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Topic: Logos = Universal Algorithm
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chimp
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posted 02. April 2004 02:09
Here is the definition of "algorithm":
http://en.wikipedia.org/wiki/Algorithm
quote:
"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?
quote:
"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)
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chimp
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posted 04. April 2004 05:54
http://www.blc.arizona.edu/Molecular_Graphics/DNA_Structure/DNA_Tutorial.HTML#Components
quote:
DNA is a polymer. The monomer units of DNA are nucleotides, and the polymer is known as a "polynucleotide." Each nucleotide consists of a 5-carbon sugar (deoxyribose), a nitrogen containing base attached to the sugar, and a phosphate group. There are four different types of nucleotides found in DNA, differing only in the nitrogenous base. The four nucleotides are given one letter abbreviations as shorthand for the four bases.
A is for adenine
G is for guanine
C is for cytosine
T is for thymine
AGCT looks like code to me... DNA? = information?
Physicist Stephen Hawking writes:
quote:
DNA is the basis of all life on Earth. It has a double helix structure, like a spiral staircase...
[...]
There are four bases in DNA: adenine, guuanine, thymine, and cytosene. The order in which they occur along the spiral staircase carries the genetic information that enables the DNA to assemble an organism around it and reproduce itself...
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?
This assumption seems to hint for a designed universe, or even stranger still, a universe that is a type of life form...???
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
quote:
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?
Interesting...
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chimp
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posted 11. April 2004 06:45
Dx and Dp are the uncertainties in position and momentum, represented as probabiliuty distributions; h is Planck's constant and C is another constant related to the Planck scale.
There is a minimum size that can be probed in string theory. An absolute limit to the precision that any object can be located in space. Ergo, according to M-theory, space cannot be continuous; an infinite amount of information cannot be packed into a finite volume of space.
According to conventional theories, the surface area of the horizon surrounding a black hole, measures its entropy, where entropy is defined as a measure of the number of internal states that the black hole can be in without looking different to an outside observer, who must measure only mass, rotation, and charge. Another theory states that the maximum entropy of any closed region of space can never exceed one quarter of the area of the circumscribing surface, with the entropy being the measure of the total information contained by the system.
S' = S_m + A/4
So the "black hole" theorists came to realize that the information associated with all phenomena in the three dimensional world, can be stored on a two dimensional boundary, analogous to the storing of a holographic image.
The set of all dogs is itself "not" a dog. It is not a member of itself. Sets that are not members of themselves leads to a contradiction in the construction of a universal set. The "set of all sets" cannot exist under these limiting conditions.
DNA is also defined as an algorithm. A finite set of instructions, a step by step problem solving procedure.
The information contained in DNA can construct a carbon based life form.
So the "DNA" contains the life form analogously to the way a blueprint contains a house.
The life form contains the DNA in the topological sense, while the DNA contains the life form in the "abstract" sense.
The Universal Algorithm contains the Universe in the abstract sense, while the Universe contains the algorithm in the topological sense.
[<-[->[U]<-]->]
The universal set.
The abstract contains the concrete and the concrete contains the abstract.
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chimp
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posted 18. April 2004 06:10
Three equidistant[comoving] points form an equilateral triangle ABC
Rotate the equilateral triangle to BCA, CAB, it is invariant to ABC
A B C
B C A
C A B
the invariance of rotation for comoving points A,B,C appears to correspond to an array of elements in a 2D[square] matrix. Information is encoded on the surface of space.
According to Hawking, the maximum entropy of a closed region of space cannot exceed 1/4 of the area of the circumscribing surface A/4 .
So information is stored on the 2 dimensional boundary of space analogously to the way a 3D holgram can be encoded on a 2D surface.
The classical theories can't be quite right with regards to absolute determinism, as evidenced by the presence of Heisenberg uncertainty. Matter-energy in the universe, is subject to fluctuations, and a particle's position/momentum cannot be predicted precisely. Hence, quantum theory enters the picture in order to "quantify" the uncertainty. There is yet to be a full quantum theory of gravity, but string theory appears to be making progress towards that goal.
According to Stephen Hawking, all of the events on a worldline have a timelike connection to each other. A worldline is defined as a continuous stream of events occurring to a physical object. Basically, the worldine of an object is a timelike curve/path through space-time.
Wormholes: Theoretically speaking, by going through a wormhole, an object can return to an event a second time. A wormhole is a nontrivial connection through curved space-time. A shortcut that allows vast interstellar travel, and even "time" travel.
All sorts of time paradoxes can be envisioned via the time travel scenarios. Now if reverse time travel becomes possible in our future, why aren't we flooded with tourists and historians FROM the future?
Back to the topic, if everything is information, processed by a gigantic multiverse computer simulation, then by travelling bacwards in time, just the presence of our atoms starts a chain of cause and effect that drastically alters the future events, creating a new timeline.
So if the intelligent design theory is to get off the ground, it must recognize the utility of the multiverse/computation model.
The universe could be a gigantic computation, exploring/observing every possible quantum event.
Universal Algorithms.
[ 18. April 2004, 06:13: Message edited by: Russell E. Rierson ]
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chimp
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posted 25. April 2004 04:19
An isometry on spacetime is a diffeomorphism which leaves the metric g_ab invariant. The action on a connected spacetime is determined by its action on a single point, along with the induced action on the tangent space at the point, since isometries map geodesics onto geodesics.
For a two dimensional manifold, the antisymmetric tensor determines the value of the field at the point of two intersecting null planes. If the metric has a Riemannian signature, the equations of action are equal to the action of an infinitesimal rotation in flat Euclidean space. It follows that the map is simply an ordinary rotation on a tangent space.
In a Schwarzchild spacetime via an analogue of the Schwarzchild spacetime of the Rindler vacuum state, for which static observers detect no particles, the expected stress-energy tensor becomes singular on two distinct portions of the intersecting null planes. This is known as the Hartle-Hawking vacuum, and the vacuum state will become a thermal state with respect to the notion of time translations with temperature T = hbar*c^3 / 8pi*k*G*M .
The vacuum state gives rise to a generalized entropy law, where the entropy S never decreases:
S' = S_m + A/4
The area of a spacetime surface and the maximum amount of information contained in a finite region of space, cannot be greater than one quarter of the area in Planck units. Spin networks can describe the quantum geometry of space at the intersection of horizon boundaries, where the spin networks intersect with the boundary at a finite number of points.
There is a finite amount of energy contained by a given region of spacetime. A finite amount of information. A finite number of quantum phase entanglements and random fluctuations.
A phenomenon is random if individual outcomes are uncertain but there is a regular distribution of outcomes in a large number of repetitions.
The Hawking-Unruh effect is possibly the consequence of the noise spectrum for a massless scalar field along an accelerated trajectory in Minkowski space. It would appear to be a Fermi-Dirac form.
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