The earlier article the Universe Aug. 20, 2007 showed why we feel humankind needs to begin searching for a new paradigm based on the experience or observations we can make in three-dimensional space instead of using abstract mathematics.

Mathematics is an important tool for science to quantify our experience however, it should not replace them.

The following example explains why.

If someone was asked to devise a mathematical model defining why there were two apples left a grocery bag after some had been removed he or she could say that originally, there were four apples and two were taken away. However, it would also be possible to say that there were six apples and four were taken away.

Both of the mathematical models give the same the accurate results but are ambiguous as to the reasons. (In one mathematical model, there were originally six apples, while in the other there were four.)

The only way to confirm which one of them is correct would be to know how many apples were originally in the bag.

However, the experience of someone who had shopped at the store where the apples bought would know they can only be purchased in packages of four.

This would give a model based on the premise that there were originally four apples a firm foundation in his experiences.

This same concept could and should be applied to validate mathematical mechanisms scientists feel may be responsible for the physical laws of nature. In other words, scientists should use their experiences along with results of of their abstract equations to validate their mathematical models.

For example, string theorists have devised very accurate quantitative mathematical models of the physical laws based on the existence of higher “curled” dimensions. However, the existence of higher curled dimension has no basis in our experiences because no one has ever observed or experienced a higher “curled” dimension. Therefore, string theorists cannot be sure that these curled dimensions exist.

Abstract mathematical equations paint a picture of universe, which can be interpreted by our imaginations. But we must be careful not to assume that just because they give the correct end result that they define reality because, as the earlier example showed it is possible to mathematical define a correct solution of that problem based on the non-reality of six apples.

We will spend the upcoming weeks, months and years showing how one can extrapolate his or her experiences in our three-dimensional world to one of four *spatial* dimensions not only explain and predict the existence of Dark Matter and Dark Energy but to use those experience to validity the equations used to quantify them.

Later Jeff

Copyright Jeffrey O’Callaghan 2007

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