kavaris

The relationship between SU(2) and SO(4) is captured by the double cover.... ^so i found some really weird sht goin on with this idea starting w.. S(3) —> S(2), and then you begin asking questions, nd find out that there are like, perfect configuration spaces for what im calling, perfect relationships, and perfect identity, where S(2) is itself representative of the viewer (a single dot is the point on the sphere which is closest to the viewer—granted the sphere could have multiple circles at every point if it wanted, but ignore that for now) viewing the space of all possible S(2)'s (multiple 3D things) ... you can take the questions further thereafter.

... is math discovered or invented.... For Plato, the physical world is just an imperfect "shadow" of this mathematical reality. A circle drawn in sand is a flawed copy of the perfect Form of Circle. Mathematicians don't create mathematical truths - they uncover pre-existing relationships in this realm of Forms. Aristotle took a more empirical view - mathematics is abstracted from physical experience, but he's less clear on whether it's purely invented or discovered. He believed mathematical concepts arise when we notice patterns and relationships in the physical world, then strip away the material aspects to focus on pure form and quantity. For Aristotle, there's no separate realm of mathematical Forms. Instead mathematical objects are abstractions from sensible objects. When we see many triangular things and abstract the concept of triangle, we're doing something that's part discovery (the patterns exist in nature) and part invention (the pure abstraction is our mental construction - conceptual space) To me, they are both speaking on two different things, one is about the nature of the circular form (the nature of reality at that) or the perfect circle becoming this flawed copy, and the other is speaking on the process of abstraction, and how to navigate the space of thinking about these things, which is where we get more rigorous and inventive ideas coming out of... But you need to be asking those Plato questions too, because that is sometimes where you get a different understanding of the fundamentals, if you can straddle that line of assessing reality and math at the same time.

Okay im learning more about the geometry of this thing... alas, theres alot going on with the simple idea of a fiber bundle w/ the structure (S(1) —> S(3) —> S(2)) ), ... And, im skipping over everything to ask what we mean by saying: each point on S(2) corresponding to a "circle" (S(1)) in —> S(3) in the Hopf fibration ((S(3) —> S(2)) note: im also not looking at any of the math/physics areas, as i only know about a very small part of the traditional math story part of it u might say... 1. Pick any point (p) on the 2 sphere (S(2)) 2. Look at ALL the points in S(3) that the Hopf-map sends to that particular point (p) Those points form a complete circle (S(1)) sitting inside (S(3)) This means S(3)) is "foliated" by circles - it's completely filled up by non-intersecting circles, and each circle corresponds to exactly one point on S(2)... "Foliated" means that a space is partitioned into disjoint subspaces (called "leaves") of the same dimension, and this partition has a smooth, regular structure. -------------- So we have to talk about something very math theoretic, where a foliation of dimension k on an n-dimensional manifold M is a partition of M into k-dimensional submanifolds (the leaves) such that: Each point has a neighborhood that looks like a "product" of a k-dimensional piece (the leaf direction) and an (n-k)-dimensional piece (the "transverse" direction) -Transverse direction refers to directions that are perpendicular or complementary to the foliation leaves. The partition varies smoothly from place to place So when we say S(3) is "foliated by circles," we mean: (1) Every point in S(3) belongs to exactly one circle. These circles are the 1-dimensional leaves. Locally, the structure looks like S(1) × R(2) (or, circle × 2D transverse space, or a subspace that intersects the foliation leaves transversally (perpendicularly)) The Hopf map π: S(3) → S(2) essentially "projects out" the circular direction, leaving just the transverse S(2) base. You know what it makes me think of is like, those like "growing circles" of equal shape and size, i wanna say its a scene in the matrix or something... but i also wonder if we are suppose to imagine that, these things are all moving, so the instance ((S(3) —> S(2)) is growing equally, and moving equally. Talking to ClaudeAI, it adds, "Yes. And this dynamic view is closer to how the Hopf fibration appears in physics (like in quantum mechanics with spin states) - as its not standing still, but is flowing geometry where the bundle structure evolves coherently through time"...

heres the new lecture, but again, you gtta have a strong backround in tlkin bout those like... gauge invariance and tensors as they are used in physics nd, u know, all that stuff-since hes drawing parallels between like, "heres wat it was, but heres wat it is". p.s. the furthest in math i got was S(2) tlkin bout a 2-sphere (which is like a ball—but unit quaternions are themselves in 4 dimensions, so they are describing the exact points on a 3-sphere S(3) which youll have to look up ...) but SU(2) to illustrate something is tlkin bout special unitary group of degree 2 SU(2) is a Lie group, isomorphic to the group of unit quaternions, so you are working with quaternions nd the realm of physics, and topological space that have specific parameters... stuff like that

yeaa, i did see it. its kindve an awkward thing to watch, they on two different pages, and no one else is professional math+physics expertise ppl, but if there is, they are likely much more intrigued by it nd can confirm those chiral this that nd SU2 × SU2 × U1 p.s. theres a new lecture out w eric goin over geometric unity. but, i get the sense sean carol is more about beautfuly reciting his quantum physics lessons, nd eric is horrible at explainin this new generation of whatever the fk that it is to be the new way of thinking about math and physics, but again, you gotta b up on that stuff to follow it anyway.

I dont get it. on lsd, its like, the entirety of life had been awaiting/ and predicated on this one coincidental thought and moment i had had, at that very point in time, like... in other words, its not like im analyzing the assumption of every single thing and thought—leading up, and to, that which becomes the experience (and breaking everything in terms of whats logically available to) but still, it proceeds as if that is what just happened, even when its not. like, i dont get it, like, what is the thing that is doing the assumption breaking if its not the analysis of what its suppose to be, leading up to...

Vortex, or no vortex This is a question, sortve. not really Definition: The universe encompasses everything that exists: all space, time, matter, and energy. It includes everything from galaxies and stars to planets and even you. What we call galaxies and universes i think is slightly mis categorizing what i think it should be called, which is either a vortex (from the vantage point, a swirling area of space time that has a very bright light at the center—which is all of the recently expelled galaxies filled with bright light), or, not-a-vortex (parts from a vantage point that appear dissonant) and these galaxies dont only drift into nothingness, though, that is part of what they do... they are consumed by black holes, which spits out some material, and the materials go somewhere... there isnt a wall though, so unfortunately everything just gotta drift on endlessly, but its proportional to everything else that had drifted, like whoever was the first thing out first is leading the way on being at the edge of lonliness, and is also THE SLOWEST. Its unclear how anything forms though, and how you get lots of energy holding hands so tospeak, and i think at some point someones gotta look at it and be like (this dont make any sense) and the amount of sense that it doesnt make outweighs everything we think we know, and we're just waiting til everyone realizes it. Its either, vortex or no vortex, waitin til everyone realizes it dont make sense. And what their opinion is on, like if things dont make sense,t 🤔 WHatnow?-type questions.

I been ruminating on different questions—like brain teasers to get ppl thinking (feel free to come up w your own, as thats the idea of the thread) and i been on this one as of lately, and that is... Does anything exist without a ground level (or without being gravitational pointed towards a source, like a planet/blackhole, thus giving rise to ground levels) iuno, basically, just think of weird questions like that, is the idea

Im slightly diverging off topic into a scenario of psychedelic/consciousness, but returning to the very initial question of something v nothing — the nothing-thing that always exists, and is always w/ us in like, the grand illusionist that awaits us, slightly staggered in some regard — is the question we finally ask that we were tryina think of, that we realize (coincidentally) it turns out its like, "woops that was truth... i didnt want that", lol... Therefore, the beginning is the beginning that exists now; however it doesnt mean there couldnt have been a prior non-everything, or something that wasnt this, it just means theres no dependencies. Suffice to say, the question to ask is like, what is the real question that gets to the heart of this, that we dont remember we are avoiding, such that its like, to realize it is to be in a bit of an coincidence. Im just assuming theres always something that is a bit deeper than the very first level, however it might have more abstractness around it, as opposed to a straight forward thing that can be brought to realization through natural means. There is specific qualities too that make it like, tuning into a busy radio frequency, type've thing.

@The Caretaker Definitely fits. I'll add to that somethin' i was thinking today, now that its like the 7th day in a row that its rained here, its like, the rain makes me feel, not great (as do other ppl) and so its like, on one hand, rain and electricity is amazing, but seven days in a row not so much (its hard to think... brain dont work) I always say how like, theres moisture, as well as a little electricity in the air, like a sortve *static effect*, that is sortve like the sub atomic, super fast, super frantic conductive nature of electricity, but a little dampened so its not like electric explosions in the air... Then it mademe feel like, electricity is sortve like, one of those products/phenomenons that you can derive everything else from, including a pseudo-like gravity (i think theres a such thing as electrocuting a non-magnet material to make it behave magnetic), then there the fact that you can derive light and power from electricity, among other things like its use in chemistry.. and whatever else. its like, dang... wtf else can you discover by starting with electricity, and then trying to find other sorts of phenomenon that exist due to these frantic whatever things (iuno what happens to make things spontaneously electric.. i asked ChatGPT the othe day and i already forget)

Master's Understanding of Numbers Numbers are our attempt to map language constructs to more precise things like the shape of the coffee table, or the time it takes for the seasons to come. Its like, a way to say things about many things, like a repititious thing—used for countably many things—and formal, as well as practical; like, you can more easily think of concepts when theyve been granted an *amount of some number...* Numbers usually imply insight (the understanding of cause and effect within a particular context), observing and finding inherent relationships, similarities and differences;alas, theyre like, the introduction to such things. I think of things in artistic terms alot, like, the study of roundness (smoothness) versus jaggedness (nd how numbers might exist as products of, and vice versa), and i feel as though we are too far in the area of trying to draw/count things in regards to a smooth and cylindrical nature. Rough, scratchy, jaggedness needsa come back now. Alongside numbers are shapes, structure and change — and the relationships between them. Its almost like our natural language, but its just directed towards a different kindve thing. Numbers serve as your first collection of symbols, and your first means to think explicitly about the nature of things, and if/when represented by numbers, how they might combine, divide, subtract or multiply. Unlike our natural language which we can use to form sentences, numbers are explicitly building and/or deriving... like, you dont write downa word, and then build words or phrases by canceling them out, or like erasing it to make it present-tense, because youve ostensibly written it out exactlyas you had thought of. Numbers are always evolving in that sense, as you need to add terms, cancel out terms, break them up, re-write them out, crossing the exponent out such that your left with two expressions, its like, thats numbers. Then theres things like PI, and PI doesnt make sense (as it depends on perfect roundness and many other things, that which have very weak underpinnings), though its a standard, a constant, and numbers are one way of labeling such things (the potential w/ numbers is great, we just have to use them to our advantage) *p.s. numbers have to come from your soul... whats that line in the Oppenheimer movie, 'Can you hear the music?'.. Its like that, 'Can you see the numbers?'

I take comprehension as a context based verb, like, its a personal, local grasp on the meaning, atleast as it sits relatively. In the global sense, comprehension falls apart as it enters the area of more questions than answers. If we take things from the metaphysics/mystical sense, although personal, we can still communicate about how we feel about it, and how frequently we are faced, as theres a weighing of significance between the real and the unreal picturesques we are painting. Everything is a form of judgement, in a personal (like a, "dont take it personally) typeve thing. We are putting our judgements on everything, and its like a feedback loop, people judging others, bouncing back as receptive judgements. Its difficult to then pull judgement apart from anything else, alas we can just try to present judgements in a way thats open, that gives room for others to do of what they wish. Beyond that, i see a spectrum: What might be comprehension at first, turns into internalization — which turns into becoming — which turns into further processes, inside, outside, whatever it seems to best serve — which lead into something, riffing... or de-compressing — jamming on new ideas, perhaps breaking the initial topics of which we had done all the comprehending on.

Theres also the fact the everything is biologic in the sense that its going through temporal sequences and such, so its like, you can only track things in a snapshot sorta way,and then what you have is a very diluted, concentrated image... so on one hand its like, it is that we could come atit from multiple angles, or is that, its like, its tryina describe the thing as you're experiencing the thing, and it feels like its very much biting off more than we can reason about, try as we might to keep tryin, as right off the bat we are workin on somethin'—else we're languishing in some depressed, against-our-nature condition.

Theres probably more than one way to describe reality/physics... like if you really wanted.. but then, isnt that weird then, its like... lets ignore the fact that theres several ways to describe a happening, and just talk about it as if its a fixed rule that we discovered.. its like, suppose theres so many ways to reach the same thing, then its like, the thing that we are describing is a little less interesting now, nd instead it like... wtf was the thing they used to describe the thing... THAT shits crazy, cause it can pretty much talk about anything — in any conceptual space. Then its just like, how do we fortify THAT, and guard the attentions drawn therein...

Can we play a game where we get other ppl in on it, as well as Leo.., where we all pick someone thats not ever mentioned in the same breath as like, a person who is devine (in the sense that everyone worships/talks about them) and we instead act like they are the smartest and coolest, like a god send-like, 'thank god for such & such...', they have to be fairly well known, and on the edge of saying things that have thought put into em (and even better if they are someone despised) or it aint gonna be as funny, like its gotta be someone like; iuno.. who was that guy thats like the smartest man in the world recently... somethin like that, but NOT that guy cause they will know its a joke, as thats like the quintessential tell that everyone is being funny.. So someones whos atleast as famous, but not someone whos associated with like smartest-man & smart trophies, etc.

Im tryina find like, a classical *solar system simulation* on youtube, or any sortve simulation of things in orbit, that which are portraying gravity's innate behavior, but its like, i cant find it—if someone happens to come across one, post it here so we can look & feel it, to understand it, conceptually and internally (note: a bonus would be, if theres a marker of relation—that can show how the sun is not only rotating but also moving directionally, around the milky way which is also moving directionally..)

Like, "What did i eat for lunch last tuesday" that could be an origin story, or it could be a progression. OR it could be the exact question we need to be asking ourselves atm As science is better understood, then we can start asking the right questions, at which point the problems might be more clear... Even still, we can illustrate things to each other, and get across like, *this is what i might imagine happening with this, or, this might be what im imagining happening with that...*

What im tryina get at is like, what if the thing we think is progression in science is akin to asking "what was the first memory i had" type questions, like maybe the answer is more of an origin story, less of a progression in science. So, i have this thing im callin Sean Theory, and its just like, what is the most practical way we can both internalize and express a thing, such that the destination is more aligned with progression, less about the origin... and i think it makes more sense conceptually if you frame every question as leaning too far in either direction... p.s. my names not sean

I had a thought (but its more of a question—that leads into an answer that im working on, as like, the best way to think of our current stuff..) but first i need to know if, like... First off, let me preface by saying: what if we dont have any actual values for anything? In other words, what if everything we have is about proportions, like *this thing we know must be proportional to that*, and so theres no actual point where a value appears, and it leads to us running on circular logic, and our whole understanding of things being based on the relationship of a prior thing, and not about what the thing might be geometrically or numerically. of course, we have electrical sinewaves, and locally scoped, electrical circuits, but do we have a way to get to the space stuff? (the space of both the big and the small) obviously i dont mean like, some theory that is like, an amalgam, i mean, this. Are there actually pieces of real things that we can point to (and i dont mean to invoke the nature of everything, in its like, insurmountable identity of posdibilities where nothing is real) but rather, we assume realness, and then, we ask: Do we have a value for a thing, that which isnt in the context of a circuit, or can we only ever say things about electricity? I think at this point i should mention that gravity is akin to the thing that demands spaces attention, like conceptually, a thing that is like, a product of the mapping of spaces, or something like that, and everything goes towards it, centripedal force, like, arrows pointing at the center. We can elaborate on this once we understand like..., is it that, we're lost because, the nature of the problem is already circular logic, or is it that we do have values, and its those famous, commercial science areas that are all the problem?

Iuno, i keep thinkin bout the fact that like, there arent edges... in other words, the moment you find yourself trying to add things to the equation, its likely you need to be doing subtraction instead, in order to understand it all, cause its always a paradox at the center, and it undulates between adding, subtracting, adding, subtracting, etc, etc, forever and ever. but remember, theres no edges, its just one continuous flow, and so there are levels to the paradox, and just holding onto the paradox is like, level1 of being trapped in a paradox.... then you need to forget your in a paradox, otherwise it challenges the thing you are doing while you are doing it, which is part of the centipedes dilemma... but thats how it all works, you need to challenge your reality, then forget, then challenge your reality, then forget, and all around that is like, things that look like words, and trees, and lollipops, and fudge factories, and ships~in~a~bottle, etc. nd so, you cant ever assume you know anything, cause its like, the very thing you are doing, is itself the only thing that there is—that can be known—and everything is like, a higher order experiment, on a lower order, fundamental realization.

its like the infinite vacuum cycle, that is, the loop goes inward, on & on & on, how many layers deep? who knows. it seems to just be an unrealized-how-deep-the-loop loop ---- That might even be how the original book goes... who knows; havent read it in awhile....

The white rabbit is just Alice-ah—Beth's desire—pulling her towards Wonderland. The twins are like the introduction (Tweedledee & Tweedledum) to a foreign-land. She has a crush on whathisface, Townes aka the cheshire cat (who sometimes appears as the caterpillar)."Eccentric tea party host" who could that be? Benny Watts is the religious-interlude (at one part in the movie, she tells her mom to stop listening to Alan Watts) The mad hatter-and his obsession w/ his black hat, who acts as an intermediary for her—wherein, shes gotta think about what shes even doin', like what is up-down, left-right. Where is wonderland (is it in russia?) how does she get there? Harry Beltik, he could be any number of the original alice in wonderland characters: dodo, the doorknob. Anyway, in the end, Beth is her own Queen of Hearts, her own villain that she has to overcome. The movie ends w/ her playing public chess w/ a random group of ppl—a chess match within a chess match.

oh wait a minute..

yes, love as well as drugs... doing drugs cause they didnt receive love, or some just do it for escapism reasons " and such... sometimes its just like, the infinite realization is what it is... and then search is, well its unusual. Iuno, alls i know is that its like episodes: (1) The cat in the hat (prequel), (2) Magic mushroom initialization of some kind, (3) Queens gambit/alice n wonderland (ep.1), (3) ... to be continued...

The only thing about Queens Gambit, is that Benny Watts hairstyle is too modern looking. I cant imagine anyone would have hair like that in 1940, til atleast like 1970... but i suppose its possible... Although if longer hair was a thing hundreds of years ago, i guesse tis possible... Maybe its tryina capture the reocurring nature of hairstyles (that which returns every 33 years)