Hopf Fibration Explained Better than Eric Weinstein on Joe Rogan

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Hopf fiber bundle topology is taught as simply as possible. Physicist Roger Penrose called the Hopf fibration, "An element of the architecture of our world." Essential in at least 8 different physics applications, the Hopf fibration is a map from a hypersphere in 4D onto a sphere in 3D. Many visualizations are displayed herein. Mathematician Eric Weinstein commented on the structure on Joe Rogan's podcast as, "The most important object in the entire universe."
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Chapters
0:00 Intro
1:08 Defining the Hopf fibration
1:42 Stereographic projection
3:24 Mapping the Hopf fibration
5:33 Hopf facts
7:11 Rotating in 4D
8:30 3D magic eye stereogram
For full length magic eye, Hennigan (2014): • Hopf Fibration Stereog...
If you're not yet familiar with higher dimensional shapes, you may want to first watch my video explaining a 4D hypercube known as the tesseract:
• 4th Dimension Explaine...
The initial outline for this video was over 25 minutes, so I trimmed details of n-spheres for the sake of brevity. Including here for those interested:
S0 0-sphere | Pair of points | Bounded by lines
S1 1-sphere | Circle | Bounded by pairs of points (S0)
S2 2-sphere | Sphere | Bounded by circles (S1)
S3 3-sphere | Hypersphere | Bounded by spheres (S2)
So the pair of points at the ends of a 1D line segment is considered a 0-sphere, or S0. It's hard to visualize, but a straight line is an arc of a circle whose radius is infinite.
Now, a circle is bounded by those pairs of points. We say a circle is S1, or a 1-sphere, sitting in 2D space.
A sphere is bounded by circles. We say a sphere is S2, or a 2-sphere, sitting in 3D space.
You are probably noticing an important pattern here. Each of these structures are one dimension lower than the Euclidian space they are embedded within. This is because we are only concerned with the boundaries of each shape.
So for a circle, we look at just the 1-dimensional circumference. Thus, S1.
For a sphere, the surface is actually 2-dimensional. Thus, S2.
Now, we are navigating beyond the limits of human perception.
A hypersphere is bounded by spheres. We say a hypersphere is S3, or a 3-sphere, sitting in 4D space. This is technically impossible to visualize.
At 2:58, I've included two visualizations of a hypersphere. The first is the shadow of a wire-frame surface of a hypersphere, projected in 3D. A perfect model would be an opaque object, so this cage gives you a sense of the hypersphere composed of spheres. The second is a highly polished version with a few vertices in view. Neither version is perfect, but they are the next best things compared to Hopf maps:
commons.wikimedia.org/wiki/Fi...
Seemann (2017) vimeo.com/210631891
🚩 Nerd Alert 🚩
The interactive Hopf map visualizer by Nico Belmonte (@philogb)
philogb.github.io/page/hopf/#
Read this paper about the 8+ physics applications
www.fuw.edu.pl/~suszek/pdf/Ur...
🚾 Works Cited
dimensions-math.org/ "Dimensions" series by Jos Leys
/ josleys
Niles Johnson (2011), www.nilesjohnson.net
• Hopf fibration -- fibe...
Guido Wugi, Wugi's 4D World Series (2020)
• Wugi's 4D world- The 3...
Joe Rogan Experience No. 1203 (2018) | Eric Weinstein
Hennigan (2013) • Hopf Fibration
Dror Bar-Natan
www.math.toronto.edu/~drorbn/G...
Azadi (2020) • Hopf Flower
Roice Nelson roice3.org/h3/isometries/
www.joerg-enderlein.de/stereo...
3Blue1Brown (2018): Visualizing quaternions (4d numbers) with stereographic projection • Visualizing quaternion...
WBlut (2020) wblut.com/images/hopf-tubes-a...
Non-Euclidean Dreamer (2019) • Train Ride through the...
🚨 Legal
Copyright Disclaimer under section 107 of the Copyright Act 1976, allowance is made for “fair use” for purposes such as criticism, comment, news reporting, teaching, scholarship, education and research. Fair use is a use permitted by copyright statute that might otherwise be infringing. No copyright is claimed herein and to the extent that material may appear to be infringed, I assert that such alleged infringement is permissible under fair use principles in U.S. copyright laws. Content may be amended.
🚀 What is this Channel?
Exploring Truth in philosophy, science, & art.
We'll uncover concepts from psychology, mythology, spirituality, literature, media, and more. If you like Lex Fridman or Curt Jaimungal, you'll love this educational channel.
Channel Trailer • Channel Trailer for Pe...
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p.s. Please subscribe! Young channel here. =)
#hopf #jre #topology #math #hopffibration #physics #hopfion #4d #hypersphere #dimensions #reality #toe #beauty #fiberbundle

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24 май 2024

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Комментарии : 2,7 тыс.

@Carlos.Explains 2 года назад

What's your favorite geometric/topological structure and why? 😀

@finnbrewer8986 2 года назад

A square, because I relate to them

@Nah_Bohdi 2 года назад

Triangle...because I tried. 🥺

@____uncompetative 2 года назад

@RobAgrees 2 года назад

You didn't actually explain its utility.

@wugionyoutube 2 года назад

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.

@joedirty6543 9 месяцев назад

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.

@sylvesterhurt447 8 месяцев назад

Yea, what does this thing mean or do?

@jasonwrner 8 месяцев назад

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.

@Runthemjewels 8 месяцев назад

@@jasonwrner…did you watch this video? He explained exactly what it is, what it does, and even recommended how to better grasp the structure

@joedirty6543 8 месяцев назад

Poop@@Runthemjewels

@kathleennorton2228 8 месяцев назад

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.

@archimedesobservatory 2 года назад

This guy really talks to anyone on his show and I'm glad he that even gives the mathematics community a chance too.

@Carlos.Explains 2 года назад

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!).

@zoro8117 Год назад

Joe rogan audience is def. Not zhe right for that on average. They rather spend tile talking about conspiracy theoriesy flat earth etc.

@leonlee8524 Год назад

@@zoro8117 obvious bait is obvious

@mitsuracer87 Год назад

@Zo Ro keep living in the past bud

@Kosmopoli Год назад

@@zoro8117 learn how to spell

@mikebarriga 10 месяцев назад

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.

@thatsovietspy1974 10 месяцев назад

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.

@TheMerryPrangster 3 месяца назад

@WinrichNaujoks 3 месяца назад

Wouldn't have one tablet been enough?

@cFull_Rtrd 3 месяца назад

@@WinrichNaujoks depends on who was selling it, lsd can be diluted just like cocaine can be cut.

@GTF85 2 месяца назад

@@WinrichNaujoksnot a tablet - just saying

@ChunskieFartFilms Месяц назад

Same, LSD + jazz ballin

@kummer45 Год назад

I cried watching this. Finally someone exposes and resumes a Hopf fibration in full detail. People do not understand HOW IMPORTANT this concept is.

@HkLY45 Год назад

You are right. I don't understand how this is important. Explain it?

@kummer45 Год назад

@@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.

@HkLY45 Год назад

@@kummer45 thanks for the explanation. I see it's important to people involved in science. I understood practically 0% of what you said. 🤣

@patrickstewart6260 Год назад

@@HkLY45 It means we get cool shit in the future bro.

@HkLY45 Год назад

@@patrickstewart6260 that's fuckin rad bro.

@JuBerryLive 2 года назад

Dude. Thank you. This is the first time I actually have a good intuition of what a higherdimension representation is.

@Carlos.Explains 2 года назад

Thank you, Ju! Glad you enjoyed it. 😀

@JeffCaplan313 2 года назад

Read Flatland.

@esco51030 Год назад

Same. It hit me like one of Rogan's DMT trips. Thanks man.

@gabedamack Год назад

Fr, Ive always thought that the universe was a torus

@archlich4489 Год назад

Check out "10 Dimensions in 2 Minutes"

@guitar0wnz 10 месяцев назад

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.

@just2genders668 9 месяцев назад

To be fair, he was in a podcast. You can’t just explain this type of stuff in words alone.

@misssly253 3 месяца назад

I guess that's why there's visuals attached to this podcast.?@@just2genders668

@dudeistpriest1 3 месяца назад

I am way too high and drunk to understand any of this.

@residentevil4freek 3 месяца назад

Samesies

@f13edz 2 месяца назад

I'm sober and still not able to understand this.

@unktheunk1428 2 года назад

I don't think I actually learned anything about the math, but the visuals are worth it on their own

@Carlos.Explains Год назад

I'll accept partial credit. :)

@angryskidmark653 Год назад

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.

@Cespinozas 8 месяцев назад

same I remember asking LSD where creativity came from and I saw this too :D Ommmm

@geo_no_go2657 7 месяцев назад

How old were you?

@angryskidmark653 7 месяцев назад

@@geo_no_go2657 14

@marshallfischer3667 3 месяца назад

This came out of nowhere 2 years later and I love it! Thanks so much.

@amarug Месяц назад

As someone named Hopf I always wondered where my addiction to mathematics came from 😂

@Chris-rw7zh Год назад

8:00 made me think of something funny where each of those spherical points are a planet that got pulled into a black hole and they are lines due to spaghettification as they rotating around the mass

@Shinryakugun 2 года назад

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!

@Carlos.Explains 2 года назад

Thank you, Aubrey!! 😄

@Sapientiaa Год назад

@@Carlos.Explains How do these manifolds interact with 1 dimensional strings? I thought strings were fundamental.

@Carlos.Explains Год назад

@@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."

@pfzht Год назад

@@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.

@Carlos.Explains Год назад

@@pfzht Thanks!

@TheAdrenaline85 11 месяцев назад

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.

@dawsonlamasbass 10 месяцев назад

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.

@roobysoho 3 месяца назад

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

@Justyn219 3 месяца назад

sup homie, can we compare trips? same shit happened to me.

@High-Strangeness 4 месяца назад

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...

@TheRealBozz Год назад

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.

@giovanniamore7532 Год назад

we never die..

@TheRealBozz Год назад

@@giovanniamore7532 Life Eternal with Hopf Fibration!

@christopherlocke9616 Год назад

I’m so confused, does this explain the space we are in. Where is 3D space connected to 4D space, just tell me that.

@JayceFisher Год назад

Um so this solves horneyness when muma is grumpy? Please explain

@TheRealBozz Год назад

@@christopherlocke9616 My doctor prescribed Hopf Fibration™ to treat my arthritis. It's done wonders!

@Tobikoyum7 Год назад

I had a psychedelic experience when I was 12 where I saw this. It was basically the translucent manifestation of space that every now and then I would catch out of the corner of my eye. At first I had thought it was dust or a mosquito buzzing about. Then I started to catch glimpses of it and realized it was something that I shouldn't be able to see but felt comforted by it nonetheless. Thanks for making this video because the math is something I've never been able to fathom.

@rudyz193 Год назад

You sure tripping at 12 isn't just having you constantly try tripping? That's a medical condition

@Carlos.Explains Год назад

Thanks for sharing, lala. I had a somewhat similar experience about a year ago. For about half an hour, I kept seeing closed strings when I blinked. I tested this in a few different light configurations, and it kept happening. Not as mind blowing as a hopf fibration, but the experience really stuck with me. I was deep into Jung's Red Book at the time.

@deadjoey77 Год назад

one time i ate 10 hits of acid and zoned out so hard all i remember was doing crazy math while flying through a wormhole with all sorts of geometric shapes and lines around me.

@Trey_Cole Год назад

@@rudyz193 Huh

@Trey_Cole Год назад

@@rudyz193 Did you not bother proofreading your comment before posting or do you not know how to form sentences others can understand completely?

@lesleysprague1158 3 дня назад

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.

@Embassy_of_Jupiter 12 дней назад

bro you can't talk about this. we all agreed that we wouldn't reveal any real phyiscs discoveries anymore after 1960. you're spoiling all the hard work we all put in so far.

@dirtylabrat958 Год назад

You did a thing that is rare on RU-vid. Delivered on your thumbnail! Great explanation and visuals.

@Carlos.Explains Год назад

Thanks DLR! Beware of men in white lab coats...

@rsanchez9865 Год назад

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.

@00SEVEN28 Год назад

Leelu Dallas: Multipass

@Carlos.Explains Год назад

@@00SEVEN28 & R Sanchez, thanks for the references!

@frankdimeglio8216 10 месяцев назад

@@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

@cosmicraysshotsintothelight 10 месяцев назад

You left out the Prometheus engineer. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-vDOj9XEezDQ.html

@spyder7758 4 месяца назад

I'm picking up HOPF Fibration, it's giving me extradimentional sensations oom bop bop oom HOPF Fibration

@WhoThisMonkey 2 месяца назад

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."

@Hug_life Год назад

Last year I took 5meo DMT with 2 spiritual guides and it was the most intense out of body experience I have ever experienced. I immediately left my body and felt like my energy or soul traveled through various wormholes and I’ve never been able to accurately explain what that looked like because my eyes were closed and I wasn’t in my body. It’s hard to explain but I felt the vast intense universe I was apart of and it was this!! The minute I saw it all come together my jaw dropped as if I was there again! Wild!

@crappycomputer77t1 Год назад

Maybe you got a glimpse at the substructure of the universe.

@firstlast2762 Год назад

Which makes sense. Psychedelic chemicals removes the “physical” construct containing the conscious light within, allowing that light to flow from the physical 3 dimensional plane, into higher or lower planes based on one’s vibrational frequencies. Everything from Transcendental Meditation to Mushrooms, DMT and beyond all allow this passage into various extensions of the ALL. ✌️👁️

@armorykittington Год назад

Yup.

@michaelvette7659 Год назад

What do you mean, "with 2 spiritual guides". Well didn't know 5meo either, but looked it up. Or else I would've gone down to the city and just asked, "hey who got the DMT" LOL

@lylechipperson3407 Год назад

for me it just allowed me to speak with my dead father, which felt good and relieving but i have to assume it was just a figment of my imagination.

@chrisholt5964 Год назад

Many thanks for a great explanation! And much respect to the creators of these amazing visuals.

@Carlos.Explains Год назад

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. 🐰🕳

@kathleennorton2228 8 месяцев назад

Much respect to the Creator, whose mind is beyond searching.

@Asstronomical_AB 6 месяцев назад

8:30 What song/music is playing at the very end? I would love to have that song to listen to 8:30

@Carlos.Explains 6 месяцев назад

Hey Alex, it's Nemesis by Albis: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Znuftxau-oE.html

@ForLorNVuLgaR 11 месяцев назад

Thank you for this. It was about time to take the next step. Its been a couple years since exploring the tesseract, Im glad the circle was next

@maxiegawehn4685 Год назад

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.

@caseyczarnomski8054 11 месяцев назад

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

@myview5840 11 месяцев назад

Can it grow food, and build houses

@LuIsSaNcHeZ510 11 месяцев назад

@@Repo-Mandumbass

@kinbolluck476 11 месяцев назад

FUCK ME SILLY

@BringDHouseDown 11 месяцев назад

@@Repo-Man oh this is gonna age well

@moneyhooligan03 Год назад

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!

@Carlos.Explains Год назад

Thanks, you so money and you don't even know it!

@KingEst87 9 месяцев назад

This Video was like a Brain/ Consciousness level exercise Thanks for the video ! Production was great also

@OnlyOnePlaylist 4 месяца назад

Hey! Amazing video. Could I get the name of the song at 7:17? Thank you so much!

@killianthegrunt Год назад

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.

@djangokinley4284 Год назад

What’s your substance of choice

@Carlos.Explains Год назад

Cheers @@djangokinley4284 and @killianthegrunt, what'd you see as the backend of reality?

@Carlos.Explains Год назад

Oh and praise be the algorithm!

@cat_sniffer Год назад

@@Carlos.Explains yeah I wanna know too

@killianthegrunt Год назад

@@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 🍻

@cunningba Год назад

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.

@PatrickPease Год назад

Id like to see that, but I don't understand math very well. Would you kindly provide a web link?

@rudyz193 Год назад

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.

@Carlos.Explains Год назад

I'm with @@PatrickPease ! Barry, do you have a link?

@Carlos.Explains Год назад

@@rudyz193 That vanity plate is commitment. Honk if you love the Hopf. :)

@cosmicraysshotsintothelight 10 месяцев назад

This will help you cope further with the science... ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-spkFNvp1lEc.html

@WalterSamuels 11 месяцев назад

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!

@diggysoze2897 10 месяцев назад

You’re lucky. I’m just adsorbing the info.

@gregoryallen0001 7 месяцев назад

before the century is over i bet a non-professional scientist is gonna make a great theory or discovery.. like in rhe old days 🔮

@someonelse9 11 месяцев назад

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

@leontobi7521 10 месяцев назад

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 10 месяцев назад

You're lucky. I only see demons in my sleep paralysis episodes

@someonelse9 10 месяцев назад

@@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

@kl7514 9 месяцев назад

@@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

@Schachtens 4 месяца назад

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.

@Mantelar Год назад

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.

@luceatlux7087 Год назад

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 11 месяцев назад

@@luceatlux7087 welcome to earth

@luceatlux7087 11 месяцев назад

@@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')

@GimbalLocksOnly 4 месяца назад

Not a scientist and I feel like my mind fractured years ago.

@logicomamk2848 2 года назад

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

@Carlos.Explains 2 года назад

Thank you so much! Be sure to share it with your friend 😀

@CarolH2O Год назад

Fascinating Eric. A silly question i have though: How does the Hopf vibration connect, if at all, with the Mandelbrot? (sp?)

@ragewilly7355 11 дней назад

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

@akiraarcas5969 10 дней назад

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

@GGPlex_ Год назад

It feels good to unintentionally learn something this insane

@mitchellbuzzard6666 Год назад

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

@alexbrestowski4131 Год назад

Clever

@vystorm Год назад

I too recommend this visualization tool

@pliktl Год назад

DMT didn’t show me the “Flower of Life” as mystics call it -instead everything turned into animated Mayan symbols, explaining their function. I saw the flower twice otherwise: once when hiking (everything, for a split second, turned to light and rushing energy) and the second in sweat lodge, when i was meditating on the face of Love. Pretty amazing being shoved out of your body see such a thing, then trying to make sense of it upon return. I have been figuring out a drawing to explain it simply. This video fills in some blanks. So exciting!

@Carlos.Explains Год назад

Thanks Mitchell. So many other folks in this thread have had a similar experience.

@Carlos.Explains Год назад

@@alexbrestowski4131 What would you like this channel to cover in the future?

@Godwinsname 8 дней назад

My intuition: A 4d sphere then is not just spherical in left-right, up-down and back-forward directions but also in in-out directions. Fun. And we humans can navigate 4d somewhat too then, by going within, or without.

@Neventual 6 месяцев назад

After too many attempts to count and many days trying, I finally was able to build this. It's total trial and error. Patience and a very delicate yet focused touch are essential. I'm terrified to touch the cube for fear of having to build it again.

@aleksandarjovic4275 Год назад

Lovely animations and concisely described, curious to check out the rest of your channel!

@abf9596 Год назад

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.

@angerbob9665 Год назад

same, im worse than you at math. but learning stuff about our universe is fascinating even if you dont undestand.

@Jay_Hendrix Год назад

👽

@ronniehdable Год назад

@@justotalkalottashit8392 wow

@ChaoticNeutralMatt Год назад

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

@Carlos.Explains Год назад

@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.

@patrickobrien2092 4 месяца назад

I’m thoroughly confused!

@Autovetus Месяц назад

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 🦾

@madderhat5852 2 года назад

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.

@Carlos.Explains 2 года назад

Thanks MadderHat! Trust me, sometimes I am tempted to offer people their money back... 😆

@madderhat5852 2 года назад

@@Carlos.Explains 🤣

@Tstorm731 2 года назад

What an amazing video. Thanks for the hard work.

@Carlos.Explains 2 года назад

Thanks Jason! Much appreciated. 😀

@davidmn3696 11 месяцев назад

Wow your illustration of this through visuals is quite amazing. Nice job 👍

@realkabecio 8 месяцев назад

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

@jamesboaz4787 Год назад

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

@jaredcrayk259 Год назад

Yes. Except the pervading shape/form representation for the veneration of most, if not all, of Christian dogma over the past 1600 years has been the Lower-case , t shape. The Cross. So is the cross the deceptive image of the beast as spoken in the Book of Revelation? 🤔

@jaredcrayk259 Год назад

It’s almost as if the final revelation of the Bible itself warns against it. I will also add that if you read scripture Old and New Testament and you apply Hopf and Toroid principles to the words that are spoken, they take on a new meaning.

@jaredcrayk259 Год назад

The Hebrew language was generated using hand movements. See: Stan Tenen

@meinbherpieg4723 Год назад

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.

@Carlos.Explains Год назад

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.

@Wilverine99 Год назад

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.

@Wilverine99 Год назад

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-UnURElCzGc0.html

@Wilverine99 Год назад

I forgot about this Carl Sagan video! Exactly what I was trying to explain! It came on right after this one! Lol

@Abacoot 3 месяца назад

Minds like this is why mankind still has hope. No ego or wild bias; just incredible understanding and innovation in thinking.

@user-rj5ps3iw4l 3 месяца назад

can tectonic plates possibly follow this pattern? almost seems antarctica is a doughnut at the bottom and we view the north pole as actually having a pole in stories. is there some type of silver lining to that?

@user-ut4vl8bw2k Год назад

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?

@mikedevyatov3213 7 месяцев назад

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.

@user-ut4vl8bw2k 7 месяцев назад

@@mikedevyatov3213 based

@snoosebaum995 Год назад

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

@Carlos.Explains Год назад

I wish I knew... I'm trying to get a physicist on for an interview to explain!

@joelrodriguez9820 9 месяцев назад

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.

@jocsanabdala9456 4 месяца назад

I’m f I zoom in to the edge of a circle, would it ever become a straight line or would its curvature infinitely decrease ?

@mkultra6664 8 месяцев назад

The magic eye stereogram at the end was awesome!

@callmedeno 2 года назад

Is it kind of like how you can cartesian product 2 circles to get a torus? Like a perpendicular circle at every point on another circle

@Carlos.Explains 2 года назад

I believe this is correct. The best visual can be found here (timestamped too): ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-10sDqSUjXHc.html

@callmedeno 2 года назад

@@Carlos.Explains thanks for that link, very interesting channel I'd not seen before

@callmedeno 2 года назад

@Russell Phelan On an unrelated note, I'm thinking about why sqrt(-1) is i, aside from the application or problem it solves. What strikes me in learning about isometries is that inverses are extremely important. If multiplication is compound addition, and exponents are compound multiplication, then the sqrt(-1) seems like a connection point, joining the inverse of the two fundamental operations, something like the (compound) multiplicative inverse of the additive inverse. Is there anything to this line of thought on an algebraic level as to why sqrt(-1) is so important?

@reverendoz Год назад

wow, swim once saw exactly this while on dmt, and everything was crystal clear but at the same time swim wasn't able to describe it with words. Thanks for explanation.

@d3adc0ps Год назад

check this out...I (I got nothing to hide) saw this exact thing the other day on DMT and was able to walk into it. It was everywhere around me. A friend was in the room with me and I tried to describe it to her while it was happening but I couldn't put the words together to be able to explain it in any meaningful way. I flipped when I saw it in the thumbnail of this video. Because of it, I was able to describe what happened much better...as well as one might be able to express the inexpressible. Similar thing happened to me on salvia 10 or 12 years ago, but that time I was inside of a giant donut hurtling through the void. The next day I randomly came across a video talking about the Merkabah and its Toroidal energy field...

@anacharsis93 3 месяца назад

the commercial started right when I was about to understand, lol

@Carlos.Explains 3 месяца назад

I suspect this speaks to a deeper meaning as to why we're here...

@ghostdogzx-1474 11 месяцев назад

I kept thinking I was opening the wrong video because I expected someone explaining it to Joe Rohan in an interview format. I’m still confused why Rogan is in the thumbnail. In any case, this is amazing, but wish I able to grasp more of it.

@MrSknottykid 11 месяцев назад

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

@mpjstuff Год назад

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.

@jakeburroughs6854 7 месяцев назад

Please reply with the suggested link video mentioned in this video. Thanks

@themartdog Месяц назад

Are there any VR explanations of this? I feel like trying to understand projecting from 4D to 3D is hard to grasp on a 2D screen

@Celler2 Год назад

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.

@Carlos.Explains Год назад

Thanks Celler2. I don't know of any software similar to that, but would love to check something like that out.

@christopherneufelt8971 10 месяцев назад

Comsol might be interesting for you, but you might need to program in finite elements the dynamic equations in many dimensions of interest (where you look for interactions) and then look for points of convergence between two or three dimensions of interest where there are possible solutions. Another possibility of course could be knot software evaluating such dynamic equations (for the more hardcore guys that have enough time, I don't). P.S. I work with Octave for dynamic systems evaluation but these are tools of Satan that want to betray Jesus and to make us all paranoid. I am not, they are just looking for me.

@FractalPrism. Год назад

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

@khaledchoucri1567 9 месяцев назад

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.

@The_Makers_Prerogative 11 месяцев назад

Great Video! This shape kind of gives me stellarator vibes as well as makes me wonder if black holes share similar symmetry

@jaredjamesimages Год назад

Interesting! This is how I see the suns light if partially blocked by a solid object, or reflected by glass at an angle.

@Carlos.Explains Год назад

Interesting indeed!

@jahleajahlou8588 7 месяцев назад

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.

@Carlos.Explains 7 месяцев назад

What a dream!

@davidbarkhuizen 4 месяца назад

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.

@davidbarkhuizen 4 месяца назад

Is the whole atomic model then just a higher order harmonic resonance in an infinitely dimensioned space projected into 4d space thay we perceive?

@Einimas 3 месяца назад

When are 5d projected into 4d projected into 3d is available?

@davidhuffman4036 10 месяцев назад

This reminds me of that stencil set in the 80s i used to make these shapes. Love geometry and all its mysteries.

@gabriell3446 3 месяца назад

The Spirograph, gonna have to get another one

@thisismyname7284 2 года назад

Fibonacci, the flower of life and other symbols like “alpha and omega” now make sense. Incredible video

@Carlos.Explains 2 года назад

Thank you Vivian! Much appreciated =)

@koba_Lyle 2 месяца назад

@Carlos.Explains What is a Hopf Vibration made of?? The shapes, geometry, and projections of such are representing what? What is the geometry representing?

@Carlos.Explains Месяц назад

Hey Koba! Best to think of it as a mapping of a hypersphere to a "regular" sphere. I don't know of what they would represent, the "shapes" themselves are as fundamental as we know.

@jdiv69 3 месяца назад

I hate I could never have the mind to contribute to these fascinating wonders. I truly appreciate people like you.

@Carlos.Explains 3 месяца назад

We are all limited... be content to always push your boundaries. :)

@drawingmomentum 2 года назад

I have been making drawings of these universal strands (pearls) for years... 👍

@siriuswobble1453 Год назад

great video. i really appreciate your effort to explain this mystery, broken down to a enjoyable simplicity. jah bless.

@Carlos.Explains Год назад

Thanks SIRIUS!

@eliasmann7381 11 месяцев назад

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

@oliumantis3272 11 месяцев назад

Processing: int N = 400; // Anzahl der Punkte pro Kreis int M = 50; // Anzahl der Fasern (Kreise) void setup() { size(800, 800, P3D); } void draw() { background(0); translate(width/2, height/2, -200); rotateX(frameCount * 0.01f); rotateY(frameCount * 0.02f); for(int i=0; i

@Co-hi8gc День назад

Wut

@cainmorningstar2989 2 года назад

So far you can square a god, you can cube a god, you can tesseract that god these are simply god multipliers.

@djeddy1987 2 года назад

Nice work Carlos!

@Carlos.Explains 2 года назад

Thanks buddy! Miss your dj spins on BRU! 🎵

@Ghostee61 7 месяцев назад

Hi Eric and thanks. Stupid question... why is it called a vibration? In the complete hypersphere, is something moving back and forth? 😊

@RQFumbles 6 месяцев назад

Finished Loki season 2 and it makes sense as to why "time" didn't want a circle ring. "Time" wants a circle through infinity. Halfway from ring to straight line, it becomes a tree.

@midplanewanderer9507 Год назад

Okay that's mind-blowing. Open question: is the Hopf Fibration, with variants thereof, the basic schematic used for describing particle 'spin?'

@Carlos.Explains Год назад

I believe it's related: nilesjohnson.net/hopf-articles/Hongwan_Liu-Hopf_fibration.pdf

@nicolasrossi5978 10 месяцев назад

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!

@drrichardpaul 7 месяцев назад

All space, at all times, is always expanding and folding upon itself simultaneously. Just because we cannot see it with our eyes doesn’t mean it’s not happening. This Theory is just one of those that have a tiered view of what my opening statement was.

@getrightincbuff Год назад

so is due north or due south or the point where all fibers meet where time reside and why we can't break into that dimension.

@orionspur Год назад

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.

@kornholyjo666 4 месяца назад

Hi, Whats the music starting at 7:15?

@geometerfpv2804 10 месяцев назад

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

@Carlos.Explains 7 месяцев назад

Amazing, thank you for the thorough explanation!!

@greatoak7661 2 года назад

Someone with WAY more math skills than me try combining the current M-Theory and Hopf fibration. planck length Hopf fibration as the unit of the M-Theory.

@____uncompetative 2 года назад

I think out of the five identified E8 x E8 Heterotic most likely corresponds to a superset of the mathematics within which our physical universe resides. I doubt there is a way to "travel" to the other four multiverses. Those behind M-Theory were suggesting that each of these multiverses interacted with each other as a complex, but my hunch is that they are isolated exouniverses we don't need to worry about. _Geometric Unity_ takes the 4-dimensional manifold with space-time signature (3, 1) and a geometry defined by mathematician Bernard Riemann which is familiar to those working with Albert Einstein's _General Relativity,_ throws out some architectural assumptions, and then grows a 14-dimensional manifold with space time signature (7, 7) and a geometry defined by mathematician Charles Ehresmann which is familiar to those working with Georgi-Glashow's SO(10) _Grand Unified Theory_ a Special Orthogonal group which contains the Special Unitary group SU(5) which in turn contains the product of SU(3) x SU(2) x U(1) which the _Quantum Field Theory_ of the current experimentally verified _Standard Model_ uses to model the Strong and Weak nuclear forces (governing nuclear cohesion and decay), and Electromagnetism (which includes microwaves, infrared, light, ultraviolet, radio waves, X-rays, and gamma rays). Eric noticed that the geometry of Ehresmann and Riemann were incompatible and it wasn't possible to devise a geometry which could replace both and harmonise what gravitation needed in 4-dimensional space-time and what 14-dimensional space-time needed as a place for the subatomic particles to exist, expressed consistently in terms of relativistic fields. This led Eric to find a way to join both manifolds and make _Geometric Unity_ as simple as possible, but no simpler. When you subtract signatures you get: (7, 7) - (3, 1) = (6, 4) = 10-dimensional Hypersphere of Hopf fibration defined with Ehresmannian geometry for SO(10) GUT Theory. However, it is a TOE as it also connects this to (3, 1) to get a theory that incorporates gravitation and geometrises the quantum rather than attempt to quantise gravity, which seems to be a deformation in the (3, 1) manifold rather than an exchange of hypothetical yet to be discovered "graviton" particles. SO(10) is plenty for the Universe we are familiar with, but the latter part of Eric's paper seems to explore very high energy SO(14), SU(7, 7) and Spin(7, 7) territory, where 2^7 => 128 x 128 matrices containing 144 new particles which unify with the third generation of matter particles (the Top and Bottom quark) which is why he calls this third generation an imposter. This is early universe stuff, so might not be possible to confirm in a particle collider. These are objects called Spinors that we only see a part of in out (3, 1) Universe. Eric seems to be unifying the C P and maybe even T broken symmetries at higher energies, as he talks about Chirality quite a lot. Go earlier in history and antimatter and matter were more in balanced proportion prior their one annihilating the other and becoming more abundant. Same goes for handedness being a bias in observed characteristics of low energy matter, the right handed counterpart could show up fully at higher energies, revealing more symmetry the closer one got to the Big Bang. Unidirectional T may itself be part of a broken symmetry where the question "What happened before the Big Bang?" is meaningless, not because there was no time before the Big Bang, but no clear direction of time, as it went both backwards and forwards in different forms of primordial energy, then picked one and it became possible to measure the direction of time as entropy increases in the future. Something about this pre-Universe must be defined to degenerate otherwise it would still be like that and we wouldn't now have the unbalanced broken symmetries which allow for chemistry, evolution, and life.

@NicholasPool Год назад

Yes i think that 8:06 zero dimensional points inside the hopf fibration is literally planck length but within each "sphere" is a tiny hopf fibration

@NicholasPool Год назад

Our perception of reality at any given time places an image of a specific point within the hopf fibration and its continuity without an observar sectioning its "state" is how the quantum World interacts

@NicholasPool Год назад

Plus the geometric shape of a hopf fibration i think is the graphical representation of combinatorials in ruleial space

@NicholasPool Год назад

Not sure of anything but im doubting what i said about every sphere having a tiny hopf fibration because that implies infinity or true computational irriducibility

@ka9dgx 2 года назад

Is this what the "spin" of an electron actually looks like?

@paulishism 2 года назад

I like to think of it as a clockwise or counter clockwise turn.

@Carlos.Explains 2 года назад

Hey Mike, I don't think so. I'll follow up if I discover otherwise. :)

@mzaidaliraja 3 месяца назад

im in marketing, why am i watching this? but if i was in physics i would travel across the world to have you as my teacher.

@lunicpilot1566 11 месяцев назад

I wonder if being in the fourth would be like being in a mash 3d world with scattered bits of 3d all around forming different places and times. The interaction you would have is something to the effect of being in all places in the 3rd dimension and at all times at once as a whole and also being in every place and time individually, at once. If that makes sense... if we are interdimensonal beings, our life time in this 3d world could very well also be a part of a 4th dimension beings life too. We would be this portion of their reality.

@coreyfreeman6226 Год назад

fascinating stuff. Very well explained even for someone not in this field but fascinated by it. Makes you realize the Architect that made our universe would be the perfect teacher. This is very intentional amazingly beautiful math.

@Carlos.Explains Год назад

Thanks Outlander! I hope it's not the architect from the Matrix 3...

@Lincoln_Bio 2 года назад

Yeah it just maps a 3-sphere to a 2-sphere with circles, but Eric Weinstein wouldn't sound clever enough if he explained it properly would he? You bring up an excellent counter-example in Niles Johnson, it was one of his lectures that made it click for me, I was like, "Oh, is that all it is? Cool." Haha. Great video!

@Carlos.Explains 2 года назад

Thanks Lincoln! Agreed, Niles Johnson's visual is superb.