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.
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, fN(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) = V0(sin(w0t)) where the oscillator output v(t) is a perfect sinusoid of amplitude V0 and frequency w0. 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.