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To illustrate Ed's teaching approach, suppose we want to perform seven events in the time of five beats. (If this would be too easy for you, imagine doing this on an accelerando, or against dotted quarters, or further subdividing the middle three events, or whatnot. It is hard to imagine being so good at 7:5 that this is never worth revisiting.)
To start with, we pull out what is probably the most frequently used concept in
the book: the HAMn (pronounced “ham"), an acronym for Harkins'
Alignment MNemonic. This is a sequence of numbers that count how many
(equally-spaced) events should fall on or after each of the five beats. If
there are, for instance, 60 beats per minute (at 1, 2, 
, 5 seconds), the
events should approximately fall at times 1, 1.71, 2.42, 3.14, 3.86, 4.57, and
5.28. The pnob, or Presumed Next On-Beat (the acronym is pronounced
with the “P" silent) arrives at 6 seconds. The HAMn is 21211, that
is, there are 2 events on or after the first beat (1 and 1.71), one after the
second, two after the third, and one each after the last two.
To perform this we can start by performing 3:2 (Hamn 21) followed immediately by 4:3 (Hamn 211). This isn't exact but is close enough that many listeners won't hear the difference (one year when Ed demonstrated this, only one student out of about 12 heard the truth). Specifically, the fourth event of the seven falls at time 3 instead of 3.17, 1/7 beat early. The first four are spaced too closely together and the last five (from 3 to the pnob at 6) are too far apart. We fix this with a noodgie (nudge): simply perform the 3:2 a bit slower and catch up during the 4:3. Once you get the eight time points (the seven onsets plus the pnob) evenly spaced, you have mastered 7 against five.
This is not quite as easy as it sounds since it involves carrying out two tasks (performing 3:2 and 4:3 inexactly, while simultaneously listening for the even spacing of the eight attacks). Developing this ability to listen simultaneously to two or more aspects of a rhythm, in real time, is a central aspect of the technique that Ed's book seeks to impart. For example, in the the book's first exercise (106, Pat 1st), although the left hand plays a steady beat, that beat is unfortunately a dotted eighth note so that everything in the right hand sounds as triplets—including two written triplets which are four and two ninths of a beat. If there were three of you, one could be listening to the dotted eighths and the bar lines, another in duple time (4.5 beats per measure except for one 6-beat one), and a third could verify the uniformity of, first, the repeating 5-quarter-note figure that hockets against the bar lines in measures 5-8, and later the 2:1 division of the first triplet compared to the second one.
Ed himself can pick up any of these exercises and perform it on call, as a student can learn by referring to any one of them out of context. Before the conversation proceeds Ed will helpfully freshen our memory of it.