Coming up through the ranks, we always wondered why the uphill escape from kesagatame was called the "uphill" escape. We joked that the Kodokan must have been built on a slope, so they must have had an escape for uphill and one for downhill - and probably a sideways escape. Well, that question stuck with me for some years until a few years ago I came upon a satisfactory answer - I don't know if this is the right answer, but it is satisfactory to me.
The uphill escape is the opposite motion in a lot of ways from the bridge&roll escape, so I got to wondering why the bridge&roll escape wasn't called the "downhill escape." Well, it turns out that the bridge&roll is the downhill escape.
When you are lying on your back, in a cross-sectional view from above your head, your chest looks like a hill, sloping downward from your sternum across your ribs to either side. If you plan to roll the guy down the far side of the hill (as in bridge&roll), the easiest way to do it is to start with him on the very top of the hill (resting on your sternum). The easiest way to get them onto your sternum is to turn to face them, loosen their grip on your shoulder a bit, place your sternum against their ribs, and use your free hand to hold them there. Then when they press your shoulders back to the ground, this places them resting on your sternum right on top of the hill, ready for you to start them rolling down the far side when you bridge.
This explanation of bridge&roll as the "downhill escape" makes the naming of the uphill escape make sense. If the holder is not on the top of the hill, you can't roll them downhill without first picking them up onto the top of the hill (inefficient). So, if they are on the uphill side of you, you do the uphill escape instead of lifting them to the top of the hill. But if they are already on the very top of the hill (or if you can get them there easily), then roll them down the far side of the hill (bridge&roll).
Photo courtesy of Simmr
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Patrick Parker www.mokurendojo.com