The journey into the 4th Dimension 4/19/12 Nature of Math The world we live in today is a world of 3-dimensions filled with objects that are zero, one and two dimensions. We all walk around in our 3-dimensional world thinking there could be no other dimensions. But would you believe me if I were to tell you that there is a 4th dimension that lies past our daily experience? The truth is that there is a 4th dimension and it’s not that far away, the crazy thing is that there could be an infinite number of other dimensions out there as well that we will never see and that our minds cannot even begin to fathom.
In order for you to fully understand the possibility of a 4th and possibly other dimensions I first need to explain the three prior and how they work. Let’s start with 0 –dimensions. When we classify an object’s dimensions we classify it according to the number of degrees of freedom it has. Therefore a 0-dimensional object would have zero degrees of freedom and would be represented as a point. With 0-dimensions you do not need any information to locate a point within that dimension. This is true because any 0-dimensional object has no length width or height.
Now think about taking that point and simply sweeping it to the left like you are drawing a line with the point. By sweeping the point in a line you have just taken a zero dimensional point and created a 1-dimensional line. All of 1-dimensional space is a line. Within a line there is only one degree of freedom, or one direction in which the line is capable of moving. It may seem like a line should be classified as a 2-dimensional object because it can move left and right but really it is based on how many different directions the line travels, which is one left and right. Now think about a line as your street.
Your specific house would only be one point on that street and in order to find it you would only need to tell one number in order for it to be found. Now if we take the 1 dimensional object and try and make it into a 2-dimensional object all we have to do is repeat the same process as before, take the line and find a new direction it can move. In the case of the second dimension we are going to take the line and move it vertically (perpendicular to the original line) in a sweeping motion, thus creating a plane. Along with creating a plane you have also just created the 2-dimension.
Inside of this world of 2-dimensions you now have the freedom to go left and right and up and down. 2-dimensional objects are all around us, squares, triangles, circles. A 2 dimensional world would be one where everything is flat, people would not be able to see depth or width we could only see what is in front of us in our flat world. Crazy huh? You may have noticed the trend by now on how we move into new dimensions by simply sweeping the current dimension in a new direction. So when we take our 2-dimensional plane and sweep it up and down it will form a cube. This creates the move from 2nd to 3rd dimension.
The 3rd dimension is one in which I am assuming you are fairly familiar with considering we live in a 3-dimensional world. Anything in our world that is tangible would be something 3-dimensional, so for example your cat, your favorite pants, a cube. Three dimensional object now have the ability not only to move left and right or up and down on a plane but can also incorporate depth and width into the picture You may now be asking “well if we live in the 3rd dimension where is the 4th dimension and what is it? ” Great Question! We would make the 4th dimension the same way as we have made all of the others.
Simply take the third dimension (for our sake lets say a cube) and slide it into a new direction perpendicular to all three previous directions. This may seem tough because we do not know any other directions aside from the three we are confined to in our world. But supposing we drag our 3-d cube in this new direction, then the 3-d cube now becomes 4-dimensional. We know this is true because in order to locate a point on this new figure we would need four different directions. This shows that there very well could be a 4th dimension out there somewhere.
Some people believe that time could be the 4th dimension, but it is still not determined. Also it could mean that there are hundreds of millions of other possibilities for dimensions as well. And while we can’t see the fourth dimension or wrap our minds around it we can now depict it to others. I chose this topic for my presentation because dimensions were my favorite topic of the class this year. They intrigued me, and made me question a lot about the world I perceive and live in. Also dimensions made me want to further pursue math and see how it relates to me in other ways that I didn’t realize.