https://benebsworth.com Software, platform & hardware engineer · Writing on Kubernetes, distributed systems, electrical engineering, and AI · Melbourne, Australia en-AU © 2026 Ben Ebsworth Tue, 23 Jun 2026 06:01:08 GMT https://benebsworth.com/icon.svg https://benebsworth.com https://benebsworth.com/blog/backprop-is-just-the-chain-rule/ https://benebsworth.com/blog/backprop-is-just-the-chain-rule/ Tue, 23 Jun 2026 00:00:00 GMT ben.ebsworth@gmail.com (Ben Ebsworth) Training a neural network sounds mystical, but the engine underneath is one idea from first-year calculus: the chain rule, applied backwards through a computation graph and reusing its work. We trace a forward and backward pass through a tiny graph, see why we run it in reverse, and connect it to the downhill step that actually does the learning. Software software machine-learning calculus https://benebsworth.com/blog/how-to-paint-with-noise/ https://benebsworth.com/blog/how-to-paint-with-noise/ Tue, 23 Jun 2026 00:00:00 GMT ben.ebsworth@gmail.com (Ben Ebsworth) Image generators start from pure TV static and end with a photo. The trick that makes it possible is wonderfully sneaky: don't learn to paint, learn to remove a little noise, then run that backwards from static. We build the forward noising process step by step, see the signal-versus-noise schedule, and work out why predicting noise is such a clever thing to train. Software software machine-learning diffusion generative-ai https://benebsworth.com/blog/three-rules-build-a-computer/ https://benebsworth.com/blog/three-rules-build-a-computer/ Tue, 23 Jun 2026 00:00:00 GMT ben.ebsworth@gmail.com (Ben Ebsworth) Conway's Game of Life has three rules and a grid of on-or-off cells, and nothing else. From that, gliders crawl, guns fire, and — astonishingly — you can build a working computer. We play with the rules, watch structure emerge that nobody designed, and follow the thread to its unsettling end: a system this simple can be impossible to predict. Software software emergence cellular-automata https://benebsworth.com/blog/what-jpeg-throws-away/ https://benebsworth.com/blog/what-jpeg-throws-away/ Tue, 23 Jun 2026 00:00:00 GMT ben.ebsworth@gmail.com (Ben Ebsworth) A JPEG is often a tenth the size of the raw image and you can't see the difference. Where did ninety percent of the data go? We follow an 8×8 block through the discrete cosine transform and quantisation to find out: JPEG sorts a picture by spatial frequency, then quietly bins the fine detail your eyes barely register. Electrical Eng electrical-engineering signals compression https://benebsworth.com/blog/why-everything-becomes-a-bell-curve/ https://benebsworth.com/blog/why-everything-becomes-a-bell-curve/ Tue, 23 Jun 2026 00:00:00 GMT ben.ebsworth@gmail.com (Ben Ebsworth) The bell curve turns up in heights, measurement errors, exam marks and sensor noise, and that is not a coincidence — it is a theorem. We work through the central limit theorem with a Galton board and a random walk: why adding up enough independent things, almost whatever they are, always lands on the same curve, and when it doesn't. Mathematics mathematics statistics probability https://benebsworth.com/blog/why-time-only-runs-forwards/ https://benebsworth.com/blog/why-time-only-runs-forwards/ Tue, 23 Jun 2026 00:00:00 GMT ben.ebsworth@gmail.com (Ben Ebsworth) The microscopic laws of physics run the same forwards and backwards, yet eggs never unscramble and gases never un-mix. We resolve the paradox with a box of mixing particles: the arrow of time isn't a force, it's a counting argument — there are overwhelmingly more messy arrangements than tidy ones, so disorder wins by sheer weight of numbers. Physics physics thermodynamics entropy https://benebsworth.com/blog/why-your-shower-temperature-oscillates/ https://benebsworth.com/blog/why-your-shower-temperature-oscillates/ Tue, 23 Jun 2026 00:00:00 GMT ben.ebsworth@gmail.com (Ben Ebsworth) The scalding-then-freezing shower dance isn't you being bad at taps — it's a feedback loop fighting a time delay, and it has a name. We meet the PID controller behind thermostats, cruise control and showers, tune one live, and find out why a little lag turns sensible corrections into oscillation. Electrical Eng electrical-engineering control feedback https://benebsworth.com/blog/a-transformer-reads-everything-at-once/ https://benebsworth.com/blog/a-transformer-reads-everything-at-once/ Mon, 22 Jun 2026 00:00:00 GMT ben.ebsworth@gmail.com (Ben Ebsworth) The transformer's one real trick is reading every token at once and letting each decide what matters. We put the whole machine on the bench — embeddings, positions, the residual stream, the feed-forward step — and work out why reading everything at once was such a departure, and why something so architecturally dull keeps getting smarter the more we feed it. With an interactive animation for every piece. Software software machine-learning deep-learning transformers https://benebsworth.com/blog/repair-is-just-solving/ https://benebsworth.com/blog/repair-is-just-solving/ Sun, 21 Jun 2026 00:00:00 GMT ben.ebsworth@gmail.com (Ben Ebsworth) I gave a 160M-parameter Go model a reflect-and-fix loop so it could bootstrap past its own ceiling. It fixed zero bugs. The reason runs deeper than the code — and it taught me my model had been memorising all along. Software machine-learning llm https://benebsworth.com/blog/filters-from-poles-and-zeros/ https://benebsworth.com/blog/filters-from-poles-and-zeros/ Fri, 19 Jun 2026 12:00:00 GMT ben.ebsworth@gmail.com (Ben Ebsworth) A filter is two polynomials, and the roots of those polynomials are the whole story. Place a few points in the complex plane and you can read the entire frequency response straight off the geometry — no calculus required at the point of use. Electrical Eng ee signals filters https://benebsworth.com/blog/learning-by-rolling-downhill/ https://benebsworth.com/blog/learning-by-rolling-downhill/ Fri, 19 Jun 2026 00:00:00 GMT ben.ebsworth@gmail.com (Ben Ebsworth) Every neural network you've ever used was trained by the oldest trick in calculus: to minimise a function, walk downhill. The whole story of modern optimisers is a list of the specific ways plain downhill walking fails, and the patch for each. Software software machine learning optimization https://benebsworth.com/blog/quantum-tunnelling-you-can-see/ https://benebsworth.com/blog/quantum-tunnelling-you-can-see/ Thu, 18 Jun 2026 12:00:00 GMT ben.ebsworth@gmail.com (Ben Ebsworth) Quantum tunnelling isn't an energy loophole: a wave decays through a wall instead of stopping. Watch a packet split, and see the exponential that keeps the Sun lit. Physics physics quantum quantum mechanics https://benebsworth.com/blog/how-the-leopard-got-its-spots/ https://benebsworth.com/blog/how-the-leopard-got-its-spots/ Thu, 18 Jun 2026 00:00:00 GMT ben.ebsworth@gmail.com (Ben Ebsworth) Two chemicals that do nothing but react and spread can break a blank sheet into spots, stripes, and mazes. Turing's last great idea was that diffusion, the great smoother, is also where pattern comes from. Mathematics maths nonlinear dynamics pattern formation https://benebsworth.com/blog/shrinking-the-kv-cache/ https://benebsworth.com/blog/shrinking-the-kv-cache/ Thu, 18 Jun 2026 00:00:00 GMT ben.ebsworth@gmail.com (Ben Ebsworth) A transformer's KV cache is a four-dimensional tensor, and every compression trick — quantisation, eviction, cross-layer sharing, linear attention — attacks one of its axes. Here is the tour, and the cautionary tale of a tiny code model whose accuracy fell 20 points because a smoke test never exercised the one axis that bites. Software software machine-learning llm transformers https://benebsworth.com/blog/a-star-search-visually/ https://benebsworth.com/blog/a-star-search-visually/ Wed, 17 Jun 2026 00:00:00 GMT ben.ebsworth@gmail.com (Ben Ebsworth) A* is not a clever algorithm so much as Dijkstra plus a bet about the future. The same code becomes Dijkstra, greedy best-first, or A* depending on one term in the priority key — and admissibility is the single property that buys optimality. Software software algorithms computer science ai https://benebsworth.com/blog/am-fm-qam-the-modulation-zoo/ https://benebsworth.com/blog/am-fm-qam-the-modulation-zoo/ Wed, 17 Jun 2026 00:00:00 GMT ben.ebsworth@gmail.com (Ben Ebsworth) Every modulation scheme is the same act — painting information onto a carrier — and they differ only in which property of the carrier you paint on. Plotted as a constellation, AM is a line, FM is a circle, and QAM is a grid. Electrical Eng electrical engineering communications modulation dsp https://benebsworth.com/blog/b-trees-vs-lsm-trees/ https://benebsworth.com/blog/b-trees-vs-lsm-trees/ Wed, 17 Jun 2026 00:00:00 GMT ben.ebsworth@gmail.com (Ben Ebsworth) Every database you use bets on one of two storage engines: B-trees (read-optimised, update-in-place) or LSM-trees (write-optimised, append-and-compact). The choice isn't about speed but about which kind of amplification you're willing to pay. Software software databases data structures systems https://benebsworth.com/blog/band-gaps-are-bragg-reflection/ https://benebsworth.com/blog/band-gaps-are-bragg-reflection/ Wed, 17 Jun 2026 00:00:00 GMT ben.ebsworth@gmail.com (Ben Ebsworth) The forbidden energy gap that makes a semiconductor a semiconductor is not a quantum mystery. It is the exact same wave interference that makes an X-ray diffract off a crystal or a soap film show colour. Physics physics condensed matter solid state quantum https://benebsworth.com/blog/every-qubit-gate-is-a-rotation/ https://benebsworth.com/blog/every-qubit-gate-is-a-rotation/ Wed, 17 Jun 2026 00:00:00 GMT ben.ebsworth@gmail.com (Ben Ebsworth) Quantum computing is taught as alien linear algebra. On the Bloch sphere it collapses to one homely fact: a qubit is an arrow on a ball, and every operation you can do to it is a rotation of that arrow. Physics physics quantum quantum computing https://benebsworth.com/blog/every-wave-is-a-circle/ https://benebsworth.com/blog/every-wave-is-a-circle/ Wed, 17 Jun 2026 00:00:00 GMT ben.ebsworth@gmail.com (Ben Ebsworth) We are taught Fourier as an integral to memorise. The geometric truth is older and stranger: any periodic signal, however square or spiky, is drawn by a stack of spinning circles — the same epicycles Ptolemy used for the planets. Mathematics mathematics fourier analysis signal processing https://benebsworth.com/blog/every-wire-is-an-rlc-circuit/ https://benebsworth.com/blog/every-wire-is-an-rlc-circuit/ Wed, 17 Jun 2026 00:00:00 GMT ben.ebsworth@gmail.com (Ben Ebsworth) There is no such thing as a digital signal at the physical layer. The clean trapezoid you draw is a fiction; every trace is a distributed RLC network, and the ringing and reflections are the lumped RLC step response playing out at picosecond timescales. Electrical Eng electrical engineering signal integrity circuits rf https://benebsworth.com/blog/how-python-dicts-really-work/ https://benebsworth.com/blog/how-python-dicts-really-work/ Wed, 17 Jun 2026 00:00:00 GMT ben.ebsworth@gmail.com (Ben Ebsworth) The dict is the most-used data structure in Python and almost nobody knows it uses open addressing, not chaining — so a single deletion leaves a tombstone, and a simple hash table is really a careful dance between load factor, probe sequences, and cache lines. Software software data structures python computer science https://benebsworth.com/blog/lorenz-and-the-limits-of-prediction/ https://benebsworth.com/blog/lorenz-and-the-limits-of-prediction/ Wed, 17 Jun 2026 00:00:00 GMT ben.ebsworth@gmail.com (Ben Ebsworth) Determinism does not imply predictability. Lorenz's three-equation toy weather model is fully deterministic yet unknowable past a horizon you can compute — a geometric fact, not an engineering failure. Mathematics mathematics chaos dynamical systems physics https://benebsworth.com/blog/normal-modes-to-chaos/ https://benebsworth.com/blog/normal-modes-to-chaos/ Wed, 17 Jun 2026 00:00:00 GMT ben.ebsworth@gmail.com (Ben Ebsworth) Two pendulums linked by a spring look hopelessly complicated. But there is a change of coordinates in which the same system is just two independent pendulums that never talk to each other. The mess is an illusion of the basis you chose. Physics physics mechanics normal modes chaos https://benebsworth.com/blog/phase-portraits-of-differential-equations/ https://benebsworth.com/blog/phase-portraits-of-differential-equations/ Wed, 17 Jun 2026 00:00:00 GMT ben.ebsworth@gmail.com (Ben Ebsworth) Most nonlinear ODEs have no formula, yet their fate is readable from the vector field. Poincare's trick: classify fixed points, limit cycles, and chaos by geometry. Mathematics mathematics dynamical systems differential equations https://benebsworth.com/blog/software-defined-radio-in-100-lines/ https://benebsworth.com/blog/software-defined-radio-in-100-lines/ Wed, 17 Jun 2026 00:00:00 GMT ben.ebsworth@gmail.com (Ben Ebsworth) A radio is no longer hardware. Once you sample the antenna fast enough, every classic RF block — mixer, filter, demodulator — becomes a few lines of arithmetic on a stream of complex numbers. The antenna is the last analog component. Electrical Eng electrical engineering sdr dsp radio https://benebsworth.com/blog/attention-from-the-inside-out/ https://benebsworth.com/blog/attention-from-the-inside-out/ Sun, 14 Jun 2026 00:00:00 GMT ben.ebsworth@gmail.com (Ben Ebsworth) Attention is just a weighted average whose weights the data computes by asking itself questions. A worked tour through scaled dot-product attention, temperature and sampling, and what a representative 46B-active / 1T-total Mixture-of-Experts spec actually means — with live matrices you can poke. Algorithms technology algorithms machine-learning deep-learning https://benebsworth.com/blog/pll-from-first-principles/ https://benebsworth.com/blog/pll-from-first-principles/ Wed, 10 Jun 2026 00:00:00 GMT ben.ebsworth@gmail.com (Ben Ebsworth) A phase-locked loop is a control system with a phase detector instead of a summing junction. The intuition you can build with the lab above is more durable than the textbook derivations. Electrical Eng technology algorithms physics electrical engineering signal processing https://benebsworth.com/blog/smith-chart-is-geometry/ https://benebsworth.com/blog/smith-chart-is-geometry/ Wed, 10 Jun 2026 00:00:00 GMT ben.ebsworth@gmail.com (Ben Ebsworth) What looks like a chart for radio engineers is really a Möbius transform drawn on the complex plane. A visual essay on why impedance matching is a question of circles, lines, and rotations. Electrical Eng technology algorithms physics electrical engineering https://benebsworth.com/blog/neural-network-zoo-explained/ https://benebsworth.com/blog/neural-network-zoo-explained/ Mon, 08 Jun 2026 00:00:00 GMT ben.ebsworth@gmail.com (Ben Ebsworth) A guided tour through the Asimov Institute's Neural Network Zoo — every architecture from the poster, with intuition for what each one is actually for and an interactive SVG diagram for the major families. Algorithms algorithms machine-learning deep-learning https://benebsworth.com/blog/istio-patterns/ https://benebsworth.com/blog/istio-patterns/ Fri, 03 Jul 2020 22:12:03 GMT ben.ebsworth@gmail.com (Ben Ebsworth) Overview of some common Istio Service Mesh topologies and configuration examples and diagrams Service Mesh technology kubernetes service mesh istio https://benebsworth.com/blog/gke-development-auto-scale-down/ https://benebsworth.com/blog/gke-development-auto-scale-down/ Mon, 23 Sep 2019 22:12:03 GMT ben.ebsworth@gmail.com (Ben Ebsworth) How to sleep at night when actively developing on Google Kubernetes Engine (GKE) using Google Cloud Scheduler Google Cloud technology GCP kubernetes https://benebsworth.com/blog/kubernetes-cicd-part-2/ https://benebsworth.com/blog/kubernetes-cicd-part-2/ Sat, 21 Sep 2019 22:12:03 GMT ben.ebsworth@gmail.com (Ben Ebsworth) An overview of the current kubernetes-native ci/cd ecosystem, With a demonstration of an end-to-end Tekton based workflow for build, test and deployment of a fullstack application Kubernetes technology CI/CD GCP kubernetes kaniko developer experience istio knative tekton skaffold https://benebsworth.com/blog/kubernetes-cicd-part-1/ https://benebsworth.com/blog/kubernetes-cicd-part-1/ Thu, 22 Aug 2019 22:12:03 GMT ben.ebsworth@gmail.com (Ben Ebsworth) How we can get closer to unifying the local developer experience with production-grade kubernetes run-time environments Kubernetes technology GCP kubernetes containers developer experience knative skaffold kustomize https://benebsworth.com/blog/two-number-sum/ https://benebsworth.com/blog/two-number-sum/ Mon, 27 May 2019 22:12:03 GMT ben.ebsworth@gmail.com (Ben Ebsworth) Three solutions to Two Number Sum, from O(n^2) brute force to an O(n) hash set to an O(1)-space two-pointer scan — and the memory-vs-compute trade-off behind each. Algorithms algorithms personal go python https://benebsworth.com/blog/getting-started-with-tekton/ https://benebsworth.com/blog/getting-started-with-tekton/ Sun, 12 May 2019 22:12:03 GMT ben.ebsworth@gmail.com (Ben Ebsworth) Developing basic CI and CD pipelines in Tekton and deploying this both to local and cloud based environments CI/CD · Tekton technology CI/CD GCP kubernetes containers kaniko developer experience https://benebsworth.com/blog/install-minikube/ https://benebsworth.com/blog/install-minikube/ Sun, 05 May 2019 22:12:03 GMT ben.ebsworth@gmail.com (Ben Ebsworth) Instructions for the installation, upgrade and other customization of a Minikube install on MacOS. As well as a basic example of deploying a service and exposing it for local access Local Dev technology kubernetes developer experience https://benebsworth.com/blog/using-helm/ https://benebsworth.com/blog/using-helm/ Mon, 29 Apr 2019 22:12:03 GMT ben.ebsworth@gmail.com (Ben Ebsworth) A practical look at Helm, the Kubernetes package manager — what a chart is, how Go templating and Sprig drive value substitution, how releases and revisions work, and when to reach for Helm over Kustomize Kubernetes technology kubernetes developer experience https://benebsworth.com/blog/using-kapitan/ https://benebsworth.com/blog/using-kapitan/ Mon, 29 Apr 2019 22:12:03 GMT ben.ebsworth@gmail.com (Ben Ebsworth) Exploring Kapitan as a generic configuration management tool: its reclass-style inventory, multiple input types, and the single-source-of-truth model that compiles one set of parameters into many outputs Kubernetes technology kubernetes developer experience https://benebsworth.com/blog/common-hooks/ https://benebsworth.com/blog/common-hooks/ Sat, 20 Apr 2019 22:12:03 GMT ben.ebsworth@gmail.com (Ben Ebsworth) Working React Hooks examples — a stale-closure-proof counter and a custom useResizeObserver — plus when useReducer replaces Redux and why ResizeObserver beats IntersectionObserver. React technology react https://benebsworth.com/blog/hello-world/ https://benebsworth.com/blog/hello-world/ Tue, 16 Apr 2019 22:12:03 GMT ben.ebsworth@gmail.com (Ben Ebsworth) The first post on Ben Ebsworth's blog: a living, personal-wiki space for exploring technologies, capturing learnings, and refining ideas over time. Field Notes general personal