This is NOT a Tesseract.
ฝัง
- เผยแพร่เมื่อ 21 มิ.ย. 2024
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There are thousands of visualizations of the “4th dimension” online, the most famous being pictures of so-called “hypercubes” and “tesseracts.” Unfortunately, most of these images also imply that you are in fact seeing a 4-D object. But that’s not true. That’s impossible. Three-dimensional math Zaddy Kyle Hill coming to you from a two-dimensional TH-cam video is here to help.
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Best man!
Rocking the cave man beard!
Not hating but am curious as to what made you want to grow it out?
This video is hilarious bro great job
I think you’re forgetting buckaroo bonsai who went across the eighth dimension. It’s pretty cool John Lithgow and Chris Lloyd are there but they’re aliens OK and they’re not good guys so don’t ask for an autograph
Kyle. Play 4D toys, if you have not. You would find it interesting at the least.
Seeing even professional mathematicians, who work with 4d and higher, lament that they can't visualize higher dimensions made me realize it's probably a human limitation.
It is entirely that. We don't see infrared or ultraviolet light because we never evolved a need. Similar premise, we've never evolved to experience fourth dimensional space, the difference being fourth dimensional space doesn't exist around us like ultraviolet or infrared light.
It's pretty easy, TBH. Just imagine a space with N dimensions and then set N equal to 4.
That's the point of a lot of math and science. To put on paper what we cannot experience in reality, yet it exists anyway. In practice, the W-axis for our universe is time, we can see, to a limited degree, that axis but only in one direction, the past. But the other direction, the future, is invisible to us. Likewise, we can travel through that W-axis in one direction only, the future, but the past is forever locked away. The only theoretical exception being space-time bending phenomena like black holes and wormholes, 4D objects that manifest at the absolute extremes of our understanding of physics and the universe at large.
We have the need to draw low resolution penis in 4 dimensions
@@cadekachelmeier7251 Cool, it works thanks!
I did as instructed and pointed in the fourth dimension direction.
My finger broke into several pieces. and the sky was torn asunder.
Then a Creature appeared, from the fourth dimension insisting i need to pay my fine for destroying time and space across the past. whilst slapping me with a goldfish. before vanishing back into its ear.
My finger is still broken.
Help
Hasta la vista baby
hahaha this needs to be pinned lol
Seems like you wound up into the warp, don't worry I am calling the Inquisition. Remember the Emperor Protects.
yes, inquisitor. that one over there!
you need a four dimensional bandage
“He’s so open minded that his brain fell out a long time ago”
😂😂😂😂😂😂😂
Shots been fired 🔥
More like made the same joke hes made in multiple other videos😂@TiagoEgas
@@jamalkjamison214
Pointed at Rogan or other people?
@@jamalkjamison214are you getting defensive over Joe Rogan!?
It's not a new joke. Why does that fact make you think anything about Rogan?@@aries4378
As someone who’s stared at the 4D wiki page and felt lost every time, I feel grateful to hear someone say, “It’s fine no one can see it.”
The best guess is time. As in (in theory)...
Nothingness (Absolute and Non Absolute)
Dot (Singularity and Non Singularity)
Line (Parallel Connection or Isolated)
2d Plane (Perpendicular Connection or Isolated)
3d Plane (Hyper Directional Connection or Isolated)
4d Omniscient Time (Greater Singularity or Hyper Infinite Directional Connection)
5th Dimensional Alternate Time (Axiom Directional Connection or Axiom Isolated)
6th Dimensional Origin Points (Infinite Origin Alpha(s) and Omega(s) Directional Connection or Isolated)
7th Dimensional Conceptual Directional (Major Singularity or Axiom Alpha Omega Connection)
8th Dimension (True Singularity or Alpha Omni Reality)
9th Dimension (Absolute Omni Singularity or Omni Directional Connection)
In other words, this is...
Null Universe
Universe
Universe+
Universe Infinite
Universe Axiom
Universe Omni
Then, fold that reality again on repeat. Until you form the Matrix. But it doesn't stop there. Fold the Matrix into itself to form the Matrix Sequences. You'll hit an Omni Level where Add Infinitus Axiom becomes Extra Dimensional and stops becoming a Core Dimension.
People just realizing you cannot see the 4th dimension is actually kind of worrying.. Like did you not think that out? Also the 4th dimension is most likely just time in the 3rd dimension, Kyle and some of science thinks about it differently and lots of contradictions, and it's mostly throwing around ideas and what shapes MIGHT look like, yeah majority of this stuff might not even be real at all. What is more likely is we are in the 3rd/4th dimension and the higher dimensions (5d+) is far beyond anything we could comprehend, there's no point in trying in this life. Anyway yeah it's not that hard to realize these things on your own, if a 2d creature could not see the 3d world, WHICH CAN BE VISUALIZED, that tells you all you need to kno. Anyway this video is very click bait, the fact people needed a video for this is kind of sad really, I think most people knew this already but it's still just astounding people think you can visualize something that we have never seen, or measured. It's completely made up and romanticized. A lot of the 4D shapes you see are just cool looking 3D shapes that have weird connections and are often stacked inside each other, that aren't in the natural world.
Me trying to look at a four dimensional object on a two dimensional screen. 😕
Damn, u beat me to it 😂
Trying to look at a four dimensional object represented by a three dimensional model on a two dimensional screen fed by a one dimensional string of 1's and 0's.
Me trying to look at a 3d representation of a 4d cube with my 2d eyes D:
Just do it!
I wonder if I could use VR to better have an intuitive understanding of a 3d projection of a 4d object. Much like we can project 3d on to 2d screens and understand them.
"so open-minded his brain fell out"
That´s one of the best disses I´ve ever heard, will absolutely save for future use
There's a Tim Minchin skit called "If you open your mind too much your brain will fall out" which is where I first heard it.
Is old but good and first time heard from the mighty thorbun
Describes alot of liberals
@@mason6883 And even more conservatives
It is a pretty sick burn. 🔥 😎
The short story "and he built a crooked house" by Robert Heinlein does a pretty good job of taking you on a tour of the inside of a tesseract.
Today I should be getting the original magazine that this was in. To me, it’s synchronicity that this video came out and I just watched it.
It was a joke. A house shaped like an unfolded tesseract that folds across the 4th dimension into a real one, because, iirc, an earthquake? Heinlein probably laughed his ass off writing that one.
I have a new Chuck Norris joke: "Chuck Norris can point his finger on the W-axis direction."
I'ma head out....
Chuck Norris so bad ass he can kick in 4d😂
One more thing worth noting is that these animation aren't even 3d representations… because they're flat. They are representations of 4d in 2d. Our brains fill in the missing dimension.
1 of them at least. Filling in both is significantly harder.
Yes, "Depth Perception" and Video Trickery!
I mean, that’s what he said in the video
We don't even see in true 3D to begin with, we cross reference two 2D images taken by our eyes and simulate the depth inside our brains.
We are 3D creatures, in a 3D world, that can only see in 2D. Our ability to see in 3D being an illusion.
This applies to EVERY sense, animals have two nostrils and two ears for the exact same reason as having 2 eyes, it allows them to determine the direction of sensory information in three dimensional space, and even determine the shapes of objects with certain species.
A 4D being would likely be the same, their senses and perception would perceive the world in 3D, and cross reference sensory information from multiple angles to determine four dimensional depth.
@@Cri_Jackal Perceiving a world in actual 3D is such a wild concept to comprehend. We are limited by a 2D plane of a object in our eyes, thus it has hidden sides. But to a 4D creature, there is no such thing.
I think my favorite way I've heard someone explain that the classic cube-inside-cube "Tesseract", is that it is the equivalent of lining up three rhombuses together into a hexagon and calling that a "Cube". The lines from the rhombuses make it appear similar to one perspective of a cube, but it is not a cube, it's still 2D shapes, the 3 rhombuses are still only making a hexagon.
with the cubes, the 3D model as a whole looks like you're viewing one perspective of a Tesseract, but it is still not a Tesseract, it's still only 2 cubes with the corners connected. turning the 3D model around and looking at it from different angles never changes what perspective you're seeing the "Tesseract" from, in the same way rotating the combined rhombuses around together doesn't change what perspective you can see the "Cube" from.
We can't visualize or comprehend a 4D space or object, and the only way to understand or explain it is by comparing it down a step to a 2D perspective of a 3D object, since that we CAN visualize and understand in full; It's how our eyes work.
Actually, the cube-inside-cube would be the analog of a square inside a square with the nearest pairs of diagonals connected. (Think about a cube that was just a wireframe along the edges, this is what it would look like if your eye was just above the top, looking down.)
The rhombi-inside-hexagon would correspond to one of the other common Hypercube projections, the two offset cubes connected at the diagonals. In this model, the two "normal" cubes are the same size, just offset from each other in some direction, usually along a diagonal.
“A cube hiding behind a square” blew my mind way more then I ever thought it could
Yeah, but it's a poor image. Do you imagine a cube as a square hiding behind a line segment? Doesn't make sense. A hollow hypercube is comprised of 8 (3D) cubes folded across a theoretical 4th spatial (hyper-spatial?) dimension, not just a cube and a square in any way.
@joesterling4299 when you are aligned to the side of the cube you see a square and the 4 segments of the 4 lateral faces which you are seeing by the side. What the guy said (can't remember the name rn) was that the representation we see of a tesseract on google, when rightly aligned (I suppose on all 4 axis), looks like a cube. Otherwise it looks like that mess in 3 dimensions just like a misaligned cube would look in 2 dimensions.
Lol have you never went outside and realized perspective?
"We have Thor at Home" seemed to have a lot of fun with this one. Had a real tough day and it got a smile outta me so nice work
I didn't realize people who ever bothered thinking about the tesseract animation didn't know it was a 2D embedding of a 3D embedding of a W axis rotation.
Same. I guess it doesn't surprise me that at some point some scientific miscommunication might have happened, but all the discussion I've ever seen regarding higher dimensional space has been careful to acknowledge human limitations.
That's because there are a lot of people who think they're a lot smarter than they are after a combination of weed and TH-cam algorithmic autoplay.
Whats the w axis
Same, cuz if you dig yourself into a hole of sci-comm then it’s not that difficult to come across explanations that match with the lower dimensions. But then I realised I’d heard worse, putting possible worlds into the mix, I can see how people are not already familiar with all the concepts can get confused by a single gif with no explanation
@@leoelliondeux
So basically you have up-down, left-right, forward-backward, aka the x, y and z axis, but we don’t really have the label for the 4 orthogonal axis because we simply cannot perceive it even if it physically exists, so we gave it the name w axis
It’s funny how this guy looks like Thor and he’s explaining what a teaseract is
Tbh, he's got the dark beard and the little vertical line thru his right eyebrow, those are more Aquaman vibes. Thor doesn't mess with his eyebrows lol
@@himynameisjeff the missing soulpatch tho...that is what throws me off. He rocks the long hair, then has bald spots in the beard. 🥺
Who better to explain it?
@@himynameisjeff Aquagardian!
Walmart version of Thor
When I visualize the net of that tesseract being folded into a higher dimension as a 3D flat lander, I imagine each cube suddenly disappearing as it’s rotated about its edge on an axis which no known form of mass-energy can traverse. Probably the most accurate visualization of 4D objects I’ve ever seen was a depiction of one passing through our 3 dimensional plane. It would seem to suddenly appear, then constantly (appear to) morph as it continues to move along the W axis, showing different 3 dimensional cross sections of its 4D geometry before just as suddenly disappearing as the last 3D monolayer of the object passes through our plane.
Exactly. I came across a TikTok video recently that helped it all click for me. They challenged us to imagine what it might look like in a 2-D plane if you were to pass a sphere through it. All they can see is lines, so it would be a point that appears out of nowhere and starts extending into a line. The line gets increasingly long before it starts contracting again, ultimately disappearing as the sphere completes its trip through their plane. So yeah, it totally stands to reason that the same concept would apply with a 4-D object being passed through a 3-D plane
So if you imagine the 3rd dimension as simple volume, an outline of a shape. Imagine the 4th dimension as density, then keep putting empty boxes inside themselves, pushing, squeezing, "folding", until you have a 4th dimensional box that for all intents and purpose has the same external volume in 3 dimensions, despite actually containing multiple boxes within.
Think about it, you can never truly look inside of something, you're just peeling back layers, but always on the outside. Like an onion, or any matter, what's the matter
There's one way to look at it. The smaller cube is not getting smaller. It's getting further away from you through 4th dimension.
The wildest thing about 4D shapes is that my brain always feels like it’s JUST MICRONS AWAY from getting there. Like understanding is juuuuuust barely out of reach. It’s an insane feeling
Lol yeah like I keep understanding three at a time... but then when I reach out for the fourth one, I reach so far that I lose my grasp on the first one. And as the fourth one comes into focus the first one fades away, and I'm left with only 3 again. Always 3.
Try to visualize 2D.
Atoms and particles are 3d, light is 3d
It has (picking 2) height and width, but no depth. What does it look like? Nothing
What is it? Nothing
Even empty space is 3d
Light cannot reflect off 2d, it cannot be made of anything we've observed, in fact cannot exist in any way we know of.
What does that look like? Visualize it.
One needs to disregard reality to believe they've seen anything in 2d.
Now, hold on to reality and attempt to perceive 4d... you can't do both.
so real
I experience literal brain strain, like my head muscles tense up and I start to get a headache. Lol
You've just described exactly how I feel about this subject. I keep coming back to videos about 4D space because I think I'll have finally cracked the code somehow. Unfortunately, what ends up happening is I get a headache instead 😂
It's quite a leap too, because I, like everyone else, can't even see in 3D! If I could, I'd probably be a 4D being trying to conceptualize 5D while not being able to see in 4D.
Dude the shadow thing just blew my mind. So could that mean that if four dimensional beings exist we could see their shadows in our dimension as three dimensional objects?
Short answer, yes.
It would only be visible if their shadow happened to land on our 3D plane of existence. If 4D space exists then that means that infinite 3D planes must also exist, in other words, infinite parallel universes.
@@anthonyward8853
> infinite parallel universes
not really. it would be one _single_ universe, which we (potentially) just live on a flat slice of. notably, we would be affected by e.g. 4d gravity, unless this universe is like, on a sheet of paper flat on the ground.
@@anthonyward8853
> It would only be visible if their shadow happened to land on our 3D plane of existence
note that the shadow would need to land on something for us to be able to see it, otherwise it would pass _though_ our plane. so you'd still need like a fog for the shadow to land on
That's what shadow people are.
If the 4th dimensional being/object happens to intersect our "flat" 3D space. Imagine a 2D being living on a piece of paper and there is a 3D pen going through it. At first the being won't see anything because the pen is not touching the paper. Then the pen starts penetrating the paper and the being sees the line of surface of the pen that is in contact with the paper. As the pen keeps going through the paper, the contact area changes and the shape that the being sees also changes. Then the pen is all the way through and no longer intersects the paper. 3D beings can still see the pen, however to the 2D being the intersection appeared out of nowhere, changed shapes for some time, and then disappeared again.
If a 2D being looks at a drawing of a building, it will only see the lines that are not occluded. The being can't see what's inside and behind the house. But a 3D creature would be able to see what's inside and behind the house. That means that a 4D creature theoretically can see the insides of a living human being and any machinery that we manufacture without the need of xray or CT scanning.
0:50 This is not what the 4th dimension actually looks like. No, this is just a tribute 🎸🤘
Me before video: I mean, Carl Sagan explained it perfectly
Me after video: Nothing has changed
Honestly, if this means we should start calling so-called hypercubes/tesseracts (the 3d shadows people have been mistaking for the real thing) hypercube shadows/tesseract shadows, I'm all for that, makes them sound even cooler :P
Then by that logic, when you see your car you should refer to it as a car shadow. Because you can't see the actual 3D car.
@@HyperCubistYeah, we should start doing that
@@HyperCubist The actual shadows are the images of the car that your eyeballs capture. Your brain derives the information of the car from the shadows of the car that it received from your eyeballs.
So no, the car is still the car.
@@fluffrier There really are no shadows, just 2D projections. But as you point out, that's all we see - the 2D projections our brain uses to get an idea of a 3D object. But we don't see in 3D, otherwise we'd be able to look at all sides at once, and see the interior of a solid object. Similarly, the tesseract model is a single 3D projection of an ideal 4D object. In turn, we see that projection via 2D projections. That means we can see 2D projections of 3D objects OR 4D objects. You can't argue that we can only see "shadows" of 4D objects, but we can see actual 3D objects. Either way, we see 2D projections of the object.
The way I kinda wrapped my brain around it, a 4D creature could see 4D by overlaying 2 3D images of the same space, but seeing from slightly different 4D angles
We are 4d creatures... we move through 4 dimensions. Height, depth, width, and time...
Maybe they have 3 eyes
@@PositiveOnly-dm3rx in the context of the vid Time does not count as a spacial dimension.
@@yeahitskimmel Possibly, I wouldn't know
@@PositiveOnly-dm3rx There are issues with time supposedly being a forth spatial dimension. The main one, in my opinion, being that there are two directions in each the three agreed-to spatial dimensions. Time only has one direction.
I can now imagine a 4D Kyle Hill explaining why he can’t show the 5th dimension
I have never seen this supposed science miscommunication about 4d
"Fourth Dimension? I cant picture that. Youre dumb!"
- Bender 'Bending' Rodriguez
4th dimension? Bah. I saw a documentary about a dude who physically traveled to the NINTH dimension!
This lesson really brings to mind Plato's "The Man in the Cave". If all of reality is but a shadow to what actually exists fed to us by the limitations of our Simian brains, then one has to wonder what the world looks like in the sun and what kind of evolution has to occur to escape the cave we live in
That's exactly the story I use to try to explain to people the concept of multiple dimensions
plato came up with the allegory of the cave, not aristotle
@@millenniummouse, thanks! Fixed
@@caelumvaldovinos5318 no prob!
Apparently I’m so late to the party that I didn’t get to see the utter face plant of crediting the cave to Aristotle! 🤦
That was the first lesson in the first lecture of my first class in college 1990.
Then I went home and drank beer.
Good times, good times…
Okay- here’s why I think it could be possible to one day imagine the 4th dimension.
So okay- people with aphantasia can’t imagine actual objects in their brains, can’t physically rotate them BUT they still can understand the concept of that object. They can understand the sides that make up that object and the properties of that object without seeing it in the conventional sense.
So here’s where things get weird. If we can figure out a method to train our brains to perceive a 3D object- all sides to it, THEN we’ll start getting really close to imagining the 4th dimension.
The easiest objects would be things like cubes and pyramids since we know what they look like inside out. BUT, we can begin the process by color coding each side and trying to comprehend each side at the same time- without unfolding it, or rotating the object.
Understanding it more like a computer would. When a computer loads up a cube in blender, it’s not seeing it from one side- it loads in the whole thing and shows us that one angle we can currently understand.
Once we figure out a method of doing this, then we can potentially start doing more complex objects and from there- we’d have mastered an understanding of the concept of the 3rd dimension.
From there, again we’ll have figured out a few new pathways of understanding what the 4th dimension could look like- in not looking at an object literally like looking at a photo, but understanding how it works
Hey, I actually have some degree of aphantasia myself! (Not sure how severe because it's self-diagnosed and I only realized like a year ago.) And I agree, I can never "picture" anything in my mind but I can understand the concepts of things just fine. As a result, while it's obviously more difficult, it's possible for me to get the "feel" of stuff like a hypercube to a degree.
It's easiest for me to conceptualize a vague "object" that as it moves in 4-D space changes what parts of it we can see in 3-D space, even if a specific example like a tessaract/hypercube is a bit too difficult for me. Probably because, while in college I understood multivariable calculus just fine, I really struggled with linear algebra (not knowing much about vector spaces and matrices before the class definitely made it hard lol).
Kyle, you wouldn't actually be able to perceive me pointing in the direction you ask unless you took the mushrooms with me.
Imagine a circle falling through 1D land on it's side. The inhabitants of 1D land "see" a dot that grows to a longer and longer line that then recedes to a dot then disappears.
Now, magine a sphere falling through 2D land. The inhabitants of 2D land "see" a dot that grows to a larger and larger circle that then recedes to a dot then disappears.
Finally, you can't imagine a hypersphere falling through our 3D world. However, we of 3D land "see" a dot that grows to a larger and large sphere that then shrinks back to a dot then disappears.
wouldn't ball be better word, as dot is inly 2D?
@@krekolos421 dot is 1D, circle is 2D, ball is 3D, ball presented in the fabric of time, including future, is 4D... Object that casts a shadow shaped as a ball... 5D! And yes, that would be 5D and not 4D opposing to what Kyle said. And anything beyond 4D can't cast a shadow higher than 3D.
@@Qassu78 Oh yeah I probably misstyped. Nontheless, thank you for the correction and also the explanation
That's what was missing in the video. BTW that username rings a very old bell, Reviewing the Kanji forums haha, what a coincidence.
In one dimension you wouldn't 'see' anything because there would be no there dimensions to look to and from (i.e. left to right.) You're somewhat taking what Carl Sagan famously said using Flatland by Edwin Abbott Abbott as an example, but you're overthinking the explanation. A two dimensional creature watching a three dimensional object pass in front of it would indeed see a dot expand to a line and reduce again to a dot. If we were to see a four dimensional object pass through our world, we would only see a three dimensional segment of that object (I.e. a sphere, if we use a four-dimensional 'spheroid' as in your example.)
One part that I think is super cool and mind melting is that we can't even see the net of the 4d cube properly. Someone who can perceive 4d objects would be able to see all of the cubes which make the net up all at the same time. When we view it there is always a cube that we can't see (the one in the 'center' of the 'cross' section), plus multiple are often partially obstructed. Someone who can view a 4d object would be able to see all of the cubes, completely all at once. The same way when we look at the net of a 3d object then we can see all of the surface area, all at once.
Cool video bro, but as for your promotion of surf shark, have you not seen the new internal exploit which allows a threat actor to to funnel all your traffic, unencrypted through a device of their choice. It also forwards your request and completes it, meaning if this is happening or not, you would never know. Every vpn currently available now; is not secure. You can hide your locality, you can bypass checks with your isp. But its still not secure. Someone internal to the company has a way to view your data without alerting either you, or the company they work for to suspicious activity.
@@jasonrodwell5316 why did you comment this on another comment?
@@jasonrodwell5316No kidding, a proxy can see the traffic it forwards? Guys, this is a very serious problem, we might have to shut down the Internet...
Yeah, same as if you could only percieve two dimensions you wouldn't be able to see the middle square in the unfolded cube, it would be behind the ones to the sides
@aysnov nope, not the company but there is an undetectable way to funnel you 'encrypted' and 'private' data through a pipeline so that a malicious person can see all that private encrypted data unencrypted. So yes, this is a very big problem. It's undetectable by you or the company hosting the network. They complete the transaction so your none the wiser, but ALL of your traffic pushed through a vpn can be seen by someone with malicious intent and its undetectable. Look up the exploit. So your saying that's not a problem? Tell that to a company pushing private company data through a vpn that now is running straight through someone's device unencrypted with full access to EVERYTHING. And I will reiterate, not for legitimate use. This is an exploit, why would a company run an exploit on their own network? they can see your data to encrypt it. I mean, someone who should not have access to your data can see it. So yes, very big problem! These vpns are being marketed as an extra layer of security when in actual fact any and all vpns now, thanks to this exploit, are an easy target for someone trying to gain unlawful access to your data.
Me during the video: OK I can’t see in 4D but at least I can see in 3D.
Me by the end: damn, you’re gonna take that away from me too??
Carl Sagan said that tesseract model is what a shadow of a 4D tesseract would look like. He said this a loooooong time ago. Trying to draw an analogy to what a cube on paper(a 2d plane) and
What a tesseract may look like as a shadow projected into our 3D reality
If people wanted to verify if something is a tesseract, they should just get Red Skull to examine it. It's not that hard.
A cool way to think of that tesseract figure is that it appears mishapen because it's 3D cubical faces (as opposed to 2d square faces of a cube) are angled in the fourth dimension. Just like a 2d representation of an angled cube has its faces look like diamons or rhombi.
Underrated comment
@@MonoKyrios thank you!
The angles in the 3d projection actually result from perspective. The inner cube is smaller in the model because it’s further away in the 4th dimension. In the 4D hypercube, every edge is the same length, every face is a square and all the angles are right angles.
True! But even if they appear distorted, they are still just as much cubes as our usual visual understanding. If we want to consider four dimensions, we simply have to update our visual rules for what cubes look like.
I just finished making a 3d tesseract, the way I got it to look like the “shape” was projecting its shadow into 3d from a 4d light source.
Fourth Dimensional Plato laughing at all of us chained in the three dimesional cave
Ceci n'est pas une tesseract.
Just as a painting of a pipe is not actually a pipe, a projection of a tesseract is not a tesseract. However, that doesn't make it not useful as a visual aid to explain what a tesseract would look like to our 3D eyes.
I laughed so hard from "Thor if you tried to draw him from memory". My lord.
The moving cube, did not expect the morphing to actually be just rotation
This reminds me of an animated film featuring a Square in a 2D world with the citizens being 2D geometric shapes. There was a hierarchy of shapes determined by complexity (number of corners "determined" intellect, iirc), with the circles being the top. They were hiding the rotating cube intersecting with their world, and forbidding knowledge or speculation about the third dimension. The Square had an octagonal daughter who was speculating about the 3rd dimension, which he dismissed and discouraged until he encountered a sphere character who opened the Square's perspective on dimensions.
I forgot the name of the animated feature, but it was an artistic means to convey this lesson.
That is an adaptation of _Flatland: A Romance of Many Dimensions_ by Edwin Abbot (1884)
I came here thinking "I swear... If he just says 'this is not a tesseract, it is just a shadow' I'll leave a dislike and go out of the video"
You should've done the sphere through 2D "Flatland" analogy with the shadow wall to really drive home the point, and that the Tessaract is merely a 3D shadow of a 4D "cube" passing through our world. Just as we can look at the 2D world and see inside everything because their world allows us to (or our perspective allows us to). The 4D world would allow them to see inside everything in the 3D world (ours) for the same reason.
That would have helped explain the shadow of the tessaract and how we see the shadow of it. As it turns around, it turns inside out as it rotates, then right side in and so on. Solid video nonetheless.
Yeah, I'm glad I'm not the only one who has read Flatland by Edwin Abbott Abbott
That's a cross-section rather than a shadow, but without specialised equipment that can pierce objects, we don't see 3D in 2D cross sections either; we see 3D as 2D shadows, which is a decent part of why I prefer visualising 4D as shadows rather than cross-sections, or worse shadows _of_ cross sections (because that's ultimately what things like 4D Toys use).
I was honestly wondering why Flatland never got brought up. It’s a fascinating metaphor to try to comprehend the concept of 4D, even knowing you can’t see it.
Carl Sagan used the Flatland example when talking about the 3rd and 4th dimensions, and it made it so much easier to understand the concept (which Kyle also alluded to when showing the snipped of Cosmos that had the bit I'm talking about). I tend to tell people to watch Cosmos and that episode (episode 10 if anyone was wondering) in particular.
The best representation of the 4th dimension I've seen is "4D Golf". A minigolf game that takes place in genuine 4D space (3 horizontal axes and 1 vertical/gravity axis), made by the youtuber Code Parade, the same guy who made Hyperbolica.
He's done an incredible job with the projection visualization and by providing multiple different projection variants. I think has done the best job at helping me intuit 4D space of anything I've ever seen. Hyperbolica did the same for hyperbolic and spherical geometry.
There is no such thing as 4 dimensions there are 3 please for the love of god stop this insane bs.
There are three very very discernible axis and there will never be room for a 4th.
Yup, if you want to get a "feel for" four dimensional space, 4D golf is an incredible way to do that.
@@BrandonDenny-we1rw
Mathematically, you can describe a space with however many dimensions you want.
There's nothing inherently incorrect about even talking about a space with 43 dimensions. Or 12. Or 538. Or 1.
@@BrandonDenny-we1rw Physically, you might be right. But we can play "but what if?" and do the math of what a fourth dimension might be like. Which is possible, the math can do it. 4D Golf does the math and projects it down to 3D/2D. Much like Kyle's shadow is a 2D projection of his 3D self, the game projects what an imaginary 4D space might be like down to a 3D space, then our graphics cards project it down for our 2D screens. I'm not saying it actually exists - but we can still pretend.
@@clapanse Except physically there is.
Which is where I am. In reality.
Me, trying to understand 4D cubes, represented in 3D, on a 2D screen with a 1D brain
@kylehill if you want to imagine a "4d cube", start backwards.
You can't imagine infinity, but you can imagine the Idea of it by visualizing unending. You do this by starting in the middle and Never allow your mind to find a beginning or end. Just relax your mind and never let the loop end.
If you get stuck, just remember that your brain already does this. You don't remember time before your birth and you don't remember time after your death.
Now, Imagine a 3d cube and visualize all the plane lines inward.
Don't let your brain "shrink" the cube. The cube is Not moving.
Then continue the trajector and "exit" outside the inside of the cube.
This the is primer.
Now, use the same technique and reverse it. Image the cube and visualize the plane lines outward. Don't let your brain visualize the cube Expanding. The cube is Not moving. Relax your mind and allow the cubes plane lines Outward.
If you get hung up, think think about infinity and the time before and after your life. Substitute yourself with a cube and substitute time for movement. Stop trying to visualize time before and after your death and stop trying to image the cube shrinking and growing.
That's a "4D" object. You know you've got it when the derealization kicks in and everything looks, sounds and feels fake.
Try not to have a panic attack.
Were you high when writing this?
This actually led to a meditative state for me lol
4D beings are face palming at our tesseracts. It's like 2D beings showing a cube as a square within a square.
If one face of a 3d wireframe cube is directly facing you, the 2d projection, accounting for perspective, does in fact appear as a square within a square. The inner square is smaller because it’s further away. In the classic 3d tesseract model, the inner cube is smaller because it’s further away in the 4th dimension.
The animation of it rolling around like a strange donut IS nonsense worthy of a facepalm, though.
not even a square within a square, since they would see a 1d projection of 2d objects
Sorry but this is wrong. It's **literally** the 3D shadow a 4D being would see in their 4D world of their 4D object. Think of shining a light onto a 3D cube and looking at the 2D shadow on the wall behind it. That shadow is the shape you would show a 2D being and tell them its from a cube in the third dimension. The 2D being would see the same exact shadow we see. And as you rotate the 3D cube in the light, the shadow on the wall changes shape. This is why the 3D tesseract we see changes shape as the actual 4D object is rotated, but it's exactly the same shadow a 4D being sees
@@calabraisNow I’m trying to visualize the 4D light needed for a 3d shadow. The dreams are going to be strange tonight.
@@calabrais this is 100000% wrong as there is literally no such thing as a "4th" dimension.
None. Zero. Nada. It doesnt exist.
look at the side of a line, you get a dot
look at the side of a cube, get a square
look at the side of a hypercube, you see the entire cube at once, from one receptor... we cant do that lol
Isn't seeing a dot or a line impossible? A dot is an infinitely small point and therefore invisible (and arguably actually inconceivable) and a line is simply a series of points but it has only length and no width (also invisible and inconceivable). A 2d object would be visible but without any depth it's also inconceivable beyond viewing it perpendicularly (and therefore from a 3rd angle, also even light has some depth). So we see in 2d but always perpendicular to that plane and move in 3d. But cannot see in any lower dimension nor move in a lower dimension.
I like how my math teacher described it: if we look at a 2 dimensional drawing, we can see the inner part of the shape. A being living in a 2d plane would see a line and the inner part is hidden to them. They see darker and lighter parts to give depth cues, but their vision is 1d so they cannot see the whole thing and the inner part is hidden. Similarly, if a 4d being looked at a cube drawing, their vision would be 3d, so they'd see the whole cube at same time including inside and back. When we look at a cube, we're only seeing a 2d projection of it, so the inside is hidden and the front blocks the back from view
it depends on the angle.
@@josecarlosmoreno9731 I mean, in 3D you can also tilt a square so that you can't see it, because it is still infinitely thin.
@@cameron7374 It's only invisible to the human eye, but all things that are visible have some physical depth to them, even light.
The best way I ever thought about the fourth dimension was: Imagine two objects occupying or intersecting the same space, but not touching one another
It really makes me wonder what would happen if humans could comprehend the 3rd and 4th dimensions optionally or simultaneously.
Google 4D Miner - a Mincraft clone that takes place in actual 4D space. The way it works is that your player and POV are 3D, but the world is 4D. You have the added ability to rotate the 4th dimensional axis, which then gives you the ability to move into 3D space that was previously parallel to the 3D space you were in before. It sounds weird, but it just applies the same math and logic used in 3D but with 1 additional dimension added. The crazy part is that the mobs in the game are actually 4D and are perfectly capable of navigating 4D space - even having the ability to sense the player through all 4 dimensions and path through 4D space into something like a closed 3D box. To make a fully safe house, you would have to build an actual tesseract-shaped house!
I was also about to comment this
Still not "true" 4d just a extra 3rd dimension that slides between each other. I may be wrong so feel free to correct me
The way I see it is imagine if we existed in 2 dimensions and we theorized about a 3rd dimension in our 2d world we make a game called 3d miner which adds an extra dimension but we can't possibly know or comprehend this 3rd dimension so we add a 2nd dimension and call it 3d because we a sliding between two parallel planes of the same dimension geometry wise.
@TheWorldWarrior I'm fairly certain that a 4th spacial dimension is exactly what 4D is. As the explanation in the video shows, we don't even have true 3D visual perception, but we do have the ability to navigate in 3 dimensions. As far as our vision goes, what we perceive is stereoscopic 2D projections of 3D space based on our current viewpoint. When we move our point of view, the projection we see changes. In the game, We're getting a 2D projection of a 3D projection of a 4D world (or just a 2D projection of a 4D world for simplicity). Because the game gives us the ability to navigate 4D space, we're able to see it from a different point of view which changes how the 3D projection appears.
@@Caffin8tor Thanks for explanation I've been at work so I haven't been able to watch this video yet definitely want to dig in and research more.
🤯
I enjoy the fact that in a number of your videos you can admit that we don’t know or can’t do something. It leaves room for growth. So many presenters could learn from this.
As someone who has been consuming 4D game devs and other contents for a while, I see this as a win win! More quality 4D Content!
Stay tuned on my channel. Lots of 4d content coming soon.
4D miner is an awesome game
@@damienasmodeus928 fr
@@HyperCubist nice, will check
"...and Thor, when you try to draw him from memory"!! 😂
There was an episode of Dr. Who called "Boneless" (correction: the creatures were called the boneless by The Doctor. The Episode was Flatline. Thank you @damienasmodeus928) that involved 2d creatures trying to comprehend our 3d existence. Similar vein just one dimensional lower.
name of the episode is flatline
@@damienasmodeus928 good catch. Thanks.
I was going to mention it too
I would be so afraid I would squish them. But they are "unsquishable"
@babomberman They actually got the idea from an old The Outer Limits episode.
Fun fact: in 4 dimensions there would be four possible doughnut shapes because instead of the one torus shape (doughnut shape) we have in three dimensions, there are four different tori shapes in 4 dimensions, in 5 dimensions you could have 11 doughnut shapes.
i wanna eat a 4D donut 🤤
Except we live in a 4 dimensional universe and that's not true... time is a dimension. Don't belive me? Then try to catch a ball that was thrown 25 years ago. If you don't use all 4 dimensions then you can't do anything. Try meeting a friend without discussing the time...
There is also 3 types of cylinders in 4D :>
@@PositiveOnly-dm3rxthere’s two types of dimensionality, temporal dimensions that you experience linearly, and spatial dimensions that can be moved through freely, we live in a 3 spatial 1 temporal dimensional universe, but what I in my comment and also Kyle in this video are referring to is a hypothetical 4 spatial 1 temporal dimensional universe.
@@thecalicodragon4103thank you for sparing me from having to write the same reply, a lot of people in the comments here seem to not understand this distinction.
I think it's cool to think that we're the shadow of a universe-sized 4D object/creature etc, which naturally could be the shadow of a 5D thing etc
I love that my favorite band and album just came up when looking for videos explaining Tesseract.
"he's so open minded his brain fell out a long time ago"... Well that's one asthma attack I'm willing to forgive!
"This dot..." shows a filled red circle
3 games that have definitely helped me understand a bit more about 4 dimensions are: 4d maze, where you navigate a multidimensional maze (the cool part about this one is that it has a viewing mode that allows you to uncross/cross your eyes and put together 2 pictures to create a 3d projection, which is trippy when you are able to make it work), 4d miner, a mining/crafting voxel game where you play on a 3d slice of a 4d world and you can move your slice/viewpoint. It also has spiders, and the best way to build a house is to either dig into the ground, or you have to completely fill in the sides of your house (though my mind is wondering if rounding off the ends of the 4-dimensional sides of the house would be less resource-intensive). The last one is 4d golf, which is minigolf in 4 dimensions, and the cool thing is, is that you have two main viewing modes for golfing (with toggleable shadows of the hidden areas in higher dimensions)- your normal view, and the other is replacing your y-axis with the w-axis, having a more volumetric view. The last section, however, goes into 5 dimensions, and that's even more trippy, though each section has somewhat of a gimmick to each of them.
In spite of this, it's an amazingly fun game, all of these are.
we need more of Kyle's Carl Sagan impression.
What's most interesting to me about this topic is that as far as I know, no object or particle in our universe behaves like the shadow of a higher dimensional object. If it did, it would likely disobey one or all of the many laws of conservation that we believe to be true. I'm convinced that higher spatial dimensions (other than time) don't exist, and these hyper-gons are just useful mathematical constructs for describing things other than space.
Hmm I think that some things dont follow the laws of conservation of energy that we have, some things are also breaking of the various symmetries we've put in place over time so thats interesting as well
I'm a mathematician and that what me and a few other math folks thinks. N-space geometry is just a more helpful way to organize variables in order for the math to be easier and to find different solutions. I'm gonna hate to say it, but it like complex numbers. They again are an abstract concept meant to find different solutions to 2 variable problems in calculus and linear algebra that can be though in the math of geometry. Because geometry is some of the simplest math, and hard multivariable calculus could use it. Greens theorem anyone?
This is actually 1 of the theories to explain dark matter & dark energy. We can see the effects (extra gravity in the universe & the universe is expanding) but we can't detect the stuff causing it. Some scientists think it's because some matter exists in higher dimensions or in other universes & still affects 3D stuff in our universe.
Much of electricity and electronics theory require the existence of a 4th special dimension to explain observations.
We call them "imaginary numbers".
@@Chad_Thundercock Usually we call that 4th dimension _time._ However, within those 4 dimensions, it's possible to construct an abstract 16-dimensional space, where linear, volumetric, and planar dimensions are treated separately. As it turns out, planar dimensions between two spatial directions behave suspiciously like "pure" quaternions.
That Sagan voice 🥲
I truly love that you don't think your viewers are dumb
5:14 This was personal 😂
But it is true
4d golf is a good way to get used to the fourth dimension
Probably the best one I've played so far. Then again, the pickings are pretty slim to begin with.
"How many dimensions are there?"
"IDK, at least 3"
love how the suggestions after this video are all depicting that hypercube
I'm sad you didn't mention 4d golf, it's probably the best current analogy we have of 4d (and 5d)
SOMEONE ELSE KNOWS ABOUT THIS GAME!!!!!
I came here to make pretty much that exact statement.. CodeParade has done great work with 4D Golf
4d golf is unbelievably good
Absolutely! Also -parabolica dangit- Hyperbolica for intuitive understanding of non-euclidean 3d spaces.
@@puskajussi37 You may mean Hyperbolica
There is a video called "4D Toys" that I think gives a pretty good idea of what 4D object will behave in 3D world, and show how bizarre it is.
Also I honestly believe that if an individual could somehow "gain vision" to see and comprehend 4D space, he/she is very likely to go mad immediately.
4D Golf
4D Toys is actually an app made by someone who is now working on an actual 4D game called Miegakure, which is "coming soon" on Steam (and has been for like a decade lmao)
4d Toys is a VR game, not just a video. Give it a try
Whatever reason you think somebody would go mad after gaining that perception would probably be wrong unless it's about how they can now permanently see the insides and all surfaces of all 3d objects, including people and other living things, without a way to turn it off.
oh and don't even get me started with 5D chess with multiverse and time travel.
I can only imagine that stepping into a fourth dimension is painful since theres gonna be 8 me's folded into eachother.
You aren’t a forth dimensional object, therefore there won’t be an extra seven of you. Like how a stickman wouldn’t gain more mass if it managed to get into the 3rd dimension.
@@assassinunknown6664 Heh, i anticipated a comment like this, but you missed the point. In order to perceive a 4th dimension, you have to become four-dimensional. Just like a stickman has to gain a 3rd dimension in order to see the 3rd dimension, otherwise he would still only see 2D. And idk if the process is painful or not, but i can imagine it's at least unpleasant.
@@dazley8021 well you could perceive the 4th dimension if you had a way to move through it like if you gave a stickman the ability to rotate left and right, the stickman would think it was tripping but it would be experiencing the 3rd dimension, just in really small parts that it can comprehend. There was a Minecraft themed game that did this and it can probably explain it much better
@@assassinunknown6664 All the stickman would see is lines coming and goint. A stickman would never see the 3D world the way we see it, unless it becomes like us. Same for us and the hypothetical 4D world.
I pointed to it. It's currently 90° behind me, in the past.
did people actually think that the tesseract representation was actually 4d? I thought it was obvious that it was just a shadow
Yes! It merely gives us a framework to imagine the perspective required to actually experience 4D.
Yeah, it's just a visual representation of a data structure
Um - everything you see in the world is a shadow. You can't see 3D, only 2D projections of 3D objects. We can just as easily see 2D projections of 4D objects. You can't say that we can ONLY see projections of 4D objects, but CAN see the "real" 3D objects. They're both projections, it's just a question of how many dimensions we're projecting down.
0:41 tesseract isn't a shape. It's a wonderful band 🤘
Altered state getting that couple seconds fame :p
4:40 aria saying "bruh"
9:45 "Duuude."
Im convinced vsauce and Kyle hill have fused into V-Kyle. They are now one, and unstoppable.
8:06 - "Did that help?" Actually, yeah it kind of did a little. What I'm picturing is seeing that weird shape-shifting illusion, but as this shape performs its rotations within actual 3D space right in front of me. The way the 3D cube's faces distort when being rotated on a 2D surface is the same type of distortion that'd manifest itself in 3 Dimensions if you were able to perceive a 4D cube rotating on a 3D surface. That also, I believe, could be one of the things that helps me visualize it - to think of the 3rd dimension not as a space, but rather as a surface. I love thinking about this sort of stuff, it feels like your mind is like just on the cusp of understanding it, but the understanding always manages to just escape you.
I picture 8 different-coloured cubes all existing in the same 3-dimensional space at once.
But I'm also content with that just being one particular flavour of wrong.
Okay, so this is a niche nitpick BUT: there was a study conducted at Princeton in the 2000s (by someone named Graziano? Maybe? Its been a minute since I read the paper) that put forward the possibility that with sufficient practice interacting with 4d spaces human brains can actually be taught to reason natively in 4 dimensions (as opposed to just simulating or approximating it in 3 dimensions). If memory serves they did this with 4d puzzles or mazes on computers.
It is far from conclusive evidence that that is possible, but it is a hint from a reputable source that it *might* be possible. And I just find that stupendously cool and tantalizing.
Seems logical that we could evolve to or learn to comprehend it with sufficient exposure to it, but the point remains that there is no way to get exposure to anything in 4D.
@@pieflies Videogames can simulate it.
Those multithreaded cuda processors are designed to project 3D objects into 2D screens to interact and play with "3D" simulated objects. Put on a headset and they simulate 3D objects into a 3D visual for humans with 2 eyes.
We can do this in fact. It would be insane though.
@@Aaron.Thomas You don't even need VR headsets. Everything we see is 2D. I've made tons of 4D models that you can rotate in 4D, shown on a screen. It doesn't take to much practice to learn to think four-dimensionally.
I would be interested to see if we could figure out/isolate what atypical brain activity in particular is responsible for the sometimes reported higher-dimensional perceptory experiences very specific psychedelics can cause and precisely induce it without psychotropic substances in a controlled setting to see if the ability to visualize higher dimensions can be temporarily activated. If it could from there it would follow that with proper care and methodology an intuition could likely be cultivated with repeated exposure. My curiosity stems from a 15 minute portion of a longer experience I had in my youth which left me 100% confident that our brains are fully capable of perfectly visualizing at very least 4d spaces given the proper circumstances, just that it is completely useless to survival and therefore not a default ability we develop. That said my guess is that it is only possible with either a restructuring of the brain or the brain misfiring/cross-talking/mixing signals like crazy (such as what is reductively happening on psychedelics) either of which are almost guaranteed have unpredictable additional cognitive effects.
@@Aaron.Thomasbut if we don’t really know what 4D looks like and can’t visualise it how would we create simulations of it that are accurate?
Unless I’m just missing the point, your comment seems to be talking about VR displaying 3D objects, which is not the same as realistically simulating 4D objects.
the best way ive figured to visualize a 4D object in person was thanks to an old, low budget computer animated movie called "flatland". In the story, a 2D charcter interprets a 3D spherical guest as a circle growing larger and larger until it shrinks and disappears. Likewise, if a 4D cube where to intersect with our 3D world, it would appear as tiny microscopic cube popping into existence gowing larger and larger until stopping and beginning to shrik again until it disappeared.
which makes you wonder about some subatomic particles like quarks and such.
I don't know if anyone else pointed it out but your mention of how humans perceive 3D by using two 2D images raises an interesting question...
If a 4D being existed would their equivalent of eyes use multiple 3D images to perceive its 4D environment? 🤔
Kyle: “You can’t…..but try”
My brain just exploded.
It must have worked if you are able to come back to a time pre-brain explosion (since you are able to type) to tell us about it while still knowing that your brain did explode and that it simultaneously is just exploding.
I thought everyone knew that these were just lower dimensional representations. Knowing this channel’s audience this video may as well be preaching to the choir.
New people are constantly coming to the stage of their life where this sort of thing is brought to their attention as a concept or becomes interesting enough to want to dig a little deeper. Some people have boundless curiosity but bad access to information in school and home to even know what there is to be curious about so having this topic in a location that someone with budding yet malnourished curiosity very well may find themselves is nothing but beneficial. It isn't always about us already here but rather those yet to arrive.
yeah, me too. the net thing was a good explanation, though
@@SurfTheSkylineIt's always weird when someone thinks "everyone already knows this" when people are getting older and born all the time
@@SurfTheSkyline you are infringing on OP’s smug sense of superiority. I can see his brow furrowing under the brim of his fedora as we speak
The entire existence of that sculpture is just a single SnapShot of a shadow of a fourth dimensional object.
I took some mushrooms once and thought I saw the fourth dimension.
This takes me back to reading "The boy who reversed himself" as a child.
sounds hot lol
@@dusk2308 I suppose steamy talk about nth space, extra dimensions and their geometry can be a little sexy. Not to a 7 year old though lol.
@@dusk2308 😂
I loved that book so much I introduced it to my kids as soon as they were old enough to start wondering about higher dimensions.
@@jxmink Yes!
It sent 7 year old me down a rabbit hole from "Ana" and "Kata", to Charles Howard Hinton and Tesseracts full speed into a fascination with spatial directions that dropped young me into the lap of (super)string theory, which I had to revisit when I was a little older lol.
Books like that are a great foundation for scientific curiosity and will always have a special place in my heart. I'll be giving it to my kids too.
So when is Kyle gonna play 4D Golf?
Sí all the way
One metaphor that helps me understand 4-d is the room analogy.
A cube is a grid of square rooms that connect in a way impossible in 2-d. travel in a straight line and you end up where you started after going through four doors to the next room. keep turning 90-degrees to the left or 90-degrees to the right without changing direction, and you end up back where you started after only 3 turns instead of the usual four.
similar holds for the tesseract, but instead of square rooms in what a 2-d being would assume is an infinite grid until they end up back where they started in an impossible fashion, you have cubical rooms in what a 3-d being would assume is a cubic honeycomb until you return to the start.
Using the 3-d Cross as a reference, if you exit the top cube through it's ceiling, you would enter the bottom most cube through its floor, and if you exit the front cube though it's front, you'd enter the bottom most cube through it's front... and the 4 side cubes are a loop, but you would travel in a straight line as you went from front to right to back to left and back to front... no matter which of the 8 cubes you are in, there are doors in all six faces and each one goes directly to a different cube, with only the 8th cube two rooms away, and in a straight line in every direction(e.g. if you where in the central cube that's completely hidden in the 3-d cross, going two rooms stright up or down will get you to the bottom most cube, but so will going two rooms stright forward or back or stright left/right... Of course, a 4-d being could just move in the fourth dimension to drill stright to the bottom most cube from the central cube, like driling from the top of a cube to its bottom instead of traveling along it's surface. I forget what it's called, but there's a short story out there about a man who lives in a pentachoron that has five tetrahedral rooms with 3 walls and a floor, a door in each wall and a trapdoor in the floor, and every room can be accessed directly from any other room. I've also used this to comprehend polyhedral pyramids(the pentachoron is a tetrahedral pyramid), prisms(the tesseract is a cubic prism), duoprisms(the tesseract is a 4,4 duoprism), and even 4-d cupolae... Don't quite have a grasp of the 16-cell, 24-cell, 120-cell, or 600-cell, even though I've built zome modelsof the latter two... though the 120-cell would have dodecahedral rooms, 12 doors each, and you would retrun to your starting point after travelling in a straight line for 10 rooms... and I get that 5 loops kind of spiral around the one you hold straight, and there are two such complexes of 60 dodecahedra, but the connections are just a bit too complex for me to wrap my mind around yet.
And kind of a shame that these rotating models of 4-d shadows are hard to build in actual 3-d(it's been done using telescoping struts for ball and stick models, but you had to be rather methodical manipulating them if memory serves, they couldn't do the 4-d rotations smoothly like in the wireframe animations.
Out there are 4 dimensional beings wondering why those stick figures are so obsessed with their cubes.
The shadow comparison really solidified the idea in my mind, great analogy!
2:01
when you go from an epic cutscene to a dance fight
Sagan said this is the closest we will get to viewing the 4th Dimension, we will only be able to see the 'shadow' of a 4D Object.
Just play 4D golf, you may not see the whole course at once but you can scan through it and put it together in your head while playing
the 4d Golf engine is unironically the current cutting edge in 4d visualization
When I played it I never felt like I understood the space I was in, and yet I still managed to build enough intuition to finish the game.
I have always just shifted down a dimension to conceptualize.
If you move a 3D cube through a 2D plane, you get a 2D square at each point.
If you move 4D cube through a "3D plane" you get a cube at each point.
(Assuming nothing is rotated)
The quotes "Right angles to reality" from Douglas Adams and "Down is the way your feet are pointing" from Robert A Heinlen spring to mind.
I was under the impression that the fourth dimension was time so I was always confused when people tried to represent it with a tesseract.
MAN KYLE YOU MISSED A CHANCE! You could've said that reality is "more than meets the eye" AND YOU DIDN'T
Unforgivable
What is as mind-blowing is that the line you made to represent 1D space is actually a 2D representation of a line, it has an actual width as well as length. It is virtually impossible to represent 1D space.
It’s more about conceptualizing the concept, not replicating it. I see this flavor of pedanticism all over these comments and it’s missing the point
The map is not the territory.
When he started talking about a fourth dimensional object casting a three-dimensional shadow, all I could think of was Adventure Time when Finn created a black hole!! What an excellent episode!
When I was learning engineering print reading about 30 years ago, I extrapolated the rules to add a fourth spatial dimension, and designed a few parts in 4D for fun.
TH-cam deleted my comment for some reason, but 4D Golf exists
Not only that, but the devlogs as well (i guess i can't put the developer here because TH-cam)
It's $20 on steam. The Steam Summer Sale is in 2 days.