Potential infinity is defined as a limit via Newton's calculus, while actual infinity is a Cantorian Cardinal number, which is a Platonic form, which is also a type of potential.
[abstract representation]--->[semantic mapping]--->[represented system]
[axiomatic]--->[Isomorphism]<---[Induction]
An abstract representation is exactly that, "abstract". It is not a space, or time, but is instead a product of consciousness, or a mental construct; topologically it is equivalent to a "point". The abstract description contains the concrete topology. Likewise, the concrete contains the abstract.
A duality?
A point contains an infinite expanse of space and time?
Could it be, that the "absolute" infinity, is actually a dimensionless point?
[point]/[set of points] = point ?
0/N = 0
Since it is possible for a "computation" to be self aware, there must be platonic forms that are types of self aware algorithms:
The description of any entity inside the real universe can only be with reference to other things in the universe. Space is then relational, and the universe, self referential. For example, if an object has a momentum, that momentum can only be explained with respect to another object within the universe. Space then becomes an aspect of the relationships between things in reality. It becomes analogous to a sentence, and it is absurd to say that a sentence has no words in it. So the grammatical structure of each sentence[space] is defined by the relationships that hold between the words in it. For example, relationships like object-subject or adjective-noun. So there are many different grammatical structures composed of different arrangements of words, and the varied relationships between them.
Langauge describes the universe, because the universe is isomorphic to a description on some level, and reality can only refer to itself, because, there is nothing outside of ..."total existence" which becomes equivalent to a self referential system, which must be a self aware system. Since descriptions make distinctions, or references to other entities, and distinctions are tautologically logical, [A or ~A], reality is logical, in that its contents can be described by a language. The contents within reality are distinctive entities, individually different from the others, yet consisting of the same foundational substance.
[<-[->[<-
->]<-]->]
Universe = Zero
On one level of stratification, two photons are separate. On another level, of stratification, the photons have zero separation.
Instantaneous communication between two objects, separated by a distance interval, is equivalent to zero separation[zero boundary] between the two objects.
According to the book "Gravitation", chapter 15, geometry of spacetime gives instructions to matter telling matter to follow the straightest path, which is a geodesic. Matter in turn, tells spacetime geometry how to curve in such a way, as to guarantee the conservation of momentum and energy. The Einstein tensor[geometric feature-description] is also conserved in this relationship between matter and the spacetime geometry. Eli Cartan's "boundary of a boundary equals zero."
Einstein's equation basically says
Einstein Tensor [G] = Stress-Energy Tensor [T]
[spacetime geometry] determines [matter-energy's path] = geodesic.
[Matter-energy] determines [spacetime geometry] = non-Euclidean geometry.
.
Conservation of momentum energy is explained as an automatic consequence of the zero boundary of a boundary. Where conservation of energy-momentum means no creation or destruction of energy momentum in a 4D region of spacetime [4D cube] The integral of "creation events" i.e. the integral of
d*T for energy momentum, over the 4D region is required to be zero, and gives the conservation of momentum energy. The mathematical machinery for identically meeting the conservation laws is the boundary of a boundary equals zero.
[spacetime tells mass]<===[geodesic path for particle]===>[mass tells spacetime]
Waves are ripples in a basic medium. Einstein explains that the ether is unecessary as a medium, so the ripples are vibrations of spacetime itself, if, mass-energy is a form of condensed space-time.
As the ripples intersect with each other, it becomes a domino effect with the ripples continually increasing in density. Very similar to taking a penny and doubling it as an iterative sequence.
2, 4, 8, 16, 32, 64, 128, 256, ... 2^n
Since the ripples are increasing in density they are "compressed" . As spacetime becomes compressed, matter is re-configured as a balancing effect, so the force of gravity and accelerations are perceived as they presently are.
[<->[<->[<-><->]<->]<->]
The increasing spacetime density must be background independent.
Actually, spacetime does not really need to be "sliced up" in that it can proceed in discrete steps, yet, still be continuous.
[density 1]--->[density 2]--->[density 3]---> ... --->[density n]
A quote from the book "The Expanding Universe" by Sir Arthur Eddington:
All change is relative. The universe is expanding relatively to our common standards; our common standards are shrinking relatively to the size of the universe. The theory of the "expanding universe" might also be called the theory of the "shrinking atom" .
Quantum mechanics leads us to the realization that all matter-energy can be explained in terms of "waves". In a confined region(i.e. a closed universe or a black hole) the waves exists as STANDING WAVES In a closed system, the entropy never decreases.
The analogy with black holes is an interesting one but if there is nothing outside the universe, then it cannot be radiating energy outside itself as black holes are explained to be. So the amount of information i.e. "quantum states" in the universe is increasing. We see it as entropy, but to an information processor with huge computational capabilities, it is compressible information.
Quantum field theory calculations where imaginary time is periodic, with period 1/T are equivalent to statistical mechanics calculations where the temperature is T. The periodic waveforms that are opposed yet "in phase" would be at standing wave resonance, giving the action.
Periodicity is a symmetry. Rotate into the complex plane and we have
real numbers on the horizonal axis and imaginary numbers on the
vertical axis. So a periodic function could exist with periodicity
along both the imaginary AND the real axis. Such functions would have
amazing symmetries. Functions that remain unchanged, when the complex
variable "z" is changed.
f(z)---->f(az+b/cz+d)
Where the elements a,b,c,d, are arranged as a matrix, forming an
algebraic group. An infinite number of possible variations that
commute with each other as the function f, is invariant under group
transformations. These functions are known as "automorphic forms".
Topologically speaking, the wormhole transformations must be
invariant with regards to time travel. In other words, by traveling
backwards in time, we "complete" the future, and no paradoxes are
created.
So when spacetime tears and a wormhole is created, it must obey
certain transformative rules, which probably appear to be
discontinuities from a "3-D" perspective, but really, these
transformations are continuous?
[v1+v2]/[1+ v1v2/c^2]
c+c = c
aleph_0 + aleph_0 = aleph_0
0 + 0 = 0
Gravity exists because the information density of space-time is increasing. This creates a "pressure force" where processed space, compresses mass-energy, and mass-energy reacts by compressing space. The process is "time", which becomes dilated due to the increased information density of massive objects.
Stephen Hawking's excellent book, "Universe in a Nutshell", explains holography as a phenomenon of interference of wave patterns. Light from a laser is split into two separate beams, one bounces off the object and gets reflected onto a photo-sensitized plate. The other beam is reflected into a lens and collides with the reflected light of the object. When a laser is shone through the developed plate, a fully three dimensional image of the original object is created.
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 can only measure mass, rotation and charge. This leads to another theory which 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. So the theorists came to realize that the information associated with all phenomena in the three dimensional world, can be stored on its two dimensional boundary, like a holographic image.
S' = S_m + A/4
Since entropy can also be defined as the number of states within a region of space, and the entropy of the universe must always increase, the next logical step is to realize that the spacetime density, i.e. the information encoded within a circumscribed region of space, must be increasing in the thermodynamic direction of time.
Entropy of thermodynamics and entropy of Shannon, are equivalent concepts, because the number of arrangements that are counted by Boltzmann entropy reflects the amount of Shannon information needed to implement any particular combination, or arrangement. The two entropies also appear to have differences, superficially. Thermodynamic entropy interpreted in units of energy divided by temperature, while, the Shannon entropy is interpreted in terms of bits, being essentially dimensionless. The difference is a matter of convention.
