Where does dimensionality come from?

Question: Where does dimensionality come from!?
Best Answer - Chosen by Asker:

An attempt to classify that which presents itself to us in the form of a particular distinctive perspective!.Www@QuestionHome@Com

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We live in a space with three different degrees of freedom for movement!. We can go to the left or to the right!. We can go forward or backward!. We can go up or we can go down!. We are allowed no more options!. Any movement we make must be some combination of these degrees of freedom!.

Any point in our space can be reached by combining the three possible types of motion!. Up / down motions are hard for humans!. We are tied to the surface of the Earth by gravity!. Hence it is not hard for us to walk along the surface anywhere not obstructed by objects, but we find it difficult to soar upwards and then downwards!. Space is more 3-D for a bird or a fish than it is for us!.
Brief history of ideas on dimensionality!.

Euclid: In the formulation of Euclidean geometry a fourth dimension was not even considered!.

Aristotle: He was the first person to state categorically that the fourth dimension is impossible!. In his work 'On Heaven' he wrote, "The line has magnitude in one way, the plane in two ways, and the solid in three ways, and beyond these there is no other magnitude because the three are all!."

Ptolemy:(A!.D!.150) In his book 'On Distance' Ptolemy gave a 'proof' that the fourth dimension is impossible!. Draw three mutually perpendicular lines he suggested!. Try to draw another line perpendicular to all of these lines!. It is impossible!. The fourth perpendicular line is "entirely without measure and without definition!." The fourth dimension is impossible!. This is really not a legitimate proof of the 4th dimension!. It is merely a proof that we cannot visualize the 4th dimension!.

Riemann: On June 10, 1854 a new way of looking at geometry was put forward in a famous lecture by the mathematician Bernhard Riemann!. He generalized Euclidean geometry to a non-Euclidean geometry allowing for curved surfaces and any number of higher dimensions!.

Riemann's ideas started many people thinking about higher dimensions!. People found that the ramifications of the existence of higher dimensions were astounding!. If you could manipulate the fourth or higher dimensions you would have god-like powers!.

You could walk in such a way that no wall
could stop you!.
You would appear to others to be passing
through walls or doors!.
When hungry you could simply reach into the
refrigerator, without opening the door!.
You could extract a section of an orange
without peeling it!.
You could do surgery without cutting skin!.
You could disappear and reappear at will!.
You would be able to see people who
had been buried by an avalanche!.

The standard method by which people try to understand higher dimensions is to try to see how a lower-dimensional creature would see a three-dimensional world!. For this purpose 2-D worlds are often used!. Let us consider a 2-D world!. To jail a criminal in such a world a circular boundary would have to be placed around the criminal!. To extricate the criminal, all a 3-D creature has to do is to peel him off the 2-D world, and redeposit him elsewhere on his world!. This feat, which is quite ordinary in 3-D, appears fantastic in 2-D!. No one in the 2-D world understands what the up direction means!. The internal organs of a 2-D creature would be visible to us!. It would be trivial to reach inside a 2-D creature and perform surgery without cutting the skin!. Viewing this 2-D flatland, notice that we are omnipotent!. The 2-D creature cannot hide from us!. He would see us as having magical powers!.

In the later part of the 1800's the idea of a fourth dimension became very popular!. In 1877, a scandalous trial in London gave the idea of extra dimensions international notoriety!. A magician and psychic by the name of Henry Slade was arrested for fraudulently using palmistry, etc, to deceive his clients!. Prominent physicists of the time came to Slade's defense claiming that his psychic feats actually proved that he could summon spirits from the fourth dimension!. Detractors said that scientists, because they are trained to trust their senses, are the worst possible people to evaluate a magician!. To objectively test a magician/psychic you need another magician!. They will know when any tricks are being made!.Www@QuestionHome@Com