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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: Thank you for that suggestion !! I actually did find something which sounds a lot like what I've been claiming.

    Quoting Wikipedia's article on Modal Logic
    "Likewise, a prefixed "diamond" () denotes "possibly p". Regardless of notation, each of these operators is definable in terms of the other:
    [square p] (necessarily p) is equivalent to [not diamond not p] ("not possible that not-p")
    [diamond p] (possibly p) is equivalent to [not square not p] ("not necessarily not-p")"

    This is strikingly similar to what I have been proposing. The only differences I can see (at this point) is that modal logic is typically used in epistemology and I dont know whather this has been applied to physics as of yet. It is possible, but I need to search for that in the literature.

    The other main difference I can see is that I am creating a very robust analogy to probablity theory. There may be a bridge from modal logic to probability theory, but Im not aware of it. More research needed on my end. Additionally, in my view the Law of Excluded Middle is just a model of existence. While modal logic seems to be more concerned with semantics or epistemology, my approach explicitly looks at tangible things. Law of Excluded Middle is one model, the Exclusive Middle is another model. Fuzzy logic combines them into a cohesive theory, while I would let them stand apart and simply say that they are equivalent.

    Thanks for that excellent comment and I'll have to research whether this has ever been applied in physics or math. I think that it should be. It seems very near to what Ive been arguing, there is an application of equivalence, but did they ever connect the dots to relativity ? I kind of doubt that. I think it's worth a look.
    • Sep 30 2012: Hi there William,

      I've had a course in this on my university but I was pretty bad at it. The field of model logic is used a bit in the artificial intelligence for computer scientists. I'll try to help you out by saying what I know about it.

      There are lots of proofs based upon these axioms. I've had to go through them all at some point in time. The language itself is "sound" and "complete" (although I don't quite remember what they mean heheh... there are proofs of it though).

      I know that there have been some (not that many) papers about introducing probability theory but I don't believe they resulted in a lot. Basically there are 2 ways of adding probability.
      1) just give chances to the diamond and then use math from there (aka you add in rules for multiply, add, substract etc)
      2) you make a model where 'worlds' are 'reachable' where each 'world' represents a combination of facts (aka p, q, x where in world 1 (p v q) is true while in world 2 this is not the case). Then you can add facts of "the real world" which then falsifies a whole bunch of theoretical ones and you simply remove them. Then probability would be "from all current worlds which I deem possible, how many different worlds can I reach".
      This is the most used way I think... it's kinda hard to explain in just 1 post ;)

      I'm not gonna explain everything about modal logic here though as I'm not a great teacher nor do I know everything of it myself. But it's nice that it sounds very close to your idea.

      As it's application in physics... I don't know that it has been. As far as I know it's a purely mathematical/logics field.

      I have a book of it called "Epistemic Logic for AI and Computer Science" by J.J.Ch. Meyer and W. van der Hoek. It contains all proofs and quite a few theoretical examples of other types of logics.

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