Impossible Universe

Possible Worlds

Possible Worlds Semantics refers to a branch of mathematics exploring the consistency of models of possible worlds. These models define information describing elements making up possible worlds and their sub-systems.

Anyone who has read a dictionary likely know that definitions can be incomplete or self referencing. E.g. "Swine"="See Pork"  "Pork" =  "See Pig" "Pig = "See Swine"

Such definitions may be confusing to someone who has never seen a the object in question (e.g. said pig) but even if you didn't know what a pig was you would admit the dictionary didn't contradict itself.

When physicists form their theories they try to self-consistent propose possible worlds that fit experimental observations.  Such models normally have "building block" assumptions that are not explained in the model, or have recursive definitions with no base. The key feature of possible worlds mathematics is it looks at wether there are any contradictions in the dictionary describing the model/system.

These definitions or rules may be as complicated self referencing fractals which can turn seeds into trees or simple one to one statements like pig=swine. If we add, change or remove a rule/definition we get a different possible world. Adding new definitions makes it possible to generate or describe new or more detailed aspects of our possible world. New rules or clarifying definitions however also take away possibilities. E.g. Many dictionaries define "Big Cats" as cats with a certain type of paw because rather than cats that grow to a certain size. Thus we can have a large cat with the wrong paw type but not a "Big Cat" with that kind of paw.

Blind Spots

This "Blind Spot Principle" crops up in in many areas of science and is perhaps related to the problem of ultimate foundation or cause or Godel's Incompleteness Theorem.

In computer science we see it in the problem of virus checkers going into endless loops when they check the part that is  checking the part that is checking itself. It is like looking into a mirror to check out flaws in a mirror. It takes forever to check every mirror for flaws, if you check each mirror singularly. In biology we see it in the eyes need a blind spot in order to see.

In Quantum Mechanics it shows up in mixed states and Heisenberg's Uncertainty Principle.

In General Relativity (GR) each observers position and frame of reference has blind spots everywhere beyond their event horizon. The same term is also used to refer to the region of blackness around a black hole where light cannot escape from. In Cybernetics or Psychology we see otherwise intelligent people who can not see their own flaws or strengths. This is most apparent in anorexics who believe themselves to be overweight yet accurately judge the weight problems of others who are too skinny.

The Blind Spot Principle suggests every perspective or person has something unique that they can understand or see, and something that they alone can not see.

Another aspect is the more we try to pin down what the world is like the more we find the pins hiding natures true nature.

Godel's Incompleteness Theorem

Sometime in the 1970s () there was a push for computers to model perfect simulations of real world situations. This was stopped short when Kurt Godel proved that any such models must be either incomplete and/or inconsistent. Someone (Richard Dreyfus?) suggested that computers couldn't dodge such blind spots because they don't have a human "soul" but (as discussed) humans seem also bound by contradictory or incomplete thinking.

If Godel's limitations on computer simulations also apply to models in Physics, it may turn out to be impossible to find a GUT or TOE that describes everything.

I suspect the problem may be greater. The mixed states of QM and the role of observation seeming to make things real rather than just revealing set states, suggests reality itself and may also be also subject to the incompleteness problems of models.

If this is true. reality (and logic ?) would be incomplete or inconsistent.