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.

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.

Deception-detection and machine intelligence in practical Turing tests

Deception-detection is the crux of Turing’s experiment to examine machine thinking conveyed through a capacity to respond with sustained and satisfactory answers to unrestricted questions put by a human interrogator. However, in 60 years to the month since the publication of Computing Machinery and Intelligence little agreement exists for a canonical format for Turing’s textual game of imitation, deception and machine intelligence. This research raises from the trapped mine of philosophical claims, counter-claims and rebuttals Turing’s own distinct five minutes question-answer imitation game, which he envisioned practicalised in two different ways: a) A two-participant, interrogator-witness viva voce, b) A three-participant, comparison of a machine with a human both questioned simultaneously by a human interrogator. Using Loebner’s 18th Prize for Artificial Intelligence contest, and Colby et al.’s 1972 transcript analysis paradigm, this research practicalised Turing’s imitation game with over 400 human participants and 13 machines across three original experiments. Results show that, at the current state of technology, a deception rate of 8.33% was achieved by machines in 60 human-machine simultaneous comparison tests. Results also show more than 1 in 3 Reviewers succumbed to hidden interlocutor misidentification after reading transcripts from experiment 2. Deception-detection is essential to uncover the increasing number of malfeasant programmes, such as CyberLover, developed to steal identity and financially defraud users in chatrooms across the Internet. Practicalising Turing’s two tests can assist in understanding natural dialogue and mitigate the risk from cybercrime.

Turing Test: Mindless Game?

The Turing Test, originally configured for a human to distinguish between an unseen man and unseen woman through a text-based conversational measure of gender, is the ultimate test for thinking. So conceived Alan Turing when he replaced the woman with a machine. His assertion, that once a machine deceived a human judge into believing that they were the human, then that machine should be attributed with intelligence. But is the Turing Test nothing more than a mindless game? We present results from recent Loebner Prizes, a platform for the Turing Test, and find that machines in the contest appear conversationally worse rather than better, from 2004 to 2006, showing a downward trend in highest scores awarded to them by human judges. Thus the machines are not thinking in the same way as a human intelligent entity would.

Hidden interlocutor misidentification in practical Turing Tests

Based on insufficient evidence, and inadequate research, Floridi and his students report inaccuracies and draw false conclusions in their Minds and Machines evaluation, which this paper aims to clarify. Acting as invited judges, Floridi et al. participated in nine, of the ninety-six, Turing tests staged in the finals of the 18th Loebner Prize for Artificial Intelligence in October 2008. From the transcripts it appears that they used power over solidarity as an interrogation technique. As a result, they were fooled on several occasions into believing that a machine was a human and that a human was a machine. Worse still, they did not realise their mistake. This resulted in a combined correct identification rate of less than 56%. In their paper they assumed that they had made correct identifications when they in fact had been incorrect.

Testing Turing's five minutes, parallel-paired imitation game

Purpose – The purpose of this paper is to consider Turing's two tests for machine intelligence: the parallel-paired, three-participants game presented in his 1950 paper, and the “jury-service” one-to-one measure described two years later in a radio broadcast. Both versions were instantiated in practical Turing tests during the 18th Loebner Prize for artificial intelligence hosted at the University of Reading, UK, in October 2008. This involved jury-service tests in the preliminary phase and parallel-paired in the final phase. Design/methodology/approach – Almost 100 test results from the final have been evaluated and this paper reports some intriguing nuances which arose as a result of the unique contest. Findings – In the 2008 competition, Turing's 30 per cent pass rate is not achieved by any machine in the parallel-paired tests but Turing's modified prediction: “at least in a hundred years time” is remembered. Originality/value – The paper presents actual responses from “modern Elizas” to human interrogators during contest dialogues that show considerable improvement in artificial conversational entities (ACE). Unlike their ancestor – Weizenbaum's natural language understanding system – ACE are now able to recall, share information and disclose personal interests.

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.

Not another look at the Turing Test!

Practical application of the Turing Test throws up all sorts of questions regarding the nature of intelligence in both machines and humans. For example - Can machines tell original jokes? What would this mean to a machine if it did so? It has been found that acting as an interrogator even top philosophers can be fooled into thinking a machine is human and/or a human is a machine - why is this? Is it that the machine is performing well or is it that the philosopher is performing badly? All these questions, and more, will be considered. Just what does the Turing test tell us about machines and humans? Actual transcripts will be considered with startling results.

Some implications of a sample of practical Turing tests

A series of imitation games involving 3-participant (simultaneous comparison of two hidden entities) and 2-participant (direct interrogation of a hidden entity) were conducted at Bletchley Park on the 100th anniversary of Alan Turing’s birth: 23 June 2012. From the ongoing analysis of over 150 games involving (expert and non-expert, males and females, adults and child) judges, machines and hidden humans (foils for the machines), we present six particular conversations that took place between human judges and a hidden entity that produced unexpected results. From this sample we focus on features of Turing’s machine intelligence test that the mathematician/code breaker did not consider in his examination for machine thinking: the subjective nature of attributing intelligence to another mind.

Human misidentification in Turing tests

This paper presents some important issues on misidentification of human interlocutors in text-based communication during practical Turing tests. The study here presents transcripts in which human judges succumbed to theconfederate effect, misidentifying hidden human foils for machines. An attempt is made to assess the reasons for this. The practical Turing tests in question were held on 23 June 2012 at Bletchley Park, England. A selection of actual full transcripts from the tests is shown and an analysis is given in each case. As a result of these tests, conclusions are drawn with regard to the sort of strategies which can perhaps lead to erroneous conclusions when one is involved as an interrogator. Such results also serve to indicate conversational directions to avoid for those machine designers who wish to create a conversational entity that performs well on the Turing test.

Effects of lying in practical Turing tests

Interpretation of utterances affects an interrogator’s determination of human from machine during live Turing tests. Here, we consider transcripts realised as a result of a series of practical Turing tests that were held on 23 June 2012 at Bletchley Park, England. The focus in this paper is to consider the effects of lying and truth-telling on the human judges by the hidden entities, whether human or a machine. Turing test transcripts provide a glimpse into short text communication, the type that occurs in emails: how does the reader determine truth from the content of a stranger’s textual message? Different types of lying in the conversations are explored, and the judge’s attribution of human or machine is investigated in each test.