Algebra and Arithmetic

Algebra and Arithmetic
Andre Willers
16 Jun 2011

Synopsis :
Algebraic systems are a subset of Arithmetical systems . Statements true in algebra is always true in Arithmetic , but some statements true in Arithmetic can not be adduced in Algebra . A consequence of Godel's Theorem .

Discussion :
Of major consequence in the digital age . Digital systems like the brain (on-off neural systems) have characteristics that cannot even in theory be modeled by abstractions .
Or AI's . for that matter .

Why ?
Sweet and Simple :
Algebra's have meaning ceiling is at Octonions (8 dimensions)
http://www.google.co.za/search?aq=f&sourceid=chrome&ie=UTF-8&q=octonions+wiki
, while Arithmetical systems have a ceiling of 26 + 1 dimensions .
See http://en.wikipedia.org/wiki/Formula_for_primes

This has been discussed before .
An ArithI + ArithII Universe needs a minimum necessary sufficient number of primary dimensions of at least 27 .
Algebra's meaning ceiling is 8 dimensions , before it gets so complicated that humans give up in an algebraic sense . The patterns are too complicated . So , in typical human fashion , they think there are no more Arithmetical patterns . But they are lurking there , waiting to zap you !

You too can create a true statement in Arithmetic that is contradictory in Algebraic terms . Just use between 9 and 25 number dimensions .

The enormous gap is about (27 – 8 ) ! ~ 19 ! . A measure of human ignorance , not even taking into account Beth(1+) effects .

Now add dimensional rotations and spins (the two are not the same , though they are cousins )

The complexities are in the rotations and spins .

Feel stupid ?
Now you know how I feel all the time .

Andre