How did they get over the catch-22 that if they used the information that Nazis could guess it came from breaking the code but if they didn’t use the information there was no point in having it.
EDIT. I tagged this as mathematics because the movie suggests the use of mathematics, but does not explain how you use mathematics to do it (it’s a movie!). I am wondering for example if they made a slight tweak to random search patterns so that they still looked random but “coincidentally” found what we already knew was there. It would be extremely hard to detect the difference between a genuinely random pattern and then almost genuinely random pattern.
In: Mathematics
Yes I looked to CGPT to form a cogent response… feel free to pick it apart…
The equation used to determine how to conceal breaking the Enigma code is related to game theory and probability, specifically the concept of expected value. The key challenge was to continue decrypting messages without making it obvious to the Germans that the Enigma code had been broken. The British used a strategy to balance the need to act on critical information and the necessity to avoid raising suspicion.
One simplified representation of this problem is:
EV(A) = P(D) . V(A|D) + P(ND) . V(A|ND)
Where:
(EV(A) is the expected value of taking action A.
(P(D) is the probability that the Germans will discover the code has been broken if action A is taken.
(V(A|D) is the value (or cost) of action A given the code is discovered.
(P(ND) is the probability that the Germans will not discover the code has been broken if action A is taken.
(V(A|ND) is the value of action A given the code is not discovered.
The goal was to maximize the expected value, considering both the benefits of acting on decrypted information and the risks of revealing the intelligence breakthrough. This involved careful selection of actions based on the intelligence gathered, sometimes letting minor attacks happen to protect the larger secret.
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