Things that stay counterintuitive no matter how many times you meet them, and where each one actually shows up.
Not open questions. These are settled, named, and older than me. I keep them because I meet the same shapes in the work and forget, every time, that they already have names.
Each one has a setup and a bite. The setup is the paradox. The bite is where I have actually run into it, which is the part I would not find by looking it up.
A heap of sand stays a heap if you remove one grain. Remove grains one at a time and at some point it is not a heap, but no single grain was the one that made the difference.
Where it bites This is the entity resolution threshold problem, exactly. At 0.99 similarity two records are the same person. At 0.10 they are not. There is no principled grain anywhere in between, which is why the honest answer is a review queue rather than a cleverer cutoff.
Replace every plank of a ship, one at a time, and you have a ship made of entirely new material. Is it the same ship? Now rebuild the original from the discarded planks. Which one is it?
Where it bites Identity over time, which most systems ignore entirely. A clinic is rebuilt, a cooperative reforms under a new name, a person changes theirs after marriage. Co-reference asks whether two mentions point at one thing now. This asks whether the thing survived, and nothing in a matcher answers it.
A trend can hold in every subgroup and reverse when the groups are combined. Both halves of the data say one thing, the whole says the opposite, and neither is a mistake.
Where it bites Attribution. A channel looks good in every segment and bad overall, or the reverse, and whichever number reached the meeting first becomes the truth. Worth remembering that the aggregate is a choice, not a fact.
In a room of 23 people there is roughly an even chance two share a birthday. It feels far too few, because intuition counts people rather than pairs, and pairs grow quadratically.
Where it bites Collisions arrive much sooner than anyone expects. It sets how long a hash prefix has to be before it identifies anything, and it is why blocking on a low-cardinality key produces enormous candidate sets from what looked like a reasonable rule.
Adding a road to a network can make everyone's journey slower, because individually rational route choices produce a worse equilibrium.
Where it bites Adding a data source can make resolution worse. One low-quality feed injects false links, those links propagate through transitive closure, and the merged result is less trustworthy than before the source arrived. More data is not monotonically better.
Improving the efficiency of a resource tends to increase its total consumption rather than reduce it. Coal was the original case.
Where it bites Cheaper inference does not mean less compute. It means inference gets put in places nobody would previously have justified, and total spend rises. Useful antidote to any plan whose savings depend on a per-unit cost falling.
Things that feel hard to humans, like chess or arithmetic, turn out to be easy for machines. Things a toddler does without thinking, like perception and judgement, turn out to be very hard.
Where it bites Comparing a million record pairs is trivial and no one is impressed. Knowing which of those comparisons actually matters, and when to stop and ask a person, is the part still unsolved. The easy-looking half is where the difficulty lives.
Selecting a sample on a combination of traits creates a correlation between those traits inside the sample that does not exist in the population.
Where it bites The records that survived matching are a selected sample. Anything learned from the merged set, about which fields agree or how often, is a statement about records that matched, not about the world. Easy to forget when the merged table is the only one anyone looks at.