I agree with Doug’s caution about the problem with ignoring away the “dependent” variables — values f[t] — and paying attention only to “zero”-crossings. As Adrian would point out as well, this already encodes many assumptions on what is a significant event. For example, that’s the basic problem with the “pluck” detector that Navid has coded and used
(More precisely, for a fixed y, the intervals in the inverse image of y under f: { f^(-1)[y] }, assuming f is C0).)
But I have a fundamental reason which is to deliberately lever us away from mono-sense-modality-ness. It’s a very crude but hopefully effective method to get us to pay attention to the phenomenology of temporality.
Keeping in mind the modal bracketing that’s being performed by looking at intervals as Julian’s kit provides.
There are more sophisticated approaches — as Pavan pointed out in an AME seminar last month: well known in signal processing 101 as passing to frequency (time) domain. That raises other fundamental issues when the signal cannot be assumed to have a significant periodic component.
And so it goes. Meanwhile I say, let’s get crude and palpably relevant experiments working first, palaver later! Xin Wei