dimensions

 yep for warp invention idea ->

- so need to decode the parameter of grp which 3d spatial dimensions emerge as kernel normal subgroup. 

 and integrate to poset lattices where the poset lattices somehow goes in cohesive and a time poset lattice ordered direction.

 so some category theory and grp thry revisiting checking time.  

of reviewing cohesionless grp definitions like banach tarski's idea to cohesion having emerged universe where possibly spatial dimensions are a normal subgroup kernel members how so that dunno hadnt figured out yet.  that when figured out the thought of this idea would be nearly ready to be axiomated and formulated completely. 

hmm.  

yep for developing atilgan's tech we need to figure out these. if turns out its 0 dimensions (multiverse)

yep now reread banach tarski theorem to revisit it to remember it goes from free groups concept and uses the notion of emerged identity element of groups generated group members  of the generated overall grp.

so what i  conceptualize as 3 members of normal subgroup kernel set  in my silly theory is tackled differently in banach tarski side of spatiality on attempts using generators of free groups with hmm SO(3) rotators.  (even if thats important in e.g. in lie grps) 

so  snce i forgot about SO(3) alike grps and so i need to revisit. 

but hmm my initial idea with beign these topics i need to relearn,  I think my initial idea differs and of course banach tarski's conceptualization of spatiality with free groups also has a point of a possible conceptual framework for depicting spatiality.  

if that were the case, then the generators parameters of the group generated's physical cohesion emergence and the lack of finitely additive measure applicance due to paradoxicality would be the investigation thingy of the idea there. i mean how from such actual paradoxical noncohesive definition the physical perceived cohesive universe emerges would be the thing to check.  but it would not initially define why its 3d either imho initially and i mean why not 4d that would also be need to be investigated.

so the banach tarski spatial definition set could be also a second spatial dimensions idea to check and in that,  what needs to be checked of whether if dimensions and euclidean coordinate system of 3d were generated from such SO(3) like free groups with generators, then  checking out why they do not go in paradoxical sheaves of the same definition but a sheave definition which generates the cohesive physical universe?  i mean if theere were free groups of banach tarski behind the perceived universe, then what to investigate in that would been, why   some sheaves become dominantly in cohesive perceived universe direction of crystallization and why such cohesive direction is the crystallization direction?  

so upon reading banach tarski, I understood that, different to my idea (which is more rigid idea of spatiality, since in my starting idea,  the dimensions is like a naturally emerged kernel normal subgroup of a cardinality of n (E.g 3d->kernel's count  is 3 group elements)) there i also the banach tarski perspect which is an alternate definiton which free group behaviour results in 3d dimensions generation and not only that the paradoxical (e.g. not supporting lebesgue or banach finite additive measures) type paradoxical versions of sheaves that could generate the resultant parameters of generated free group members of a subset of it  that paradoxical versions somehow eliminate due to some dynamics in universe crystallizaton so that resultant perceived universe is cohesive.

e.g. that for a subset it could been generated by possible subsets of generators transformed versions. so it could come from various sheaves of originating different generator combinations of the parameter of grp. --> so in this possible paradoxical many sheaves versions  some sheaves gets dominant when universe multiverse is crystallizing to a set of universes and thats a cohesive universe. 

so if we considered the banach tarski based spatialization idea unlike my starting idea, thats also an alternate idea to investigate. in that, how the paradoxical sheaves do not get the high prboiabiluty but the perceived universe gets the high probabiluty is the investigation topic /check topic of such ideas.

so how could 3d emerge from banach tarskian perspect ?

it could mean-> from generators some generators are having the higher probability in universe crystallization and somehow those generators have SO(3) alike limited to 3d.  so the sheaves in which generators of subgroups which results in limited 3d somehow become the predominant sheaves and not only that,  those could also have paradoxical sheaves as theorem shows of nonexistence of a finite additive banach measure,   and not only that the sheaves that is limited to generating 3d gets dominant in universe crystallization but also that generators also paradoxical versions also do not crystallize which would give a meaning to some relatedness to generators to the universe crystallization strangely. 

how so a generator would have a relation to universe crystallization? this now initially hadnt understood yet, but as told, i need to study restudy these topics since i had forgotten SO(3) or have to restudy and i hadnt fully studied before also either just the initial studies introduction had not get phd knowledge of yet.  

so -> hmm so thanks to banach tarski for extending my imagination to their idea. my starting idea started with a kernel size for dimension concept.  but it could also be alike banahc tarski thought.  

hmm. 

so as visible as you see, i need to restudy to these topics since had not studied phd alike and had forgotten also what i studied alot since gave pause to these studies for a while of category theory etc etc. but has been resuming as mentioned. 

hmm.

there might be third definition to spatiality and what dimension is. 

and that might be related to grp orbits topics where hmm it might be a set of group members where is distincted to 3 orbits by a group action  and these 3 orbits each self has its generators and identity element so. so in this alternate defintion spatiality would be not alike above definitions exactly but rather a group action attempted to a set (which is also a group itself) and the orbits of the set partition to 3 orbits which has its own generator logic in its partitioned set and identity element etc.  

 yep so in this third theory, 3d comes from not the set of the parameter but rather some combing of a set to such count sets of subgroups.  where each subgroup has its own generator. so in this third theory,  the dimension emerges from not any related to the perceived parameter but rather a group action on parameter.  

 

so these are the initial 3 theories thought upon how spatial 3d dimension thingy is in generator universe.  of 0 dimension actual universe theories ideas. there could be more such ideas thought but later. i think first lets investigate how these initial theories of 0 dimension generator universe could be along with posets ordering of time and that creates Lorentz theory wise perception. 

so in this initial idea set, spatial and time dimension is different concepts. one is a group parameter of kernel type or subgroup or set of group members,    other is poset ordering related to this initial spatial grp.

but maybe  its not like that. maybe time is also a parameter of such spatial defintion.  

so but we start ideas like that that time is not a parameter but ordering. or maybe in third theorem, time is the group action which both creates spatiality and both iterates such each grp's grp members. but latter seems more continuous definition whereas time is something that could go somewhere in 0 time like photon.  and on observer of photon sees it in light speed which is also ordered weirdly. so i think the latter theory lacks explaining time behaviour indeed. unless we add an additional generator grp to the group action grp there which is alike a generator grp alike banach theorems and that which could have generate either a measure concept  which effects the group action.  but then in suhc additional generator grp addition,  when some speed increase happens time slows for that reference frame so that universe crystallization somehow switches to group action (generated by such additional grp again as added ) for that reference frame gets selected of a infinite generated group member type.

i mean its something like

G is group action and A is the set of spatial parameters which is in crystallized universe version is distinctive to 3 subgroups (group action creating orbit of subgroups in a set)

then but this as told suffices to describe photon. 

so we add a new group  which is like Banach group generators  which is binded to G (generates G) 

and this grp behind G has various generator configs that generates G.   and not only a single g of G could be generated from many alternate generator configs (alternate sheaves) also it can be generated to a different g either. 

so then this then would explain why photon would take 0 time to move from somewhere to else config. since in that case the G group action would have a g that is that much large  (generator over infinity )  that would take photon instantly to any config. any distance parameter value of spatial dimensions. 

then that must be related to the speed of the reference frame also where it reaches light speed alike. 

in that light speed or near light speed spatial dimension could go in a very less time go to any spatial config and reason time flows less there is because the group action already is iterating the spatial config as velocity where under such group  action photon goes an ordered poset sets mcuh longer length in same moment where a slower velocity item has passed thereby to the longer poset set is more hysteresis and slower time perception and the slower item has less poset sets and less hysteresis of generation and regeneration of free group strings of posets of universe crystallizations over and over of a near probability set of universe cluster strings of posets and where there is more config the free group generator there has a much more string diversity and there by a metaphorical hysteresis of universe iteration which is perceived as slowed time.  

so hmm i still did not liked this idea since gave time a lebesgue measure or such  aspect. i usually dont initially favor such ideas since it would align exactly with perceived universe version but we are here to understand what is the actuality? of course perceived might be similar to actuality either but still that limits warp invention capabilities. so we are to understand how different it could be. i mean perceived universe versus actual multiverse.

so i think possibly multiverse crystallization to universe sets is like following metaphorical to free groups behaviour of generators   being generating some near probable universe crystallizations.

when the poset count is long in that then the somehow dynamics of that generators generate some what a constantly more hysteresis nearprobable universe sets.

so reason i disliked  this idea is because it gave time a lebesgue aspect. 

in initial idea i thoiught, time were just simply any order but then somehow multiverse crystallization would order it alike a poset. 

 

but so here we are:  we can not exclude this idea from ideas.  that time is actually something like that. where hmm in multiverse crystallization it crystallizes in an iterative posets under group action effector but in crystallization due to larger paramedter space it goes more alternate universe crystallizations versions which are all near probable and very similar. so then there is that increase of alternate universe counts is the slowing of time hysteresis of time where one universe version can loop from one to other alot frequently -> thereby slowing of time.

but in the slower reference frame, there is less posets iterated by group action and then in less parameter space, there is somehow crystallization of multiverse goes more focused and less hysteresis.

so seems as universe crystallization dynamics also seems as possibly a free group behaviour alike maybe.  lets put that idea aside. since might be relevant.  i mean maybe that group is not just simply probabilistic calculation expectation max alike probabilitistic sheaves prioritizing but rather also a group generator is involved not just probabilistic calculations be the thingy of why some sheaves gets prioritized (Crystallized metaphorically)

but maybe the probability calculation logic itself behaves like that exactly some group logic due to the overall effector group actions. yep. which also has a generator group itslef also. 

  so i disliked this idea because it has constants. so why the group action group  G generates 3 orbits?  why so? 

but it could be related to G's generator either which might be a free group. 

I mean 3 must be something thats caused alike -> it could been 4 dimensions  but the probability calculations there limited the group action grp to behave like that. 

i mean it must be an lower bound that 3 dimensions. caused by some maths there. 

i mean otherwise there is no meaning of constant there why it generates 3 orbits.

no i dont like the ideas alike string theory which says some parameter config creates constants.

I dont like that thought method.  why that constant is there?  it must be created somehow. by some maths system there. 

so i very dislike thought method of string theory due to that. its incomplete imho.  why would universe behave such mechanical alike? i mean there is this distinc parametrization and that different version. 

why so? 

unless that were an eigenstate distinctification behaviour (parameter config creation behaviour), it would made  no sense at all. 

every constant config must be created by something.  

its not the hmm cartesian thought method where some parameter set defines a platitude of configs and where each config can create some alternate.  i mean an eigenstate might behave like that. but a theory which tries to say universe behaves like that with some such multidimensional thingy, seems severely cartesian tradition and severely cartesian/dualist and i dislike it due to.

I think universe must be very complex not defineable by a unit entity which its parameters defines overall universe  behaviour \s one pattern.

thats too cartesian. 

i mean ofcourse occam's razor favors the simplistic thought method, but i think in universe decoding i dislike such cartesian thought somehow.  

its ok to eigenstates to behave simplistic like that but for defining overall universe like that seems oversimplification most possibly.  

i would rather think e.g. that even if i disliked the group action based time and spatiality definition (although defined yet incompletely) i definitely dislike it much less than string theory's oversimplified idea/definition.  

but maybe i am wrong in that. maybe string theory is correct. dunno.  i am just not very knowledgeable in these topics yet of cosmology alike and i might very err in my ideas either.   so take my refutations of ideas like string theory with some skeptiscm please since i am not an expert in ideas aof this knowledge domain any yet very much.  there somewhere but not expert any yet.  (some amateur warp inventor yep. which iterates amateurishly in warp invention ideas yet  whom does not have neither bsc nor msc nor phd in this cosmology  domain)   although i believe even amateurish i could invent warp idea. i believe even i can invent without needing help of to be invented ml algos. but in case i can not invent, there ml algos would invent the tech of atilgan.  yep! but i believe i can also invent even being amateur in this cosmology domain.  (but still  when i refute an idea in the domain e.g. when i refuted string theory idea, please take it with some skepticsm please. since i am not expert in this knowledge domain) 

but i just my thoughts prioritize alternate theories investigations first. of starting with first such 3 ideas.