Thursday, January 15, 2009

AWT, theories and Gödel's incompleteness theorems

By AWT the scientific (i.e. causality logics based) theories are simply density fluctuations of Aether scale invariant environment like others. Human understanding is energy density driven, and the theories are accelerating the speed of energy/information propagation through environment (a human society) by the same way, like the asymmetric density fluctuations (a gradients) are accelerating the asymmetric energy spreading in transversal waves through particle environment.

Being a physical artifacts, even the seemingly abstract theories have independent tangible impact to observable reality. For example, the aerial view bellow illustrates the appearance of two neighboring countries (Austria and former Czechoslovakia), which differs just only by their theories of social arrangement, not by natural conditions. The appearance of landscape in country, which is applying socially oriented theory leading to less diversity is apparently less divergent as well. It still doesn't mean, the more divergent theory is necessarily better, though, because it's suited just for more rich and divergent environment - but this is another story.

Because the scope of density fluctuations inside of nested field of density fluctuations is always limited, the scope of theories must remain limited as well. This is because every theory is based on at least single causal/logical connection between two or more axioms/postulates/assumptions, i.e. an implication tensor definning the cardinality and compactness/consistency of formal logic system built upon implication. But the consistency of two different postulates can be never confirmed with certainty - or we could replace them by single one and we could never have some implication between them anymore, but a tautology. By such way, the scope of every logics is limited, because it remains based on insintrically inconsistent axioms - or we couldn't have some logics at all. In particular, at the moment, when TOE defines a time arrow, it becomes tautological, because validity of every implication depends on time arrow vector of antecedent and consequent. Such conclusion leads us to the understanding, every Theory Of Everything (a TOE based on no assumptions) is necessarily tautological by its very nature by the same way, like dual concept of God - and as such not very useful in causual perspective for the rest of society.

Gödel's incompleteness theorems (GITs) show that, for any sufficiently complex set of mathematical systems, one of the following two statements is true. Either
  1. There are true statements, expressible within the mathematical system, that cannot be proven from the axioms of that mathematical system. Or:
  2. There are false statements, expressible within the mathematical system, that can be proven from the axioms of that mathematical system.
Most mathematicians lean towards (1), because (2) would basically imply that formal math is BS (causual bifurcations related to imaginary numbers or division by zero are particularly good for it). But (1) is just a limitation upon what can be proven by mathematics: There are true statements, which you can perfectly describe in mathematical terms, which cannot be proven by mathematics.

Whole GITs are about this dilemma, but the explanation of AWT appears more intuitive and general. GITs were derived for theory of natural number set based on eleven axioms of Peano algebra, which is supposedly best defined human theory (of countable units) so far. The existence of other theories is based on more fuzzy logic, including the definition of theory itself. We can still consider AWT theory more general, then any other number theory, because the (natural) number concept is based on countable units, i.s. singular zero-dimensional particles colliding mutually in infinitely dimensional space, whereas the differential calculus is based upon concept of Aether density gradients driven observable reality.

Without particle concept the number concept is unthinkable - until we accept, we are composed just from pure numbers - which doesn't appear very probable, because number theory is product of human evolution and as such is much younger, then the Universe - not vice-versa. By such way, the AWT is working even at the case of singular geometry and fuzzy algebras.

Donald Rumsfeld: "As we know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns - the ones we don't know we don't know."