by Parodites » Sun May 02, 2021 5:37 pm
Hinton has the concept of the 'world-line', which he utilizes to intuit and visualize higher-dimensional geometry. It is integral for a philosopher to be able to reach ever higher levels of pure abstraction, and I would provide an overview of the ten possible levels available to humans. Each one is more difficult to conceive than the last, but it is possible, and the concept of the world-line is perhaps the most useful tool for accomplishing the task.
Imagine a stack of 2-d planes, and above them, a superpositional structure from which 'world-lines' radiate in all directions, with these lines intersecting the planes. The points of intersection are what we see as atomic particles. A world line intersecting any given plane, as it keeps going outward, will intersect those below it at slightly different angles: thus, imagining myself as one such world-line, moving up and down through this stack of 2-d planes would 'move' me into different snapshots of the universe. That is what time is, it is just another spatial dimension, the fourth, in which you can either go down or up through this stack of 2-d planes. All particles and all collections of particles ('objects') are simply world-lines intersecting the planes, radiating outward from a 5-dimensional hyperobject in which all the matter of our universe is in a compressed state of superposition, enfolded on itself in a higher-dimensional structure.
Just as "Parodites" is, for example, a world-line passing through these planes from a 4-d projection of the 5-d hyperobject, creating a constellation through these 2-d planes at points of intersection which I consciously experience in one direction, so this entire universe is simply a world-line passing through a 3-d sphere from a 5-d projection. The 5d object's world-lines are universes, and collectively, they form all the parallel universes associated with an initial condition matching that of our present universe. In other words, it contains all the possible branching-universes generated by the initial condition of our big bang. As you can only move up and down through the 2d-planes to move forward and backward through time in one universe, so you can simply rotate the 3-d sphere while the stationary world lines, instead of intersecting planes at different angles, instantly jump between different universes across the surface of the sphere's (the Reimann-sphere's) higher geometry. As moving up and down through the stack of 2-d planes progresses you through time in a single universe, so rotating that sphere moves you through parallel universes branching off from our own big bang.
But then that sphere, upon whose surface all the parallel universes of the many-worlds are projected, is itself a world-line passing through a 4-d tesseract from a 6-d projection. That tesseract contains all possible universes- the multiverse in other words, in which every universe sprouting from every possible initial condition is contained. So not just the universes branching off from our big bang: but all possible big bangs and their respective daughter-universes.
But that tesseract is itself a world-line passing through a 5-d hyperobject (one of the hintonian hyperobjects, a 'brane' in string-theory) from a 7-d projection: that hyperobject contains all possible multiverses,- multiverses in which, not just the initial big bang conditions are varied, but in which the physical constants themselves like gravity are completely different, in which the structure of atomic particles is different, etc.
Past this point, we are in the realm of digital physics and essentially dealing with pure informational structures, for this 'omniverse' of multiverses of universes is itself a world-line passing through a 6-d object from an 8-d projection: that 6-d object contains an infinite number of possible states of binary urs, * and represents the infinite 'time' in which universes can be generated from their own big bangs, evolve, and pass away.
But then this omniverse is simply a world-line passing through a 7-d object from a 9-d projection. That 7-d object contains all the parabose tensors of the binary urs I just referred to.
Finally, that aggregate of all parabose tensors on ur-collectives is constituted by a world-line passing through an 8-d object from a 9-d projection. That 8-d object contains the quantum field within which all possible integrated ur-collectives are described, that is, a purely informational transfinite structure in which the infinite number of the infinite strings of binary-urs is contained, like the Cantorian infinite, ie. the set of all sets. One infinity can be bigger than another in set theory, here we are simply talking about the 'biggest' infinity, ie. the one that contains all other infinities.
At last, this quantum field is a world-line passing through a 9-d structure from a 10-d projection. That 9-d structure contains every permutation and combination of the strings of binary-urs within the formerly noted 8-d structure. They call those 9-d structures, projected from a 10th dimension, "strings". It is not possible to go any further, there is nowhere left. We accounted for time, infinite time, the universe, all its parallel branching universes, the multiverse of different initial conditions, all the multiverses of different physical constants, and then the omniverse in which all possible multiverses exist in all possible states, described purely in terms of binary-urs and their parabose tensors. Universe, multiverse, omniverse: if you can think of a higher abstraction to get to, be my guest, but this is the end as far as I conceive it.
--
* I describe what Urs and tensors are in one of my books, here:
" In short, the theory of ur-alternatives reconstructs physics from 1-bit informational units, and IIT
reconstructs consciousness from 1-bit informational units. Combining the two, one arrives at a
theory of consciousness and its emergence from a flattened spacetime, occupying its own
'intrinsic space',- an intrinsicity that is, essentially, what we call time, or an as yet ungraspable
fourth-dimension. Following the theory of Urs, the first three dimensions appear during the
reconstruction of physics: ur-alternatives, then elementary particles as parabose tensors of urs,
and finally quantum field theory, in which the particles constituted by the 2nd dimension here
considered become merely syntactic elements within a higher semantic content,- namely, the
semantic content given by particles which become field quanta, at the third-dimensional level. At
this dimension, ur-collectives give way to un-readable (a la. the no-teleportation theorem)
quantum information whose continuous-valued trajectory (in terms of the typical representation
of spacetime in vector-space, as opposed to the algebraic representation proposed here, or even
that suggested by Baylis' treatment of electrodynamics; in particular, note the following paper:
Spinors in the hyperbolic algebra, S. Ulyrch. 2005: "The algebraic representation of geometry
has in general advantages compared to the conventional description in terms of column vectors
and matrices. ..." ) on the Bloch sphere demands a reformulation of emergent ur-collectives as
"paracomplex structures on a 2n-dimensional" [See: Cruceanu, Fortuny, and Gadea's Survey on
Paracomplex Geometry.] projective Hilbert space, that is, a correspondence of pure quantum
states, by way of Hopf fibration, to spinors on Riemann's extended complex plane, granting a
diffeomorphism of the urs and finally, a model of differentiable manifolds that may be useful in
theoretically reconstructing different semantic levels as symplectic manifolds, like those derived
from the Hamiltonian definition of the total set of a system's possible configurations (the total set
of a system's possible configurations would refer here to all the possible ur-collectives which
could be structurally bound as equivalent cause-effect spaces enclosed at the semantic level) as
modeled by a manifold whose cotangent bundle describes its phase-space. Thus we move toward
the fourth dimension, which would arise from the interactions of these fields: this dimension, not
yet understood by man, is that in which 'time' appears, (meaning, that in which time is
syntactically organized from a higher semantic level) and therefor, the intrinsic space occupied
by what IIT would call- 'consciousness', amounting to an enclosed cause-effect space operating
upon itself. The interaction of these fields within 'time', given the combination of the two
theories, would imply an interaction of enclosed cause-effect spaces, each constituting a certain
level of consciousness in the Kochian or panpsychic sense, from the causal universe of the
faintest consciousness, that is, the consciousness of a hydrogen atom, to the most developed
consciousness in a human being. How exactly these fields interact to produce an intrinsically
grounded temporal consciousness out of an atemporal fourth-dimensional composite of
interacting and enclosed fields within the third-dimension (quantum field theory) is of course not
yet understood, though Hinton long ago proposed that particles moving within the three
dimensions we would associate here with the third semantic level of the quantum fields, might be
succeeding cross sections of an un-moving, eternal, static fourth-dimensional architecture within
a fourth semantic-level consisting of world-lines passing through a three-dimensional plane.
Hinton even believed that man could access this eternal fourth-dimensional construct through a
kenotic process by which the self might rid itself of ideas like right, left, up, or down by utilizing
certain meditative techniques."
In the same text I briefly summarize the first four dimensions:
" 1. The 1-dimensional perspective: the 'infernal plane', the Real. The domain of the urs, or an expansive, infinitely extended atomic informational
structure composed of discrete 1-bit digital minima. All the parallel realities or many-worlds are 'fused' here; they are not differentiable. It is
what fills the liminal spaces, the 'site of exception', across whose chiasmus we invoke our 'gods'.
2. The 2-dimensional perspective: 'parabose tensors of the urs', 'multiple quantization', etc. Here, the worlds are differentiated into separate
universes, which are essentially massive ur-collectives, or ur-collectives of maximal size but minimal complexity: the many worlds of
string-theory and certain interpretations of quantum mechanics. The multiverse. The 1-d plane is given 2-d depth, meaning that it can be
subdivided into multiple 1-d planes, that is, multiple universes.
3. The 3-dimensional perspective: We know this one the best, because it's the one we live and move around in. Here, particles emerge, and with
them, the quantum fields. The quantum fields interact in such a way as to produce an 'intrinsicity', within which consciousness unfolds... in Time.
We cannot, from this perspective, understand how exactly the fields interact to produce this temporality, or consciousness with it: that requires
higher-dimensional thought.
4. The 4-dimensional perspective: The universe becomes a flattened spacetime, the observable sphere of our world is transformed into a
deterministic loop, a circle. But here, the other worlds become flat membranes as well, all stacked on top of one another, stretching toward
infinity. And above our flat time-horizon, and above all the others, there is a... "fourth-dimensional construct", as Hinton refers to it. It is
composed not only of all the matter in our universe, but all the 'matter' of all universes. It is the Ontos. It is Being, un-differentiated; eternal,
static, unmoving, unchanging; the ultimate; it is the Dragon, the Demiurge, Leviathan and Behemoth; it is Yaldabaoth, Samael, the Blind Lion;
the Serpent, the Fallen Angel; the God of Flesh, of Matter, and Time. From it, world-lines radiate, and these world-lines intersect all the now flat
planes, which are the 'many-worlds'. The point at which one of these lines intersects one of the planes, becomes a 'point particle', the elementary
particles constituting matter, from the 3-d perspective of those occupying the planes. And because the quantum fields overlap, sometimes one of
these world lines passes through the plane and crosses two or more fields at once. So the mystery of how the quantum fields interact to produce
Time is: they don't interact. What happens is, the same world-line passes through two or more fields simultaneously, so that the point-particle it
produces at its point of intersection has characteristics governed by all the quantum fields that were crossed by that world-line; we see this as an
interaction inside an enclosed 3-d spacetime, that is, as an interaction within time- but time is a predetermined circle from this 4-d perspective.
At any rate, this is how all the empty spacetimes of the 'many worlds' are populated with matter- with particles. This is how the quantum fields
'interact' to produce temporality and consciousness."
Qui non intelligit, aut taceat, aut discat.
BTHYS TOU ANAHAT KHYA-PANDEMAI.
-- Hermaedion, in: the Liber Endumiaskia.
ΑΝΤΗΡΟΠΑΡΙΟΝ,
in formis perisseia mutilata in omnia perisarkos mutilatum;
omniformis protosseia immutilatum in protosarkos immutilata.
Measure the breaking of the Flesh in the flesh that is broken.
[ The Ecstasies of Zosimos, Tablet
the First.]