Alan Shapiro on Tue, 4 Aug 2009 15:19:06 +0200 (CEST) |
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<nettime> The New Computer Science |
Dear nettime, Choreograph.net just published the essay "A Proposal for Developing Quantum Computing in Software", by Alan N. Shapiro and Alexis Clancy (see link below). This is an essay on the new computer science, which is based on new mathematics. I am sending you one-fourth of the text to publish on nettime. If you decide to publish it (i hope so), please include the link to the full text at Choreograph.net. Best regards, Alan N. Shapiro "A Proposal for Developing Quantum Computing in Software" published here: http://www.choreograph.net/ A Proposal for Developing Quantum Computing in Software by Alan N. Shapiro and Alexis Clancy [We] 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. 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. 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'. 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. 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 (1). I am inspired by Goethe's quote: Search nothing beyond the phenomena, they themselves are the theory. 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. 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. 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. 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. 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. 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. NOTES 1 - 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). # distributed via <nettime>: no commercial use without permission # <nettime> is a moderated mailing list for net criticism, # collaborative text filtering and cultural politics of the nets # more info: http://mail.kein.org/mailman/listinfo/nettime-l # archive: http://www.nettime.org contact: nettime@kein.org