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Self-reference systems http://www.ltn.lv/~dainize/MathPages/self.systems.pdf Dainis Zeps University of Latvia Institution of Mathematics and Computer Science 2007. Self-reference systems in nature Self-reference system, or idem (pron. ’aid ə m) =

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Self-reference frameworks http://www.ltn.lv/~dainize/MathPages/self.systems.pdf Dainis Zeps University of Latvia Institution of Mathematics and Computer Science 2007.

Self-reference frameworks in nature Self-reference framework, or idem (pron. âaid É m) = <state in se | state particula collidens > Particle in se does not know anything about the external world unless impact happens with other molecule which causes molecule, now in state particula collidens, to think about the external world. Molecule becomes acquainted with about world outside itself Particula collidens Particula in se meditans does not know anything about world outside itself

Idems in PC programming Procedure as self-reference framework or idem = <set of directions: particula in se meditans | through variablesâ association with other system body: particula collidens > The angle meditans for particula in se is a result of calculation, i.e., instructionsâ execution by PC running, or, if there should arise an occurrence of procedureâs invariant consistent comprehention of truth. Technique in exceptionally characteristic path swings to act naturally reference framework with life in itself, i.e., calculations inside of itself, and time to time exchanging data with external world, i.e., worldwide project body.

Quantum self-reference frameworks Lifetime for idem = every single conceivable state particula collidens ; For idem <s 1 |s 2 > relating quantum idem <s 1 | lifetime = all conceivable s 2 > Quantum self-reference framework = < particula in se meditans | particulae collidendae or collidentes > Aspect meditans include experience of lifetime. Angle collidendae =particles that ought to be met, is interchangable with collidentes = particleâs self states by crashes in lifetime. Taking after Feymanâs way vital idea we sum up lifetime history of numerous particles to one particleâs life: see next slide. At the point when idem runs every single conceivable state through which it interfaces with world outside, it as though characterizes its essential amount called quantum idem .

Feynmanâs way essential methodology Having numerous particlesâ (occasions) framework, we may consider each particleâs lifetime story as one particleâs way vital and all particlesâ lifetime story in the framework along these way integrals giving one possible molecule with numerous beginnings and closures (for single particles) where by mix we didnât take single particles more than ones. What we got? The lifetime story of the framework is as though one way necessary of a solitary (multi-) molecule unless it begins in each poin of the complex it lives in and comparatively closes in every conceivable purpose of this complex. Further we see that by making so as to associate end with beginnings, i.e., complete structure patterned, we can credit to our lifetime structure decent scientific structure unless we don't request that what sense ascribe to this recognizable proof or basically say that in nontemporal angle it doesnt much matter what such distinguishing proof could mean. Beginning to keep running from each purpose of the space along each way in the space and completion with each point, we get the same result in the event that we measure these runnings by crashes with the same particles doing likewise work.

Example of quantum particleâs lifetime story Let us have molecule moving in the field, where field be imitated by multiparticle: Let us characterize important lifetime story of the quantum molecule; Particle meditans lives in, say, Euclid space with no field and collidens is guided (by some other molecule) along geodesics of the genuine field Elementary idem is <...|action of the field depicted as association of two single particles>; Quantum idem is <...| particleâs way fundamental over the lifetime story> State meditans is really field in Euclid space, i.e., with Cartesian geodesics Quantum idem mirrors in infinitisimal scales real fieldâs activity as though blended with little bits of Euclid field. What might it be able to give for counts? Perhaps it is as of now common for scientists, yet it could be additional inspiration for them to discover comparing easier idems: for this situation: the activity of two basic particles in type of some power which give s as way vital over lifetime story the genuine field activity. In this manner, for quantum idem field there ought to exist basic activity: power between two particles . For idem power we ought to get quantum idem field of this power activity.

Quantum idems in arithmetic Let us have some class where items are states in se and circular segments are states particula collidens : For instance, for gathering hypothesis state in se is âelementâ and state collidens is âgroup operationâ,then for quantum idem ought to stand idem bunch. This is not yet definition on the grounds that we must indicate state âgroup operationâ which ought to be idem itself. Classifications best of all express thought around quantum self-reference framework. Let hypothesis be envisioned as an idem. It as of now is quantum idem in light of its inclination to be dynamic and relevant to its lifetime statesâ set. This brings up an issue: would we be able to dependably discover relating rudimentary idem for any hypothesis considered as a quantum idem? On the off chance that quantum idem is identic with itâs basic idem then it would be as of now a decent arrangement, i.e., where lifetime set is minor. Hypothesis in science is a quantum idem as a result of its deliberation from more straightforward realities: would we be able to perceive those less difficult truths to say where from our hypothesis came and detail them as idems either? Its an issue.

What is arithmetic? Science is manufactured from quantum self-reference frameworks. Science is not fabricated from prophet frameworks, i.e. âcomplete picturesâ from nature, or, we don't have resourses for such observation. It is not barred that arithmetic could needs some rudimentary prophet frameworks, say, number one or zero keeping in mind the end goal to manufacture a few frameworks, e.g., for whole numbers. Science is fabricated from refinements and their speculation - quantum qualifications that would and ought to remain for our most basic deliberations. We contend that science is fabricated from straightforward refinements, i.e., idems and for the most part broad deliberations in arithmetic are quantum qualifications, i.e., quantum idems. Really, it may end up being some broad pattern just; we don't have the foggiest idea, what it could mean exactly.

What this all speaks the truth? Is the self-reference systemsâ state of mind: a sort of theory? giving consequent paradigmatic ways to deal with gainful supposing in arithmetic? giving some consequent strategy, that ought to be produced and/or discovered where it as of now is available in arithmetic, so as to work with, e.g., in training of science? We trust that things depicted here could discover some application to training of arithmetic. Give us a chance to see the thought's improvement. Could this methodology of self-reference frameworks and their lifetime stories give some advantage for science? We trust that this mentality as of now works in some aberrant way, yet we speak the truth to realize it in the predetermined here way. We are for timeâs rejection from our thinking. Arithmetic does it. Do we know this? Arithmetic is cleverer than its developers.

Let us have a lifetime story of 4 balls portrayed as a multigraph where to one side it can be coded as combinatorial guide, yet to one side, without understood connections or sinchronized occasions, ought to be coded utilizing groups of stars, i.e. combinatorial guide of higher request, both being two approaches to depict multigraph. see Lando Sergei K., Zvonkin Alexander K., Graphs on Surphaces and Their Applications. Springer, 2003. This lifetime story of four ballsâ shared impacts can be considered as one idem too, unless we are enticed to consider it as an independent or prophet framework. Four ballsâ crash story can be charachterized by multigraph that may be further separated by more particular combinatorial structures.

Manifold of reality comparing to lifetime story Let us have two holomorphic capacities such that they are negligible that have the multigraph relating to lifetime story in two conceivable blueprints as an invariant in the sense ramified covers are depicted in Riemann geometry [see Lando, Zvonkin]. The two potential outcomes relate to two posibilities to synchronize occasions by single idems and in diverse models we may have distinctive synchronizations; for us here it doesnât matter much. Give us a chance to call these capacities manifolds of reality relating to the lifetime story. Discrete structure that portrays the lifetime story can be further described with a smooth capacity that gangs this discrete structure as some invariant. This smooth capacity we are going to call complex of reality.

Lifetime stories and models of universe Either four ballsâ hitting history or the same number of occasions as in lifetime of entire universe, we utilize the same discription for the idem of lifetime and relating to it the complex of reality. We bless our universe with speculation angle considering idems that constitute it having viewpoint meditans . Why? Our universe model is urgently without time viewpoint at all aside from representing causal groupings and notwithstanding permitting cycles. Keeping in mind the end goal to represent this nontemporal angle we bless our model with viewpoint meditans and, taking Descartes cogito hence aggregate model in record , cogitans thus existens perspective . In this way, keeping in mind the end goal to better express nontemporality and closiness in oneself, and materialness to intellectual regions, e.g., in arithmetic, we talk about cogitans hence existens model of universe, i.e., the universe that is as though considering in oneself. We consid