Reflections on phenomenic descriptions of the real part 1

Idea and conceptualization of the mathematics and the content behind the post : pondering physics, the mechanisms behind every possible system, the boundaries within which all things become true (the manner that the system proves itself by its own principles and since the system is contingent by itself,the way it proves itself is the principles to which he is in and for itself). But what does it mean to give a consistent self-critical system to physics, to motion? What does it mean to truly impart motion to the system, or give it existence? Since to exist is to exist in time, and to move means to have time, to be time, to produce time, to be beholden by time,to behold time,to create a worldline with local/global increments in time/by time—a way fold,to emerge and ascend from the inner abyssal nothingness (and yes, that's an important aspect of the response within the question itself).

For me, time has always been something to contemplate, to reflect upon. It seems that all cycles of existence come in packages of indexed continuous or discrete congruences of time, space, whatever loci's (particle-like), global (field/wave realization), and global/loci relations (curvature or second form), like quantum  geodesics (quantum states of spacetime itself) merging with their other comrades, friends of mutual nature/contextual relations. Not just thinking about time, but information—the singularity of perception or (most of the time, I mean logically non-exclusive 'or') apperception (the form of information is a touch with the holy unity; information is purely relative in its definition, a theorem on digression).

When I read things like "it from bit" from Wheeler and the quantum; the thermodynamic, marasms of the 20th century, all attempting to discern how entropy works, what entropy means to be, what information is (Shannon, Gibbs, Carnot, Boltzmann, Wiener, Prigogine, Clausius, Kolmogorov, Rényi, Schrödinger, Bateson—all of them), how particles could be field-affected entities or field-effect entities (meaning that the tension between particle and field is the only reality to behold)—truly attempting to grasp the functioning of the artificial interface that we see (the holographic leaves of zero equalizer), these small spots of consciousness. "All the world's a stage, and all the men and women merely excitations of an M field: they have their lowerings and their risings as second forms and then they vanish back to nothingness," the science of systems has since then converged to Lagrangian descriptions or Feynman ones if you want, meaning that Euler-Lagrange equations were and still are the current classical and possibly the quantum paradigm by quantum groups extensions that we have. And to be sure, no one really seems to know how Hamilton's principle states itself as a philosophical reason, not entirely at least, so let's delve further into all the points I can (note that there may be some problems in it, because I'm terrible at algebraic operations and algebraic manipulation, but I'll try to give my best at it).

---------------------------------------------------------------------------

First of all, I'm going to provide a quote that will at least show that I'm not alone in this, by Musès (if you don't know him, you should know, as he will be a very important figure to talk about):

"The action tends to be minimal in physical processes: the famous Principle of Least Action. On other occasions, we have pointed out that this principle is rooted in an even deeper one, which may be stated as follows: In any physical process, the time rate of change of entropy (dH/dt) is always minimized, yet the integral (H) of that rate of change always exceeds zero by a finite amount.

We also define dH/dt as the rate at which a quantity of available energy is made inaccessible (usually by dissipation as unrecoverable heat or radiation)."

To be sure, it can be maximum, so in general, a physical emanation is a tiny tip step away from and into stationarity, not minimization. The other quote is by Wiener, whom I have recently recognized as a truly incredible man:

“Information is information; it is neither matter nor energy.”

This is an important concept we should keep in mind: that matter and energy do not equate to information. At least cognitively, we should think that way. This creates a duality from the quantitative/equal/infinitely divisible/non-unitary/appearance/aspect/arbitrary part of a thing or an undirectionated derivative to the qualitative/unequal/discrete or self-contained/unitary or communicatively meaningful/essential aspect/a sub-idea of the actual/the chosen part or the directional derivative. This should also provide us with a background to idealize the problems with General Relativity.

In relation to abstraction, there's really no math to it, no proof or anything—it's a truly epistemological observation with a math thing or other in it. That, in itself, should be its own aspect of formalization (meaning that intuition is the important here, not the inverse). As Wiener says:

"Science is a way of life which can only flourish when men are free to have faith."

But if you want to see it, that's the point of this post—to show inconsistencies with the linear physical paradigm, the stakes of pure formalism, the empirical external things/externalities. These are things that some people still want to call science (pure or applied). Wiener's phrase comes to mind again:

"What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead."

I'll discuss basic diffeomorphic spaces, non-diffeomorphic ones, categorical points of view, and the meaning of M in M-theory (it's not just an inference for a unified theory; it's more than that and has a deeper meaning to it), string theory points of view, and some formalizations—basically showing ideas, proofs, notions for what we call real.

$$J_t, \space z \in \text{LieAlg}(T), \space R_{J_t, z} \simeq \lim \frac{\prod_\square P \circ z - z}{\delta A} \in \text{hol}(T)$$

$$\omega^i = \Omega^{i}_{T\space j} dy^j + N^{i}_{n\space j}dk^j$$

$$T = \Gamma (\text{Diff Manf}=Q, \text{Riem Manf}=M, \text{Sympt Manf}=K, \text{Riem Sympt Manf}=N)$$

The reason I'm defining these quantities (thus acquiring importance to them) is that we are investigating the idea of motion, varying through the matrix of 'infinitude,' the little infinity,  the big infinity ,the middle infinity (infinitely centered), the propositions of stiffness to geometry. Lie algebra offers a way of defining the directional,the orientation, structure of a manifold; curvature gives a way to measure how the manifold is embedded in $\mathbb{R}^n$ and how it's intrinsically differentiated from the Euclidean embedding space. Also, the connections provide multiple transformations by which the coordinates vary (infinitely centered between the Euclidean and the non-Euclidean). So, it's a way to abstract the multiple coordinate choices by which a manifold's motion can be set, how the phase becomes different in local hills when we talk about phase connections/momentum space connections; what happens when the surface is curved and the path is asymmetric, like a half parabola/paraboloid one may see, so direction would be provided by the momentum curvature as the tangent curvature provides(a grasp to the equivalence btw intrinsic ans extrinsic and the duality between them). This curvature is a combination of normal vector curvature and tangent ones (which in a surface case can be approached by $R_{J_{y_t}, z_k}$ and $R_{J_k, y_{t}, z_y}$, where $k$ is the orthogonal part to the $y$ surface part, so $J_{k_t}$ is the normal variation field and $J_{y_t}$ is the tangent). It can be proved that both sections of curvature and connections are interrelated in each of their singular dual relations, so they are inseparable—it's the duality extrinsic/intrinsic as said before, in both the sections of connections and in the sections of curvature rationed in the division of normal and tangent frames.

So, in quantitative terms, a presymplectic form should be defined,a phase connection too. In differentiable non-Riemannian manifolds, it's not unique as the metric and whatever derived constructions are not. So, an estereotypical quantity (assuming an enriched hom-set of forms);to ensure the uniqueness and thus the non-degeneracy of the form—the enriched hom-set of forms has to be a terminal object as the enriched hom-set of connection forms, so $Q$ becomes $M$ (the becoming of being is the becoming of geometry, and the becoming of geometry is the becoming of being).

 

Just to explain better, the hom set being terminal is the same as $\Gamma$ being unique; a connection's uniqueness means a metric's uniqueness (can be proved by thinking otherwise—I'm not going to do it because it's simple to do, and yeah, I have problems with algebra). That's a Riemannian manifold $M$, so now we can define the symplectic form quantitatively? Yes, it would be possible, but we are not just talking about the determined quantity. There's a continuum(pure quantity)of adjoint qualitative time preorders that still have a Riemannian manifold as a target, and even that, we have the possibility of defining it by the time in integration Riemannian curves. This is not time; we are not at pseudo-Riemannian manifolds, yet, so sometimes the end $\mathbb D$ of $\mathbb D ^3\times \mathbb D$ is sufficiently different that it's not possible to define a symplectic form $\omega$, just a presymplectic form (if we are assuming time to be a variable from Euler-Lagrange equations). Now comes the most exciting part: to finally define a symplectic form from the presymplectic form.

The problem to why we are not being capable of having the sympletic form here is simple,its because euler lagrange equations can have dissipations,chaos,holonomic,semiholonomic and non holonomic constraints,to which all reduce to semiholonomic,holonomic and non holonomic constraints,equations that gives boundarys,conditions and potentials to the manifold,it can be a cliff at some point,or a hill,maybe it could be a velocity restriction relating frictions and drag,a virtual work force leveling the motion to a specified  molded moduleted manifold,obviously it will give unexpected zeros,unexpected non uniqueness,the lagrangian is being used to set in place external contracts,the problem is the same here for external gauge conditions(that can be moduleted by above constraints too),note that the reason eletromagnetism has well known behavior at lagrangian and hamiltonian is because of it's form, a symbiosis with the non potentiated lagrangian(the free lagrangian) to form another free lagrangian (free functor),so in that way there's no external things and its all counted inside the inner degrees of freedom,the inner  dynamics,note that this symbiosis sometimes is not as well done as we would want,in certain ways it would break dimensionality ,would not be a kinetic term,would break important symetrys,thats the part where i say how to do better.

deeping into Hamiltonian we see that it has no accommodation for dissipations,chaos,anything beyond the simple $\mathcal L =T(\dot q^2)+V(q)$,

the reason why it fails is because $\mathcal H$ is not the natural territory of time,instead its $\mathcal L$ and $E$,first lets give an important result to see this,if $\mathcal L$ has no explicity time dependence(a thing we all know its physical ensurement,at least most of the times),$E$ is conserved,thats a point,but i ask you,now suposing you understanded the ideas i got here before(that all or has been based on theorem's proofs or my self reasons and proofs),we supose that we really have the sympletic form(or even presympletic,for this following argument doenst matter) that accounts for the dynamic of the system,so it would be a sympletic  form of the lagrangian,the lagrangian as said before would ensure the time,and time gives the slices of a phase space,so here time transformations($f_{t}$) are the same as presymplectomorphisms, and the aplication of it gives the presympletic/sympletic form $\Omega$ its invariant form.

jus to be clear:

if $(K,\Omega)$ a $2n$-sympletic manifold and $f$ a presympletictomorphism,$f_{t}$ a

chronomorphism,$f^*\Omega=f_{t}^*\Omega=\Omega$.

to me from this seems clear that $E$ and $L$ equations would be the same,both run trough the same phase space,$E$ conservation means that it runs trough all phase space and that this space is the only space where it runs trough,same for $\mathcal L$.$\Omega$ construction becomes something about $\mathcal L$ and $E$,not about $\mathcal H$,and since both $\mathcal L$ and $E$ equations are the same we can say that conservation of energy is the same as hamilton principle(in case there's no explicity time dependence,a thing that we may talk later,since its a symptom of a big problem in math),other thing i want to go back is about using curvature in sympletic manifolds or the riemannian sympletic manifolds that its the same as real kahler  manifolds(to which i mean all properties including the almost complex structure)

$$T = \Gamma (\text{Diff Manf}=Q, \text{Riem Manf}=M, \text{Sympt Manf}=K,\text{Real Kahler Manf} =\text{Riem Sympt Manf}=N)$$

curvature may be not possible in sympletic manifolds due to Darboux theorem(i guess is a possible somewhat viewed missintepretation,i may be wrong),and thats the point i want to talk,to stress about,Darboux theorem is about sympletic forms on sympletic manifolds,it says that there's no local invariants on it that are not made flat by symplectomorphisms,but here we are not talking just of symplectomorphism ,we here are talking about 'isometric symplectomorphisms',ones that preserve not just the sympletic form criteria but that its inside the manifold(also meaning that sympletic criteria is not physical criteria).

    Something that can be done to creating physical criteria is create the $N$ manifold(its the only one that satisfies above conditions,also all analysis that i made with relation to the geometrical quantitys that parametrize more deep behaviors apply here, something that should be clear before but if not now it should),so curvature becomes ensured on it and the same analysis for what is curvature can be done here to analyse the sympletic phase space,to see how it acquires the many topologies of genic origin(relative to genus,relative to birth itself, individuality and transgression),now the phase space almost have its form.

probably the image imported as low quality ,the left up equations are about how to define the real Kahler manifold correctly with compatibility and  equivariant time indexing,and the red parts are the fields in the dual manifolds(both the sphere and the N manifold related can be seen as nuclei cartesian closed profunctors),so in a way the right manifold for physics is one that satisfies Real Kahler manifold conditions,or Complex Kahler manifold conditions,they are the same and the $J^2=-1$ condition is a almost complex condition as the name sugests,observe that this is the same tide that minkowski space has to time,meaning that space and motion in phase space are tied as time is to space in minskowski space,see the paralel?this should be obvious at first time for who studies chronotopic relations,motion is time so the anacronic or rather cronic behavior of  motion should be the same as time,this would state phenomenic boundarys, to which the dynamic object is a limitation as much as its living environment,so now the symbiosis ocours at the fundamental level and as a dialetic unfolding btw both,a infinitely centered spatial context to the separated earlier defined infinitys of the space(pure homogeneity) and the time(pure heterogeneity),this way we just jump from one to another,the space just assumes motion as time,or more metaphysical,the object as its emanance.Just to continue the disserting about complex behavior,something that is very present at Musès articles and books,it's that the imaginary is the real,just to paraphrase the post name,we are trying to grasp the heuristica of the real,and the imaginary is much as real as the vague kind stupid notion of real,the imaginary relates deep dimensionality that's behind the bare logic of apearance,the steganography of space and maybe of time if we include it to be space,but even time seems to be imaginary,its out of reach and again as Musès says its an different dimension as the other ones(what he calls negadimension),thats a thing to say that time is a restriction to space and vice versa,so the positive of one is the negative of the other,just as information is the negative of entropy(a thing that i know by myself and by Wiener),so it comes to form bounded frames to space,closed by time,as time progresses space shrinks in size,as space progresses time shrinks in size,we as age evolves begin to interact less,move trough less space,when we change too fast(time expands) we think too little,so mostly we do nothing(space contracts), when we get too far from were we are we tend to go back to it in some way due the imense irrupitive motion,time shrinks(we see less of ourselfs,loss of identity),in each time section there's all space(given that each time is a moment of the space,so its seemly to say that inside time there's all time or others divisions of it),they are clearly oposite to each other in some way:

"Mathematically put, if $kt^1 = kt$ denotes $k$ units of duration, then 

$kt^0 = k\times 1$ denotes $k$ units of space. And space is seen as the zeroth dimension 

of time. Thus all of physical space, of however high dimensionality, is 

included in but a point (moment) of time. 

The talented writer Italo Calvino in his story Ti con zero ("t with zero 

subscript") grasped this fact poetically when he wrote that what must be 

simultaneously considered is the totality of points contained in the universe 

in that moment to, not excluding a single one."

Musès

one point of time means more space since we exist in time and time have to begin to build a relation,meaning that all is initiated,unitiated,ended or unended,one big nut/shell(to relate to the pure,meaning that this idea is pure abstract,so not a mean of thinking),to add to it i would say that negadimensions are the way they are because $t^-1=1/t\simeq s\rightarrow s/t=c$,so here as $s^1$ positive dimensionality means extensive $dx+dy+dz$,$t^1$, negative dimensionality means intensive $-dt_1-dt_2-\cdots $,and to be more general both ideas follow for volume,this is easy to prove.This relates to the above point about complexity in the way that this time diference can be encoded as a imaginary number at time($dy=dx+idt$),$dy^2=dx^2-dt^2$,metric is the same as before but time is modified,is propositally differentiated to include the $i^2$ orbit(the well known imaginary time that makes the dimension go positive by $-dτ^2=dt^2$,and yes all is about the metric,not length exacly), negative intensive relations stills there,just in a isomorphic manner to which vectors aren't the same(or they are?),they can be related to the previous ones to give same relations but now dimensions interact in this almost complexified manner,is almost the same relation Complex Kahler manifold has to Real Kahler manifold,they have the same physical relations,are isomorphic,can be produced from each other,the almost here just means that its not really complexified(to complexify $\rightarrow$ $g\simeq g(\frac{\partial}{\partial z},\frac{\partial}{\partial z})$),in any way the structure has all these fixed point relations,imaginarys is no any less real than reals,the vision of space was just deturped by empiricist,logicistic,formalistic,bare rationalists point of view,the rigid seguiment of views of iluministic time.The idea so would be to come with equivariant unique isomorphic adjunctions/ hom spaces,and the foci would be symetry's,the morphisms,the quintessent structures(groupoid/group-like relations,internal cosmic relations(cosmos also being somewhat semiotic and somewhat mathematical)).

list of spaces with the same order of sameness:

• specific matrix induced spaces(order of $u_0+u_1$ by Musès)
• specific of Cayley Dickson first construction and other visions of complex extension of the reals
• isometric covariant phase space(covariantly here i mean non singular,reciprocal,complementar, concurrent,exteriorly irreductible,that by the talk above means more or less the same as what nlab states,but to he sure covariant phase space for itself to me means what isometric covariant phase space means,but im not wanting to confuse any more than it might be to some people)
• lagrangian isometric submanifolds/lagrangian isometric zero equalizers
• $\mathbb R$or $\mathbb C$ specific Riemannian manifolds.
• Kahler Complex manifolds
• Kahler Real Manifolds
• Entropy,information symplectomorphism coadjointness(information geometry)
• Stochastic probability lower limit spaces
• Energy phase-isoparametric submanifolds
• Relativistic and generalized extensional spaces lower limit spaces
• finite poset top limit dimensional anomaly correction model spaces(mostly seem at string theory)
• dialetical derived time constructions
• ying/yang,taoistic,hinduistic,buddhistic,teistic cohesion finite poset top limit models
• finite Tower like G-spaces limit space
• Transfinite Ordinal $ω^2$ spaces
• Twistor space("It turns out that vector bundles with self-dual connections on $\mathbb R^4$ (instantons) correspond bijectively to holomorphic vector bundles on complex projective 3-space $\mathbb {CP} ^{3}$" Wikipedia twistor space)
• quotient of the sympletic $Sp(2n,F)$,or specific equivalent's quotient subgroup of $U(2n)$.
• First order integral of U(2n) group(its holonomy special group)
• Calabi Yau orientation morphism inverse image(or maybe we want the Kahler Manifold to be Calabi Yau)
• quotient of $T^n$ or(the non exclusive 'or' apearing again)$\mathbb P \mathbb R^n$ or even some other antinomic/homonomic derivative of modal dynamics(regarded as a branch of cronotopology and temporal geometric logic)
• others possible topological time group realizations(from the above entitys in cobordism relations)
• Phase slice of compact conjugation compatible spaces
• Phase Euler characteristic molified integral via pffafian(not literal riemannian,lebesgue one,as before was not a riemannian,lebesgue integral)in its $\mathbb C$,$\mathbb R$ forms
• Dynamic topology-diffeology  univalent Spatiation(built on topology-diffeology duality that has a wonderful unity at riemannian manifolds,when our known topology becomes differential)
• Ergogical non degenerated dynamical space (ressembles Kahler manifold as the others do)
• conformal non degenerated dynamical space

We now have trampled at the boundarys of diffeomorphic domains,we have showed that this domain can flourish at all points of the continuos analytic reality(since we had solved all physical contradictions by requiring a still diffeomorphic system,or we have almost solved them,depends,to me we are still to solve them,but you may as me be little confused by it if you deep too much in the boundarys of this two realms),by constructing what we cant break from ours codimension(what anciently they probably called realism,a thing that we know claim to be the oposite),so a space built in basic fundamental and rudimentar social construct,the spatial selfdirected and indirected reflection of the conection between all pointed objects(the same spurious one that relates to the idea that every material is non ideal/non astral/non non material(related to classical logical mathematical laws too)or purely a source of non teleological determinism),that coined the real numeric rationalistic point of view to form complete stupid deductions,such as needing to prove 1+1=2 in 162 pages,or asserting itself to prove it using more than 40,60 pages (the bad infinity),we here are trying to set out this views but doing so by accepting it as an directed graph guideline/mediated expansion point,to absorb learnings from this structure as our self-aligned piece of consciouness emanance,all is part of all and etc(something that comes as we begin to know how to exclude things without deleting it but absorbing it internally,as something that could go back again in some different way,and that Immediately does it)

 Reals by itself could be made to construct all pointed related categories and more non pointed ones as adjoint ones,the fact is that our plane of existence is one that is in constant change and alloteric comunication,such that a site could mean other in relation to the understanding of our psyques,points,morphisms and symetry's,all of them being interchanged all the time,all the time you are concerning new ego's,our barriers are changing all the time,so giving this basic state of the nature of my/ours loci's(here to mean the variational path space),the related foci should ordinalize the set of convergence correctly,it should give the correct neuroinformative comutative diagram/neuroinformative pair composition,should filter information in order to have it,so by excluding uncertainty(that here we mean a non paralelized relation with deleting it as before,so exclude here would be like picking it and putting in the correct paste,the negativity here is to give importance to the fact that we should be  pratical as much we are thinkable beings,avoiding static tingences) or in other form to say, turning uncertainty into aporiac notions(a Motivated battle), organizing uncertainty,what gets back to the beggining of this post,so to continue on the meta quality of it and of the post itself:

"To live effectively is to live with adequate information. Thus, communication and control belong to the essence of man's inner life, even as they belong to his life in society."

Norbert Wiener

We are informational beings,and so our destiny is to come back to information,partially because of this outdoor scratching our mind we are in such a lonely society,so should be also a fact that we should ourselfs have love towards all the alloterys of being and the sinful behaviors of the same,we have gone too far,and this give's us the right to see things no one could,or that everyone should,so far that is too dificult to share it,sometimes we are so crumbled in our own defficiencies that we forget the worlds own defficiencies living as we are the most problematic being in the instantiated thought of self guided misery, that's the fact that we are forgeting sometimes,we should all the time prepare to die and to be alone in our own arms,to be in our own faith when no one is,when no one believes in it,to know the imaginable and be able to bare the impulse to count/tell(the paralel of aforistic and arithmetic cycles as said at the blog introduction)for everyone,in a way to just be able to mediate the connection,in order to create own axes of support.

Back to the subject,real numbers,diffeomorphic constructions and diffeomorphic guiding/convergence(or to be sure,divergence) have seen to give semiogenesis for the indispensable alteric parallels with topological,categorical,metaphysical,epistemological,social,possibly political too extensions/or constructions,formulations of timelike ocurrence

and recurrency,a thing that we wanted so far in order to have our own guiding path(gnogenesis or autopoieses).

 I want to go by this line,giving the reasons i gaved lines before,from now we should go from riemannian point of view to the non riemannian point of view or from the local point of view to the non local/global point of view without cutting the ties to local/continuous ideals(mathematical ideals i mean here giving some cover of them),so better state would be:tracing parallels to quantum physics,more algebraic geometry,and more algebraic points of view,relating theories and frameworks,and forming new models giving the already given ones of diffeomorphic physics that i said before and the reader already knows.

One thing i didn't said before but since we will stress things related to string theory i must stress now is that the oriented Kahler Manifold is a Calabi Yau manifold,the  strangeness of this lies in Calabi Yau manifolds being a topic of string theory and now coming to be the only "closely consistent" physical system,to me its really interesting to think that way,seems that we are getting to the bottom so quickly by just giving some presuposes.

Giving such strangeness lets dive the superficial parallels to solve the principles,if the reader knows string theory he knows that Calabi Yau manifolds are used for renormalizability porpuoses/supersymetry porpuoses ,these manifolds are used there due to the proposal of being diffeomorphic/isomorphic to the real ones and having well defined structure so it can have supersymetry and whatever, its simple to see,extra dimension is just too little to see but supersymetry is a hypernumber thing,it can be any small as we want,still holds,and as we know complex is just extension of reals in all the levels i gaved before and many more others(probably is in nlab if anyone wants to make more parallels),so reals can be returned by taking imaginary part to zero,thats really other interesting thing,in string theory we are on the real/complex/hypernumeric boundarys,we can go from any part to any part,so another fixed point to us think about mereologically,this is a way of having a glimpse of how physics and math are interconnected with one being a theory for another,directing bridges between disciplines,and i'll dissert more in it on the right time.

In GR flat energy can be expanded by connection terms to the curved tensorial energy,so killing vectors turn into a symbiotic entity with spacetime,the curvature assumes identity with the object in it being submmited,it has to be considered to encompass overall information:

$E_{\text{flat}}=K_{\mu}ξ^{\mu},E_{\text{curved}}=\lim E_{\text{flat}}=T_{\text{particle or body}}^{00}$

$\frac{dE}{d\tau}=\frac{dT^{00}}{d\tau}=J_{\tau}\cdot \nabla T^{00}=0$

Can be related to the hamiltonian formalism or ADM formalism,energy is conserved,also of course there's constraints to the energy momentum tensor in order to have a correct conservation(as said before,time seems to still being considered as kind external , lagrangian needing ensurance for energy be conserved, physical constraints to which is not emerged but given),anyway im not in this tangent,the point is about the expansion of curvature being an external artefact,when you expand energy metric is something that is being directed towards,metric is a resolution of the curvature gaved by an body,so what about non linear mutual dynamics,when both bodys are non stationary,if we would trace it we would go back to infinity,an body that can affect itself would be atracting itself infinitely,the atraction is infinite because the differentiable and gravitational conditions set the object to a singular condition,we are comparing infinitys(im not saying that dynamics can't be extracted),infinity atracting infinity and etc giving a finite result like if infinitys we being measured in the nous mind of the unknown,little hidden patterns just like with all algebraic extension some way getting to submerge at its non extensioned conjugated part,some way this gets me back to cantor and set theory when comparing different ordinals,we had to extent the basis of numbers to have a more lot of iterable repetitive infinitys by addition of some axioms,just to see that there are infinity of them,to see that the self description of infinity is a independent axiom,here are the same case,trying to stick with these infinitys would be trying to prove things by contradictions,when we does it we does by the sack of transcendenting the mortality and the void presented in the infinity, infinity being imaginary, infinity being a real,infinity being a integer,being a zero,being a singular matrix,being a non instanton solution,being an independent seemly consistent axiom,an teseu/lawvere derived contradictory axiom,a source of the deeper subworld of non discovered maths seemly apearing from nothing else beyond the own assumed complete structure,how can be something be more beatiful than this,even being a ordinality its just beatiful to uncover hidden patterns,exploring the liminality of laws in order of being a citizen of nowhere,your norms are not defined just like at some pos octonion hypernumbers.To recall,relativity can describe self dynamics but needs to do it by the other,we need coupled equations in the middle of infinitys to uncover the depths of mutual relations,the dynamics stills about how one afects the other by the vision of the absolute self,the other is not a part of the self because the other stills an absolute external as were before in newton formalism,the internal description comes so by recalling that the laws is given to be about both selfs as one really covariant conscience/synomos(with+science/framework,or  with +nomic,synomic),the self so is constructed by a relational dynamics as the other is,the other is the self,the self is the other,a contingent non fixed point of view(i like to see here contingent really as the idea that the self is being painted in the basis of its own painting,an undirectionated or multidirected self actualization,also undirected relates to the Kahler manifold,something to be oriented,that doenst have a already made one,as it is the problem is to the reason, theory/model is not everything),this construction would be like the one called by tesla,smolin,bohm,wheeler,wolfram(in some ways),rovelli,feynman(at some ways again),schrodinguer,nottale,koestler,also about a couple of the theories i want to mimic a bit to give the wanted synomic behaviors:

• quantum mechanics(caste of the quantum)
• quantum field theory(caste of the field)
• hiduism(no self,self is a selfish memetic creation)
• buddhism quaternity principles(no self,self is a selfish memetic idealization)
• taoism yin yang nature(no self,self is a selfish memetic idealization)
• teism trynity foundation(no self,self is a selfish memetic idealization)
• kabalah(afirmation of nature numeric valued cycles,presented also in tesla combinatory theory)
• tesla theory
• vibrational dynamics/wave dynamics as hamilton equations non self expansion with kolgomorov theorem (the probably most direct way of regularizing infinitys at einstein theory)
• vibrational dynamics/wave dynamics as signal fourier wave theory
• string net/vibrational net/topological nets/field nets/state nets theories(relatives with unitys group (nlab based),picard group,braid group,brauer group, cobordism group,thom spectrum,...,fock unitys group(one example of what i mean by nlab based,everything can be at the unitys group))
• non stable/non linear/non riemannian/non differentiable dynamic systems
• fractal topology's and fractal scale theorys
• naturally chaotic systems
• metalinguistic models and metamodels in general
• informational directed graphs
• entropic group setting and integral
• liminal terminal objects(liminal subobject spectrum)/extreme stable terminal object system setting(extremal here relating to turing completeness,completeness or coadjointness)
• continuation of previous non ended limits of the infinity rope(since here we are going by true infinity we can get over any number of infinity limits,we will always have another and another,the links goes indefinitely and i dont have words to describe it)
• more (probably there's a ton of others equivalent theories that i could add as before had)

from this im again remembered of previous showned wiener quote :

"What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead."

Such amount of richness in the systematic ontoeidogenesis itself besides the quantitative applications.

just to end this part ,quantum theory can be seen as a flat Complex Kahler manifold/vector space(to be sure can be curved if we're considering $\mathbb P \mathbb C^n$),due to $U(n)$ in the manifold(sometimes seen directly trough the map $2n---->2n$), relating to the generators algebra,born algebra,deformation algebra,also metric(quadratic form) is the important degree of freedom (i said it before,not length,the quadratic form,resembles interaction),it gives projection,density,codensity, measure/mensurement local from non local behavior,correspondence principle shuts dimensions to a specific number(just like in string theory when higher dimension terms turn to low dimension),and deformation algebra reduces to poisson algebra,basic simple rules(imaginary extension to cover time recurrency as an universal),anyway thats the idea,Hilbert spaces,$L^2$,$l^2$ Complex spaces,$\infty$ functional vector spaces(somewhat present in GR,wave/geodesic paralels,both as harmonic/solitonic expansion of inner dimensions) and quantum information by dagger compact categories (if one absorbed the introduction and the end will know that information is the key to raise from GR decrepitc body).

part 2 its going to expand on mathematics,mathematical physics,quantum channels,topological channels,informational channels,information theory,universal causality,more about cybernetic principles,granularity,granularity and supersymetry,granularity and information,hypernumbers,hypernumbers and supersymetry,more modal ontological principles,gut's,supergravity,string theory,unification theories,dualities,...