I find the 3-dimensional world sufficiently complex as it is. Still, it is interesting to think of adding 1 more dimension to it.
I once read that to imagine a 4 dimensional world, think of every point in 3-dimensional space as a sphere.
Isn’t that adding too many dimesnsions?
Shouldn’t it be stated that you should picture every point in 3-D space as a line?
I remember seeing something on TV about how a four demensional object would make a three demensional shadow.
Hey! Think about this! If the glasses they give you at the movies allow you to see three dimensions on a two dimensional plane and you wear them outside, would you see into the fourth dimension?
Humans can’t really see four dimensions. If you think you can, you’re fooling yourself with a projection. All humans can see is three dimensions, so we’d see three-dimensional objects that are `really’ the pieces of four-dimensional objects that happen to share a three-brane with us.
To better visualize this, remove a dimension and imagine two-dimensional beings looking at three-dimensional objects. How would a two-dimensional creature see a sphere? As a circle. What kind of circle? The kind of circle that corresponds to the part of the sphere that intrudes upon his two-dimensional membrane (or two-brane, in shorthand). We are just as limited as the two-dimensional beings viewing three-dimensional objects when we try to see four-dimensional objects.
Actually, the world is only 3D if you were to take a greyscale snapshot from both eyes. Add time, color, and numerous other dimensions that the visual system readily processes at the level of the cortex and you have a 7 dimensional world–at a minimum.
What does the 4th dimension represent in this model?
homercles: No, not correct. In this thread, dimension' has the standard meaning of a spatial dimension.’
Oh that would be time, right?
I suppose it does seem a bit strange, but surely you mean “imagine a mathematical model of a 4-dimensional world”? It takes no effort at all to imagine the world as it is.
So be it, i suppose i may not have read the OP very closely.
BTW, youre in Havre, Montana? I was born in Harlem. Part of the Walsh clan.
Meta-Gumble: As I said, in this thread, I think the OP is referring to a fourth spatial dimension, not a timelike dimension. There’s no such thing as the fourth dimension, just various mathematical models that call up different numbers of dimensions, spatial and timelike, to explain what we observe. To use an oft-referenced example, string theory implies eleven spatial dimensions in its equations, and not one of those eleven can be equated with time.
homercles: Not familiar with the Walsh clan, but I do live close to Harlem.
There’s no one best way to visualize 4-D, and I’ve yet to be convinced that anyone can. However, thinking of a 4-D point as a 3-D sphere is not necessarily bad off. A 3-D point requires three “dimensional values” to describe it: x, y, and z, if you like. Similarly, a 4-D point requires four. A 3-D sphere also requires four: x, y, z, and R. Although it’s crude, you can think of “point size” as the fourth dimension to help you visualize. For instance, you can imagine a line going from point A to point B, and as it went along, the “points” got bigger, so that you had small spheres at point A and big spheres at point B. This is sort of like a line in 4-D.
Can’t visualize 4 dimensions? What are you talking about? There’s an entire generation of people that can see 4 dimensions. They’re the ones that took all the LSD back in the '60s.
Okay, thanks for all of your replies. And yes I was talking about a spatial 4th dimension. Achernar I like your explanation of “point size” being a sphere in the 4th dimension.
I too learned (many years ago) that time, the passage of time anyway, was a fourth dimension. My information is pretty old, though. Probably 30-40 years. I read about it, but can’t remember what or by whom. The same article claimed the impossibility of only two (spacial) dimensions.
Four dimensions (x,y,z,t) or oblivion, take your pick. 
Peace,
mangeorge
mangeorge: Well, time is a timelike dimension, and therefore different from a spatial dimension. For example, information can only travel in the time dimension in one direction, and entropy is directional only in the time dimension. In a fourth spatial dimension, information could travel it both directions and entropy wouldn’t exibit any tendancies along it.
I can perceive a 5-dimensional world every time I listen to “Age of Aquarius” or “Up, Up and Away.”
<obligatory Flatland reference.>
Consider:
A zero-dimensional point, extruded through one dimension describes a one-dimensional line.
A one-dimensional line, extruded through a second dimension (perpendicular to the first) describes a two-dimensional plane square.
A two-dimensional plane square, extruded through a third dimension (perpendicular to the other two) describes a three-dimensional solid cube.
A three-dimensional silod cube, extruded through a fourth dimension (perpendicular to the other tthree) describes a four-dimensional 'hyper’solid Metacube.
Trouble is that is is very difficult to visualise the fourth extrusion; usually, the mind’s eye will see it as an extrusion in some vector composed of the existing three dimensions.
Another thing:
To a resident of a two-dimensional universe (Flatland), a one-dimensional line is visible in full - the resident of the one-dimensional universe (Lineland) can only observe the points on the line adjacent to his own position.
To a resident of a three-dimensional universe (Spaceland), a two-dimensional plane figure is visible in full - the resident of the two-dimensional universe (Flatland) can only observe the sides facing to his own position.
To a resident of a four-dimensional universe (Hyperland), a three-dimensional solid figure is visible in full - the resident of the three-dimensional universe (Spaceland) can only observe the faces presented toward to his own position. - From a vantage point in the fourth spatial dimension, all six faces of a three-dimensional cube would be visible at the same time.
I always felt like we see the world in two dimensions, and our brains interpret the depth aspect.
A 2D person would NOT see a sphere as a circle. That would require being “above” the plane to see the entire circle. (Flatland is a good book for this concept.) A sphere would appear as a line that got “fuzzy” toward the edges.
In much the same way as a 3D object (sphere) appears to a 2D creature as a 1D object (line), we see the world in 2D and “interpret” the third. Just my $0.02. (Hmmm…is this IMHO or GQ?)
Damn Mangetout, you beat me to the simulpost. You win the Flatland reference race. But I’ll be back, I tell ya!
Damn, both Ellis Dee and Mangetout beat me to it. Damn you all! Every single both of you!
Seriously, you should read the actual Flatland book, it’s dirt cheap and, well, just plain weird.
