Interesting insight. My attempt at canonicalization would be that, therefore, the orientation of the frontal and sagittal planes (attitude and azimuth of the heads) are functions of the degree of engagement. Engagement is a measure of the alignment of those vectors.
Galton was a brilliant thinker and a deeply horrible human being.
I miss the Futility Closet podcast. Well worth listening to their back catalogue. IIRC one of the founders had health issues. I hope they are doing ok now.
One of my Crazy Fringe Ideas that anybody who wants can take (because I've got no practical way of monetizing this) is having large video conferences analyze the facial expressions of the participants, and synthesizing it into a small number of representative faces for the presenter to see how the crowd is taking it. For instance, if everyone is engaged, the sample faces would be engaged, but if some people started to drift away, one of the faces would become disinterested. There's a variety of interesting uses this could be put to to help a presenter at least somewhat engage with a crowd as if they were more live and in person.
Of course, this may turn out to be a case of too much truth shattering too many illusions. Maybe we can have a surreptitious CEO mode where all the faces at the multi-thousand-person "all hands" meetings just automatically are smiling and engaged. "Oh, yes, they were all hanging on your every word and deeply excited about your new initiative to engage in thought leadership for advancing synergy in the world market."
You might like the plot of the (pseudonymous Neal Stephenson collaboration novel), "Interface", by Stephen Bury. There's definitely a parallel to what you're describing applied to politics.
I have a friend who worked in computer vision at Carnegie Mellon and talked about automatically estimating focus levels. I'm not aware of any successful product that gathers these metrics though. Here's some papers from a quick web search:
They announced closing up shop — but apparently that sabbatical lasted only a handful of months. (Sadly, I had stopped visiting in the interim and didn't realize they were back until recently.)
