The EEG records the brain's spontaneous electrical activity.<quoted text> True, that would seeing your dream RR, We know that isn't possible, but the dreams are observed with the EEG, brain waves and such, just not in the "visual" sense that you must be talking about. you said it there, "somewhat measurable" . The observation of dreams are measured and seen by brainwave activity..I think the studying of them is more of why now as opposed to how!
When you're hooked up to one and are listening to music, watching images on a TV, playing a guitar, etc, those things are objective to not only the test person but the scientists as well.
While hooked up to one and dreaming, the dream itself is completely subjective to the dreamer only. The scientists see the REM combined with the electrical activity they see on their monitors and assume that they're witnessing the brain's activity while the test person is dreaming.
The state of dreaming is detectable, the dream itself is not.
Dreams cannot be measured today.