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To revolutionize both math and physics by the grassroots popularization of a new quantitative tool which is introduced below.

We start with the Law of the Excluded Middle. Consider it's complement and call this new law the Law of the Exclusive Middle. Let these two laws be equivalent. You now have something similar to Fuzzy Math, but it is very different. These two laws are connected by equivalence which is very different than Fuzzy Math.

Next consider Descartes "I think therefore I am". We reverse engineer this into a statement which reflects our foundation (above), to derive "Maybe I think therefore maybe I am". We keep both of these statements and set them as equivalent.

We then proceed to all of the standard tools of mathematics which are used for the analytic quantification of magnitudes. In math, things are said to exist. In our new system things are regarded as "maybe existing". We keep both of these tools and regard them as being equivalent. We will call one of them Mathematics, and the other should be called something like Conjectural Modeling to reflect that it is based entirely on absolute indeterminacy.

We now have a quantitative tool which is split down the middle, essentially a kind of mirror image. On one side, absolute determinacy. On the other side, absolute indeterminacy. Both sides held together by equivalence.

We now have a tool which is capable of addressing both the equivalence inherent to relativity, and the indeterminacy which is inherent to Quantum Mechanics.

We can write correct and accurate quantitative models using either system. In fact, for every possible question there should be two solutions. One based on determinacy, and the other based on randomness. These two answers are equivalent. As an example, whether I know with absolute certainty that I have 10 dollars, this is quantitatively identical to not knowing but "expecting" that I have 10 dollars where 10 is an expected value instead of a value known with absolute certainty.

I have many examples and a lot of math to reinforce these views. I am convinced that this solution is extremely important.

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  • Sep 29 2012: Yes, it is a bit different. Currently, in mathematics it is believed that stochastic and non-stochastic processes are two very different things. Indeed they are. It is difficult to call them opposites, but may be considered complementary by some.

    In my view these would be considered equivalent processes. Equivalent in the same sense that two completely different frames of reference can be regarded as being equivalent in relativity.

    I have several worked examples which illustrate why we can say that random and non-random processes can be regarded as being equivalent. This applies to physical as well as mathematical processes.

    The best way to explain these examples is with a short video. I have two videos on YouTube and I will try to link to them here:

    The first video should play automatically at this link. It is called "Two Physicists Walk Into A Bar"
    http://www.youtube.com/user/HeliumXenonKrypton?feature=mhee

    The second video concerns the Sierpinski Triangle, a very famous fractal:
    http://www.youtube.com/watch?v=aM95mNEQsY0&list=UUpxczJY6eD7lNBzfOATQLyg&index=3&feature=plcp

    This general approach is a valid application and extension of the methods of Relativity. Because it is so closely related to randomness, it should be clear that it provides a way to connect General Relativity with Quantum Mechanics.
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      Sep 29 2012: The Sierpinski Triangle - when viewed through the randomness method - does not provide a duplicate of the Sierpinski Triangle. You will have triangle points left over. Thus the Sierpinski approximation of the Sierpinski triangle is not equal. The equivalence that is mentioned in the video you offered is based on a provable fallacy.
      • Sep 29 2012: Incorrect. When generated by the random algorithm, you let the process go through infinitely many iterations to generate the triangle. The two fractals, generated by their respective algorithms are identical with the possible exception of a few points needed to start the random process, but that can be eliminated by selecting a starting point properly.
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          Sep 29 2012: If your starting point is not random, then you have violated the entire randomness method. Those exceptions (the extra points) are important if you are putting a theory together. Random =/= deliberate just as approximate =/= exact.

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