From the ground up
2020

This 2020 sequence rebuilds computation from switching, state, logic, and addition.

It starts from low-level geometry that allows control, then builds a hierarchy of algorithms from the ground up. The exercises are meant to stay close to the physical substrate: relay switches, CMOS transistors, FPGAs, and GPU shaders are different materials for the same logical discipline.

(No "cheating" involved! We will be able to reproduce these algorithms virtually anywhere, from relay switches and CMOS transistors, to FPGAs and GPU shaders.)

Computation sequenceThis page collects the early browser-native lessons.

Included: scaffolding, minimum WebGL, history/control, logic, and addition.

Boundary: this is not a complete modern WebGPU/GPGPU curriculum or a full introduction to Cartilage.

Introduction

The streams of computation let us define and run computation in arbitrary media, including water pipes, billiard balls, dominos processors, GPUs, FPGAs, ordinary CPUs, then quantum computers, and even time machines.

The concepts we are about to explore will unfold for us in a straightforward manner, where we will be using code to fixate our memory.

Analogies

In mathematics, one must to memorize and execute in their head all axioms and theoremes. We will use computer to memorize those for us. We will use ordinary browser available without any installations in every laptop, and even smartphone.

The principles we are about to explore, will help us to design efficient streams of computations and run sophisticated predictive simulations virtually anywhere, from toy models in browser; up to Vulkan, CUDA, RDNA, ROCm, OpenCL, Verilog, FPGA, and supercomputing large-scale simulations.

We will move through arithmetics, then over numeric methods of mathematics, and running physical simulations in an attempt to learn how to predict and control the reality around us.

Math Symbol Reference

∀ ∂ ∃ ∅ ∇ ∈ ∉ ∋ ∏ ∑ ϶ ϵ ϱ ϰ ϝ Ϝ ϖ ϕ ϒ ϑ α β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ ς σ τ υ φ χ ψ ω ℝ Even more math HTML entities

Use This Sequence For

The useful thread is the climb from controlled switching to logic and addition. Read it as a substrate-first path into computation, not as a polished course outline.