Visualizing 4D Pt.1
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- čas přidán 11. 09. 2024
- The first video in a multi-part series on understanding and visualizing the 4th dimension, from a mathematical point-of-view. We'll understand where a 4th dimension lies, what 4D space is, and learn a powerful way to visualize 4D objects.
![Visualizing 4D Geometry - A Journey Into the 4th Dimension [Part 2]](http://i.ytimg.com/vi/4URVJ3D8e8k/mqdefault.jpg)
![Visualizing 4D Geometry - A Journey Into the 4th Dimension [Part 2]](/img/tr.png)
[Edited periodically]
[Update: Still working on part 2, thanks for your patience! Based on the response to part 1 I realized I had to reframe some concepts and present things a bit differently. But I promise it's coming soon!]
Hi all - HyperCubist here. Just wanted to address a couple points. But first, I'm really glad this is blowing up! I've been envisioning this series for several years, it's why I started this math channel last year in the first place. It's great to finally get these ideas out of my and share it with CZcams. Thanks for all the really wonderful comments - as someone who's been obsessed with 4D exploration for a while, it's really nice to engage with similar thinkers. Everyone seems to have their own personal take on what 4D is, which is really cool to see and discuss. I'll try to answer as many sensible comments as I can.
Is it even possible to "visualize" 4D? In my view that's an emphatic YES. This is an argument I'll lay out as the videos progress. The upshot is that you WILL be able to see all 4 dimensions on a 2D screen in a mathematically justifiable way, rotate around in 4D space, and get comfortable with 4D geometry - just as we already do with 3D, by projecting down information into our 2D field of view and navigating around in 3D. These visualization techniques are very well-known and understood, though I do have a (I believe) fresh interpretation of what we see. This is just the intro video, and I haven't yet shown how to truly bring the 4th axis into view that's why everything looks like regular 3D cubes stacked on each other.
Do I have any credentials? I have a BS in Mechanical Engineering, and about 25 years experience tutoring math and physics at all levels through college undergrad. Above that, just a lot of self-taught math and physics over the years.
Am I full of $*it? If you disagree with how I present things, that's fine. Just please be courteous in the comments, I don't mind engaging with a well-argued post.
Am I using the same methods as 4D Toys or 4D Golf? No - there are two standard ways of showing 4D - the intersection method and the projection method. 4D Toys, 4D Golf, and similar games use the intersection method - where you see one 3D 'slice' of 4D objects at a time, and shift along the 4th dimension with the world changing around you. It's a fantastic way to start thinking in 4D. But I'll focus on the projection method, basically projecting 4D into our field of view (much more on this in later videos).
Is the Deck of Cards model new? Thinking about 3D slices of 4D is very standard, but I've never seen it exactly in that handy form anywhere else. It came from me trying to visualize a hypersphere in a way we can understand. And it's not just a hack, I'll show that it's a special case of a valid way to rotate cross sections of 4D objects in space, which IS standard. Still I'd be surprised if I was the first person to use that model (please let me know if you've come across it before).
Do higher dimensions _exist_ ? That's a can of worms I'm not interested in (at least here). I make no claims about the nature of our physical universe. Ideas of parallel universes or other sci-fi or ideas are fun to think about but have no bearing here. And concepts like flatland or 4D beings are simply useful thought experiments. I'm really only interested in the mathematical idea of dimensions and visualizing 4D geometry. This is after all a math channel.
Am I using an AI voice? Nope, 100% me, maybe just a bit over-annunciated and edited.
What software am I using? Mostly Geogebra 3D for the animations - a little pit of Vpython. Outside of that just Apple Keynote for slides.
What's next? The next video is a bit different - we'll learn how to rotate objects in 4D, and how to truly bring the hidden w axis into view. And we'll start to learn the "new visual framework" I allude to in this video. We'll do it in the form of a simple game, and use our understating of the analogy to wrap our heads around 4D rotation. It''ll require some patience, but we'll be able to see hyperplanes and 4D objects in a whole new way.
When's it coming? Further along the time axis ;)
How many videos in the series? I'm planning on at least about a dozen to cover what I want to show, but depending on how it goes there could be more.
Is there a Discord or Patreon? Not yet, but we'll see ....
Where can I learn more? There's tons of info all over the web, but I found this blog particularly useful when I first started diving into this: www.qfbox.info/4d/vis/vis
Glad to have you all onboard! See you in part 2!!
(For anyone wondering I cut out the red pill / pledge in the intro)
how often do you plan to make each upload for this series? i'm very interested
@@arkanon8661 Ideally once a week - I have a few in the tank already, but there will be gaps I'm sure as I make new content.
@@HyperCubist have you ever read the culture series? I’m currently developing a version of the 4D house the hyper intelligent “Minds” from the series use to communicate with each other. Also, there’s a few videos by TheLazyEngineer that has some helpful ideas :)
@@mnrvaprjct Haven't read it. But I HAVE seen TheLazyEngineers' videos, they were some of the best 4D videos I had seen when I was first diving into all of this.
Thank you very much for this video. I have thought about extra dimensions a lot myself. In particular I would imagine a cube the normal way and then the fourth would be cubes lined up in a row and the 5th would be the cubes assorted in a square and the 6th would be them assorted into a cube. Kind of like reusing the three spatial dimensions we have over again. But I was never able to wrap my mind around rotating these objects and truly understanding them. Can’t wait for new videos.
You put a whole terms of service to gatekeep the 4th dimension. Respect.
Hahaha
Hahaha
@@baconheadhair6938hahahhHHA
Hahaha
type text of laughter if you're an npc
So scared of accidentally moving a meter through the fourth dimension and never being able to return home
I always thought that lol, probably kept me up at night a couple of times just thinking about it
Super Paper Mario has this exact scenario with a 2D character being lost in the 3rd dimension.
i think the opposite. i'm intrigued that unlocking that dimension would trigger an infinite expansion to my universe, and that would make me a god-like being, but there will already be others there. think about it, the mere fact you could move in a fourth spatial dimension means you would be literally invincible. you could have "invisibility", "Invulnerability", "teleportation", x-ray vision and "telekinesis" just by merely moving in 4d against a 3d foe.
@@GraveUypoothers I understand but could you explain the 'invulnerability' part. You're still flesh and blood, just moving through the 4th dimension.
I hate it when that happens.
HOLY FUCK THAT DECK OF CARDS MODEL IS SO SIMPLE YET GENIUS
how the hell has no one ever used that before??
I'm assuming we're used to draw in whiteboard, we haven't fully explore our digital screen.
5D needs hologram/VR for sure.
@@nabieladrian honestly the deck of cards method is probably useful for 5D and beyond as well. Just project 4 dimensions into 2D and then treat depth as the fifth dimension. Granted, it probably gets to be a bit of a mess once you reach 10 dimensions, but 10 dimensions themselves are kind of inherently a mess anyway.
i actually came up with it seperately in 3rd grade. i was a smart kid. it's not too hard to come up with, it's just like "how do you squish 3 dimensions into a 2d plane? how do you add a 4th dimension?"
A lot of people represent 4th dimension as time, and time as frames.
this is all metaphor
I absolutely love how the introduction made me feel like I was in a mission brief for an objectively impossible challenge
Haha yes!
I felt I was taking an oath that conspiracy theorists/Creationists call religion. ~sigh~ 😕😞
@@NotSoMuchFrankly Yeah I cut those parts 🤦♂
that's the part of the conspiracy-fantasy rabbit whole. it makes YOU feel like the hero. classic cult tactic. feeling into the ego and grandiose feelings.
I mean youre not wrong
Hey, that deck of cards idea is really powerful. Thanks!
After I finished watching I was sure this was some month-old video with at least a couple hundred thousand views. It shocked me that this is only a few hours old and has not yet reached a larger audience. This video neeeeds to get viral!!! The deck of cards visuals in the end just clicked in a way that made my brain melt down. This is insane and I just subscribed, waiting impatiently for the rest of this
@@PimmelBerger-nl6zy Thanks so much! I really hope it takes off and reaches a wide audience as well. But mostly I want to make this series to get these ideas out of my head, and documented for anyone who appreciates this topic.
@@HyperCubist Just have to share that I found the deck of cards idea incredibly helpful as well! I've seen a lot of hypercube visualizations and have heard several different analogies / explanations that I can accept as valid but which do not help with visualization. The deck of cards finally really, really helped in a breakthrough sort of way! Much respect and appreciation :)
Same. Having a 3D projection on a card and extruding the card - so obvious once you've seen it - suddenly demystifies what's going on in a typical hypercube visualization.
This is what sold me. I saw for the first time that the stereotypical symmetrical hypercube, the one which appears to show a small cube _centered inside_ a larger one, is counterintuitive and why I've been processing it wrong. Thanks to the card, I realized that in those representations, smaller cubes are _always_ further from the viewer, countering the visual intuition that the smaller cube is centered inside.
Again, it seems obvious in retrospect, but I needed a reference frame, a bar to hold onto while the room spins, and the card model was that bar. Huge thanks, and excellent production value to boot.
Yeah that's the first time a hypercube has ever actually made sense to me. Absolutely great analogy.
In a job interview...
Boss: So what is your special skill?
Applicant: I can visualize 4D
The "deck of cards" method is the first time I actually even partially understood the 4th dimension. In all the other visualizations my brain always goes "That's not ACTUALLY a new axis, it's just a line drawn through the original 3 dimensions!" which made it very hard to actually "believe" the representation is accurate, but when you abstracted it like that, it finally clicked
I'm glad that made it click for you (and apparently many others too). And you're right, aside from the cards, I haven't yet shown the 'actual' new axis. Parts 2 and 3 will show how we can do this in a mathematically consistent and logical way.
Yeah, even though, I always was quite comfortable with the causally unconnected moments in time analogy,
This "deck of cards" model surprised me in how simple and intuitive it is.
From what I understand, in any given number of dimensions, the last one will always act as time. And for any number dimensional being, time is always one up from that. Like in a flip book, a character's world is 2d, but the "depth" that we have acts as their time. For anyone able to view our time, the forth dimension, I would think that it might look as if every instance of our world's existance is superimposed on itself, unlike a flipbook, but they would still be able to peruse it at will with whatever they use to sense and interact with the forth dimension.
Yet it doesn't help me understand or visualize the 4th dimension direction. To truly visualize it you would need to be able to see and understand the 4th dimension axis while visualizing a 3d cube, not a 2d representation of one. I don't believe that is possible.
@@karaokehammick5215 Why doesn't it help you visualize it?
You can imagine a stack of cubes. Or even just multiple cubes near each other that are connected.
It's different from actually seeing into the fourth dimension and being able to actually see every angle of every cube at the same time, but it's a start.
Nice to see a useful and accurate explanation! I think Duocylinders/Tigers are definitely the hardest to visualize, so I'm curious if you plan to cover those. I also find it challenging to visualize how objects connect, like why 2 spheritorus can't form a link, but a spheritorus and torisphere can.
omg Code Parade, hi!
hey code parade! nice seeing you here with yout 4d golf game, it looks really sick, keep up the good work!
CodeParade! Thanks so much! I plan on covering all the basic shapes - prisms, sphereinders, hypersperes, etc - and will definitely cover duocylinders. I may do a breakdown of all the 'advanced' tori in a video, though I still have to wrap my head around some of them myself. Stay tuned!
Playing 4D golf really gave me an intuition on 4D and the Beyond course helped a lot too.
Also, maybe you can try 2 time dimensions as your next game?
4D visualization gang 💪💝💝💝
This video explains 4D better than any Ive ever seen
"imagine something 3D projecting on a flat surface", literally everyone watching this on a flat screen lol
With your 1 dimensional brain
(I hope someone watches sciencephile to get the joke)
@@denifnaf5874 I see some humor even without the reference.... (never heard of sciencephile...8-)
but back in focus.. I used to watch 2D images on a CRT, a box that used a lot of 3D space.
Now I have several flat (2D) screens that can show 3D pictures...
hmmm, should i 'flatten' some 3D printers to print some thing in 4D ?
That's the 5th dimension. All in 2D.
This is quite possibly the single best 4D explainer video on all of CZcams. I had to figure out all this stuff the hard way, but future 4D explorers now can get a head start! I’m looking forward to learning even more in future videos
Thank you!! I've had to figure out a lot of this stuff for myself as well over the last couple years. And I've watched a LOT of 4D content on CZcams (and other sources) myself - most of which were useless, but some of which was brilliant. I'm really trying to layout everything I've come to understand in a one-stop-shop series that hopefully anyone who's interested enough can learn. Glad you're onboard!
@@HyperCubistHypercubist
@@HyperCubist Still, the fact that it is possible to visualise 4d and potentially even more dimensions blows my mind, let’s just keep exploring
Wow, did not expect to get pinned! Thanks!
@@HyperCubist I've always wondered if you can use VR goggles to help visualize 4D objects. I mean, we use 2D screens to help visualize 3D objects, so why can't we use a 3D interface to help visualize 4D objects.
The deck of cards model broke my mind, and I finally understand why every hypercube render I've ever seen looks like it does. Thank you!
as seemingly the only person in the comments who isn't experienced with visualizing 4D space, I found the explanations extremely intuitive and I can't wait for the next ep.
Thank you! I really wanted this to be accessible to people who had never tried to visualize 4D before, as well as keep it interesting for folks who are well-versed.
To be fair, it's only a couple of days old, and the channel only has ~7.5k subscribers :P It stands to reason that it would mostly have only been watched by people who are already interested in 4D topics rather than a broader audience. But holy cow was this so much easier to understand than any other 4D explanation I've ever seen! I would love to see it reach a much wider audience; it strikes me as one of the few videos that _could_ be received by a wider audience.
And you're not alone! I've seen demonstrations of hypercubes before and am familiar with the Flatland analogy (just watched the movie last night; you should check it out if you haven't seen it! The director put it on CZcams for anyone to watch for free), but I cannot in any way visualize 4D space lol. Hoping to change that here :) The deck of 3D cards really helped!
count me in...
in the unexperienced lot I mean
@@HyperCubist You casually glossed over one point that for me made everything come together: the notion that the cube discussed beginning at 10:30 is a three dimensional object -- and the *period of the cube's existence* is a fourth dimensional object! That helped immeasurably to break apart the brain's stubborn prejudice about time.
this is nothing short of mindblowing. i never expected to even comprehend 4D logic as it is, but here i am realizing that from 4D logic, we're flat. it now makes complete sense why time cant be used to full extent because 3D planes dont exist in a moment, they exist all at once just like how 2D planes form a 3D plane all at once. amazing and well done, this video is truly the gem of youtube for me
Thta was. Atheory of mine! I swear sonce 15 yold i formulated that theory by myself, but its just in a notepad
This is why I feel like I just found my community in the comments of this video. Who else spent their teens trying to visualize higher dimensions and speculating things about them? Hi 👋 yeah I got notepads too
Yeah, but I think that’s if we use time as the 4th dimension; then we’re just long meat spirals that start from a small point, growing into a baby, to child, to adult until we die, and while doing this we swirl through the ever expanding universe.
Pretty insane and very beautiful
Which means 2d objects in our 3d world will be 3d in the 4th dimension like our shadows will be 3d
3D isn't formed of 2D planes. And 2D isn't formed of 1D planes. Everything is formed of 3D planes. There is no evidence for the existence of 2D planes or 1D planes.
Once in college, I tried to visualize 4D space
I started by crafting a 2D plane in my head, the same one used to describe gravity (like at 9:05), and expanded it out to 3D, did this for like half and hour until it was so vivid it was as if I was actually seeing it with my actual eyes
I tried to then imagine a wormhole in this 3D space, and how it would fold on itself through the 4th dimension, starting with a projection into the 3D space and attempting to expand it into a proper 4th direction, I swear I got really close to figuring it out, when suddenly the entire mental image was engulfed in a flash of light, my eyes forcibly opened, and I had a massive headache that lasted for a couple of hours
I have never been able to do this again, no matter how hard I tried
You are going to love part 3.
Hey I had the headache thing too that's really interesting. I've been studying 4d geometry for a while and had my breakthrough when looking at a tesseract that was drawn with 4d perspective. I was switching back and forth between a 2d drawing of a cube and a tesseract in perspective when my brain finally interpreted the tesseract correctly. I could actually feel the 4th dimension sort of "pop out" of the paper. It made my head "buzz" and gave me a headache for a minute.
Absolutely stunning graphic - thank you, I'm a 70 year old retired Physics teacher and I think this is a wonderful explanation of 4-space. I first read about flatland when I was in my twenties and this helped a lot but your final graphic was just brilliant.
Thank you sir - really appreciate the comment. I'm a former Mechanical Engineer, but most of my career I've been teaching / tutoring math and physics. 4D is such a fascinating concept, and after a lot of frustration with the lack of good explainers on CZcams I knew I needed to make my own. Glad to have you onboard!
6:33 "Take the red pill" these are jelly beans my guy
Shhhhhh! ;)
It's a 4D pill
The red one contains acid
@@kuroshite That ain't gonna go down easy -- especially for Freddie!
Good one hahaha @@KenLieck
man WHERE WERE YOU when I was 15 years old and insanely curious?! I am 29 years old now, and when I was browsing youtube in 2009, I was always trying to find videos on 4d stuff, and only managed to find carl sagan's flatland example we are all familiar with. This video had so many "aha" moments! Seriously love this
Right there with you my friend. Had to figure out most of this for myself. Part 2 is going to blow your mind.
I’m just realising how lucky I am to be watching this as a 15 year old lol, huge thanks to the creator!!!
@@aoifedeborha2420Omg same !!😭😭
@aoifedeborha2420well played, you are making the right decisions! Remember, when you learn younger you have more time for the knowledge to compound over time.
One analogy i like to use to visualize 4D is by having a 3D object cast a shadow on the 2D plane that a flatlander can see, but go right through, the closer the object is to the plane the darker the shadow, until it intersects, creating a pure shadow since no light be it in the plane or in 3D space can enter that area (and it's now touchable since the object is actually intersecting the plane), i like using a cone because when it approaches bottom first it produces a circle, while when it approaches tip first it produces a circle shadow that is darker closer to the center and lighter close to the edges.
For a flatlander in this model they can use these shadows darkness as a stand in for the distance they cant directly see, as they are directly correlated.
If we the extend the example to a hypercone approaching a triplane, if it approaches bottom first you will see a shadow sphere slowly fade in, but if it approaches tip first you will see a faint shadow point that expands as the hypercone gets closer to the triplane, producing a spherical shadow that is darkest near the center and lightest near the surface; In this sense we can use the darkness of the 3D shadow as a stand in for the distance we can't directly see.
Reminds me of the color shift in 4d golf
Wow dude! That's almost exactly how I imagined the 4th dimension when the narrator talked about t being parallel to all the 3 dimensions we see... But I imagined it more like the opposite: being like a point of light, in which we perceive as a very bright point that expands it's rays outward getting brighter then shrinks and dimmer as it moves away. Not quite like a sphere, but a "light", really, that's also physically touchable
Whoa never thought about it, I love it, I'll try to imagine this hyperlight, thanks!
I'm having a lillte trouble visualizing what you're saying. But I think it would be helpful to me if I could. Any chance there's a video to help me see what I fail to glean from your words?
Dude that’s wild. Love it
For forty years I've been trying to grasp 4D. Can confirm this video lives up to the promise made.
Red pill team for the algorithm 👇
Thanks! And really, this is just the intro. So much more to come. Next video we'll show a logical framework for rotating the 4th axis into view.
I understood all the concepts you introduced in the video. When they all visually coalesced together in the deck of cards mental model with the particle moving in virtual 4D space... That gave me a child-like grin on my face. Such a simple yet effective way to visualize it, thanks for this video.
I think it's so cool that for all the difficulty most visualizations have showing our 3 dimensional space, clearly having mastered that skill (with such clean animations) you prepare to move to another dimension, and in so doing share it with us. It's beautiful!
Thanks so much! Yes there is great beauty in imagining the 'impossible'.
You are punching above your weight for a small channel with this video quality. Keep it up! I cant wait for the next video.
Appreciate that, thanks!
As a design foundations educator, the explanation of projection 3 dimensional objects onto 2d surfaces can often break students confidence and motivation. The fact we can rely on basic math and geometry to reference for understanding and identify proof is what helps students reconcile their own internal struggles with fully comprehending they can represent ideas of 3d on 2d surfaces.
Your biggest struggle will be helping those who are not inclined to comprehend more sophisticated math build the confidence that they can trust their own representation of 4d "______" within 3d volume. Love it and am interested to see your approach.
The fact that 1/10th of the people who saw this left a like is a testament to how clear this explanation was
The introduction to this feels like the one in those mangas and manhwas where the MC has been a nobody all his life and now he's being offered a chance to get everything he ever wanted and I'm freaking here for it, will be looking forward to your new videos.
This was also a really good watch
The deck of cards visualization is the greatest assisting demonstration of this I have ever seen.
This video has a very 'timeless' aesthetic
I see what you've done here.
no pun intended
I still don’t get it why do people think the fourth dimension is time?? Like oh we have Length, Width, Height/Depth, AND TIME?? DOES THAT NOT SOUND OUT OF PLACE?? HOW DOES THAT EVEN WORK?
@ABTContinentallyProblematic Because people trying to explain general relativity to people who are not theoretical physicists said the 4th dimension is time. More specifically, relativistic motion when trying to conceptualize time travel. More specifically, travelling forward in time, by use of near-light speed travel.
(The idea that matter is always moving at the speed of light, but a lot of that motion is across the dimension of time, so the faster you move through the other spacial dimension, the less time you will experience when compared to slower-moving objects ... essentially pushing you forward in time.)
Far as I can tell, the only reason that the "4D=3D+time" is deeply engrained in people's minds is just because people who don't know modern physics want to build a time machines.
@ABTContinentallyProblematic time IS a fourth dimension. Like the video explained, anything with four describable "positions" is in four dimensions in one way or another. Time is an axis we can move across, and we are moving across it all the time, we just don't have control over it.
I was having a hard time visualizing what he was saying in the video until he used the, “deck of cards” visualization, it was genuinely really helpful
11:30 A sense that is coming to me is a sense of continuity within the inside of the cube to the four dimensional progression of the cube in a single slice of 3D space. Just as there is a sense of connection of points on a line, points in a plane, points in a volume, there is also a regional locality of points along the hyperspace continuum.
Exactly. And that's what the deck-of-cards model is trying to suggest - all the 3D slices (regardless of how you slice) form a continuum, all stacked up like cards to form the (4D) deck.
One could even argue circling it back around to time. I made a comment previously about how the deck of cards metaphor helped visualize extrusion of 3d space: there's an angle where 3d space is flat. Our perception of time is that it's a continuous experience. Each moment fluidly leads to the next, and each space is inherently different. A superposition of every single event in a 3d space along its 4th dimension would form its 4d correlate
As a fellow 4D addict, I didn't really learn anything new from this video, but I just wanted to leave a comment to support the algorithm, as you did really great on this video here! Everything was explained neatly and I love how you think about 4D the same way I do. I hope in future episodes you cover rotation, as rotation allows you to see the fourth dimension in 3D. Also if you talk about ground view for visualizing 4D space (swapping the vertical and w axis, so that you see the floor as a 3D space), I think that would help new people as well. Anyway, I really loved your video and I think it's a great contribution to the 4D community. :)
Thanks so much! Yes, this is just an intro video to lay down some basics, and get people on board who may not have invested a lot of time thinking about this before, as well as correcting a lot of the BS that's out there. I'm intending this ongoing series to be a "one-stop-shop" for understanding 4D from the ground up. I'll start covering 4D rotation (at least my take on it) in the 2nd video. I've thought a lot about the "3D floor" idea, with gravity in the w-direction, but it may be a while before I dive into those kinds of analogies. Trying to find the "correct" logical order to present ideas in the most accessible way is a challenge in and of itself. And even people like us who have though a lot about this have different takes on what makes sense and what doesn't, so I'll be curious as to your thoughts as we progress. Glad you're onboard!
@@HyperCubist I've tried my hand at explaining it all, but taking years of knowledge and presenting it in a fast and sensical manner is quite a challenge and requires skill. I was working on a video script a while ago but haven't touched it since. My video focused more on the math and geometry side, and kind of rushed through the mythbusting and explanatory parts, and I was thinking later videos in the series will cover more world buildy/biological aspects, like walking patterns in 4D and maybe even 4D chemistry.
@@ziggyzoggin Hi. Are you the writer of "Elsewhere - Everyday Life on a Hyper Geometric Earth?"
@@gonegahgah I haven’t heard of that book unfortunately, but I was planning on writing a book that explores how everyday life and stuff changes in 4D, so now I’m sad that that already exists
@@ziggyzoggin That is true. However, his work is more a treatise on everyday things in 4D rather than a story story. Also the author makes an excellent effort but is still a little trapped in 3D think. So, the opportunity for you still remains... I am curious to see how @HyperCubist progresses here to see if it crosses any of my previous developments...
I've been trying to understand this for years and while watching this video I literally felt it click. You need a patrean you deserve to make money from this. This is the best visualization of tesseract video on CZcams.
The way I always tried to visualize 4D with the help of time is like: think of one of those timelapse videos of a closed flowerbud gradually blooming. One frame shows you a 3D shape that represents the flower's appearance at one moment in time, say, half-bloomed. But this momentary appearance of a half-bloomed flower is but a slice of the flower's "total appearance" which includes the closed bud, the fully-bloomed flower, and everything in between. In our 3D reality, we can't see "total appearance" all at once; we just scrobble through time viewing one slice at a time. Scrobbling through many slices quickly one after another gets us the timelapse video. Our 3D brains understand the flower's "total appearance" as motion or animation through time.
In 4D space, you would not need a video to show the "total appearance" of the flower from closed bud to fully bloomed all at once. This "total appearance" is just a regular 4D shape.
Imagine holding that 4D shape in your hand. You would see and feel the entire existence of the flower from closed bud to fully bloomed as a still, stationary object. Cut it with a knife really(infinitely) thinly, and you get a 3D solid, e.g. a half-bloomed flower.
Yup - that's using time as the 4th dimension, as I show with the cube moving through time. And it's a great entry point to 4D thinking. But I try to steer away from time to focus on a purely spatial 4th dimension, though I do use time as a crutch when it's helpful.
@@HyperCubistyou could convert this from time to space by imagining the flower as more of a flip book. we have flip books where 3d space is used to visualise time, flicking between 2d planes to show movement. In that sense, the transformation over time of the image has been captured into the dimension of space - in other words, the 3rd spatial dimension is just being used to demonstrate time. In the same sense you could imagine a 4D being creating a 3D flip book of a flower, in which all the 3D states exist at once, parallel to each other, so they can be quickly viewed to give the illusion of the 3D flower blooming the same way we use 3D flip books to give the illusion of a 2D character dancing
@@HyperCubist Isn't OP just describing a flower "extruded" along the extra 4D axis (rather than a static cube extruded along that same axis)? Maybe I'm still stuck in the "entry point" that you're talking about, but I've always thought of "time" as just the way we measure 4D space. Like, inches themselves aren't "3D space" but they're our units for measuring 3D space. Similarly, aren't seconds (or moments, or minutes, or hours, or whatever) just units we, from our 3D POV, use to measure distance along the 4D axis, a distance over which things like flowers (from our 3D pov) come into existence, bloom, and die but really just exist as one hyper-shape?
Whatever the reason is that *we* seem limited to experiencing (or mentally processing) that axis in the direction of entropy (giving us the illusion of one-directional movement through it), that still seems to be the axis we're talking about when we're talking about 4D. Isn't it?
If not, what is the basis for detaching the 4th dimension from time and assuming there's a 4th physical dimension that isn't time (or related to time)? And does that 4D space also "move" through time?
My apologies if this is something that you're planning to cover in future videos. It's just that, even though I heard you say in the video you were only going to use time as the 4th dimension as a crutch and as much as I thought your deck of cards method was genius, I still came out of the video assuming that we were talking about an axis situated in the direction of entropy (for reasons that are obviously beyond both our understanding and the scope of this video).
This is _exactly_ the video I've been looking for for a long time. I can't wait to see how the series turns out.
This is a great great great GREAT video. The deck of cards concept is absolutely genius.
I’ve always understood the slice concept after my first brush with flatland when I first became interested in visualizing 4D. I think it’s what most of us interested in the topic decide upon after thinking about flatland for way too long.
I’ve always felt like you needed virtual reality to really wrap your head around the 3D slices by having all 3D slices exist at the same time to really conceptualize the extrusion. For example, throw a cube in VR space, and observe all the 3D slices frozen in the air as the cube leaves them behind(essentially a virtual 3D version of your 2D card method) as it travels the entire trajectory of the throw, cube rotation/spin included, which you could then virtually walk around and observe in the virtual space. Extrusion is an elegant way to put it.
The other concept I’ve tried to use to explain what is happening is the optical illusion of spinning “flat” coin, creating the illusion of a “3D” sphere where all “2D” coin slices exist and overlap on the same rotational axis at the same time.
But to show how to visualize 4D while I watch on the flat plane of my computer screen on youtube, no VR headset required? Absolutely genius.
blud I can’t even visualize three dimensions cmon
bro is a flatlander
@@zerq4558 calling someone a flatlander is equivalent to smooth brain
What in God’s green, flat Earth are you talking about
It's funny that people watching a video about visualising 4D don't even realise that they typically imagine a 2D image representation such as the kind their retina usually provides to their brain, but they're making fun of you
@@luthandomdadaneyeah, having 3d imagination already takes high level of artistic skill or sport skill, most people just can't do it
I have looked at a lot of videos trying to understand the geometry of a 4th dimension of space, and while this didn't go into much of anything I didn't already know the one thing that helped me more than those other videos was the mention of extrusion, and although it should have been obvious to think about I never really had a mental model of how that extrusion should look.
Man I feel like this is the best explanation on youtube. It's always been a very abstract thought, but now in a lot of ways, my understanding feels very fundamental. Thank you for imparting that wisdom on me! Can't wait for part 2.
I can visualize being a 3D being in a 4d world but I cannot understand being a 4th dimensional being. This video, however, made me understand just a little bit more. Thank you.
That's becouse using geometric shapes is "cheating" to get it easier. You just say the hypercube has the same length alongside the w-axis, becouse that is the natural extension of that shape, and each 3d slice (perpendicular to the w-axis) in the 4d space is a cube of the same size. But the 4d shapes can be wild. Not only the length on the w-axis doesn't have to be the same (imagine half a hypercube) but the shape can change compeltely. If we used hypersphere instead of hypercube, each slice would still be a sphere but the diameter of would change. But the shapes can be wild and there seems to be no "natural extansion" of human body into 4d space. You would probably have to have infinitely many 3d arms for example. One way to imagine it would be probably something like in the film Everything Everywhere All At Once. But it still doesn't capture the possible complexity.
IDK if you were the innovator of the Deck of Cards, but this is brilliant. Thanks for making this.
I know that taking 3D slices of a 4D object is a pretty common way of dealing with 4D, but the idea using 2D projections OF the 3D slices and stacking them up in a "deck" occurred to me while trying to visualize a hypersphere. I haven't seen that elsewhere, but it wouldn't surprise me if that's been presented before.
@@HyperCubist I remember seeing a youtube video mention how projecting 3D objects onto 2D and drawing a line perpendicular to the 2D plane is a good way to visualize the 4th dimension a long time ago which led me to a similar deck of cards method back when I was like 10 or something, however I've never seen anyone else mention the stacking of said visualizations or something similar before seeing this video.
@@HyperCubisti thought of something like that once before as an infinite number of dx’s stacked together (i just took calculus that year), but I didnt have the imagination/visualization chops to really go through with it (cant imagine a spinning red apple and such)
@@jasoncola6071 Yeah it's basically a calculus type argument. Volume is integrated area, Hyper-volume (bulk) is integrated volume. By the way if you haven't seen them, I have a few calc-related videos on my channel you might like.
I’ve been trying to explain this concept to people but most don’t understand, thank you for simplifying this idea in an understandable way
*Me, an Aphantasic:* I'm skeptical... but still intrigued
[Update] Ok, just finished watching it. I'll admit, it's a handy mental tool to conceptualize 4D Space. I won't be able to use it to make an _actual_ mental picture, but it can certainly help with conprehensive models and, for example, drawing out something I understand.
So I guess the problem most people have in explaining how 4D is supposed to "look" is that they just weren't...
... _playing with a full deck._
But puns aside, it *does* give a certain perspective regarding, for example, Space-Time. If you take the Card Deck model, and consider depicting the "past" as the stack of "3D Cards" and the "Deck" as the Time axis, then it's kind of like we're all seated in a car (or train, rocket, whatever vehicle suits you) facing *backwards* looking at the past. You can access information from those cards behind the vehicle (and in front of _you_ since you're seated backwards). But the "Cards" in front of the vehicle are not visible. They may not even _exist_ yet; they might very well be procedurally generated as the vehicle moves forward (behind you). Moreover, it "warps" the shape of space around it; the "Card" will be "pinched in" towards the vehicle, meaning it will be shaped more like a cone... a "Light Cone" if you will... than a totally flat card.
And moving around in the 3D volume of your Card would also ever so slightly slow the speed of the vehicle through the deck, too. It has a fixed overall speed and whatever it spends moving _within_ a Card *must* be taken from its speed through the Deck.
What I would really love to see is path tracing simulation in 4D. Typically 4 dimensions visualized with 3D slices or simply edges of the objects. But this is not how a creature would "see" in 4 dimensions. To see things we need to collect photons that are scattered from different surfaces and this is exactly what path tracing allows us to do. To see reflections, shadows and specular lights in 4D might be much more informative than all other ways to visualize four dimensions. I know for sure that technically it is possible but I have never seen anyone actually doing it.
once i saw a video of hyperbolic path tracing so it's definitely possible
@@elbonnieto8929 hyperbolic space isnt the same as 4D space though, right? Isnt hyperbolic space just, having more space crammed into the same 3D space than is normally allowed by euclidean geometry?
I'd like to see what this would look like. Are there any examples?
Understanding the 4d axis will be integral for interstellar travel. Well done, may you be remembered as an icon for the future.
8:25 if you're the person that just hits "agree" on Terms of Service.
Legendary thank you
Selection leads your action -
Blue pill : u are not subscribing
Red pill : going to subscribe
This is one of the best 4D videos I've ever seen. I cannot wait for more.
I've seen so many videos on 4d space and this is the only one that's ever made it "click" for me, incredible video
THANK YOU! I've been thinking about 4d for a while and it is kind of annoying when people say you can't visualize it, because you definitely can. Your "deck of cards" model is interesting, but not the way I'd go about it.
the way I've been visualizing 4d is taking a 3d slice at a number of integer (or integers over some number, e.g. ℤ/10={...-0.3,-0.2,-0.1,0.1,0.2,0.3...}) coordinates, and putting those next to eachother in 3d space. this works very well once you understand how rotation works along this new axis (which you can sort of visualize as "transferring" material from one slice to its neighbors in a specific way). This method also generalizes to higher dimensions; you can add another axis of slices for the fifth, and another for the sixth. now, just copypaste the whole cube of slices past the end of it to get to the seventh, and to the eight and ninth just again fill the other axes. you can do this recursively to go up to an arbitrary number of dimensions (I don't know if that made sense at all, kinda hard to convey thru text). I wanna make a video about this at some point but haven't gotten around to it yet.
also I'm glad you'll be talking about graphs of complex functions because viewing them in their actual four-dimensionality reveals a lot of cool things about them. I made a tool to graph complex functions in four dimensions before and I gained a lot of intuition about them from it. the graph of e^x specifically is very interesting.
Thanks! In your visualization, are you putting the 3D slices side by side in 3D space, or do they overlap? Is it similar to what I have at 16:48 ? And yeah, complex graphs are pretty cool. The way that I do it, e^x looks like a flat sheet in one direction, and and exponentially growing helix in another. But as you rotate around in 4D its shape can vary. I probably won't get into this until the later videos.
@@HyperCubist I place them side-by-side. overlapping them (as you did) clobbers information on one slice with another, making it hard to tell what's going on.
the first thing I did before that also was to do the same thing but one dimension lower (where I'm taking 2d slices of 3d) which built my intuition before moving to 4
I love all attempts at explaining 4-D, but I feel that so far this has to best one. The narration, explanation, anecdotes and animations have really helped this 3D'er experience 4D.
I'm only at 1:45 in the video, but I've been working on worldbuilding for a 4d fantasy setting, and I've thus far been visualizing the world as a pair of perpendicular, hyper-planar cross sections. It helps that the main character in the story I'm making for this setting is a 3d being who (at first unknowingly) lives on the surface of a 4d "ocean".
Ooh I'm interested already!
@@Wonderhoy-er The world is shaped like a double-layered Klein bottle, and the 3d world is sorta between it's inner and outer surface (even though they're the same surface). The cross sections I use to visuallize it are one of the 3d world as the protagonist perceives it, and another where the ocean is visible, its surface being a 2d slice of the 3d world, so that the 3rd spacial axis can be w. From this view, the world looks like a giant double-helix mobius strip (since it's a slice of a klein bottle) encircling a (hyper)spherical sun. The edges of the helix are massive mountain ranges (actually a single range, if you follow it all the way around) and the "floating orbs" of stone that exist in the 3d world are actually islands on the strip of "ether" that exists in the valley between the two mountain ranges.
Looking forward to the next video! A quick comment on the impossibility of 'visualizing' 4D--
I like to think that I have a pretty solid intuition for 4D, and that I'm able to pretty effectively conceptualize the visuals in my head, whether that be a projection into 3-space, or thinking of it as 3D slices, or sometimes with a lower dimensional analogy. However, I think what people mean when they say it's impossible to visualize the fourth dimension is more along the lines of-- well, it's impossible to see more colors than the ones our human eyes can see. I can still mentally consider those colors, and form intuition around them, etc, but I can't actually imagine a new color and see it in my mind's eye-- my brain isn't equipped to do that.
This is definitely a bit of a pedantic point, though-- I do look forward to seeing how you try to de-mystify and make these concepts more accessible!
Interestingly the cones in our eyes have the potential to see colors that don’t appear in real life, but it’s not really feasible because of overlap between what activates each cone. For example if we could activate the green cone to full extent and the other cones not at all we would perceive what is known as hyper green, but a light of the frequency to fully active the green cones also activates the others to lesser extent.
@@MeshremMath This is how we see "purple", actually. There is no single "purple" wavelength, it's just what our brains guess seeing red and blue light together must mean.
@@MeshremMath I've heard that it's actually possible to perceive these, if you're willing to stretch the definition a little bit. Look up 'chimerical colors'-- basically, since our eyes are designed to see colors in a relative sense, by looking at one color for a while, it raises the threshold for that cone to activate, and you can 'tire out' that color, so that when you look at the next one, it's something you couldn't otherwise experience.
Some people cant even see normal colors in their minds eye (aphantasia)
Thanks! I get what you're saying. Much of "visualizing" 4D is simply teaching yourself to THINK in 4D, but there is definitely a real visual component to it as well. It's all about learning new visual rules for interpreting what you see, and abandoning old ones. And part of it will rely on semantics and updating definitions. But once you spend enough time visualizing 4D this way, it becomes automatic, and we can learn to see 4D the same way we can see 3D - by projecting onto a 2D plane.
15:23 This is my breakthrough moment. ANY axis at 0 technically IS perpendicular to each other! The law didn't even break!
I also have to say, your explanation of "offset" is also as brilliant!
0:38 i am expecting my mind to be blown
And?
Same
@HyperCubist Well his mind exploded so he did not survive
@@lightpro7 🤯
@@HyperCubistliterally.
I was hoping this video was a year old so i could binge watch the entire series. Now I’m going through red pill withdrawal 😂. Awesome explainer video
Totally agree!!!
Deck of cards model is absolutely stunning! It feels like I've seen a hypercube properly for the first time in my life. Thank you!!!
5D now please
Imagine Fredy imagining 4d
It's would be exactly as hard as it would be for him
I beleive 5D deals with our brain and consciousness in the universe
@@Poisontooth why?
@theguyshetellsunottoworryabout I believe the mind and the universe is ultimately connected.
@@Poisontooth okay but why ? You wake up one day and you just believed? Or something made you believe that?
This video has been on my recommended page for a while and I was kinda reluctent to click it, because more often than not this kind of video just repeats things I saw or read elsewhere in a slightly different way. Needless to say, I was pleasently surprised. I am looking forward to the rest of this series!
It does cover a lot of basics, but I'm glad you found some fresh insights!
My curiosity on this topic started when i watched a video about imagining 10-D on youtube a long time ago.
I'd often doodle hypercubes during class, but it's been a while since I've drawn one.
This video has resparked that curiosity, and im so glad it popped up on my recommendation.
Thank you for making this so digestible and fun to watch. Subscribed!
Thank you. I promise you that once this series is complete, you'll be doodling cubinders, hyperspheres, duocylinders and lots of other shapes, and understand them in great detail.
Everyone get this video viral, it’s super good and informative, everyone like the video and share it with your friends :D
fax
Algorithm is treating this guy well. Well deserved!
This is a very quick and easy-to-follow video! Most tutorials only cover the Freddie part, but this tutorial covers so much more, and it’s also a very engaging tutorial as well (especially the deck of cards). I can’t wait to see this video evolve into a world-changing series, thank you for making it!
Thank you! Yes I'm planning on going waaaaay beyond the usual stuff you see in your typical 4D explainer videos. I really hope it does change the popular conversation around 4D.
@@HyperCubist Thanks, and I bet it will. I can’t wait to watch the rest of series!
I'm so glad you're making this series and actually learning to visualize in higher dimensions has been instrumental for actually understanding physics and abstract math. Marc ten Bosch's explanations of GA rotors and his 4D Toys app are what lead to me going down these rabbit holes myself. I expect this video series will aid my understanding and fundamentally change others'. I'm not a people person nor a fan of the education system, but things like this show how much better maths education can be, and almost inspire me to pursue teaching.
Last year in physics there were times when someone asked me for help on a problem and I remembered that most people don't think that _visualizing a 4d volume in spacetime and applying the Leibniz rule using the faces of the volume (which are 3d volumes embedded in 4d spacetime, but can also be thought of as snapshots of a cube at two points in time, plus integrals of surface of that cube over the period of time)..._ is making the problem any easier to solve.
Oh my god I was so ready to binge the ever living shit out of this series until I realized this is the only video out right now. Good job! Looking forward to the next one!!
coming soon!
yeah me too
@@HyperCubist can’t wait!
@@KSJuneI was about to look for the second video. I'll take a deep breath instead.
Me too!
17:48 “Everything that has passed, can never be again. All these moments in time will be lost, like tears in rain.”
Don’t mind me, I’ll just be sitting and staring out the window for the next 2 hours.
My favorite movie quote of all time
@@luks303 it’s from a movie?
@@AllHailZeppelin Out of place in a math video imo.
@@AllHailZeppelin its from blade runner
@@arab6745 nah I thought it was funny
Projecting the 3D space on layered 2D planes to explain 4th dimension is pure genius. Thanks.
Can't wait for the next one. I have had the ability to visualize four dimensions and toy with hyperspatial entities mentally for quite some time, and having more intuition built up and knowing 'what flies' vs what doesn't always helps. Please keep up the great work :)
Interesting. DMT?
what how would you visualize 4D before this video existed?
@@calculator_gamingdrugs
@@calculator_gaming honestly, I watched enough versions of flatland as a kid that I basically arrived independently at the same intuitions described in the video. Also a shitload of weed helps with the whole "radical acceptance" part if you can't get past the initial anxiety of "but that feels wrong"
@@calculator_gaming some people just think they can visualize it while not realizing they are doing it wrong
Time is a measurement of motion through space. Multiple cubes spread out along a time line, extruded objects, stacked two dimensional objects and any other trick you want to demonstrate, are all just three dimensional objects. The source of "time is a dimension" comes from mathematical formulations (translations, rotations, boundaries, etc) using common geometrical functions. That is the only place that time exists as a dimension.
Actually it's even worse - these are all just two dimensional objects on a screen.
@@HyperCubistand the hypercube depicted is just a 2d representation of the 3d shadow of a 4d hypercube.
The deck of cards analogy made me actually understand the shape of the common hypercube you see when you look up "4d"
An i right in thinking the 'smaller' cube in the 'center' only looks that way because it's further from us in the fourth dimension? Like how the farther edge of a 3d cube looks shorter than the edge closest to us?
Is it just 4d foreshortening?
Exactly! We'll do a deep dive on this when we talk about perspective down the line.
The idea of frames comes to mind. Since the advent of 3 dimensional representation on computer screens or even television/film, we now accept that if we stack the frames and flip through them forward or back, we see movement in 3 dimensions through an optical illusion. Like your paper stacking analogy, each "frame" is the 4th dimension. if you overlay the frames and see them all at once, you'd see "tracers" or "trails" of anything that moved. If the camera (frame of reference) is still, it's easy to look at it an see an object moving frame to frame making almost a snakelike shape of itself.
But, if you move the camera (frame of reference) and move some objects, then roll the film forward, suddenly everything has trails (walls, floors, painting on the walls all have trails as well as the snake trails from the moving objects) and the brain loses the ability to make sense of what is happening. The trick to save the brain from losing the is to slow the framerate down, changing only once every few seconds. It still hurts but if you watch long enough suddenly the brain adjusts and can track it all again (which is exactly what you did with the paper analogy at the end).
Time as a 4th dimension is just an extrusion of all points in a 3 d world along one direction of a 4th axis. And it's not that the past doesn't exist, it's more that we cannot move in that direction and seem to be compelled to move forward. But if you slow time to examine one frame at a time (which is how we live, but more like 30 frames at a time per second) the future isn't available to us either beyond the current set of frames we can handle. Both directions on the time axis exist, we are the ones that can't go too far one way or the other.
In a way, our minds act like a microscope for viewing 4 dimensional space 30 frames at a time. Maybe other minds have a longer view an d can "zoom" out to 100, 1000, 10,000,000 up to maybe ALL frames at a glance, seeing what to us would be past, present and future in one solid block of 4 d space.
The challenge is navigating a 4D cave in 4D Minecraft without getting lost.
I took the red pill over 2 years ago, I'm all for this series ✊
A universe projection over a hyperplane for time would be a killer piece of art.
I'm excited for the next videos in the series !
This is unexpected
@@AZALI00013 It's that part where you suddenly see someone you've known before on a topic completely unrelated to what you know them for
(This happened with ITR at least 2 or 3 times :P)
4D beats… coming soon… ;)
MY GOAT
Finding Azali on random vids chosen by the algorithm
2/?
This was very cool and helpful in further visualizing the 4th dimension. Through viewing higher dimension conceptual videos, I had some of it worked out already, but this gives me more to ponder on. Thanks and I hope the algorithm doesn't fail me when the new video drops.
As a senior now this brings me back to my early years as a young teen, with an obsession with my hair. I was lucky enough to have a mirrored medicine cabinet with two movable side mirrors, we also had a mirror hung on the wall perpendicular to the medicine cabinet.
So visualizing a fourth dimension came easy to me, but since the reflection is backwards I remember having a hard time coordinating my finger to a certain spot on my head. My brain had a hard time adjusting to it.
All this led me too using a ruler to draw the perfect three dimensional box on a flat piece of paper and I've been hooked on geometry and angles ever since. But your slice or slide method is much better especially for those who never had a bathroom full of mirrors...
Me a 3D person trying to understand the 4th dimension by seeing this video on a 2D screen
Video starts at 8:20
thx
you skipped a third of the the video
@@alert2 I didn't, but go off. All of it before that is just a preface to it. I'm not a fan of reading the entire iTunes agreement before I click accept.
The card visualization just blew my mind and Im all here for it!!!! Can’t wait for more, this is my introduction to visualizing 4D space and I have to say you’re doing amazing so far!
Anyone else coming back daily to check for part 2?
22:55 most useful part of the video
THANK YOU!! I’ve been trying to explain dimensionality like this to friends and family for the longest time now; I just about fell out of my chair when I saw the video thumbnail! I was like “YO THAT’S IT, THAT’S WHAT I’VE BEEN SAYING!!”
I haven’t actually watched the video yet, but I used the metaphor of how we can use frames of 2D images to represent the passage of time, snapshot samples of an ever-growing stack along the Z-axis representing time. And the fact that we can “project” 3D onto a two dimensional frame. So therefore, we can “project” 4D into 3D space. Best visualized with VR headsets, although we can re-project that 3D projection of the 4D object onto a 2D space (a computer monitor) if we really had to.
Which I imagine is exactly what this video is!
Yeah, the thumbnail kinda tells the whole story instead of me yappin' ;)
Ohk video starts here 3:51
Visualizing the 4d on a screen is like visualizing the 3d on a line. It's pointless because it takes away all the information.
I've already been working on visualizing 4d by testing new mental models and building new intuitions via 4d simulations and games like 4d Golf and 4d Miner, and they are great tools for this! Everyone should do this! Expand your mind!
thank you for the information
after watching this video I went to sleep and I dreamed about the fourth dimension
I can now see inside my house and my friends everything is flat. I can see the whole 6 sides of a cube, and I can see a 4 dimensional cube with 8 sides.
this really help me understand and become higher dimensional being. this helped me connect to a math at a spiritual level(this is a joke LOL)🙏
Rather than seeing the 6 sides of the cube. as a 4D being you will see the entirety of the cube. This is just like we can see the entirety of a square. But just like we can turn a square side on and only see it as an edge (1 or 2 edge lines visible), likewise a 4D being can turn a cube edge on and only see it as an edge (1, 2 or 3 squares visible). So think of that and keep the dreams coming...
Wrong. I have aphantasia, so can’t visualise anything regardless of number of dimensions!
finally someone who gets it, i guess for us aphants this should help us conceptualize it at least
Your inability does not affect the inherent truth of reality.
There is still light even blind people exist.
"Me, me, me" 🙄
@@pierremarcotte6299 ‘twas a joke.
@@pierremarcotte6299 also, they were referring to the thumbnail which says “yes, you can visualize 4D!”. The use of the word “you” there means that’s literally a false statement when spoken to someone with aphantasia, hence the joke, which, again, is just a joke. It’s sort of funny for one to pretend they don’t understand that the word “you” wasn’t specifically literally referring to them and is actually just a general statement about people’s ability to visualize 4D. Anyway, sorry I’ve totally butchered this joke through insane over-explanation now but hopefully you understand
I don’t know if that exist as a real thing. I see the entire idea as different cultures in the ancient past, especially those of higher advanced cultures all had like but separate ways of imagining the functioning of a number. Given no extensive training on how to calculate will lend itself towards individual perceptions
the deck of cards model is awesome actually. it uses our visual perception to simulate a 3rd spatial dimension, even though the cards are 2d. That frees up the 3rd dimension to represent the 4D axis. Really, really clever usage of our perception. Bravo
Played a game called 4D golf a few months ago. It really helps to visualize a fourth special dimension with rotations rather than translations.
400k Views in two weeks off of 23k subsccribers. Good Lord. Even youtube couldnt deny the genius blend of ASMR, Education and entertainment that is this video.
Bravo. Bravo.
The best video I have seen on this concept. After I read Flatland, watched at least a dozen videos on 4D. But this is the 1st time i felt at home, while you kept explaining the concept and adding more information for a general viewer. Please carry on and I am eagerly looking forward to your next video on this topic. Thank you 🙏🏻
Sounds like cult to me 7:20
They done drank the cool aid
😅😂
I have also thought about this a lot, and although I agree with the fact that four dimensions can be visualised using the slice method, I think this visualisation doesn't properly convey the symmetries of four dimensional space, the fourth axes is different that the other three axis, an issue shared when the fourth dimension is time or temperature.
And just having four components only has permutational symmetry.
Do you think it is possible to visualise all four dimensional rotation?
it's sort of possible to visualize 4d rotation; you just have to completely change the way you think about rotation. it's still going to be asymmetric but you can improve it (or worsen it depending on who you are) by visualizing 4d as a grid of 2d slices, then it's still asymmetric but now you have two axes in which you rotate in the normal method, and two axes in which you rotate in a different method.
@@thezipcreator In a way, you are either contructing ℝ⁴ as ℝ³⨯ℝ or as ℝ²⨯ℝ².
This matters, because both contructions are also constructions of 4D rotations, this space is 3 dimensional in (3,1) and 4 dimensional in (2,2).
Since ℝ⁴ has a six dimensional space of rotatations, this still seems far from the full picture.
What rotation isn't 4 dimensional?
@caspermadlener4191 "Do you think it is possible to visualise all four dimensional rotation?" I feel that it may be. I look forward to seeing if this is the case.
First dimention, front and back.
Second: left and right
Third: up and down
Fourt: inside and outside
0:03 fun fact: people who timestamp their unrelated comments to the start of the video need to get a life
😂 so u
Looking forward to the next video man
Oh wow, that deck of cards model is simply brilliant! I always forget how much of my understanding of dimensional spaces above 3 relies heavily on mathematical abstraction, only reminded of the fact when I'm trying to explain that jump from 3 to 4 dimensions in introductory terms. I love this so much because it let's me use the same tools/ideas gathered in building up from 1 to 3 dimensions to enter the 4th; and it gives the feeling of a natural progression that I've always struggled to communicate when the topic has come up. Thank you for sharing this, definitely looking forward to part 2 and on!
I've been looking for a video like this
Start watching at 13:00 to skip the introduction.
But you would miss the pledge making the entire video series useless.
@@seisveintiocho-x9eI second this.
Every time I've seen someone say "you can't conceptualize 4 dimensions" what they have *meant* is that you can conceptualize it directly and must instead rely on a projection of 4 dimensions into 3, which is exactly what this video does too.
It's actually worse than that. We can't conceptualize 3D directly, and must instead rely on a projection of 3 dimensions onto 2 - our 2D field of vision.
@HyperCubist our vision is 2d dimensional, but that for me is what made me even try visualizing 4D space in the first place. If we have already been visualizing the entire 3rd dimension from a 2D representation then we already have the tools to visualize higher dimensions in our heads. The trick is taking those tools and sharpening them to handle 4D as well.
@@austinzitterich8389 You've got it. This is exactly the mode of thinking that resulted in this video. Part 2 explores this idea to develop a new mental framework for visualizing 4D.
@HyperCubist looking forward to part 2. I'm excited to see what you cover. There's just so much to it. One of my favorites was recognizing what 4d corners are and visualizing them. A corner on a cube is two 2D squares coming together at right angles at a 1D line, so the corner of a tesseract is two 3D cubes coming together at a right angle at a 2D square. Realizing that a 1D line on a cube acts the same way as a 2D square on a tesseract helped so much with visualizing a tesseract.
Bro is yapping about 4 dimensions when his video doesnt even have more than 2
By definition a video is a series of images separated by time
So 3 dimensions