Dualities - Cs.purdue.edu
Dualities(Each duality has its particular characteristics fortransformation back and forth)Material / InformationPractice / TheoryWave / ParticleFourier transformProjection (reversed by generalised inverse matrix)Real situation / Language descriptionTranslation (Russian/English language)Phenotype / genotype (Protein / DNA)
Test of theory is practice. A good theory has Survival value.
Physical WorldInformation structuresArrangements of atoms MathematicsSuperposition of wavesLanguageInteracting systemsData structures(both dynamic and static)ParticleWave function (“the unreasonable effectiveness of mathematics” Eugene Wigner 1960)
Orthodox (“classical”) crystallography- equilibrium structures- ‘absolute’ identity of units and of surroundings- long range order, 230 Space groupsBeyond crystals- dissipative structures, energy fluxes, SYSTEMS- local energy minima located by information (address)- curved structures; hierarchic structures; process- local order; local symmetries; approx. identity
Observation of structure (static and dynamic)Orthodox crystallography- X-ray crystal structure analysis (XRD)Generalised structure analysis- Electron microscopy (and AFM developments)(Resistance to novelty: resistance of microscopists toAbbe’s theory: late recognition of Zernike’s phasecontrast microscopy as extending Abbe’s theories.Resistance of XRD people to use of phases ofscattered radiation).
A CRYSTALis a structure, the description of which is very muchsmaller than the structure itself.(Most general definition)(The International Union of Crystallography give a retrogradedefinition of a crystal as a structure giving a diffraction patternwith discrete points. That is, with periodicities) Thischaracterises a structure by the method for observing it andimposes the characteristic limitations of the observer.
Structure of Mg32(Al,Zn)49 found by Pauling’s “stochastic”method but where is the information ? Is there a “gene” ?
Aspects of the physical world may be represented asmathematics.Informational structures may be represented as physicalstructures.Manipulation in the physical world - trial and error,experiment, measurement.Manipulation in the informational world– discussion, computation, “data mining”. (e.g. If a set ofassumptions leads to a contradiction then something iswrong.- A. Turing and the Enigma machine)
“DIALECTICS”the emergence oftruth from theconfrontation ofopposing arguments- resolution withcritical experiment(following FrancisBacon) as the judge.DIALECTIC Method used by Ancient Greeks, Jesuits, G. F. W.Hegel, Marx and Engels, and doctorate examiners, Proposer v.Advocatus diaboli, leads to a solution at a local optimum.
Dialectical DevelopmentReal SpaceRepresentational SpaceMATERIAL INFORMATIONProjection ComparisonManipulation Restoration
Informational structures:(above) the Ogham alphabet.(Ireland 9th cent.)(economy!)(up. right) Mayan inscriptionfrom Mexico. (redundancy!)Abacus - metastable structure
A.D.Booth and his machineat Birkbeck College, Londonabout 1952“The Computer”- for the manipulation ofinformation and thecontrol of machinery
Energy landscapesWaddington’s epigenetic landscapeN-dimensional Configuration space(with increasing complexity a phase diagrambecomes useless and is replaced by anaddress in configuration space).Morse characterisation of its topology.
How to search for solutions:EVOLUTION has evolved because it is the bestsystem for exploring configuration space. Itrequires a separation between structure anddescription, which engage in a dialogue.The GENETIC ALGORITHM. (JohnHolland)(the mathematical equivalent of biologicalevolution)but, will quantum computing go straight to theanswer ?
DARWINIAN EVOLUTION – ininformation space“How do you get so many good ideas,Dr. Pauling ?” - “I just take all my ideasand throw away the bad ones”.
Curved surfaces (excluded by periodicity)- two sides, which may be structurally different- importance of micelles defining inside and outside- curvature componentsbend, twist, splay from local forces- Gaussian curvature k1 k2 (k 1/(radius of curvature))- Mean curvature (k1 k2 )/2- Topology (Euler characteristic, etc.)
Living materials- symbiotic and hierarchic mixture of structural andinformational components- flux of energy and material structuration- an INSIDE and an OUTSIDE (Vesicles)- “It is not birth, marriage, or death, butgastrulation, which is truly the most important timein your life.” (Lewis Wolpert, 1986) ( local controlof curvature leads to morphogenesis.)
A. Kleinschmidt(1962)T4 bacteriophage(with negative staining)The first visualisation ofan informational structure
Poliomyelitisvirus particleR.Franklin and A.Klug, 1958(model by JohnErnest) (A virusrepresents ashort circuitdown an energygradient in thebiochemicalpathways space.)
TobaccoMosaicVirus[TMV](Rosalind Franklin,Aaron Klug, KenHolmes)(Model by JohnErnest 1958)(The informationalsub-structure hasalso a structuralrole.)
What information is there in the structure ?What information is there in theinorganic structure?Factor analysis of data banksPlace in phase diagramConformational entropy ? W. H. Zurek ?Algorithmic ComplexityDescription of structureCellular automaton as a generalisation oflocal interactions in an energy flux De-localised information
Systems Belousov-Zhabotinski reactionsCellular automata (Wolfram)Chaotic solutionsVirusesCraig Venter and “Synthia”Robotics (nanoscale upwards)Self-reproduction (v. Neumann)(separatereproduction of material and of program)
FreemanDyson’sVision(New York Review of Books 19 July 2007)(N. Goldenfield and C. Woese, Nature, 445, 369, (25 Jan. 2007)Dialogue of material/information is at a newstage. NanotechnologyBoth information and material are transmittedand transformed with unprecedented speedthrough the actions of human beings. Perhapseven, there may be eventually no otherspecies.Human culture is transmitted as open source,non-Darwinian software.
Three stages over 4 billion years1) Initial period of ‘life’Archaeo-bacteria with common gene pool(rapid ‘horizontal gene transfer’)(“Primitive Communism”)2) Sequestration of genes in individuals.Slow Darwinian evolution.(“Private intellectual property”)3) Modern synthetic biology. Control of genesand proteins. Rapid production of novelorganisms in biological eco-systems(“Utopian communism ? Totalitarianism ? Global capitalism ? ”)
The Quantum Substrate– perhaps solution and synthesis Observer subsumed into landscape ?Evolution of self-consciousness ?Wave/particle duality resolved ?Artificial intelligence ?Quantum computation, (A. Zeilinger) ?
Now St. Petersburg, August 2007 !
R.Franklin and A. Klug, 1958 (model by John Ernest) (A virus represents a short circuit down an energy gradient in the biochemical pathways space.) Tobacco MosaicVirus [TMV] (Rosalind Franklin, Aaron Klug, Ken Holmes) (Model by John Ernest 1958) . through the actions of human beings. Perhaps even, there may be eventually no other
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