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ISEGORIABenjamin Haire
日本語

About me

Hi, I’m Benjamin Haire.

This site is a collection of esoterica I find interesting, and an account of how I go about it.

What holds my attention: cellular automata, algebraic varieties, differential geometry. On the engineering side, game engine technology, particularly AI integration in modern engines, and real-time simulation of fluids and constrained bodies: XPBD and the wider family of position-based and implicit solvers, particle-grid hybrids, and what has to be given up to hit a frame budget.

More about me

My route here has been a slightly winding one. I did a BSc with first class honours in pure mathematics at the University of Melbourne, then an SM in pure mathematics at the Massachusetts Institute of Technology, and somewhere along the way picked up a Diploma of Languages in Japanese and the JLPT N3. After that I spent a stretch as a project manager at a medical laboratory in Melbourne developing cancer immunotherapies, before going back to medical school, which is where I am now.

In my spare time I enjoy playing video games (particularly survival horror), and being a very enthusiastic, yet very mediocre, violinist. I have perhaps an unhealthy attachment to my Steam Deck. I currently hold memberships in Mensa and the Prometheus Society (perhaps obnoxious self-aggrandisement, but what else is this page for?)

Benjamin Michael Haire
Australia

Latest work

Updated 13 October 2026

What I have been working on most recently, newest first. Everything here also lives in the sections below, filed by subject.

New·13 October 2026 C++23, Metal and ARM64 field guides Three typeset booklets for writing a Metal C++ engine on Apple silicon: modern C++23 with pointers explained slowly, graphics with Metal 4, and arm64 assembly. PDF
The Longevity Stack Creatine, cold exposure, fasting, aerobic and resistance training, and melatonin: the mechanisms, how good the human evidence is for each, and what I think they might do together. English / 日本語PDF Weekly Putnam: The odd one out The squares of 2027 points on the unit circle cancel exactly. Solution PDFEnglish / 日本語 Nanite and Lumen How Unreal Engine 5 draws film-density geometry at one triangle per pixel and lights a fully dynamic world with multi-bounce global illumination, with ten diagrams: the cluster DAG and its one-pixel error cut, software rasterization, the surface cache, distance fields, screen probes and the tracing ladder. English / 日本語PDF Weekly Putnam: Integer moments need room A continuous function whose first 2026 power integrals are all integers cannot live inside a short interval. Solution PDFEnglish / 日本語

All preoccupations →

Math encyclopedia

Six subjects · 85 entries

Mathematical explainers, experiments, and reference material in one place. Browse by subject, open the reference sheets, or try this week’s Putnam problem, with its full worked solution.

Foundations and algebra15 entries: Set theory, Discrete mathematics, Logic and computability, Cellular automata, Category theory, and 10 moreTopology and analysis14 entries: Analysis Atlas, Lebesgue vs Riemann integration, Lebesgue integration, Lebesgue Integration Lab, Measure theory, and 9 moreGeometry and transformations13 entries: Differential geometry, Hyperbolic geometry, Knot theory, Differential forms, Push-forward and pullback, and 8 moreProbability, computation, and reference14 entries: Probability, Statistics and inference, Markov chains, Stochastic processes, Information theory, and 9 morePhysics21 entries: Classical mechanics, Hamiltonian mechanics, Rigid-body dynamics, Electromagnetism, Optics, and 16 moreEngineering: watches and sound8 entries: Oscillators and escapements, Gears and mechanisms, Piston engines, Quartz resonators, Loudspeakers, and 3 more

Interactive explainers

25 entries

Mechanisms and devices taken apart and made operable in the browser. Turn something and watch the physics answer.

How a perpetual calendar works A 48-month cam perpetual calendar you can step night by night: the 24-hour wheel, the grand lever, the date and day stars, the snail that drags a short month round to the 1st, and the moon disc. English / 日本語 How a tourbillon works A one-minute flying tourbillon taken apart and run in the browser: the cage, the fixed wheel that makes the escape wheel turn, the escapement in slow motion, and why the whole thing averages out gravity. English / 日本語 Inside an Automatic Chronograph: the Whole Movement, Turning A complete automatic chronograph calibre built part by part and set running in the browser: rotor and winding, barrel and going train, lever escapement and balance, keyless works, motion works and date, and a column-wheel, vertical-clutch chronograph, every wheel at its true ratio. English / 日本語 The Bladeless Fan How a ring with a one-millimetre slot moves fifteen times more air than its motor pushes: an operable cutaway of the air multiplier, with the jet laws that set the number and why the ratio flatters a narrow slot. English / 日本語 How my headphones measure my ears What the CustomTune chime measures, and how the noise cancelling and the EQ are refitted to one ear. English / 日本語 Inside the Kuru Toga Three cams, half a tooth at a time, and a wear simulation of what the turning is actually worth. English / 日本語Interactive 3D Inside every M-series die All 20 M-series chips as interactive top-down floorplans, from die photographs where they exist, with side-by-side comparison. English / 日本語 Model benchmark atlas Astra, Fable 5.1 and Opus 5 across every reasoning-effort setting: measured quality against cost and response time. English / 日本語Interactive Nicotine dose curve A first-order elimination model over 24 hours, comparing cigarette boluses against vape micro-doses at a matched daily dose. English / 日本語Interactive + PDF DualSense: inside the feel Take the PS5 controller apart in 3D: left and right haptics, voice-coil motion, and adaptive trigger resistance you can load by hand. English / 日本語Interactive 3D Laurent series × Bessel functions An interactive lesson on annuli, contour coefficients, radial differential equations, and convergent worked examples. Interactive Apple silicon: the M-series atlas Explore all 20 announced M-series chips through top-down architecture views, generation comparisons, memory and parallelism experiments, and illustrated PDF guides. English / 日本語Interactive + PDF The Writing Lab: JETSTREAM & KURU TOGA DIVEInspect both instruments in 3D, explore Lite touch ink chemistry, and experiment with lead rotation and automatic feeding.English / 日本語Interactive 3DCold, explained: How a refrigerator worksOpen a 3D refrigerator, follow its refrigerant circuit, and experiment with energy use and thermostat control. Skin Deep · Oral versus Topical Melatonin Topical melatonin makes an exponential gradient through the dermis and oral melatonin makes a flat plateau. English / 日本語PDF KEF Coda W: Inside Uni-Q Explore the speaker in 3D, separate the Uni-Q components, and see how source geometry changes off-axis path differences. Interactive 3D Carrera Panda: A Study in Precision Nine exploded mechanism views, 36 guided stages and hands-on experiments explain automatic winding, timekeeping and the chronograph alongside a detailed Carrera model. Interactive 3DWatch study Membrane: A Living Action Potential A 3D neuron with live membrane voltage, sodium and potassium flow, and voltage-gated channels. Interactive 3DReact · Three.js Inside an Automatic Watch Follow energy from rotor and mainspring through the going train to escapement, balance, and hands. Interactive Mechanical Watch Atlas Step through automatic winding, chronographs, calendars, moon phases, tides, repeaters, and other complications. InteractiveEnglish / 日本語PDF Automatic Watch Deep Lab A larger movement, gear-train, escapement, and hairspring simulation. Interactive Quartz Watch Lab The piezoelectric tuning fork, the Pierce oscillator, the fifteen-stage divider, and the Lavet stepper motor that moves the hands. InteractivePDF Electricity, Quartz, Motor Where energy actually changes form between the battery and the hands: two transductions, and one gap that nothing physical crosses. InteractivePDF OLED — A panel made of lightExplore the OLED layer stack in 3D, follow electron–hole recombination, and mix RGB subpixels.Interactive 3DEnglish / 日本語 Apple Watch: A heartbeat, seen in light Explore a 3D watch and wrist cutaway, then change heart rate, light source and noise to see how an optical pulse becomes beats per minute. Interactive 3DEnglish / 日本語 Heat, moved: Split-system engineering Switch between heating and cooling, inspect the refrigerant circuit and compressor in 3D, and explore thermodynamics, electricity use and running costs. Interactive 3DEnglish / 日本語 SodaStream ART: Inside the fizz Inspect the SodaStream ART in 3D, follow the gas path from cylinder to bottle, and explore dissolved CO₂, bubbles and the chemistry of carbonation. Interactive 3DEnglish / 日本語 Studio Display: Sound in a thin space Inspect the 2022 internals in 3D, isolate the speaker chambers, and explore force cancellation, wavelength and spatial hearing. Interactive 3DEnglish / 日本語PDF

Preoccupations

Twenty-four · Research and explainers

Questions I followed further than I needed to, and wrote up. Pharmacology, acoustics, graphics, game engines, and the insides of watches.

The Longevity Stack Creatine, cold exposure, fasting, aerobic and resistance training, and melatonin: the mechanisms, how good the human evidence is for each, and what I think they might do together. English / 日本語PDF Nanite and Lumen How Unreal Engine 5 draws film-density geometry at one triangle per pixel and lights a fully dynamic world with multi-bounce global illumination, with ten diagrams: the cluster DAG and its one-pixel error cut, software rasterization, the surface cache, distance fields, screen probes and the tracing ladder. English / 日本語PDF Can Concerta and Intuniv ease heartbreak? The neurobiology of romantic loss and the case that methylphenidate and guanfacine ER could help people function through it: the circuit, an hour-by-hour occupancy model of Concerta 54 mg and 108 mg, and the strongest objections. English / 日本語PDF What Fable 5.1 still buys you over Opus 5.5 Opus 5.5 matches or beats Fable 5.1 on most published measures for under half the price. English / 日本語PDF Cold Water and the Mind What a cold shower does to mood, anxiety and attention, from skin receptor to randomised trial. English / 日本語PDF What the Diamond in uni NanoDia Does What nanodiamond physically does inside uni NanoDia lead, and whether it beats Pentel Ain. English / 日本語PDF The Gamepad Froze in 2005. The Hardware Did Not. Fifty-four years of game controllers, and why no input feature added since 2005 has reached all three console makers. English / 日本語PDF Threads: agreement, disagreement, praise and criticismAn anonymized observational study of reply stance, account patterns, praise and criticism, with context from four behavioral studies.English / 日本語PDF Creatine, longevity and the central nervous system A research report on energy buffering, healthy aging, cognition and mood, separating plausible mechanisms from demonstrated human benefits. English / 日本語PDF The Dislike of AI Art Is Not Aesthetic Looking at art is inference about a mind. English / 日本語PDF Violin Études de perfectionnement Original violin études for the first level on Michel Sogny's model: one technical target per study, a bilingual instruction page with the practice variants notated, and a minimum duration. English / 日本語PDF Creatine, Amphetamine and the Shape of the Load Amphetamine adds an ATP cost that no action potential switches off, and lowers dopamine-neuron firing rate rather than raising it. English / 日本語PDF Coding Reasoning: Astra, Sol and FableReasoning-level curves, coding benchmarks, token use, cost and latency. Expanded PDF and interactive comparisons. Concerta: Extracellular NE and DA A dose–time model I kept inside what the evidence can actually carry: OROS exposure, transporter occupancy, and relative catecholamine signals. Creatine, the Brain, and Cognition Where I think the evidence holds and where it gives way: brain energy, cognition under sleep loss, neurological disease, and safety. Two Routes to a Cheaper Brain Vortioxetine, creatine, and whether a lower BOLD signal is really evidence of a more efficient brain. The Menstrual Cycle and ADHD Catecholamine signalling across the cycle, eight competing hypotheses, and why the dopamine story outruns its evidence. English / 日本語PDF The Best Argument for T-Rex Vortioxetine plus brexpiprazole, audited for cognition, mood and anxiety, and what the dendrite claim actually rests on. Real-Time Natural Worlds Where procedural terrain, procedural flora, and water rendering in videogames have actually got to, as far as I could establish. Frontier Coding Atlas Models, reasoning effort, published coding evidence, and what parallel subagents actually change. Interactive reportPDF A Closed-Book Knowledge Probe Thirty short-answer items, an answer key, and a scoring scheme that reports what a model knows minus what it confidently invents. English / 日本語PDF The effort dial runs out before the money does Claude Opus 5, Claude Fable 5.1 and GPT-6 Astra across all five reasoning-effort settings: where the marginal return on deliberation reaches zero, and which model is cheapest at a given score. English / 日本語PDF Computational Acoustics A patent-led comparison of Apple HomePod 2 and Bose Lifestyle Ultra, with interactive acoustic-path diagrams. Soulblighter Internals A field guide to the simulation architecture of Myth II: integer physics, tag graphs, and deterministic lockstep.

Books

3 entries

The pieces I wanted to exist as a book rather than a page. Typeset properly, and free to download and keep.

C++23, Metal and ARM64 field guides Three typeset booklets for writing a Metal C++ engine on Apple silicon: modern C++23 with pointers explained slowly, graphics with Metal 4, and arm64 assembly. PDF Game Design as the Dynamics of Learning My book arguing that games are systems regulating the rate at which players reduce uncertainty, that fun is that reduction at an optimal rate, and that the learning gradient is the primary design metric. Web editionEPUBPDF Integrated Medical Foundations Bilingual English and Japanese textbook editions, with EPUB and PDF downloads. EPUBPDFEN / 日本語 Inside a Quartz Watch The print edition of the quartz lab. PDF

Selected software

All repositories →

Material Lab A photograph in, editable PBR texture maps out, entirely on the Mac. Learned geometry, a seam-cut tiler and GTAO occlusion. macOS · iOS · CLI World Model MCP Local research memory with evidence, human review, and revision history. MCP · TypeScript Game Development Studio Local-first asset production, vendoring, visual debugging, and performance tooling. TypeScript Game Debug MCP Sealed-frame evidence, first-divergence diagnosis, and identity-safe performance comparison. MCP · CLI Systems Lab A native workspace for drawing schematics, simulating systems, and plotting Modelica results. macOS Structure Studio Turns text descriptions into fully authored 3D building structures. macOS Neural Biped Trainer A standalone animation trainer built on SwiftUI, Metal, MuJoCo, and Apple Silicon worker tooling. Python Algebraic Varieties A visual primer on algebraic varieties with an interactive curve laboratory. Interactive

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Why the name

Isegoria means an equal right to speak.

I chose it because I want this to be an equal invitation into technical conversation, whatever the subject. I am not trying to take the sophistication out, only the needless opacity.

Read the approach →