At the boards, someone fits a curve through every point of a day’s tide data — a wild polynomial that misses nothing — and announces “perfect fit”. Is it a good model? Trace it one hour past the data and it promises a forty-metre tide by midnight. Meanwhile the group beside them has a gentle sine curve that misses every single point by a little — and correctly predicts tomorrow. Between “passes through the points” and “tells the truth about what comes next” runs the gap this conversation is about, and it is strangely lopsided: fitting the past is easy, and it proves almost nothing about the future.
Questions worth arguing about:
- What exactly has the perfect-fitter shown, and what have they not? Is hitting every data point evidence of anything?
- The sine curve’s parameters mean something: its amplitude is half the tidal range, its period is the time between high tides, its axis is the harbour’s average depth. Why does a model whose knobs have names deserve more trust than one whose knobs do nothing but fit?
- Every model has an expiry: paper cannot be folded a hundred times, a population cannot double forever, an interest rate will not hold for a century. Whose job is it to say where a model stops being true — the equation’s, or the person wielding it?
- When is simple-but-slightly-wrong the better choice than complicated-but-close? Would you rather your bank used the first kind or the second?
- “All models are wrong, but some are useful.” Prosecute or defend this claim — and decide what “useful” has to mean for it to survive.
This stops being talk at Double or Nothing and The Tide Problem, where your group must choose a family of functions, defend every parameter, and say out loud where your model stops deserving belief. The habit of asking what a graph’s shape claims starts small, every morning, in Graph Talks.