Out of curiosity I looked up the meaning of asymptote[always eager to educate myself].Having looked at the answer I have a glazed look on my face. How Tenyu can imply that this tunes in somehow with Aikido I do not know.I defy anyone to make sense of Tenyus article.The first guy to give me a rationale of what Tenyu is saying I will send him /her a coconut[in a figuratively speaking . sense].I await a horde of answers with bated breath. Cheers, Joe.
Tom Read, who applied the concept to aikido, explains it as this: you have a runner running in a straight line as fast as he can. You tell him to turn right, maintaining his speed. He can't make a 90 degree turn at full speed. He has to curve. A stronger person can curve more sharply, but there's a limit to how much turn he can make with his mass and speed, and that curve is the "asymptote". He can't possibly pass that "barrier" described by the curve. So it's not a physical "thing" but it is a physical limit.
Applied to aikido, at least on one level, the attacker comes at you and you move to his side. He can turn toward you, but there's a limit to how sharply he can turn toward you and if you're on the other side of the "asymptote" line, he can't reach you. He can conceivably put his arm through that space, but not with full power because he's working against himself.
I'm not exactly clear on how this applies to the staff.
But I think that's the basic idea.
Best to you.