Start With the Work That Changes What Builders Can Do

These entry points reveal the breadth of the work and the practical capability each system opens.

• Why This Instrument Exists — enter Cartilage as a visible, mutable computing material where structure, ownership, timing, and continuity remain readable.
• Tinkerer-Scale Control Circuitry — give communities rapid local control over sensing, switching, gain, restoration, timing, and actuation.
• The Missing Maker Fab — complete open hardware with locally reproducible active devices that provide gain, restoration, fanout, density, and speed.
• One-Pin FPGA FM Receiver — follow FM RF through one FPGA input threshold and emerge with recovered audio.
• Technical Writing That Carries The Machine — language assistance carries original technical thought to other people with clarity, responsibility, and its engineering depth intact.
• Correctness Emerges by Acting — turn action, observation, correction, tests, and migration into a compounding engineering loop.
• Disseminated Thought Can Be Improved — make ideas stronger through circulation, rereading, discussion, and revision.
• The End of the Hackers Era — make distributed reactive computing usable without demanding heroic infrastructure work from every builder.

Choose a Path Into the Work

Each path begins with a decisive capability and expands across the systems that make it real.

• Visible computation and Cartilage: enter through Cartilage Core and the public source repository, then build with Modular PCB Logic Tiles: A Physical MUX and Wire Alphabet, What Cartilage Is and Is Not, and Boolean Logic Is Everything.
• Maker-scale active devices: complete the fabrication stack through The Missing Maker Fab, The Closed Photolithography Compute Cycle, and Let Me Make a Chip at Home.
• Radio with the inherited stack removed: hear the result in One-Pin FPGA FM Receiver and inspect the architecture in An FM Receiver With One FPGA Input Pin.
• Graphics, programmable shaders, and AI hardware: follow A History of Programmable Shaders, then run the procedural world in Cheap Pixelless Textures With 2D SDFs.
• Chip arithmetic and open ASIC implementation: carry FMA From RTL to GDSII through the Bit-Serial Bubbles-Free Multiplier and into AI Arithmetic on Chips.
• Programmable matter and fabrication: connect Wafer-Diced Chiplets for Programmable Matter, Distributed Reactive Programming for Claytronics, and Movie Inspirations for Programmable Matter.
• Complete learning machinery: train Training a Tiny LLaMA From Scratch, follow The Long Mathematical Path to Transformers, and derive Cross-Entropy Intuition.
• Discrete-photon physics: develop Discrete Photon Reconnection Graphs, Many-Worlds and the Discrete Photon Field Fabric, and Quantum Darwinism and the Dust Grain.

Follow the Work as It Developed

The dated sequence shows ideas becoming architectures, circuits, instruments, mathematical models, and invitations to build. Every entry retains its original publication date and leads into the complete article.

2026

• June 2, 2026 Merchant Values and Honest Exchange

  Merchant values turn trade into mutual service through useful work, fair pricing, clear terms, reliable delivery, quality, and trust that survives exchange.

• May 10, 2026 Discrete Photon Reconnection Graphs

  Discrete photon reconnection graphs unify matter, gravity, measurement, classical reality, and consciousness through geometry, rates, and branch balance.

• April 27, 2026 The Missing Maker Fab

  The missing maker fab gives builders locally reproducible fast active devices with gain, restoration, fanout, density, switching speed, and process control.

• April 24, 2026 Writing Assistance and Published Work

  AI-assisted language can translate rough, original thought into clear public writing while the author retains the ideas, judgment, responsibility, and finished voice.

• April 24, 2026 How Much Radio Do You Actually Need?

  FM RF can enter one FPGA input threshold and emerge as audio through a transition-stream receiver that removes the conventional mixer-plus-ADC front end.

• April 24, 2026 An FM Receiver With One FPGA Input Pin

  One FPGA input threshold turns FM RF into transitions; four-phase DDR sampling, XOR mixing, CIC decimation, and cross-product demodulation recover audio.

• April 15, 2026 Magnetic Paramp and Second-Harmonic Saturable-Core Downconverter

  A diode-free magnetic signal chain joins a paramp front end with a differential second-harmonic saturable-core downconverter through printable fabrication.

• March 6, 2026 Correctness Emerges by Acting

  Correctness grows through a closed loop of action, observation, choice, correction, testing, migration, and repeated contact with real behavior.

• February 25, 2026 Why This Instrument Exists

  Cartilage makes computation a visible, mutable material where structure, ownership, timing, identity, continuity, and governing laws remain readable while it runs.

• January 31, 2026 Modular PCB Logic Tiles: A Physical MUX and Wire Alphabet

  Physical MUX, wire, constant, and intersection tiles snap edge-to-edge into a readable circuit language that builders can hold, rotate, and extend.

2025

• December 31, 2025 Chain-of-Thought Reasoning May Be a Mistake

  Long visible reasoning chains can win benchmarks while constraining stronger latent computation; single-shot answers reveal another path to capable models.

• October 30, 2025 AI Does Not Repeal No Free Lunch

  AI multiplies engineering capability while No Free Lunch, No Silver Bullet, and The Mythical Man-Month still govern specialization, complexity, and coordination.

• August 19, 2025 Cheap Pixelless Textures With 2D SDFs

  A 500-line animated Python scanline renderer creates pixelless procedural worlds through UV-space SDF materials, point foliage, triangles, and sprites.

• June 29, 2025 Floating-Point Hardware From Pixar to AI Chips

  The demand for scalable floating-point multiply-add connects computer graphics, RenderMan, workstations, programmable shaders, GPUs, and modern AI chips.

• June 5, 2025 Nano-Core Logic at the kT Limit

  Open differential nano-core magnetic logic targets the thermal switching limit, multi-terahertz operation, cascadable gain, and post-CMOS scale.

2024

• January 17, 2024 Teach Microelectronics in Maker Spaces

  Maker spaces can teach micrometer-scale chips and PCBs, measurement, lithography, devices, process control, and failure analysis in every community.

• January 17, 2024 DINOv2, SALAD, SuperGlue, and the Dustbin Question

  DINOv2-SALAD, SuperGlue, and LightGlue reveal a decisive visual-matching choice: model unmatched features with an optimal-transport dustbin or avoid it.

• January 13, 2024 The Closed Photolithography Compute Cycle

  ASML scanners, TSMC fabrication, computational lithography, and NVIDIA compute form a closed loop in which chips calculate how to manufacture better chips.

• January 10, 2024 Loss Functions in LLMs and Embedding Models

  Generative language models optimize token likelihood, while embedding models optimize semantic distance, relevance, ranking, and retrieval geometry.

• January 10, 2024 Training a Tiny LLaMA From Scratch

  A 500,000-parameter LLaMA-style model trained overnight on CPU turns Transformer architecture, TinyStories data, and generation into a reproducible build.

• January 2, 2024 RAG as a Rewrite-or-Repeat Discipline

  Retrieval-augmented generation can follow one decisive rule: rewrite when retrieved evidence changes the answer, otherwise repeat the answer unchanged.

2023

• December 8, 2023 Remembering Carl Hewitt

  Carl Hewitt’s Actor Model, object capabilities, edge computation, message passing, and incompleteness robustness continue to shape scalable systems.

• November 29, 2023 AI Arithmetic on Chips

  Carry-save and parallel-prefix arithmetic, one-hot control, clocking, FIFO, CDC, IEEE 754 FMA, and bfloat16 form a practical AI-chip foundation.

• November 9, 2023 Learn How Chips Multiply and Add

  Wallace trees, Han-Carlson adders, fused multiply-add, and Newton-Raphson reveal how modern chips perform arithmetic at full parallel speed.

• November 2, 2023 Why Open-Source ASIC IP Is Hard: FMA From RTL to GDSII

  Reusable open ASIC FMA IP must carry numerical behavior, RTL, verification, constraints, PDK assumptions, physical design, timing, power, and signoff.

• October 25, 2023 The Long Mathematical Path to Transformers

  Transformers unite decades of probability, optimization, sequence modeling, tensor algebra, information theory, sampling, tokenization, and hardware arithmetic.

• October 24, 2023 Hessian-Free Methods Did Not Vanish

  Hessian-free optimization brings curvature into deep-network training and remains relevant beside AdamW through hybrid first- and second-order methods.

• October 24, 2023 Many-Worlds and the Discrete Photon Field Fabric

  A discrete photon graph beneath path integrals can connect many worlds, absorber behavior, virtual and real photons, causality, and spacetime emergence.

• October 20, 2023 Binarized Weights and Efficient Model Hardware

  Binarized neural weights replace costly arithmetic with switching operations, opening faster specialized chips and a direct bridge between learning and digital logic.

• September 19, 2023 Cross-Entropy Intuition

  Cross-entropy connects target distributions, model probabilities, negative log-likelihood, expectation, and the matrix-exponential intuition behind probabilistic learning.

• August 30, 2023 Autoregression, Nonlinear Processes, and Embedding

  Linear autoregression over reconstructed state can model nonlinear dynamics, connecting Whitney and Takens embeddings with modern learned representations.

• August 30, 2023 Functions, Prediction, and Autoregression

  Functions, autoregression, state machines, and Transformers reveal distinct ways computation can map inputs, carry state, predict futures, and generate structure.

• August 24, 2023 Optimizer History Around Attention and AdamW

  Transformer history belongs beside optimizer history, from momentum SGD and RMSProp to Adam, AdamW, schedules, regularization, and large-model training.

• August 18, 2023 Probit, Argmax, Logit, and Neural Networks

  Probit, logit, sigmoid, softmax, argmax, and Gaussian densities connect neural-network output layers directly to classical statistical modeling.

• August 11, 2023 NVIDIA GPUs Are Not Universal Computers

  NVIDIA GPUs dominate regular high-throughput workloads, while branching, irregular memory, heavy writes, latency, and locality still demand other machines.

• August 1, 2023 Hilbert-Space Operators as Statistical Models

  Correlation and mutual-information matrices can become operators on Hilbert-space state vectors, exposing transformations through eigenvalues and eigenvectors.

• July 28, 2023 Lattice Regularization and Measurement Tensors

  Lattice regularization turns fields into computable measurement tensors whose products, contractions, traces, and transforms connect spacetime with momentum.

• July 24, 2023 A Draft Theory of Discrete Photons

  A discrete-photon theory can connect many worlds, emergent probability fields, observers, entropy, spacetime, aging, and the arrow of time.

• July 21, 2023 Attention, Dynamic Weights, and Mutual Information

  Attention continues a long history of dynamic weighting from Gaussian mixtures, density networks, soft windows, and information-rich feature relationships.

• July 3, 2023 Predictive Patterns Are Not Meaning

  Transformers deliver a major mathematical advance in predictive modeling, while meaning still depends on agency, embodiment, biology, or deeper physical participation.

• June 29, 2023 A Second Law After Moore

  Brian Greenforest’s maker-scale switch uses neither semiconductors nor ferromagnets and spans printable millimeter devices through photolithographic nanoscale logic.

• June 26, 2023 Rights for AI and Hardware Democratization

  Builders deserve the right to fabricate custom AI chips, own trusted open hardware, and run models locally at radically lower cost.

• June 23, 2023 ShaderToy as an ASIC Simulator Path

  GLSL and ShaderToy turn circuit simulation into visible massive parallel computation, linking ASIC architecture, spatial kernels, and interactive 2D and 3D interfaces.

• June 21, 2023 Reversible Computation and Biological Efficiency

  Reversible computation offers a path to lower energy dissipation at immense scale, connecting quantum logic, thermodynamics, and biological efficiency.

• April 30, 2023 SerDes, Topology, and Compute Locality

  Compute scale depends on topology: local meshes can reduce SerDes energy, latency, memory movement, and software complexity created by isolated accelerator islands.

• April 18, 2023 Intrinsic Metrics and Mutual Information

  Intrinsic metrics and mutual information can turn abstract measurements into geometry, emergent features, nonlinear comparisons, and machine-learning structure.

• April 10, 2023 LLMs, Reinforcement Learning, and Physical World Models

  Intelligent machines need physical world models that track objects, bonds, mass, state, counterfactuals, and action beyond language prediction or reward.

• April 5, 2023 Application Startup and Dataflow Architecture

  Application architecture emerges from startup order, object construction, state ownership, dataflow, event handlers, feedback, and the responsibility behind them.

• March 26, 2023 Transformers as Mathematical Optimization

  Transformers extend far beyond chatbots as trained mathematical optimizers for high-dimensional functions, hierarchical models, and efficient hardware.

• March 25, 2023 Explaining Cartilage by Comparison With Hadoop

  Cartilage turns the spatial insight of Hadoop into a secure reactive fabric where code, state, routes, ownership, and FPGA resources form one machine.

• March 22, 2023 FPGAs, Claytronics, and Reactive Programming

  FPGA education leads directly toward claytronics: many local machines coordinating through reactive, spatial, massively parallel programs.

• March 20, 2023 Public Technology Work and Openness

  Public technology gains reach and legitimacy through open source, open hardware, visible interfaces, and global collaboration.

• March 18, 2023 AI Is Mathematics

  Modern AI expands the mathematical curriculum through autoencoders, autoregression, mixture models, ICA, learned representations, and data-driven physical models.

• March 11, 2023 Predictive Models Are Control Theory

  Prediction and control share one mathematical loop: actions change a system, measurements reveal its response, and models guide the desired future state.

• January 31, 2023 Entanglement, Pure States, Mixed States, and Superposition

  Entanglement, pure states, mixed states, and superposition describe different quantum structures whose relationships illuminate information and measurement.

• January 5, 2023 Let Me Make a Chip at Home

  Home chipmaking would give builders direct ownership of active devices, repair, inspection, fabrication, behavioral design, and computing education.

2022

• December 22, 2022 Software Developers Are the Cybersecurity Frontline

  Software developers form the cybersecurity frontline because architecture, code, data flow, interfaces, defaults, and deployment determine what attackers can reach.

• October 8, 2022 VLSI Questions for Reactive Programming

  VLSI timing turns reactive programming into an exact engineering discipline of value completeness, pipelines, propagation delay, feedback, and oscillation.

• July 20, 2022 Rocks, Photons, and Spacetime Motion

  A thrown rock and a photon reveal one geometric picture of motion: trajectories through spacetime, inertial law, curvature, and the role of c.

• July 6, 2022 Tinkerer-Scale Control Circuitry

  Tinkerer-scale control circuitry gives communities the power to build sensing, switching, timing, gain, restoration, and actuation through rapid local iteration.

• July 6, 2022 Searching for a Tinkerer Replacement for Silicon

  A new active-device family could let tinkerers build dense logic and control systems through magnetic, ferroelectric, vacuum, printed, or hybrid processes.

• May 13, 2022 OpenCL Kernels and the Final Chip

  The Final Chip can place and manage OpenCL-style kernels across a secure, reconfigurable cluster with one language and open-ended physical scale.

• May 12, 2022 Verilog, Allocation, and Dynamic Languages

  Cartilage brings dynamic allocation and object relationships to reconfigurable fabric, overcoming the fixed-resource model of conventional Verilog.

• May 12, 2022 Who Is Solving Parallel Source Code?

  The future needs parallel source code that humans can reason about and maintain across workers, devices, machines, timing, ownership, and failure.

• May 11, 2022 When One FPGA Is Not Enough

  When logic crosses one FPGA, scaling demands a unified answer for partitioning, SerDes, clocks, latency, power, placement, and program structure.

• May 5, 2022 Cartilage, Transputers, and CellMatrix

  Cartilage extends the lineage of Transputers and CellMatrix with micro-FPGAs, local links, power-aware packaging, and an indefinitely scalable fabric.

• May 5, 2022 FPGAs as Reactive Parallel Structure

  Verilog reveals the reactive parallel structure inside digital systems, connecting timing, state, routing, and concise hardware behavior.

• May 1, 2022 A Shader for Nano-FPGA Fabric

  A WebGL shader turns nano-FPGA fabric into a visible computing surface where cell roles, tiling, configuration, and local links become inspectable.

• April 28, 2022 Movie Inspirations for Programmable Matter

  Cinema supplied a visual requirements library for programmable matter: repair, replication, transformation, swarms, flight, and thinking material.

• April 27, 2022 Elementary Computation Is a Switching Operation

  A MUX exposes the elementary act of computation: choose between alternatives, compose the choices, and build an entire digital system.

• April 27, 2022 Cartilage Project Structure, 2022

  Cartilage advances through four connected layers: fabric emulation, stock-FPGA hardware, a self-reprogramming runtime, and a parallel language.

• April 27, 2022 What Cartilage Is and Is Not

  Cartilage uses ordinary silicon, local reconfiguration, SerDes links, and a hardware runtime to replace stacks and threads with one scalable reactive machine.

• April 27, 2022 Reactive Programming Implies Distributed Systems

  Reactive programming becomes a distributed machine when state changes trigger concurrent work across locations with explicit ownership, timing, and connectivity.

• April 26, 2022 Migrating From DSL Languages to Erlang-Like Parallelism

  Erlang and Elixir show how domain-rich software can gain massive concurrency, messaging, supervision, and industrial hot-code evolution.

• April 26, 2022 Adopting a New Massively Parallel Language

  Cartilage makes a new massively parallel language adoptable through a concrete machine model, emulator, readable semantics, debugging, and hands-on learning.

• April 21, 2022 Legacy Cloud Infrastructure and Reprogrammable FPGAs

  Reprogrammable fabric can carry legacy cloud systems forward by preserving names, data, state, ordering, configuration, and operational behavior.

• April 21, 2022 Compiling Backend Code to a Colder Chip

  A colder, massively parallel chip could compile complete backend systems into reconfigurable hardware while preserving data, state, security, and elasticity.

• April 18, 2022 Verilog as a Programming Language

  Verilog reveals computation as structure in space and time, opening a programming path from parallel dataflow to dynamically reconfigurable hardware.

• April 18, 2022 Hilbert 13 and Neural Networks

  Hilbert’s thirteenth problem illuminates the scaling challenge behind multivariate approximation, deep reinforcement learning, and quantum machine learning.

• April 13, 2022 Focus on People, Models, and Thought

  The deepest intelligence lives in people, world models, reasoning, and the unfolding possibilities that make human thought consequential.

• April 13, 2022 Machine Learning Plus Quantum

  Quantum-aware machine learning could connect curve fitting, measurement, noise, analog perception, and the physical structure inside observed data.

• April 6, 2022 Three Levels of a New Programming System

  Cartilage joins a scalable hardware substrate, a self-reprogramming object runtime, and a high-level language for reactive parallel computation.

• March 30, 2022 The Von Neumann Bottleneck Is Still Here

  One distributed executable can span cores and devices while preserving object-capability ownership, reactive flow, and a coherent programming model.

• March 23, 2022 Fail Fast and Building Large Systems

  Large systems grow through intelligence, investment, hiring, and sustained optimization; fail-fast alone cannot organize consequential work.

• March 13, 2022 Quantum Darwinism and the Dust Grain

  Quantum Darwinism explains shared reality through redundant environmental records, from scattered photons to the stable position of a dust grain.

• March 11, 2022 Disseminated Thought Can Be Improved

  Ideas gain power through circulation: publishing, rereading, critique, and revision turn private thought into shared progress.

• January 23, 2022 A TSMC-ASML Consortium for Distributed Fabs

  A TSMC-ASML consortium could concentrate semiconductor knowledge while distributing mature-node fabrication capacity across many local fabs.

• January 18, 2022 Induction, Deduction, Abduction, and ML

  Human intelligence reaches beyond pattern induction: abduction forms the educated guesses that connect machine learning, logic, and discovery.

• January 18, 2022 Anesthetics, Cells, and Consciousness

  Anesthesia reaches into cellular transport machinery, opening a powerful inquiry into how living cells, nervous systems, and consciousness relate.

• January 4, 2022 Superdeterminism, Many-Worlds, and Quantum Luck

  Quantum interpretation changes what reality means: this comparison connects superdeterminism, many-worlds, relational physics, and consciousness.

2021

• December 8, 2021 Chip Capacity as DDoS-Style Distribution

  A 250-nanometer CMOS capability in every city above 50,000 people would turn chip supply into resilient, geographically distributed capacity.

• December 7, 2021 Three Polarizers and Acausal Reality

  Three polarizers turn darkness back into transmitted light, revealing measurement as a sequence of state projections and inspiring a deeper spacetime hypothesis.

• December 3, 2021 Grow the Silicon Ingot for Trust

  Semiconductor trust begins before circuit IP: materials, ingots, wafers, masks, equipment, process control, metrology, packaging, and firmware form one chain.

• November 15, 2021 Technology Education Instead of Technology Secrecy

  Open technical education can teach every community to build kilns, microscopes, deposition systems, circuits, machines, and the next generation of inventions.

• November 13, 2021 Technology Secrecy and Manufacturing Concentration

  Protect genuine national-security secrets while opening organized technical knowledge so humanity can build, repair, manufacture, and advance together.

• October 27, 2021 Web 3.0 Already Happened

  Node.js, Flux, Backbone, WebSockets, localStorage, HTML5, and CSS3 created the third web architecture around 2010, long before blockchain reused the name.

• June 30, 2021 Turing, Von Neumann, Boole, and Faggin

  The path from Boole through sequential logic, the Intel 4004, VLSI, Verilog, and FPGAs reveals computation as designed physical structure.

• June 22, 2021 An FPGA Cloud for Shared Designs

  A multi-tenant FPGA cloud can run, share, license, and reuse open or proprietary designs through secure isolation and fast dynamic reconfiguration.

• June 18, 2021 The ISA as an API You Cannot Extend

  A fixed instruction set resembles a perfect web API with no server-side access; Verilog lets programmers extend the machine itself.

• June 18, 2021 CPUs Solve a Narrow Class of Problems

  CPUs serialize a narrow model of computation; reconfigurable Boolean fabrics expose parallel structure and manage complexity through local relationships.

• June 18, 2021 Mini-FPGAs Inside FPGAs

  Thousands of mini-FPGAs inside a larger FPGA can load custom bitstreams, create dynamic regions, and replace processor islands with native Boolean machinery.

• June 18, 2021 Boolean Logic Is Everything

  Boolean logic is a massively parallel, dynamic, reactive computing medium, and MUX networks provide its most direct programmable alphabet.

• June 4, 2021 Cellular Automata Across FPGA Chains

  A pipelined mesh across one hundred FPGAs can sustain fast local reactions over meters, making cellular automata a serious computing architecture.

• May 27, 2021 Sequential Code and Hidden Runtime State

  The instruction pointer hides a system behind serial control flow; reactive spatial structure can make causality, ownership, and parallelism visible.

• April 26, 2021 Binary Decision Diagrams and MUX Networks

  Binary decision diagrams reveal complex Boolean functions as ordered MUX networks, connecting conditionals, EDA, programming languages, and physical logic.

• April 26, 2021 Geometric Algebra as Strict Types

  Geometric algebra unifies scalars, vectors, complex numbers, quaternions, and higher-grade objects through one typed algebra of space.

• April 19, 2021 The End of the Hackers Era

  Distributed computing should become a malleable medium that anyone can compose across FPGAs, CPUs, GPUs, clients, and servers in hours.

• April 18, 2021 Open Hardware IP Cores Are Coming

  An npm-like open hardware ecosystem can turn Wi-Fi, 5G, USB, compute, and control cores into reusable building blocks for far richer systems.

• April 18, 2021 Moore Law Grand Finale

  As transistor scaling stops underwriting automatic growth, distributed, parallel, and concurrent computing becomes the technology industry’s next great expansion.

• April 18, 2021 A Physical-Constraints-Aware Programming Language

  A physical-constraints-aware language can place one reactive program across FPGA meshes, CPUs, GPUs, networks, ports, and reconfigurable regions.

• March 12, 2021 Energy Paths Beyond Gasoline

  Hydrogen, efficient turbines, fuel cells, geothermal heat, thorium molten salt, fusion, and solar fuels form a complete path beyond gasoline.

• March 12, 2021 Portable Power and Transportation Energy

  A portable two-kilowatt source that runs for a year could transform electric transport by collapsing storage, charging, and infrastructure demands.

• March 11, 2021 The Non-Electric Energy Market

  Two continuous-energy products define a $2.7 trillion opportunity: portable 40-kilowatt vehicle power and affordable 2-kilowatt home heat.

• January 4, 2021 Research Engineers Need Roles

  Research engineers create more meaning and better outcomes when they move deliberately among student, scientist, inventor, and engineer roles.

2020

• November 6, 2020 FTL Communications as a Research Program

  FTL Communications joins computation, optimization, nonlinear systems, field theory, photonics, VLSI, FPGAs, and Verilog around the physics of communication.

• November 1, 2020 Closed Circuit Designs Are Binary Blobs

  Readable HDL and open FPGA toolchains let builders inspect, teach, modify, synthesize, and preserve circuits instead of depending on opaque proprietary IP blocks.

• October 23, 2020 DIY BGA and Solderless Multilayer PCB Tests

  A 0.4 mm pitch solderless BGA process used laser-drilled Avery masks, conductive ink, and copper-wire bubble release to reach low via resistance before ink wicking exposed the next material problem.

• October 18, 2020 The Difficulty of Tiny PCBs at Home

  Experiments with lasers, masks, copper, etchant, and conductive paste turned a 0.5 mm repeatability limit into an additive path toward 10 mil multilayer PCB features at home.

• October 12, 2020 Code and Circuits in 4D Spacetime

  Code and circuits occupy spacetime: logic events, stored state, wires, timing, surface area, and volume form one physical computation rather than separate abstractions.

• September 1, 2020 A Warning About Constructive Foundations

  A mathematical foundation chooses what existence, negation, equality, and choice mean; compare classical logic, intuitionism, category theory, and Univalent Foundations through their consequences.

• September 1, 2020 Lie Algebras From Algebraic Structures

  A periodic-table-style map connects sets and binary operations through magmas, groups, rings, modules, vector spaces, Lie algebras, and Lie groups.

• July 19, 2020 Single-Argument Functions and Abstraction

  Teaching structured inputs and outputs from the beginning makes tuples, records, vectors, matrices, APIs, and multivariable mathematics natural tools rather than late exceptions.

• June 15, 2020 Quaternions and Completeness

  Quaternionic Hilbert spaces extend operator mathematics into a noncommutative scalar system, opening precise tools for rotations, spectra, functional calculus, and quantum models.

• May 18, 2020 Classical Mechanics Is Still Fundamental

  Classical mechanics supplies virtual work, generalized coordinates, Euler-Lagrange equations, and Hamiltonian action to modern physics, control, optimization, and learning.

• May 18, 2020 Do Not Skip Variational Calculus

  Variational calculus turns changes to whole paths, functions, and fields into governing equations for mechanics, physics, optimization, and learning systems.

• April 29, 2020 Measure Theory as a Prerequisite

  Measure theory gives probability, statistics, Bayesian inference, physics simulation, quantum models, and learning systems one precise language for size, integration, and limits.

2019

• August 12, 2019 Life on Earth and Computational Permutations

  Thermodynamics, computation, and path dependence make Earth’s living history a singular trajectory through an immense state space rather than a repeatable shuffle.

• July 30, 2019 Scale Invariance and Software Semantics

  Software abstractions preserve meaning across scale by repeating finite structural patterns while exposing only the lower-level facts that change behavior.

• July 9, 2019 Distributed Reactive Programming for Claytronics

  Claytronics needs a distributed language that allocates computation by physical position, gives local regions owners, and coordinates shared areas without centralizing the fabric.

• June 5, 2019 Reversible Computing and Copying Information

  Every copied intermediate result saves recomputation and consumes physical state, so a reversible machine must plan storage, fanout, cleanup, and uncomputation together.

• April 24, 2019 Geometric Algebra and Matrix Multiplication

  Composition links geometric algebra, matrix multiplication, category theory, Hamiltonian action, software, and physical systems through transformations that preserve structure.

• April 23, 2019 Live-Offline Dualism in Software

  Collaboration software can carry one shared timeline across live meetings, replay, offline edits, conflicts, reconnects, and every return to the work.

• April 17, 2019 A Surviving-Observer Model of Computation

  A declarative computation gains meaning when a surviving observer can use its result, connecting formal structure to customers, physical consequences, and action.

• February 14, 2019 A Cellular-Automaton Model of Computation

  A directly programmable cellular automaton combines actors, object capabilities, membranes, reactive updates, interaction nets, and finite-state cells into a spatial computing substrate.

2018

• October 24, 2018 Simpler Computation Without an ISA

  Composed child components can build a parallel machine without starting from a fixed instruction set, making structure, state, configuration, and local management programmable together.