cannot be accurately measured

I want to clarify that the “cannot” here refers not to the inadequacy of our tools (which hypothetically could have been fixed in the future by building better tools), but by a fundamental prohibition of the quantum mechanics theory. Practically, the single-photon lasers and detectors used here are like 90%+ efficient - plenty good enough to distinguish between the two monkey scenarios. But some observables in quantum mechanics are “orthogonal” - you can measure one or the other, but not both at the same time - the math will not allow it. The typical example of that is “position” and “momentum” of a particle.

The math is quite beautiful actually, the analogy I’d use is something like asking “Which way is east at the North Pole?” In your head you can either know “This direction is east.” or “I am standing at the North Pole.” but you cannot hold both pieces of knowledge in your head at the same time.

The orthogonal observables in this experiment are the “which-way top/bottom slit” information and the “which-interference-category Pattern 4/Pattern 5” information. It’s even more beautiful in the delayed choice quantum eraser experiment that I was ranting about here. There, both pieces of information are stored orthogonally in a single photon. You can choose at a later time to either measure it one way, which will tell you the which-way info, or in a different way, which will tell you the interference category info, but there is no hypothetical way to measure it in both. The only way you can get the category info out to allow your computer to draw the interference pattern is if you guarantee that the which-way information has been irrecoverably erased. It is as if the whole universe conspires to censor this information from you! But it’s just the consequence of the math rules in use.