My logo :) It's a 4D surface representing the complex Circle-Hyperbola, showing that these two conics are, in complex coordinates, the same manifold in different orientations, and the 'real' curves are part of it. It's the first of a whole series of complex functions' 4D surfaces I've visualised on my channel.
Yes exactly, the title says explained better. But in reality he barely even attempted to explain it. He spent more time discussing the visuals, the programs used to create the visuals and the people that created the visuals.
Yes. Practical application. From looking at it I think it is involved with the flight of various creatures. I wouldn't be surprised if there are hidden secrets of flight within it.
Agreed, some of the most brilliant minds in math & physics are exposed to such a large audience - an audience that loves to learn, and for many about topics beyond the limits of their current understanding (which I think is great!).
Hey, you weren't kidding! Vastly improved delivery! This is the type of stuff that continues to fuel my ambition to do this for as many concepts in physics as possible in optimally intuitive and visual detail. Thanks for the video.
@@HkLY45 This is a central topic in theoretical physics and mathematics. It's a new tool that helps us build a better model about many things in applied physics. It is a landmark discovery in topology and one of the main building blocks in the theory of Lie groups. The Hopf fibration has applications in the theory of magnetic monopoles, rigid body mechanics, and quantum information theory among other fields of applied physics.
the Goethe quote comes to mind "architecture is frozen music" the flowing forces of physics, as chaotic as it may all seem, is akin to a symphony. measured and balanced by the laws that keep everything in it's right place...
Thank you! I have been trying to describe this in 2D, 3D cardboard models and even mirrored snail shells since I read Chandrakasar’s (sp?) description of a 4D sphere, then had vivid dreams about it while taking 1st year physics. I solved a bonus question on a midterm with basic math using the 4D sphere I was seeing in my head. I was able to pull it back to two sets of x,y,z coordinates overlapping each other to find the sign. I was the only one to get the question correct but prof refused me the points as I didn’t use calculus. Two weeks later, I was awarded the points as no one else in 1st or 2nd year managed to solve the problem. I knew I was onto something and it became a hobby/obsession. I kept looking through topology sites etc once the internet and things like YT became available. Interested in Klein Bottles etc. I bored friends and family rambling on about toruses/torii shoved through each other but not touching. I stared at donuts 🍩. What I saw in my mind was the simpler version with 3 rings (so happy for that simulation) I knew there was more but that was way too mind blowing. I still think there might be something intrinsically important about the direction of “flow” to the perception of space/time. Thank you for pointing me in the right direction I’ve been an ant on a Möbius strip for too long. That reminds me, have you tried twisting those toruses into infinity toruses? I’d really love to see that simulation. Twists my mind back in on itself trying to envision.
You sound like someone with savant syndrome who "sees math" wherever he looks, combined with an obsessed programmer dreaming the code he was trying to figure out, after finally getting some sleep. I hope you nurture this hobby/obsession well!
I agree with you and experienced the same. Mine kicked off with lucid dreaming when very young. High dimensional shapes come almost intuitively in that realm.
@@lesleysprague1158 Polaris is part of the small Dipper, mirror image Big Dipper in the sam sky. We are all in tune with the point in which the energy has to try to turn around and leave underneath your feet but new energy continues to flood the system. It's the hypersphere mapped through Infinity. At the very center singularity in the middle of the Earth where longitude is equal to latitude and undefined as zero if I asked you to look up 90° and tell me latitude and longitude upon arrival, you wouldn't know if you were in the Northern or Southern hemisphere.
Thank you! I love watching Eric so much but when he talks about math it often goes over my head. Definitely subscribing, cant wait to see what else you have in store!
@@Sapientiaa I'm not sure... from the paper linked in the description, this is what I could find regarding the link. Very technical, alas: "In the relativistic regime, the relevant wave equation is the Dirac equation. We shall point out here that the Hopf fibration has significance also in this context.Most directly this comes about when one considers the analog of the Dirac equation in two-dimensional space-times in their Euclideanized and compactified versions, which is done either when studying field theories in two space-time dimensions for their own sake, or in (super)string theory. In this context, S2 ∼= CP1 is just the simplest example of such a space-time or string world-sheet, more complicated ones being Riemann surfaces corresponding to algebraic curves [37]. The concept of spinor field, to be subjected to a Dirac equation, requires that of a spin structure, which is a 2:1 covering of the space-time’s bundle of oriented orthonormal tangent frames (see, e.g., [44] for detailed exposition suitable in the present context). Now the assignment z → Z(z) used in Section 2 to graphically represent state vectors in the Bloch sphere picture of pure states shows that the Hopf bundle yields a 2:1 covering of the bundle of oriented orthonormal tangent frames of the 2-sphere, the structure group U(1) playing the role of the spin group covering the frame bundle’s structure group SO(2). Indeed one verifies by elementary calculation that P(z) = RZ(z), Q(z) := IZ(z) satisfy P2 = Q2 = 1, P · Q = 0, P × Q = R. Thus the Hopf bundle is the spin bundle of the 2-sphere."
@@Sapientiaa likely overlapping fundamentality, which sounds paradoxical in a non-eternal universe. The ocean churns, spilling from one waterway to the next. To clarify, they are interlaced emergent properties of each other at different points on their journey.
I recommend a visualizing tool called DMT I've seen this before it moves very rapidly and also can have numbers in areas that collapse in on each other and correspond to idk what but this visual tool also had the beautiful rotating rainbows colors...too hard to explain in words but apparently Hopf vibration is a dimension away from that DMT tool method
I suspect that quantum entanglement is due to effects from hyper dimensions. It's the only thing that explains faster than light communications (i.e.instantaneous), because of their connection in the hyper dimensions.
That is genuinely mind blowing, I had very similar hallucinations while I took LSD and didn't know how to interpret their origin within my brain : - how did my brain ended up letting me see theses structures that I never saw ever ? That I couldn't imagine myself ? So this video is a key of understanding of this phenomenon due to mathematics and it is amazing that I have been able to literally experience 4th dimensional concepts making the theory of higher dimensions very much more tangible than complex math equations. Still didn't get a lot of what this is about but helped me make more sense in my journey of understanding reality mixing math's and psychedelics dope video
I think you might be the missing key of our understanding of how the universe might work. If you are willing to contact me, we should be able to get you at NREC for further exchanges about your theories. The commity already sent you an mail, Looking forward to work with you From Z and our sharesholders
At 7:33 that is exactly what I saw when I took DMT and I broke through.I have always been facinated by these topics and live to try and understand. I use to watch the science channel everyday when it came on premium cable and all I did was watch stuff like this. I love learning bout the universe. You got a subscriber.
I agree 100%, this stuff as well as Mandelbrot's findings pop up in psychedelic experiences even without prior knowledge to the concepts. I think these concepts, math, psychedelics and the universe all are correlated. I have had DMT trips like this, as well as Psilocybin and LSD trips that all contain similar complex geometry.
yes! I have seen very similar geometry on similar substances... And was really upset afterwards when I couldn't explain it to myself or anyone else, because I didn't have the words or brainpower.... Thank fuck for smrt peple. lol and science
"A sphere through infinity", 4:37, looks exactly like the throat of a black hole - if Eric is right (which he is) and this is "the most important shape in the Universe", then implications are implied automatically. Knowing which ones are right is trickier.
Dude, I can't thank you or the algorithm enough for this video. I've been writing a paper (hopefully book) on what I've seen as the "backend" of reality during my out of body experiences. Wish me luck.
@@Carlos.Explains @Django Kinley @Connor Mcleaney I've been writing and rewriting my reply for this because I don't want to give away too much. I will reply here again once I've posted or published my findings. But just know that we are all one. We are all part of something greater and are helping build it (not in a physical sense). Live your life with a burning heart, helping hand, and an open mind. Thanks for the motivation! Much love, and cheers 🍻
The Hopf fibration is a mathematical mapping that describes the relationship between two 3-dimensional spheres. It is named after Heinz Hopf, who discovered it in 1931.
This is a great representation of M Theory/Super String Theory. The vibration frequencies and rotation patterns could be the solidification of energy into matter and explain a ToE
I have a Epileptic AuDHD brain. If I dont take my epilepsy medication, I see these behind my eyelids everywhere all at once. Its looks like I'm seeing reality coming out of reality. The problem is, I can't determine if thats what I'm seeing, or if i am just seeing the transfering of information from my eyeballs down my retinas to my brain. Its one of those things ill just sit and watch and know I'll never understand. It is beautiful. I used to call them hyperspheres, but this is a far better explanation of what I am seeing. I remember when I took my first epilepsy test, and they were blasting light into my eyes. I had an epiphany moment, where I saw myself being pulled backwards out of a water lilly, out of the very centre, and in my mind I thought, that's how everything comes to be. It curves out from behind reality. When an human egg is hatched by a sperm, that very conception point when the inside of the egg the fetus begins, it curls out from behind the bend of reality. When a plant starts to grow inside a seed, the very centre of that growth is pulled out wards from behind that same curve. Almost like a reverse black hole, but it can happen absolutely anywhere in the space we see around us. I only discovered I had an epileptic AuDHD brain after dropping acid a bunch of times. This is all just the ravings of the thoughts ive had, but it's still a profoundly fascinating concept for me. Whats interesting, when I had the waterlilly epiphany, my brain was being monitored by a nurse, and she said "Are you okay?" Straight afterwards. When the test was done, I asked her why she had asked, and she said "well, your entire brain had just lit up, and I thought you were having seizure." The biggest riddle in all of this, was "are these thoughts being given to me from without, or are they are my own thoughts." I think that's a riddle that many have different answers for. It's likely what religious people would call visions. I personally understand I don't have a causal link to make any conclusions, I'm happy with "I don't know."
this was dope lol, my adhd test is coming up. we type similarly. a whole lotta good acid will def hav u being birthed by water lillies hahah its insane how i even got to ur comment. i've been scrolling for so long to find the comment that popped up in the recommend comment section? idk what that singular comment section is called but the comment was just "mind 🍬" which i thought was super clean/super fresh. i click in to give the comment a like and stupid fucking youtube has it BURIED. Why would it pop a comment up right there in that singular, recommended-like section but make it impossible to find??? what kind of POOR POOOR design is that??? Loll😂 im literally going back to digging even further for that comment now. youtube is designed by dumb idiot douchebaggs.. hope i find it soon before i give up. i hyperfixate really quickly so im stuck till i find. its 1:00AM and ive spent 15mins on this. LOL stay safe my brother in mental illness and mental exploration❤
great , draw a bunch of lines , very simple but how does this relate to the structure of the universe ? one thing i love about roger penrose , he often has said that these things should be understandable
Maybe it might help you visualize what a black hole looks like if you could look at it in someway... Almost like looking at something impossible to look at unimaginable, undescribable.
I have seen something very similar to this during a sleep paralysis where I was going through something like this as if it was the part you get sucked into or out of but after this you go out of your body into this astral plane. But during all of the transition you hear static and music (like A.m radio frequencies. I have a hypothesis that some music hits come from there. The muse of you wanna call it that. When you are able to “vibrate out” of this tunnel you astral project your body and are able to travel but I find myself waking up quite quickly after this because it’s hard to control because of over stimulation or something. Idk but this has happened to me since I was 6 or so , I’m 35 now
This is het exactly what happens on DMT, which is the psychedelic chemical that is released in your brain when you’re born and when you die. I am convinced that it is the path into and out of your body
@@briansutton2176 that’s what it was like for me in the beginning but as I got older and had them frequently I wasn’t letting the “ fear take over “ . When you feel it coming over you , you go with it confidently that you won’t let it control you but “vibrate” out of it . Physicist Michio Kaku said it’s about lowering your frequency to 4 ohms. Idk but I’m putting things together and it’s insane
@@someonelse9this is called lucid dreaming, uve accidentally stumbled upon a hard technique to master called WILD, yes the vibrations is when the transition to the dream hsppens
It depends on what you actually have in your mind. If demons show up, you still struggle with general fear. Fear about money, life stuff, fear death. Let it all go and just vibe with life. It's what it's all about.
Reminds me of the scene in "Fifth Element" when the scientist describes the DNA chains "more of them and tightly packed". Thank you for this wonderful video.
@@Carlos.ExplainsI have the most integrated and extensive unification and understanding regarding physics/physical experience and TIME. What is GRAVITY is, ON BALANCE, an INTERACTION that cannot be shielded or blocked. CLEARLY, gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites (ON BALANCE); AS WHAT IS E=MC2 IS GRAVITY; AS the rotation of WHAT IS THE MOON matches the revolution; AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). Consider TIME AND time dilation ON BALANCE. INDEED, consider what is THE EYE ON BALANCE; AS c squared CLEARLY AND NECESSARILY represents a dimension of SPACE ON BALANCE. This explains the fourth dimension. CLEARLY, gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites (ON BALANCE); AS the stars AND PLANETS are POINTS in the night sky; AS the rotation of WHAT IS THE MOON matches the revolution. Consider TIME AND time dilation ON BALANCE, AS WHAT IS E=MC2 is taken directly from F=ma; AS a given PLANET (including WHAT IS THE EARTH) sweeps out equal area in equal TIME. What is GRAVITY is, ON BALANCE, an INTERACTION that cannot be shielded or blocked, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE); AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE. Great !!!! Notice what is the TRANSLUCENT AND BLUE sky ON BALANCE. CLEARLY, ON BALANCE, I have mathematically proven (and explained) what is the fourth dimension. Magnificent. By Frank Martin DiMeglio
For me, it looks like a 3d fractal. I see similar patterns and forms that I noticed in the Mandelbrot fractal and in the bifurcation diagram, especially on the stereographic projection from 2:32 and visualization on the sphere at 1:24 and on a plane at 3:52 . I have reasons to believe they are linked and using same mathematic laws. Is there some mathematics here to confirm or disproof?
Not a mathematician but I think it’s a mixed bag of similarities and differences. Hyperspheres have more dimensions than a Mandelbrot set which as it is radically changes the way it’s variables interact with the generic sphere formula. On the other hand, the base shape of a hypersphere is very simple compared to a Mandelbrot set despite the Mandelbrot set being flat. Under Mandelbrots definition, an n-sphere is not a fractal but it is self similar under different scales and has infinite “complexity” due to its fractal curve. I highly recommend you look at the formulas yourself though, there’s no way to fully grasp these concepts geometrically and these sort of projections cause substantial information loss to force extra dimensions to be represented in a three dimensional abstraction. Ultimately, what you’re looking at is how different variables interact with each other as one or more of them is adjusted.
I NEED TO KNOW MORE. I MUST KNOW MORE. This explanation is excellent for my simple brain. I have a question though. Consider the HF to be a physical skin like a soccer ball. What would the effect on the Hopf Fibratoon be if it were to suddenly be in motion like a spinning basket ball that's been dropped from a great height. What would it look like or what would it do if it were to suddenly be in freefall? Much like a tiny moving ball falling into a bottomless pit. Would it form a definitive "shape" like the moon? 😊😊😊
Thank you very much! I appreciate your work more than one can imagine. Unfortunately for me, I had difficulty understand both this video and the one on the tesseract. However, I will keep trying to understand. In the course of my life, I have come to intuitively understand the significance of a torus. I hoped that in this day and age that I could quickly learn about it, but maybe it will be harder for me than the average person. By the way, I am good at many aspects of math, but mostly the simpler ones, such as the ones taught through high school. I am trying to connect a lot of (truly) scientific and (ontologically) spiritual bodies of knowledge together to work first hand on my personal development. Anyway, I will quit rambing for now. Thanks again. Like, subscribed and hit the notification bell. Take care.
It appears we are a parallel journey through different points in 4D space :P this is only one of many aspects I'm considering, including my religious and spiritual and philosophical understanding
@abf, thanks for the comment! And I plan on covering the torus in the future. :) The hopf fibration and tesseract are complicated! Kudos to you for following your curiosity. I hope to provide better explainers going forward.
Great Video. Could you maybe try to explain how these fiber bundles are used within Weinstein's Geometric Unity? From what I could make out during his lecture, which is on his website, it seems like these bundles are some kind of bridge that collapses higher dimensional symmetries down to lower dimensional projections, or that these higher dimensions provide the necessary "rulers and protractors" that go into creating the 3-dimensional world we see. I'm still kind of fuzzy on his theory, or E8 symmetry as well.
Thanks Meinbher! I might do a follow-up on his Geometric Unity. Admittedly much of this is way over my head, I'd like to have him on for an interview as I think that would be more fruitful.
I try to imagine being on a 2d plane world where somehow you can see a cube drawn that looks 3d. It’s impossible to fully comprehend the paradox from a 2d perspective but some how we strive to imagine it. These geometries and visualizations are the “rulers and protractors” that are used to guide the pencil in drawing 3d on a 2d plane (or 4D in a 3D environment). That’s my interpretation at least haha.
Thanks Chris! And yes, great credit goes to the folks who made these visuals. All works are cited in the description, if any folks are interested in going further down the rabbit hole. 🐰🕳
Thank you for this, was trying to explain this to friend when I heard it on JRE, didnt go well. This explanation is a lot better, but now you have to test it with stoned Rogan in the room haha : D
I think if I were smart enough to understand the mathematics of this, and be able to apply it to describe various aspects of physical reality, I’d go insane.
sho' 'nuff! the more you know, the more you come to know that you don't know and the more you see how much the common person tends to completely inaccurately overgeneralize everything in life. at some point (even just a couple steps past "common sense" territory), the equations of life become too complex to continue considering in a fluid way. everything breaks down into increasingly separate tasks and your mental workload keeps exponentially increasing and your mind starts to fracture... i imagine these are some of the truths on which the 'mad scientist' or the 'absent minded professor' archetypes are based.
@@Princetantaneous yeah uh.. i don't like it tbh. it could be cool, but i won't get into what stops it from being cool. i wanna get off the ride! only, who's to say the other option won't be immeasurably worse? what a racket. (jk... sorta')
My favorite "visualization" of the Hopf fibration is as the restriction of the tautological line bundle over CP^1 to the unit sphere in C^2: S^3 --> CP^1. I've loved it since taking Frank Peterson's seminar in Homotopy Theory in Spring, 1969. My Ohio vanity plate is PI3S2Z.
From this visualization it looks like what we have called atomic orbitals are actually subsets of the hopf fibration, and the apparent transitions the electrons make as they fill up the orbitals are just discontinuities in the mapping from higher d to 4 d space.
This seems to me like a thought exercise. Suitable to create a drawing or a mapping of, via computer simulation(as was shown) ,or writing out/figuring out, the math (geometry?) that illustrates the concept in order to challenge ones thinking. It is attractive to look at ,with all the colors used to indicate or graph points in space, but is it just a clever and beautiful concept and thought exercise, or is there some real world applicability or practical problem solving usage? I mean I used to enjoy playing with a 'Spyrograph' as a kid with the multi colored pens too, or using straight lines between points on a graph (or various colored threads to illustrate trajectories, and pins as the points) to eventually create curves at their intersections, but beyond the artistic pleasure taken from these activities and a better understanding (through firsthand visualization and tactile participation) of how a series of points in space can be manipulated to make curves or circles or even spheres, I don't think there was any 'takeaway' as to how this exercise or the recipe for doing them could be made useful. It just seemed like an interesting way to pass the time, a byproduct of which might be a pretty drawing or mapping at the end. Is there more? What does it tell us, or inform? Thanks in any, case it was enjoyable!
This is the shape I was imagining for quantum particles - I imagined them as a torus made of a dimension that pulled itself inside out. The torus keeps engulfing itself. But the lines never cross. In inside of the particle may not be inside our Universe - or more precisely, they may share the same outer boundary. This is sort of the opposite of a black hole but, similar concept of an event horizon- not sharing our space. So the outside of a black hole is a bit like the inside of a quark and vice versa. It’s how particles are made without any substance.
For something perhaps easier to visualize, connect the two ends of a Slinky (a long spring) to make a donut shape. Now twist (roll) the spring so that the donut shape is preserved, but the surface is moving, and also free to bounce around. This is a 1-dimensional object (spring) mapped onto a 2-dimensional surface (torus) oscillating in 3-dimensional space. It is also the 3-dimensional the shadow of a 4-dimensional Hopf-like object.
Pretty good! You may not have realized, but you neglected to explain the total space is the 3-sphere in 4-space, you just called it "a hypersphere". I think it's worth defining this object rigorously, it has no pre-requisites besides cartesian coordinates. It's also easy to explain the "circle at infinity" using the more intuitive 2-sphere stereographic projection: any geodesic circle through the north pole is projected to a line. Any circle on the 2 sphere that doesn't touch the north pole makes a (topological) circle in the plane. Same concept with the 3 sphere. Another fun thing: I see you have exposited the 4-d cube as a "join" of two 3-d cubes: the union of the two cubes as well as all segments between them. The 3 sphere is the "join" of two circles. They may be taken to be the two "distinguished" circles in the hopf fibration: the geodesic unit circle in the xy plane where the torus collapses, and the circle at infinity. If you take these two circles, draw every segment joining points from the two, and put the distance induced by the spherical law of cosines on the segments and round metric on the circles, you have the 3-sphere (that one is a bit of a deep cut...the only place I've seen it written out is an unpublished paper of Perelman on Alexandrov spaces 😉) A great video, the explanation on Rogan was...not great. Glad someone made a good follow up. - a mathematician
Cool vid. New subscriber here. Looking forward to more videos & also reviewing prior content -really want to understand ( 8:11 ) how the Hopf Fibration is actually a “fundamental element” 🤔….
My first time ever tripping, I took 2 tabs of LSD and saw this hopf thing. I didn’t know how to explain it well but this is it. The visuals in the first minute are it. It undoubtedly has great significance in my mind.
Honestly it looks like many geometric art pieces found across time in religious books and on some church walls and it also looks alot like some of the things you can see on ACID or Shrooms, makes me wonder about our minds being from a higher dimension
Same here. Which is why I'm gonna watch all his vids , and than I'm gonna be like : bit** , shut up , I'm thinking in 4 dimensions ! You can't comprehend this 🦾
Towards the end the hypersphere projection began looking like the Ring Nebula. Excellent visualization and music. Very inspiring to me, a non-physicist but someone who is interested in intuitively understanding these kinds of ideas. Your presentation fully allows for that kind of perception. Thank you so much
So glad I found your channel man. Literally absorbing everything you have on here, it's taking a lot of time but I'm getting through it! KNOWLEDGE ASSIMILATION!
As someone who has no background in all of this I'd just like to ask at some point doesn't this mimic the torus sphere? Should I just be viewing the torus sphere as a stepping stone to understanding the hopf? Also wouldn't that mean that all torus spheres have some sort of unseen element that unknowingly to us makes it a hopf? Edit: Just an after thought wouldn't this intersect it self at some point like a klien bottle if enough circles are added?
Awesome! Loved it! So, the source was always from the northern most point of the sphere, right? Would the illustrations change if the source wasoved to a lower point on the sphere? And, would it also make a difference if the source was closer to the outer edge or to the most inner part of the sphere?
I was just looking around and saw the Hopf and was stunned. 3 days after the CERN collider was started back up I had a dream. Three Hopf (now I know what it was, didn't know until seeing this) "units" were presented to me. Each one was getting progressively smaller. The Hopf "units" were all distorted and deflated and in the dream I knew this was not right. Additionally the surface of the Hopf "units" had melted distorted chimera like imagery of all of the worlds flags (3 were predominate). Under that layer were all of the worlds corporate logos also completed melted, distorted and chimera like. I quit looking into the layers at that point. When I woke up I didn't have an opinion, but within a few days I realized it pertained to CERN.
This is exactly what I was looking for. I only imagined that idea and here you are showing it. More interestingly, is there software that lets you see how shapes transition from one dimension to the next. Also looking for a way to have an image wrapped around sphere in 3D and sterographically force it on to 2D surface to see what the image will look like.
What does this vibration dictate in physical reality, and at what level of physics? Is it under the fabric of space time? Is it beyond the Planck length, Planck time, Planck temperature
So a race around a hypersphere would start at a non skewed circle and end at an infinite finish line. Now the question is, is there such thing as a start or finish? Or would we see the hole race all at once?
When I was a child I was given psychedelic mushrooms. When I looked into the sky I saw this but from the inside as if we were passing through it. This was long before I had any clue that such things existed.
when the red infinity circle was shown as a vanishing point into the center of the image i felt like i understood some of how the 4th dimensional objects make sense; the hypercube came to mind and it felt better to look at. at the same moment i also felt i had an intution for how anything 5th dimensional might be shown. what a great vid. thank you
Reminds me of what I see during a dmt session. It's like flying through one of these on the way to... Wherever you go. Everything is covered by a fractal film that responds to stimuli... Once you learn how to look, you'll see.
So what does it do? How is it useful? Practical application? Without the spinning 4d modeling it looks like the field strength of radio waves that widen transmitting in all directions or flatten out into a focused ground plane depending on antenna height from the ground.
This is just an interesting visualization of a hypersphere as circles drawn on its surface. What is meant by "vibration". It would be more interesting to talk about how it relates to those physics topics. I assume it is also related to electron spin state.
When I was in high school I used to take adderall. One day I took the adderall and payed on the couch and rested my eyes. I didn’t drift off into sleep(i think). I was concentrating on nothing except a pressure in the middle of my head. I was intentionally doing so. As I lay there I believe I began to see a myriad of color (almost like an oil slick produces when light shines upon it) passing underneath me and going up the hopfi walls behind me. I began to look forward and saw a shape that I have never seen since. It was a solid and semi solidly with hard edges and smooth liquid like surfaces( poor description I know) it was constantly moving and changing the shape. It spoke and said everything is okay in a voice that sounded like Optimus prime. I said whatever you say Optimus prime then my heart rate began to raise and I opened my eyes and was laying on the couch again. It was either a hopfi or a toroidal shape. I’m more keen to say it was a toroidal bc the center object had a stream going into it and out of it from the top and bottom
Cool how the hypersphere looks like a wormhole as the circle gets closer to passing through infinity. Could black holes be circles through infinity on a hypersphere?
I'm not educated on the math, but I've always had the idea that a "particle" is two or more quantum fields trapped within each other. Which, given the angles of those fields relative to each other, would seem to me to necessitate them "turning inside out around each other". This video illustrates perfectly what I could never put into words.
1. 🔥comment 2. it took me probably 3 full minutes of non-stop scrolling through the comment section to find this. im literally so pissed/frustrated at youtube. 3. This comment popped up in the singular comment section as i was watching the video vertically on my phone. 4. Why would youtube bury a recommeded comment??? that makes no sense, ZERO SENSE. I had to hyperfixate and utilize my ADHD powers to get here and put this into reality. 5. i apologize for being crass in this intellectual domain but jesus christ youtube is retarded for this.
all i wanted to do was give a like and a "fire comment" to the comment that POPPED UP. why did i need to scroll so much and get literally upset/obsessed for somthing that should hav been at the top if it was what made me click in. im sorry i lack the proper tech lingo but i hope i've at least expressed how unreasonable the design of this app/comment situation is. sorry to the original comment and the video channel. my rage towards the incompetent/lazy/careless web designers at youtube knows no bounds
It felt like watching a black hole or quasar or supernova. All those magneto electric entanglements. Vibrational portals or wormholes ....... fascinating.
And that all those who conclude, after looking at al levels of reality, and cannot see that there "exists" ( quotation marks, because if only the narrow definition of, "to exist", means, " some scientific instrument can be used to detect it " is used ...) a Creative Superintelligence behind, above , beneath, and within our reality, they must be willfully blind.
I found out that kinetic energy is part of it. KE = mvˇ2/2 is basically same as the volume of torus (m being the r1 big radius, and v being cirumference of small radius). But as KE is simple Newtonian, then adding features to it extends the torus to new dimensions where Hopf fibration awaits on every step again and again. Universe is bunch or perpendicular radii, circles. Although it could be interpreted as waves, because waves and circles are all about number Pii.
So basically, if we took this concept to the 5th Dimension each one of those linked circles would instead be spheres instead, intersecting probably an infinite amount of times right?
Laser dot (the infinity point) hits a mirror the mirror can spread out that dot into a 2 dimensional plane.. the image is a continuous positive and negative.. when this is reflected onto a second mirror adding another dimension all manner of 2d and 3d shapes can be manifest as a projection yet uninterrupted from a source that has the ability to scale up to a maximum size limited by throw distance and mirror angle but also reduced in size back to an original infinite dot... the image projected out can also can have added dimensions governed by the geometry of that space. Just thought of all that as I watched your video and felt it may help give me or you or anyone another way of understanding the Hopf Fibration. It may not be anything??
What's your favorite geometric/topological structure and why? 😀
A square, because I relate to them
Triangle...because I tried.
🥺
.
You didn't actually explain its utility.
My logo :) It's a 4D surface representing the complex Circle-Hyperbola, showing that these two conics are, in complex coordinates, the same manifold in different orientations, and the 'real' curves are part of it. It's the first of a whole series of complex functions' 4D surfaces I've visualised on my channel.
I think it would have really helped to go into more depth on the importance of this structure and why it matters so much. Otherwise, phenomenal video.
Yea, what does this thing mean or do?
Yes exactly, the title says explained better. But in reality he barely even attempted to explain it. He spent more time discussing the visuals, the programs used to create the visuals and the people that created the visuals.
@@jasonwrner…did you watch this video? He explained exactly what it is, what it does, and even recommended how to better grasp the structure
Poop@@Runthemjewels
Yes. Practical application.
From looking at it I think it is involved with the flight of various creatures. I wouldn't be surprised if there are hidden secrets of flight within it.
This guy really talks to anyone on his show and I'm glad he that even gives the mathematics community a chance too.
Agreed, some of the most brilliant minds in math & physics are exposed to such a large audience - an audience that loves to learn, and for many about topics beyond the limits of their current understanding (which I think is great!).
Joe rogan audience is def. Not zhe right for that on average.
They rather spend tile talking about conspiracy theoriesy flat earth etc.
@@zoro8117 obvious bait is obvious
@Zo Ro keep living in the past bud
@@zoro8117 learn how to spell
I’m listening to this really loud so my girlfriend thinks I’m smart. Waffles are so good. That’s what I want for dinner.
Haha I’m actually interested in this shit but she doesn’t care about my smart side 😢😂
🤣😂🤣🤣🤣🤣🤣😂
you are so cool and quirky dood wow!
Stop trying to impress her. She's only using you and doesn't care. And soon she'll be gone and you'll be forgotten.
@@SelectCircle😮💨kid,go out,touch some grass
Hey, you weren't kidding! Vastly improved delivery! This is the type of stuff that continues to fuel my ambition to do this for as many concepts in physics as possible in optimally intuitive and visual detail. Thanks for the video.
To be fair, he was in a podcast. You can’t just explain this type of stuff in words alone.
I guess that's why there's visuals attached to this podcast.?@@just2genders668
That's a good point. I should mention that Eric's episodes are some of my favorites, especially that one when it came out.
Dude. Thank you. This is the first time I actually have a good intuition of what a higherdimension representation is.
Thank you, Ju! Glad you enjoyed it. 😀
Read Flatland.
Same. It hit me like one of Rogan's DMT trips. Thanks man.
Fr, Ive always thought that the universe was a torus
Check out "10 Dimensions in 2 Minutes"
I cried watching this.
Finally someone exposes and resumes a Hopf fibration in full detail. People do not understand HOW IMPORTANT this concept is.
You are right. I don't understand how this is important. Explain it?
@@HkLY45 This is a central topic in theoretical physics and mathematics. It's a new tool that helps us build a better model about many things in applied physics. It is a landmark discovery in topology and one of the main building blocks in the theory of Lie groups. The Hopf fibration has applications in the theory of magnetic monopoles, rigid body mechanics, and quantum information theory among other fields of applied physics.
@@kummer45 thanks for the explanation. I see it's important to people involved in science. I understood practically 0% of what you said. 🤣
@@HkLY45 It means we get cool shit in the future bro.
@@patrickstewart6260 that's fuckin rad bro.
the Goethe quote comes to mind "architecture is frozen music"
the flowing forces of physics, as chaotic as it may all seem,
is akin to a symphony. measured and balanced by the laws that keep everything in it's right place...
Thank you! I have been trying to describe this in 2D, 3D cardboard models and even mirrored snail shells since I read Chandrakasar’s (sp?) description of a 4D sphere, then had vivid dreams about it while taking 1st year physics. I solved a bonus question on a midterm with basic math using the 4D sphere I was seeing in my head. I was able to pull it back to two sets of x,y,z coordinates overlapping each other to find the sign. I was the only one to get the question correct but prof refused me the points as I didn’t use calculus. Two weeks later, I was awarded the points as no one else in 1st or 2nd year managed to solve the problem.
I knew I was onto something and it became a hobby/obsession. I kept looking through topology sites etc once the internet and things like YT became available. Interested in Klein Bottles etc. I bored friends and family rambling on about toruses/torii shoved through each other but not touching. I stared at donuts 🍩. What I saw in my mind was the simpler version with 3 rings (so happy for that simulation) I knew there was more but that was way too mind blowing. I still think there might be something intrinsically important about the direction of “flow” to the perception of space/time. Thank you for pointing me in the right direction I’ve been an ant on a Möbius strip for too long. That reminds me, have you tried twisting those toruses into infinity toruses? I’d really love to see that simulation. Twists my mind back in on itself trying to envision.
You sound like someone with savant syndrome who "sees math" wherever he looks, combined with an obsessed programmer dreaming the code he was trying to figure out, after finally getting some sleep. I hope you nurture this hobby/obsession well!
I agree with you and experienced the same. Mine kicked off with lucid dreaming when very young. High dimensional shapes come almost intuitively in that realm.
@@lesleysprague1158 Polaris is part of the small Dipper, mirror image Big Dipper in the sam sky. We are all in tune with the point in which the energy has to try to turn around and leave underneath your feet but new energy continues to flood the system. It's the hypersphere mapped through Infinity. At the very center singularity in the middle of the Earth where longitude is equal to latitude and undefined as zero if I asked you to look up 90° and tell me latitude and longitude upon arrival, you wouldn't know if you were in the Northern or Southern hemisphere.
Are you male or female?
Enjoyed your comment, btw.
So basically this oroves higher dimensions exist
I am way too high and drunk to understand any of this.
Samesies
I'm sober and still not able to understand this.
It'll all start to click when we hear our activation phrases
@@niconicotinenebula7104huh⁉️
You did a thing that is rare on UA-cam. Delivered on your thumbnail! Great explanation and visuals.
Thanks DLR! Beware of men in white lab coats...
Thank you! I love watching Eric so much but when he talks about math it often goes over my head. Definitely subscribing, cant wait to see what else you have in store!
Thank you, Aubrey!! 😄
@@Carlos.Explains How do these manifolds interact with 1 dimensional strings? I thought strings were fundamental.
@@Sapientiaa I'm not sure... from the paper linked in the description, this is what I could find regarding the link. Very technical, alas:
"In the relativistic regime, the relevant wave equation is the Dirac equation. We shall point out here that the Hopf fibration has significance also in this context.Most directly this comes about when one considers the analog of the Dirac equation in two-dimensional space-times in their Euclideanized and compactified versions, which is done either when studying field theories in two space-time dimensions for their
own sake, or in (super)string theory. In this context, S2 ∼= CP1 is just the simplest example of such a space-time or string world-sheet, more complicated ones being Riemann surfaces corresponding to algebraic curves [37].
The concept of spinor field, to be subjected to a Dirac equation, requires that of a spin structure, which is a 2:1 covering of the space-time’s bundle of oriented orthonormal tangent frames (see, e.g., [44] for detailed exposition suitable in the present context). Now the assignment z → Z(z) used in Section 2 to graphically represent state vectors in the Bloch sphere picture of pure states shows that the Hopf bundle yields a 2:1 covering of the bundle of oriented orthonormal tangent frames of the 2-sphere, the structure group U(1) playing the role of the spin group covering the frame bundle’s structure group SO(2). Indeed one verifies by elementary calculation that P(z) = RZ(z), Q(z) := IZ(z) satisfy P2 = Q2 = 1, P · Q = 0, P × Q = R. Thus the Hopf bundle is the
spin bundle of the 2-sphere."
@@Sapientiaa likely overlapping fundamentality, which sounds paradoxical in a non-eternal universe. The ocean churns, spilling from one waterway to the next. To clarify, they are interlaced emergent properties of each other at different points on their journey.
@@pfzht Thanks!
I recommend a visualizing tool called DMT
I've seen this before it moves very rapidly and also can have numbers in areas that collapse in on each other and correspond to idk what but this visual tool also had the beautiful rotating rainbows colors...too hard to explain in words but apparently Hopf vibration is a dimension away from that DMT tool method
Clever
I too recommend this visualization tool
Thanks Mitchell. So many other folks in this thread have had a similar experience.
@@alexbrestowski4131 What would you like this channel to cover in the future?
@@vystorm care to share your experience?
This came out of nowhere 2 years later and I love it! Thanks so much.
I suspect that quantum entanglement is due to effects from hyper dimensions. It's the only thing that explains faster than light communications (i.e.instantaneous), because of their connection in the hyper dimensions.
That is genuinely mind blowing, I had very similar hallucinations while I took LSD and didn't know how to interpret their origin within my brain :
- how did my brain ended up letting me see theses structures that I never saw ever ? That I couldn't imagine myself ?
So this video is a key of understanding of this phenomenon due to mathematics and it is amazing that I have been able to literally experience 4th dimensional concepts making the theory of higher dimensions very much more tangible than complex math equations.
Still didn't get a lot of what this is about but helped me make more sense in my journey of understanding reality mixing math's and psychedelics
dope video
I think you might be the missing key of our understanding of how the universe might work. If you are willing to contact me, we should be able to get you at NREC for further exchanges about your theories.
The commity already sent you an mail,
Looking forward to work with you
From Z and our sharesholders
At 7:33 that is exactly what I saw when I took DMT and I broke through.I have always been facinated by these topics and live to try and understand. I use to watch the science channel everyday when it came on premium cable and all I did was watch stuff like this. I love learning bout the universe. You got a subscriber.
I agree 100%, this stuff as well as Mandelbrot's findings pop up in psychedelic experiences even without prior knowledge to the concepts. I think these concepts, math, psychedelics and the universe all are correlated. I have had DMT trips like this, as well as Psilocybin and LSD trips that all contain similar complex geometry.
yes! I have seen very similar geometry on similar substances... And was really upset afterwards when I couldn't explain it to myself or anyone else, because I didn't have the words or brainpower.... Thank fuck for smrt peple. lol and science
sup homie, can we compare trips? same shit happened to me.
I don't think I actually learned anything about the math, but the visuals are worth it on their own
I'll accept partial credit. :)
This is all well and good but can I get it as a screen saver?
"A sphere through infinity", 4:37, looks exactly like the throat of a black hole - if Eric is right (which he is) and this is "the most important shape in the Universe", then implications are implied automatically. Knowing which ones are right is trickier.
It feels good to unintentionally learn something this insane
Dude, I can't thank you or the algorithm enough for this video. I've been writing a paper (hopefully book) on what I've seen as the "backend" of reality during my out of body experiences.
Wish me luck.
What’s your substance of choice
Cheers @@djangokinley4284 and @killianthegrunt, what'd you see as the backend of reality?
Oh and praise be the algorithm!
@@Carlos.Explains yeah I wanna know too
@@Carlos.Explains @Django Kinley @Connor Mcleaney I've been writing and rewriting my reply for this because I don't want to give away too much. I will reply here again once I've posted or published my findings.
But just know that we are all one. We are all part of something greater and are helping build it (not in a physical sense).
Live your life with a burning heart, helping hand, and an open mind.
Thanks for the motivation! Much love, and cheers 🍻
The Hopf fibration is a mathematical mapping that describes the relationship between two 3-dimensional spheres. It is named after Heinz Hopf, who discovered it in 1931.
This is a great representation of M Theory/Super String Theory. The vibration frequencies and rotation patterns could be the solidification of energy into matter and explain a ToE
Can it grow food, and build houses
@Repo-Mandumbass
FUCK ME SILLY
@Repo-Man oh this is gonna age well
I have a Epileptic AuDHD brain.
If I dont take my epilepsy medication, I see these behind my eyelids everywhere all at once.
Its looks like I'm seeing reality coming out of reality.
The problem is, I can't determine if thats what I'm seeing, or if i am just seeing the transfering of information from my eyeballs down my retinas to my brain.
Its one of those things ill just sit and watch and know I'll never understand.
It is beautiful.
I used to call them hyperspheres, but this is a far better explanation of what I am seeing.
I remember when I took my first epilepsy test, and they were blasting light into my eyes.
I had an epiphany moment, where I saw myself being pulled backwards out of a water lilly, out of the very centre, and in my mind I thought, that's how everything comes to be.
It curves out from behind reality.
When an human egg is hatched by a sperm, that very conception point when the inside of the egg the fetus begins, it curls out from behind the bend of reality.
When a plant starts to grow inside a seed, the very centre of that growth is pulled out wards from behind that same curve.
Almost like a reverse black hole, but it can happen absolutely anywhere in the space we see around us.
I only discovered I had an epileptic AuDHD brain after dropping acid a bunch of times.
This is all just the ravings of the thoughts ive had, but it's still a profoundly fascinating concept for me.
Whats interesting, when I had the waterlilly epiphany, my brain was being monitored by a nurse, and she said "Are you okay?" Straight afterwards.
When the test was done, I asked her why she had asked, and she said "well, your entire brain had just lit up, and I thought you were having seizure."
The biggest riddle in all of this, was "are these thoughts being given to me from without, or are they are my own thoughts."
I think that's a riddle that many have different answers for.
It's likely what religious people would call visions.
I personally understand I don't have a causal link to make any conclusions, I'm happy with "I don't know."
this was dope lol, my adhd test is coming up. we type similarly.
a whole lotta good acid will def hav u being birthed by water lillies hahah
its insane how i even got to ur comment. i've been scrolling for so long to find the comment that popped up in the recommend comment section? idk what that singular comment section is called but the comment was just
"mind 🍬"
which i thought was super clean/super fresh.
i click in to give the comment a like and stupid fucking youtube has it BURIED.
Why would it pop a comment up right there in that singular, recommended-like section but make it impossible to find??? what kind of POOR POOOR design is that???
Loll😂 im literally going back to digging even further for that comment now. youtube is designed by dumb idiot douchebaggs.. hope i find it soon before i give up. i hyperfixate really quickly so im stuck till i find. its 1:00AM and ive spent 15mins on this. LOL stay safe my brother in mental illness and mental exploration❤
Could you please elaborate on your experience? Sounds very interesting
I'm comletely lost at 3:25, what is this levitating circle on the left???? why are you plotting this weird shape at 3:45???
great , draw a bunch of lines , very simple but how does this relate to the structure of the universe ? one thing i love about roger penrose , he often has said that these things should be understandable
I wish I knew... I'm trying to get a physicist on for an interview to explain!
Maybe it might help you visualize what a black hole looks like if you could look at it in someway...
Almost like looking at something impossible to look at unimaginable, undescribable.
I have seen something very similar to this during a sleep paralysis where I was going through something like this as if it was the part you get sucked into or out of but after this you go out of your body into this astral plane. But during all of the transition you hear static and music (like A.m radio frequencies. I have a hypothesis that some music hits come from there. The muse of you wanna call it that.
When you are able to “vibrate out” of this tunnel you astral project your body and are able to travel but I find myself waking up quite quickly after this because it’s hard to control because of over stimulation or something. Idk but this has happened to me since I was 6 or so , I’m 35 now
This is het exactly what happens on DMT, which is the psychedelic chemical that is released in your brain when you’re born and when you die. I am convinced that it is the path into and out of your body
You're lucky. I only see demons in my sleep paralysis episodes
@@briansutton2176 that’s what it was like for me in the beginning but as I got older and had them frequently I wasn’t letting the “ fear take over “ . When you feel it coming over you , you go with it confidently that you won’t let it control you but “vibrate” out of it . Physicist Michio Kaku said it’s about lowering your frequency to 4 ohms. Idk but I’m putting things together and it’s insane
@@someonelse9this is called lucid dreaming, uve accidentally stumbled upon a hard technique to master called WILD, yes the vibrations is when the transition to the dream hsppens
It depends on what you actually have in your mind. If demons show up, you still struggle with general fear. Fear about money, life stuff, fear death. Let it all go and just vibe with life. It's what it's all about.
Reminds me of the scene in "Fifth Element" when the scientist describes the DNA chains "more of them and tightly packed". Thank you for this wonderful video.
Leelu Dallas: Multipass
@@00SEVEN28 & R Sanchez, thanks for the references!
@@Carlos.ExplainsI have the most integrated and extensive unification and understanding regarding physics/physical experience and TIME.
What is GRAVITY is, ON BALANCE, an INTERACTION that cannot be shielded or blocked. CLEARLY, gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites (ON BALANCE); AS WHAT IS E=MC2 IS GRAVITY; AS the rotation of WHAT IS THE MOON matches the revolution; AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). Consider TIME AND time dilation ON BALANCE. INDEED, consider what is THE EYE ON BALANCE; AS c squared CLEARLY AND NECESSARILY represents a dimension of SPACE ON BALANCE. This explains the fourth dimension. CLEARLY, gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites (ON BALANCE); AS the stars AND PLANETS are POINTS in the night sky; AS the rotation of WHAT IS THE MOON matches the revolution. Consider TIME AND time dilation ON BALANCE, AS WHAT IS E=MC2 is taken directly from F=ma; AS a given PLANET (including WHAT IS THE EARTH) sweeps out equal area in equal TIME. What is GRAVITY is, ON BALANCE, an INTERACTION that cannot be shielded or blocked, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE); AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE. Great !!!! Notice what is the TRANSLUCENT AND BLUE sky ON BALANCE. CLEARLY, ON BALANCE, I have mathematically proven (and explained) what is the fourth dimension. Magnificent.
By Frank Martin DiMeglio
You left out the Prometheus engineer. ua-cam.com/video/vDOj9XEezDQ/v-deo.html
Love your videos my bro! I always watch them and chill before I go to bed. Thanks for making them.
@@g-dad1472 thanks for watching! sweet dreams
Thank you for your time. Ps I like how you answer to negative comments. I don't see why people need to be rude when commenting in these forums.
Thanks MadderHat! Trust me, sometimes I am tempted to offer people their money back... 😆
@@Carlos.Explains 🤣
For me, it looks like a 3d fractal. I see similar patterns and forms that I noticed in the Mandelbrot fractal and in the bifurcation diagram, especially on the stereographic projection from 2:32 and visualization on the sphere at 1:24 and on a plane at 3:52 . I have reasons to believe they are linked and using same mathematic laws. Is there some mathematics here to confirm or disproof?
Not a mathematician but I think it’s a mixed bag of similarities and differences. Hyperspheres have more dimensions than a Mandelbrot set which as it is radically changes the way it’s variables interact with the generic sphere formula. On the other hand, the base shape of a hypersphere is very simple compared to a Mandelbrot set despite the Mandelbrot set being flat. Under Mandelbrots definition, an n-sphere is not a fractal but it is self similar under different scales and has infinite “complexity” due to its fractal curve. I highly recommend you look at the formulas yourself though, there’s no way to fully grasp these concepts geometrically and these sort of projections cause substantial information loss to force extra dimensions to be represented in a three dimensional abstraction. Ultimately, what you’re looking at is how different variables interact with each other as one or more of them is adjusted.
@@mikedevyatov3213 based
THIS is what I've been missing my entire life! Hopf Fibration FINALLY explained in a manner that I can understand!
Now I can die happy.
we never die..
@@giovanniamore7532 Life Eternal with Hopf Fibration!
I’m so confused, does this explain the space we are in. Where is 3D space connected to 4D space, just tell me that.
Um so this solves horneyness when muma is grumpy? Please explain
@@christopherlocke9616 My doctor prescribed Hopf Fibration™ to treat my arthritis. It's done wonders!
I'm picking up HOPF Fibration, it's giving me extradimentional sensations oom bop bop oom HOPF Fibration
I NEED TO KNOW MORE.
I MUST KNOW MORE.
This explanation is excellent for my simple brain.
I have a question though.
Consider the HF to be a physical skin like a soccer ball.
What would the effect on the Hopf Fibratoon be if it were to suddenly be in motion like a spinning basket ball that's been dropped from a great height.
What would it look like or what would it do if it were to suddenly be in freefall?
Much like a tiny moving ball falling into a bottomless pit.
Would it form a definitive "shape" like the moon? 😊😊😊
Thank you very much! I appreciate your work more than one can imagine. Unfortunately for me, I had difficulty understand both this video and the one on the tesseract. However, I will keep trying to understand. In the course of my life, I have come to intuitively understand the significance of a torus. I hoped that in this day and age that I could quickly learn about it, but maybe it will be harder for me than the average person. By the way, I am good at many aspects of math, but mostly the simpler ones, such as the ones taught through high school. I am trying to connect a lot of (truly) scientific and (ontologically) spiritual bodies of knowledge together to work first hand on my personal development. Anyway, I will quit rambing for now. Thanks again. Like, subscribed and hit the notification bell. Take care.
same, im worse than you at math. but learning stuff about our universe is fascinating even if you dont undestand.
👽
@@justotalkalottashit8392 wow
It appears we are a parallel journey through different points in 4D space :P this is only one of many aspects I'm considering, including my religious and spiritual and philosophical understanding
@abf, thanks for the comment! And I plan on covering the torus in the future. :)
The hopf fibration and tesseract are complicated! Kudos to you for following your curiosity. I hope to provide better explainers going forward.
Great Video. Could you maybe try to explain how these fiber bundles are used within Weinstein's Geometric Unity? From what I could make out during his lecture, which is on his website, it seems like these bundles are some kind of bridge that collapses higher dimensional symmetries down to lower dimensional projections, or that these higher dimensions provide the necessary "rulers and protractors" that go into creating the 3-dimensional world we see. I'm still kind of fuzzy on his theory, or E8 symmetry as well.
Thanks Meinbher! I might do a follow-up on his Geometric Unity. Admittedly much of this is way over my head, I'd like to have him on for an interview as I think that would be more fruitful.
I try to imagine being on a 2d plane world where somehow you can see a cube drawn that looks 3d. It’s impossible to fully comprehend the paradox from a 2d perspective but some how we strive to imagine it. These geometries and visualizations are the “rulers and protractors” that are used to guide the pencil in drawing 3d on a 2d plane (or 4D in a 3D environment). That’s my interpretation at least haha.
ua-cam.com/video/UnURElCzGc0/v-deo.html
I forgot about this Carl Sagan video! Exactly what I was trying to explain! It came on right after this one! Lol
Many thanks for a great explanation! And much respect to the creators of these amazing visuals.
Thanks Chris! And yes, great credit goes to the folks who made these visuals. All works are cited in the description, if any folks are interested in going further down the rabbit hole. 🐰🕳
Much respect to the Creator, whose mind is beyond searching.
This Video was like a Brain/ Consciousness level exercise Thanks for the video ! Production was great also
At 7:10 doesn’t it resemble a pulsar? What if pulsars are the 3d representation of a hyper sphere?
Thank you for this, was trying to explain this to friend when I heard it on JRE, didnt go well.
This explanation is a lot better, but now you have to test it with stoned Rogan in the room haha : D
Thank you so much! Be sure to share it with your friend 😀
I think if I were smart enough to understand the mathematics of this, and be able to apply it to describe various aspects of physical reality, I’d go insane.
sho' 'nuff!
the more you know, the more you come to know that you don't know and the more you see how much the common person tends to completely inaccurately overgeneralize everything in life.
at some point (even just a couple steps past "common sense" territory), the equations of life become too complex to continue considering in a fluid way. everything breaks down into increasingly separate tasks and your mental workload keeps exponentially increasing and your mind starts to fracture... i imagine these are some of the truths on which the 'mad scientist' or the 'absent minded professor' archetypes are based.
@@luceatlux7087 welcome to earth
@@Princetantaneous yeah uh.. i don't like it tbh. it could be cool, but i won't get into what stops it from being cool.
i wanna get off the ride! only, who's to say the other option won't be immeasurably worse? what a racket.
(jk... sorta')
Not a scientist and I feel like my mind fractured years ago.
My favorite "visualization" of the Hopf fibration is as the restriction of the tautological line bundle over CP^1 to the unit sphere in C^2: S^3 --> CP^1.
I've loved it since taking Frank Peterson's seminar in Homotopy Theory in Spring, 1969.
My Ohio vanity plate is PI3S2Z.
Id like to see that, but I don't understand math very well. Would you kindly provide a web link?
I'm high as shit lol idk any if what you just said, but you're a nerd and shouldn't ever change. Its beautiful.
I'm with @@PatrickPease ! Barry, do you have a link?
@@WiZArdx4s That vanity plate is commitment. Honk if you love the Hopf. :)
This will help you cope further with the science... ua-cam.com/video/spkFNvp1lEc/v-deo.html
From this visualization it looks like what we have called atomic orbitals are actually subsets of the hopf fibration, and the apparent transitions the electrons make as they fill up the orbitals are just discontinuities in the mapping from higher d to 4 d space.
Is the whole atomic model then just a higher order harmonic resonance in an infinitely dimensioned space projected into 4d space thay we perceive?
This seems to me like a thought exercise. Suitable to create a drawing or a mapping of, via computer simulation(as was shown) ,or writing out/figuring out, the math (geometry?) that illustrates the concept in order to challenge ones thinking. It is attractive to look at ,with all the colors used to indicate or graph points in space, but is it just a clever and beautiful concept and thought exercise, or is there some real world applicability or practical problem solving usage? I mean I used to enjoy playing with a 'Spyrograph' as a kid with the multi colored pens too, or using straight lines between points on a graph (or various colored threads to illustrate trajectories, and pins as the points) to eventually create curves at their intersections, but beyond the artistic pleasure taken from these activities and a better understanding (through firsthand visualization and tactile participation) of how a series of points in space can be manipulated to make curves or circles or even spheres, I don't think there was any 'takeaway' as to how this exercise or the recipe for doing them could be made useful. It just seemed like an interesting way to pass the time, a byproduct of which might be a pretty drawing or mapping at the end. Is there more? What does it tell us, or inform? Thanks in any, case it was enjoyable!
What a great job explaining so much in this bite sized piece of golden content! You know I subscribed! Awesome production thru and thru as well!
Thanks, you so money and you don't even know it!
This is the shape I was imagining for quantum particles - I imagined them as a torus made of a dimension that pulled itself inside out. The torus keeps engulfing itself. But the lines never cross. In inside of the particle may not be inside our Universe - or more precisely, they may share the same outer boundary. This is sort of the opposite of a black hole but, similar concept of an event horizon- not sharing our space. So the outside of a black hole is a bit like the inside of a quark and vice versa.
It’s how particles are made without any substance.
For something perhaps easier to visualize, connect the two ends of a Slinky (a long spring) to make a donut shape. Now twist (roll) the spring so that the donut shape is preserved, but the surface is moving, and also free to bounce around. This is a 1-dimensional object (spring) mapped onto a 2-dimensional surface (torus) oscillating in 3-dimensional space. It is also the 3-dimensional the shadow of a 4-dimensional Hopf-like object.
Pretty good! You may not have realized, but you neglected to explain the total space is the 3-sphere in 4-space, you just called it "a hypersphere". I think it's worth defining this object rigorously, it has no pre-requisites besides cartesian coordinates.
It's also easy to explain the "circle at infinity" using the more intuitive 2-sphere stereographic projection: any geodesic circle through the north pole is projected to a line. Any circle on the 2 sphere that doesn't touch the north pole makes a (topological) circle in the plane. Same concept with the 3 sphere.
Another fun thing: I see you have exposited the 4-d cube as a "join" of two 3-d cubes: the union of the two cubes as well as all segments between them. The 3 sphere is the "join" of two circles. They may be taken to be the two "distinguished" circles in the hopf fibration: the geodesic unit circle in the xy plane where the torus collapses, and the circle at infinity. If you take these two circles, draw every segment joining points from the two, and put the distance induced by the spherical law of cosines on the segments and round metric on the circles, you have the 3-sphere (that one is a bit of a deep cut...the only place I've seen it written out is an unpublished paper of Perelman on Alexandrov spaces 😉)
A great video, the explanation on Rogan was...not great. Glad someone made a good follow up. - a mathematician
Amazing, thank you for the thorough explanation!!
Cool vid. New subscriber here. Looking forward to more videos & also reviewing prior content -really want to understand ( 8:11 ) how the Hopf Fibration is actually a “fundamental element”
🤔….
My first time ever tripping, I took 2 tabs of LSD and saw this hopf thing. I didn’t know how to explain it well but this is it. The visuals in the first minute are it. It undoubtedly has great significance in my mind.
Ok
Wouldn't have one tablet been enough?
@@WinrichNaujoks depends on who was selling it, lsd can be diluted just like cocaine can be cut.
@@WinrichNaujoksnot a tablet - just saying
Same, LSD + jazz ballin
Honestly it looks like many geometric art pieces found across time in religious books and on some church walls and it also looks alot like some of the things you can see on ACID or Shrooms, makes me wonder about our minds being from a higher dimension
I gotta say this was really comprehensive. As a “math illiterate” person some of these concepts keep evading me. I have a better grasp. Thanks
As someone named Hopf I always wondered where my addiction to mathematics came from 😂
8:30 What song/music is playing at the very end? I would love to have that song to listen to
8:30
Hey Alex, it's Nemesis by Albis: ua-cam.com/video/Znuftxau-oE/v-deo.html
I’m thoroughly confused!
Same here. Which is why I'm gonna watch all his vids , and than I'm gonna be like : bit** , shut up , I'm thinking in 4 dimensions ! You can't comprehend this 🦾
🤣😂🤣 same... I'm just gonna keep with it until it clicks.
Towards the end the hypersphere projection began looking like the Ring Nebula. Excellent visualization and music. Very inspiring to me, a non-physicist but someone who is interested in intuitively understanding these kinds of ideas. Your presentation fully allows for that kind of perception. Thank you so much
What an amazing video. Thanks for the hard work.
Thanks Jason! Much appreciated. 😀
The thumbnail is gold
The magic eye stereogram at the end was awesome!
So glad I found your channel man. Literally absorbing everything you have on here, it's taking a lot of time but I'm getting through it! KNOWLEDGE ASSIMILATION!
You’re lucky. I’m just adsorbing the info.
before the century is over i bet a non-professional scientist is gonna make a great theory or discovery.. like in rhe old days 🔮
Lovely animations and concisely described, curious to check out the rest of your channel!
This reminds me of that stencil set in the 80s i used to make these shapes. Love geometry and all its mysteries.
The Spirograph, gonna have to get another one
As someone who has no background in all of this I'd just like to ask at some point doesn't this mimic the torus sphere? Should I just be viewing the torus sphere as a stepping stone to understanding the hopf? Also wouldn't that mean that all torus spheres have some sort of unseen element that unknowingly to us makes it a hopf?
Edit: Just an after thought wouldn't this intersect it self at some point like a klien bottle if enough circles are added?
Excellent video; perfection editing for the YT physics fan. Everything makes more and more sense, the less it makes sense really 🤷♂Love it, subbed
Awesome! Loved it!
So, the source was always from the northern most point of the sphere, right? Would the illustrations change if the source wasoved to a lower point on the sphere? And, would it also make a difference if the source was closer to the outer edge or to the most inner part of the sphere?
I was just looking around and saw the Hopf and was stunned. 3 days after the CERN collider was started back up I had a dream. Three Hopf (now I know what it was, didn't know until seeing this) "units" were presented to me. Each one was getting progressively smaller. The Hopf "units" were all distorted and deflated and in the dream I knew this was not right. Additionally the surface of the Hopf "units" had melted distorted chimera like imagery of all of the worlds flags (3 were predominate). Under that layer were all of the worlds corporate logos also completed melted, distorted and chimera like. I quit looking into the layers at that point. When I woke up I didn't have an opinion, but within a few days I realized it pertained to CERN.
What a dream!
I have been making drawings of these universal strands (pearls) for years... 👍
This is exactly what I was looking for. I only imagined that idea and here you are showing it. More interestingly, is there software that lets you see how shapes transition from one dimension to the next. Also looking for a way to have an image wrapped around sphere in 3D and sterographically force it on to 2D surface to see what the image will look like.
Thanks Celler2. I don't know of any software similar to that, but would love to check something like that out.
2:15 Isn't the circle only larger because of the point of reference?
What does this vibration dictate in physical reality, and at what level of physics? Is it under the fabric of space time? Is it beyond the Planck length, Planck time, Planck temperature
Fibonacci, the flower of life and other symbols like “alpha and omega” now make sense. Incredible video
Thank you Vivian! Much appreciated =)
To what purpose?
If time is next dimension, you have answers
I’m too drunk for this.
So a race around a hypersphere would start at a non skewed circle and end at an infinite finish line. Now the question is, is there such thing as a start or finish? Or would we see the hole race all at once?
Well the title definitely wasn’t wrong, shame you had to use the Weinstein name to get any clicks. Really well done either way.
When I was a child I was given psychedelic mushrooms. When I looked into the sky I saw this but from the inside as if we were passing through it. This was long before I had any clue that such things existed.
same I remember asking LSD where creativity came from and I saw this too :D Ommmm
How old were you?
@@geo_no_go2657 14
when the red infinity circle was shown as a vanishing point into the center of the image i felt like i understood some of how the 4th dimensional objects make sense; the hypercube came to mind and it felt better to look at.
at the same moment i also felt i had an intution for how anything 5th dimensional might be shown.
what a great vid. thank you
I had the same exact feeling, I felt like a 4th dimensional being travelling along the red infinite line, which was both the past and the present.
Reminds me of what I see during a dmt session. It's like flying through one of these on the way to... Wherever you go. Everything is covered by a fractal film that responds to stimuli... Once you learn how to look, you'll see.
So what does it do? How is it useful? Practical application?
Without the spinning 4d modeling it looks like the field strength of radio waves that widen transmitting in all directions or flatten out into a focused ground plane depending on antenna height from the ground.
Well if we could make them on demand we could start fiddling with them
This is just an interesting visualization of a hypersphere as circles drawn on its surface. What is meant by "vibration". It would be more interesting to talk about how it relates to those physics topics. I assume it is also related to electron spin state.
Great video
Thanks, TKG!
I've seen this object before while tripping acid
Same
Same
When I was in high school I used to take adderall. One day I took the adderall and payed on the couch and rested my eyes. I didn’t drift off into sleep(i think). I was concentrating on nothing except a pressure in the middle of my head. I was intentionally doing so. As I lay there I believe I began to see a myriad of color (almost like an oil slick produces when light shines upon it) passing underneath me and going up the hopfi walls behind me. I began to look forward and saw a shape that I have never seen since. It was a solid and semi solidly with hard edges and smooth liquid like surfaces( poor description I know) it was constantly moving and changing the shape. It spoke and said everything is okay in a voice that sounded like Optimus prime. I said whatever you say Optimus prime then my heart rate began to raise and I opened my eyes and was laying on the couch again. It was either a hopfi or a toroidal shape. I’m more keen to say it was a toroidal bc the center object had a stream going into it and out of it from the top and bottom
Bro this is not simplified at all
😂😂😂😂😂😂
Cool how the hypersphere looks like a wormhole as the circle gets closer to passing through infinity.
Could black holes be circles through infinity on a hypersphere?
I'm not educated on the math, but I've always had the idea that a "particle" is two or more quantum fields trapped within each other. Which, given the angles of those fields relative to each other, would seem to me to necessitate them "turning inside out around each other". This video illustrates perfectly what I could never put into words.
Mind candy 🍬
1. 🔥comment
2. it took me probably 3 full minutes of non-stop scrolling through the comment section to find this. im literally so pissed/frustrated at youtube.
3. This comment popped up in the singular comment section as i was watching the video vertically on my phone.
4. Why would youtube bury a recommeded comment??? that makes no sense, ZERO SENSE. I had to hyperfixate and utilize my ADHD powers to get here and put this into reality.
5. i apologize for being crass in this intellectual domain but jesus christ youtube is retarded for this.
all i wanted to do was give a like and a "fire comment" to the comment that POPPED UP. why did i need to scroll so much and get literally upset/obsessed for somthing that should hav been at the top if it was what made me click in.
im sorry i lack the proper tech lingo but i hope i've at least expressed how unreasonable the design of this app/comment situation is.
sorry to the original comment and the video channel.
my rage towards the incompetent/lazy/careless web designers at youtube knows no bounds
It felt like watching a black hole or quasar or supernova. All those magneto electric entanglements. Vibrational portals or wormholes ....... fascinating.
This is more confusing than the architect scene in the matrix
Hi, Whats the music starting at 7:15?
I'm so dumb. My mind melted 2 minutes in
The uniververse is made of donuts
Uniververse made of donunuts.
What i only understand is that GOD is behind all this
And that all those who conclude, after looking at al levels of reality, and cannot see that there "exists" ( quotation marks, because if only the narrow definition of, "to exist", means, " some scientific instrument can be used to detect it " is used ...) a Creative Superintelligence behind, above , beneath, and within our reality, they must be willfully blind.
Thanks for the 3d at the end! Really good video, I subbed up xx
I found out that kinetic energy is part of it.
KE = mvˇ2/2
is basically same as the volume of torus (m being the r1 big radius, and v being cirumference of small radius). But as KE is simple Newtonian, then adding features to it extends the torus to new dimensions where Hopf fibration awaits on every step again and again.
Universe is bunch or perpendicular radii, circles. Although it could be interpreted as waves, because waves and circles are all about number Pii.
Hey! Amazing video. Could I get the name of the song at 7:17? Thank you so much!
So basically, if we took this concept to the 5th Dimension each one of those linked circles would instead be spheres instead, intersecting probably an infinite amount of times right?
Atomism vs. Fieldtheory: ua-cam.com/video/aq-oluWt_kY/v-deo.html
Laser dot (the infinity point) hits a mirror the mirror can spread out that dot into a 2 dimensional plane.. the image is a continuous positive and negative.. when this is reflected onto a second mirror adding another dimension all manner of 2d and 3d shapes can be manifest as a projection yet uninterrupted from a source that has the ability to scale up to a maximum size limited by throw distance and mirror angle but also reduced in size back to an original infinite dot... the image projected out can also can have added dimensions governed by the geometry of that space.
Just thought of all that as I watched your video and felt it may help give me or you or anyone another way of understanding the Hopf Fibration. It may not be anything??
Can you explain why this is an essential feature of the universe? Is this the shape of our universe?
Ohh a get new Hopf for the future now and a Tothempole means a energy output from the wind for me now! /Mikael