Lama said:
What I suggest is very simple:
The language of Mathematics...
A description is an abstract representation of a concrete physical instantiation.
Mathematics is a meta-language, highly abstract. A description contains the concrete physical instantiation in the abstract sense and the concrete object contains the description in the physical sense.
Here is the definition of "algorithm":
http://en.wikipedia.org/wiki/Algorithm
"Algorithm
From Wikipedia, the free encyclopedia.
Broadly-defined, an algorithm is an interpretable, finite set of instructions for dealing with contingencies and accomplishing some task which can be anything that has a recognizable end-state, end-point, or result for all inputs. (contrast with heuristic). Algorithms often have steps that repeat (iterate) or require decisions (logic and comparison) until the task is completed."
DNA is an algorithm, a finite set of instructions, which can construct a carbon based life form.
The life form physically contains the DNA and the DNA contains the life form in an "abstract" sense.
At a fundamental level of existence, it is postulated that "nature" could be constructed of tiny strings, and those strings, loops, or branes, could even be constructed of string "bits".
These bits could encode information, analogous to the universe's "DNA"? A set of instructions built into the fabric of space/time and mass/energy?
"If, then, it is true that the axiomatic basis of theoretical physics cannot be extracted from experience but must be freely invented, can we ever hope to find the right way? I answer without hesitation that there is, in my opinion, a right way, and that we are capable of finding it. I hold it true that pure thought can grasp reality, as the ancients dreamed." (Albert Einstein, 1954)
At the most fundamental length scales, the fundamental paticles, called "strings", could be constructed of even more basic units i.e. bits? analogous to a computer code?
1010100010...etc.
Universal algorithms?
Some interesting ideas on "string bits":
http://xxx.lanl.gov/PS_cache/hep-th/pdf/9607/9607183.pdf
http://xxx.lanl.gov/PS_cache/hep-th/pdf/9707/9707048.pdf
Introduction
In string-bit models, string is viewed as a polymer molecule, a bound system of point-like constituents which enjoy a Galilei invariant dynamics. This can be consistent with Poincar´e invariant string, because the Galilei invariance of string-bit dynamics is precisely that of the transverse space of light-cone quantization. If the string-bit description of string is correct, ordinary nonrelativistic many-body quantum mechanics is the appropriate framework for string dynamics. Of course, for superstring-bits, this quantum mechanics must be made supersymmetric.
According to string theory, the uncertainty in position is given by:
Dx < h/Dp + C*Dp
Which points towards a type of "discrete" spacetime?
A metric space has distance function r(x,y), characterized by involvement with the real numbers, R, such that the metric space and R are embedded simultaneously in the full structure of manifold M. A topological space consists of sets of points which are defined[in this case] to be the intersections of cotangent bundles.
If space is *quantized* yet also continuous, then it too, has the property called "wave-particle" duality. If space consists of indivisible units, then a measurement of space means that Fermat's last theorem holds, for it.
According to the Pythagorean theorem:
x^2 + y^2 = z^2
All possible integer solutions are then rerpresented as:
[a^2 - b^2]^2 + [2ab]^2 = [a^2 + b^2]^2
a^4 -2(ab)^2 + b^4 + 4(ab)^2 =
a^4 + 2(ab)^2 + b^4 = [a^2 + b^2]^2
all odd numbers can be represented as:
[a^2 - b^2] or Z^p - Y^p
if Y is an "even" natural n and Z is odd, same for a and b .
Fermat's last theorem, for integers a,b,Z,Y,p:
[a^2 - b^2]^p + Y^p = Z^p
[a^2 - b^2]^p = Z^p - Y^p
a^2 - b^2 = [Z^p - Y^p]^[1/p]
When Z^p - Y^p is a prime number, it cannot have an integer root.
a^2 - b^2 is not an integer, for [Z^p - Y^p]^[1/p] , for a,b,Z,Y,p, unless p = 2.
To every set A and every condition S(x) there corresponds a set B whose elements are exactly those elements x of A for which S(x) holds. This is the axiom that leads to Russell's paradox. For if we let the condition S(x) be: not(x element of x), then B = {x in A such that x is not in x}. Is B a member of B? If it is, then it isn't; and if it isn't, then it is. Therefore B cannot be in A, meaning that nothing contains everything.
This means that relativity holds in the "topological" sense and T-duality is correct.
Quantum entities are described as probability distributions, which are attributes of an underlying phase space, where the properties-attributes such as "spin" and "charge" are not the attributes of individual particles, but they are universally distributive entities, being the attributes of a "coherent wave function". It is this wave-distribution property that then "decoheres" into the ostensible "wave function collapse", as waves become localized particles that are "in phase" creating standing-spherical-wave resonances, which are condensations of space itself. The continual collapse-condensation of space into matter-energy is the continual "change", i.e. the property called "time". The spherical waves, or probability distributions are represented by the Schrodinger wave function, "psi".
The information density of the universal system must be increasing. The increase of information density is analogous to a pressure gradient.
[density 1]--->[density 2]--->[density 3]---> ... --->[density n]
[<-[->[<-[->
<-]->]<-]->]
Intersecting wavefronts = increasing density of spacelike slices
As the wavefronts intersect, it becomes a mathematical computation:
2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, ...2^n
