The Book Flatland Refering To The Book How Can Time Be Considered Another Dimension?

Question

Another Question My Teazher Asked Me This What Two Dimensional Shapes Can Result When Various Three Dimensional Objects Are Sliced

Answer 1

Flatland is the famous book that proposes the view of a 2D world when a 3D creature enters it. This would explain how we would react to a possible 4D creature.

According to Einstein’s equations there are at least 11 dimensions, and according to String Theory there could be 20 so the higher dimensions are there, we just can't see them.

According to Einstein space time is the fabric of space. So time isn't a dimension it is part of space. However, most people think of time as the fourth dimension.

A 2D creature would have the area of itself as its volume. So if a sphere entered a room with a circle the 2D circle would see a circle with an expanding radius. He would only see part of the 3D sphere at a time. If a 4D creature appeared to us then we would only see a fraction of it at one time. If time was the fourth dimension then it would be like one huge worm that started when it was created and finishes when it dies or is destroyed. We would only see one segment of the worm at a time; about 1 second's worth.

To create a 3D shape you take a 2D shape and rotate it through the third dimension. Therefore slices of that 3D shape would be just like the original 2D shape that the shape was rotated from. For example if you rotate a square through the third dimension you would have a cube; with slices of it being squares. If you rotated a circle through the third dimension you would create a sphere and when you saw parts of it you would see slices of a circle.

Now if you take a cube, a 3D object, and rotate it into a higher dimension then you would create a tesseract: http://en.wikipedia.org/wiki/Tesseract.
This imaginary shape would be a strange one and slices of it would be cubes. It would be like taking 6 cubes and putting them into the space of 1 cube, along with the original space of the inside of the cube. You see as you increase the number of dimensions the volume dramatically increases.

Answer 2

Imagine a 3d pencil passing through 2d space. First you see a black dot (pencil tip), then a brown circle appears around the dot (the sharpened wood), first the circle grows slightly and then abruptly changes into a yellow hexagon (the six flat sides of a yellow pencil). The thin (because it's just paint) yellow hexagon surrounds a thicker brown hexagon (the wood) and in the center a small round black dot (the pencil lead). After a while the hexagon disappears and is replaced by a metal circle surrounding a pink rubber disk (the eraser). Very quickly the metal circle is gone and only the pink disk remains. Shortly afterwards this completely disappears and nothing is left. This whole process took place over a period of TIME.

If the 3d pencil passed completely through the 2d space at a constant rate (not stopping or changing speed) then a 2d person observing this strange object that appeared out of nowhere, changed shape and color, and then disappeared, might be able to think of time as a third dimension and picture in her imagination an overall strange (3d) shape that all at the same time possessed the different changing shapes that appeared as simple 2d objects. In other words, by thinking of time as a third dimension the 2d person can picture what we would think of as simple 3d object, a pencil.

We, as 3d people, can do this if we imagine a changing process that takes place over time as existing simultaneously in all of its different aspects. Imagine yourself as a baby, a child, a young adult, a mature adult, and an old adult. Now imagine yourself as a long, stretched out object that at one end is a baby and at the other end is an old person, all at the same time. This is one way of considering or picturing time as another dimension.

Second question: Use your imagination to picture it, or just look up "Conic Sections" for some famous examples.

Answer 3

time can be considered