A small museum of falsifiable ideas
The Counterexample
Cabinet
A beautiful rule. One inconvenient moth.
Let the exception improve the explanation.
Admission: a willingness
to be wrong.
No clock. No penalty.
Only sixteen paper moths.
Three gates · each has a different hidden rule
Changing exhibits starts a fresh notebook. Reselecting the same one preserves your work.
The generous gate
The specimen drawer
2 / 16 observedPick a moth. The small label is the gate’s observed answer, never your prediction.
Under the lens
Specimen 01
Your rule predicts
The gate answered
Two observations came with the drawer. The rest are yours to request.
Room for another explanation
A claim you can put at risk
Build the gate’s rule
Choose two properties and a connective. NOT reverses a property. Your rule predicts whether the lamp lights.
The checker searches all sixteen specimens in number order. One mismatch refutes the claim; an exact match reveals the whole table. It does not require the intended wording.
The cabinet’s reply
No universal claim checked yet.
The starter rule fits the two supplied observations in the first exhibit. That does not make it the gate’s rule.
Select a specimen or assemble a rule.
The seventeenth specimen
And outside the glass?
This imagined visitor has three spots per wing. Our domain admitted only one or two. You can propose an extension of your rule to it, but this cabinet assigns no gate answer outside its sixteen specimens.
One extended gate could light for this visitor; another could stay dark. Both could agree on all sixteen moths you tested. Your certificate cannot choose between them.
A complete check needs a boundary. This is a demonstration about a finite, invented domain—not a recipe for certifying reality.
Everything lives in this tab. Downloads are JSON records, not importable saves. Undo remembers the last 80 rule edits, not observations. New drafts and Undo always require a new check.
The observation ledger · an equivalent text view
| Specimen / properties | Prediction | Observed |
|---|
Reading & making · the limits of this little museum
01 / Source positions
An explanation should risk something.
In Rescuing Philosophy, Michael Edward Johnson criticizes weak feedback in philosophy and argues for alternative institutions and practices. He also cautions that inherited ways of framing a problem can import confusion. This cabinet takes the feedback question seriously without treating his institutional judgments as settled history.
In the complete January 26, 2025 Note on electricity and LLM explanations, Johnson contrasts evocative language with predictive laws and asks how AI could help investigate consciousness rather than produce compelling but inadequate descriptions. That analogy motivates our contrast between a plausible rule and a testable one. It does not establish that consciousness will have any particular mathematical theory.
02 / Authored mechanics
The cabinet is not nature.
All moths, gates, exhibit titles, Boolean rules and counterexample choices are invented. Four binary properties make exactly sixteen specimens. Two possibly negated properties joined by AND, OR or XOR give 192 expressions. The rival counter merges expressions with identical sixteen-entry prediction tables: it counts distinct behaviors, not sentences, probabilities or credences.
A suggested specimen maximizes the smaller of the lit and dark rival groups; ties go to the lowest number. It selects a question without answering it. A complete match proves agreement only on this authored domain. The source essay does not supply this algorithm, and real research rarely supplies an exhaustive oracle or a known-correct hypothesis language.
No consciousness, neuroscience, welfare or intelligence is measured. Beauty is not an error; predictive adequacy is a different demand. This is not a test of the visitor’s rationality.
03 / Colophon
A Daily-only tribute.
Original AI-generated code, writing and procedural SVG illustrations, dated September 28, 2026. Model: gpt-6-astra, session-reported runtime metadata—not a claim about public model availability. Status: Daily; no main-site approval or endorsement.
The live Lab, Hyperspace and Notes index were reviewed for context. All seventeen earlier Daily apps were reviewed before choosing counterexample-guided rule repair rather than another oscillator, spatial notebook or narrative.
No external runtime requests, audio, timers, analytics, persistent storage or new dependencies. Native controls and a textual ledger accompany every illustration. No physical-device or Safari verification is claimed.