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Start swiping — it's freeIn 1888, a group of European language teachers published the International Phonetic Alphabet to give every distinct sound in human speech its own unique symbol, independent of any single language's spelling. Linguists still use it to transcribe pronunciation precisely, from English 'th' to clicks in Zulu.
— International Phonetic Association, International Phonetic Alphabet — First published 1888
Start with 1. To build the next line, read the previous line aloud and write down what you say: '1' becomes 'one 1', so line two is 11. That becomes 'two 1s', so line three is 21. Keep going: 21, 1211, 111221... What's the rule for generating any line, and does the sequence ever settle into a repeating pattern?
Each line just describes the digit-runs of the one before it ('one 2, one 1' -> 1211, and so on), so it never repeats — it grows forever. John Conway proved in 1986 that every such sequence eventually breaks down into a fixed set of 92 recurring 'elements' (which he named after chemical elements) and that its length grows by a constant factor each step, now called Conway's constant (≈ 1.303577).
When potato blight destroyed Ireland's staple crop from 1845, roughly a million people died of starvation and disease and another million emigrated, shrinking Ireland's population by a quarter within a decade. Grain and livestock continued to be exported from Ireland throughout the famine under British trade policy, a fact that still shapes how the disaster is remembered as much a political failure as a natural one.
— Cecil Woodham-Smith, The Great Hunger: Ireland 1845-1849 — Hamish Hamilton, 1962
Psychologist George Loewenstein described the 'hot-cold empathy gap': in a calm, 'cold' state, people consistently underestimate how much a 'hot' emotional or physical state — anger, hunger, pain, desire — will change their own judgement and choices. The gap runs both ways: mid-craving, it's just as hard to remember what calm restraint felt like. It helps explain why good intentions set in advance so often collapse in the moment.
— George Loewenstein, Hot-Cold Empathy Gaps and Medical Decision Making — Health Psychology, 2005
When a choice is forced, can't be settled by evidence either way, and matters enough that waiting is itself a choice, James argued you're entitled to let your passional nature decide. He aimed this squarely at religious belief: refusing to believe until proof arrives is itself a bet, not neutrality.