Four Strokes or Three
A normalization rule can make two records look identical by removing the marks that kept them apart. Scripts and language records make the loss visible because they retain the original form alongside a reading.
collision
9 entries
combinatorial designs graph algorithms
No Two Walked Together Twice
A shortest or cheapest route can look diversified because it has many hops while repeatedly relying on one untested pairing. Combinatorial designs supply the coverage constraint that graph optimization does not.
Nothing Happened to the Spelling
Names are evidence of identity, not identity itself. Naming systems preserve crossovers, spelling variation and publication thresholds that make a clean join look more certain than it is.
historical geography historical places
One Place, Five Authorities
A name can survive a border change, a conquest and a map revision while the thing it denotes changes. Historical geography makes the mapping explicit; a time series should do the same before it compares locations across years.
The Letter Reached the Printer
A total can change because the world changed or because membership was redefined. Set theory made the membership rule explicit because unrestricted collection creates contradictions; data universes need the same discipline.
regression historical geography
Thirty-Nine, Then Twenty-Five
When the reporting unit changes, aggregation can manufacture a discontinuity even if every underlying place changed smoothly. Regression can quantify the apparent effect; historical geography says to repair the unit first.
Thirty-Seven Million Descriptions
A growing catalogue can mean that more records were described, not that more underlying material exists. Archives and documentary editions keep these counts apart because the object being counted changes with the record system.
Two Rows Became One Row
A split can create two institutions that both claim an older identity. Treating one as the continuation and the other as a new entrant manufactures a clean history that the record does not supply.
No Integer Satisfies Both
Every leap rule is a congruence system. So is every settlement calendar. Whether two of them can be jointly satisfied depends on a number nobody computes.