yayyy thinking of some eigenvector configurations with this noncompact notion mentioned:
there when you dont have exact values for eigenvectors do you still can observe the light's energy iterations related to wavelength? thinking sp configurations and their relevant experimental results,
it makes it that as if there is compactness also when considering this exact eigenvalue eigenvector configurations of energy changes of regarding to wavelength.
hmm so maybe compactness exists in physical world? but I tend to check the contrary first, of whether if e slight configuration distances of the exact eigenvector configuration could result similarly in such similar behavior.
it could be like when its not exact eigenvector, it could turn out to be like if its 3 dimensional matrix, it could be scaled continuously until 2 dimensions become the main dimension and one dimension becomes less effective due to noncompact vectors data there of numbers with not rational or integer type compact version. it could be also like iteration to become 2 dimensions diminsih and 1 dimension result in the eigen vector if consecutively applied.
so how this noncompactness would effect the schrodinger equation? it would not break it it would not change the equation but add more variety of changesets to there. though thinking these energy levels are calculated along the various sp configurations, one just simply wonders if there is compactness in there or not?
my initial impression is that: nope the noncompact representation wont break that much existing formulations but add more variety to it.
so i were just for a wbhile wondering whether if this my whether everything is noncompact and integer number type or rational number type with compact placement in number line, is just delusional could be delusional to think there exists compactness e.g. in quantum mechanics type idea I have. but this definitely would add more complexity to the calculation of quantum mechanics diff equations. but i want to look to this topic in this aspect also that it might be that we could have numbers with infinite series representations always and wondered how it would work with schrodinger equation or default expected sp configurations energy level calculations, i believe it wont change alot or break the usual eigenvector mechanisics that much but might add some variety to the eigenvector system there even with changes of its dimensionality etc.
hmm if we thought more dimension having matrix, we might end up again more variety in how eigenvector would bheave from its usual non direction nondimensionality changing behavior.
hmm i think noncompact number system (my various maths grammar's one version would have such noncompact number system with infinitely expoinentiation part ) wont break schrodingers equation or sp calculated energy level changes from usual calculated sp related data.
and if we add extra dimensions to that matrix, we might even understand came up new space time notions to alter this eigenvector behavior. that be the extension point to quantum mechanics such definition this noncompact number system might bring. it enhances the variety of eigenvectors' slight divergent eigenvector behavior not anymore any compactnes having system nor the exact eigenvector. but would definitely have helped adding new dimensions to space time system there or trying to do that in terms of quantum mechanics perspective to investigate. maybe one of the such dimensions might be then used to even do time travel. maybe aliens time travel machines to commuincate from star trek (i have such idea) uses such noncompact number system to alter the hidden dimensions of these systems and using tricks to alter such eigenvector iteration in those extra dimensions to warp through space time and also in positive or negative direction in time. but this might be just point transfer if you work on a point it might work but normally we are many mnoles of matter so if we have to transfer us with such time machinery system of noncompact maths based differential equations based dynamics, there might come up some discrepancies among parts of moles of matter which might not be any stable thing.
but this is a starting point. to my investigation of whether if compactness concept people invented is actually a delusional system? that there is no compactness even in eigenvectors in schrodinger's equation. and so, we could easily extend dimensionality count of existing matrices in schrodingers equations to include extra dimensions that also alters that eigenvector movement behavior. we could at least investigate such extra dimensions of such physical systems sydnamics. maybe there is not maybe there is. its a topic to investigate. but is the only initial starting point of this alternative math ontologies study. yayy first ontology version would consider compactness concept delusional. another secondary ontology concept might include compactness but might still be with not same ontology of maths.
its just so fun to define new math ontologies. not that i studied alot today just gave some couple of minutes thought to place this noncompactness to schrodinger equation to understand whether its compaticble with quantum mechanics existing observed behaviors. I understood its compatible most possibly from my initial not thorough analysis. and it also adds new possibilities like easily adding more extra dimensions to matrix systems there of known force energy systems that also might be connected having relation to time dimensions. so this noncompact math version compiler/language would be the very first math grammar to create and carry existing formulations theorems axioms to. then as mentioned i would check the quantum mechanics with such perspective.
because i tjhink aliens have communicated with me with time machines and I understand that this might be another method to build a time machine. hypothethically i mean such noncompact math might enabnle building time machine maybe.
its only a hypothesis not proven. not axiomatic. i just only believe and very believe because i seen alot coincidences to believe existence of time machines, i believe aliens have time machiens and communicated withme throguh star trek movie but its my belief and its a belief.
but better investigate whether this noncompact math ontology might enable such extra dimension additions to matrixes of quantum mechanics and with still keeping up compatibility with sp energy values data that were proven by experimental physicsts.
yuppp so that now that i dont have sleep yet, I think i would stop laziness of today's lazy evening mood and would resume abstract algebra study to continue revising necessary math knowledge to build my initial ontology layers/initial parser definition in this math compiler topic to build my own intrinsic language to investigate cosmology/quantum mechanics like topics. i need to read/learn alot in particle physics specficically adn also later special/general relativity but i think i would i have necessary enough material/documents/books to study from so it would be possible.
hmm if we would then have quantum gravity versions of gravity force, there then we might with if such extra dimensinos existed, with this noncompact maths version might figure out even altering gravity force's eimpact and momentum location change etc. so this also has some prospects in quantum gravity side in topics of building such spaceships. but not to have early such hopes high in the sense, it might be point wise applicable but might be very hard to keep up apply such intrinsic more elaborate eigenvector iterations to many moles e.g. space ship to move against usual gravity force dynamics. it needs to be checked whether it could be also used in such configurations like space ships then yayyyy if it all turns out possible/feasible (most possibly it wont because i mean in science i mean the first hypothesis theorem you think of might not work out but lets see maybe it might work) wovvv then I could build spaceships that defies gravity force.
so math ontology layer studies has huge prospects in cosmology and quantum mechanics studies imho.
but i might be thibking all incompetently since i am not that expert in these topics any but i believe i would keep up take expertise throiugh this study. yuppp. nice. cool i liked this prospects of this very first ontology version. first ontology version's manifest is to claim " compactness is delusion". :)
chapter 1 -- first ontology --- first paagraph starts with:
" compactness is all delusional,"
:)
there would be surelyt many such various math grammar versions to build and actually I wish to intend to later generatively build extra grammars wishfully. or maybe that might be hard to do. i can't project whether that generative grammar design would be a feasible task or not. i am sure to ai when ai would be ready it would have been feasible. but to me, the non ai, i dont know if i can build such generative grammar designer but i am sure the ai would be able to build. since woulkd be much more intelligent than me. yuppp.
but until ai is ready, lets have this fun of first noncompact maths ontology definition.
yayyy defining a new language is so fun! :D some abstact algebra study fun now. since it has passed long time i studied that book, its no boring but definitely every math study became very bnoring exactly 1 year ago since i were constantly doing math studying and i think i got overwhelmedn. now that i gave pause a year to math studies, its no more boring and i could restudy with curiosity again. yuppp.
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