A continuous spatial automaton is analogous to a cellular automaton, except that the cells form a continuum, as do the possible states of the cells. After an informal mathematical description of spatial automata, we describe in detail a continuous analog of Conway’s “Life,” and show how the automaton can be implemented using the basic operations of field computation.

In this report we develop the basic properties of a set of functions analogous to the circular and hyperbolic functions, but based on L p circles. The resulting identities may simplify analysis in L p spaces in much the way that the circular functions do in Euclidean space. In any case, they are a pleasing example of mathematical generalization.

The title of my talk, “Living Neoplatonism,” is intentionally ambiguous, for it can refer, first, to Neoplatonism as a living philosophy rather than as a historical artifact embodied in the writings of Plotinus, Proclus, and the rest. And second, it can refer to the practice of living Neoplatonically as a modern way of life. But why Neoplatonism, as opposed to some other philosophy? From my perspective as a scientist I will explain why I think Neoplatonism is especially suited to provide (...) a spiritual complement to the contemporary scientific worldview, which is otherwise materialistic in orientation and ill-equipped to deal with many peoples’ spiritual concerns. (shrink)

This article is a reflection on the significance of the recent struggle in Brisbane to prevent a two-year-old refugee child, Asha, from being taken from hospital and deported. The child was suffering from burns and after her treatment the doctors refused to sign a release form as her safety could not be guaranteed in the refugee camp. The stance of the doctors produced widespread support from the people of Brisbane and the rest of Australia forcing the government to temporarily back (...) down and allow the child and her parents to be placed in community detention in Australia rather than off-shore. (shrink)

Hypatia was the most famous female spiritual teacher of ancient Alexandria. The mix of classical philosophies she taught to Pagans, Jews, and Christians in the fourth century CE forms the very foundation of Western magic and mysticism as we know it today. The Wisdom of Hypatia offers a progressive, nine month programme based on the teachings of this inspiring Pagan philosopher. Discover how to bring purpose, tranquillity, and spiritual depth to your life through exercises and techniques divided into three stages (...) of wisdom: Epicureanism, Stoicism, and Neoplatonism. This virtual course in philosophy, well-being, and divine union is an essential and practical introduction to the ancient wisdom of the West. (shrink)

Use of quantum probability as a top-down model of cognition will be enhanced by consideration of the underlying complex-valued wave function, which allows a better account of interference effects and of the structure of learned and ad hoc question operators. Furthermore, the treatment of incompatible questions can be made more quantitative by analyzing them as non-commutative operators.

It has been argued that neural networks and other forms of analog computation may transcend the limits of Turing-machine computation; proofs have been offered on both sides, subject to differing assumptions. In this article I argue that the important comparisons between the two models of computation are not so much mathematical as epistemological. The Turing-machine model makes assumptions about information representation and processing that are badly matched to the realities of natural computation (information representation and processing in or inspired by (...) natural systems). This points to the need for new models of computation addressing issues orthogonal to those that have occupied the traditional theory of computation. (shrink)

The issue of symbol grounding is not essentially different in analog and digital computation. The principal difference between the two is that in analog computers continuous variables change continuously, whereas in digital computers discrete variables change in discrete steps (at the relevant level of analysis). Interpretations are imposed on analog computations just as on digital computations: by attaching meanings to the variables and the processes defined over them. As Harnad (2001) claims, states acquire intrinsic meaning through their relation to the (...) real (physical) environment, for example, through transduction. However, this is independent of the question of the continuity or discreteness of the variables or the transduction processes. (shrink)

The worldview emerging from neurophenomenology is consistent with the phenomenological insights obtained by Neoplatonic theurgical operations. For example, gods and daimons are phenomenologically equivalent to the archetypes and complexes investigated in Jungian psychology and explicated by evolutionary psychology. Jung understood the unconscious mind and physical reality to have a common root in an unus mundus. Parallel reductions in the phenomenological and neurological domain imply elementary constituents of consciousness associated with simple physical systems, that is, natural processes experienced both externally and (...) internally. Analysis reveals they have both an eternal formal structure and a material substrate that allows the formal structure to evolve in time with both phenomenal and physical aspects. Since all physical processes fit this description, a form of panpsychism is implied. These developments can inform our understanding of the Forms, the World Soul, and individual souls in Neoplatonism. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:uippraisals from the 'Past THE CLEAREST INTELLECT OF OUR AGEl H UGH MACLENNAN 19°7-199° R cently I have been rereading Bertrand Russell, and in so doing I suddenly realized that lowe to this man a good deal of such happiness as I enjoy. Over the years I had forgotten how great my debt was, but when I reread one of his books which I first read as a (...) student, I understood the extent to which he had liberated me from the psychological sadism of Calvin and Knox, to whom I had been unduly exposed when young. It is probably impossible for anyone entirely to escape once these two have got their hands around his throat, but Russell enabled me to escape a litde. 1 [This essay was recently discovered during the cataloguing for BRACERS of an obscure class of correspondence. Mr. Joseph w. Devine had sent Russell a clipping of the essay's appearance in' the Philadelphia Sunday But/etin, of 15 July 1962. I had long thought, from reading Elspeth Cameron's Hugh MacLennan: a Writers Life (1981), that he showed signs not only of having been influenced by Russell but of being the sOrt of person who is attracted to Russell's way of thinking. A promising tide in the same scholar's bibliography ofMacLennan turned out to be a fuller version of the clipping. "The Clearest Intellect of Our Age" is reprinted from The Montreal Star, 14 July 1962, "Entertainments" sec., p. 5. Russell did influence MacLennan. Neither the Russell Archives nor the inventory of the Maclennan papers at the Universiry of Calgary reveals personal contact berween the rwo. I wish I had asked MacLennan about contacts and influence seventeen years ago, when I sent him an early issue of Russell He commented: ''1 found your journal fascinating and never before had read that beautiful thing Russell wrote in his early days with Whitehead:" He is referring to the essay on the status of women in No.6, now in Papers 12.-Ed.] russell: the Journal ofthe Benrand Russell Archives McMaster Unive..ity Libraty Press noS. 11 (summer 1991): 83-5 ISSN 00,6-01631 84 HUGH MACLENNAN I suppose he really is the greatest man alive, in the sense that his teaching grows and his teaching is good, but it is pointless to argue the point between him and Churchill. It is wonderful, however, that many think he is our greatest man and that he has become an international hero to millions of the thoughtful youth. He must be the first pure logician who ever was that. Until he took his stand against nuclear war, he never appealed to the passions. He lacked the aggressions which youth admires. He never said: "Come live with me and I will be your master"; or, "Follow me and I will purge you of your sins." He had no use for self-sacrifice as such. He simply said, in effect: "Happiness is good. If you desire it, you must be reasonable." As he was intelligent enough to know that anyone who teaches that happiness is good, and teaches how to achieve it, is sute to be considered subversive to a Christian-commercial society, he bore no personal resentment when society persecuted him. The young know, of course, that Russell is now assumed by the experts to be the most important philosopher since Hume, but that is not why they love him. They love him for the sublime civilization of his courage, for his refusal to let an intensely kind nature blunt his respect for truth. They love him because he loves life even in the twentieth century; and they love him most of all because he is engage. And of course they also love the wit which refuses to be made tongue-tied by those who insist that whenever one speaks of sex or religion one must be solemn. Russell's wit is worth the study of any writer. It is based on mathematics, and Russell would agree, I think, with the remark Camillien Houde once made to me when I asked the famous mayor of Montreal how he was always able to make people laugh. Houde replied... (shrink)

to small scales. Further, it is often useful to describe motor control and sensorimotor coordination in terms of external elds such as force elds and sensory images. We survey the basic concepts of eld computation, including both feed-forward eld operations and eld dynamics resulting from recurrent connections. Adaptive and learning mechanisms are discussed brie y. The application of eld computation to motor control is illustrated by several examples: external force elds associated with spinal neurons, population coding of direction in motor (...) cortex, continuous transformation of direction elds, and linear gain elds and coordinate transformations in posterior parietal cortex. Next we survey some eld-based representations of motion, including direct, Fourier, Gabor and wavelet or multiresolution representations. Finally we consider brie y the application of these representations to constraint satisfaction, which has many applications in motor control. (shrink)

The central claim of computationalism is generally taken to be that the brain is a computer, and that any computer implementing the appropriate program would ipso facto have a mind. In this paper I argue for the following propositions: (1) The central claim of computationalism is not about computers, a concept too imprecise for a scientific claim of this sort, but is about physical calculi (instantiated discrete formal systems). (2) In matters of formality, interpretability, and so forth, analog computation and (...) digital computation are not essentially different, and so arguments such as Searle''s hold or not as well for one as for the other. (3) Whether or not a biological system (such as the brain) is computational is a scientific matter of fact. (4) A substantive scientific question for cognitive science is whether cognition is better modeled by discrete representations or by continuous representations. (5) Cognitive science and AI need a theoretical construct that is the continuous analog of a calculus. The discussion of these propositions will illuminate several terminology traps, in which it''s all too easy to become ensnared. (shrink)

The idea that democracy is under threat, after being largely dormant for at least 40 years, is looming increasingly large in public discourse. Complex systems theory offers a range of powerful new tools to analyse the stability of social institutions in general, and democracy in particular. What makes a democracy stable? And which processes potentially lead to instability of a democratic system? This paper offers a complex systems perspective on this question, informed by areas of the mathematical, natural, and social (...) sciences. We explain the meaning of the term 'stability' in different disciplines and discuss how laws, rules, and regulations, but also norms, conventions, and expectations are decisive for the stability of a social institution such as democracy. (shrink)

I discuss neuroscientific and phenomenological arguments in support of Millikan's thesis. I then consider invariance as a unifying theme in perceptual and conceptual tracking, and how invariants may be extracted from the environment. Finally, some wider implications of Millikan's nondescriptionist approach to language are presented, with specific application to color terms.

Richard Kilborn and John Izod _An Introduction to Television Documentary: Confronting Reality_ Manchester: Manchester University Press, 1997 ISBN: 0719048923(hbk) 0719048931 (pbk) 258 pp.

The ‘hard problem’ is hard because of the special epistemological status of consciousness, which does not, however, preclude its scientific investigation. Data from phenomenologically trained observers can be combined with neurological investigations to establish the relation between experience and neurodynamics. Although experience cannot be reduced to physical phenomena, parallel phenomenological and neurological analyses allow the structure of experience to be related to the structure of the brain. Such an analysis suggests a theoretical entity, an elementary unit of experience, the protophenomenon, (...) which corresponds to an activity site in the brain. The structure of experience is determined by connections between these activity sites; the connections correspond to temporal patterns among the elementary units of experience, which can be expressed mathematically. This theoretical framework illuminates several issues, including degrees of consciousness, nonbiological consciousness, sensory inversions, unity of consciousness and the unconscious mind. (shrink)

The principal problem of consciousness is how brain processes cause subjective awareness. Since this problem involves subjectivity, ordinary scientific methods, applicable only to objective phenomena, cannot be used. Instead, by parallel application of phenomenological and scientific methods, we may establish a correspondence between the subjective and the objective. This correspondence is effected by the construction of a theoretical entity, essentially an elementary unit of consciousness, the intensity of which corresponds to electrochemical activity in a synapse. Dendritic networks correspond to causal (...) dependencies between these subjective units. Therefore, the structure of conscious experience is derived from synaptic connectivity. This parallel phenomenal/neural analysis provides a framework for the investigation of a number of problems, including sensory inversions, the unity of consciousness, and the nature of nonhuman consciousness. (shrink)

Despite tensions between Tillich's category of belief-ful realism and a view of science that embraces metaphysical and epistemological realism, a constructive relationship can be developed between the two. Both are based on common understandings about reality. Belief-ful or theonomous realism, thus, affirms scientific realism. On the other hand, scientific realism is open to the ecstatic, self-transcending elements of belief-ful realism. Finally, Tillich's formulation of the relationship between culture and religion can be reformulated specifically to include scientific and technological culture.

In the first part of this commentary I argue that a neurophenomenological analysis of color reveals additional asymmetries that preclude undetectable color transformations, without appealing to weak arguments based on Basic Color Categories (BCCs); that is, I suggest additional factors that must be included in “an empirically accurate model of color experience,” and which break the remaining asymmetries. In the second part I discuss the “isomorphism constraint” and the extent to which we may predict the subjective quality of experience from (...) its neurological correlates. Protophenomena are discussed as a way of capturing in a relational structure all of qualitative experience except for the bare fact of subjectivity. (shrink)

For all animals, color is an indicator of the substance and state of objects, for which purpose reflectance is just one among many relevant optical properties. This broader meaning of color is confirmed by linguistic evidence. Rather than reducing color to a simple physical property, it is more realistic to embrace its full phenomenology.

Ausgehend von Erkenntnissen der Evolutionären Psychologie untersucht dieser Beitrag wichtige Funktionen, die das Bewusstsein autonomer Roboter ausfüllen kann. Gemeint sind willkürlich kontrolliertes Handeln, bewusstes Wahrnehmen, Eigenwahrnehmung, Metaerkenntnis sowie Bewusstsein des eigenen Selbst. Der Verfasser unterscheidet zwischen intrinsischer Intentionalität und Bewusstsein, führt jedoch das Argument ins Feld, dass es ebenso wichtig sei, die Erkenntnisweise eines Roboters zu verstehen. Abschließend wird, aus dem Blickwinkel der Theorie von den Protophänomenen, das für Roboter „schwierige Problem” untersucht, d.h. die Frage, ob sie zu subjektiver Wahrnehmung (...) fähig sind. (shrink)

The central claim of computationalism is generally taken to be that the brain is a computer, and that any computer implementing the appropriate program would ipso facto have a mind. In this paper I argue for the following propositions: (1) The central claim of computationalism is not about computers, a concept too imprecise for a scienti c claim of this sort, but is about physical calculi (instantiated discrete formal systems). (2) In matters of formality, interpretability, and so forth, analog computation (...) and digital computation are not essentially di erent, and so arguments such as Searle's hold or not as well for one as for the other. (3) Whether or not a biological system (such as the brain) is computational is a scienti c matter of fact. (4) A substantive scienti c question for cognitive science is whether cognition is better modeled by discrete representations or by continuous representations. (5) Cognitive science and AI need a theoretical construct that is the continuous analog of a calculus. The discussion of these propositions will illuminate several terminology traps, in which it's all too easy to become ensnared. (shrink)

on Documentary Film Classics by William Rothman.