Gustafson's Law and the Universal Scalability Law

Symptom Two measurements that both look like they break the previous post. The first: your Spark job takes four hours on ten nodes. You move it to a hundred nodes and it still takes four hours — but it is now processing ten times the data. T081 said the ceiling was 20×, and nobody hit a ceiling. ...

Amdahl's Law

Symptom The profile was unambiguous: 94% of wall-clock time in one loop, and the loop’s iterations are independent. You parallelise it across sixteen cores, the flame graph flattens exactly as predicted, and the end-to-end time goes from 40 seconds to 17. ...

No Universal Lossless Compressor

Symptom Someone sends you a pitch deck. The claim is a compression algorithm that reduces any file by a guaranteed ratio, and — this is always the tell — that it can be applied repeatedly. Four gigabytes down to one, then one down to two fifty, and so on until the whole film is a few hundred bytes and a clever decoder. ...

The Pigeonhole Principle

Symptom You are asked to build a cache key. You have a 64-bit hash, and someone on the team says: “collisions are basically impossible, there are eighteen quintillion values.” Or: your service assigns short IDs to uploads, six characters of base-36, and you are wondering when you need to worry. ...