Finding the Perfect Nib: A Binary Search

When adjusting a fountain pen’s nib, you’re hunting for that sweet spot where ink flows smoothly without flooding or skipping. Too much pressure bends the tines apart; too little leaves scratchy lines. The secret is methodical refinement—testing the middle ground, then halving your adjustment based on results.

This mirrors binary search perfectly. Instead of checking every possible adjustment linearly, you leap to the centre of your range, test, then eliminate half the possibilities. It’s the difference between tediously trying every setting versus intelligently converging on perfection.

function findOptimalPressure(testWrite, minPressure, maxPressure, tolerance = 0.1) {
  while (maxPressure - minPressure > tolerance) {
    const midPressure = (minPressure + maxPressure) / 2;
    const result = testWrite(midPressure);
    
    if (result === 'perfect') return midPressure;
    if (result === 'too_light') minPressure = midPressure;
    else maxPressure = midPressure;
  }
  return (minPressure + maxPressure) / 2;
}

JavaScript’s imperative style mirrors the hands-on nature of nib adjustment—direct manipulation of ranges until convergence.

Erlang approaches this through pattern matching and tail recursion, embodying the methodical patience restoration demands:

find_pressure(TestFn, Min, Max, Tolerance) when Max - Min =< Tolerance ->
    (Min + Max) / 2;
find_pressure(TestFn, Min, Max, Tolerance) ->
    Mid = (Min + Max) / 2,
    case TestFn(Mid) of
        perfect -> Mid;
        too_light -> find_pressure(TestFn, Mid, Max, Tolerance);
        too_heavy -> find_pressure(TestFn, Min, Mid, Tolerance)
    end.

Binary search emerged in the 1950s as computers needed efficient ways to locate data in sorted arrays. Like a master restorer who instinctively knows where to start testing a nib, binary search eliminates half the possibilities with each iteration, achieving O(log n) efficiency.

The algorithm’s elegance lies in its restraint—resisting the urge to check everything, instead trusting in systematic reduction. Whether tuning a 1920s Waterman or searching a million-record database, the principle remains: find the middle, test, and halve your uncertainty.