Assumption of knowledge and the Chinese Room in Turing test interrogation

Whilst common sense knowledge has been well researched in terms of intelligence and (in particular) artificial intelligence, specific, factual knowledge also plays a critical part in practice. When it comes to testing for intelligence, testing for factual knowledge is, in every-day life, frequently used as a front line tool. This paper presents new results which were the outcome of a series of practical Turing tests held on 23rd June 2012 at Bletchley Park, England. The focus of this paper is on the employment of specific knowledge testing by interrogators. Of interest are prejudiced assumptions made by interrogators as to what they believe should be widely known and subsequently the conclusions drawn if an entity does or does not appear to know a particular fact known to the interrogator. The paper is not at all about the performance of machines or hidden humans but rather the strategies based on assumptions of Turing test interrogators. Full, unedited transcripts from the tests are shown for the reader as working examples. As a result, it might be possible to draw critical conclusions with regard to the nature of human concepts of intelligence, in terms of the role played by specific, factual knowledge in our understanding of intelligence, whether this is exhibited by a human or a machine. This is specifically intended as a position paper, firstly by claiming that practicalising Turing's test is a useful exercise throwing light on how we humans think, and secondly, by taking a potentially controversial stance, because some interrogators adopt a solipsist questioning style of hidden entities with a view that it is a thinking intelligent human if it thinks like them and knows what they know. The paper is aimed at opening discussion with regard to the different aspects considered.

ken

From the beginning, the world of game-playing by machine has been fortunate in attracting contributions from the leading names of computer science. Charles Babbage, Konrad Zuse, Claude Shannon, Alan Turing, John von Neumann, John McCarthy, Alan Newell, Herb Simon and Ken Thompson all come to mind, and each reader will wish to add to this list. Recently, the Journal has saluted both Claude Shannon and Herb Simon. Ken’s retirement from Lucent Technologies’ Bell Labs to the start-up Entrisphere is also a good moment for reflection.

Truth in complex adaptive systems models should be based on truth by constructive verification

It is argued that the truth status of emergent properties of complex adaptive systems models should be based on an epistemology of proof by constructive verification and therefore on the ontological axioms of a non-realist logical system such as constructivism or intuitionism. ‘Emergent’ properties of complex adaptive systems (CAS) models create particular epistemological and ontological challenges. These challenges bear directly on current debates in the philosophy of mathematics and in theoretical computer science. CAS research, with its emphasis on computer simulation, is heavily reliant on models which explore the entailments of Formal Axiomatic Systems (FAS). The incompleteness results of Gödel, the incomputability results of Turing, and the Algorithmic Information Theory results of Chaitin, undermine a realist (platonic) truth model of emergent properties. These same findings support the hegemony of epistemology over ontology and point to alternative truth models such as intuitionism, constructivism and quasi-empiricism.

Perspex machine VII: The universal perspex machine

The perspex machine arose from the unification of projective geometry with the Turing machine. It uses a total arithmetic, called transreal arithmetic, that contains real arithmetic and allows division by zero. Transreal arithmetic is redefined here. The new arithmetic has both a positive and a negative infinity which lie at the extremes of the number line, and a number nullity that lies off the number line. We prove that nullity, 0/0, is a number. Hence a number may have one of four signs: negative, zero, positive, or nullity. It is, therefore, impossible to encode the sign of a number in one bit, as floating-, point arithmetic attempts to do, resulting in the difficulty of having both positive and negative zeros and NaNs. Transrational arithmetic is consistent with Cantor arithmetic. In an extension to real arithmetic, the product of zero, an infinity, or nullity with its reciprocal is nullity, not unity. This avoids the usual contradictions that follow from allowing division by zero. Transreal arithmetic has a fixed algebraic structure and does not admit options as IEEE, floating-point arithmetic does. Most significantly, nullity has a simple semantics that is related to zero. Zero means "no value" and nullity means "no information." We argue that nullity is as useful to a manufactured computer as zero is to a human computer. The perspex machine is intended to offer one solution to the mind-body problem by showing how the computable aspects of mind and. perhaps, the whole of mind relates to the geometrical aspects of body and, perhaps, the whole of body. We review some of Turing's writings and show that he held the view that his machine has spatial properties. In particular, that it has the property of being a 7D lattice of compact spaces. Thus, we read Turing as believing that his machine relates computation to geometrical bodies. We simplify the perspex machine by substituting an augmented Euclidean geometry for projective geometry. This leads to a general-linear perspex-machine which is very much easier to pro-ram than the original perspex-machine. We then show how to map the whole of perspex space into a unit cube. This allows us to construct a fractal of perspex machines with the cardinality of a real-numbered line or space. This fractal is the universal perspex machine. It can solve, in unit time, the halting problem for itself and for all perspex machines instantiated in real-numbered space, including all Turing machines. We cite an experiment that has been proposed to test the physical reality of the perspex machine's model of time, but we make no claim that the physical universe works this way or that it has the cardinality of the perspex machine. We leave it that the perspex machine provides an upper bound on the computational properties of physical things, including manufactured computers and biological organisms, that have a cardinality no greater than the real-number line.

Perspex machine IX: transreal analysis

We introduce transreal analysis as a generalisation of real analysis. We find that the generalisation of the real exponential and logarithmic functions is well defined for all transreal numbers. Hence, we derive well defined values of all transreal powers of all non-negative transreal numbers. In particular, we find a well defined value for zero to the power of zero. We also note that the computation of products via the transreal logarithm is identical to the transreal product, as expected. We then generalise all of the common, real, trigonometric functions to transreal functions and show that transreal (sin x)/x is well defined everywhere. This raises the possibility that transreal analysis is total, in other words, that every function and every limit is everywhere well defined. If so, transreal analysis should be an adequate mathematical basis for analysing the perspex machine - a theoretical, super-Turing machine that operates on a total geometry. We go on to dispel all of the standard counter "proofs" that purport to show that division by zero is impossible. This is done simply by carrying the proof through in transreal arithmetic or transreal analysis. We find that either the supposed counter proof has no content or else that it supports the contention that division by zero is possible. The supposed counter proofs rely on extending the standard systems in arbitrary and inconsistent ways and then showing, tautologously, that the chosen extensions are not consistent. This shows only that the chosen extensions are inconsistent and does not bear on the question of whether division by zero is logically possible. By contrast, transreal arithmetic is total and consistent so it defeats any possible "straw man" argument. Finally, we show how to arrange that a function has finite or else unmeasurable (nullity) values, but no infinite values. This arithmetical arrangement might prove useful in mathematical physics because it outlaws naked singularities in all equations.

Perspex machine VIII: axioms of transreal arithmetic

Transreal arithmetic is a total arithmetic that contains real arithmetic, but which has no arithmetical exceptions. It allows the specification of the Universal Perspex Machine which unifies geometry with the Turing Machine. Here we axiomatise the algebraic structure of transreal arithmetic so that it provides a total arithmetic on any appropriate set of numbers. This opens up the possibility of specifying a version of floating-point arithmetic that does not have any arithmetical exceptions and in which every number is a first-class citizen. We find that literal numbers in the axioms are distinct. In other words, the axiomatisation does not require special axioms to force non-triviality. It follows that transreal arithmetic must be defined on a set of numbers that contains{-8,-1,0,1,8,&pphi;} as a proper subset. We note that the axioms have been shown to be consistent by machine proof.

Chatterbox challenge as a test-bed for synthetic emotions

Chatterbox Challenge is an annual web-based contest for artificial conversational systems, ACE. The 2010 instantiation was the tenth consecutive contest held between March and June in the 60th year following the publication of Alan Turing’s influential disquisition ‘computing machinery and intelligence’. Loosely based on Turing’s viva voca interrogator-hidden witness imitation game, a thought experiment to ascertain a machine’s capacity to respond satisfactorily to unrestricted questions, the contest provides a platform for technology comparison and evaluation. This paper provides an insight into emotion content in the entries since the 2005 Chatterbox Challenge. The authors find that synthetic textual systems, none of which are backed by academic or industry funding, are, on the whole and more than half a century since Weizenbaum’s natural language understanding experiment, little further than Eliza in terms of expressing emotion in dialogue. This may be a failure on the part of the academic AI community for ignoring the Turing test as an engineering challenge.

From the buzzing in Turing’s head to machine intelligence contests

This paper presents an analysis of three major contests for machine intelligence. We conclude that a new era for Turing’s test requires a fillip in the guise of a committed sponsor, not unlike DARPA, funders of the successful 2007 Urban Challenge.

Perspex machine

We introduce the perspex machine which unifies projective geometry and the Turing machine, resulting in a supra-Turing machine. Specifically, we show that a Universal Register Machine (URM) can be implemented as a conditional series of whole numbered projective transformations. This leads naturally to a suggestion that it might be possible to construct a perspex machine as a series of pin-holes and stops. A rough calculation shows that an ultraviolet perspex machine might operate up to the petahertz range of operations per second. Surprisingly, we find that perspex space is irreversible in time, which might make it a candidate for an anisotropic spacetime geometry in physical theories. We make a bold hypothesis that the apparent irreversibility of physical time is due to the random nature of quantum events, but suggest that a sum over histories might be achieved by sampling fluctuations in the direction of time flow. We propose an experiment, based on the Casimir apparatus, that should measure fluctuations of time flow with respect to time duration- if such fluctuations exist.

Robot free will

We introduce the perspex machine which unifies projective geometry and Turing computation and results in a supra-Turing machine. We show two ways in which the perspex machine unifies symbolic and non-symbolic AI. Firstly, we describe concrete geometrical models that map perspexes onto neural networks, some of which perform only symbolic operations. Secondly, we describe an abstract continuum of perspex logics that includes both symbolic logics and a new class of continuous logics. We argue that an axiom in symbolic logic can be the conclusion of a perspex theorem. That is, the atoms of symbolic logic can be the conclusions of sub-atomic theorems. We argue that perspex space can be mapped onto the spacetime of the universe we inhabit. This allows us to discuss how a robot might be conscious, feel, and have free will in a deterministic, or semi-deterministic, universe. We ground the reality of our universe in existence. On a theistic point, we argue that preordination and free will are compatible. On a theological point, we argue that it is not heretical for us to give robots free will. Finally, we give a pragmatic warning as to the double-edged risks of creating robots that do, or alternatively do not, have free will.

Adaptation-induced collective dynamics of a single-cell protozoan

We investigate the behavior of a single-cell protozoan in a narrow tubular ring. This environment forces them to swim under a one-dimensional periodic boundary condition. Above a critical density, single-cell protozoa aggregate spontaneously without external stimulation. The high-density zone of swimming cells exhibits a characteristic collective dynamics including translation and boundary fluctuation. We analyzed the velocity distribution and turn rate of swimming cells and found that the regulation of the turing rate leads to a stable aggregation and that acceleration of velocity triggers instability of aggregation. These two opposing effects may help to explain the spontaneous dynamics of collective behavior. We also propose a stochastic model for the mechanism underlying the collective behavior of swimming cells.

Axonal velocity distributions in neural feld equations

By modelling the average activity of large neuronal populations, continuum mean field models (MFMs) have become an increasingly important theoretical tool for understanding the emergent activity of cortical tissue. In order to be computationally tractable, long-range propagation of activity in MFMs is often approximated with partial differential equations (PDEs). However, PDE approximations in current use correspond to underlying axonal velocity distributions incompatible with experimental measurements. In order to rectify this deficiency, we here introduce novel propagation PDEs that give rise to smooth unimodal distributions of axonal conduction velocities. We also argue that velocities estimated from fibre diameters in slice and from latency measurements, respectively, relate quite differently to such distributions, a significant point for any phenomenological description. Our PDEs are then successfully fit to fibre diameter data from human corpus callosum and rat subcortical white matter. This allows for the first time to simulate long-range conduction in the mammalian brain with realistic, convenient PDEs. Furthermore, the obtained results suggest that the propagation of activity in rat and human differs significantly beyond mere scaling. The dynamical consequences of our new formulation are investigated in the context of a well known neural field model. On the basis of Turing instability analyses, we conclude that pattern formation is more easily initiated using our more realistic propagator. By increasing characteristic conduction velocities, a smooth transition can occur from self-sustaining bulk oscillations to travelling waves of various wavelengths, which may influence axonal growth during development. Our analytic results are also corroborated numerically using simulations on a large spatial grid. Thus we provide here a comprehensive analysis of empirically constrained activity propagation in the context of MFMs, which will allow more realistic studies of mammalian brain activity in the future.

Modeling electrocortical activity through improved local approximations of integral neural field equations

Neural field models of firing rate activity typically take the form of integral equations with space-dependent axonal delays. Under natural assumptions on the synaptic connectivity we show how one can derive an equivalent partial differential equation (PDE) model that properly treats the axonal delay terms of the integral formulation. Our analysis avoids the so-called long-wavelength approximation that has previously been used to formulate PDE models for neural activity in two spatial dimensions. Direct numerical simulations of this PDE model show instabilities of the homogeneous steady state that are in full agreement with a Turing instability analysis of the original integral model. We discuss the benefits of such a local model and its usefulness in modeling electrocortical activity. In particular, we are able to treat “patchy” connections, whereby a homogeneous and isotropic system is modulated in a spatially periodic fashion. In this case the emergence of a “lattice-directed” traveling wave predicted by a linear instability analysis is confirmed by the numerical simulation of an appropriate set of coupled PDEs.

Spatial interaction among nontoxic phytoplankton, toxic phytoplankton and zooplankton: emergence in space and time

In homogeneous environments, by overturning the possibility of competitive exclusion among phytoplankton species, and by regulating the dynamics of overall plankton population, toxin-producing phytoplankton (TPP) potentially help in maintaining plankton diversity—a result shown recently. Here, I explore the competitive effects of TPP on phytoplankton and zooplankton species undergoing spatial movements in the subsurface water. The spatial interactions among the species are represented in the form of reaction-diffusion equations. Suitable parametric conditions under which Turing patterns may or may not evolve are investigated. Spatiotemporal distributions of species biomass are simulated using the diffusivity assumptions realistic for natural planktonic systems. The study demonstrates that spatial movements of planktonic systems in the presence of TPP generate and maintain inhomogeneous biomass distribution of competing phytoplankton, as well as grazer zooplankton, thereby ensuring the persistence of multiple species in space and time. The overall results may potentially explain the sustainability of biodiversity and the spatiotemporal emergence of phytoplankton and zooplankton species under the influence of TPP combined with their physical movement in the subsurface water.