The Semantics of Jitter in Anticipating Time Itself within Nano-Databases Michael Heather and Nick Rossiter CEIS, Northumbria University, Newcastle NE1 8ST /

INVITED SESSION 6.3. THURSDAY AUGUST 9, 8:30-12:30, ROOM 138 Logic and Semantics in Front of Nanoscale Physics Chairman: Salvatore Santoli - Co-Chairman: Peter J. Marcer Dialoguing – Delusion or Physical Reality?, Salvatore Santoli (Italy) Intent, Future, Anticipation: A Semiotic, Transdisciplinary Approach, Hellmut K. Loeckenhoff (Germany) Semantics and Selforganization in Nanoscale Physics, Mikhail B. Ignatyev (Russia) Computers, Nanotechnology and Mind, Bertil Ekdahl (Sweden) The Mind of the Scientist, Otto van Nieuwenhuijze (The Netherlands) The Semantics of Jitter in Anticipating Time Itself Within Nano-Databases, Michael Heather, Nick Rossiter (United Kingdom)

Nano-technology Development of nano-technology –careful examination of anticipatory systems at this small scale –in particular characteristics of time at the boundary between classical and quantum domains quite critical for the advancement of the new technology

Nature of Time Time is not absolute –even in classical subjects like navigation and dynamics –idealised concepts used to iron out fluctuations solar time and Newton's dynamical time –astronomy cannot relate sideral and solar time by exact formulism relies on experimental methods. International Atomic time is a convention –relying on a naturally occurring but arbitrarily selected frequency

Temporal Problems Any temporal component for anticipation –even more problematic for anticipatory systems of modern physics Einstein postulated in his Special Theory that –simultaneity is indeterminable and in 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 –Everett’s Theory of Parallel Universes –variety of bubbling universes

Time is Data 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

Russell on Time as Logic Dr. Whitehead, at this stage, persuaded me to abandon points of space, instance of time, and particles of matter, substituting for them logical constructions composed of events. In the end, it seemed to result that none of the raw material of the world has smooth logical properties, but that whatever appears to have such properties is constructed artificially in order to have them. B. Russell, The Principles of Mathematics, 2nd ed, p.xi, 1937

Effect of Gödel 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 Classical methods of formal mathematics give only weak anticipation –subject to Gödel undecidability –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

Interoperability of Time Domains 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

Clock Domain A Clock Domain B Clock Domain C Clock Domain D Clock Domain E Example of Problem: Multiple Time Domains and Signals transferring Data from one Domain to Another From Cohen, D, & Banks, C, Taking the Risk out of Multi-clock Design, Electronics Weekly no p (2007).

Industry Practice Practice in industry –treat uncertainty as noise –provide a clock conditioner designed to generate an ideal time based on a classical model for a sinusoid oscillator additive phase noise,  N (t): [equation 2.28 in the National Semiconductor’s Clock Conditioner Owner's Manual for winter 2006]

Time Correction It follows that the (weak) anticipatory time correction is: Amplitude noise in addition to additive phase noise may be expressed as:

Amplitude Noise Amplitude noise in addition to additive phase noise may be expressed as: with the optimal behaviour given by –v(t) = V 0 (sin(  0 t)) –where oscillator output v(t) is a perfect sinusoid of amplitude V 0 and frequency  0 This provides a higher order component of anticipation

Jitter Capture of time data in databases at this level –exhibits the limitations of weak anticipation –derived by statistical data modeling Noise gives rise to jitter –measure of the displacement from the anticipated phase cycle Jitter has two components: –deterministic –random Jitter causes problems which are difficult to cure

Cycle-to-Cycle Period Jitter This figure from Clock Conditioner Owner’s Manual

Deterministic/Random Deterministic –relates to behaviour that is predictable and determinable Random –relates 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 –fundamental difficulty is that jitter is represented using numbers giving rise to undecidability and incompleteness according to Gödel’s theorems In single local time system, jitter may not be a problem –inevitable offence of Gödel though in multiple time systems as interoperability is needed with higher-order operations

This diagram and next from Clock Conditioners Owner’s Manual Cycle-to-Cycle Period Jitter

Period Jitter

Categorical Form Advanced categorical form –calls for the use of adjointness –time jitter is measurable as unit of adjunction counit of adjunction These measures (units) are not a number and are therefore Gödel free

Unit/Counit Measures Similar to those used to achieve simultaneity in database transactions –Rossiter, Heather & Sisiaridis in Process as a World Transaction, Proceedings ANPA 27, (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. Undecidability –as in transactions with non-deterministic aspects –cannot completely decide how a transaction will behave –random part is undecidable: part of our understanding

Adjointness between Functors F and G mapping Categories L and R F ┤ G

Composition Triangles in Detail a) unit of adjunction  ; b) co-unit of adjunction  Coherence (true time) is when two triangles are satisfied

is eta from η from reference time view ε from actual time view Period Jitter from Categorial Viewpoint

Reference Time L Actual Time R F G η: 1 L  GF(L) ε: FG(R)  1 R Categorial View for η (unit) and ε (counit) of adjunction

Adjointness between Functors F and G: Use of Multiple ‘Cycles’ Three ‘cycles’ GFGFGF: to measure unit in L; counit in R; overall consistency. Performed simultaneously.

Can also be viewed as Monad Monad = where T = GF Comonad would look at dual perspective (FG) CGNR1: Could put categorial version of magazine diagram from earlier CGNR1: Could put categorial version of magazine diagram from earlier

Summary Clock article is example of problems with jitter Different time domains gives problems in interoperability Should be adjointness between the time domains Coherence is achieved when two triangles (for unit and counit) are satisfied Potential of 3-’cycle’ Approaches