Asymptote is a mathematical concept. it's a line that a curve approaches but never intersects. e.g., the asymptote for y=1/x is a straight line at y=0.
What are you trying to say in plain, jargon-free English?
Maybe this will help you understand what he is talking about.
'Aikido Aikibojitsu and the Structure of Natural Law'
by John Thomas Read
"Surfaces of Intent
Suppose someone is running across a large
field and is suddenly instructed to turn right (make
a right angle turn.) He will find it impossible to do
so; his actual path will be a curve. If he is relatively
weak, the curve will be more gradual; if he is
relatively strong, the curve will be more sharp.
If stronger and stronger individuals were to
attempt this, their efforts would produce sharper
curves, closer approximations to a right angle. At
the same time, the curves of stronger individuals
would become closer and closer together (the
difference between the attempt curves becoming
less and less (Figure 09.)
As the strongest individuals attempt the turn,
it becomes apparent that a limit of curvature is
being approached, a limit that is, in the end, fundamentally
beyond human strength to surpass.
"An asymptotic boundary is a limiting surface that is
only approachable, never crossable, as impenetrable
as hardest steel, yet without any real physical
"On a theoretical level, the set of technical
moves of Aikido and Aikibojitsu are based upon
nage continually moving in such a way as to occupy
space that is denied to uke by asymptotic boundary.
Since uke cannot pass through the boundary, nage
is essentially protected by the boundary's impenetrable,
reflective asymptotic surface.1
"When nage moves in such a way as to deny
uke’s center of mass access, nage’s technical
positions are buttressed by the upstream causal
power of asymptotic determinative structure.
Ueshiba Sensei was a true master of this, able to
control multiple armed attackers by continually
moving to space simultaneously denied to all of
"1. More precisely, it is uke's center of mass that is
blocked by asymptotic boundary. It might still be possible
for uke to reach through or perhaps strike through
the boundary (albeit relatively inefficiently) with arms or
weapon. Note that such a reach or strike would itself be
bound by asymptotic determinative surfaces.
Waveguides are used to control extremely high
(microwave) frequency energy by deliberately
using energy's reluctance to stay within the
conduit's metallic structure. The desire of the
energy to avoid re-entering the conductive walls of
a waveguide provides a means to guide and contain
it. In a waveguide, energy is introduced into the
guidant conduit by a small antenna placed within
the conduit, from which the input energy radiates,
propagating down the waveguide toward the ends,
bouncing off the walls as it goes.
One interesting thing about waveguides is
that, if properly designed, the waveguide’s ends
may be open, but there still will be no loss of
energy from the system! Such a waveguide would
be constructed of an actual tube of metal, open on
both ends. Even if very high levels of energy are
input to the waveguide by way of a precisely placed
transmitting antenna, the input energy will not
leave the waveguide structure through the open
This is because the open ends of the
waveguide act as asymptotic mirrors to the
energy that is travelling toward them, even though
there is no physical mirror, or for that matter any
conductive material there at all. Energy that
reaches the open ends of the waveguide finds in the
‘nothing’ at the end, an infinite impedance, and is
reflected back the other way.1
The notion of asymptotic reflection and
precise placement of the energy generator, is not
limited to electrical waveguides. Aikibojitsu treats
the staff as a resonant entity, a carrier of energy that
doesn't differ in principle from a waveguide.
In Aikibojitsu, choice and location of hand
position, is precisely determined by nodal location
of harmonic preformal wave patterns within the
staff. Control of high levels of energy in the staff is
based upon asymptotic reflection and nonresistant
redirection of energy both outward into
space, and inward to asymptotic ground.
Hand placement and sequencing, with respect
to the waveforms of the resonant staff, is called
Tracking Pattern, a matter considered in detail in
the chapter Technical Aikibojitsu II.
The Asymptotic Channel."
1. Asymptotic reflection from the open end of the conduit
is based upon wavelength of the energy to be contained.
Length of conduit, and precise placement of the
radiant antenna are calculated with respect to the wavelength
of the energy to be contained.
Waveguide (metallic conduit)
Impedance = Voltage/Current
At either end of the waveguide, where current is 0, impedance is infinite,
causing energy to be reflected back the other way."