If I ask a physicist to sketch out a solution to a problem, I'll be willing to accept that they may need to look up some constants or formulas along the way, because knowing how to attack the problem and memorizing a bunch of numbers are two very different things; the latter is useful from time to time, but it's the former that I care about if I'm interviewing you.
Why, then, do so many interview processes assume that the ability to, essentially, vomit rote-memorized bits of syntax, argument orders, etc. onto a whiteboard is so important that any "real programmer" should be able to do it on command?
See Tim Bray doesn't know operator precedence rules. It's perfectly possible to live and work and thrive without memorizing everything. This is what being an engineer is all about. Yet the FUD that goes into interview & recruitment processes (as well as other aspects of a programmer's work, but that's a longer story) is astonishing.
Why, then, do so many interview processes assume that the ability to, essentially, vomit rote-memorized bits of syntax, argument orders, etc. onto a whiteboard is so important that any "real programmer" should be able to do it on command?