Devlog #33 — Wave 13 & Simulations in the Classroom

All Three Wave 13 Posts

Wave 13 spans June–July 2028. The three posts cover two Spotlights and one Learning entry — the smallest wave yet in terms of post count, but perhaps the most mathematically dense. Each one required significantly more research time than earlier posts; the Schwarzschild metric section in Learning #23 alone went through four drafts to get the notation consistent and the GPS correction calculation exactly right.

Simulations in the Classroom

Over the past year we have received more email from educators than in any previous period. Physics teachers embedding simulations in lesson plans, university lecturers linking from course pages, and maths instructors using topology and statistics simulations to supplement lectures. This section is a summary of what we have learned from those conversations.

Which Simulations Appear in Syllabi

The most frequently mentioned simulations in educator emails are, in rough order of frequency:

1. Time Dilation and Twin Paradox — virtually every A-level and university-first-year special relativity module. The clock-rate visualisation resolves the twin paradox confusion faster than any written explanation, according to several teachers.
2. Projectile Motion / Ballistics — the first simulation most physics teachers find. Used at GCSE and A-level for the kinematic equations; drag toggle appreciated.
3. Blackbody Radiation — popular in chemistry and physics at A-level. The Planck curve slider that changes temperature and shows the peak shifting is exactly what textbook diagrams cannot do.
4. Carnot Cycle — thermodynamics. The animated PV diagram with the four-step cycle identified by colour is used in a number of engineering thermodynamics courses as a supplement to static diagrams.
5. Diffraction and Diffraction Grating — optics at A-level and university. The continuous wavelength slider showing the grating pattern change in real time.
6. Central Limit Theorem — statistics. Used in social science methods courses and economics as well as mathematics.
7. Lorenz Attractor and Bifurcation Diagram — chaos theory modules at university. The butterfly effect is intuitive with the attractor trajectory; bifurcation diagram gives the logistic map a visual grounding.

Less popular but mentioned consistently by university-level educators: the Hodgkin-Huxley neuron (computational neuroscience), Schwarzschild geodesics (GR courses), and crystal structures (materials science undergraduates needing a 3D view of BCC vs FCC).

Common Classroom Patterns

Three usage patterns come up repeatedly in educator feedback:

1. Pre-lecture preview. Students are asked to play with a simulation before a lecture so they arrive with an intuitive sense of the phenomenon. For time dilation, several teachers report that students who explored the simulation in advance ask much better questions about the relativity of simultaneity — because they have already noticed that "something strange happens" with the simultaneity lines and want to understand why.

2. In-class demonstration. The teacher projects the simulation and adjusts parameters while explaining, pausing at key values (e.g., the ISCO radius for Schwarzschild geodesics, or the eutectic point on an alloy phase diagram). The animation removes the need to redraw graphs repeatedly, freeing whiteboard time for derivations.

3. Post-lecture exploration task. Students are given a specific question that requires using a simulation to answer. For example: "What is the deflection angle for the gravitational lensing simulation when the impact parameter equals the Einstein radius? Does the simulation match the formula?" This bridges the gap between textbook exercise and interactive exploration.

Writing Process for Wave 13

Materials Science — Breadth Without Shallowness

Spotlight #26 covers six distinct sub-fields: crystallography, diffusion, mechanical properties, dislocation theory, phase equilibria and semiconductor physics. Each of these is a semester-long university course. The challenge was to pick the one or two equations that actually connect to what the simulation shows, and explain them without misrepresenting the depth of the underlying theory.

The decision to include the Hall-Petch equation (σ_y = σ₀ + k/√d) was deliberate: it is rarely seen outside metallurgy textbooks but is one of the most surprising results in materials science. Smaller grain size means stronger metal — the opposite of what most people intuitively expect — and the square-root dependence on grain diameter is non-obvious and experimentally robust. Putting that in the math box next to the stress-strain curve gives mathematically inclined readers something concrete to look up.

General Relativity — GPS as the Anchor

Learning #23 is the longest Wave 13 post at around 5 800 words. The decision to use GPS as the anchor example for gravitational time dilation came from classroom feedback: abstract "clocks near a black hole" examples are hard to connect to. But GPS — something every student uses daily, something that would fail visibly and immediately without a general-relativistic correction — makes the stakes concrete. The +38.7 µs/day net correction (gravitational minus special-relativistic) has been independently checked against multiple sources and is correct to the figure precision quoted.

Topology — Keeping the Physics Connection

Topology is the post most likely to be read by pure mathematics students. The risk was writing something too abstract. To counter this, every section ends with a physical consequence: Möbius strip → topological insulators; Klein bottle → homology and quantum field theory; torus → KAM theorem and phase space; knot theory → DNA topoisomerases and Chern-Simons theory; minimal surfaces → butterflies and architecture. The mathematics is never introduced without a reason to care about it.

Blog Series Status After Wave 13

After Wave 13, here is where each series stands:

• Category Spotlight — 27 posts published. Remaining major gaps: photonics/optics deep-dive, plasma physics, cell biology, civil and structural engineering, acoustics.
• Learning with Simulations — 23 posts published. Remaining: quantum field theory introduction, thermodynamics deep-dive, network science / graph theory, numerical methods.
• Devlog — 33 posts published. Next milestone devlog at 350 simulations (close — currently 345 live).
• Tips & Tricks — 12 posts published. A performance optimisation post for Three.js scenes with many instanced meshes is drafted.
• Announcements — 15 posts published. A post announcing the sharable-link parameter feature will ship alongside the feature itself.

Wave 14 Outlook

Wave 14 is being planned for August–September 2028. Current candidates under discussion:

• Spotlight #28: Acoustics & Music — standing waves, room acoustics, concert hall reverberation, Chladni patterns, cochlear resonance
• Learning #24: Thermodynamics — entropy, the second law, Maxwell's demon, phase transitions and the Ising model
• Spotlight #29: Plasma Physics — Debye shielding, magnetohydrodynamics, aurora, fusion confinement
• Devlog #34: 350 simulations milestone retrospective

The sharable-link feature (pre-set parameter URLs) will ship during Wave 14. Once live, it will be announced here with a guide on how educators can use it to build custom classroom activities directly from the blog.