Beckett was himself unhappy with the manoeuvre that they need to do in the middle to avoid hitting each other, but didn't take the obvious step of putting in a fifth person and using a pentagram. The maths in his original version is interesting. He uses combinations and permutations to have all possible groups of two and three walkers. The geometrical path is also exhaustive in some way. However there are repetitions.
My idea is to have 5 walkers, use the pentagram. This means each walker will trace the pentagram path from their particular point. We will do these circuits:
1 circuit with no walkers
5 separate circuits, each with one walker
10 circuits with 2 walkers
10 circuits with 3 walkers
5 circuits with 4 walkers
1 with all 5.
I wonder how long this will take?
Musically we can give each walker a refrain on a different instrument. This can be added afterwards to the video. We would get every possible combination of the sounds. Hopefully some rather interesting clashes.
For the 10 circuits of 2, I would use: 1&2, 3&4, 5&1, 2&3, 4&5, 1&3, 2&4, 3&5, 4&1, 5&2
For the three, we use their negative. How will the walkers remember this?
Can we film it in several different locations and cut it together later?
Maths footnote.
The shape may be the most interesting geometrical figure there is. Certainly historically. For the Pythagoreans it held within it the secret of the universe. They kept its dark secret to themselves and killed the two people who discovered it. It is possible to date the beginning of disciplined abstract thought from this moment. The discovery that it is not true that "All is Number" shook the sect, and in turn, the world. In my view the most important discovery ever made. I may be overstating this a bit.
Of course, as well as the Golden Ratio and the discovery of the irrational, the shape is the simplest rational sided shape, having exactly 2 1/2 sides.
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