iolinked.com Ajai's space
Announcement

What is this website about?

Robotics, microcontrollers & industrial automation, AI & machine learning — and the maths & algorithms underneath it all. Learned from first principles, documented end to end.

Self-driving robots, smart factories, and the maths underneath — studied in the open, one layer at a time.

Probability, algorithms, cryptography, operating-system internals, machine learning, systems thinking — different vocabularies, same machinery. A PID controller and a neural-network training loop both work the same way: measure an error, feed it back, shrink it. A language model and a zip file are both bets about which symbol comes next. Underneath, it's one subject: mathematics, wearing different clothes — and every course here climbs down to the layer where they meet.

For as long as I can remember, I've needed to know how things work — really work, the layer beneath the layer, until there's nothing left to take apart. This site is that habit written down: I pick a concept, learn it until it stops being fog, and document the path while the climb is still fresh.

Robotics, factory automation, AI, the maths underneath — one story told at different depths. A sensor reading is a voltage; an ADC turns it into an integer; firmware turns the integer into a message on a bus; a filter turns noisy messages into a state estimate; a planner turns the estimate into a decision — and an equation at every joint says why the hand-off is legal. The courses here walk stretches of that chain and refuse to hand-wave the joints, because the joints are where understanding actually lives.

The projects run end to end. A small self-driving robot — perception, planning, control — trained in simulation, then debugged on real hardware, where timing jitter, sensor noise and a sagging battery teach things no simulator will. Industrial systems where microcontrollers and PLCs meet the right comms protocols until IT and OT share one picture of the plant. The write-ups keep the failures in, because the failure is usually the moment the concept clicked.

Under the builds sit the ideas I keep returning to: the algorithms, transformers and RAG, the way a quant prices risk, the mathematics holding the structure up. ROS, STM32, Isaac Lab, training loops — good tools, but tools age fast and ideas don't: attention is from 2017, the Kalman filter from 1960, Bayes' rule from 1763 — and all three are running in production right now. These pages spend their effort on the part that lasts.

Since so much of this site orbits AI, here is what the word means, mechanically. A neural network is a huge pile of numbers, tuned by showing it examples and nudging every number in the direction that shrinks the error — the nudge is a gradient, and repeating it billions of times is all "training" is. Generative AI is a model that has learned the shape of its data well enough to sample from it: a language model does one thing — it predicts the next token — and attention is the mechanism that lets every word weigh every other word while it decides. Chat, reasoning, working code: all of it falls out of that one loop run at scale. Agentic AI puts the model inside a loop — a goal, tools it can call, memory of what just happened — so prediction becomes behaviour. And look closely at that loop: sense → decide → act. It's a control system. Control engineers have been shipping that loop since 1922, when it first steered ships — the plant just got stranger.

People sometimes ask why one site covers circuits, factories, models and markets. Because the walls between them are thinner than the job titles suggest. Feedback, probability, optimisation, information — the same four ideas run the robot, the plant, the model and the trading book, and each field keeps rediscovering them under new names. I didn't set out to connect these subjects; the connections were already there. Writing is how I catch them in the act.

The thread that ties it together

Learn the machine. One layer at a time.

The habit underneath every page here: when something matters, learn the machine under it. Programming is one factor in that — a strong one, because code forces you to say exactly what you mean and shows you, mercilessly, when you didn't. But the same training comes from circuits, from control loops, from proofs: break the problem into testable pieces, find the assumption that's lying to you, fix that first. Machines will soon draft most of the code; reading the diff still takes someone who knows what the code is for.

That training transfers with no paperwork. The discipline that corners a firmware bug is the one that untangles a factory line, a trading model, a research paper — isolate, instrument, change one thing. Generated code is cheap now; understanding is the part that never got cheaper. First principles are the slow road in and the only one that compounds: each layer you actually understand makes the next one cheaper to learn.

So the courses start at the transistor and try not to skip steps. A sensor reading becomes firmware, firmware becomes an algorithm, an algorithm becomes a decision made by a machine — and each hand-off is shown, not asserted. I write the chapters while learning the material properly myself, which keeps me honest about which steps need explaining: the gaps most tutorials skip are usually the ones I just climbed out of.

Everything here is built in the open and traced through its layers, so you can follow along, check the working, and build your own. Where something's wrong, say so — the next revision gets sharper. Pull up a chair; let's make and break things.

None of it stays theoretical for long — three arenas on this site put the ideas to work:

What connects everything

one answer: mathematics

Strip the casing off anything on this site — a drone, a factory line, a trading bot, a language model — and just before the physics you find the same thing: mathematics. The top row is that maths in its own words. The bottom row is what it looks like soldered down.

the climb probability (the bedrock)algorithms (structure on the math)cryptography (maths doing the work of trust)OS internals (how machines actually run)machine learning (how machines learn)systems thinking (how parts become wholes)math to mind.

the zoom from microcontrollers & edge devices, through robotics & industrial automation, up to AI & financechip to world. Same language, every altitude.

the spectrum deterministic → non-deterministic: machine code (every step exact)a program (precise by construction)legal wording (precise, yet argued over)everyday English (ambiguity doing the work)a poem (meaning lives between the words) — the same road runs from program to AI, from machine to human mind. Trace3 lives at one end of this road; the Mind IO-Reactor at the other.

Probability

The art of being precisely unsure.

Appears in
  • sensor fusion in robotics
  • risk models in trading
  • uncertainty in ML

Algorithms

Recipes that don’t care what they cook.

Appears in
  • game loops & physics
  • robot planning
  • trade execution

Cryptography

Maths you can bet a fortune on.

Appears in
  • Bitcoin & the blockchain
  • embedded authentication
  • secure systems

Systems thinking

Where parts start acting like a creature.

Appears in
  • robot coordination
  • multi-agent AI
  • industrial automation, IT ⇄ OT

Communication protocols

How machines agree on meaning.

Appears in
  • CAN & Modbus on the factory floor
  • UART · SPI · I²C between chips
  • MQTT bridging IT ⇄ OT

Microcontrollers

Where code meets silicon.

Appears in
  • bare-metal firmware & RTOSes
  • motor drives & sensor loops
  • PLCs sequencing the plant

Electronics

Every signal starts as physics.

Appears in
  • sensor front-ends & ADCs
  • power stages & motor drivers
  • the PCB under every robot

A Kalman filter steering a drone runs the same probability math as a trading desk's risk model. Both lean on systems thinking. Both are algorithms built from first principles. And every bit of it eventually lands on copper and silicon — a sensor, a bus, a microcontroller — where the math starts moving real machines.

Even games are load-bearing here. The GPU was invented to draw them, Monte-Carlo tree search was built to win them, and reinforcement learning grew up chasing high scores — and that exact stack went on to fold proteins (AlphaGo → AlphaFold) and now screens molecules for drug discovery. A game engine and a molecular-dynamics simulator are the same machine running at different timesteps. Play is how the tools of discovery get built — and that's exactly why games get first-class treatment on this site: every arcade here is a physics engine, a state machine and an algorithm you can feel.

Browse by topic

complete explorations from first principles — not tutorials
No posts match that search yet.

build systems · think deeply · innovate anywhere