26th January 2014
The perception of the space is based on how we as humans view our surroundings. We try to develop our understanding of the basic mechanism based on our observations. The science teaches us how to be precise in our observations by making measurements. One of the implicit assumptions is that whatever we observe is the extent of reality. The measurements are interpreted based on our sensory inputs, mainly visual, which result in the (t, x, y, z) description we call continuous. One of the most critical component of any description is the definition of the origin. How we measure an origin therefore becomes crucial in developing a scientific description. If we think about it, we can not accurately measure the value of zero. We can assign a value "zero" based on our instruments limitations, but that is merely the lower limit. Therefore the description is restricted to the lower and the upper limits. Measuring an accurate zero is as difficult as measuring an infinite, measurements which really test the limits of our capabilities.
When providing a theoretical description, rather than restricting ourselves to any specific coordinate system, we should first try to define what our optimum coordinate system will consist of. The definition of origin or the measurement of zero is the most crucial stage of our description. But the problem is that we know that we are limited in our capabilities and hence an origin which can be used as an accurate reference, is not available. This represents a fundamental problem which basically leads to the introduction of the concept of the symmetry. We will discuss symmetries and their implications later on, but to describe a system by an observer with a limited capability, we need to introduce a pair of observers instead of just one. And that implies that such measurement space is discrete in nature i.e. two observers defining an action rather than just one. For details please refer to the chapter ORIGIN. Please note that we are not getting into the argument of continuous versus discrete. We are merely stating that an observer of finite capability will not be able to determine origin accurately and hence we need a measurement space which is discrete in nature to explain the observer's results.
On a lighter note, the movie Gravity has been nominated for various BAFTA and Academy awards. Great special effects but we feel that Sulu and Chekov did a much better job pushing those clunky buttons.
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KoopMandooka 8Jan 2014