User blog comment:Nayuta Ito/Ordinal Ruler/@comment-11227630-20180308062944/@comment-30754445-20180308125627

@Hyp Cos

I think the idea is to only use the algorithm for ordinals we haven't yet placed on the ruler. The order in which we do things would still become important, though. So if you want the process to be non-arbitrary, we need to specify this order.

Intuitively, at any rate, it is easy to see how to do things:

In your example, ω2 should go at 1/2 and ω×2 should go at 1/4. The correct ordinal for 5/8 would, of-course, be ω2×2.