I always imagine that walking in a fourth dimensional world was kinda like swimming, it would be in a way, but it also wouldn't be, because you'd have gravity pulling you and no boyancy
I actually have an idea/theory. In the 5th dimension maybe Ur eyes can span in the shape of a cube, that means Ur sight range would be able to capture every single inch of an objecy
it's really easy with circles, spheres, hyperspheres, and above, because the perimeter / surface area / whatever is just the derivative of the area / volume / whatever
1D: a line 2D: a square: two lines with their corresponding endpoints connected by lines 3D: a cube: two squares with their corresponding lines connected by squares 4D: a hyper cube: two cubes with their corresponding faces (squares) area connected by cubes
Physically, no there most likely isn’t (gravity would act all wonky) but the concept works mathematically and higher-dimensional geometry is actually useful in error correction in binary messages
If you consider this for n dimension general formula for this two things will be, 2(n)L^(n-1) and L^n. But if you look just closely, Differentiation of L^n with respect to L is nL^(n-1) d(L^n)/dL = nL^(n-1) And the first thing is just two times that. So basically it's two things, L^n and 2(d(L^n)/dL).
Yea this can be proved by the power rule as well. x^n th object's surface attribute will be 2x the derivative of x^n which would be 2 times nx^n-1. The power rule itself comes from binomial theorem.
Interestingly going a dimension lower seems to take another derivative (like the 1D measurement of the edges is the derivative of the surface area, which is 12L)
Large misconception people seem to be getting from this. There are two different types of dimensions in physics, spatial and geometrical. Spatial refers to time and energy and the overall body we are describing, such as universes and possibilities. Geometrical refers to the actual shape itself, where you have lines, squares, and cubes for whatnot. They are not the same, and this video talks about geometrical dimensions not spatial. Also the existence of the fourth dimension isn’t proven, and by the very laws of physics as we know of them, can’t be proven as we cannot interact with the 4th dimension (geometrical one) since you can’t interact with things in a dimension above you.
Everything spoken about the fourth dimension is purely conceptual. In reality, we have no idea whether or not a fourth dimension actually exists (and could not in any way interact with it unless we somehow found and tripped over a fourth dimensional object and clipped into the backrooms)
If you look at that 4d projection, it kind of looks like the beginning and end states of a moving cube connected by lines... which I think is what it would be if the fourth dimension was time.
I told the same thing to my maths teacher in 8th grade and I got 1 week vacation for my discovery, principal called my dad and said"your son is suspended for 1 week, because he entered in toilet when maths teacher was there
Imagine that we are experiments of 4D Beings in a 4D world, and they're observing what a creature that can only see and comprehend 3D or below lives like.
Look at a tesseract, focus on the impossible 90° lines. The ones that connect the inner cube with the outer cube and count the areas between those lines including the inner and outer cube. You get 8 areas, therefore it's 8 cubes
@@Ace_BlackStar That's the boring theory. If that was the case, our world would be like 70D at least, you can't point at something and call it a dimention...
For the volume, the calculation can be different.... Like for cube , its area of square(2d) expanded in direction of line(1d) i.e. (l*l)*l... In the same way volume of 4th dimension will be volume of 3 dimension extended to 2 dimensions direction = (l*l*l)*(l*l) i.e. l to the power of 5.
The math for going from dimension to dimension doesn't fully work out, even though it looks like it should. The coefficient for L, L^2, etc isn't calculated just by L+1, since a one dimensional object has a perimeter of 1L, which doesn't translate into 4L but instead into 2L.
Maybe that thing really is what 4th dim mention looks like. 5th would go backwards, creating a “plate” of this things. then 6th dimension could go up, thus creating a square of many squares that are connected
@@coconutpog596 why? It makes sense? Each dimension can experience the next higher dimension but cannot travel through the next higher dimension, so logically time would be the 4th as well experience it but can not travel through it. It also deals with the direction issue, as each dimension adds a direction we cannot add another to the 3rd normally except for time, so rather than a measure of where the 4th adds a measure of when or at least what we perceive as when.
I guess I would imagine there are (we don't know how many) spacial dimensions and then there are dimensions of time We have 3 dimensions of space and one dimension of time
If there is a 4d object then it'll have a 4th property to see how increasing the number of dimensions increases the number of properties in 1d 2d and 3d objects.
that's confirmed because if you use the perspective version of the tesseract, you can see 8 Cubes. 6 "side cubes", an inner cube, and an outer cube. The "hypervolume" of a tesseract is just L⁴ because there are 4 dimensions/directions, x(length(long)), y(width(wide)), z(height(high)), and w(depth(deep)).
Not quite. You just can't image it. We've got so used and adapted to the 3D world we live in, that when you have the 3 axis, lenght, height and depth you just have no idea where would the next 90° turn be
You don't see in 2D. You see in 2D only when you close one eye, that small distance between your eyes makes the difference needed to call it 3D. The thinf about 4D is that it literally doesn't exist for us. You have 3 lines our world is composed of - length, height and depth. Now try to think, where will the next 90° turn be? That's 4D...
@@Wojtek1250XD You see 2D images which are then interpreted into a 3D model of your environment. This interpretation uses parallax from multiple 2D images (whether from moving or binocular vision), lighting, occlusion, relative sizes, and even non-vision senses like sound and touch combined with proprioception. _All_ of these come together to provide a 3D perception of the world.
4 dimension have the visual of all the face of the cube, like holding a Rubik's cube, u see all the face in every position, the details the prospective etc...
Yea but it’s impossible to comprehend because every new dim you add a new way like length then width then height and what he shows as “4d” is just the width line extended
You can’t just assume that the fourth dimension has or only has 2 extra sides just because there are four sides on a square and two extra sides on a cube ( being front and back). The fourth dimension could just as easily be a complete mirror of a cube giving 6 x 2 = 12 sides or a mirror in each plane giving 6 x 6 = 36 sides.
Put on a Cartesian plane, the Tesseract can be plotted quite easily on the x y and z axis which means it is still a 3D object. I don't think we can perceive 4D because it exists beyond our scope or just doesn't exist at all.
what you are thinking is a tesseract is actually just one 3d projection of a tesseract. projecting a 4d object onto (into?) a 3d space makes a 3d projection, just like projecting a 3d object onto a 2d plane makes a 2d projection. the tesseract has many 3d projections. I recommend looking them up, they’re pretty cool!
The tesseract isn't 3d, you're probably thinking of the projection on 3d space since there is no possible w axis in 3d space, also, 3d space isn't called cartesian plane, you're confusing it with 2d space
Surface area and volume manifest in third dimension representing space Fourth dimension is not spacial...so the mechanics doesn't represent When you look at how causality works in Fourth (and higher) dimension to work out a sense of higher dimensions in a useful way
Everybody’s talking about how cool this is, but this man just drew his check BACKWARDS.
Saw that, thought that the video was mirrored , but nope.
@@DeletedUser73926 yeah, I figured
@@DeletedUser73926 as a lefty, I disagree as I just do the check flipped. And ive seen other lefties do the same as I so he's just weird
Shit had me jittery
Huh interesting
"Surface Volume" is cursed af lmao
IKR🤣
jumping game enjoyer:
@@Yusuketh443 squares and triangles
@@Yusuketh443 yes the game that somehow crashes your game more than many others out there for some reason
I always imagine that walking in a fourth dimensional world was kinda like swimming, it would be in a way, but it also wouldn't be, because you'd have gravity pulling you and no boyancy
Meanwhile in the 4D: how to measure in 5D(theory)
In 5D how to measure 6D(Theory)
@@Patriotic_BoyATT in 6D: how to measure in 7D (theory)
Surface: 2nL^(n-1)
Interior: L^n
There, that's how you measure in 42D.
In all x dimensions: How to calculate stuff in (x+1)d.
Dont want to be that guy but 4d would prob be making videos about 6d as 5d is time travel
the 4th dimension watching us:
they're doing math now. that's cute.
Bruh
Are 4D dimension beings real?
@@soultr549 everything is possible
@@soultr549 not that we know of
The 5th dimension is watching the 4th
"I may not be able to see it, but I can math it!"
Astrophysics in a nutshell
*meth it
@@АлександърСтойнов-ф2ч damn right
@@АлександърСтойнов-ф2чyeah, science!
This man’s mic quality is changing every second
The only difference between his shorts is the microphone.
It's travelling through dimensions
He sounds like the Announcer from Portal 2
The sound waves change thought dimensions
Man just said Surface Volume and it made perfect sense
Frrr 🤣
Stop giving the mathematicians weed and alone time
The fact we have alone time is probably linked to the fact we spend it doing math for fun.
Dude turned himself into the god then he teaching other how to become god 🙏🤣
BWAHAHAG THIS.
I actually have an idea/theory. In the 5th dimension maybe Ur eyes can span in the shape of a cube, that means Ur sight range would be able to capture every single inch of an objecy
@@Spidsle Wow! That sounds cool!
I’m learning more from these shorts then school ngl
Actual Found footage of SCP-055
I feel like in a couple years your gonna teach us about the multi verse and 10D
Bro Nicholas you are so good at making this videos I love them
Keep making videos about higher dimensions please. I really like how you explain things.
it's really easy with circles, spheres, hyperspheres, and above, because the perimeter / surface area / whatever is just the derivative of the area / volume / whatever
1D: a line
2D: a square: two lines with their corresponding endpoints connected by lines
3D: a cube: two squares with their corresponding lines connected by squares
4D: a hyper cube: two cubes with their corresponding faces (squares) area connected by cubes
Surface volume is a cursed phrase if ive ever heard one
Plot twist: there is no fourth dimension and they're just messing with us.
Physically, no there most likely isn’t (gravity would act all wonky) but the concept works mathematically and higher-dimensional geometry is actually useful in error correction in binary messages
In our world? That is the case, there is no 4D for us, but math can easily replicate how it would be
If you consider this for n dimension general formula for this two things will be, 2(n)L^(n-1) and L^n.
But if you look just closely,
Differentiation of L^n with respect to L is nL^(n-1)
d(L^n)/dL = nL^(n-1)
And the first thing is just two times that.
So basically it's two things, L^n and 2(d(L^n)/dL).
Yea this can be proved by the power rule as well. x^n th object's surface attribute will be 2x the derivative of x^n which would be 2 times nx^n-1.
The power rule itself comes from binomial theorem.
Interestingly going a dimension lower seems to take another derivative (like the 1D measurement of the edges is the derivative of the surface area, which is 12L)
Just watching this short is Giving me more knowledge than what 10 years of school has taught me
Me: Your really good at math
Also me: 🤨
Quick and concise, good resource! 👍🏼
Large misconception people seem to be getting from this. There are two different types of dimensions in physics, spatial and geometrical. Spatial refers to time and energy and the overall body we are describing, such as universes and possibilities. Geometrical refers to the actual shape itself, where you have lines, squares, and cubes for whatnot. They are not the same, and this video talks about geometrical dimensions not spatial. Also the existence of the fourth dimension isn’t proven, and by the very laws of physics as we know of them, can’t be proven as we cannot interact with the 4th dimension (geometrical one) since you can’t interact with things in a dimension above you.
Everything spoken about the fourth dimension is purely conceptual. In reality, we have no idea whether or not a fourth dimension actually exists (and could not in any way interact with it unless we somehow found and tripped over a fourth dimensional object and clipped into the backrooms)
This is the 3rd time i got this guy randomly while I was scrolling through shorts
And it's all chronological
I feel like that should have been shown more rigorously, but yeah, it's all correct
If you look at that 4d projection, it kind of looks like the beginning and end states of a moving cube connected by lines... which I think is what it would be if the fourth dimension was time.
Usually we say bulk instead of hypervolume, and use hypervolume for 5d and above
We be out here just learning 4 dimensions while there's 8d music in TH-cam and other platforms
The length from opposite corners of a perfect tesseract with a edge length of 1 is 2 because it is the square root of 4
What i learnt from this is that speculation can sound nice
I told the same thing to my maths teacher in 8th grade and I got 1 week vacation for my discovery, principal called my dad and said"your son is suspended for 1 week, because he entered in toilet when maths teacher was there
And it is all in accordance with analogy
Imagine that we are experiments of 4D Beings in a 4D world, and they're observing what a creature that can only see and comprehend 3D or below lives like.
Finally, someone who makes math fun
At the end i didn't understand but left a like, like i did
For the surface volume it could be 9L instead of 8 as it may be x1.5
Look at a tesseract, focus on the impossible 90° lines. The ones that connect the inner cube with the outer cube and count the areas between those lines including the inner and outer cube. You get 8 areas, therefore it's 8 cubes
it isnt that simple to just multiply it
I can’t wait for people to make stuff out of that or I might be dead by then who knows
You are underrated
Imagine 4D turns out to be way different then the original sequence.
The forth dimension is just time T
@@Ace_BlackStar That's the boring theory. If that was the case, our world would be like 70D at least, you can't point at something and call it a dimention...
@@Ace_BlackStar This is about spatial dimensions
This guy is going to make money
Thanks for *Facts*
It could be different when we somehow begin to comprehend 4D, but this seems pretty viable
He sure loves saying tesseract
"it's just a theory"
"A SCIENCE THEORY"
Him: but the math of 4th dimension is actually pretty simple.
Me 30 seconds later :🤯my f***ing mind is smoking
Huh?
For the volume, the calculation can be different.... Like for cube , its area of square(2d) expanded in direction of line(1d) i.e. (l*l)*l... In the same way volume of 4th dimension will be volume of 3 dimension extended to 2 dimensions direction = (l*l*l)*(l*l) i.e. l to the power of 5.
The math for going from dimension to dimension doesn't fully work out, even though it looks like it should. The coefficient for L, L^2, etc isn't calculated just by L+1, since a one dimensional object has a perimeter of 1L, which doesn't translate into 4L but instead into 2L.
But the perimeter of a 2d object IS 4L?
Also the n dimensional measure isn't calculated by L+1, it's calculated by L^dimension
I love how I understand the math but as soon as you show the 4D object my brain shorts out
My brain is too small for this
I was only waiting for the hypervolume, tys.
Dang that’s cool
we are in 3rd dimension and will never truly comprehend what 4th dimension is
Maybe that thing really is what 4th dim mention looks like. 5th would go backwards, creating a “plate” of this things. then 6th dimension could go up, thus creating a square of many squares that are connected
Beautiful!!
This is like Mumbo Jumbo trying to explain redstone
I just imagine the fourth dimension as time, for it moves alongside the other 3 dimensions. Makes it easier to think about.
4th dimesion is time but they are talking about 'spatial' dimentions wguch is different from time dimensions.
We'll only have one shot to figure it out tho
Dude, the whole time 4d thing is stupid
@@coconutpog596 why? It makes sense?
Each dimension can experience the next higher dimension but cannot travel through the next higher dimension, so logically time would be the 4th as well experience it but can not travel through it. It also deals with the direction issue, as each dimension adds a direction we cannot add another to the 3rd normally except for time, so rather than a measure of where the 4th adds a measure of when or at least what we perceive as when.
I guess
I would imagine there are (we don't know how many) spacial dimensions and then there are dimensions of time
We have 3 dimensions of space and one dimension of time
Really cool
A line segment has a surface consisting of 2 points. So its surface size is 2L^0.
Yup. It's 2. Not 2 meters or 2 inches or whatever. Just 2.
If there is a 4d object then it'll have a 4th property to see how increasing the number of dimensions increases the number of properties in 1d 2d and 3d objects.
I like your funny wordsss magiicc maaann
Well by definition a tesseract has measure (4D volume) proportional to its length to the fourth power such that a unit tesseract has unit measure.
that's confirmed because if you use the perspective version of the tesseract, you can see 8 Cubes.
6 "side cubes", an inner cube, and an outer cube.
The "hypervolume" of a tesseract is just L⁴ because there are 4 dimensions/directions, x(length(long)), y(width(wide)), z(height(high)), and w(depth(deep)).
Our eyes are made to see 3D but our brain is limitless
Not quite. You just can't image it. We've got so used and adapted to the 3D world we live in, that when you have the 3 axis, lenght, height and depth you just have no idea where would the next 90° turn be
That check mark scares me because it’s backwards
I actually figured this out in history class when I was bored and thinking about other dimensions. I was amazed at how simple and obvious it was
Using our 2D eyes to understand 4D is like using a 2D creatures’s 1D eyes to try and understand 3D.
You don't see in 2D. You see in 2D only when you close one eye, that small distance between your eyes makes the difference needed to call it 3D. The thinf about 4D is that it literally doesn't exist for us. You have 3 lines our world is composed of - length, height and depth. Now try to think, where will the next 90° turn be? That's 4D...
@@Wojtek1250XD You see 2D images which are then interpreted into a 3D model of your environment. This interpretation uses parallax from multiple 2D images (whether from moving or binocular vision), lighting, occlusion, relative sizes, and even non-vision senses like sound and touch combined with proprioception.
_All_ of these come together to provide a 3D perception of the world.
Me : who couldnt understand a thing but still watched his full video
4 dimension have the visual of all the face of the cube, like holding a Rubik's cube, u see all the face in every position, the details the prospective etc...
Yes, including the inside of it
Interesting.
NASA HIRE THIS MAN ASAP!!!👨🔬👨🔬👨🔬
5th dimensional penteract:
surface volume: 10L^4
volume: L^5
This is just geometry 101 at the Secret 🤫 School 🏫🎒
I talked about the 4th dimension ONCE and this is the second video in a 15 minute timespand
So when I was on the train track of the other side of fabric of reality and I say our planet on the other side this explains nicely how I saw it
Now casually bring up Hilbert spaces
Thanks Quandale
Yea but it’s impossible to comprehend because every new dim you add a new way like length then width then height and what he shows as “4d” is just the width line extended
The math is making it actually easier to understand the concept
You are explaining these things so well good god even though I love my math teachers their explanations pale in comparison
You can’t just assume that the fourth dimension has or only has 2 extra sides just because there are four sides on a square and two extra sides on a cube ( being front and back). The fourth dimension could just as easily be a complete mirror of a cube giving 6 x 2 = 12 sides or a mirror in each plane giving 6 x 6 = 36 sides.
This is how you enter the fourth dimension
Go forwards backwards left right upside down and right side up
Put on a Cartesian plane, the Tesseract can be plotted quite easily on the x y and z axis which means it is still a 3D object. I don't think we can perceive 4D because it exists beyond our scope or just doesn't exist at all.
what you are thinking is a tesseract is actually just one 3d projection of a tesseract. projecting a 4d object onto (into?) a 3d space makes a 3d projection, just like projecting a 3d object onto a 2d plane makes a 2d projection. the tesseract has many 3d projections. I recommend looking them up, they’re pretty cool!
The tesseract isn't 3d, you're probably thinking of the projection on 3d space since there is no possible w axis in 3d space, also, 3d space isn't called cartesian plane, you're confusing it with 2d space
I don't understand this but it's entertaining
What perfect timing i was just thinking about that. But I want to ask is a 4D Pyramid/Triangle "Volume Volume" 1/4 Base×Height?
Now the only problem is we dont have a tesseract
I hope you get a real good job about quantum mech
Dude is on to something
Hey math folks remind me why the derivative of the volume is twice the surface area of a cube. Where did the *2 come from?
The tesaract sounds like the mcguffin from the transformers movie
The only time math is easier then the actual thing you are applying math to
One thing is missing though every other dimension added another parameter ie y for 2d and z for 3d
First steps in dem hoping
its jus deptg of something like seeing a depth of a wall ur looking u just have a wallhack but cant see behind
My brain: [INSERT DIAL UP MODEM NOISE HERE]
Surface area and volume manifest in third dimension representing space
Fourth dimension is not spacial...so the mechanics doesn't represent
When you look at how causality works in Fourth (and higher) dimension to work out a sense of higher dimensions in a useful way
Wow!
I usually imagine 4th dimension as a set of 3 dimensional objects that have only one of them being shown up at a time
Yeah, that's a great method for imagining the 4th axis. The tricky part is thinking through how the object rotates as a whole
surface volume sounds so cursed lol
Ik the fourth dimension, it's time. Because we cannot comprehend all of time at once in tern, time is a line too
Try do subdimensions (0.5D. 0.2D. 1.3D)
The f**k is a 0.5D? What's a halfway point between a line and a dot?