I recently read a book about the Enigma code machine that the Germans used in World War II (Seizing the Enigma: The Race to Break the German U-Boat Codes by David Kahn). Famously, the British cracked this code and used the information gained thereby to help win the war. That’s the shorthand version of the story, anyway. But the long version of the story is, as you might expect, more subtle. Did cracking Enigma really shorten the war? Here’s a related but little-known fact: The British and US navies often used shoddy encryption that German analysts cracked on a regular basis. Why didn’t that help Germany win the war? Why aren’t there movies and museums about clever German analysts?
It turns out that much of the initial work cracking Enigma was done by some brilliant Polish mathematicians early in the war, before Poland was invaded and defeated. This work was eventually passed on to the British to jumpstart their own cryptanalysis efforts. On the eve of the German invasion of Poland, Polish cryptanalysts were essentially reading the German battle plans and sending them to the Polish high command. Why didn’t it help?
It’s easy to think that accurate information is the only thing that matters. But it’s one thing to possess information. It’s another thing entirely to be able to capitalize on it. The Polish army was so weak relative to the Wehrmacht, that even perfect information about the motives and dispositions of their enemy was ultimately of little use. They lacked the ability to capitalize.
Some information is trivial. You can act on it, but it doesn’t matter. Some information is vast. Knowing about it doesn’t allow you to take action that matters. Only in the small subset between these extremes can you change the world. There is a “Goldilocks Radius” for information. Too small, too big, too bad. It needs to be just right. What do you know that matters, given your ability to act right now?
Boil it down, and you end up with something like Reinhold Niebuhr’s Serenity Prayer: “God, grant me the serenity to accept the things I cannot change, the courage to change the things I can, and the wisdom to know the difference.” The value of what you know depends on the nature of what you can do. Whether you view this with serenity or wretched angst is something else entirely.
Did cracking Enigma shorten the war? It certainly made a difference. But the final answer is more equivocal than you might expect. The most important factor is that Allied force of arms put them in the position for that secret knowledge to make a difference.