Basics of Dimensions
Introduction to Dimensions
According to Basics of Dimensions in different theories, we can visualise higher dimensions and the geometrical structure of higher dimensions. We might be living in higher dimensions unknowingly and what supernatural powers a being of higher dimensions would possess.
First of all let’s understand what we mean by Basics of Dimensions? Dimension of a point is defined as the minimum number of coordinates that are needed to specify that point in it. For example, to specify a sheet of paper we need two coordinates only; length and breadth. Therefore it is a two dimensional object. But to specify a cube in space; 3 coordinates are needed. these are- length breadth and height. We call it a three dimensional object.
According to classical physics there are 3 Basics of Dimensions with space; length, breadth and height and one dimension is of time. String theory requires 10 dimensions; but as per M theory total dimensions are 11. In Bosonic string theory, Space-time is 26 dimensional. But now the Question arises, if there are so many dimensions in existence then why we are not able to perceive them. Why we cannot feel the presence of higher dimensions?
Limitations in Basics of Dimensions
Actually We might be living in higher dimensions without being aware of it. But because of the limitations of our brain and senses we may not be able to perceive them. According to some researches extra dimensions may be “curled up” at extremely small scales. This scale is so small that we cannot see them with our experiments based on current technologies.
As far Basics of Dimensions; we live in a three dimensional world, it’s very hard for our 3 dimensional brain to visualize higher dimensions. There is a process known as Compactification, where higher dimensions are curled in on themselves. On changing our reference frame and going into microscopic level we will find higher dimensions.
Understanding Basics of Dimensions
Let us understand Basics of Dimensions with the help of a simple example; suppose we are looking at a rope from some distance which is tied between two rocks. From this distance we will see only one dimension of the rope i.e. length. Now Imagine that an ant is crawling onto the rope.
So from the frame of reference of ant, the rope is at least 2 dimensional as it can see it’s breadth and thickness also along with its length. The ant can also feel the grooves and roughness of the rope. If we go to microscopic level and see from the reference frame of atoms then we will see a whole new world of 3 dimensional atoms having solid nucleus and electrons revolving around it in 3 dimensional space.
As per some physicists everything in this universe is made up of tiny vibrating loops known as strings, according to string theory. So now you can understand how we can find higher dimensions at the microscopic level.
Understanding Basics of Dimensions; There is no length, no breadth and no height of an object in the zeroth dimension. Example of zeroth dimension is a point. Lets imagine someone is living in the zeroth dimension then he would neither have any body nor any shape. He can not move in any direction like forward, reverse, up or down. zeroth dimension is the basis of all the higher dimensions.
An object in first dimension has only one dimension i.e. length. A straight line is an example in Basics of Dimensions of first dimensional object. We can get straight line by joining two points. A one Dimensional being can move only in a straight line. It cannot move in other dimensions like left, right and upward or downwards directions.
Second Dimension (2D) objects also known as two dimensional or 2D objects are flat shapes. Some common examples of two dimensional shapes are squares and triangles. As the name denotes, two dimensional objects are made up of two dimensions length and breadth. There is no third dimension of height or depth. Therefore these objects are flat figures having non-zero area but zero volume.
Basics of Dimensions indicates If someone is living in two dimensions, then he would be able to move only on a surface without being able to move in up or down directions. He will not have any idea of the third dimension which is height. Can you imagine what will happen when a 3 dimensional object enters into the world of two dimensional being? Let’s understand it with an interesting example.
Basics of Dimensions; 2 Dimensional Being Watching 3D Apple
Suppose a two dimensional being present in his two dimensional space is watching a three-dimensional apple entering into his flatland world on a vertical axis perpendicular to the plane of the flatlander. But as we know a two dimensional being cannot see a three dimensional object.
So how would that 3 dimensional apple look like from the frame of reference of that flatlander? He cannot see the Apple untill it touches his 2 dimensional plane as it’s above his flatland and he cannot see anything which is above or below his 2 dimensional plane world. but as the Apple just touches the plane, he will see a dot which is nothing but the point of contact of the Apple to the plane.
Now as the Apple goes below his plane world, he sees a circle growing in size on his plane and the size of the circle is maximum when half of the Apple is above and half is below the plane and then the circle size becomes smaller and smaller and then a point and finally it disappears for him. It means the 2 dimensional being sees only the cross sectional view of the Apple that is cut by his 2 dimensional plane at that moment.
So for a person living in a particular dimension, objects of higher dimensions suddenly may appear from nowhere, may change shapes and size and then disappear into space. It may appear supernatural or kind of magic for a lower dimensional being but for that higher dimensional object it’s nothing special. It just moves in dimensions that are not perceived by him.
Third dimension (3D)
On adding one more dimension to 2 dimensional objects we enter into the world of three dimensions. This third dimension is of height. Therefore to represent three dimensional or 3D objects we need three coordinates length, breadth and height. that two dimensional objects are plane figures therefore have zero volume. But three dimensional objects are solid objects and therefore have non zero volume.
Some common daily life examples of three dimensional things are balls, chair, car and we humans. We live in a three dimensional world. This is the reason we can move in forward, reverse, up and down directions easily. As we have full control over the three dimensions of space. Fourth dimension Time is considered the fourth dimension. A four Dimensional being can move freely in time dimension. It would have full control over time. He would be able to move in any desired direction in time; past or future.