Physicist: If you think of a shadow as the lack of light created by an object blocking a light source, then shadows are 3-D. After all, it’s dark everywhere behind an object, not just on the surface of another object.
Is a shadow the dark volume behind stuff, or the dark surface on other things?
If, on the other hand, you define a shadow to be what we see and intuitively think of (the dark, parroting person on the wall, with whom you can shadow box) and not the volume in between, then shadows are 2-D.
However, that second definition is a little abstract, because there’s no real physical significance. You could say that the border between countries is a one dimensional line along the ground, but there are no physical laws that have anything to do with national borders, so it doesn’t matter.
Defining exactly where the surface of an object is (what with all of their atoms) is like trying to define exactly where the surface of a ball pit is.
It’s impossible to get something that’s genuinely 2-D in our universe for several reasons, the simplest of which is that atoms themselves are 3-D. So even the flattest flat thing will still have some 3-D-ness (at least a quarter of a nanometer or more). That said, there are innumerable examples of things that behave as though they were 2-D. In situations where one direction is restricted compared to the others you’ll often find that the physics follows suit.
Hurricanes and other very-large-scale weather phenomena roughly obey 2-dimensional physics.
For example, ripples on the surface of water are an example of 2-D waves that behave very differently from ordinary 3-D waves. Weather systems that are substantially bigger across than they are tall, like hurricanes (e.g., Sandy was about 800 miles across, and only about 5-10 miles high), roughly obey 2-D fluid dynamics. Normally the energy in a fluid (or gas) starts out with big eddies and moves into smaller and smaller eddies (you can see this if you pour cream into some coffee and then stare at it). However, very weirdly, in a 2-D fluid you find that the opposite tends to be true: energy starts out in small eddies and moves to larger.
If it weren’t for the flatness of the atmosphere (and some obscure math involving “entropy flow” in 2-D fluids) we wouldn’t get hurricanes!
Orbits of planets and moons seem to be 2d. I’m no astrophysicist though.
I believe this “However, very weirdly, in a 2-D fluid you find that the opposite tends to be true: energy starts out in small eddies and moves to larger” part needs an answer gravy.
It really does need some gravy. Unfortunately I can’t remember where I read that particular derivation. It’s in a book or paper or some notes or “other” on “non-equilibrium statistical mechanics” (which is like thermodynamics, but totally off the hook). It was something like; start with the Fokker-Planck and Navier-Stokes equations, and conservation of mass, then re-write all of it in terms of their the Fourier transforms.
Then, after a day or two, ask for help (because that mess is pretty tricky). You find that in two dimensions the Fourier spectrum tends to “drift down” over time, which means that the size of the “structures” in the fluid get bigger.
Could you post what the final Forrier transformation looks like?
Again, from a risk management point of view, it is a terrible idea to assert that the existence of hurricanes (physical reality) is dependent on concepts in people’s heads, i.e.: “obscure math involving “entropy flow” in 2-D fluids”.
This violates a basic foundation of science, that reality exists independent of our perception, and given the profound impact of language on cognition, the “just an expression” justification does not stand in light of persistent, fundamental mysteries.
Wouldn’t rainbows or the the resultant prismatic effects of refraction two-D?
If you have a projector and you project an image onto a screen, that image is 2D.
I think rainbows and the projector would fall in the same category as the shadow. There is depth to both the rainbow and the projector if you consider the space between the source ( the projector lense) and your eyes or camera iris.
Are there any examples of anything other than 3 dimensional structures or systems in the universe?
A shadow is not a thing, it is the lack of a thing. And in the universe, an object is also the lack of every other object in the same space. That does not make the lack of everything else a 2-dimensional object.
The image on the projector screen would still have to form to the contours of the screen itself, which if looked at closely would have an uneven surface due to the rise and fall of the atoms that compose it.
The same for a rainbow, only the canvas would be rain droplets in the sky instead of a projector screen.
For examples of extra dimensional objects in our 3 dimensional world I figure black holes might come up. *I am so not ready for that can of wormholes…er uh worms*
I imagine a 2d object escaping it’s constraints by bending the space it occupies; dot on a paper can’t move up or down unless you bend the page. So if a black hole rips through the 3d space we occupy, does it punch through to the 4th dimension? Are atoms compressed so tightly within a blackhole’s center they are smooshed into a 2d or 1d universe? I don’t figgin know! But it’s fun to think about. lol
I’ve always imagined that at some point within the sub-atomic level as matter gradually transitions into energy strings there are real 2-D particles with energy strings being 1-D. The pure thought or pure information level that programs our reality could be considered 0-D.
Mike you are absolutely correct about 0-D ,I have been thinking about similar stuff myself.
Discounting the surface an image is projected onto as having dimension simply because the image clings to that dimension, but is not part of that structure, and discounting the “space between” a light source and it’s shadow as an entirely different structure than the image, I don’t see why both a shadow, a projected image, or the image on the shroud of Turin would not be considered 2D.
I think it would be hard to conclude that it would be 2-d. Since we are aware of 2-d models I think we are biased in a way to be able to imagine 2d information out of patterns like the dark spot made by an object blocking light. The space in the shadow is exactly the same space sans photons traveling through it in reality. We may ultimately see that process as a darken triangle given the proper perspective. Also since an object like the shroud of Turin is made up of atoms which themselves are 3 dimensional structures it would be impossible for the combination of 3d structures to yield 2dimensional outcomes.
Just to keep this going, the shadow and rainbows are also technically illusions that our brains construct to give a useful sense of depth and place in space.
The shadow is just a tonal shift in the base color of the object cast in shadow. The tonal shifts are obviously due the the amount of light reflecting off its surface. The rainbow as stated above is a collection or system of droplets being struck with light which gives the rainbow effect. It only seems 2d because of our perspective from the ground. It has other notable qualities which are all visual effects and dependent on water droplets. It seems infinte but…… 🙂
Couldnt we consider that an object beeing 2 dimensional or 3 dimensional depends on the observers view?
Lets say I move towards a 3d cube with constant velocity. With increasing velocity, I would measure the depth of the cube more and more decreased (lets say the depth of the cube is aligned with my direction of movement) . The faster I move towards the cube, the lesser its depth…so it increasingly appears to be a 2d object.
Taking this to the limit v–> c, I would think that the cube has no depth at all and thus must be a 2d object. So, would the concept of dimension be a relativistic concept?
Marvin,, we can objectively look at a cube and agree that it has a length a depth and a width . Those are the qualifiers to make something 3D absent of our perspective. So unless we do a lot of mental gymnastics to redefine what 3D means we can be sure it is not a relative experience. I would be more inclined to believe your view regarding color but not mechanical structures in the universe.
As a fifth grade math/science teacher, kids asked me what a 2 dimensional object was. I told them that the shadow on the ground was 2D. The image seen on a TV screen was 2D. The image on the surface of a picture or movie screen was 2D. How wrong was I? I heard another teacher tell them that paper, actually an index card, was 2D, and I was appalled. Luckily, the kids understood the concept I had explained well enough to argue with that teacher, and say that the card was 3D. I did define 2D, but the kids wanted an example. What should I have said?
Mez,
You are teaching fifth graders, so your answers are about as good as it’s going to get. I would not just say you are wrong in what you said. But if I may give my understanding of it. I think I can offer a bit to at least think about.
The world we live in is “3 dimensional”. There is not a single thing in our existence that is actually 2 dimensional. The shadow is just the lack of light. It’s not an object. It isn’t a thing. It’s the lack of light. The idea of the shadow is just that; an idea we made up because the light landed every else more than it landed there. The image on the television? That is actually just the light energy entering your eyes. The image doesn’t really exist in it’s own right, it is just a bunch of tiny lights shining red, green and blue. It’s just a trick. But what are all those tiny lights? The lights are 3D. The light emitting out of it is a wave of energy that you see. But what part of it is actually “2D”?
I argue that there is no such thing as actual 2D. We use 2D in math as an explanation of certain functions, but even the numbers are really non existent, right? They are just for measurement, but measuring what? Every idea and thought to ever enter our 3 dimensional minds was 3 dimensional. Even the brain cells and neurons that made the thought in the first place. If there is a 2D world, I don’t think we will ever know anything about it. Ever.
Lite.. itself is 2 dimentional.. and it exists in our 3 dimentional world.. as far as i know it is the only thing that is truely 2 dimentional and exists in our 3 dimentional world..
I have not much math background. Unknowing prior to the realization that there is really nothing 2D at all not in this universe but this does been our universe is in a very special state, and I didn’t think that nothing was 2D because Adams are still three-dimensional but I thought that there’s nothing 2-D because something truly two-dimensional would have to have nothing on the other side of it and there cannot be nothing anywhere in our universe. Also you can always look on the other side of anything and everything. Think about this if we are truly in the third dimension right now then at its most basic roots mathematics are wrong and we really I truly think need to rethink dimensionality because if the first dimension is a point in the second dimension is a line well you would need those first two things hypothetically in order to get to that third step so what division are we really in here think about that try to answer that mathematically maybe for me. Or maybe try to tell others it’s wrong using some mathematical equation that none of them you’re telling really understand anyway. But the smartest guys in the room are always the ones who are best able at selling the perception that they are the smartest and understand the most easiest
Also Michael lights are made up of photons and you can see on the other side of light like in the comments above stated there is nothing truly to dimensional in our universe because if something were truly too dimensional then on the other side of that something that would be nothing and once again nothing can exist in our universe
When I first thought of there being nothing truly two-dimensional in the universe I had no notion or idea that anybody else had thought that or felt that way I had no previous knowledge of that whatsoever and when I looked on Google about it the first time a few years ago there was nothing about things not being too dimensional in fact the only thing that I’ve seen close to it was recently
If we look at the formation of a shadow at the inverse speed of light the idea that a shadow is a two dimensional projection in three dimensions becomes more clear.
Using a cube with the light hitting one side exactly, and the source of light being slowed to 1/c, we can envision a two dimensional square shadow projection moving through three space eventually hitting a surface that we can see the shadow on. Yes, I conceded that the shadow is only visible because of it’s interaction with the third dimension, but I would argue that shadows and reflections are projections of the second dimension in the third dimension.
It has been suggested that this shadow space has a volume. I would also say that those who would like to take the volume of the shadow space are misguided. When looking at it from the speed of 1/c, there is nothing to take the volume of- it is a projection, not an object containing volume.
Looking at this further, we can argue it is the third dimension that warps the time-space of the second dimension. If the surface the shadow is projected on is a corner space, the singular shadow plane is broken into three planes- the singular dimension of two space is broken into three separate, but unified, planes of two dimensional projections.
We can also identify the first dimension with this example. It is the line between the dense presence of photons and the less dense presence of photons, the border of the shadow… and we can see how the second dimension is the force that bends the first dimension in the same sense that the third dimension is the force that bends the second dimension.
We can say, “The limit of the first dimension is the second dimension, at any point, and the zero vector,” and we can say, “The limit of the second dimension, at any point, is the third dimension on one side and the first dimension on the other.” The question then becomes, “Is it the fourth dimension that is the limit of the third, on one end, and the second dimension as the limit on the other end, at any point?” I think it is, but I do not have the qualification to prove it is. What I do know is that Einstein proved that anything with mass warps our own timespace. I speculate that the source of force (universal; Gravity, electro-magnitism, strong/weak nuclear force) is a projection of the fourth dimension onto the third.
There has been objection that the second dimension can not exist in the third dimension, and this is true, but we can speculate that two space can be projected into three space. That is what a square, or a circle, or a triangle is. We can not actually make a square, but we know six squares aligned in the proper way is a cube (I.E. the infinite elements of the second dimension make the third dimension). And we are back to the beginning.
Dimensions are not separate from one another, but tangential. It takes all infinity of prior dimensions to make an extra-dimensional space. In layman’s terms: If you stacked all infinite first dimensions, you get a plane; if you stack all infinite second dimensions, you get the third; if you stack all third dimensions, you get the fourth. How would one stack the third dimension? I’m glad you asked.
Left, right, up, down, forward, backwards- thats the third dimension. The part that is missing, and here’s the kicker, is infinite expansion and infinite shrinkage. And what seems to express infinite expansion? Electrons, Stars, Red Shift. What seems to express infinite shrinkage? Protons, Black Holes, Blue Shift. The source of force within the third dimension is a projection of the fourth dimension into the third. This is a bold statement, but it stands to reason that it is reasonable.
What do you guys think is the source of the Universal forces? All of this is speculation so any input would be valued.
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I can’t believe not one person thought to even mention the Mobius device. Please explain to me how a non-orientable surface doesn’t qualify as a two-dimensional construct. And that’s all it took to shut down this entire conversation. Adding a chirality to a piece of paper and attaching it to itself. What’s really kind of scary is how passionate many of you trusted opinions are on the fact that a two-dimensional construct cannot exist. First of all, ninjas are real dragons are real even cool mathematicians are real. Two dimensions is real. I’m obvious device is real. And y it is much more than a classroom demonstration