When moving from the artificially perfect world of (excluded-middle) mathematics back into the real world, we encounter significant changes to our expectations for how things work. Or, as seen from the other directions, pure math feels "liberating" because we don't have to worry about all the pesky details associated with including middles that happens in real life. There is an interesting analogy to this transition found in networking lore:
L. Peter Deutsch’s 8 fallacies of distributed computing presents a set of incorrect assumptions which many new to the space frequently make:
- The network is reliable.
- Latency is zero.
- Bandwidth is infinite.
- The network is secure.
- Topology doesn’t change.
- There is one administrator.
- Transport cost is zero.
- The network is homogeneous.
https://en.wikipedia.org/wiki/Fallacies_of_distributed_computing