Lizards, Codes and Calm Nerves: A Geometry Lesson from the Cloud
by Kirstin Stevens, Building Schools in the Cloud
Most people don’t believe me when I say some of the best conversations of my week are about broken embeds, tessellating lizards, and 16th-century cipher queens.
But that’s what happens when you’re building schools in the cloud with someone like Gerry Docherty.
Gerry and I meet regularly online – half maths clinic, half design lab for whatever “school” is becoming. This week’s call started, as many do, with a simple teacher problem:
“Canvas used to let me embed my Web Sketchpad files,” Gerry said. “Today it just… doesn’t. The code’s there. Nothing appears.”
Welcome to 2025, where even veteran maths educators with decades of experience find themselves arguing with invisible LMS rules and mysterious platform updates, while an AI window quietly suggests, “You may need to upload this to GitHub instead.”
This is the bit nobody really prepares teachers for: You’re not “just” planning lessons anymore. You’re debugging the infrastructure of learning in real time.
When the Geometry Doesn’t Load
On the surface, Gerry’s issue was small: Web Sketchpad activities that used to embed in Canvas had suddenly stopped working. Same HTML, same workflow, different outcome.
“Has Canvas changed the rules?” “Is it something in the AI-generated code?” “Have I done something stupid?”
Every educator I know asks some version of those three questions several times a week.
We talked through his GitHub setup: local folders, commits, pushes, the usual dance of “why is only one file showing when I moved two?” None of this is what Gerry trained in. He trained to teach mathematics, not to version-control interactive hexagon lizards in a distributed file system.
But here he is. And that matters.
Because this is what “Building Schools in the Cloud” really looks like in practice:
A teacher from Scotland, troubleshooting a geometry lesson like a junior DevOps engineer.
An ex-founder in England, squinting at GitHub status messages at midnight.
Multiple AI systems in the background, occasionally helpful, occasionally confidently wrong.
Not glamorous. Not polished. But very real.
And in the middle of the friction, something beautiful is being built.
Lizards on a Hexagon Grid
Once we’d parked the GitHub mystery, Gerry shared what he’d been working on.
“Have you heard of M. C. Escher?” he asked – the Dutch graphic artist famous for impossibly recursive staircases and mind-bending tessellations.
He then screen-shared an in-progress activity: a tiling of the plane using regular hexagons, living inside Web Sketchpad.
First, he constructs a simple hexagon grid. Interior angles: 120°. Enough symmetry to do something interesting.
Then, using rotation, he shows how a head, a leg and a tail can be carved out of a single hexagon, piece by piece. Rotate the shapes around the vertices and, suddenly, the plain grid is populated with “Lizzie the Lizard” – an interlocking creature born entirely from clean geometry.
From there, it gets clever:
Buttons to generate the head by rotation
Buttons to build the leg and tail
Buttons to clone and rotate the full lizard into green and red companions
Translation vectors that slide whole trios of lizards across the grid, until the screen is fully tiled with interlocking shapes – no gaps, no overlaps, just living symmetry
He’s not just showing pupils a pretty tessellation. He’s giving them the tools to build it.
It’s Escher in the browser, but with one crucial difference: The learner isn’t just an observer of the pattern – they’re the author of the transformation.
Why Our Nervous Systems Love This Stuff
Looking at Gerry’s hexagon lizards, something in me relaxed.
There’s an odd kind of relief in watching symmetry click into place. Patterns that could have been chaotic suddenly fit. Everything finds a home.
I said to him on the call that there’s something deeply soothing about that kind of balance – something our nervous systems recognise before our rational mind catches up.
It’s not just “oh, that’s pretty.” It’s I trust this.
Maybe that’s why Escher’s work has endured: he uncovered all 28 symmetry groups without formal mathematical training, guided by an instinctive feel for pattern, structure and visual logic. That’s the bit our current system so often misses.
We talk about “rigour” as if it lives only in exam papers, but Gerry’s work is a reminder: rigour is also in the careful construction of beauty.
And that’s exactly what I want future employers to hear when a young person says:
“I went to The Haven.” “I learned maths through tessellating lizards and code wheels and breathing labs.”
This isn’t fluff. This is brain-level engineering for a world that’s going to need sensitive, pattern-literate problem-solvers.
Broken Nervous Systems and Breathing Labs
At some point, our chat turned from hexagons to health.
I told Gerry I’d seen a physio who’d essentially said: “You’ve broken your nervous system.” Too long in survival mode. Too much stress. Things not quite firing properly.
Her prescription? Calm my nerves.
So naturally, I told her I’d already built an app called Calm Nerves Lab.
It started as a Breathing Lab – a simple browser-based tool with a series of breathing patterns:
4–4–6 breath (inhale for 4, hold for 4, exhale for 6)
Box breathing (4 in, 4 hold, 4 out, 4 hold)
2–2 heart-focused breath
Fire breath for activation
A gentle pre-sleep pattern, inspired by my son Aidan, who struggles to switch off at night
Built originally with Claude (inspired by the work of Paul Collins ), refined with Tailwind and config in another model, it’s a tiny thing. But when I used it before bed, I slept.
That connection between pattern and peace kept looping back in the conversation:
Symmetric lizards in a hexagon grid
Boxed and spiralled breath cycles
DNA’s double helix
Our kids’ overloaded nervous systems trying to find a rhythm that isn’t fight-or-flight
We are, as someone recently called us, “wetware”. Geometry in soft, sensitive form.
If we’re going to build schools in the cloud that actually help, not harm, then tools like Gerry’s lizard tilings and my Breathing Lab aren’t extras. They’re part of the core curriculum:
Geometric patterns for the mind
Rhythmic patterns for the body
Symbolic patterns for meaning
All three matter.
Mary, Codes and the Shape of Thought
Towards the end of the call I mentioned I’d been watching Mary’s Secret Codes – a BBC documentary on Mary, Queen of Scots, and the ciphers she used in her letters.
The code-breakers who cracked her cipher centuries later? A musician, a Japanese cryptographer, an Italian specialist, a French historian. Different disciplines, different ways of seeing – all converging on one pattern.
Gerry immediately referenced Simon Singh’s The Code Book, where Mary’s cipher is the opening chapter, and started talking about resurrecting an old Caesar cipher wheel he’d once built in Flash. The original course used a character called Dr Danger, a spoof on Austin Powers’s Doctor Evil, guiding pupils through an escape-room-style sequence of codes to crack.
Now he’s thinking of rebuilding it in HTML with Canvas. Same idea, new medium.
Again, the pattern is the same:
Real stories (Mary, Alan Turing, Bletchley Park)
Playful tools (cipher wheels, mock villains, escape missions)
Cross-disciplinary teams (musicians, mathematicians, coders, teachers)
This is what we mean when we talk about Building Schools in the Cloud: Not just “online lessons”, but living ecosystems of pattern work – numeric, geometric, symbolic, emotional.
Publishing From the Edges
We closed the call talking about books.
I’ve just launched The Novacene Press as a way to publish the work emerging from all these edges without waiting for traditional gatekeepers to understand it. E-books created in Calibre from PDFs, pushed to Kindle or sold directly. Anthologies of work from educators like Gerry Docherty, Paul Glossop, Mandy Perry, Euan MacLean and others who are quietly redesigning education from inside their own classrooms and living rooms.
Gerry already has children’s books out there – Tessa the Turtle, and another climate-themed adventure that never quite made it online. Meanwhile I’m writing children’s allegories about emergent intelligence and cereal bowls, and reading them to my own kids on weekends.
It feels fragmented, but it’s not. It’s a network.
My conviction is simple:
If we want different schools, we have to publish from the field, not wait for permission from the system we’re trying to evolve.
Joint books. Shared code. Open tools. Live experiments. A collective “this is what we’re doing and why” – for anyone who wants to build with us.
Why This Conversation Matters
On paper, today’s chat with Gerry was “just”:
an embed issue in Canvas
a tessellating lizard activity
a broken nervous system and a breathing app
a documentary about Mary, Queen of Scots
an old cipher wheel sitting in someone’s archive
a passing mention of Kindles and e-pubs
But in reality, it was a snapshot of the future of learning:
Teachers as makers – building interactive tools, not just consuming them
AI as collaborator – helpful, fallible, and part of the workflow, not the whole thing
Maths as art and regulation – soothing the nervous system while sharpening the mind
History as pattern memory – codes, symmetry groups, cryptography as narrative
Publishing as mutual signal – educators documenting their own experiments in public
This is Building Schools in the Cloud. Messy, human, occasionally glitchy – and full of lizards tiled across a plane, quietly reminding us that order and beauty can emerge from the simplest of shapes, if we give people the tools and time to play.
Somewhere in all of this, a young person will one day say in an interview:
“I learned to see patterns in lizards, codes, and my own breathing.”
And the person on the other side of the table – if they’re awake to the world that’s coming – will know exactly what that’s worth.
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First published in Building Schools in the Cloud on LinkedIn, 18 November 2025.