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Dimensions 101 (for mathematicians only)
Is there a difference between a dimension and a coordinate, between width and latitude? If so, the mathematicians are unware of it. Of course, it is no wonder that they conclude that you live within a four-dimensional sphere.
Relativists confuse dimensions with coordinates
It is entirely inexplicable that in the last 10,000 years the mathematicians have not realized that there is a difference between a dimension, a coordinate, and a vector. The three dimensions are known as length, width, and height and have to do with architecture and orientation. The three coordinates are known as longitude, latitude, and altitude and have to do with location. Dimensions point outward from an object. Coordinates point inward toward an object. The three vectors are known as depth, breadth, and elevation. They describe the mutually orthogonal directions in which an object may move. No rational person would confuse length (orientation) with longitude (location) or with depth (motion)!
One could argue that the mathematicians simply have a different definition of the word dimension: "the number of coordinates." But then, this definition leads them to amusing conclusions that by far surpass the centuries-old supernatural explanations proposed by traditional religions. Relativists claim that, according to the mathematical definition of dimension, the Universe is four-dimensional.
How is this possible if we cannot even imagine such a monster? Are they simply putting understanding of the Universe beyond the reach of humans to justify their own ignorance? (i.e., God works in mysterious ways!)
The mathematicians claim that in addition to length, width and height (dimensions) we need an extra 'dimension' known as time to specify an object's LOCATION in space!
There are so many conceptual errors in this breathtaking statement that one doesn't know where to begin. Are the mathematicians talking about locating an object on the surface of another object? If so, why do they use dimensions and not coordinates? (Oh, I forgot. A mathematician doesn't understand the difference between a dimension and a coordinate. Scratch that!) Is time a dimension? If so, in what ways is time similar to height?
To make a long story short, it turns out that the mathematicians are NOT talking about dimensions, coordinates, or vectors. Mathematics has no use for such qualitative concepts. A mathematician deals exclusively with number lines. The mathematicians simply got into the bad habit of calling their number lines dimensions, coordinates, and vectors.
Number lines have at least one important property that dimensions, coordinates, and vectors lack: magnitude. Dimensions, coordinates, and vectors have at least two properties that number lines don't have: direction and orthogonality. In what direction does a series of numbers point, anyway? To what does a set of numbers run perpendicular?
Therefore, when relativists propose that we live within an unimaginable 4D sphere, the D in '4D' does not allude to dimensions, but to number lines. The 11 and 26 'dimensional' worlds talked about in String Theory are no different.
However, the spherical '4D' universe of relativity suffers from an even more fundamental fatal problem. What contours and gives shape to the sphere?
Relativists have three irreconcilable answers to this question, take your pick:
1. It is an invalid question like asking what's north of the North Pole.
2. It is an unscientific question because we have no way to test the hypothesis. The question is philosophical
3. It is not expanding into anything. The closed space is all there is.
The correct answer is that relativists don't understand the Scientific Method. In Science, it is the responsibility of the presenter to propose a rational hypothesis that makes or breaks his or her theory, not for the philosophers at the other side of campus to figure it out.
It is as a result of misdefining the crucial term in their presentation -- 'dimension' -- that the mathemagicians ended up with four dimensional (4D) spacetime. Einstein got the part about length, width and height right, but he incongruously applied these terms to space rather than to objects. In the religion of Mathemagix, it is not the table which has length, width, and height, but rather the empty space that it 'occupies' or 'displaces'. The mathemagicians think of space as an ocean, as a volume of water. Carl Sagan referred to space as the 'Cosmic Ocean'. A mathemagician is not interested in objects such as tables and rocks and trees. He focuses on and works with the empty part of the glass. He is hypnotized by the 'half empty' side of 'physics'.
The mathemagicians also made mess of the 'time' part of their presentation. They refer to time as a 'dimension' when time is neither a dimension nor a coordinate. Time is definitely a number line. Time lacks direction and orthogonality and has what no dimension has: magnitude. What is the magnitude of width? If you reply that you have to measure the table in order to tell me, you are clearly referring to a number line: a series of tick marks on a graph line.
What Einstein and his generation did is merge and blend two irreconcilable notions: 3D objects with the number line known as time. He stirred heart with love and came up with spacetime. He preempts your next question by saying that you should not try to visualize this 4D monster because we petty humans, with our limited intelligence, are stuck in 3D and will never be able to see the glory of God. We can only relate to 4D spacetime through analogy. You have to travel to Flatland and think of a Flatlander trying to imagine our 3D world. The stealthy way in which Einstein does it is to replace the dimension of height on his graph with the 'dimension' of time, leaving you with either 2 or 3 dimensions on the graph throughout his presentation.
Is it rational to pit the single dimension width against time?
The Math Asylum says it is.