Dimensions - Sixty Symbols
Вставка
- Опубліковано 8 чер 2024
- What would life be like with just two (or four) dimensions?
More on extra dimensions with Ed Copeland... • Extra Dimensions - Six...
Flatland: A Romance of Many Dimensions by Edwin Abbott.
The Planiverse by A. K. Dewdney
Visit our website at www.sixtysymbols.com/
We're on Facebook at / sixtysymbols
And Twitter at #!/periodicvideos
This project features scientists from The University of Nottingham
www.nottingham.ac.uk/physics/i...
Sixty Symbols videos by Brady Haran
A run-down of Brady's channels: bit.ly/bradychannels - Наука та технологія
The sphere versus a circle that changes sizes is very insightful but got glossed over pretty quickly. XD
true!
So in 4 spacial dimensions, escape velocity would be easier to achieve than it is in 3?
i would imagine its 1/8th
Yep 2^3
yep and no stable orbits , planets all quickly, escape each others grasp, no dancing around holding hands. only 2d and 3d can have planet systems and LIFE finds a way to do the rest. In 2D no escape velocity, rocket engines and/ or solar sails got to be on or you will fall back unless you are past about halfway to the next sun then you can fall into that. but you can use the other planets as a slingshot Gravity is expressed as flux like that is an approximation of the force of gravity. unless relativistic curved space effects are much stronger or speed of light is slower in the universe the law is 1/distrance * ( num dimensions -1).
Ok
thanks - you can show Pete (the artist) some love by checking the link in the video description!
This video was fascinating. You should consider having Mike do a video explaining what the problems with the Kepler spacecraft were/are. Maybe something about what that this might mean for its future and for the engineering of other spacecraft.
Two questions, it would be great of someone could explain them to me
1) For the escape velocity example, wouldn't that be working on the assumption that the mass of the 2D object is the same as that of the 3D object? In 2D it would have far less mass, so while the rate of gravitation drop-off would be less, the actual amount of gravity you are having to overcome is also less.
2) Is graphene REALLY only 2D? Yes it's only 1 layer of atoms thick, but atoms are 3D. The electron orbitals don't all line up in one 2D plane, they go out in all directions. So while the distance across would be extremely small, it is not zero.
In physics if something is reaaaly small then you can make a model that explains the behavior without taking account of that small value.
@@Radianx001 aaaaand thats how we got to the dark matter and dark energy woo woo smh
By far being an expert, but this is my guess:
1) Does not matter about the amount of mass, the acceleration needed would be the same. In our 3D Newtonian universe, the gravitational acceleration is the same regardless of mass. A feather falls as fast as a hammer (excluding air resistance).
2) Where is the other dimension for the electron to go? Yes, the orbits are spatial 3D, but if you think about applying an electrical current, the electrons can only behave as though graphene was 2D, length and width (or whatever you label the dimensions). Graphene is like Flatland
Graphene still has probability to has its electrons outside the 2D plane. And if you break it, you will definitely be convinced it is 3D. One thing that is always 2D is shadow, but the problem with shadows is that they don't really exist. The concept of a shadow only exist in our heads, because we are capable of perceiving lower dimensional spaces, even though they do not exist.
Those animated segments are a marvelous addition to these videos!
"...eleven spacial dimensions."
*spits out drink*
I love the sixty symbols videos, thank you so much for making them. I would like to make one suggestion. It would really be nice to know the name of the person speaking. Perhaps you could place a bar with the person's name beside or below them in the video .
Great vid but I wish they would have explained a 4th dimension more.
I think our limited human comprehension makes it harder to see what we are missing that could be had with four dimensions. Each additional dimension is less of a leap than the last.
+ganondorfchampin The most interesting I can think about is how in 3d dimensions our projections are all 2d. Like are vision is really 2d, just with a 3d points assigned to each 2d point. We don't really see our world in all three dimensions, we just see the 2d surfaces of objects. A single projection, like what you get from a drawing or keeping one eye closed, gives you part of surface from a single viewpoint; getting all the view points from all perspectives at once only gives the complete surface. A 4d being would see not only from all perspectives at once, but they'd see all layers of us simultaneously. They'll see are guts, our hearts, our brains, our skin, all at once. It's sort of incomprehensible. Even most are presentations of 2d dimensions fail to take this into account, implying a 3rd dimension that is simply not seen.
You only see in 2 dimensions if you only have one eye. Or close your other one, if you have 2. It is true, that both eyes only see 2 dimensions, but 2 pictures of 2 dimensions can be turned in to a 3 dimensional picture, which is what our brains do all the time.
Sup3rman1c Nope. We don't actually see in 3D, it's just an illusion. Our visual field is completely 2D, we just perceive objects within the 2D array as having depth by combing information from two different projections, but we are still only seeing the surfaces of things. I already covered that in my last comment, you added absolutely nothing to the conversation. Closing one eye doesn't completely remove depth perception either, as their are other visual cues the brain uses to infer depth.
Sup3rman1c It's like this: if we actually saw things 3D dimensionally, than paintings wouldn't work. At all. It's the difference between reducing a color image to a black and white one, to reducing a color image to just a line. You can tell what the black and white image is, but not what the line is.
Thank you for telling me about The Planiverse! I have since read the whole thing and loved it.
To give half an example, one point in a 4D cube can be viewed as 4 points on a line segment, where the single coordinate of each of the 4 points corresponds with one coordinate in the 4D space. If the 4 dimensions aren't the same size/shape, you can use 4 separate line segments, and if one dimension depends on the location in another (e.g. surface of a cone; height on it affects radius of circle around other direction), you can vary even the size/topology of each as necessary.
You could use the same orifice for eating and.... exiting out what's left after digestion.
+911gpd Yep, that's how the Nsana do it in the novel.
Like jellyfish?
911gp -- That is exactly how animals like jellyfish and coral, and flat worms do their digestive business.. only one opening for both shipping and receiving.
yum yum
Why not just have its body be able digest anything it comes in contact with
I don't understand why a two dimensional being wouldn't be able to lift a plank. Can somebody help me out here?
Sage Llivokin Look at the picture at 1:12 - His feet are on the ground and the hand is touching the plank. with this, he created a closed space between his feet/body/arm/plank/ground in 2D. So if he tries to lift the plank, he is creating a vacuume, making it uttelry hard if not impossible to lift it. get it? ;) he basically needs to jump up or wobble his feet to let the air through between his feet and the ground.
Adam Flow I don't think I understand the physics of a vacuum then.
Oh, I see. Thank you.
It won't be a vacuum, though, just a lower "pressure", so he'll be able to lift it a bit. Also he could squeeze air into it.
jimpozcaner "lower pressure" is essentially what a vaccum is.
Excellent video. I love stuff like this. It makes you see the most mundane aspects of your existence in a whole new way.
It is very good of you to question these things, this makes a good scientist. You kinda have to get into these mathematics and suprisingly you'll start getting a feeling for certain problems and know from the start what the answer will look like. Experience mixed with talent/intuition is key.
Escape velocity would be achievable! It would just be nearly impossible to reach it. Also, by the logic that in two dimensions, Gravity is one over distance, then gravity does not dissipate in one dimension.
I loved Flatland. :D It was cute and funny enough that I think kids would like it, but it also brings up a lot of interesting ideas about perspective and reality. Very cool book.
Fantastic interesting videos. I think the 4th dimension is worth exploring a bit more in depth with your explaining vids Brady :)
In even more detail than the already made extra dimensions video
This video was really interesting. I hope they do more like this
I don't understand what one means when they say a dimension is 'small' or 'bunched up'.
String theory imagines that the most elementary building blocks of matter, like quarks and electrons and photons are actually multi-dimensional vibrating strings. This string can vibrate in the xyz directions that we know of, and also in up to 8 extra directions, but those dimensions are really only accessible to the string itself for the purposes of this vibration. The string can't move through these extra dimensions from one place to another like it can in the 3 "regular" dimensions. It's pretty much impossible to picture visually.
Imagine a 2 dimensional universe that is really 3 dimensions. It looks flat, but if you looked at the universe under a microscope there would be some thickness, although small.
What the hell would a 4th dimension look like? Like if I were to pop into one right now, what would I see?
first you would die instantly because your body is not meant for higher dimensions. idk what will happen after that but 4d entities will probably be laughing at you
Well, you know the three dimensions your familiar with? Imagine one more. There's just another 2 directions at right angles to the others. Also, there would be nothing holding your guts in so you'd die pretty quickly.
That is an excellent question....and an old one.
And i don't think there is a single person on this planet with the adequate knowledge to answer it...
Though i wish there was.
You'd see everything. If you had for example a cube, you'd see all of the cube at once, like you can now see all of a square at once, but flatlanders can't
Apologies if this has already been mentioned, but from what I've learned: If a tesseract (4-D cube) moved through you would see a cube grow and then shrink in size. Remember the video when the sphere moved through Flatland, it appeared to be a circle starting out as a point, growing to a circle, then collapsing back to a point. The tesseract, or hypersphere, or what-have-you, would project whatever 3-D information it had as its 4-D body passed through that region of 3-D space.
I would love to see this conversation cover more dimensions and go on longer than 7 and a half minute. I could listen to a 45 minute talk about the subject and I would rather enjoy it very much!!!!!
Another excellent video Brady thanks for this!
That Planck's constant pun, though..kudos.
0:51 Vihart!
Thank you very much for your efforts in making these videos.... This is GREAT culture, so interesting and brain-teasing! Really glad that a lot of people follow this channel.
Brilliant video. Put a massive smile on my face.
"The plank's constant" HAHAHA.
What about 4D cinemas?
the 4D refers to the puffs of air and water and stuff, like its "adding a new dimension" as the marketers like to put it.
+Tom Goldberg lol. I know. Just having a go.
+Antony Karlytzky I first saw "What about 4D enemas?"
+Antony Karlytzky congratulations, you totally parker squared that comment :)
In a sense a regular movie is already 3D, time being a dimension.
This was so fascinating!
in a video on this topic, what did you expect!? :)
if you live in 2d you can draw only in 1d we live in 3d and can only draw in 2d can something in 4d draw in 3 etc? stoner thoughts
im probably assuming something i shouldnt
We can draw in three dimensions.
We can draw three dimensional things in two dimensions*
Drawing in 3 dimensions is called sculpting.
***** We live in 4d and we can draw in 3d, 2d, 1d, or even 0d... a sculpture, a plane, a line, or a point.
koolguy728 idiot. When you are drawing a point, it isnt 0D. Its atleast an atom wide, long, and high. Any single thing drawn or made can be measured using 3 Dimensions.
heres a time for me to look thick on youtube:
(all in my opinion)
a spacial 2D universe would not be possible as a 3rd dimension is needed for the 2D shapes to exist on.
my theory is that in our universe we are within has 27 dimensions (not just spacial dimensions), each dimension of the 3 dimensions we see has 2 other dimensions which allow for space and time. for example when you pick an object up by the length of it, the force that is allowing that to move are the 2 other dimensions at work, curving space and allowing time for that object to move.
this probably sounds like bull, but you try explaining something rather complex through youtube comments
One of many brilliant comments left by gifted people who take this stuff seriously and try to understand it.
Thank you for your excellent theory, sir.
Splendid animations!
Lovely animations!
2d space can only be seen when we look at it from the third dimension. The hypothetical creatures that would live in such a world wouldn't see anything. They would inhabit a completely flat surface. A surface that has no height is invisible when you look at it from the side.
Terminator4004 That only applies to 3d creatures. A 2d creature would see 2d photons and 2d objects just fine, because everything would be equally "wide" and perfectly aligned.
Joshua Pearce You can't see photons though. They might exist, but they wouldn't do anything.
+Connor Skudlarek But the effects of the wavelengths of Photons interacting with the sensor cells of the eyes is the reason why we see anything at all, they are the only things that touch our eyes.
Bungis Albondigas Yes.
+Terminator4004
If there was a form of "2d light" then a 2d creature could see a line of visual information. This is in contrast to the planes us 3d creatures see.
Though does that mean a 4d creature might see in volumes?
Gravity has a longer range except for the fact that there is no gravity.
Gravity is fractionated each dimension.
+OpportunisticHunter On the one hand, we could think of gravity somehow spreading out the further it gets from the source. This would make sense if it were carried by some kind of particle emitted by the source. Using such a model, we'd get a Newtonian style relationship whereby the force is proportional to _r_^(1-_n_) where _r_ is the distance and _n_ is the number of dimensions. This is the idea he first discussed when he was referring to escape velocity. I suppose that this may be what you mean by its being "fractionated".
On the other hand, he mentions that general relativity doesn't work in 2 dimensions.
Of course, we might just as well call it all metaphysics anyway.
jimpozcaner
The event horizon on black holes reach the infinite gravity and time is stretched to the limit where from our perspective the substance on the spiraling disk never goes any further as some kind of 2D world projectioned on a sphere.
No no.
Newtonian Gravity in 2D has a longer range.
Meanwhile General relativity in 2D doesn't work. These are two different ways of extending gravity from 3D to 2D.
This is a fantastic video explaining dimensions
Carl Sagan also had a great segment about 'flat-land' on the show Cosmos. Very similar to the opening discussion on this clip. Really enjoyed this topic Brady.
You can't have anything in two dimension. Even the carbon example is at least one atom thick...
You couldn't even an an operation of light or vision because that requires a 3rd dimension of thickness/width within 2 dimensional X and Y. Seeing would be impossible. Only way to discern distance would be to touch things.
Perhaps there is a third dimension but it's extremely small. So for all intents and purposes there are 2D, but in actuality there's however many small, non-extended dimensions needed to make the whole thing work?
jmitterii2
Not even that, touching things is electromagnetic interaction, therefore fundamentally the same thing as light.
and he never said contrary!
the thickness would be small enough to consider it as having no thickness :)
Or a 2d universe can just have very different physics.
I second this! The prof said that thinking from the perspective of two dimensions gives an insight into how higher dimensions could be. The animation there really made that clear.
This was just a really fascinating video. Thanks!
great video! love the animations!
The animations are superb!
Especially the one at 6:45
Higher dimensions has problems too. Knots that cannot be untied by themselves (need somebody to unravel them so that they can hold things together solidly by themselves) cannot be made, from what I saw in a video once, which greatly removes many things we can do in 3 dimensions. (Turns out things like knots are important in many, many things!)
Thank you Bradey, you are great
Love the animations in this video :D
See link in video description for a chance to get some of Pete's original artwork in this video!
Nice video and nice animations!
Extremely interesting stuff, thanks!
I remember that book! It blew my mind. I still have it, waiting for my kids to be old enough to get into it.
TO SHORT! It was getting really interesting and then it was over??? Great episode! :)
I think I already read about this book in a high-school geometry textbook, it sounded nice but I never would have thought of those implications!
thanks Alan!
Really interesting video, keep up the good work!
It's not just for gravity, the power law applies to anything that radiates from a point (so, for instance, electromagnetism also decreases like 1/r^2 in 3d and 1/r in 2d, same thing for sound, circular water waves, etc). Like AlanKey said, what matters is that you are spreading out over the area of the surface of a sphere, which grows likes r^2 in 3d. In 4d it would go like r^3 because that's the area of a "3-Sphere", etc. If you want to know the maths just google "Gauss Law".
Love the vid, but well your videos are always great guys. :)
Great work :)
This is my understanding of it, explained with an example (don't shoot me if I'm wrong)
Imagine looking at a very long straw held vertically. If you look at it up close, you can see it's surface has two dimensions: up adn down along the length of the straw, and a circular dimension around the straw. If you look at it from further, the second, circular dimension becomes unnoticable: you can only see the length-wise dimension. The second dimension is therefore called 'smaller' than the first one.
The amimation is beyond belive! Well done. Hugely inspirational 2D creatures!
planiverse was my favourite book when i was 12. it was a big influence on my young mind.
very interesting video, thanks!
Thanks very much, lots of work went into them. Although I have to say the designs for the creatures themselves were based on the characters in Dewdeny's Planiverse book.
utterly fascinating.
please do a video on higher dimensions, and teleporting and time travelling etc... I'm really confused with all that and craving to know more
Flatland is one of my favourite books. I actually managed to get it on my English literature list back in high-school.
Look the sixtysymbols video called "Extra Dimensions". It touches on the idea of small dimensions.
Extremely interesting. I would love to hear more on the topic of extra dimensions. Minute physics mentioned that stable gravitational orbits can only exist in 3 spatial dimensions a while ago. Could you possibly ask how we know gravity decreases with 1/distance in a 2 spatially dimensioned universe? It really does seem fascinating.
The generalization of cross-product in higher dimensions is what is known as "exterior product". See wikipedia article "Exterior_algebra".
Thank you feedback means a lot! Check the link in the description, I'm selling the original artwork in the hope I'll be able to afford to keep working on Brady's projects.
Not sure, but I'd very much recommend checking out the two books linked in the description.
Did I understand it correctly if I think, that spatial dimensions aren't straight, but they loop, so when you've moved a distance in one dimension, you'll get back to the same point again?
Do you mean that you don't have to travel very far before you get back to the same place, when you say that a dimension can be small?
Thanks that's very kind of you! Believe it or not, I'm actually very new to animating in this way and doing these few videos for Brady has made me think of the many possibilities there are for working like this. If you would like (and are able) to support there's a link in the description to ebay where I'm selling the original artwork. Tänan!
@Brady Came across this cool idea "the curse of dimensionality" in sci am a while back , that has some interesting counter intuitive properties, probably a fun topic for such a video like this.
next video please do the 11 dimensions! Also like someone else asked; how can these extra dimensions be small, dimensions are just planes of direction perpendicular to all the other dimensions, what defines their size?
Hi, I have a question. @ 4:55 you talked about grafine being an example of two-dimensional object, but atoms and electrons are not three dimensional particles / waves?
I would much rather have a 7:20 minute ad that I can skip then a 20 second ad that I must watch. Lots of ads are better than the videos that follow.
BTW, I'm halfway through reading The Planiverse and it's so exciting that sometimes I have to turn on the hrabx.
Loved this video right up until the end. I remain convinced there are at least 4 spacial dimensions in the universe in which we live.
It is the same way we consider things written on a piece of paper as 2-D. The thickness is insignificant compared to the other dimensions.
There are spacial dimensions (vectors/axes) and temporal dimensions. Both are dimensions, but different kinds of dimensions. To quote Wikipedia: "A temporal dimension is one way to measure physical change. It is perceived differently from the three spatial dimensions in that there is only one of it, and that we cannot move freely in time but subjectively move in one direction."
nice animations!
Thanks for reply. I was confused, because when I learned about gravity I was told exactly what I said and it worked well for 10 years. I really liked your analogy. Is green paint gravitons that are theorised to be gravity medium or is it just a metaphor for gravity itself? Because that would make it even better.
Very cool video
A lot of people consider time to be the 4th dimension. Time isn't a spacial dimension, though it is a dimension. Here's the thing, there aren't a specific 11 dimensions. You can have 11 dimensions, but they can be space, time, or I suppose a combination of anything you would want to call a dimension.
If you're concerned with dimensions that are spacial, such as that described in the video (not the 11 dimensions people are talking about), look up hypercubes.
great video
I like these new animations.
Logically equivalent to that statement is:
Through any three non-collinear points there is exactly one plane.
Through any four non-coplanar points there is exactly one solid (3-plane).
Through any n points that do not lie on the same (n - 2)-plane there is exactly one (n - 1)-plane.
Which seems more self-evident to you?
I think this is your best 60 symbols yet.
This may seem like a silly question but which direction does the 4th dimension face? Like a 3d object has an x y and z axis, what is the 4th axis?
I think in the video he was talking about the electrons being restricted to the plane by the conditions in that certain arrangement of particles.
How are those tear shaped (with the hole) attachments on the binders behind him used?
I think it's impossible to imagine. Like if you imagine swinging your arm and pointing in every single direction you still haven't pointed in the fourth spatial dimension (assuming there is one). In four dimensions if you're inside a solid cube you could just walk out, but you don't walk through the cube. It's so crazy to even think about that my brain hurts.
Channels like this make me want to go to university... I want to learn what makes the world work ^_^.
The dimension you are talking about are Cartesian dimensions, which are only a special type. One of the easiest examples of "not-straight line" dimension would be a cylindrical co-ordinate system.
Is the rule about infraction range decaying at (x^{y-1}) applicable to an arbitrary number of dimensions upwards?
I love where your imagination can take you once you apply this concept to a fourth dimensional being interacting with a third dimensional being. Mind blowing stuff this subject.
What they were saying is that electrons between the layers move in near-as-makes-no-difference 2 dimensions, so electricity could still be conducted through gaps in a material just like they are in 3D.