image by Maths Mateo Imagining the 4th Dimension. Small note: the above image is a four dimensional hypercube, or at least the best representation of one we can make in the third dimension. Things to read by me also: Klein Bottle Mobius Strip The first dimension. A point. Right there, just one. Remember these from geometry? No? Well that’s okay; it’s much like a coordinate. Coordinates give the location of something, a certain point where something is, but that point does not have any dimensions, it has no size and is therefore imaginary. Quite like a coordinate, it’s not like you can see what they look like; they only give the position in a system. Secondly, we add another point of unknowable size and draw a line between the two. This is a first dimensional shape, it has length only. The second dimension. For the purpose of this we shall imagine that the first dimension is the line up one side of a rectangle (except there’s nothing else), now, to get to the second dimension we simply add in another side, much like giving a line at 90 degrees from this rectangle, branching off as such. This allows us to see how we may form a two dimensional shape. A two dimensional shape has length and width, but no depth. If you were a flatlander (common name for hypothetical two dimensional creatures) you could perceive the third dimension but only in two dimensions. For example, a ball would appear as a small point which grows inexplicably larger as it passes by until it shrinks again and disappears from sight. The third dimension. Pfft, easy, you’re thinking. Well yes, we do understand this one very well, as we spend our lives in it. Length, width and height. Here’s another way to think about it: a fly walking across a newspaper can be thought as a flatlander, of two dimensions. The third dimension would be if we could magically fold the paper, allowing the fly to cross from any one point to another completely different point. To make our lives easier, it will help if you imagine the third dimension like this: the one you fold through to jump from one point to another in the dimension below. The fourth dimension. If we can designate the first three dimensions, length width and height (respectively) then what could we designate the fourth dimension? An appropriate word seems to be ‘duration’ as we can imagine the fourth dimension as a line between two points in the third dimension. For example, a line drawn between a snapshot of yourself a minute ago and yourself now would be a line in the fourth dimension. If you were to see yourself in the fourth dimension you would look not unlike a snake or a slinky, with your first stages of growth at one end and you in a casket at the other. Much like our two dimensional flatlanders, we can only see cross-sections of the dimension above, so if we are not unlike an undulating snake in the 4thdimension, then as third dimensional creatures we can only see a cross section of ourselves. Do you remember my previous article about the Möbius strip? Well, if you take a strip of paper loop it in a circle but turning one of the ends 180 degrees and draw a line around it you will end up where you started: it miraculously only has one side. Now, if we imagine ourselves as a flatlander walking along this Möbius strip, only being able to perceive things in two dimensions we would not be aware that as we walk along this ‘flat’ surface, in the dimension above (3rd) the Möbius strip is actually curving and looping. Hence we can see that we can be unaware of our own movement in the third dimension. This relates to us in the third dimension, as we experience life as a linear pathway, start and end. Yet, as we experience these three dimensional cross-sections of snake-like selves in the 4th dimension in a linear progression, we are unaware of how these cross-sections amount to a twisting and turning 4th dimensional self. I just thought I’d make you a recap diagram as well, so here you go:

image by Maths Mateo

Imagining the 4th Dimension.

Small note: the above image is a four dimensional hypercube, or at least the best representation of one we can make in the third dimension.

Things to read by me also:

The first dimension.

A point. Right there, just one. Remember these from geometry? No? Well that’s okay; it’s much like a coordinate. Coordinates give the location of something, a certain point where something is, but that point does not have any dimensions, it has no size and is therefore imaginary. Quite like a coordinate, it’s not like you can see what they look like; they only give the position in a system.

Secondly, we add another point of unknowable size and draw a line between the two. This is a first dimensional shape, it has length only.

The second dimension.

For the purpose of this we shall imagine that the first dimension is the line up one side of a rectangle (except there’s nothing else), now, to get to the second dimension we simply add in another side, much like giving a line at 90 degrees from this rectangle, branching off as such. This allows us to see how we may form a two dimensional shape. A two dimensional shape has length and width, but no depth.

If you were a flatlander (common name for hypothetical two dimensional creatures) you could perceive the third dimension but only in two dimensions. For example, a ball would appear as a small point which grows inexplicably larger as it passes by until it shrinks again and disappears from sight.

The third dimension.

Pfft, easy, you’re thinking. Well yes, we do understand this one very well, as we spend our lives in it. Length, width and height. Here’s another way to think about it: a fly walking across a newspaper can be thought as a flatlander, of two dimensions. The third dimension would be if we could magically fold the paper, allowing the fly to cross from any one point to another completely different point.

To make our lives easier, it will help if you imagine the third dimension like this: the one you fold through to jump from one point to another in the dimension below.

The fourth dimension.

If we can designate the first three dimensions, length width and height (respectively) then what could we designate the fourth dimension? An appropriate word seems to be ‘duration’ as we can imagine the fourth dimension as a line between two points in the third dimension. For example, a line drawn between a snapshot of yourself a minute ago and yourself now would be a line in the fourth dimension.

If you were to see yourself in the fourth dimension you would look not unlike a snake or a slinky, with your first stages of growth at one end and you in a casket at the other.

Much like our two dimensional flatlanders, we can only see cross-sections of the dimension above, so if we are not unlike an undulating snake in the 4thdimension, then as third dimensional creatures we can only see a cross section of ourselves.

Do you remember my previous article about the Möbius strip? Well, if you take a strip of paper loop it in a circle but turning one of the ends 180 degrees and draw a line around it you will end up where you started: it miraculously only has one side. Now, if we imagine ourselves as a flatlander walking along this Möbius strip, only being able to perceive things in two dimensions we would not be aware that as we walk along this ‘flat’ surface, in the dimension above (3rd) the Möbius strip is actually curving and looping. Hence we can see that we can be unaware of our own movement in the third dimension.

This relates to us in the third dimension, as we experience life as a linear pathway, start and end. Yet, as we experience these three dimensional cross-sections of snake-like selves in the 4th dimension in a linear progression, we are unaware of how these cross-sections amount to a twisting and turning 4th dimensional self.
I just thought I’d make you a recap diagram as well, so here you go: