Say what? Yep: We spent a lot of time getting nowhere, just like the zeroth dimension! A line is one- dimensional 1D as it only extends one way like this sentence, which you can only read forward or backward.
A plane is two dimensional 2D ; it has length and width. A block is three-dimensional 3D ; it has length, width, and depth. Before we get started, let's be clear what we mean by a dimension. As a simple definition, adimension is a measure of extent. The dimensions of an object no, not a plain old object, buta monkey with Rainbow-colored fur, so this won't read like some boring math textbook refer to different directions in which an object extends.
The monkey has height how tall she is of course she's a girl, what else would she be? However, there are different kinds of dimensions, like space and time or if you want to getexotic, we can talk about the dimensionality of your thoughts or even your body odor. Weneed to explore the concept of a dimension a little further, so that you'll know exactly whichtype of dimensions we are discussing in this book. Let's begin with a simple geometric example. An infinitesimal point has zero dimensions 0D; that's "zero dee," not "oh dee".
Yeah, infinitesimal. Like that word? Surely you know the word infinity the largest number, right? If it were a number, you could add one to it and find a larger number. Infinity represents the concept that you can keep counting. If you want the previous picture to look less boring, you have to use your brain and imagine that it consists of from left to right a monkey's thought, a monkey's tail, a monkey's shadow, and a monkey. Any other direction is a combination of these.
So that's why we think of space as being 3D. Space appears to be 3D, but space-time is 4D. Time is a dimension in the sense that it is also a measure of extent it is a duration. But time is clearly a different type of dimension than length, width, and depth.
In this report, we're interested in a fourth dimension of space. That is, a fourth dimension that is very much like length, width, and depth, but not a combination of these i. String theory actually predicts that our universe has more than just three dimensions of space. Our universe might actually have 9 dimensions of space. Let's begin with the zeroth dimension. A 0D object is just a mathematical point. A single object in a 0D universe would take up all of the space.
Motion wouldn't be possible. It would be the ultimate prison, where you could only "do time," as the. You couldn't do anything physical in 0D, but it might suffice for a purely philosophical or spiritual world. The first dimension could be a line, but it could also be a curve like a parabola or a circle.
Curves are effectively 1D because any object living in such a space would have the same limited freedom that a line has: You can only go forward or backward. A plane is 2D, but a 2D world doesn't need to be flat; it could be curved like a sphere or a cylinder. Walking around in an open field is a largely 2D human activity. Notice that two lines intersect at a point and two planes intersect at a line.
We can use patterns like this to predict what the fourth dimension might be like. For example, by analogy, if two 3D universes hyperplanes were to intersect, they would meet at a plane. A 2D world would actually be quite unlike 2D drawings that we often draw on paper. When we draw a 2D picture on a piece of paper, we often draw the surface of a 3D object that we see with our eyes. Besides pure curiosity, 4D visualization has a wide variety of useful applications.
Mathematicians have long wondered how to visualize 4D space. In calculus, a very useful method of understanding functions is to graph them. We can plot a real-valued function of one variable on a piece of graph paper, which is 2D.
We can also plot a real-valued function of two variables using a 3D graph. However, we run into trouble with even the simplest complex-valued function of 1 complex argument: every complex number has two parts, the real part and the imaginary part, and requires 2 dimensions to be fully depicted.
This means that we need 4 dimensions to plot the graph of the complex function. But to see the resulting graph, one must be able to visualize 4D. Einstein's theory of Special Relativity postulates that space and time are interrelated, forming a space-time continuum of 3 spatial dimensions and 1 temporal dimension.
For example, the distance between two events is the distance between two 4D points. The light-cone also has a particular shape that can only be adequately visualized as a 4D object. Furthermore, Einstein's theory of General Relativity describes curvature in space-time. While it may not actually be a curvature into a physical spatial dimension, it is helpful to visualize it as such, so that we can see how space curves in 4D as a 3-manifold.
If space in the universe had positive curvature, for example, it would be in the shape of a 4D hypersphere—but what exactly does that look like? Many other interesting mathematical objects also require 4D visualization to be appreciated fully.
In , Edwin A. Abbot published a novel that depicts the problem of seeing dimensions beyond your own. Living in 2-D means that the square is surrounded by circles, triangles and rectangles, but all the square sees are other lines. One day, the square is visited by a sphere. On first glance, the sphere just looks like a circle to the square, and the square can't comprehend what the sphere means when he explains 3-D objects.
Eventually, the sphere takes the square to the 3-D world, and the square understands. He sees not just lines, but entire shapes that have depth. Emboldened, the square asks the sphere what exists beyond the 3-D world; the sphere is appalled.
The sphere can't comprehend a world beyond this, and in this way, stands in for the reader. Our brains aren't trained to see anything other than our world, and it will likely take something from another dimension to make us understand.
But what is this other dimension? Mystics used to see it as a place where spirits lived, since they weren't bound by our earthly rules. In his theory of special relativity, Einstein called the fourth dimension time, but noted that time is inseparable from space. Science fiction aficionados may recognize that union as space-time , and indeed, the idea of a space-time continuum has been popularized by science fiction writers for centuries [source: Overbye ].
Einstein described gravity as a bend in space-time. Sign me up for the newsletter! Don't worry will send you cool content only a few times a month! Skip to content.
A hypercube with its vertices numbered 1 to 16 This drawing of a tesseract does not perfectly represent what it looks like because what we have above are two dimensional drawings since they are on a computer screen of three-dimensional models of a four-dimensional tesseract.
An hourglass timeclock with sand Modern scientific theories such as string theory demand the existence of higher dimensions and this particular theory requires 10 dimensions. References 1. About the Author Shiven is a secondary school student who is enthused by science, and especially physics. Leave a Reply Cancel reply Your email address will not be published. This website uses cookies to improve your experience. We'll assume you're ok with this, but you can opt-out if you wish.
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