March 20, 2017

Can manifolds change; or are they invariant?

Filed under: Letters from Ionia — Tags: , — zankaon @ 5:12 pm

Manifold concept can, in a simplified sense, be refered to as just a surface. Thus shape is irrelevant; hence change in shape is not pertinent.

Manifold can be rendered as continuum; that is an inbetweeness quality, wherein one has a mapping of nearby elements of respective sets. Can one even have a minimum number (3) of elements required to define closeness and inbetweeness?

So can a manifold change; that is change it’s continuum? Or add additional inclusive new continua vis a product space construction, giving successively a new higher dimensional space?

Would bifurcation and merging of manifolds be impossible, even of same continua? Exemplified by no merging of hot Jupiters’ with respective star, even over billion of years? Thus also consistent with no coalescence of compact objects? Also would above be compatable with no bifurcating of manifolds, as in eternal chaotic inflation, nor with merging of 3-branes, nor of patches of different manifold arising within a given manifold, nor of non-manifold suddenly appearing i.e. singularity etc.?

Thus are manifolds stable? Thus no creation nor destruction of manifolds. Hence for example, consistent with a divergent set of entangled always disjoint manifolds?

Would all of this seem consistent with concept of manifolds being truculent, and difficult to deal with? As if they want to be left alone; perhaps because they are not capable of change i.e. always invariant? 

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May 18, 2014

Plato’s musings: a larger more general pattern (i.e. form) descriptive of nature?

Filed under: Letters from Ionia — Tags: , , , , , , , — zankaon @ 1:14 pm

In step with Plato’s musings in regards to Forms i.e. patterns, might there be a most general pattern in a description of nature? Entropy, in it’s various renditions, and as the Second Law of thermodynamics, is very general, and survived the quantum and relativistic revolutions. Might one generalize further from such entropy construct; thus perhaps resulting in a broader applicability?

MSM (Modified Set Model) Generality:   an ongoing maximizing (or tendency toward maximizing) of the cardinality of sets (in comparison to alternative scenarios), for all stages and for all scales of manifold(s). 

Even though entropy and information is just locally generated in the model, still the construct entropy summation for over a positive definite MGS instant, has been utilized sparingly as a modified global interdependent variable. However the alleged divergent non-smooth finer than Planck scale, and alleged divergent analytical temporal sequence, such as for System S{UT, …}, and thus set of MGSs (Modified Global Simultaneity) i.e. common cosmic time, could be considered as consistent with such Generality. Thus such Generality would seem to apply to both M3m and M1m manifolds i.e for all scales and for all stages of endless evolving System S{UT, …}.

MSM Generality is considered as an abstraction and generalization from entropy concept. That is, for greater cardinality of a set, then more re-arrangements, and hence increased contribution to alleged always monotonically increasing entropy generation. Likewise allegedly a concomitant ongoing maximizing of information generation in comparison to alternative scenarios; even though entropy can be defined as a loss of information, and information can be described as a loss of entropy. ∆s1≡-∆Iand ∆IΞ-∆s2 respectively, with allegedly always ∆s1>∆I2 .

A practical example of such ongoing maximizing of entropy and information, would be us, and our ingestion of food (energy); most of which is broken down into smaller more numerous parts, and radiated as infrared radiation, in order for us to maintain a constant core etc. body temperature i.e. homothermic. Approximately 5% is utilized as free energy i.e. work, for structure and function (physiology); that is information generation.

What might be further predictions of such a model? The fermion mass spectrum would seem consistent with such MSM Generality. Also the modified black hole with polar jets, would seem consistent, and a prediction of, such model. That is, both scenarios would seem consistent with a further increasing entropy in comparison to alternative scenarios. For example, the increased surface area of such modified BH, with respective polar vertices, would be consistent with an increased entropy generation. Also the constraint of polar jets would seem to enhance information generation.

In addition, the presence of longitudinal polarization and thus mass in the universe, allows for more interactions, and hence is consistent with more entropy generation. Thus obviating the query as to the origin of mass. That is, MSM Generality would seem consistent with always the presence of mass, such as fermion mass spectrum, even at the extreme of rm minimum stage of 3-manifold evolution.

Also MSM Generality would seem consistent with the System rendered as an evolving set of manifolds; and not consistent with the complement (i.e. null set) of such System, in domain of discourse. Thus MSM Generality would not seem consistent with a special condition scenario for the System (i.e. quanta and manifold) or number set, being generated from null set. In fact the null set would represent the minimizing of cardinality of a set; the antithesis i.e. opposite, of MSM Generality.

In context of the model, one might further compare the System and it’s complement, null set. What do they have in common; they both are sets. What do they not have in common? The System set(s) has elements; whereas the complement does not. For the System, one allegedly has MSM Generality: an ongoing maximizing of cardinality of elements of sets; whereas the complement has a minimizing of elements of a set. Also the System has a manifold (i.e. topology) description, in the form of a mixed continuity, consisting of M3m and M1m manifolds; whereas the complement does not have a continuity description. So other than set construct, the System and it’s complement, not-System, would seem to define each other, in the domain of discourse.  TMM

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the opposite of a great truth is also a great truth.

                                                 T. Mann                                                      

October 8, 2013

Just a marble rolling about in a bowl – a sufficient local description? Rationale for 3-dimensions?

Is a 3-surface model a sufficient description of local motion? Might not curved 3-surface (3-space), together with MTC Modified Time Construct Δ2V3L for example, change in rate of Hubble expansion of 3-volume, suffice to describe not only how a 3-volume evolves, but also describe local motion in such 3-surface? Might it be somewhat like ( product space?) so-called neo-Newtonian space and time model, but instead using change in rate of Hubble expansion  ΔH  as cosmic time tc ? Would an equation with stress tensor and 3-curvature suffice? Radio signal delay and curvilinear null geodesics in 3-dimension gravitational field, would still seem suitable. Still limit of finite velocity of light, with increasing inertia, and hence mass. Could one dispense with light cone; hence no space-like and time-like description? Yet still 3-dimensional shortest null geodesic. Could one still have a 3-dimensional black hole description? Although possible deformation of 3-surface, still wouldn’t gravity wave description seem more suitable in 4-dimension? Overall then is such curved 3-surface description simpler and more realistic for a gravitation description? That is, although 4-surface model is useful, don’t we live in an evolving 3-surface?

The latter being consistent with mathematical statement that the number of ways in which to smooth a manifold is greatest in 3 or fewer dimensions. Entropic flavor? Also non-abelian for 3-dimensions (rather than just 2-D) description would seem consistent with MSM Modified Set Generality: alleged ongoing maximizing of cardinality of set for all stages and for all scales of System?

Is our 3-volume regional volume Vyoung or old? The LSS (large scale streaming) of our small cluster (Local Group) is ~630 km/sec, and change in rate of Hubble parameter ΔH is undetected (i.e. linear) out to at least redshift z~ .3-.4  i.e. ~5 billion years? But if always exponentially changing, then never any detectable non-linear change? Likewise for similar duration in future, since far out on log spiral curve, with always alleged exponential decline of change in Hubble parameter. So considering these two factors, there would seem to be a very slow deceleration of expansion, but still a quite high large scale peculiar velocity, a tangent vector to log spiral modified global trajectory in SRM model. Therefore the duration of our 3-manifold (3-volume) would seem to eventually be extremely long (trillion+ years?). Hence we would to seem to be in a very early stage of our ‘universe’, which then likely has a very atypical appearance. Perhaps only hard GRBs (gamma ray bursts from BH jetting, if such colliding (merging?) beams’ accelerator process continues for entire age of ‘universe, even if extreme?) and red dwarfs (fission stars?) detectable for such far future long quiescent stages for our 3-manifold and System? If long persistence for red dwarf fission stars, then terrestrial life would also seem persistent, and unending, even for extremely long duration 3-manifold.  TMM

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