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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 30 2012: Looks like Godel used modal logic to make some proofs of things.

    But yeah, it seems like a tool for studying logic through semantics. I'm quite shocked to find the use of equivalence here, instead of so many other places where it should be used for example in math and physics.

    If we say that the excluded middle is equivalent to the exclusive middle, it's easy to derive that random and non-random are equivalent. This equivalence would be present in the mathematical models, and would also be assumed to apply to physical reality. I have many good examples to support this, and the more I search for counterexamples it seems that all I can find is more compelling reasons to support it.

    To say that "random and nonrandom are equivalent" is a statement which begs a lot of justification. I have that justification in the form of highly credible examples and some very solid mathematics. It is all really very simple, nothing complex whatsoever. A child could understand my argument.

    And, it almost sounds absurd to say that random and nonrandom are equivalent. But the numbers dont lie. Think of how absurd it seems to say that different frames of reference are equivalent. Yet we know that Relativity is indeed correct.

    If you start with equivalence at LEM, Law of Identity and Law of Noncontradiction, then all of these results follow and I believe that Relativity itself can be explained in terms of these first principles. So, if true, this would be a very big deal. I simply cannot do it alone. I need to share the idea wherever possible and elicit as much high quality criticism as possible, and if it is wrong then so be it, but if it's right then mankind gets a great big birthday gift.
    • Sep 30 2012: I'm not quite following you but perhaps other people can.
      I will remain sceptical for now.

      On the topic of random numbers being not random... perhaps read into deterministic automata (theory behind computers). It basically shows that 'random' doesn't exist within computers.
      This doesn't really claim anything about the real world though unless you believe that people do not have free will etc. (aka everything in the universe is deterministic aka everything was already determined at the big bang or before... well whenever it started, it could be infinity ago).

      But I see that someone else has already said things about this...
      • Sep 30 2012: Law of Excluded Middle says you can only have truth values 0 and 1.

        Law of Exclusive Middle says there is no 0, there is no 1, all truth values must fall on the open interval (0, 1) noninclusive.

        Consider that 0.999... = 1. Consider 0.999... as a magnitude of truth, or an expected magnitude.

        For anything which is true, we can [a] be certain of it's truth with a certainty of 1, or [b] we can be uncertain of this truth with magnitude 0.999... . Quantitatively they are indistinguishable because .999... = 1. The only difference being qualitative. In one case we are certain, in the other we are uncertain.

        Certainty and uncertainty are equivalent in this example. We can easily generalize this and make lots of examples.

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