🌐 日本語 ｜ English
The canonical originals of “Wakaru” (“It Clicks”) — a reading series for physics-loving high-schoolers and undergraduates. Every series is managed here from now on. Each episode is a self-contained HTML page (serif type + MathJax + live canvas figures + print/PDF ready; the only external dependency is the MathJax CDN).
➡ https://yomei-o.github.io/wakaru_all/
On GitHub’s file pages (github.com/…) the HTML shows up as source. To actually read it and play with the live figures, open the published site (GitHub Pages) above. The links in the tables below also point to the published (rendered) site.
| Series | About | Read (published site) |
|---|---|---|
| c·t = const, That Clicks〔sequel to Conformal Transformations That Click〕 | On its own (c\cdot t=\text{const}) says nothing — it can be realised in any universe — which is exactly why it can be substituted into every equation there is. A notation for writing cosmology as short as it will go, with the shortness measured in bits. 50 episodes in 6 parts, complete. Part I: divide memory by operations and the equation of state falls out · two logarithmic clocks, 140 and 73, divide to give the expansion law · erase everything erasable and only a single mass is left · what shortness costs (BIC 5.37 bits, misfit 154). Part II: gravity, quantum mechanics, the atom, heat and information, light, the vacuum, fluids, phase transitions, chemistry and biology — only “size” is touched; “shape” is out of reach. Part III: the horizon problem as distributed consensus · holography as addressing (one bit ↔ 1.96 fm) · sorting identity, coincidence and physics by surprise in bits · (C\cdot t=N), exactly one memory pass per Hubble time · the wrap-up compresses 24 headline numbers into 12 inputs. Part IV: inflation, VSL, MOND, measuring the constants, CCC, the cosmon, Milne, conformal gravity and asymptotic safety on one operating table — only VSL failed to separate (A) notation from (B) an observable claim, every prediction sat in a dimensionless quantity, and six coincidences cluster in a 4-to-7-bit band (a selection effect). Part V: quantum anomalies (the breaking sits 28.7 bits above the noise) · the conformal factor problem (the ghost never disappears; it only moves) · Kerr ((\chi\le1) is in the untouchable column) · gravitational entropy (three (10^{122})s are one number) · the Weyl curvature hypothesis (the arrow of time is written in the half the tool cannot touch) · the black hole interior · the Planck scale (a smallest length is excluded by hypothesis) · discretisation (the demand was never “no scale”, only “no scale left in the answer”) · the wrap-up (it touches exactly half the curvature). Part VI, the finale: twelve ways of saying (a\propto t) come from three inputs · the 2019 SI officially declared that dimensionful is bookkeeping ((c) can be decreed, (\alpha) cannot) · beauty was a choice of prior, not a third currency · sixteen open doors in four kinds (four in ten cannot be closed by data) · the finale: only one thing moves (50 episodes → 6 tools → 2 ideas → 1). Every number was computed and run in 53 verification scripts | open |
| Conformal Transformations That Click〔sequel to Cosmology That Clicks〕 | Rewriting the universe with the one operation that swaps your ruler point by point. Weyl 1918 and Einstein’s objection (gauge once meant a ruler’s calibration) · maybe atoms are shrinking rather than space expanding · what “light slowing down” actually is (Weyl-transform c·t=const and it is the same metric read in cosmic time) · gravity becomes a single scalar (the dilaton) · the equation of state was a potential, V∝φ^(1−3w), with c·t=const exactly a mass term · is the singularity a coordinate artefact (only half) · light is conformally invariant, mass is not (Penrose’s CCC) · quantum mechanics breaks conformal symmetry (the trace anomaly = a running coupling; 99% of your body weight) · the conformal factor was a ghost · which frame is the real one. The previous series’ motto — units are bookkeeping, dimensionless is physics — becomes a decision procedure (10 episodes, complete + 1 bonus: “what happens if you run it at face value”, the verdict from nucleosynthesis) | open |
| Cosmology That Clicks | Read the universe through the speed of light, the fine-structure constant, and gauge symmetry | open |
| Relativity That Clicks | Divide everything by c. β · γ · spacetime interval · E=mc² · simultaneity · gravity = curvature · variable-c ≡ curvature (7 episodes, complete) | open |
| Quantum That Clicks | The story of ℏ. S/ℏ separates classical from quantum: grain & wave, wave function, sum over paths, Schrödinger, uncertainty, measurement (6 episodes + bonus, complete) | open |
| Fields That Click | Why forces travel at the speed of light. Reading fields as “dimensionless ratios” (8 episodes, complete) | open |
| Black Holes That Click | The diagonal of the cube (c · ℏ · G), read through information and bits: horizon · entropy = bit count · Hawking temperature · fastest computer · holography · information paradox (6 episodes + 2 bonus, complete) | open |
| Renormalization That Clicks | Why the world still works when you throw things away: coarse-graining · phase vs. decay · decoherence · universality and the renormalization group · where it breaks · the hierarchy problem · resolution as a dimension (7 episodes + 6 bonus, complete; the bonuses reach into statistics, information theory and machine learning, and link back to the cosmology and universe-as-computer series) | open |
| Temperature That Clicks | Temperature is not a property of matter; k_B is an exchange rate. How energy is shared out · heat as untracked motion · the fluctuation theorem · negative temperature · the period in imaginary time · the Unruh effect (7 episodes + 1 bonus, complete; the bonus collapses Unruh, Hawking and the cosmological horizon into one line) | open |
| Tunneling That Clicks | Getting to the far side of a wall without going over it: walking in imaginary time · why the Sun burns · climb over or slip through · the Josephson effect · superconductivity is not tunneling · what perturbation theory cannot see · vacuum decay (7 episodes + 7 bonus, complete; the bonuses compute a verdict on cold fusion, cover muon catalysis, why a single atom is visible, the unresolved tunneling time, quantum biology sorted, thirty years of room-temperature superconductivity, and instantons as spacetime geometry) | open |
| Refraction That Clicks | Refraction slows light down, so why is the speed of light still invariant? What slows is the wave, not the photon · there are two light cones (the effective metric) · the phase velocity exceeds c · reflection comes from mismatch, and total internal reflection is tunneling · refraction and absorption are one complex function glued by causality · stopping light · what you see is a map of refractive index (7 episodes, complete) | open |
| The Lattice We Build〔the build side〕 | The one series that does not explain but builds. Put a tool in the blank space and run it: enumerate all 162,931 dimensionless ratios and measure that only coincidence comes out (p = 0.67) → make spacetime a lattice and you buy an 18-order fine-tuning → the stage may stay flat (the equivalence principle comes out as a conclusion) → the memory effect and BMS → the boundary was 3-dimensional (Carroll geometry, where c = 0) → the tower of soft theorems forms w(1+∞) → the horizon is Carrollian too → write a specification for what is missing → in 3 dimensions it is already proved → BMS₄ has no central charge (dim H² = 0, computed by hand) → the area law comes for free → the degrees of freedom never needed counting → the wall was Episode 1’s own theorem → Mercury precesses on a flat lattice (42.9807″/century, ratio to GR 1.0000) → one photon settles it (112 PeV) → this way the arithmetic is easier. Four doors closed · one calculation that went through · one falsifiable number · zero new physics (19 episodes + 4 bonus, complete) | open |
| Force That Clicks | Peel back what “force” really is — down to fields, geometry, and symmetry | open |
| Mass That Clicks | What mass actually is | open |
| The Universe Is a Computer | Read the cosmos through the lens of computation | open |
| Learning That Clicks | Evolution, learning, and consciousness read through one and the same gradient | open |
| A History of UNIX That Clicks | The history of UNIX | open |
★ Map of the whole collection: The Physics Cube ── take in every series at a glance along the three axes c · ℏ · G (and the fourth axis k_B — “Temperature That Clicks”).
(English folders: wakaru-uchuron-en/ · wakaru-soutai-en/ · wakaru-ryoushi-en/ · wakaru-ba-en/ · wakaru-blackhole-en/ · wakaru-kurikomi-en/ · wakaru-ondo-en/ · wakaru-surinuke-en/ · wakaru-kussetsu-en/ · butsuri-tsukuru-en/ · wakaru-chikara-en/ · wakaru-shitsuryo-en/ · wakaru-uchu-keisanki-en/ · wakaru-gakushuron-en/ · wakaru-unix-en/)
The Japanese originals live in sibling folders and are listed in the Japanese README. Quick links: Conformal Transformations · Fields · Relativity · Quantum · Renormalization · Temperature · Tunneling · Refraction · The Lattice We Build · Cosmology · Force · Mass · Universe-as-Computer · Learning · UNIX.
Exactly one row in the table above does not say “That Clicks.” Where the “Wakaru” series explains known physics, this one flips the stance: it builds a tool, runs it, and reads the result as it comes — including the runs that failed, and the runs where the author was simply wrong. The tool it builds is a lattice: what breaks when you declare spacetime to be a lattice, and what still turns over perfectly when you keep the lattice flat.
Spine, in one line: making physics is not about predicting, but about deciding in advance how a prediction would die.
19 main episodes + 4 bonus, complete. Every episode carries an interactive figure; the check code is dependency-free pure C++ / pure Python (kuuhaku_cpp).
Negative results are published as negative, and corrections are not hidden — every episode carries a correction banner plus a ledger.
➡ English: butsuri-tsukuru-en/ ｜ Japanese original: butsuri-tsukuru/
Start from the contents page of the published site above and go to each episode. Every individual HTML file just works when opened in a browser (the only external dependency is the MathJax CDN). To print, use each page’s “Print → Save as PDF.”
wakaru-ba-en/ → ../wakaru-chikara-en/index.html), so keep each series in its sibling folder directly under the root.