(with special thanks to Jeffrey Gormly for important contributions)
[EDITORIAL NOTE: We are pleased to publish this ground-breaking paper by two of our regular contributors. while there are some technical and difficult concepts from mathematics in here, I feel that this work exemplifies how metaphors from choreography and dance as understood at choreograph.net can be used to create radical breakthroughs in non-arts based fields. JG]
Alan N. Shapiro (1): Star Trek: Technologies of Disappearance (Berlin: AVINUS Verlag, 2004), examines the relation between science fiction and the modern scientific imagination. It uncovers the influence of cultural artefacts such as Star Trek on the epistemology of generative sciences and engineering. It rigorously explores both the real science behind the futuristic technologies of Artificial Intelligence (AI), Artificial Life, Artificial Languages, cyborgs, androids, virtual reality (the Holodeck), teleportation (‘beaming’), time travel, and faster-than-light (warp) speed, and the recursive influence of these fictional projections on the possibilities for real science. The book has been, and will continue to be, recognized as rigorously consistent with, and driving of, the most advanced knowledge in fields as diverse as media studies, cultural studies, simulation technology, theoretical physics, and computer science.
This book has become the foundational text of Shapiro Technologies, a company of futurists whose mission is not only to design and build futuristic technologies, but also to seriously concern itself with the ethics of what is to be done with these technologies. The crucial question is not if Artificial Intelligence, Artificial Life, Animatic Automata, cyborgs, virtual reality, teleportation, and time travel are possible. They are indeed possible. The crucial question is what will we do with these technologies once we have them?
However, Shapiro Technologies is not based only on a foundational text but is an emergent phenomenon, growing out of a dreaming matrix of ideas of which Technologies of Disappearance is but one wild instance. Shapiro Technologies is a thinking dancing vehicle exploring and working with new ideas; it is a collaboratory social choreography within a network of similarly avant-garde entities including Daghdha Dance Company, R.I.C.E. Radical Institute of Cybernetic Epistemology, choreograph.net, and the AVINUS Press/Verlag.
I believe that the invention of a new computer science, one more powerful than that which presently exists, is possible; a more powerful computer science that often goes by the name of Artificial Intelligence. Shapiro Technologies will go beyond the digital or binary computing paradigm that has persisted since the seminal work of the Second World War generation of information theorists such as Alan Turing, John von Neumann, Norbert Wiener, and Claude Shannon, so as to achieve quantum computing.
THE CHALLENGE OF QUANTUM COMPUTING
Alan N. Shapiro: The goal of quantum computing has been clearly and explicitly defined by computer scientists, but the mathematics of how to implement qubits and superposition states does not yet exist. It should be noted right away that most efforts to realize quantum computing are, in my view, too one-sidedly hardware-centric.
A crucial characteristic of quantum mechanics known as entanglement occurs under certain experimental conditions. Subatomic particles become ‘inextricably linked’ in such a way that a change to one of them is instantly ‘reflected in its counterpart’, no matter how physically separated they are. Quantum theory postulates a superposition of states that destabilizes the intuitive sensorial notion of spatial separation. Entangled particles transcend space and remoteness. They belong to a ‘shared’ system that acts as a single entity. The distance that divides the particles no longer plays any influencing role that would lead them to be regarded as having distinct identities. Once the entanglement state is established, the subatomic duo stays forever bonded. The two particles will always have either precisely opposing or ‘elegantly complementing’ relative values of key quantum properties such as polarization direction, regardless of how far apart they travel from one another.
Quantum mechanical phenomena, such as superposition and entanglement, are made use of to perform operations on what are called quantum bits, or qubits. Instead of the classical binary or digital bit, which has the discrete value of 0 or 1, there is a qubit, which may have a third state, an in-between-state, the momentary value of which is determined by the superposition of the state of many other bits in the system.
Entanglement and superpositioning enable this third state, which can be cultivated to correspond with the anticipated choice space of the ‘user’.
EXISTING METAPHORS FOR QUANTUM COMPUTING
In a landmark article called “Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer,” MIT mathematician and computer scientist Peter W. Shor defines algorithmic sequences for quantum computing in software. Shor asserts that digital computing, contrary to common belief and to the famous statements in information theory of Alan Turing (“On computable numbers, with an application to the Entscheidungsproblem”) and Alonzo Church (“An unsolvable problem of elementary number theory”), is not an efficient universal computing device. “It is believed able to simulate any physical computing device with an increase in computation time by at most a polynomial factor,” he writes. “But this may not be true when quantum mechanics is taken into consideration.” (2)
Shor considers two mathematical problems in cryptography, factoring integers and finding discrete logarithms, which are highly challenging to implement on a digital computer. He formalizes efficient randomized algorithms for these two problems but still leaves a crucial difficulty remaining to be solved by the hypothetical quantum computer. “To compute the period of a function f, we evaluate the function at all points simultaneously.” But quantum physics imposes on us the limitation that this information is never available to us. Since the mid-twentieth century, physicists have discovered that there is a reality of quantum physics, but have had trouble observing that reality. It is up to the designers of the quantum computer now to implement the quantum property of the ‘superposition of states’.
A measurement of superpositions yields only one value, and at the same time destroys all the others. Computer scientists working on quantum computers therefore rely heavily on the Fourier transform, a mathematical operation that transforms one function of a real variable into another, called the frequency domain representation of the first function, as the hypothesized way to solve the problem. The quantum Fourier transform is primarily thought of as being implemented in hardware. A hypothetical quantum computing device would have so-called ‘reversible logic gates’ which continuously allow sequences of reversible decompositions into mathematical unitary matrices.
In January 2007, I attended the conference “Consciousness and Quantum Computers” in Lucerne, Switzerland, organized by the Swiss Biennial on Science, Technics & Aesthetics (SBSTA). In his opening remarks, René Stettler, Founder and Director of the SBSTA, talked about the trans-disciplinary work that would be involved in the project of bringing to fruition quantum computing. It is especially an expanded understanding of consciousness that would be required to gain a real grasp of quantum physics. Yet, as Stettler pointed out, universities do not even seem to be striving for this trans-disciplinary knowledge. Hans-Peter Dürr, former executive Director of the Max Planck Institute for Physics and Astrophysics, and former collaborator of Werner Heisenberg, emphasized in his keynote address that physicists do not have the philosophical training necessary to understand what quantum physics really means. The celebrated mid-twentieth century physicists who discovered quantum mechanics did not understand it, they only spoke about it in metaphors. They settled on the practice of using applied quantum physics statistically without understanding what quantum physics means.
But quantum physics, according to Dürr, is the most profound rational knowledge that we have gained about the world. The necessary expanded understanding of consciousness and action would have to come from engagement with philosophical traditions like phenomenology, Buddhism, and Hindu cosmic perspectives like Vedanta. Excellent talks on the relationship between Buddhism and the philosophy of science were given at the conference by Geshe Obsang Tenzin, a Tibetan Buddhist psychologist living in America and working on mind/body medicine, and German philosopher Christian Thomas Kohl.
A MORPHOGENETIC FIELD
The matrix that is Shapiro Technologies, by its very designation a fertile space, gives life to new and unforeseeable thoughts. This space can also be thought of as a series of overlaid morphogenetic fields:
‘First, morphogenetic fields work by imposing patterns or structures on otherwise random or indeterminate processes in the systems under their control. Second, they contain attractors, which draw systems under their influence towards future goals. Third, they evolve, along with living organisms themselves. The morphic fields of all species have history, and contain inherent memory given by the process I call morphic resonance. … Morphic resonance works across space and time, from the past to the present. Through morphic resonance, each member of a species both draws upon and contributes to a collective memory of the species.
… Morphogenetic fields are part of a larger class of fields, called morphic fields, all of which contain inherent memory given by morphic resonance. Morphic fields also underlie our perceptions, thoughts and other mental processes. The morphic fields of mental activities are called mental fields. Through mental fields, the extended mind reaches out into the environment through attention and intention, and connects with other members of social groups.’ (5)
By working with metaphor, we can create the epistemological conditions that allow us to think, and by extension design, code and implement, the quantum computer, or Artificial Life, into existence. What follows is a description of both the morphogenetic field that contains our thought work on this problem, and also an enumeration of the strange attractors in operation in this field.
NEW TOPOLOGIES, STRANGE ATTRACTORS
Alexis Clancy (3): * Third Space mechanics: I consider a model to be a dynamic series of frames. In modeling a universe, I consider two sets. First, the set F of everything that I know. Second, the set D of everything that I do not know. Something can either be known to me or unknown to me. It cannot be both. [”_F_eicte” is the Irish word for “seen.” _D_ofhiecte is the Irish word for “unseen.”]
The set F of everything that I know is characterised by collapsed wave form Kroneker Delta functions which are finite, bounded and measured. [A Kroneker Delta function is a function whose value is one at a unique instance, zero everywhere else. It best describes the collapse of a waveform on measurement, the wave collapsing to an absolute negation of probability at a certain point on this measurement.]
The set D of everything that I do not know is characterised by Schrödinger type equations, spacewise infinite and unbounded. However, the perimeter of the set F of everything that I know presents a problem, as a point on this perimeter exists in both spaces F and D [Imagine someone standing on the border of Belgium and The Netherlands – essentially, they are standing in both countries at the same time]. This contradicts the first Rule. I correct this model by introducing a small cleft about the perimeter, small yet big enough to exist. Epsilon small. I call this cleft the Epsilon Cleft. This is the Third Space.
Locally and superficially, the dimensionality of F strictly does not go beyond 2D, and it is Euclidean. The dimensionality of D is a function of time; as time progresses, symmetry breaks [i.e the character of an absolute law dictating the character of D is no longer a given. See here] and as many dimensions as are needed to patch the model are used. Ignoring the first term, the sequence (as stated previously) is 4, 11, 26, 57… The Epsilon Cleft is the source of these dimensions. My assertion that symmetry will always break (as long as there is time) dictates that the Epsilon Cleft will have an inexhaustible supply of dimensions. [This assertion is taken as a direct inference of Gödel’s Incompleteness Theorems.] It is therefore countably infinite. Adopting this attitude towards a model renders the ‘problem’ of innumerable infinites not a problem, but rather an actual contributor to an overall dynamic and evolving model.
I like to view spaces like the Epsilon Cleft as a “novelty” space. I find them to be analogous to the “No Mind” structure referred to in the Samurai Creed (“I have no sword. I make No Mind my sword.”) and the characteristic consciousness produced by Samadhi practices of Buddhist and Hindu Yogic meditation; I place my faith in the Epsilon Cleft to provide a space for novelty to emerge. In this case, we design the solution space such that the novelty that emerges is Artificial Life.
- Faith: The interesting thing to me about a probability spike, as derived and described in Shor’s paper, is that even if it hits, say, a 99.9999999999th percentile of certainty, 0.0000000001 must be taken on faith. Faith is a qualitative rather than a quantitative construct – once it is there, it is there and it becomes a fundamental aspect of the overall paradigm, contributing to the overall efficiency of the paradigm. To negate it would take an infinite amount of time. I feel that faith is critical to any sort of AI paradigm, quantum or otherwise. I remember speaking about faith with a friend of mine who is a Jesuit priest. He said that what a lot of people forget is how practical a construct faith is. Indeed, faith is a large part of the Bushido creed: faith in discipline, faith in training, faith in “No Mind,” faith in the Way or Path. Faith is a real time saver.
To have gaps in the spacetime model provides many advantages: the possibility of motion, for one, and more to the point, the capability to creatively evolve and provide the model with as many dimensions as needed. Since it exists outside spacetime mechanics, the “novelty space” is fast. Thus we have the qualities of dance: motion, creative capacity for change, speed; this is the kind of dance Choreographer Michael Klien describes as ‘a state of excitement in a system whereby change becomes possible’ (5).
- My theory of mutation relates to stochastic (a stochastic method is a method whereby a “guess” is made as to the operation of an observed phenomena and then the “guess” is “tweaked” into rigor) methods, more precisely genetic algorithms. It is an example as to how the behaviour of quantum geometries can be used in developing solutions strategies for the macro world. While I have only observed the probability of mutation as being a constant in contemporary theories, my preliminary theory tries to state otherwise. As stochastic modelling methods rely on their closeness of adherence to natural processes and phenomena, viewing mutation as a multi-variable function improves the algorithm.
I am beginning to think that this theory of Mutation is much more important than I originally surmised, as it bridges Darwinistic theories of evolution and assertions of intelligent design. Once the system comes into a bind, mutating seems like the intelligent thing to do. A shrinking probability interval and the existence of choice is key. So there is a randomness (albeit a shrinking one) and a free will paradigm at play. In terms of theology, I do not feel there is any need to delve any more to further the understanding of the model; a choice exists, that is all. So the mutation theory can stand out not just as stochastic proposal, it is also a bold illustration as to how Möbius (symmetry breaking) Incompleteness in a Riemann geometry can give rise to what can be deemed intelligent behaviour.
Consider any object in a Riemann Geometry. It is a property, a mathematical truth of this object that any line section of it is Möbius (i.e. contains a 180° half twist. See here) in structure -¬ the Riemann object can be described as a pinched S^3 sphere and, by examining it as a Clifford (Fibre) bundle of a Riemannian manifold, we can say that all sections are Möbius in character, as there exists a ‘choice of sign’ with respect to the vectors therein. The Möbius twist itself – the “interval of inflexion” – leaves a gap in the model – this concept is expounded on shortly.
In a Riemann type geometry, a conic represents a pinch of some sort. An unmolested bounded space can be taken to be a sphere but some stress on the system will render it not so – the most basic morphing will be hyperbolically conical. I state gravity to be a constraint simply due to its universality with respect to binding a system. With respect to separating the time and space factors, I feel that, as we are dealing with a spacetime metric, the mutation function is a coupled bivariable function. It is almost a rule of thumb that nature will not use a simple linear function to do anything – a simple non-linear function is generally the case. The geometry can be taken to be a quantum geometry, but I believe that most of what we experience has its origin in these kinds of spaces. I feel that the solution space metric we will design should embody these qualities and also be breathable (my term) and elastic – a mathematical weave as opposed to a mathematical covering (6). I am inspired by Goethe’s quote: Search nothing beyond the phenomena, they themselves are the theory.
Take the interval of inflexion and call it the Aleph Point. This is the point where symmetry breaks (down) in the overall section and the system is called on to evolve to a higher dimension. Now consider a closed space under some sort of constraint, gravitational or otherwise, and represent it as a conic, with a time interval T operating. Note that as we travel down the conic, taking sections at points a, b, c, and d, we can deduce, as we travel ‘down’ the conic, that the probability of an “Aleph Point” being called on increases for two reasons. First, because the section interval is shorter (|a|>|b|>|c|>|d|), so the “aleph” point is more likely to be “chosen.” Second, because the time interval is operating faster as spacetime is getting denser toward the bottom of the conic. The overall conclusion is that the greater the strain/constrain(t) on a system, the greater the probability of symmetry breaking.
With respect to genetic algorithms, I propose that symmetry breaking is analogous to mutation. The challenge lies in fabricating an appropriate metric for the solution space so that a suitable variable mutation function can be applied and a more efficient algorithm developed. It must be a Möbius weave, as opposed to a covering. It must be non-Euclidean. It must not be decimal or binary in base foundation, as, to my mind and acumen, there are no universal harmonics bound to 2 or 10. Right now, 360 seems to be the most appropriate base.
This is a very important demonstration as to how Möbius topologies, incompleteness and Riemann geometry combine in a sense that seems intelligent.
- One of the fundamental challenges with respect to our quantum computing/A-Life project surrounds waveform collapse. There is the choice space of the mind of the user and the solution space of the A-Life device. The probability space of the range of choices presented to the user collapses into a decision and the superposition of states offered by quantum computing/A-Life must collapse into the same decision.
My investigations of waveform collapse suggest that it happens due to a “well” of incomplete spaces, and collapse happens in pairs of wave potentials. This is due to the anticipation of Newton’s third law – every action has an equal and opposite reaction. So there is an “instance” (action) vector and a “shadow” (reaction) vector, one anticipating the other. In terms of the dimensionality of the event (i.e. waveform collapse), it is infinite in potential and finite in eventual unfolding – this finitude following the sequence 1, 4, 11, 26, 57, 120, 247… [see the figures ‘the symmetry breaking of aleph’] (based on dynamic patching of incomplete spaces generated by Möbius inflections). In my modelling, the only way that I could stop the well being infinite (and the event taking an eternity to happen) is by observing the origin (the origin being the ordained source of vectors of a given framework) being sucked into the event as all vectors are brought to the event’s location. There is a “kiss” of origin and event, the dimensionality of the collapse reaches a finitude, a moment of absolute parity is achieved and then the collapsed waveform unwinds.
It is this moment of parity that we must strive for – the equality of what is in the mind of the operator and the equivalent member of the solution space. I have meditated on the ‘=’ symbol for many years and the result of these contemplations is that the symbol is actually quite special and not to be used lightly. I regard it as a ‘parity license’ and, like all licenses, it must be applied for.
- Where the challenge lies is in accessing a Schrödinger waveform to “play” with. It may be of use to draw on a conjecture that I developed regarding Schrödinger’s Equations and Parametric Normal Distributions. The question I pose is this: Do statistics imitate life, or does life imitate statistics? The conjecture is based on the meditation that, because Gauss’ rigorous definition of the Normal Distribution [the ubiquitous “Bell Curve” (because it looks like a bell) seen in most statistical models, particularly in models whose elements have the possibility to chose their state] predated the development of Quantum Theory, the results of experimentation and thought experiments were mathematically retrofitted into Gauss’ model and taken to be a system of “statistical aggregates.” However, it is my view that Gauss’ Normal Distribution is a trans-dimensional fractal, mimicking in form and behaviour its quantum origins on a macro scale.
This conjecture is supported by David Bohm’s first postulate of his highly regarded quantum theory: that the Schrödinger equation is not only a mathematical object – it is also an object of form. This expansion of consciousness permits the accessing of a Schrödinger waveform through parametric data. There must be an analogue input at some instance, but the scale is not important. I feel that this search for the appropriate input could be like Edison’s search for the appropriate filament for his lightbulb.
3, or threeness, is very important with respect to escaping the tyrannies of binary/digital. Indeed, the ‘trick’ with respect to our macro q-device will be to build a device that goes beyond Turing’s definition in ‘On Computable Numbers’ of a universal computing device while using components which conform to that definition.
12 has many strengths. Its combination of three and four make it a very musical number, and it has almost self-organizing properties. This is also the case in a strong way for things divided into 360 parts. It is well to remember that base 2 and base 10 are to be seen as some sort of enemy to our thinking regarding this project.
64 is important with respect to partitioning a vector space. My research has led me to conclude that anything after a 64th part partition is meaningless. It represents the gauge of the ‘vector net’ that we are to establish. I believe that complete coverings cannot be applied to real-world scenarios as they fail to incorporate concepts of incompleteness. *Breathable metrics are what is called for*. In order to fabricate these metrics, there is a requirement for a given, acceptable tolerance to this metric and its least element. I propose that 64 be this tolerance. Although it is a classic number in binary computing, it does have a nice twelveness to it in that there are 4 parts of 8 and 8 parts of 4, and this twelveness is crucial in modelling a nexus of any given spacetime scenario.
There must be some analogue input somewhere along the way. Resonance is, as far as I know, one of the few quantum phenomena that can be experienced on a macro level. It is a way to access a Schrödinger waveform in a fractal, macro sense.
MANIFESTING QUANTUM COMPUTING
Alan N. Shapiro : As in object-oriented software development, there is the design of a model, with data and operations. Software models something in real-world processes, but what we need for quantum computation is a way that allows the model to breathe and facilitate emergence of intelligence. Breathable models, mutable axioms.
Alexis Clancy : The mathematical proposal with respect to quantum phenomena would not be best described as particle physics. It is more of a fractal investigation of the behaviour of waves with a view to creating a metric space that can “shadow” the thought of a human mind, particularly its choices. This I hold to be possible “seeding” (my term) a specially constructed metric with the appropriate fractal incompleteness. It is nearly as important to understand what we do not want to do.
Alexis Clancy and Alan N. Shapiro :
• We want incompleteness. Some methodologies exist in electronic engineering where a least element is applied to create a mesh for the mathematical space used for examining given problems. But this has little to do with Gödel’s incompleteness – it is just a method that works. Where the novelty in our proposed methodology lies is in the assertion that the “gaps” left in a given frame due to a Möbius inflection are the physical manifestation of incompleteness. This is a significant breakthrough, and it is the real way forward for Artificial Intelligence.
Alexis Clancy : Incompleteness is almost treated as a dirty word in modern physics – I am of a polar attitude. I find it to be critical, and, if harnessed properly, the way forward with respect to the development of true Artificial Intelligence. I cannot stress enough how important Gödel’s work is to my overall thesis. It throws “wobbles” into any proposition. Furthermore, on examining the epistemology of axiomatic reasoning, a rigorous examination of any axiom-based theory will inevitably reduce to an examination of the word itself. Axiom: that which can be taken as “self-evident truth.” Well, what is “truth”? It is certainly no objective matter, so, indeed, it is a matter of faith that it is taken to be “true.” Though the faith element may be considered epsilon small in dimension, it still exists, but is habitually glossed over. I have come to see axioms as totems, as opposed to hardline written-in-stone truths. In view of the incompleteness theorem, it behoves one to have mutable, evolving, breathable axioms or else the theory will be crushed by incompleteness at some later point in time and space.
• What we will practice is the strategy of reversibility – overturn the negatively connoted perception of limit into a positive opportunity. Incompleteness will be a positive program for growing embodiment and vitality. For the first time, computer programming (Java) will be extended from classical combinatorial logic to the programming of the real conditions for emergence.
The first step will be to program in Java a Universal Incompleteness Generator. This is eminently doable, since computing as we know it today can produce undecidable statements in a ‘negative’ way, starting from any set of arithmetical axioms. Any computer program can be expressed as a mathematical function, then converted into an arithmetical formula, then ‘Gödel-ized’. This ‘negative’ use of Gödel’s incompleteness theorem in computer science establishes the limit of what can be proved or disproved from axioms. Existing computer science thereby points directly to the limit of its own paradigm, and is clueless as to how to proceed further. This Universal Incompleteness Generator establishes the “stumper” (a key word for our project – many of the great advances of twentieth-century mathematics and science have stuck for a very long time on these stumpers).
• Another important aspect of the incompleteness theorem as the way to the emergence of Artificial Intelligence is dimension hopping. Dimensional history follows quantum developments, as illustrated in the below diagram, which looks at the fractal nature of incompleteness. In this diagram up to 11 dimensions are labelled, and 26 dimensions are marked but unlabeled. The aleph approaching x indicates the timeframe of the event, the hammers of the aleph ‘hopping’ over the trunk (the ‘trunk’ is the long diagonal shaft of the Aleph) represent two time lines (the instance and the shadow) that are not touching. As the main time line is fractally phased smaller, the aleph approaches x. Indicated in the diagram are the creative evolutionary properties of both Möbius and Incompleteness– the capacity to reach higher dimensions so as to ensure the survival of a system. This can be perceived as intelligence. The predicted dimensionality gives the opportunity to catch the strands of an event as it evolves.
This intelligence stems from the presence of the Möbius Pi half-twist in the frame. This has more to do with the existence of choice than anything else. From the perspective of an observer looking at the frame, there exists this inflexion in the frame for which no power can be discerned as its cause. Yet something is the cause. I [Alexis Clancy] label an operator that brings it about, and leave the rest to the imagination. I call this the aleph operator. It has an energy signature, albeit a very small one, just enough to exist – epsilon small. (7)
• We do not want a covering. A covering is a topological abstraction where the collection or union of subsets is posited as equivalent to the whole topological space. This is a self-fulfilling prophecy restricting the topology in advance to the combinatorial and the impossibility of emergence.
• We want a weave. Tailoring the weave so that Intelligence may arise is an amazingly elegant solution, infinitely superior to all of the other proposed Artificial Intelligence paradigms. It will be simple, and we will do it fast, and it will be fast. We will discover and open up to visibility the reality of non-Euclidean geometry. The topologies and the programming in software of this new geometry will be simultaneous.
• We do not want binary stasis. Binary stasis is the Endgame of computing as we know it today. However, (1) a binary model can be set up to stand in as a placeholder for holistic emergence, then (2) the suppression of radical uncertainty that is imposed by static binary simulation’s metaphysical rejection of the third term can be overturned to liberate Otherness and substantiate in fact that all is not simulation.
• We want dance. By displacing the incompleteness argument away from the semantic and more towards the semiotic and the fractal, we set motion into motion, and also free motion from symmetrical images, which are always static simulation models. Dance for us is the animation that emerges from all kinds of asymmetrical movements.
• We want to create something breathing, evolving that has the capacity to be novel. A huge aspect of modelling incompleteness is the clocking of the space. This is achieved by slowing the clocks of the other two spaces (Cartesian space and Schrödinger space). The behaviour of events pertaining to incomplete spaces, particularly with respect to symmetry breaking, is known to us on a theoretical basis, so the modelling is distinctly achievable.
PUTTING THE METAPHORS TOGETHER; DIALOGUE: AN EXPANSION OF CONSCIOUSNESS
Alan N. Shapiro : Peter W. Shor’s work on quantum computing in software is important, but I think that his approach actually represents precisely the direction that we do not want to go in. The two principal efforts in quantum computing are either to imagine a reversible gate implemented in hardware (an effort which honestly is not going anywhere) or to formalize algorithms like Shor does, thus isolating the problem to the quantum Fourier transform, which the hardware gate still must implement and (as yet, cannot) solve.
Quantum physics was never philosophically understood by its practitioners, who opted to just use it, and subsequently developed practical statistical methods for doing so. No trans-disciplinary knowledge there. So far, all that the physicists and mathematicians have done are “clever tricks.” Even the quantum teleportation experiment has to use the “clever trick” of the joint Bell-state analysis or measurement of a third particle that is independent of the entangled pair.
Shor’s algorithms and all the ideas about quantum computing in hardware continue this reductionist history of quantum physics that never tries to philosophically understand the “weirdness” of reality, the absolute fact that reality is being created anew at each moment. But this reductionism just will not do anymore!
Only with an expansion of consciousness does a protected space open up where the impossibilities of quantum mechanical observation are suspended (as an act of friendship by the divine towards us, so to speak). In this protected space, we can do transformations in a different way. It will not be the Newtonian taking of a measurement that destroys the state measured.
Alexis Clancy : I am pretty much in complete agreement with your assessment of the Shor paper – and of Western quantum thinking generally. There seems to be a satisfaction in drawing a line between the known and the unknown and leaving the rest to statistical aggregates. My fascination is with that very line.
While Shor’s paper has much merit (and is an extremely good study aid), it is hard to imagine that the decoherence problems could ever be eliminated to the point of being cost-effective. I have an issue with the quest for the true randomness criteria that the factoring algorithms are based on. I believe that, while things at a certain point in time and space may seem random, stepping out of that inertial frame of reference often reveals a pattern. I often say that 8nothing is truly random*. There is no sense in breaking our necks trying to generate true randomness. I also have a mixed attitude towards ‘noise’ – I do not think that it matters if the model is framed correctly – unless the noise is cataclysmic. (8)
Alan N. Shapiro : The way to take measurements on both sides of a created universe, of the model and its phantom, to access all of the quantum information that is going on in the system, is to have a safe, protected space in between where one is allowed to be, prior to ‘becoming (measurable).’ First, we will have a portion that conforms to the definition of a universal computing device made by Turing in “On Computable Numbers,” the q-state, the third possible state of the qubit, as a statistical aggregate of all the other states that we are interested in (for a particular systems design). That is no problem. Second, we will have a portion that goes beyond Turing’s definition. Along these lines, we want to perceive quantum states of musical resonance which are going on in the system in real-time, not just Normal Distribution stuff that existing computer science and mathematics have been able to handle.
Alexis Clancy : Just a quick word on Fermat’s Last Theorem (x^n + y^n = z^n has no integer solutions for n > 2). I’m not sure that I have told you this, but ALL my work stems from an image of a splitting Möbius band and there being a correlation between it and a solution to the theorem. What has spawned from this is an ongoing evolving body of work that should keep me busy until I die. But what occurred to me in this examination is that this is one of the most succinct mystical sign posts that the West has to offer. Whereas Wiles offered a proof for the cases of n = 3 to infinity, I look at Pythagoras as being a special case. My examination of least triangles has led me to conclude that they are bound by Kroneker Delta functions (collapsed waveforms). Any other slight deviation other than an orthogonal view leads to Möbius incompleteness. Fermat hints at this.
Once we step off a surface, the mathematical texture deviates. I have gone through Euclid’s Elements (Book VII in particular), which is the bible of the set of all definitions and postulates for classical number theory. It’s measure, measure, measure all the way … It is no great leap (I think) to suggest that it is collapsed waveforms, ‘measured’ as they are, as opposed to uncollapsed probabilistic waveforms (mathematically, Schrödinger Equations operating in a complex Hilbert space), which are at play in the formulation of nearly all of the postulates and proofs set out by Euclid, if they are to be taken in a physical sense. I actually have a problem with the concept of a Hilbert Space – I consider it to be a ‘barrel for an ashtray’ solution to housing a wave equation.
Alan N. Shapiro : Here is the answer to the riddle of quantum physics: not measure, but perceive. And an expansion of consciousness supports an expanded perception. Quantum behaviour is a reality. Physicists thought that they could not observe or measure this reality without destroying the information therein. But they conceptualized the methodology of observation conventionally. The space from which one can observe the reality of quantum behaviour without destroying the information therein is also a reality, a fact of nature. We do not have to invent this space, we only have to perceive it. This space of non-destructive observation really exists, just as quantum behaviour really exists, and we will get it working in software. To perceive this space, we have to change our consciousness. That’s all that we have to do! We have to recognize as being scientific some ways of perceiving that belong to other traditions that Western science has so far small-mindedly regarded as non-scientific. This expanded perceiving includes creative mathematics, the deconstruction of classical spacetime mechanics, Buddhist and Hinduist meditation/ontologies, Aboriginal-sacred-mystical-expanded consciousness thinking, and Continental semiotics/grammatology.
Alexis Clancy : I try to stay away from equations, as the equalto operation reduces everything to a Euclidean realm (measure, measure, measure) that really does not concern us. Most of the work is fractal, either a fractal Aleph or a Schrödinger. We do not have to prove anything, we just have to get the thing working. The equalto only exists for that brief moment within eternity when Newton’s Third law is satisfied. We are drowning in the equalto operation. It is one of the first things that has to go if we are to break our minds out of this lens space and “see things as they truly are.” (William Blake)
I do think that what lies ahead of us is developing a new type of stochastic method. I am looking forward to discovering it with you.
Alan N. Shapiro : Your idea of the Epsilon Cleft is a very good representation of that protected space which provides an extra framing dimension enabling observation of the set of bits (in a body of real numbers that is beyond Turing’s idea of what is computable) which are in a 0 state, and the set of bits which are in a 1 state. The Epsilon Cleft is safe and protected, non-destructive, a breathable space based on breathable axioms, outside spacetime mechanics.
Alexis Clancy : In terms of the Epsilon Cleft, the initial instantiation is straightforward enough to introduce the idea of a Third Space from the point of view of mathematical modeling (after all, the model is the reality, I believe), but what I have yet to formulate is the Epsilon Metric, which is how I view spacetime: as a Möbius weave with Epsilon spaces throughout. But I have more than a strong informed instinctive feeling that it has the texture and character of a fractal Aleph.
This is, I believe, the fundamental challenge that confronts our project. Harnessing what for some are considered to be ‘problems’ – symmetry breaking and incompleteness – to a mathematical model, and turning them, in relation to the overall model, into a source of zero point energy. ‘Clocking’ the metric will be fun – the spacetime of some aspects of the metric are going to be vastly different from others. It is then that the faith element comes into play, and the building of resonating phenomenal forms in this Epsilon metric. Not only is the Epsilon Space non-computable, so too is the ‘Unknown’ space, as, ultimately, the wave can collapse anywhere.
Alan N. Shapiro : So ultimately we will need much faster hardware as well, quantum computing hardware. At first, we’ll have a little bit of AI (which will already be a lot, will be worth its weight in gold), but to get lots of AI will be a long-term project.
Alexis Clancy : Here is an idea for the ‘nuts and bolts’ aspect of the project. This has emerged as the result of contemplating an Aboriginal ‘Dreamtime’ model of parallel timestreams. This is opposed to a certain model of Western narrative. We in the West operate in but one single node of the Aboriginal model, our obsession with the workaday ‘real’, leaving us bereft of many riches. In my models of quantum computing and Artificial Life, I have discerned three timelines in a given event. Two of them are vector timelines, and one is scalar. To instantiate the metric, we need three different types of clocks, three nodes of Dreamtime.
The three different types of clocks are:
• Metronome (vector).
• Elastic (vector).
• Superfast (scalar).
The Metronome clock is Cartesian and represents physical ‘real’ time.
The Elastic clock represents the time frame for the Schrödinger space. I have discerned that the spacetime compacts and decompacts at intervals. The Elastic time is complex, Möbius, and has dimensionality of 4, 11, 26, 57…, depending on symmetry breaking.
The Superfast clock time frame relates to the incomplete spaces. The Superfast time is Aleph 0 (countable), infinite in dimension, and also Möbius in character.
Both the Metronome time and the Elastic time are considerably slower than that of the superfast time. This gives us an opportunity to take advantage of simulated annealing – the stochastic method whereby the solution space provides the overall method with an opportunity to hop to a ‘better’ optimum solution.
From the hardware point of view, the STI Cell microprocessor architecture looks interesting. We will do a lot of programming in C as well as in Java. What I think is significant is that we have a very definite line of inquiry with respect to the practical implementation of quantum computing and Artificial Life in software. (9)
Alan N. Shapiro: I create a database with 65,536 entries. It’s a simple comma-delimited text file for now, one key-value pair on each line. The key is a 4-digit instruction. Each digit is a hex number ranging from 0 to F. After the comma, is a 4-digit “reply,” arbitrarily using the upper-case letters G to V. This has no meaning, only that each reply is unique. So it’s something like a John Searle “Chinese Room” or a primitive conversation database. You give an instruction and get back a reply.
Using a random shuffle or a binary search tree, whatever, I load the key-value pairs from the database to a Java TreeMap. I’ll have 8 mechanistic-conventional data structures going which handle instructions or queries that are coming in and the reply to the instruction. There will then be a 9th data structure which has the aspiration of not being mechanistic but rather holistic or quantum.
The goal is to have a new kind of data structure built on top of q-bits which can acquire values (0 or 1) by autonomously perceiving what is going on holistically in a system in real-time, going beyond the explicit setting of the values of bit-based data structures by the subject-centered programmer, which is what existing computer science is all about. This holistic perception or receiving of information from an ‘elsewhere’ has something crucially to do with the question of how does one obtain quantum information in a way that is not a statistical reduction, a statistical aggregation of many possible outcomes. Alexis hypothesizes in his unconventional mathematics that we are in effect dealing with two qualitatively non-local, albeit relatively ‘near’ quantum systems. In a very brief moment of time prior to the waveform collapse that produces the results available to us in the ‘real’ (or ‘simulation’) quantum system, there exists another system where a small edge in quantum knowing – whether an outcome is going to be 0 or 1, which of two left-right parallel slits the photon is going to pass through, whether the roulette ball is going to fall on a red or a black number – is available.
To achieve the ‘Hello World’ of the LIMERICK METRIC SPACE in software will not necessarily mean that we will then have functions in our software library that always reliably return the same calculation result. This is no longer about equations or calculations in the traditional sense, about looking up cosines in a trigonometric table, knowing the ratio of the circumference to the diameter of a circle. It is about being a sort of magician who has a sixth sense of special sequences of numbers with certain magical powers. It is about developing a sense of time, the running of unconventional clocks, which are other than linear time. Passing data through these special sequences of numbers in a data approximation transform to gain a special edge in the knowledge of outcomes, to attain that slightly more than 50% certainty that a gambler needs. Gamblers deal with gaining a special mastery over incompleteness, not with definitively overcoming incompleteness in hard results as the APIs of conventional programming language math libraries do. Thus the Limerick Metric ‘Hello World’ will perform the impossible feat of both satisfying the criterion of what software is – it will really work and really do something – and rewriting the rules of what software is in an act of wily defiance and non-deterministic trickery.
MANIFESTO: ARTIFICIAL LIFE
Artificial Life is dynamically stabilized instability. Artificial Life is a computational paradigm for biology and a biological paradigm for software engineering. The bio-informatic professional might be qualified in areas like immune system computing and genome programming. Self-replicating computer programs are said to be “alive,” according to cybernetics historian N. Katherine Hayles, through the rhetoric of biological analogies regarding complex behavior, diversity regulation mechanisms, and their abundance of “interacting adaptive agents.” With Artificial Life, the goal is to “evolve intelligence within the machine through pathways found by the ‘creatures’ themselves.” (10) Life-based systems emphasize autonomous agents without a directing layer, strange attractors, and the appearance of emergent behaviours. They have the features of unpredictability, mutability, nonlinearity, rule diversity, fuzzy functionality, and chaotic instability. They tend to operate in a state of non-equilibrium that is ‘at the edge of chaos’. Data storage structures have non-discrete holistic forms and connections. Programming languages acquire self-modifying capabilities. Computing systems coinciding with the third order of cybernetics have properties affiliated with genetic algorithms, cellular automata, and neural networks. The hyper-dynamic software makes leaps to new ‘attractor structures’ that can in turn mutate into yet further configurations.
This is a stochastic method that draws heavily on the positive inferences of Gödel’s Incompleteness Theorems by applying them to topological choice structures (i.e. Möbius structures). These inferences give rise to rich insight regarding symmetry breaking and variable mutation probability theorems. There is also a coupling with these inferences and purely mathematical “skewing” of certain basic paradigms – skewing of mathematical bases and alternate treatment of origin and infinity constructs.
1 – Alan N. Shapiro is a trans-disciplinary thinker who studied science-technology at MIT and philosophy-history-literature at Cornell University. He is the author of Technologies of Disappearance and many published essays. He is a practicing software developer, and a translator of works in new philosophy and new critical theory from German and Italian into English. He loves baseball and casino gambling.
2 – In the article abstract. This echoes the view of Humboldt University media theory professor Friedrich Kittler who pointed out in his essay “There is no Software” that Turing’s computing machine is a reduction of the body of real numbers extant in nature that we call chaos.
3 – Rupert Sheldrake, The Sense Of Being Stared At. See: A New Science of Life: The Hypothesis of Formative Causation (1981), The Presence of the Past. Morphic Resonance and the Habits of Nature (1988), and The Rebirth of Nature: The Greening of Science and God (1991), all by Rupert Sheldrake.
4 – Alexis Clancy is a young Irish artist, computer scientist, and mathematician with university degrees in mathematics and physics. He has a special genius here, and his breakthroughs stem in part from his having undertaken studies of comparative historical mathematical systems, such as Hebrew and Mayan mathematics, and Bushido dynamics.
5 – Artistic Director of Daghdha Dance Company.
6 – In mathematics, a Metric Space is a set where a specific concept of distance between elements of the set is defined and implemented. Three-dimensional Euclidean space – a way of thinking about space that belongs to the Western metaphysical ‘construction of reality’ as it was originated by the Ancient Greek thinkers – corresponds to our ‘intuitive understanding’ of space. Another example of Western metaphysics is the Aristotelian classifiying logic of “A is true or B is true,” the limits of which as an intelligent system of logic are nowadays showing more and more. The geometric properties of the Metric Space depend on the Metric chosen. By conceptualizing a different Metric, interesting Non-Euclidean Geometries can be constructed, for example, those used in the Einsteinian theory of general relativity. Metric Spaces are Topological Spaces, and there is a continuous function between Metric Spaces (small changes in input result in small changes in output).
7. What is also nifty about the Aleph operator is that its effect on a frame (and a model being a dynamic series of frames) renders it consistent with slices of a Riemann solid, and is therefore consistent with the geometry of both the quanta and the cosmic. I am not a complete expert on Riemann geometry, but I know enough to know this.
8 – [Cybernetic Epistemologist Gregory] Bateson’s .. ‘ecology of mind’ .. assumed that noise generation was creative. In Bateson’s reinterpretation, noise was ‘playful’ and creative; it became looped back into the overall system as part of the creation of new patterns. .. thus the presence of noise was by no means an error to be overcome; rather, it was a source for future adaptation.
9 – Purely mathematical objections: To model anything on a (0, ∞) interval can ultimately only give rise to serious non-sequiturs due to the incompatibility of the concepts of zero and infinity with the set of real numbers. Furthermore, the treatment of zero as a straightforward singularity to be (more or less) mathematically ignored denies the model some of the subtleties that a dynamic of the origin can offer (specifically when it comes to marshalling events and the dimensionality achieved therein).
10 – N. Katherine Hayles, How We Became Posthuman: Virtual Bodies in Cybernetics, Literature and Informatics (Chicago: University of Chicago Press, 1999); p.239