A thought occured to me as I was reading the Universe thread. It’s all this talk of extra dimensions. I’m a math guy, so I don’t have any problem with n-dimensions. But here in the physical world, do other dimensions really exist?
I don’t think anyone has ever seen a 2-D being, or a 1-D being for that matter. If 4-D beings exist, I would think they would be just as baffled as us.
Theories such as String theory depend on extra dimensions. I think General Relativity implies it. But we have no physical basis for this assumption. Only that they fit into the equations.
This sounds like one for the eggheads… I could be a smart-ass and say “I see 2 demensional beings all the time! …in my TV set” but then even that isnt TRUE 2d when you get down to small enough particles… maybe a slide show is 2d… I shouldnt even be posting for this!! Isnt the 4th demension time or something?
Beer… you might want to read Flatland - A romance of many dimensions by Edwin Abbot: http://www.alcyone.com/max/lit/flatland/ It’s a classic explanation of single, dual and multi-dimensinal thinking. I read it about 30 years ago, and have had very little trouble “visualizing” (or at least imagining I am visualizing) additional dimensions ever since.
I’ve heard about Flatland, and I intend to read it someday. It’s about visualizing 3-D from a 2-D perspective.
I have no problem attempting (if that’s what I call it) to visualize the 4th dimension (a 4th spacial dimension, not time). There is no doubt it can exist. My question is: Is it good to assume that it exists?
Beer asks: << I have no problem attempting (if that’s what I call it) to visualize the
4th dimension (a 4th spacial dimension, not time). There is no doubt it
can exist. My question is: Is it good to assume that it exists? >>
Let’s pull back for a second. The notion of a two- or three-dimensional orientation system is a mathematical notion. Just like a mathematical line, or point; they don’t “exist” in the real world as such. Any line that you draw in the real world has width and depth (from the pencil lead, say).
However, the idea of a line or a point can be a useful model of how the real world works. Similarly with the 2-, 3-, or 4-dimensional model. By thinking of the solar system as a 4-dimensional model (with time as the fourth dimension), it is possible to calculate the flight path from earth to Mars, for instance. By thinking of the United States as a 3-dimensional model, it is possible to have air traffic control. By thinking of your back lawn as a 2-dimensional model, you can figure an efficient path to mow the grass. All these models are useful – and don’t limit yourself to 3- or 4-dimensions, sometimes a multi-dimensional model is useful, thinking of temperature, electron “spin” direction, or various other elements as dimensions.
So, the answer of “is it useful”, you bet. Is it “true” – no, it’s a model of reality.
Don’t quote me on this or burn me at the stake!
I read somewhere that time is an invention of humans that portays/descibe the change of state of a three dimentional object in space. This change of state is the fourth dimension.
But these models you have suggested are based closely to natural occuring phenomena. There is no observable fourth spatial dimension. Is it safe to base our models on phenomena which cannot be proven or disproven to exist?
Aha! I finally got the point. There is actually no observable 2nd dimension. But we are free to make theories in 2-D from equations in 3-D.
I guess you’re right, CKdexthavn, a phenomena doesn’t have to exist for us to use it.
There is a 4th dimension - and many more. All entities and all events exist here and now, in the same space; we create our own reality; we create ALL reality; there is no linear time as we think of it – all events happen at the same “time” - those who have “died” are here with us- in another dimension. Anyone else read the Seth books?
Gee Sycorax, if everyone is everything, everyone knows everything, and all things are all things, why did you bother posting? We already knew what you had to say, you already said it, and if we are all of one mind, we all think you’ve said nothing of substance.
“When the going gets weird, the weird turn pro.”
“It is impossible to imagine a four-dimensional space… The surface of the earth is two-dimensional because the position of a point can be specified by two coordinates, latitude and longtitude.” Stephen Hawking, “A Brief History of Time.”
I am presently reading this book and recommend it, although it gets pretty technical. My aforementioned Seth books get into the space-time thing and are fascinating reading and that’s why I wondered if anyone else knew of them. (Slythe, Hawking and Seth are way too deep for your puny mind, so don’t even try.)
Sycorax, I assume that you Hawking quote means that it is impossible to VISUALIZE four dimensional space. It is certainly very possible to create mathematical models of 4, 5, 6, or n-dimensional spaces and to work with them. One can create solids and images of graphs (the n-dimensional equivalent of curves), one can work with formulas for distance, etc etc. Anyone who took 2nd year calculus has been exposed to n-dimensional spaces.
Sycorax, I read Hawking before Hawking was pop. I was commenting on your Seth reference.
I’m sorry, but whenever someone brings up the nonsense of everyone is everything is everywhere is always, etc. one phrase comes to mind.
Koo koo katchoo.
“When the going gets weird, the weird turn pro.”
Getting back to the OP, I remember Carl Sagan giving a demonstration of dimensional relationships that was simple yet elegant.
He used a cube made from plexiglass to cast a shadow on a flat surface to represent the cube’s appearance in 2 dimensions. There is some error in the projection, as not all the vertices join at right angles in the 2D shadow cube, but explains that this unavoidable since we are observing the 2D cube from the 3rd dimension. He calls this error the price of projection. He then shows us the projection of a tesseract (a 4D hyper-cube) & again notes that there is some error introduced since we are looking at it from the 3rd dimension. A 2D representation of a tesseract can be seen at http://pweb.netcom.com/~hjsmith/WireFrame4/tesseract.html , but remember that the real tesseract would have all vertices of equal length, and all joined at right angles.
I understand that all matter has 3 dimensions no matter how thinly we slice it, since it exhibits some degree of roughness, even if it’s only the thickness of the subatomic particles- I guess the question I have is, are shadows & other representations of light really 2D objects?
Forgive the lack of exactness of the following answer. I read a bunch of quantum cosmology books last year; and even though I’ve retained the concepts, the exact numbers elude me.
It seems that a combination of quantum theory, gravitational theory, general and specific relativity theory, electromagnetic theory, and the strong and weak force theory all work nice and neatly, if the universe has 26 (or abouts) dimensions. The exact equation to define this escapes us all for the moment.
Serendipitously, close to half those dimensions drop or cancel each other out in practice, leaving about 11 - 16 actually existing dimensions to really worry about in the final equation.
Even more convenient for us humans, all but three of those dimensions have collapsed to subatomic size. (Forget time for the moment, I’m just talkin’ spatial dimensions.)
For structures larger than subatomic particles, those extra dimensions are almost irrelevant. Trying to figure out the effects of or worry about those extra dimensions for us on a human scale would be like worrying about or factoring in the time dilation involved in a car trip – it’s inconsequential.
But for subatomic particles, they can fit in and travel in and out those extra dimensions – thats why a photon can be both a wave and a particle.
So, let’s travel to flatland for a moment. But instead of a pure two-D plane, these flantlanders are pencil drawings on a thin, 3-D piece of copper sheeting. Now, their graphite selves have thickness, but they don’t realize it, because it’s too thin for their technology to measure. They live as if they were only 2-D, when they do, in fact, have a 3-D reality about them. Now imagine their surprise when they develop the means to track an electron (which they think has no dimensions, but is a point on their supposed 2-D plane), and the electron keeps appearing and disappearing from view. The electron is, in fact, bouncing around inside the sheet of copper. Their theorists then postulate that they are really 3-D creatures, but that the third dimension is so tiny, it only has practical effects on subatomic particles.
Wa-lah! We are really 11-D (or 16-D) creatures; however, all except three dimensions are too tiny to effect us practically.
Oh, and while we’ve never seen a 2-D being, scientists have trapped electrons in a magnetic fields so strong and cold, that their ‘3-D’ wave function has collapsed to a 2-D wave. Yep, they’ve created a 2-D object (although, it still might be existing in those extra, tiny dimensions, also).