so if it were some mapping and kernel subgroup then would have somewhat homomorphism to i*j =k concept of perceived spatial dimensions.
for free groups of banach tarski side, then the generators that generate SO(3) alike spatiality then would somehow some form of free group that generates orthogonality among generator's generated groups. and that such subgroups being priotized by the equations there should have relatedness to anthropic principle. that e.g. generators which could 4d also exist, but their universe mixture flux possibly moves to 3d ffrequently. for 3d maybe the direction to 4d is more rare contravariantly. 2d would have been maybe too simple for self organized intelligence to form. (maybe not). so if it were banach tarski like free group generators based generated spatiality concept, there the generators somehow generate orthogonality concept naturally and its 3d due to some reason there of that crystallization to posets mechanism there of the probability based crystallization process of the multiverse of its spatial dimensions generators. somehow there possibly the generaots themselves have some group action that some how creates direct sum alike metaphorics alike. or multiplication metaphorics in category topic. or exp topoi metaphorics. or else its about its crystallization. for newtonian mechanics perspect, then it would be something like for an moving rolling ball without force input, it would when without friction, would go indefinitely right? there we observe some velocity with 0 acceleration right? where universe time posets crystallization happens with some generators being constantly generaing its generated spatial dimension with some poset lattice formation of some poset lattice length. lets think like that(with term like rolling ball instead of quanta), then, now change the perspect and change it to quanta. ok, then think with same analogy, ok, then, without an external influence it would constantly move with generators generating itself. then the poset crystallization would have some lattice/poset length related to inherent velocity of the quanta right? so how this could happen? then lets think about this-> e,g think of reverse newtonian force applied to rolling ball -> how does this happen that they counterbalance? its possible that the system actually switches from one state to other in case both forces are equal.
hmm and if one system has more momentum than it moves the counter ball. hmm the more velocity would mean more higher exp of the generator. and so, it might have favorance of lattice crystallization that, the higher exp are more prioritized to happen unless there is also counter side some more sheaves count by somehow mass of the ball.
hmm so if we tried to describe basic newtonian principles in such yet not frameworkized idea, hmm time would be again something related to hysteresis based slowening. of eigenstates getting lost in hysteresis loops and one that does that less has time flowing faster. so somehow the crystallization of that posets also have alternate universe versions which they do hysteresis to. somehow visibly the higher exp value of the generators have less alternate universes so then time becomes something about count of hysteresis loops there where less such count happening for that time passes faster. but this would conflict with the actual observation. where time actually slows. so that the higher exp value of the generator means more hysteresis setting possibly. yep.
so crystallization concept then becomes the following concept- >
normally for a generator to crystallize it does not make sense. i mean for a generator there is no time concept. i mean from one generated to twice generated to tree times generated it does not map to any logic of course its iteration is intuitive but it being crystallized to some poset has no natural definition/intuition on that.
but when you introduce the hysteresis factor, then there you are, thats what creates the lattice. the nodes of the hysteresis loops are where the posets are iterating.
so somehow as the speed increases (generator degree increases) somehow the hysteresis more happens.
so theere is nothing unusual about it. they could have been equal. i mean irrelevant to generator's degree. or else either related to proportional to generator degree or inversely proportional to.
so moving quanta is a quanta. not a single eigenstate, a mixture. so in higher eigenstates the quanta's somehow gets more hysteresis loops in its natural crystallization behaviour. hmm that it does not diverge to other sheaves of other eigenstates. but somehow loops frequently in some back and forth some eigenstates configs and then returns back and loops and returns back and see, so this if happens frequently this is more hysteresis. and if it has some escape value from hysteresis, than it iterates to iterated generator exp followingly. so in default the generator unless identity value it constantly increases with no speed concept/no time concept. but when hystereis is involved, then we have the crsytallization metaphor. where the hysteresis creates posets logic somehow. where metaphorically longer chain means more time. in the following perspect its like that. think that a quanta is lost in a partiallt hysteresis loop. then it is in one condition eascaped from hysteresis. both universe versions exist at the same time. so reset your single universe notion at this point of this thinking exercise again. not that its something like: quanta moves and lost in hystereis than escapes from hysteresis. no :) think of all possible such hysteresis configs and escape configs of the quanta. there -> if the exp of generator is higher somehow the hysteresis is more proibable. thereby to second quanta or third quanta, their combined possible posets iterations somehow the poset iterations where some more hysteresis and then escape of the quanta is somehow happening of the crystallized universe version. so that must be the relative time concept formation.
e.g. think of an generator having some iteration alike hysteresis hystereis (2 times hysteresis possibility) generating
and if a second one has hysteresis hysteresis hysteresis (3 times more hysteresis possibility) generating -->
then this hysteresis would be like gap concepts forming the perception of time among the quantas.hmm or not. let me rethink this silly idea again.
hmm i think the idea of lattice then is like that.
think of sheaves of an eigenstate and think of a second eigenstate or third.
then the first one has a lot of sheaves branches. in some sheaves it has loops of back and forth and some escape from hysteresis loop where loop has some possibility and escape from loop has also probability.
then -> think of a second eigenstate/third eigenstate like that. among 10 times of loop iteration maybe first one loops twice and second one loops three times and third one loops 6 times eg..
so at a moment all of these happen. but e.g.most probable for a moment is for instance to have first one not loop and then second one not loop(and iterate in its generator) and then third one loop.
for third eigenstate itself, it might most possibly loop but in some sheaves it might had not loop.
so among all these sheaves patterns, even if there is no time, all of the sheaves are probable, and for an eigenstate maximum sheaves count iterates the perceived direction for the eigenstate.
so first eigenstate would not observe third one iterate ni most cases, but in some cases might see that happen in its sheaves. so for first one as if time and generation as if stopped for third eigenstate
or else other thing could be, that the specific pattern of third eigenstate most possibly be observed by first eigenstate. if there is some interaction between eigenstates, regarding to their generator degrees then the first eigenstate might bind to due to many external effects bind from one eigenstate of third eigenstate to its second config routinely. and that is second form of hysteresis of interaction between eigenstates right? other than its own direct iteration sheaves leafs. so -> if that loop of bind/rebind happens alot there again, at a point its always probable to bind to any interacted eigenstate's config but more probable more frequently happens. but when binded ot a config then this time as mentioned could rebind to its other config. but so when there is not hysteresis but iteration, that to coincide with the third one's iteration (which has more hysteresis possibility) happens not for the first eigenstate most probably in its existing config. then might see itself iterated but the third eigenstate stayed in hysteresis. and after that in some proceeding iteration it might bind to other sheave config of third eigenstate where it also binds to the version where third eigenstate also moved in generator generating direction.
so the generator being more generated compared to third one creates the perception of time.
along this probability is like lattice formation of flux of change of eigenstates happens based on sheaves count back in past and countersheaves count in future. but that being some metaphor of probability of which sheaves happens.
so that i tried to find a definition of time from generator and hysteresis concept in this not complete banach tarski based idea set where the spatial dimensions comes from free grp where somehow some orthogonal versions have more sheaves count overall in connected past future of sheaves,
in such perspect its incomplete since formulation how banach tarski a free grp could generate orthogonal spatiality is yet not developed. but one guesses its possible to develop that I need to check some phd book and some msc book to recheck some topics and so. and then in such orthogonal groups generating free group generators, (where there only some specific set of generators crystallize most creating perception of SO(3) ) and for to have time perception happen, we figure out a relative velocity difference based on lattice shapes and hysteresis loops for the generator iterations. so that, normally byitself generator has no speed. but when there is hysteresis (loops) then there it has speed divergence of its generation. i mean its not that there is in default a time concept. but hmm there is crystallized most possible universe flux.and there, an eigenstate could bind to both versions of an external eigenstate at any time. and there that more hysteresis counts creates some algebraic properties there which speed /time concept emerges. normally to a generator there is no time. it takes no time from generator-0 to generator-1000 it is continuously an increasing dynamics by itself. but when a third one does more hystereris than the speed concept and time concept emerges. there because first one could bind to a config of third one and then after regenerated rebind to alternate universe version whihc were less probable at first moment where it binded to some config of. or somehow the generated members some of them in their egienstate interaction have some free group related behaviour of loop or revert to previous config alike. which might again has some effect of perception of time type perception it would have created.
hmm i think i hadnt yet any be able to come to relevance of scooter storm coincidence to banach tarski based initial ideaization of 3 ideas. that be left to tomorrow evening these thought ideas. currently thinking very conceptual not exactly. just thinking of possible some lattice generation and time concept generation of the second idea of one related to banach tarski ideas.
third idea were about grp action to create orbits whcih would be spatiality were the tihrd theory to check.
would check later. rest time.
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