Imagine inheriting one of the largest fortunes in Europe and giving every penny away to teach elementary school in a remote village. That is only one chapter in the life of Ludwig Wittgenstein, the Austro-British thinker who revolutionized 20th-century philosophy and then tore down his own system to start over. This deep dive begins in the Palais Wittgenstein in Vienna, where steel tycoon Karl Wittgenstein, often compared to Andrew Carnegie, ran a household with seven grand pianos, visits from Brahms and Mahler, and a suffocating demand for perfection. Three of Ludwig's four older brothers took their own lives, and the young man with absolute pitch who could whistle entire symphonies fled into engineering.

The episode follows his surprising years in aeronautics at Manchester, where he flew kites at a meteorological station and designed a ti ...