I bet It's the phi button sold it for you. :-)
Weird, isn't it. As noted in the blurb - golden ratio, visually aesthetically appealing, occurs all over the show in nature, but in music we are familiar with consonance and steady rhythms, all depending on simple arithmetic ratios. And the golden ratio is, in a very reasonable mathematical way, as far from a simple ratio as you can get. But the little video clip of it in use does sound good. My guess is that he is moving the taps a little forward or backwards to meet approximate multiples of phi mod 1 or somesuch so that the timing is a tiny bit looser and not so machine-rigid sounding, and that the choice of relating this to the "mystical properties" of that particular number was so some extent arbitrary.
(Also, oops - I now realise I was confusing the T-Resonator, which I had chanced upon some while ago, with another Jomox device I saw at the same time - the Resonator Neuronium (http://www.jayemsonic.de/homeenglish.html). Onlne shop- with yT demo here (http://www.jomox.com/product_details.php?lang=2&category=2&product_id=9).)
Anyway, enough drooling over technoporn. It's not a first pedal. The fact is there is a lot of good mileage to be had from the most basic of delays. Peter Pringle recently described the theremin as an incomplete instrument, in the sense that a complete instrument can produce rhythm, melody and harmony at the same time. Any delay or looper "completes" the theremin, in a limited way, (i.e. with the sort of limitations that can have you seriously consider spending more than the cost of the instrument on an echolution if you're that way inclined) and, with the naturally occurring pitch variations of the theremin it will give you access to interesting microtonal interactions - cluster drones, beat frequencies, and celeste-like sounds. Which is why, Goat Punishment, if you're still reading this thread, I think you'll get on fine with your Dan Echo. :-)