The Noisy-Channel Coding Theorem

Symptom Your link drops 1% of bits. You need reliable delivery, so you triple every bit and take a majority vote. Now an error needs two of three bits to flip, which happens with probability about $3 \times 10^{-4}$ — better, but you paid 3x in bandwidth and the error rate is still not zero. ...

The Two Generals Problem

Symptom You call the payment API. The request goes out. Nothing comes back. Did the charge happen? You genuinely do not know. Retrying might double-charge the customer. Not retrying might drop the payment. There is no third option available, and no amount of care in your client library creates one. ...

Hyrum's Law and Postel's Principle

Symptom You fix a typo in an error message. Four days later a customer escalates: their alerting pipeline greps for the old string and has gone quiet. Or you make a function faster, and a test suite that had been green for two years starts failing intermittently — not because the function is wrong, but because it used to be slow enough to hide a race. ...