the seeds in the center don’t get crowded and squished and the ones outside don’t fall off. This sort of exactitude, balance, and order are what we humans rarely experience but so long for.
I note that, coincidentally, the designs I didn’t design seem to work much more often than mine.
Something about the spiral and other kinds of curves makes you want to throw your arms outward and around as in the port de bras of a ballerina, with a deep breath and a long sweep of your arms, so you become a curve, too.
“And then what makes it sacred,” I told the girl, “is the life inside, its being–the snail!” I was so moved by what I had just said that I clutched my chest.
“Hmmm.” she said, opening the bag of chips.
“It breathes, it has babies, it scooches around through jet propulsion. It has memory. It can live twenty years.” I paused for effect. “Brother snail!”
When I got home from church, I went online and ordered a split nautilus shell for her, so she could see the coil of chambers, how it (and maybe we) grow.
Forgiveness grows like this, too.
It seems as though intuition might still be guiding me.
Habits of Mind
I came across this approach again through a blog post shared by the organization that certified me as a nature educator. I’ve loosely incorporated this method into what I’m building with our cooperative but got bogged down by life and administrative responsibilities for a bit. It’s nice to be to a place where I can now focus more on the quality of our outings and not just the logistical aspects–even if it is just temporarily. There’s definitely need for a more egalitarian framework for task distribution.
Through a steady diet of asking the children, “What do you notice?” and “what do you wonder?,” the children’s perception of the environment and their role in it has dramatically changed in these 12 weeks. We have moved from utilizing the space as solely playground (which is also important and valuable), to engaging with all that we see through the eyes of curiosity.
We are forming habits of mind in the forest. Beyond the skills and facts that will surely accumulate, it is the orientation toward learning that we seek to cultivate most.
Written by: Rachel Schwartzman, Director/Lead Teacher of Forest Days – http://www.erafans.org/blog/7007658
Today, I had a long conversation with a child about a clump of soil with leaves stuck to it that he had picked up and brought to me. Unprompted, he stated his observations: “The ice is never melting,” and “There are leaves stuck to this.” We looked closely with a flashlight and a hand lens to try to figure out more. His genuine curiosity about this object he had found and chosen to pick up struck me. On another day, this would easily have been passed by, but today, he is paying closer attention to the environment. He is choosing his topics of research. He is growing knowledge that will be layered on in the weeks to come. His relationship to the forest is becoming one of interest, curiosity and engagement.
There are sixteen dispositions and behaviors identified by Art Costa and Bena Kallick in their book Learning and Leading with Habits of Mind: 16 Essential Characteristics for Success. I’ve not read this book, and have only examined these through an abbreviated version produced by a forest school in the United Kingdom (https://www.kingsmoorprimaryschool.co.uk/). Most are reasonable expectations but some need adjustment for kids with disabilities, particularly ADHD.
| Learning continuously | I am always learning and always growing. Understanding that there are always new things to learn and new ways to gather information, regardless of age. Every experience can be a learning experience. |
| Thinking and communicating with clarity and precision | I think about what I am going to say before I speak so it is clear and others understand me. Think and communicate with clarity, precision and accuracy with precise language to be specific. Avoid over generalisations, distortions and exaggerations. |
| Thinking about our thinking (Metacognition) | I listen to what I think. Thinking about your own thoughts, feelings and actions and being able to identify them. Setting a plan, maintaining that plan and reflecting on it once it is finished. |
| Persisting | Don’t give up! I can do it! To stick with a task means to stick with it until it is completed. Think about the problem and try different strategies to solve it. If one method doesn’t work, try a new one and keep going. |
| Creating, imagining, Innovating | I know there is more than one way to do things. Create new and original solutions and techniques by looking at problems differently and considering it from new perspectives. |
| Gathering data through all senses | I pay attention to all my senses. Learning through all the senses; taste, sight, smell, hearing and touch to gather as much information as possible |
| Responding with awe and wonderment | My curiosity opens up new worlds. Finding special aspects of things, that others consider ordinary. Thinking is about opening up new areas for exploring and being excited about what can be found. |
| Managing impulsivity | Stop. Think. Act. Think about the problem and possible outcomes. Think about what is needed while staying calm and think of others’ actions to achieve. |
| Thinking interdependently | I work with others because together we achieve more. Working collaboratively and socially, considering the opinions and views of others and working together to achieve. |
| Striving for accuracy and precision | I take my time and always double check. Set goals for high standards and try to achieve them. Search for ways to improve and take pride in everything I do. |
| Applying past knowledge to new situations | What I already know can be used in new areas. Learning from previous experiences and adapting knowledge to new situations. See connections between experiences and transfer the knowledge from one experience to the next. |
| Taking responsible risks | I take chances and I am confident in trying. Trying new things without fear of being wrong. Be secure and confident to try new things rather than regret holding back and not trying. If it works that’s great. If it doesn’t it is something that has been learnt. |
| Finding humour | I can find a funny side of situations and laugh at myself. Being able to laugh at yourself and find the funny side of situations. Not taking things so seriously and being confident to laugh at personal mistakes. |
| Questioning and posing problems | I try to fill the gap between what I know and what I don’t. I use a range of questions to gain as much knowledge as possible. Look at the points of view of others, find connections between things and consider hypothetical outcomes. |
| Listening to others with understanding and Empathy | I try to understand others. Completely listen to other people and hear their thoughts, beliefs, opinions, emotions and think about it from their point of view without judgement |
| Thinking flexibly | I try new things and think in new ways. Thinking flexibly means being able to consider or create other options, methods or views and being able to change perspective when new information is added. |
What is this, a school for ants?
I want to facilitate a class specifically intended for obsessing over patterns in nature. – Me to Twitter (essentially my ADHD thought diary) on February 26, 2020.

in order to be easy to remember, ideas need a house, a place to live
One boy, quite a good student, was working on the problem, “If you have 6 jugs, and you want to put 2/3 of a pint of lemonade into each jug, how much lemonade will you need?” His answer was 18 pints.
I said, “How much in each jug?”
“Twothirds of a pint.”
I said, “Is that more or less that a pint?”
“Less.”
I said, “How many jugs are there?“
“Six.”
I said, “But that [the answer of 18 pints] doesn’t make any sense.”
He shrugged his shoulders and said, “Well, that’s the way the system worked out.” Holt argues: “He has long since quit expecting school to make sense. They tell you these facts and rules, and your job is to put them down on paper the way they tell you. Never mind whether they mean anything or not.
If mathematics learning is not grounded in an understanding of the nature of the problem to be solved and does not build on a student’s own reasoning and strategy development, then solving problems successfully will depend on the ability to recall memorized rules. If a student has not reviewed those rules recently (as is the case when a summer has passed), they can easily be forgotten. Without a conceptual understanding of the nature of problems and strategies for solving them, failure to retrieve learned procedures can leave a student completely at a loss.
Yet students can feel lost not only when they have forgotten, but also when they fail to ‘get it’ from the start. Many of the conventions of mathematics have been adopted for the convenience of communicating efficiently in a shared language. If students learn to memorize procedures but do not understand that the procedures are full of such conventions adopted for efficiency, they can be baffled by things that are left unexplained. If students never understand that x and y have no intrinsic meaning, but are conventional notations for labeling unknowns, they will be baffled when a z appears. When an m precedes an x in the equation of a line, students may wonder, Why m? Why not s for slope? If there is no m, then is there no slope? To someone with a secure mathematics understanding, the missing m is simply an unstated m = 1. But to a student who does not understand that the point is to write the equation efficiently, the missing m can be baffling.
Unlike language learning, in which new expressions can often be figured out because they are couched in meaningful contexts, there are few clues to help a student who is lost in mathematics. Providing a secure conceptual understanding of the mathematics enterprise that is linked to students’ sensemaking capacities is critical so that students can puzzle productively over new material, identify the source of their confusion, and ask questions when they do not understand.”
In 1960, Nobel laureate Richard Feynman,
…who was well known as an extraordinary teacher, delivered a series of lectures in introductory physics that were recorded and preserved. Feynman’s focus was on the fundamental principles of physics, not the fundamental principles of learning. But his lessons apply nonetheless.
He emphasized how little the fundamental principles of physics “as we now understand them” tell us about the complexity of the world despite the enormous importance of the insights they offer.
Feynman offered an effective analogy for the relationship between understanding general principles identified through scientific efforts and understanding the far more complex set of behaviors for which those principles provide only a broad set of constraints:
We can imagine that this complicated array of moving things which constitutes “the world” is something like a great chess game being played by the gods, and we are observers of the game. We do not know what the rules of the game are; all we are allowed to do is to watch the playing. Of course, if we watch long enough, we may eventually catch on to a few of the rules. The rules of the game are what we mean by fundamental physics. Even if we knew every rule, however, we might not be able to understand why a particular move is made in the game, merely because it is too complicated and our minds are limited. If you play chess you must know that it is easy to learn all the rules, and yet it is often very hard to select the best move or to understand why a player moves as he does. . . . Aside from not knowing all of the rules, what we really can explain in terms of those rules is very limited, because almost all situations are so enormously complicated that we cannot follow the plays of the game using the rules, much less tell what is going to happen next.
[…] what we know from research thus far is critical in defining the constraints on strategy development. […] what we expect to learn from a well-played game (in this case, what we expect to learn from well-conceptualized instruction) is not how to reproduce it. Rather, we look for insights about playing/teaching well that can be brought to one’s own game. Even if we could replicate every move, this would be of little help. In an actual game, the best move must be identified in response to another party’s move. In just such a fashion, a teacher’s “game” must respond to the rather unpredictable “moves” of the students in the classroom whose learning is the target.