Dimensions

I lay in bed. I look at the wall facing me, at the foot of the bed. I move my gaze to the right, following the wall. The wall stops, there is another wall at right angles stopping it from going any farther. There is a corner between them where they join – two walls but only one corner. I follow the corner upwards to where it hits another wall. This one is called the ceiling. It is at right angles to the other two. Now we have three walls and three corners. The three corners descend towards each other and meet to form a super corner. What is next. Ah, another wall. This one must be at right angles to the other three and, when it is in place it must produce how many corners – I suggest six. The problem is where you put this wall to satisfy the conditions. I try this wall in different positions, nothing works. Something is missing. We need another place. What is missing must be the fourth dimension. Problem solved, we have a tesseract.

Now we have to test the hypothesis.

If you unfold a square – two dimensions, you end up with four lines – one dimension.

If you unfold a cube – three dimensions, you end up with six squares – two dimensions

If you unfold a tesseract – four dimensions, you should end up with cubes in three dimensions but how many? Using the previous examples, the answer seems to be twice as many objects as there are dimensions, so eight. Now we have four dimensions in one room.

This would be a good way to build a space saving house. Build eight cubes, call them rooms and then fold them into the fourth dimension. ( You might need to hire a special tool to do this ). No corridors are needed because all of the rooms are next to each other. This house only takes up as much space as one room but it has eight rooms, each one is as big as the house.

We can draw points, lines, squares and cubes on paper in two dimensions. Can we draw a tesseract reduced by two dimensions and draw it on paper in two dimensions? The answer, surprisingly, is yes.

wikimedia.org/wikipedia/commons/4/45/Dimension_levels.svg

The most recent physics, string theory, predicts we live in a space with ten dimensions, M theory requires eleven  This is where it gets difficult. Where do you fold all these dimensions? It seems that we can just about visualise and cope with eight cubes folded into a tesseract in four dimensions but eleven dimensions? They must all be very tightly folded. Quantum physics, of course stipulates space with an infinite number of dimensions.

So far we have stayed in the room but if you start at any corner where two walls meet and then follow this corner until you come to a third wall, you will be in a super corner where the three walls meet. If you get right into the corner then you are at a point. A point has position but no dimensions. If you now go further into the corner, past the point with no dimensions you suddenly burst out into a different universe where there are no walls, no limits and no corners, only cabbages and flowers, butterflies and bees. Different rules. How many dimensions? Is colour a dimension, is smell? What about time?