4d explained
Created on: September 4th, 2006
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I have always had an easy time understand and seeing both with 'lines' and geometry a 4D shape. What I fail to understand is what relevance can this have in the super powers of reality. Easily enough, what would a 4 dimensional anything look like, if at all possible in a conceivable physical. Does this like the drawn 2nd Dimension have only a place on paper? hahaha.
cassio: Giving people a more intuitive understanding of 4-dimensional geometry gives them an advantage if they start learning either a) relativistic physics, in which you think in terms of spacetime as a united 4d manifold, or b) mathematical analysis. multidimensional models are very important for putting together statistical models. The visual interpretation is not something you'll ever manage to perceive with a real 4d object, but it helps to get your brain thinking in the right mode.
"So what happens when you stand in the middle of a railroad track..." The effect you see when standing in a railroad track doesn't happen at all in "projected" views. It happens only when using proper vanishing-point perspective.
This image uses isometric perspective, in which parallel lines remain parallel rather than meeting at a vanishing point.
And I understand what you're saying about a screen only allowing 2-D. However, in our universe at least, there are only 3 dimensions of space. Your argument makes no sense to anyone with a half decent education, and more importantly common sense. I also like how you're so smug in thinking that you're right too. Get a clue.
http://en.wikipedia.org/wiki/Fourth_dimension
Here is the wiki article on fourth dimension. Notice that nowhere does it mention time. The conjoining points of the two cubes exist simoteanously and in the exact same place in the third dimension, but not in the fourth. This would be a 4D object, which we cannot create yet. Wormholes may be an example of a natural 4D object.
In our universe, there are three or four dimensions, depending on whether or not you count time as a dimension. This does not prevent us from projecting from four dimensions into two dimensions, just as the fact that Newton was probably wrong about how the universe works doesn't prevent us from talking about and simulating Newtonian physics.
Even if time were a dimension, it would be a 'fifth' dimension in four-dimensional space. This YTMND ignores time, and focuses on space. In theorey you can imagine as many spatial dimensions as you want. A five-dimensional cube would be one of those hypercubes (or a tesseract) projected in ANOTHER direction. Going on about time is senseless.
unaidedcoder, think of the x, y, and z axis' as they would actually appear in a 3d space. also consider the planes that each axis creates. draw any line starting from the origin 90 degrees from z and you'll see that line is already defined with (x,y). and any point in that cube thing can be defined as (x,y,z).
Ok, first we take the derivative of F(x), which is F'(x) = 2x.
So now, we construct an equation for the slope of the line from a given point on F(x) to the point (1,-3). Since the Y value is F(x), which is x^2, the 'rise' component of that slope is going to be x^2 + 3. The 'run' component is super easy - run is just x - 1.
So, the formula G(x) = (x^2 + 3) / (x - 1) gives the slope of a line through that point on the graph, and through (1, -3).
I'm guessing that the only way someone on ytmnd was patient enough to explain something as "complicated" as this would be because spazdor was either allowed to fold through a line in the sixth dimension from one point in the fifth dimension to another (from a non lazy ytmnd to this one) point in the fifth dimension, or he folded through a line in the ninth dimension to reach a completely different point in the eighth dimension.
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