The Semantics of
Jitter in Anticipating Time Itself within Nano-Databases

Symposium 6: Logic
and Semantics in Front of Nanoscale Physics

Michael Heather and
Nick Rossiter,

CEIS, Northumbria
University, Newcastle NE1 8ST.

http://computing.unn.ac.uk/staff/cgnr1/

The development of
nano-technology calls for a careful examination of anticipatory systems at this
small scale. For the characteristics of time at the boundary between classical
and quantum domains are quite critical for the advancement of the new
technology.

It has long been
well recognised that time is not absolute even in classical subjects like navigation and dynamics where idealised
concepts like mean solar time and Newton's dynamical time have had to be used
to iron out the fluctuations. Astronomy cannot relate sideral and solar time by
an exact formulism but has to rely on experimental methods. International
Atomic time is a convention relying on a naturally occurring but arbitrarily
selected frequency. Any temporal component for anticipation in anticipatory
systems becomes even more problematic for anticipatory systems of modern
physics. Einstein postulated in his
Special Theory that simultaneity is indeterminable and in the General Theory of
Relativity that time is not independent of space and matter. Quantum Mechanics
places time uncertainty deeper within the laws of physics. String theory makes
the dimension of time only a potential particle. The time between multiverses
is not related whether in Everett’s Theory of Parallels to our Universe or in
the variety of bubbling universes.

Time therefore is
the data of the Universe and belongs in the semantics of its extensional form.
At the boundary between classical and quantum behaviour the uncertainty of time
data becomes a significant effect and this is why it is of great importance in
nanotechnology. The Theory of Anticipating Systems provides a method for
anticipating data classically with respect to time. In nano-phenomenon where
different time becomes apparent it is necessary to anticipate time data
independent of time itself (or themselves). Classical methods of formal
mathematics give only weak anticipation which is subject to Gödel
undecidability and consequently of limited use for nanotechnology which needs
the techniques of strong anticipation. To escape the clutches of Gödel
undecidability it is necessary to advance to mathematical categories beyond the
category of sets.

A prime example in
current nanotechnology is the interoperability of different time domains in the
ASIC hardware presently available. A lack of synchronicity results from many
different clock signals. The practice in industry is to treat the uncertainty
as noise and to provide a clock conditioner designed to generate an ideal time
based on a classical model for a sinusoid oscillator additive phase noise, f_{N}(t):

_{}_{}

[See the equation
2.28 in the National Semiconductor’s Clock Conditioner Owner's Manual for
winter 2006 at http://www.national.com/appinfo/interface/files/clk_conditioner_owners_manual.pdf.with the usual
symbols]. It follows that the (weak)
anticipatory time correction is:

_{}

Amplitude noise in
addition to additive phase
noise may be expressed as:

_{}

with the optimal behaviour given by v(t) = V_{0}(sin(w_{0}t)) where
the oscillator output v(t) is a perfect sinusoid of amplitude V_{0} and frequency w_{0.} This
provides a higher order component of anticipation.

The
capture of time data in databases at this level exhibits the limitations of
weak anticipation derived by statistical data modeling. The noise gives rise to
jitter which is a measure of the displacement from the anticipated phase cycle.
Jitter has two components: deterministic and random. The former relates to
behaviour that is predictable and determinable, the latter to phase noise.
Jitter causes a system to behave in an unpredictable fashion, a severe and
expensive problem for anticipating how time will be handled. A fundamental
difficulty is that jitter is represented using numbers, giving rise to
undecidability and incompleteness according to Gödel’s theorems.

The advanced categorical form is seen to call for the
use of adjointness where time jitter is measurable as the unit and counit of
adjunction. These measures are not a number and are therefore Gödel free. They
are similar to those used to achieve simultaneity
in database transactions as described by Rossiter, Heather & Sisiaridis in
Process as a World Transaction, Proceedings ANPA 27, 122-157 (2006). In the
categorical view, time is part of the data and is with the system, not an
external parameter. To anticipate time is a semantic operation, not a syntactic
one.