Introduction
Canonical
identification
Identification
via common rationals
Hybrid of
canonical identification and identification via common
rationals
Topics of the
chapter
Summary of the basic physical ideas
pAdic mass calculations briefly
pAdic length scale hypothesis, zero energy ontology, and hierarchy of Planck constants
pAdic physics and the notion of finite measurement resolution
pAdic numbers and the analogy of TGD with spinglass
Life as islands of rational/algebraic numbers in the seas of real and padic continua?
pAdic physics as physics of cognition and intention
pAdic numbers
Basic properties
of padic numbers
Algebraic extensions of
padic numbers
Is e an exceptional transcendental?
pAdic Numbers
and Finite Fields
What is the
correspondence between padic and real numbers?
Generalization
of the number concept
Canonical
identification
The
interpretation of canonical identification
pAdic differential
and integral calculus
pAdic
differential calculus
pAdic fractals
pAdic integral
calculus
pAdic symmetries
and Fourier analysis
pAdic
symmetries and generalization of the notion of group
pAdic Fourier
analysis: number theoretical approach
pAdic Fourier
analysis: group theoretical approach
How to define integration, padic Fourier analysis
and adic counterarts of geometric objects?
Generalization of
Riemann geometry
pAdic
Riemannian geometry depends on cognitive representations
pAdic
imbedding space
Topological
condensate as a generalized manifold
Appendix: pAdic
square root function and square root allowing extension of
padic numbers
p>2 resp. p=2
corresponds to D=4 resp. D=8 dimensional extension
pAdic square
root function for p>2
Convergence
radius for square root function
p=2 case
