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The Turing Dimension
(Karl S. Chu | X Kavya)
(v.1.0)
Abstract
The following article is a philosophical interpretation of the phenomenon of computation
by disclosing a certain complicity in the use of instrumental reason to achieve what is
essentially a gnostic quest for fulfillment. Computation is not immune to the demand
placed by the metaphysics of desire. As such, it will be transformed, in all inevitability,
into a machinic philosophy of tragic effect: a phenomenology of the spirit of universal
information processing made possible by the advent of the Universal Turing Machine.
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"Science is a differential equation. Religion a boundary condition."
Alan Turing
If tragedy, or a certain philosophical interpretation of tragedy, is the origin and matrix of
speculative thought in general, and dialech a general system of combination or the
calculable, the opposition of the ideal tone (the subjective aspiration toward the
absolute) and the heroic artistic tone of discord or agon in order to arrive at a higher
unity or resolution in the One-All through the spirit of the poetic genre. The poetic
genre, in the current situation, is about to become the only genre based on an
algorithmic conception of the world where everything enters into an extended wandering
under the unthinkable while being sustained by the elusive umbrella of the intractable.
It would eventually unfold itself into a drama of appearances and disappearances impl
Whereas for those who remain in tension toward that which cannot be encapsulated or
embodied, the green membrane of space is merely a global cockpit of architecture
directed toward the absolute infinite beyond the threshold of representation.
Nonetheless, the emerging drama signifies the coming of age of the Pythagorean
premonition of the world as numbers, and the permutation of numbers in the form of bits
would provide the new materiality necessary for a cosmopolitical drama to stage itself
on the new plane of immanence destined to rise to the level of an epic proportion.
Seen from this light, the recurrence of tragedy has been ite expression in the Universal
Turing Machine (UTM), and on the other, to enter into communion with the substance of
affects engendered by the instrumental use of reason in the first place. The tragic
effect is a dialectic of fusion of numbers and beings driven by a utopic impulse that
channels and transports the spirit of universal information processing into an epic
dramatology of transubstantiation.
In this echo of tragedy, the subject is mediated by the Universal Turing Machine, which
will, in due time, prove to be a gnostic medium that operates on ect of speculative
Idealism finds him/herself immersed into the manifold cockpit of the topological surface
now being engendered by the Universal Turing Machine. It is a trajectory, or a tragic
transport, that becomes infused with the medium by steering from within the infinite
movements of thought and lines of flight in order to overcome, through a dialectics of
transgression, the fabric of mimetology brought on by the machine of the double bind.
It is simultaneously a catharsis of the subject and of the medium that represents both
the substance of Aristotelian mimesis as a mode of poiesis and mimesis in the sense of
mimetism or imitation. It isn though it is at once the nearest and yet the farthest from
absolute fulfillment, it may require the intrusion of the caesura so that what appears is
not the alternation of representations or simulations but the limits of representation
itself.
With the publication of the paper On Computable Numbers, with an Application to the
Entscheidungsproblem in 1936, Alan Turing launched the specification for an abstract
machine that would ultimately engender a new world by laying out a new plane of
immanence specific to its mode of formal implementation. This plane is the virtual
arena upon which diagrammatic flows and constructions are instantiated by the abstion
of the Hyperzoic Era (the artificial life of self-organizing systems) by redefining the
projective content of the plane of immanence as information-theoretic in origin. It is the
harbinger of a new breed of biomechanical species and carries with it the germ of a
brave new world far more fantastic and hyperbolic than anything we have seen in the
history of human civilization. In its most significant form, the UTM is not merely another
instrument in the history of technical inventions; it is a computational monad that
redefines a new plane of immanence as the spectacle of a second order nature
transposed onto the cultural universe of humanity that is founded upon the first order
nature. As a generative mechanism, the UTM has brought to the foreground a
universe of counterfactual possibilities by showing that these potential states of affairs
are inextricably woven into the invisible fabric of realityations through the inner workings
of the Turing Dimension: a linear sequence of cells that function as the channel through
which information is processed to form the digital economy of the Universal Turing
Machine.
The UTM is a logical counterpart of Leibnizís idea of the metaphysical monad. It is a
computational monad that is founded upon the classical model of computation due its
reliance on the mechanism of classical logic for its operation. As such, the UTM is an
abstract machine composed of a linear tape, that is potentially infinite in length and is
divided into squares or cells, and a device called a head which reads and re-writes
binary digits registered on each cell according to the instruction set of the program.
The tape serves as a receptacle for storing as well as for processing binary information.
The machine is always in one of a finite number of states of mind and the operation of
the mac
*
*
*
*
Write the symbol 1 on the observed square
Delete whatever symbol appears on the observed square
Move one square to the right of the observed square
Move one square to the left of the observed square
1
0
R
L
Thus a complete instruction to the machine consists of a quadruple
(Qi, S, Op, Qj)
where Qi is the current state, S (ì0î or ì1î) is the current symbol, Op is one of the
operations described above, and Qj is the new state. The set of quadruples is defined
as a program or an abstract machine and the configuration of a Turing Machine is
referred to as an ordered triple:
(contents of the tape, scanned square, state)
The notion of universality derives from the fact that every UTM can compute, according
to the Church/Turing Thesis, anythrld by means of an internal principle that continually
modifies its internal state to arrive at a more comprehensive version of the model or
perception of the world. In other words, the UTM is a logical subset that can compute
the potential content of the larger set that is the universe itself. Consequently, by the
nature of its embeddedness, it is capable of altering the content of the universe by
further computing the numerical substance of the cosmos and staging it onto the plane
of immanence as diverse modalities of possible existence. According to Rolf Landauer
of IBM, who has done fundamental research into thvolution and transformation of the
universe at large.
The Universal Turing Machine therefore is a machinic idea of a perpetual computing
system, or an abstract evolutionary machine, that processes information through
sequential iteration of bits by registering them on the linear tape of the machine that is
potentially infinite in length. As such, it is endowed with the latent capacity to
self-organize and transforms its internal states, at least in principle, into all possible
states of a monad without end. Even though its initial design is predicated by the need
to delineate the consistency of the sequence of steps nehis is an ontological status
distinct from a condition that is dependent, as a prime mover, solely on external forces
that instantiate its will to action. In other words, the UTM is a primitive precursor of a
biomechanical species with the metaphysical ambition to embody a machinic form of
artificial life and neural intelligence. Since the UTM is the simplest and the most
general type of computing system, its internal principle or program can be made to
accommodate a generalized form of genetic algorithm that could evolve through
self-modification and optimization of itphylum of Universal Turing Machines. Even
though the Leibnizian monad continually engages in simultaneous, albeit non-linear,
modification of multiplicities as it develops into higher levels of complexity, the UTM is a
one-dimensional cellular automata that self-organizes and transforms itself by
incessantly rewriting the binary digits registered on the tape that constitutes the Turing
Dimension. It is a one-dimensional universe of monadic states generated by the
perpetually evolving code of the machine.
The Turing Dimension, together with the arrow of time, establishes tion outputted by
each scanning particle as it scans and rewrites bits along the linear sequence of cells
marked on the tape of the Turing Dimension of each machine. The scanning particle
zigzags through one domain of well-ordered sequence of bits to another by passing
through non-well-defined sequence of bits (random sequence) and by overcoming loops
and glitches as well as halting programs in order to gradually regain another sequence
of well-ordered state of the monad. Such a perpetual Turing Machine is an abstract
biological engine made to sustain itself thromension that interrupt the crazed oscillations
of the tragic effect induced by the dialectics of fusion operating in complicity with the
synthetic logic of the Universal Turing Machines.
In the brave new world that has begun to unfold, the horizons of the tragic effect will no
doubt resonate on the virtual contours of the Universal Turing Surface that is currently
expanding into potential space. The Universal Turing Surface is an active matrix or
cellular automata percolating and filtering out the universe of potential events into virtual
events and cross-pollinatinglows and singularities. Every plane of immanence is a
cross section of the configuration space of a possible world. It is a finite incarnation of
the potential infinite that is severely constrained and channeled through linear iterations
of the Universal Turing Machine. The UTM therefore is a diagrammatic machine that
rolls and unrolls the Universal Turing Surface into architectures of the manifold cockpit
that navigates by incessantly opening up a universe of possible worlds. The ambition
of the Universal Turing Machine is to encapsulate Leibnizís notion of the Principle of
Sufficient Reason by rising to the level expressive of an oracle and thereby disclosing
the hidden voice of reality on the inner Surface of the Turing Machine. This voice, the
obscure sirens of the muses from beyond, or, simply, the words within the voice, would
be an algorithmic script in the form of ing Surface as the Surface of the One-All. It is
mimesis in the most intrinsic sense in that it appeals to a formal representation of the
universe as a pre-established harmony of coordinated monads that form a plenum.
Herein lies the supreme irony of a gnostic quest that may well be usurped by the very
instrument that promises to deliver. The internal principle and the internal complexity
contained within each computational monad is dependent on the universe of
computable functions drawn from the universe of mathematics that has proven to be
irreducibly random and incomplete in its organization. As a consequence, any
algorithmic compression that reflects the matrix of the internal complexity would be a
code that is also irreducibly random, a specific kind of randomness that is qualitatively
different from any random scrambling of bits. By extension, any attempt at a
compressitin, the metamathematician from IBM, it would not be possible to prove that
the Metacode in question is the absolute minimal string that can output a maximum of
possible effects. If the totality of all possible worlds is a mirror of the infinity of possible
effects engendered by the absolute infinite cause, there are, in all likelihood, no binary
strings that can encapsulate the hidden logic of the absolute infinite in its entirety.
However, if there do exist such a Metacode, it would, by definition, pertain to all possible
worlds including those that exist outside the domain of the laws of physics that underlies
the present state of the universe. Yet Seth Lloyd of nciple, which says that it is not
possible to know in advance if a given universal computation trying to solve a particular
problem will finish and output the answer, or rather continue forever. The only possible
solution is to run the calculation and allow the ensuing stream of apparently random
binary numbers with no possibility of grasping the pattern at the end because there is no
end. Perhaps, the ultimate physical theory operates in a similar vein in that the
universe slowly reveals itself, surprise upon surprise, an endless stream of binary
numbers that are intelligible and yet random. Embedded and configured within these
seemingly random flow of numbers would bepresence and the infinite extensivity of the
tragic effect induced by the Turing Dimension, which, in turn, maps and haunts the
infinite expanse of the Universal Turing Surface ingrained with holes and vortices
amidst an hyperzoic ecology (intensive fields permeated with self-organizing systems)
teeming with artificial life forms. These holes and vortices are interruptions or caesurae
due to intractable problems derived from the incompleteness and undecidability of
certain propositions pertaining to the logic and limits of computation.
Let it suffice for the moment to say that, the Turing Dimension is the potential infinite
interspersed with breaks or interruptions that lieo finitudeî (PLL), as defined, in this
context, by the logic and limits of computability. It is at once a tragic comedy and a
machinic philosophy of the tragic effect. Nothing symbolizes the emergence of the
Hyperzoic Era more clearly and explicitly than the emergence of the Universal Turing
Surface that lays out a virtual cartography of a possible world among an infinite number
of possible worlds. Architecture is implicated in the folds of this cartography that has
become the green membrane of space suspended essentially in a twilight zone that is
everywhere and nowhere. The Universal Turing Surface is the phase space topology
enge a pause or the empty moment, the absence of moment that, if luck is with it, ìmay
allow for the intrusion of the prophetic wordî (PLL). The Universal Turing Surface is the
new plane of immanence that is, above all else, a cosmopolitical orchestration, an
onto-organology constituted by an autopoeisis: a self-generated organ of a
self-synthesized information system (John Wheeler) within demiurgic space.
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Karl S. Chu
X KAVYA