The Fourth Dimension

I just had one of those eye-opening experiences in class, and this time it was during my Calculus III class today.  We just got introduced to functions with multiple variables.  During all this time studying calculus, we have been looking at an output that is dependent upon one input.  Now, things are spiced up a bit and we are starting to look at an output that is dependent upon two, maybe even three variables.

Let’s work from the ground up.  When looking at the very first functions studied, the domain and the range were dependent upon one dimensions, or well, a line.  When we add another variable to the domain (input) this essentially produces a surface/plane depending upon the conditions of the domain.  (Some domains are all real numbers, while some have very specific conditions.)  This essentially means that the surface dictates the value of one dimension, or a line.  Which means, I am sure math has explored functions that not only have a multidimensional domain, but also a multi-dimensional range.  However, let’s keep it simple.  As numbers are picked upon the two-dimensional surface that are legitimate for the overall function (domain) a z coordinate is produced showing a three-dimensional surface if everything was plotted.

From there we went into cross sections.  Topologists (map makers) basically use this concept constantly when calculating the height (z coordinate) of surfaces.  Essentially if they can create a two-dimensional axis of x and y, they draw a line that corresponds to a constant z.  After all the z’s are recorded, a three-dimensional surface can therefore be constructed, producing three-dimensional maps of the world around us.

But….let’s get even more spicy….

What if we were to make the domain of our function dependent upon three variables or dimensions?  The output inevitably could be a minimum of one more dimension.  Which means, if one were to attempt to graph the entire system, the minimum would have to be four dimensions.

How is that possible?

My awesome teacher basically proposed the strategies of the topologists to this problem with a three-dimensional domain.  The domain was essentially a sphere.  And well, the only way the human mind (at this point) can capture the overall system, is to show a sphere that shrinks or expands depending upon the passage of time.

This is why I think many intellectuals and geniuses view the fourth dimension as time.  And well, I do not necessarily think this is the case.  I think the human mind perceives the fourth dimension as time, I do not deny that.  But just because the human mind perceives something does not mean whatever is being perceived is Truth.

Therefore, just as the fourth dimension could very well be time, I think it could just be as possible that the concept of time is just a perceivement.  Time is just the result of our brains trying to “see” a dimension that is not easily seen.

If the reader has been reading other posts of mine, in one post that I wrote I talked about the possibility of humanity to be able to fully perceive other dimensions by either evolving or deriving another sense.  In which case, if I follow the same conclusions of that post, I think it is possible for humanity to either break the boundaries of the five senses, or derive other senses using the fundamental five.  This will inevitably change our percievement, which raises the possibility of being able to perceive more dimensions past three.

So, what would the fourth dimension look like?  Would we still perceive it as the passage of time?  Or would another phenomena take place?

Today was amazing.  Not only do I understand why theoretical physicists and mathematicians think that the fourth dimension is time, but by combining other thoughts and conclusions that I have made, I have deduced that time just could be the manifestation of our percievement, which does not necessarily mean reality.

And well, this class also showed me once again how math builds upon itself.  I finally understand why finding domain and ranges are so important.  And by following the foundations of practices of functions with one variable, processes can be figured out and followed to functions with more than one.  (Derivatives, Integrals, etc.)



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