All on the Line · Series
The foundational sequence. An attempt to build a more precise language for how financial systems actually behave, piece by piece: about distributions that don’t converge, about optimization problems that resist exact solutions, about the traps that appear when a system keeps improving toward the nearest peak while a better one sits out of reach, and about what a check can and cannot establish.
The limits of verification: proving a curve optimal took mathematics 135 years; one Saturday the market priced USDC’s gap at $1.7 billion.
A sequential identifier bridges a public price and a private volume. What London did to German tanks, and does to a loan book.
Why does pro tennis set new records every week? The same combinatorics explains the explosion of ETFs, with very different consequences.
The math behind your credit card was invented in 1954. The math protecting it has never been broken. Both use arithmetic you never learned.
When the denominator is hidden, any result can look like proof. Theranos knew it. So does every hedge fund with a three-year track record.
Financial models fail not just on tails, but when they describe a world that has already changed.
The path matters as much as the outcome. More investments fail from the path than from the thesis.
Some financial systems behave like heavy-tailed distributions, where rare events dominate and the average may not exist.
Financial models compress an uncountable world. Mistaking compression for completeness is where fragility begins.
From the Traveling Salesman Problem to financial markets, why perfect optimization becomes irrational at scale.
Exploring local versus global maxima in training, business, and investing, and the mathematics of optimizing entire systems.
Why average returns mislead investors. A mathematical look at distributions, drawdowns, and what it actually takes to survive the path.
