Funny enough, the "1 plus 1 equals square root of 2?!" bit is why travelling _diagonally_ on minecart rails is faster, because Minecraft caps minecart velocity _per axis,_ not its _total_ velocity.
"If you really think time is the fourth dimension then walk over to thirty seconds ago and pick up your common sense" came up with this one myself as a joke on the directional nature of time compared to space
@@NexusOfChaos I believe time and space are indistinguishable. With my current limited knowledge it makes sense that we a forced to move along the time “axis”. The speed of our movement is even determined by matter in 3d space. So just because particles treat it differently. Is it not a dimension? Its just a number like all the others like described in this video
@@a_skyfish i mean, i did say it was a joke. thru *spacetime* everything moves at the speed of light, its just a matter of how much is thru space and how much is thru time
@@abbyofgenderpronouns Guess it's made to optimize the rotation and scale, like you first apply rotation and scale to a matrix and then you don't have to do it for each point of the model in case of 3D graphics.
In Hamiltonian and Lagrangian (Classical) Mechanics, we use as many dimensions as we have mechanical degrees of freedom in the mechanical system we're analyzing. That whole, "three space-like and one time-like dimensions" thing is the degrees of freedom for an infitesimal (0D) point floating in space with nothing interacting with it. Four numbers are all you need to describe any and all velocities in the universe. That's where it comes from... _velocity_
In an effort to explain "time" and why everyone has such a difficulty understanding it it is because it is the ocean our universe exists within. Motion is what we perceive of as time. While this "time" dimension that we speak of does involve normal motion, it also involves probabilities which is potential. But I'll get to that topic in a little while. For now, let's focus on motion. When breakdown how we keep track of and what we calculate when we discuss the topic of "time" we are only ever able to describe "time" as motion in relation to some other motion. And therefore "time" can and should be described as a change in state with a minimum of two vectors. However, in an isolated system of only two vectors and nothing else in the universe, nothing would state that there was any thing changed. The wonderful thing about our universe is that it is ripe with structures to compare motions, and so we can compare the motion of any one thing to some other thing. With this action happening around us, everything moving in relation to some other thing, all sorts of properties explode out. What we witness after everything gets moving is entropy, causality, and probabilities where if I throw a ball through the air, the momentum of my swinging arm took stored energy from me and added it to the system of the flying ball; this creates the expelling of heat which dissipates into my environment, the action is written to my memory until I forget and everyone else's memory until they forget, the movement of the ball through the air creates drag and heat which is absorbed into the air, and then finally the ball lands on a patch of dirt which scatters dirt, leaving a small pit that will be erased the next time some action moves those dirt particles. The point of this example being that all that motion, energy, mass, potential energy is recorded into the environment, and also erased by the environment. The event pops into existence momentarily, and then disappears from our perspective while blurring into memory. This is all in accordance with the weight of the matter, because in this manner, energy of the system is not effected by the scenario, and so if I throw the ball in a field while no one watches: the event dissipates quickly. But if the entire world watches while society has placed a grand outcome on the event, the example has the potential to stretch into infinity because that action of throwing the ball in front of the entire world will cause others to take action, dissipating more and more energy out into the environment until that action has fully burned away it's potential energy. This is what we describe as "time" and attempt to measure. The more accurately we can describe a scenario of the future and work towards that scenario, the more favorable the outcome. This is what we call planing. What is actually going on is we take our present environment into account, create a future potential scenario, and make things move in relation to other things until we feel satisfied that our planned outcome was achieved. Results will vary based on the accuracy of the initial survey and consequent actions afterwards, and how well the individual or individuals are able to hold that potential reality in their mind and the success of working towards that goal. So this is how we would describe as what we perceive as "future". The reality is that the vector lines of all the particles that need to move to achieve that future exist in this one infinite now as it becomes written onto the system's surroundings; and this what we perceive as the flow of time. The reason that "time" breaks down for most people when they take into account scenarios without conscious awareness involved is because they cannot understand "time" without memory or future probability, but those properties are perfectly described in the math if you consider everything within the effect of some system that is being considered. When you consider "time" as motions of particles dissipating potential energy into their effecting environment (which is the scale that that system exists at) then "time" becomes non-linear and even non-existent. The particle that has the smallest potential energy will impart its effects onto its environment, like a ripple in the water, and the motions of its environment will over take the potential energy of the particle. And at the largest of potential energy storage scale, a black hole disperses its energy potential onto the environment, but the potentiality of the singularity overwhelms everything that we know of. All potential futures of anything that falls into a singularity reach one and only one outcome: whatever the singularity's out come is because it swallows up all other outcomes. Obviously we exist somewhere in between the smallest and largest. As such, we are able to see change and observe that change, and we have so far called that "time". "Time" is an emergent property that comes from the interaction of the forces of nature, simply. As the systems of the universe interact at scale, the systems have no choice but to evolve according to their potential, absorbing or succumbing to any other potential that occurs should that system interact with something else, which the system will always interact with something else at our scale. This way of thinking does away with all sorts of paradoxes, such as: the grandfather paradox, which doesn't occur because the causes and affects of reality absorb whatever outcome, and Schrodinger's Cat goes away because the probable reality is nonsense to any other potential reality. The solution has to do with probability, but the reality is inconsequential because there are too many other causalities keeping the one causality of the living cat. (As a side note though, it may very well be all possible scenarios to any given scenario must take place so that the probable out come can occur. If that were so, this would further the idea of probability pressures that I will write on presently) These paradoxes are systems unable to cope with what I will call probability pressure that is exacted onto surrounding events that keep all probabilities intact while still interacting with the outside world. We could say certainly that each essence of something has a probability horizon to where that entity no long interacts with anything outside of that horizon. This of course continues through scales. At the smallest scale Schrodinger's Cat is waiting for a moment that requires no pressure at all, radiation will suddenly and immediately kill the cat. But at the large scale of the cat, that can't happen because of all the stuff that needs to stay intact for the entire system to keep persisting the way it already does. If the cat was alive when it when in the box, it will come out of the box alive. If was dead before it went into the box, then it will be dead when it comes out the box. Observation is nonsense in these operations. What is consistent is that particles, and your expectations are interacting through these probability pressures to keep the story going, as it were. If the scenario where we finally put a live cat into a box and it comes dead occurs, the probability pressure from all events, what you would call a timeline, always was going to have that particular cat in that particular configuration come out dead, always. The reason being is that the system of the living cat becoming a dead cat inside of the box was the only way that probabilistic outcome could occur. Alright, how does this all tie into there not being anything called "time", how does it fit into the grand scheme of things, and what the heck do we do now? From the very smallest to the very biggest, energy is moving, for whatever reasons beyond me, and this creates a sea of motion moving in two opposing directions that we ride as a wavefront while barring witness to all of the swirls and patterns and forces, all of which put pressures onto infinite probable outcomes to create a coherent universe that allows for all the beauty and wonder we witness ever moment of our lives. But what do we do now? From a day to day perspective: nothing, but there might be. For the very smart engineers and physicists, let's learn to surf and sail.
I think I might try to do something like this but make my code modular in such a way to allow setting the amount of dimensions at run time and just have it work. you could have 3d physics, 2d physics, 1d physics, 1025d physics, really any dimensional physics if you have enough RAM
Very fun video. Some things that might be practically different in 7 dimensions would be funky rotation stuff around more than a simple axis, forces and interactions dropping off at the inverse of the distance to the power of 6, and also different packing paterns and structure layouts.
A fun thing about the time dimension, in Relativity with time as the 4th dimension, it turns out distances are measured by adding the spatial dimensions, but SUBTRACTING the time dimension, which leads to all sorts of quirky effects....
I already knew all these concepts, but I adore the way you explained it because you gave my *fundamental understanding* additional support, allowing me to rebuild my intuition stemming from it in a different way, and in turn allowing me to make different connections. Man, you're a gem. Straight up. First time I've seen your content, instant sub. Keep teaching, no matter where you go. You are incredibly talented as an animator, but even more so as a speaker.
20:40 that right there is the best of the best example for the 4th dimension object in the perspective of a 3d person. I had the same example and that animation describes it precisely. Great work makit. and yes i did the vector addition from the last part.
The visualisation of a 4D object passing through a 3D space kinda reminds me of quantum mechanics, specifically the part where some particles seem to pop in and out of existence. Maybe the universe is made out of some sort of 4 dimensional spaghetti? Kinda sounds like string theory too.
This phenomenon is actually due to the way that waves are not localized to a single point in space and time. To make a long story short, you can never say that the vacuum of empty space has exactly zero energy for very breif periods of time... ... and so it doesn't. It's only zero _on average_ over long periods of time. I can explain in more detail if you want... actually, there's a really good video here on UA-cam about the "Heisenberg Uncertainty Principle" by, um, I think the name of the channel is: "Physics Explained". The UA-cam title image has a black and white photo of Heisenburg on the right side, with a bunch of colorful lines in the middle, and the title on the left. Update: I found the video: ua-cam.com/video/FRP4AqZR3UU/v-deo.html
i played around with your idea a lil but chatgpt is stubborn so according to the current understanding of physics it's a coincidence :( "Virtual Particles Virtual particles are a concept from quantum field theory. They are temporary fluctuations in quantum fields that "pop" in and out of existence, but they are not real particles in the traditional sense. Instead, they are mathematical constructs used in calculations, particularly in perturbation theory. The appearance and disappearance of virtual particles do not necessarily imply a higher-dimensional origin; they are more about the uncertainty and probabilistic nature of quantum fields. Quantum Tunneling Quantum tunneling occurs when a particle crosses an energy barrier that, according to classical physics, it shouldn't be able to overcome. This phenomenon is a result of the wave-like nature of particles and the probabilistic rules of quantum mechanics. The idea of tunneling is often explained by the particle "borrowing" energy to pass through the barrier, a process that doesn't need to invoke higher dimensions. Higher-Dimensional Theories In string theory and other speculative frameworks, higher dimensions do play a role. However, these theories don't necessarily predict that quantum tunneling or virtual particles are directly caused by interactions with higher-dimensional objects. Instead, these dimensions are often compactified or hidden in ways that don't manifest directly in our 3D experience. Coincidence or Connection? The similarity between the "popping in and out" behavior of quantum phenomena and how a higher-dimensional object might appear in lower dimensions is likely coincidental rather than causal. The quantum behaviors are well-explained within the framework of quantum mechanics without needing to invoke extra dimensions. However, the idea remains an interesting analogy and could serve as a metaphor for understanding these complex phenomena." - chatgpt
would space have infinite dimensions, and the particles in it be limited to 3? meaning there could exist particles who are limited to 3 or more other dimensions in the same space?
This is what are generally called "Brane Theories". Electromagnetic interactions are basically stuck on a 3D manifold, but our 3D manifold could be in a larger "Embedding Space". I assume that this is what you are asking about and not infinite dimensional frequency spaces like what you get out of a Fourier Transformation.
Truly exceptional content MAKiT!! Seriously, your animations are just so good and I could tell a lot of effort went into it. Don’t stop making these vids, even if the views get low..I know you can do it
Really good video (The only thing that I noticed which may just be a pet peeve of mine is how many times your text clipped into other text or the environment, such as at 6:16 with the x y vector clipping into your time variable)
Mathematically I'm pretty sure working in a vector space in 3 dimensions where the Z component is always 0 is pretty much identical to working in a vector space in 2 dimensions, if we're only talking in vectors. But when we bring in matrices, the moment one of the basis vectors earns itself a Z component... it's still flat. It still has a 2-dimensional span. It's rotated in 3 dimensions but it's still a flat surface. So while computationally we can use as many numbers as we like, fundamentally we're essentially only working in 2. See: the span of a vector space
For those watching this cool video; the question to ask yourself is about is about why dimension exists at all and why can we define spaces with an arbitrary number of dimensions to begin with. Furthermore, dimensions are isomorphic (equivalent). This is why we have say the holographic principle and projective geometry: you can construct the same objects using high or lower dimensional spaces. In fact this forms the basis of video game graphics like blender! Cheers everyone
not even nth dimension wow yknow I think you have the capability to delve deeper, you don't need to turn your findings into a video but I think you're fully capable
So about two minutes into the video but right now my mind is screaming "Vectors!" Seven dimensions? Easy! = m*. Well... doesn't look very easy, but nothing that a bit of Python or C++ can't handle.
This video is phenomenal, absolutely brilliant! Thank you! Now when I correct people on this I can just send them this video instead of tripping over myself trying to explain XD
I never connected the two, but hearing it back to back like this, at least in this narrow scope it sounds like time is a 4th spacial dimension but flat as we only perseve the present, and the past can not exist on the present plane nor the future. Interesting to think about reality having layered flat planes of high dimensions
i used to ask my friends for 20 dimensional vectors for force (i say its "force" but it was "distance" what i did) in 8th grade and calculated the total force. its nothing hard, you just apply the pythagorean theorem over and over again, but it was enough to impress my friends.
It's amazing how you explained this so simply but people still think we'll find another spacial dimension that isn't just a remix of XYZ instead of realizing that 4-6 are already available to us in a 3d space.
Now I'm curious about what would happen if any physical simulation had time work as just another axis that everything moves normally in, but without friction so the usual rate of constant motion could work.
A fourth zero dimension can be useful. Like let's supose that we have a D-dimensional vector (I'll exemplify by D =2). So we have [x, y]. Now let's say we want to do a translation of it. Well, we can add another vector [A,B]. [x,y] + [A,B] = [x+A , y + B] But if we don't want to add another vector, we can take it up a dimension into (D+1)-dimensional vector with the last dimension as one [x,y,1]. With this, we can do translations with a matrix multiplication. [x,y,1] * [ (1,0,0) , (0,1,0) , (A,B,1) ] = [x+A , y + B , 1] So we have the same translation transformation, but without doing a vector addition, but a matrix multiplication instead.
Best explanation i ever experienced brother my teacher is so dump that whenever i ask something to her she just change the topic in flow flow anyways best quality content
A friend showed me this video, and we both found it to be the best explanation of matrices we had ever seen! We're only left wondering what the purpose is of the final row of a 4x4 matrix...
I saw on russian video frome guy onigiri how he simulated over 100k dimensional space for sorting chaotic information, he just downloaded and sorted thousands of commentaries, imagine possible mass and gravity in such a space
Clinically insane how much quality is in this channel, yet it doesn't get the attention it deserves. Pleae continue enlightening us with the knowledge brother.
Love the idea, but there is a diference if we are doing phisycs in more dimensions, the cross product works, diferent, or doesnt wprk depending on your definition, also the orbits, it isnt always posible to have stable orbits depends on the power of the distance in the gravity, wich also depends on the dimension, here gravity moves in a sphere away from the mass (classical newtonian one) but in 4 spacial dimensions in moves in a hypersphere, and therefore it is proportional to lrl^(-3) so not only gravity would be weird, maxwell equations, specially the rotational wont work as usuall
Also, coriollis and centrifugal or centripetal force are derived from going drom rectilinare reference system to a spherical accelerated one, i think in more dimension you get more not li terms, also the magic numbers in the nuclear shell theory would differ, and the periodic table wpuld be different, the sphere packing thing, wich would be related to the disposition of atoms, became ... weird
What if spacetime, or the “fourth dimension” is shaped like a fractal where any given point in time is connected to any other through a theoretically infinite distance
there's a common misconception that dimensions are always spatial, but the truth is, while we live in only 3 spatial dimensions, we actually live in a lot more dimensions if you take into account subjective experiences, for example a dimension for how "blue" something is, or a dimension of how some objects texture may change as you move across the spatial dimensions
For most people, color is 3 dimensional, though there are people for whom color is either 2 or 4 dimensional. Regardless, color is an excellent way of representing 4D graphs, especially when there's cyclic behavior that maps elegantly to a polar form. 2 dimensional input (position), and then a 2D output that's a slice of the 3D color space for the output. Add in animation and you basically have an entire 5D graph on a flat screen.
Classical Physics itself uses lots of "extra dimensions" all the time. Besides a Hamiltonian phase space for the momentum allong every degree of freedom in your machine. Things like temperature and mass can be treated as their own dimensions. The whole thing about a unified 3D of space and 1D of time is that four numbers are all you need to distinctly describe the velocity of an infitesimal "0D" point anywhere in the universe. It's _velocity_ It's all velocities everywhere forever. There's a really long story about how Maxwell's Equations lead to Special Relativity, but I don't want to write a really long comment here unless someone replies to this and asks me to.
That's where our spectrum comes into play, that's because from a computational perspective, you're right. Anything that could be represented with a number we could just add to our "universe" vector, and that would be a basis for an argument that we live in an n-dimensional universe... HOWEVER That's from a computational perspective where we represent everything with a number, on the other side of the spectrum where we have physics where we differentiate between different vectors, and when we say "our world is three dimensional" OR "our world is four dimensional" we mean "In order to describe position of something we need 3 dimensions" OR "in order to describe movement of something we need 4 dimensions" So it all depends on what kind of dimensions you're talking about
When it comes to nerding out about an extremely specific involving physical models most people consider impossible to understand... don't ask for permission, wait for them to ask you to stop
Funny enough, the "1 plus 1 equals square root of 2?!" bit is why travelling _diagonally_ on minecart rails is faster, because Minecraft caps minecart velocity _per axis,_ not its _total_ velocity.
"If you really think time is the fourth dimension then walk over to thirty seconds ago and pick up your common sense"
came up with this one myself as a joke on the directional nature of time compared to space
@@NexusOfChaos I believe time and space are indistinguishable. With my current limited knowledge it makes sense that we a forced to move along the time “axis”. The speed of our movement is even determined by matter in 3d space. So just because particles treat it differently. Is it not a dimension? Its just a number like all the others like described in this video
@@a_skyfish i mean, i did say it was a joke. thru *spacetime* everything moves at the speed of light, its just a matter of how much is thru space and how much is thru time
This sounds like something Cave Johnson would say, followed by "because you're fired!"
Lol
@@NexusOfChaos i did say I have limited knowledge… thats a real good explanation
time traveler -bet! *creates an infinite loop*
With this we can finally play 5D chess with multiverse and time travel in real life with 2 dimensions to spare
"2 dimensions to spare" is a phrase
I literally c sharp minored to this.
BAAHAHAHAHAHAHHA
That's just perfect
What?
what does this mean
C*m?
Nah, he can't do physics in 7 dimensions, that's too many.
*spits out cereal*
11:34
Putting an ad right after you said "would be" is diabolical.
Fr i got it tooo
The matrix explanation is gold, I've never seen someone explain them like that
i just dont get what they are for in the first place. like why can the arrows for the directions go at angles
@@abbyofgenderpronouns Guess it's made to optimize the rotation and scale, like you first apply rotation and scale to a matrix and then you don't have to do it for each point of the model in case of 3D graphics.
@@abbyofgenderpronounsthey explain it at 14:00
In Hamiltonian and Lagrangian (Classical) Mechanics, we use as many dimensions as we have mechanical degrees of freedom in the mechanical system we're analyzing.
That whole, "three space-like and one time-like dimensions" thing is the degrees of freedom for an infitesimal (0D) point floating in space with nothing interacting with it.
Four numbers are all you need to describe any and all velocities in the universe.
That's where it comes from... _velocity_
Bro I hope you get more subscribers and views. You truly deserve it. Your content is so unique and the animations are out of the world. Don't stop!
👍.. Only thing is sometimes you talk to fast and quiet imo, so it's hard to understand what you are saying.
1:24 And then you can add another Newton of force away from the viewer and it is travelling at √3 m/s! Perpendicular dimensions are crazy, yo.
6:30 I think he's about to cover that point. Be patient.
No, he went very far afield. Interesting nonetheless.
Wait are there three franklyanogre00000? Cuz they each have independent character
Meanwhile me who can't even understand physics in 2 dimensions:
the final boss!
7 dimension
5:35 1 dimensional circle? that's so cursed terminology 💀 I think you mean the direction??
why bro cooking so hard 🗣🗣🔥🔥
video got me taking notes 😭😭
I know the effort that has gone into making this and I appreciate it a lot.
Now let me enjoy the video!
In an effort to explain "time" and why everyone has such a difficulty understanding it it is because it is the ocean our universe exists within. Motion is what we perceive of as time. While this "time" dimension that we speak of does involve normal motion, it also involves probabilities which is potential. But I'll get to that topic in a little while. For now, let's focus on motion. When breakdown how we keep track of and what we calculate when we discuss the topic of "time" we are only ever able to describe "time" as motion in relation to some other motion. And therefore "time" can and should be described as a change in state with a minimum of two vectors. However, in an isolated system of only two vectors and nothing else in the universe, nothing would state that there was any thing changed. The wonderful thing about our universe is that it is ripe with structures to compare motions, and so we can compare the motion of any one thing to some other thing. With this action happening around us, everything moving in relation to some other thing, all sorts of properties explode out. What we witness after everything gets moving is entropy, causality, and probabilities where if I throw a ball through the air, the momentum of my swinging arm took stored energy from me and added it to the system of the flying ball; this creates the expelling of heat which dissipates into my environment, the action is written to my memory until I forget and everyone else's memory until they forget, the movement of the ball through the air creates drag and heat which is absorbed into the air, and then finally the ball lands on a patch of dirt which scatters dirt, leaving a small pit that will be erased the next time some action moves those dirt particles. The point of this example being that all that motion, energy, mass, potential energy is recorded into the environment, and also erased by the environment. The event pops into existence momentarily, and then disappears from our perspective while blurring into memory. This is all in accordance with the weight of the matter, because in this manner, energy of the system is not effected by the scenario, and so if I throw the ball in a field while no one watches: the event dissipates quickly. But if the entire world watches while society has placed a grand outcome on the event, the example has the potential to stretch into infinity because that action of throwing the ball in front of the entire world will cause others to take action, dissipating more and more energy out into the environment until that action has fully burned away it's potential energy.
This is what we describe as "time" and attempt to measure. The more accurately we can describe a scenario of the future and work towards that scenario, the more favorable the outcome. This is what we call planing. What is actually going on is we take our present environment into account, create a future potential scenario, and make things move in relation to other things until we feel satisfied that our planned outcome was achieved. Results will vary based on the accuracy of the initial survey and consequent actions afterwards, and how well the individual or individuals are able to hold that potential reality in their mind and the success of working towards that goal. So this is how we would describe as what we perceive as "future". The reality is that the vector lines of all the particles that need to move to achieve that future exist in this one infinite now as it becomes written onto the system's surroundings; and this what we perceive as the flow of time.
The reason that "time" breaks down for most people when they take into account scenarios without conscious awareness involved is because they cannot understand "time" without memory or future probability, but those properties are perfectly described in the math if you consider everything within the effect of some system that is being considered.
When you consider "time" as motions of particles dissipating potential energy into their effecting environment (which is the scale that that system exists at) then "time" becomes non-linear and even non-existent. The particle that has the smallest potential energy will impart its effects onto its environment, like a ripple in the water, and the motions of its environment will over take the potential energy of the particle. And at the largest of potential energy storage scale, a black hole disperses its energy potential onto the environment, but the potentiality of the singularity overwhelms everything that we know of. All potential futures of anything that falls into a singularity reach one and only one outcome: whatever the singularity's out come is because it swallows up all other outcomes.
Obviously we exist somewhere in between the smallest and largest. As such, we are able to see change and observe that change, and we have so far called that "time". "Time" is an emergent property that comes from the interaction of the forces of nature, simply. As the systems of the universe interact at scale, the systems have no choice but to evolve according to their potential, absorbing or succumbing to any other potential that occurs should that system interact with something else, which the system will always interact with something else at our scale.
This way of thinking does away with all sorts of paradoxes, such as: the grandfather paradox, which doesn't occur because the causes and affects of reality absorb whatever outcome, and Schrodinger's Cat goes away because the probable reality is nonsense to any other potential reality. The solution has to do with probability, but the reality is inconsequential because there are too many other causalities keeping the one causality of the living cat. (As a side note though, it may very well be all possible scenarios to any given scenario must take place so that the probable out come can occur. If that were so, this would further the idea of probability pressures that I will write on presently)
These paradoxes are systems unable to cope with what I will call probability pressure that is exacted onto surrounding events that keep all probabilities intact while still interacting with the outside world. We could say certainly that each essence of something has a probability horizon to where that entity no long interacts with anything outside of that horizon. This of course continues through scales. At the smallest scale Schrodinger's Cat is waiting for a moment that requires no pressure at all, radiation will suddenly and immediately kill the cat. But at the large scale of the cat, that can't happen because of all the stuff that needs to stay intact for the entire system to keep persisting the way it already does. If the cat was alive when it when in the box, it will come out of the box alive. If was dead before it went into the box, then it will be dead when it comes out the box. Observation is nonsense in these operations. What is consistent is that particles, and your expectations are interacting through these probability pressures to keep the story going, as it were. If the scenario where we finally put a live cat into a box and it comes dead occurs, the probability pressure from all events, what you would call a timeline, always was going to have that particular cat in that particular configuration come out dead, always. The reason being is that the system of the living cat becoming a dead cat inside of the box was the only way that probabilistic outcome could occur.
Alright, how does this all tie into there not being anything called "time", how does it fit into the grand scheme of things, and what the heck do we do now? From the very smallest to the very biggest, energy is moving, for whatever reasons beyond me, and this creates a sea of motion moving in two opposing directions that we ride as a wavefront while barring witness to all of the swirls and patterns and forces, all of which put pressures onto infinite probable outcomes to create a coherent universe that allows for all the beauty and wonder we witness ever moment of our lives. But what do we do now? From a day to day perspective: nothing, but there might be. For the very smart engineers and physicists, let's learn to surf and sail.
Alternatively, draw in 3D while saying 7 to yourself repeatedly
I thought you were gonna talk about the 7 dimensional cross product
Hell yeah, another MAKiT banger
Isn´t the equation in time 9:31 wrong beacuse even if I put starting matrix in wolfram alpha than I get in upper row ax+by and in lower row cx+dy
yea it's wrong
Inventing new dimensions to fix your math is crazy
String theorists be like
6:04 you wrote acceleration as x²/t instead of x/t².
Great video btw.
Instructions unclear, i have to communicate with 8 dimensional deities.
Interesting and nicely explained. I don’t really know why your channel is not more popular. Your channel is brilliant on UA-cam!
I think I might try to do something like this but make my code modular in such a way to allow setting the amount of dimensions at run time and just have it work. you could have 3d physics, 2d physics, 1d physics, 1025d physics, really any dimensional physics if you have enough RAM
Wow, that was great! Beautiful explanation, beautiful graphics, great music. That first title card music really captured me. Well done!
Very fun video. Some things that might be practically different in 7 dimensions would be funky rotation stuff around more than a simple axis, forces and interactions dropping off at the inverse of the distance to the power of 6, and also different packing paterns and structure layouts.
A fun thing about the time dimension, in Relativity with time as the 4th dimension, it turns out distances are measured by adding the spatial dimensions, but SUBTRACTING the time dimension, which leads to all sorts of quirky effects....
I already knew all these concepts, but I adore the way you explained it because you gave my *fundamental understanding* additional support, allowing me to rebuild my intuition stemming from it in a different way, and in turn allowing me to make different connections.
Man, you're a gem. Straight up. First time I've seen your content, instant sub. Keep teaching, no matter where you go. You are incredibly talented as an animator, but even more so as a speaker.
*Combine in the sense of a Cartesian product, make it into an ordered pair
why the hell does this video not have at least a million views
Dawg no videos get 1m views in 3 days except youtube’s monoliths
20:40 that right there is the best of the best example for the 4th dimension object in the perspective of a 3d person. I had the same example and that animation describes it precisely. Great work makit. and yes i did the vector addition from the last part.
I'm happy that your channel is picking back some momentom, this one is already Makit second most viewed video!
Holy shit, your animations might just be the best I have ever seen for a presentation-type video. They are so smooth! Keep up the good work man!
Yep, this is the kind of stuff i watch for fun
Good video. I happen to be writing a physics engine currently so I knew most of this stuff, but the matrix visualization was superb!
Keep in mind if you See something In the fourth dimension, it will look like a Disk Or whatever Shape it is.
The visualisation of a 4D object passing through a 3D space kinda reminds me of quantum mechanics, specifically the part where some particles seem to pop in and out of existence. Maybe the universe is made out of some sort of 4 dimensional spaghetti? Kinda sounds like string theory too.
This phenomenon is actually due to the way that waves are not localized to a single point in space and time. To make a long story short, you can never say that the vacuum of empty space has exactly zero energy for very breif periods of time...
... and so it doesn't. It's only zero _on average_ over long periods of time.
I can explain in more detail if you want... actually, there's a really good video here on UA-cam about the "Heisenberg Uncertainty Principle" by, um, I think the name of the channel is: "Physics Explained".
The UA-cam title image has a black and white photo of Heisenburg on the right side, with a bunch of colorful lines in the middle, and the title on the left.
Update:
I found the video:
ua-cam.com/video/FRP4AqZR3UU/v-deo.html
i played around with your idea a lil but chatgpt is stubborn so according to the current understanding of physics it's a coincidence :( "Virtual Particles
Virtual particles are a concept from quantum field theory. They are temporary fluctuations in quantum fields that "pop" in and out of existence, but they are not real particles in the traditional sense. Instead, they are mathematical constructs used in calculations, particularly in perturbation theory. The appearance and disappearance of virtual particles do not necessarily imply a higher-dimensional origin; they are more about the uncertainty and probabilistic nature of quantum fields.
Quantum Tunneling
Quantum tunneling occurs when a particle crosses an energy barrier that, according to classical physics, it shouldn't be able to overcome. This phenomenon is a result of the wave-like nature of particles and the probabilistic rules of quantum mechanics. The idea of tunneling is often explained by the particle "borrowing" energy to pass through the barrier, a process that doesn't need to invoke higher dimensions.
Higher-Dimensional Theories
In string theory and other speculative frameworks, higher dimensions do play a role. However, these theories don't necessarily predict that quantum tunneling or virtual particles are directly caused by interactions with higher-dimensional objects. Instead, these dimensions are often compactified or hidden in ways that don't manifest directly in our 3D experience.
Coincidence or Connection?
The similarity between the "popping in and out" behavior of quantum phenomena and how a higher-dimensional object might appear in lower dimensions is likely coincidental rather than causal. The quantum behaviors are well-explained within the framework of quantum mechanics without needing to invoke extra dimensions. However, the idea remains an interesting analogy and could serve as a metaphor for understanding these complex phenomena." - chatgpt
I can't with the music
The content is great, but removing the music would be better.
It’s a banger what you mean
Music makes it fun!
Touhou type music
10/10 flawless video
would space have infinite dimensions, and the particles in it be limited to 3? meaning there could exist particles who are limited to 3 or more other dimensions in the same space?
This is what are generally called "Brane Theories".
Electromagnetic interactions are basically stuck on a 3D manifold, but our 3D manifold could be in a larger "Embedding Space".
I assume that this is what you are asking about and not infinite dimensional frequency spaces like what you get out of a Fourier Transformation.
@@juliavixen176 i will look into brane theories 👍
I will be really surprised if the music is still made with AI, because it sounds way too good.
it definitely is, its not bad but it has a weird noise to it on most instruments
Truly exceptional content MAKiT!! Seriously, your animations are just so good and I could tell a lot of effort went into it. Don’t stop making these vids, even if the views get low..I know you can do it
MY MIND WAS BLOWN WITH THE INTRO!?!
HOW HAVE I NEVER VISUALIZED IT LIKE THIS!!!
intro goes crazy
I now how higher dimensions work. I've played 4d golf wich had 5d golf and 4d miner.
You made learning vector physics really entertaining. I have subscribed.
I want to see the sequel where you calculate collisions in 7D
Fun fact, the seventh circle of hell was actually called that because everyone inside has to manually calculate collisions in 7D
Really good video (The only thing that I noticed which may just be a pet peeve of mine is how many times your text clipped into other text or the environment, such as at 6:16 with the x y vector clipping into your time variable)
These visuals are brilliant! Are you an editing genius or animation artisan, prolly both heh
oh my god that outro statement was GENUINELY FUCKING BRILLIANT DELIVERY AND WRITING 10/10 worth waiting to the last second
How are u still getting 100 views on this
This deserves millions of views atleast
absolutely love your videos
Mathematically I'm pretty sure working in a vector space in 3 dimensions where the Z component is always 0 is pretty much identical to working in a vector space in 2 dimensions, if we're only talking in vectors. But when we bring in matrices, the moment one of the basis vectors earns itself a Z component... it's still flat. It still has a 2-dimensional span. It's rotated in 3 dimensions but it's still a flat surface.
So while computationally we can use as many numbers as we like, fundamentally we're essentially only working in 2.
See: the span of a vector space
All vectors are infinite dimensional.
For those watching this cool video; the question to ask yourself is about is about why dimension exists at all and why can we define spaces with an arbitrary number of dimensions to begin with.
Furthermore, dimensions are isomorphic (equivalent). This is why we have say the holographic principle and projective geometry: you can construct the same objects using high or lower dimensional spaces. In fact this forms the basis of video game graphics like blender!
Cheers everyone
not even nth dimension wow
yknow I think you have the capability to delve deeper, you don't need to turn your findings into a video but I think you're fully capable
So about two minutes into the video but right now my mind is screaming "Vectors!" Seven dimensions? Easy! = m*. Well... doesn't look very easy, but nothing that a bit of Python or C++ can't handle.
squid launcher!
The joys of linear algebra.
This video is phenomenal, absolutely brilliant! Thank you!
Now when I correct people on this I can just send them this video instead of tripping over myself trying to explain XD
Yes We have seen such anomalies particels that appear out of now were, gravity and the expantion of the universe
I never connected the two, but hearing it back to back like this, at least in this narrow scope it sounds like time is a 4th spacial dimension but flat as we only perseve the present, and the past can not exist on the present plane nor the future. Interesting to think about reality having layered flat planes of high dimensions
Explaination of matrices and vectors was GOLD!
i used to ask my friends for 20 dimensional vectors for force (i say its "force" but it was "distance" what i did) in 8th grade and calculated the total force. its nothing hard, you just apply the pythagorean theorem over and over again, but it was enough to impress my friends.
It's amazing how you explained this so simply but people still think we'll find another spacial dimension that isn't just a remix of XYZ instead of realizing that 4-6 are already available to us in a 3d space.
Now I'm curious about what would happen if any physical simulation had time work as just another axis that everything moves normally in, but without friction so the usual rate of constant motion could work.
A fourth zero dimension can be useful.
Like let's supose that we have a D-dimensional vector (I'll exemplify by D =2).
So we have [x, y].
Now let's say we want to do a translation of it.
Well, we can add another vector [A,B].
[x,y] + [A,B] = [x+A , y + B]
But if we don't want to add another vector, we can take it up a dimension into (D+1)-dimensional vector with the last dimension as one [x,y,1].
With this, we can do translations with a matrix multiplication.
[x,y,1] * [ (1,0,0) , (0,1,0) , (A,B,1) ] = [x+A , y + B , 1]
So we have the same translation transformation, but without doing a vector addition, but a matrix multiplication instead.
Best explanation i ever experienced brother my teacher is so dump that whenever i ask something to her she just change the topic in flow flow anyways best quality content
Terry is about to binge watch you. Beware.
Impressive videos. This guy will be big AF soon.
A friend showed me this video, and we both found it to be the best explanation of matrices we had ever seen!
We're only left wondering what the purpose is of the final row of a 4x4 matrix...
YESSS NEW MAKIT VIDEO DROPPED!!!!
I saw on russian video frome guy onigiri how he simulated over 100k dimensional space for sorting chaotic information, he just downloaded and sorted thousands of commentaries, imagine possible mass and gravity in such a space
REALLY COOL BLENDER MAGIC ✨
Now I want to know what a five-dimensional object moving through four-dimensional space would look like... Or even higher...
Clinically insane how much quality is in this channel, yet it doesn't get the attention it deserves. Pleae continue enlightening us with the knowledge brother.
that intro goes so hard!!
a 1*1 any number of times will always have more mass than a dimension less than it but less in a dimension higher in it (ex 1*1*1*1 > 1*1*1)
that 3 numbers joke got me subbing
vector and transform vector :I got lost
i really glad you say all of that obvious things because i can understand things only when they said like this
me when 1+1 is irrational: that´s not ok... but... that´s also ok... WAIT WHAT-
for the intro alone, ya got a sub from me
n now that am done watching the video, thanx for teaching me something I never understood in school
Man, I would love to live in a 4 spacial dimensional world...
Great video
Love the idea, but there is a diference if we are doing phisycs in more dimensions, the cross product works, diferent, or doesnt wprk depending on your definition, also the orbits, it isnt always posible to have stable orbits depends on the power of the distance in the gravity, wich also depends on the dimension, here gravity moves in a sphere away from the mass (classical newtonian one) but in 4 spacial dimensions in moves in a hypersphere, and therefore it is proportional to lrl^(-3) so not only gravity would be weird, maxwell equations, specially the rotational wont work as usuall
Also, coriollis and centrifugal or centripetal force are derived from going drom rectilinare reference system to a spherical accelerated one, i think in more dimension you get more not li terms, also the magic numbers in the nuclear shell theory would differ, and the periodic table wpuld be different, the sphere packing thing, wich would be related to the disposition of atoms, became ... weird
My point being, physics in more dimensions, is neat, but it is diferent
Still loved the video
The 69 jump scare was it for me, good vid.
you show me a 4D object in 3D world on my 2D screen and I try to understand this with my 1D brain!
you know what, yes, let's do just that
Bro wanted to reinvent linear algebra 💀
i have not even the slightest clue what this means, but its fun!
What if spacetime, or the “fourth dimension” is shaped like a fractal where any given point in time is connected to any other through a theoretically infinite distance
this video is beautiful. thank you youtube algorithm gods for this
Are you God ,just kidding keep up the great work
Lets not do physics in 7Dimensions.
Physics isnt math
The square root of twotens of force
All mori9n is just hyperdimensional reflection
Most underrated channel ever.
there's a common misconception that dimensions are always spatial, but the truth is, while we live in only 3 spatial dimensions, we actually live in a lot more dimensions if you take into account subjective experiences, for example a dimension for how "blue" something is, or a dimension of how some objects texture may change as you move across the spatial dimensions
For most people, color is 3 dimensional, though there are people for whom color is either 2 or 4 dimensional.
Regardless, color is an excellent way of representing 4D graphs, especially when there's cyclic behavior that maps elegantly to a polar form. 2 dimensional input (position), and then a 2D output that's a slice of the 3D color space for the output. Add in animation and you basically have an entire 5D graph on a flat screen.
Classical Physics itself uses lots of "extra dimensions" all the time. Besides a Hamiltonian phase space for the momentum allong every degree of freedom in your machine. Things like temperature and mass can be treated as their own dimensions.
The whole thing about a unified 3D of space and 1D of time is that four numbers are all you need to distinctly describe the velocity of an infitesimal "0D" point anywhere in the universe.
It's _velocity_
It's all velocities everywhere forever.
There's a really long story about how Maxwell's Equations lead to Special Relativity, but I don't want to write a really long comment here unless someone replies to this and asks me to.
That's where our spectrum comes into play, that's because from a computational perspective, you're right.
Anything that could be represented with a number we could just add to our "universe" vector, and that would be a basis for an argument that we live in an n-dimensional universe... HOWEVER
That's from a computational perspective where we represent everything with a number, on the other side of the spectrum where we have physics where we differentiate between different vectors, and when we say "our world is three dimensional" OR "our world is four dimensional" we mean "In order to describe position of something we need 3 dimensions" OR "in order to describe movement of something we need 4 dimensions"
So it all depends on what kind of dimensions you're talking about
When it comes to nerding out about an extremely specific involving physical models most people consider impossible to understand... don't ask for permission, wait for them to ask you to stop
For the matrix explanation, why do you need a 3x3 matrix to represent the composite vector, why not use a 3x1 matrix?
Yes
I really thought u were gonna talk about 7d cross products :(
This video is incredible quality, I cant wait to see what more you do!