I have been recently looking out for tools to visualize 4 dimensional data and other higher dimensions.
It is very hard for me to visualize a 4 dimensional object. One question I have is if such a thing is possible.
I can understand the logic of specifying that a 2 dimensional object can be visualized as a collection of 1 dimensional object and 3 dimensional object as a collection of 2 dimensional object.
Trying to apply the same concept to visualize a 4 dimensional object. To visualize a 4 dimensional object I have to assume a collection of 3d objects say cubes along a fourth dimension. What could be a fourth dimension. Time is one thing that comes to my mind, but many people have done that. Before considering time i would like to consider other possibilities. Is it possible to have a fourth dimension to space itself. Suppose in our space there is a fourth dimension say x,y,z and a. What this would mean is that at given volume of space that you see could contain more than just one thing. That is if you look along the a axis upon the world you can have infinite number of things in that space having different x,y,z coordinates.
In other words say at one x,y,z coordinate in space which is a small ball in my bedroom. I am able to see only this ball. But that space could contain infinitely more elements along the a axis. I am able to see only one thing along this a axis. Possible because I am also located at the same 'a' axis value. The same problem that a circle in a two dimensional world had.
How amazing it would be if there were more dimensions to this space than 3. And it is totally possible because we cannot assume that humans have the capability to see all the dimensions possible.
Now I would like to show you a very interesting thought. Suppose there is a fourth dimension and lets denote it by axis a. You are at a particular value of a axis. I give you a velocity in the direction of a axis and send you. For you as an object you do not have understanding to know that you are moving along a axis because you dont even know what that dimension is. All that you can see is the 3d world around you at that particular a axis value. But as you are in a motion along a axis and the world is different at every a axis value you would find that the world around you is changing. Ring Bells. This is exactly the experience we have everyday. We observe that the world around us is changing.
What I am trying to show you is that it is possible that time is a fourth dimension of space and we are moving along it with a velocity. With that I would like to add that the likeliness of this is high than just a guess, because as our universe believes in symmetry it is bit out of place when we consider space as a separate kind of dimension and time as a another separate dimension not related to each other.
Now the only point left in this argument is how to define the two words we used in this article. That is motion and velocity. It is now confusing to do this as we do not have time as a coordinate. As we are moving along a axis, the motion would be a2 - a1 where a1 is our initial coordinate and a2 our final coordinate. To be honest with you there is no reference frame we know with respect to which we can calculate this velocity. The four dimensions we know is x,y,z,a and we have motion along all four of these. If we want to calculate the velocity of this motion we need a 5th dimension from which we can do that. But for the time being let us assume we have such a dimension and we can define motion and velocity with respect to this dimension.
Implications
What this implies is that the world that we see is pre determined. It bring us back to the concept of fate. It also throws up the possibility of time travel if we know how to change our velocity along the new a axis.
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