The study of cases of illusory or unstable perception of some visual stimuli allows exploration of the psychology of perception of the surrounding world. The wired construction known as “Necker cube” is one such stimulus: it can be perceived as a cube whose front face is seen higher than the back face or vice versa. The switch can occur intentionally or spontaneously. The investigations were focused on switching parameters, relation of the switching to eye position, pre-history, and (...) environment. Here we define that the kernel of the problem is recognizing the 2D drawing as a 3D Necker cube. To this end, we have expanded Gestalt's psychology methods that allow us to recognize 2D figures in drawings for recognizing 3D figure in a flat drawing (including the Necker cube). The presented algorithm for recognizing the cube based on the imitation principle allowed the development of the model of switching between two possible perceptions of the Necker cube. The paper shows that the predictions are in conformity with previously available experimental data. The results confirm the imitation principle of perception, and suggest expanding our research on perception to a wider class of 3D figures, opening a window into the internal processes of perception. (shrink)

In this sequel, linear algebra methods are used to study the Routley Functor, both in single Neckers and in Necker chains. The latter display a certain irreducible higher-order inconsistency. A definition of degree of inconsistency is given, which classifies such inconsistency correctly with other examples of local and global inconsistency.

We apply linear algebra to the study of the inconsistent figure known as the Crazy Crate. Disambiguation by means of occlusions leads to a class of sixteen such figures: consistent, complete, both and neither. Necessary and sufficien conditions for inconsistency are obtained.

We apply linear algebra to the study of the inconsistent figure known as the Crazy Crate. Disambiguation by means of occlusions leads to a class of sixteen such figures: consistent, complete, both and neither. Necessary and sufficient conditions for inconsistency are obtained.

This paper aims to distinguish and classify sixteen versions of the Necker cube. In particular, it is shown how to describe inconsistent and incomplete theories which correspond in a systematic way to these sixteen diagrams. Concerning two of these sixteen cubes, there is a natural intuition that there is a sense in which they inconsistent. It is seen that this intuition is vindicated by an analysis in which their corresponding theories turn out to be globally inconsistent but not (...) locally inconsistent, while various other cubes of the sixteen are merely locally inconsistent. The Routley functor is seen to be useful in classifying the relations between these diagrams. (shrink)

The debates about human free will are traditionally the concern of metaphysics but neuroscientists have recently entered the field arguing that acts of the will are determined by brain events themselves causal products of other events. We examine that claim through the example of free or voluntary switch of perception in relation to the Necker cube. When I am asked to see the cube in one way, I decide whether I will follow the command (or do as (...) I am asked) using skills that reason and language give to me and change my brain states accordingly. The voluntary shift of perspective in seeing the Necker cube this way or that exemplifies the top-down control exercised by a human being on the basis of the role of language and meaning in their activity. It also indicates the lived story that is at the centre of each human consciousness. In the third part of this essay, three arguments are used to undermine metaphysical objections to the very idea of top-down self control. (shrink)

Current theories assume that perception and affect are separate realms of the mind. In contrast, we argue that affect is a genuine online-component of perception instantaneously mirroring the success of different perceptual stages. Consequently, we predicted that the success (failure) of even very early and cognitively encapsulated basic visual Processing steps would trigger immediate positive (negative) affective responses. To test this assumption, simple visual stimuli that either allowed or obstructed early visual processing stages without participants being aware of this were (...) presented briefly. Across 5 experiments, we found more positive affective responses to stimuli that allowed rather than obstructed Gestalt completion at certain early visual stages (Experiments 1–3; briefest presentation 100 ms with post-mask), and visual disambiguation in possible vs. impossible Necker cubes (Experiments 4 and 5; briefest presentation 100 ms with post-mask). This effect was observed both on verbal preference ratings (Experiments 1, 2, and 4) and as facial muscle responses occurring within 2–4 s after stimulus onset (zygomaticus activity; Experiments 3 and 7). For instance, in participants unaware of spatial possibility we found affective discrimination between possible and impossible Necker cubes (the famous Freemish Crate) for 100 ms presentation timings, although a conscious discrimination took more than 2000 ms (Experiment 4). (shrink)

This work responds by tracing the details of the relationship between transcendental and practical freedom through Kant's writings.

Kant's preface: The metaphysics of morals and the strategy of the groundwork -- Of the groundwork: the good will, duty, and the derivation of the categorical imperative -- Of the groundwork: practical reason, imperatives, and their formulas -- Of the groundwork: the deduction of the categorical imperative.

The Necker cube and the productive class of related stimuli involving multiple depth interpretations driven by corner-like line junctions are often taken to be ambiguous. This idea is normally taken to be as little in need of defense as the claim that the Necker cube gives rise to multiple distinct percepts. In the philosophy of language, it is taken to be a substantive question whether a stimulus that affords multiple interpretations is a case of ambiguity. If (...) we take into account what have been identified as hallmark features of ambiguity and look at the empirical record, it appears that the Necker cube and related stimuli are not ambiguous. I argue that this raises problems for extant models of multistable perception in cognitive neuroscience insofar as they are purported to apply to these stimuli. Helpfully, similar considerations also yield reasons to suggest that the relevant models are well motivated for other instances of multistable perception. However, a different breed of model seems to be required for the Necker cube and related stimuli. I end with a sketch how one may go about designing such a model relying on oscillatory patters in neural firing. I suggest that distinctions normally confined to the philosophy of language are important for the study of perception, a perspective with a growing number of adherents. (shrink)

In the seventeenth century, the Jewish mystical tradition which is known as Kabbalah was integrated into the curriculum of studying the Hebrew Bible and the Talmud. Kabbalah became popular in these times in the wake of the dissemination of Isaac Luria’s teachings, in particular within the Jewish communities in Prague and Amsterdam, where members of the Horowitz family took a leading role. Kabbalistic psychology was applied to the whole Jewish lifestyle then, and to the understanding of Jewish tradition. Kabbalistic intentions (...) of prayer intensified the expectation of redemption, and during the messianic movement initiated by Shabtai Zvi, the kabbalistic meaning of repentance was also adapted in prayer books composed for so-called Conversos, who had to familiarize themselves with Jewish tradition. The article exemplifies this process by a Spanish anthology of prayers, Libro entitulado ensenha à pecadores, and shows the historical impact of Kabbalah in the field of Jewish education. (shrink)

This paper takes as its point of departure recent research into the possibility that human beings can perceive single photons. In order to appreciate what quantum perception may entail, we first explore several of the leading interpretations of quantum mechanics, then consider an alternative view based on the ontological phenomenology of Maurice Merleau-Ponty and Martin Heidegger. Next, the philosophical analysis is brought into sharper focus by employing a perceptual model, the Necker cube, augmented by the topology of the (...) Klein bottle. This paves the way for addressing in greater depth the paper’s central question: Just what would it take to observe the quantum reality of the photon? In formulating an answer, we examine the nature of scientific objectivity itself, along with the paradoxical properties of light. The conclusion reached is that quantum perception requires a new kind of observation, one in which the observer of the photon adopts a concretely self-reflexive observational posture that brings her into close ontological relationship with the observed. (shrink)

In this study, voluntary and involuntary visual attention focused on different interpretations of a bistable image, were investigated using magnetoencephalography. A Necker cube with sinusoidally modulated pixels' intensity in the front and rear faces with frequencies 6.67 Hz and 8.57 Hz, respectively, was presented to 12 healthy volunteers, who interpreted the cube as either left- or right-oriented. The tags of these frequencies and their second harmonics were identified in the average Fourier spectra of the MEG data recorded (...) from the visual cortex. In the first part of the experiment, the subjects were asked to voluntarily control their attention by interpreting the cube orientation as either being on the left or right. Accordingly, we observed the dominance of the corresponding spectral component, and voluntary attention performance was measured. In the second part of the experiment, the subjects were asked to focus their gaze on a red marker at the center of the cube image without putting forth effort in its interpretation. The alternation of the dominant spectral energies at the second harmonics of the stimulation frequencies was treated as changes in the cube orientation. Based on the results of the first experimental stage and using a wavelet analysis, we developed a method which allowed us to identify the currently perceived cube orientation. Finally, we characterized involuntary attention using the distribution of dominance times when focusing attention on one of the cube orientations, which was related to voluntary attention performance and brain noise. In particular, we confirmed our hypothesis that higher attention performance is associated with stronger brain noise. (shrink)

Although our eyes receive incomplete and ambiguous information, our perceptual system is usually able to successfully construct a stable representation of the world. In the case of ambiguous figures, however, perception is unstable, spontaneously alternating between equally possible outcomes. The present study compared EEG responses to ambiguous figures and their unambiguous variants. We found that slight figural changes, which turn ambiguous figures into unambiguous ones, lead to a dramatic difference in an ERP (“event-related potential”) component at around 400 ms. This (...) result was obtained across two different categories of figures, namely the geometric Necker cube stimulus and the semantic Old/Young Woman face stimulus. Our results fit well into the Bayesian inference concept, which models the evaluation of a perceptual interpretation’s reliability for subsequent action planning. This process seems to be unconscious and the late.. (shrink)

The way we represent and perceive time has crucial implications for studying temporality in conscious experience. Contrasting positions posit that temporal information is separately abstracted out like any other perceptual property through specialized mechanisms or that time is represented through the temporality of experiences themselves. To add to this debate, we investigate alterations in felt time in conditions where only conscious visual experience is altered through perceptual switches while a bistable figure remains physically unchanged. We predicted that if perceived time (...) is a function of temporally evolving conscious content, then a break in it (here via a perceptual switch) would also lead to a break in felt time. In three experiments, we showed participants a Necker cube that was manipulated to induce a perceptual switch (experiments 1(a) and 1(b)) or left to switch on its own (experiment 2). We asked participants to report both perceptual switches and felt durations (experiments 1(a) and 2) or only estimate time (experiment 1(b)). Over these three experiments, we find evidence of contraction of felt time in trials with a perceptual switch, consistent with the idea that perceived time is a function of temporally evolving conscious experience. Additionally, we present a phenomenological demonstration to support our empirical data. Overall, the study provides evidence for temporal mirroring and isomorphism in visual experience, arguing for a link between the timing of experience and time perception. (shrink)

The premise of this paper is that the goal of signifying Being central to ontological phenomenology has been tacitly subverted by the semiotic structure of conventional phenomenological writing. First it is demonstrated that the three components of the sign—sign-vehicle, object, and interpretant (C. S. Peirce)—bear an external relationship to each other when treated conventionally. This is linked to the abstractness of alphabetic language, which objectifies nature and splits subject and object. It is the subject-object divide that phenomenology must surmount if (...) it is to signify Being. To this end, we go beyond alphabetic convention and explore the use of iconic signs. Following the lead of Merleau-Ponty, the iconic expression of Being is seen as entailing paradox, and we are directed to the fields of visual geometry and topology, where we work with three paradoxical figures: the Necker cube, Moebius strip, and Klein bottle. While the Necker cube and Moebius prove to have their limitations in fully signifying Being, the Klein bottle, possessing an added dimension (made palpable via a stereogram), can embody Being more intimately, provided that it is approached in a radically non-classical way. The essay closes with the realization that the most concrete signification of Being must be a self-signification. Here the author removes his cloak of anonymity and makes his presence tangibly felt in the text. (shrink)

The aspects family -- A. the duck-rabbit -- B. the necker cube -- Faces, faces, faces -- Illusions -- E. "puzzle-pictures" -- Aspects and words -- A. introspection and experiment -- B. how we do things with words -- How we see things with words -- Aspect blindness -- A. imagination -- B. aspect blindness -- Fat wednesday -- Aspects and art -- A. experience -- B. seeing a painting -- Musical aspects -- Emergent meaning and wine -- (...) Ethics and aesthetics are one -- A. science -- B. from a religious point of view. (shrink)

This essay is written at the crossroads of intuitive holism, as typified in Eastern thought, and the discursive reflectiveness more characteristic of the West. The point of departure is the age-old human need to overcome fragmentation and realize wholeness. Three basic tasks are set forth: to provide some new insight into the underlying obstacle to wholeness, to show what would be necessary for surmounting this blockage, and to take a concrete step in that direction. At the outset, the question of (...) paradox is addressed, examined in relation to Zen meditation, the problem of language, and the thinking of Heidegger. Wholeness is to be realized through paradox, and it is shown that a complete realization requires that paradox be embodied. Drawing from the fields of visual geometry and qualitative mathematics, three concrete models of paradox are offered: the Necker cube, the Moebius surface, and the Klein bottle. In attempting to model wholeness, an important limitation is recognized: a model is a symbolic representation that maintains the division between the reality represented and the act of symbolizing that reality. It is demonstrated that while the first two models are subject to this limitation, the Klein bottle, possessing higher dimensionality, can express wholeness more completely, provided that it is approached in a radically nonclassical way. The final question of this essay concerns its own capability as an essay. It is asked whether the present text is restricted to affording a mere abstract reflection on wholeness, or whether wholeness can tangibly be delivered. (shrink)

This article explores the evolution of human attention, focusing particularly on the phylogenetic and ontogenetic implications of the work of the American social psychiatrist Trigant Burrow. Attentional development is linked to the emergence of visual perspective, and this, in turn, is related to Burrow's notion of `ditention' (divided or partitive attention). Burrow's distinction between `ditention' and `cotention' (total organismic awareness) is examined, and, expanding on this, a threefold pattern of perceptual change is identified: prototention-->ditention-->cotention. Next, ditentive visual perspective is related (...) to binocular convergence, and the author makes use of the perspectivally ambiguous, `non-convergent' Gestalt figure known as the Necker Cube to illustrate cotention. The paper concludes by proposing that the shift from the currently pervasive ditentive pattern of awareness to a cotentive mode could have a salutary effect on human society. (shrink)

In this paper, we propose to see the Necker cube phenomenon as a basis for the development of a mathematical language in accordance with Leibniz’s vision of soft logic. By the development of a new coordinate system, we make a distinction between −0 and +0. This distinction enables us to present a new model for nonstandard analysis, and to develop a calculus theory without the need of the concept of limit. We also established a connection between “Recursive Distinctioning” (...) and soft logic, and use it as a basis for a new computational model. This model has a potential to change the current computational paradigm. (shrink)

Experimental Phenomenology is a book on learning phenomenology by doing it. The format follows the progression of a number of thought-experiments which mark out the procedures and directions of phenomenological inquiry. Making use of examples of familiar optical illusions and multi-stable drawings, such as the well-known Necker cube, Professor Ihde illustrates by way of careful and disciplined step-by-step analyses how some of the main methodological procedures and epistemological concepts of phenomenology assume concrete relevance in the project of doing (...) phenomenology. Such formidable phenomenological fare as epoche, noetic and noematic analysis, apodicticity, adequacy, sedimentation, imaginative variation, field, and fringe are rendered into the currency of a quotidian commerce with the perceptual world. (shrink)

In the paper, the author analyzes and compares cube examples in Wittgenstein’s works, especially the cube from TLP and the cube from PPF. There is no direct evidence that the PPF–cube is a reaction to the “grave mistake” of the TLP–cube. Also, there is no evidence that the TLP–cube is a representation of the Necker’s cube, although it resembles the Jastrow’s cube. These are negative results. Both cubes present important ideas of (...) TLP and PPF. Also, Wittgenstein writes that he “purposely chose” the example of the cube in PI and PPF, perhaps to show one of the “grave mistakes” of the TLP–cube. By analysis of the Necker’s cube and comparison of drawings and accompanied text of the TLP–cube and the PPF–cube the author tries to explicate some possible implicit pictorial aspects of Wittgenstein’s thought and of the general nature philosophical thinking as pictorial. (shrink)

A novel conceptual framework for theoretical psychology is presented and illustrated for the example of bistable perception. A basic formal feature of this framework is the non-commutativity of operations acting on mental states. A corresponding model for the bistable perception of ambiguous stimuli, the Necker–Zeno model, is sketched and some empirical evidence for it so far is described. It is discussed how a temporal non-locality of mental states, predicted by the model, can be understood and tested.

We re-examine the problem of existential import by using classical predicate logic. Our problem is: How to distribute the existential import among the quantified propositions in order for all the relations of the logical square to be valid? After defining existential import and scrutinizing the available solutions, we distinguish between three possible cases: explicit import, implicit non-import, explicit negative import and formalize the propositions accordingly. Then, we examine the 16 combinations between the 8 propositions having the first two kinds of (...) import, the third one being trivial and rule out the squares where at least one relation does not hold. This leads to the following results: (1) three squares are valid when the domain is non-empty; (2) one of them is valid even in the empty domain: the square can thus be saved in arbitrary domains and (3) the aforementioned eight propositions give rise to a cube, which contains two more (non-classical) valid squares and several hexagons. A classical solution to the problem of existential import is thus possible, without resorting to deviant systems and merely relying upon the symbolism of First-order Logic (FOL). Aristotle’s system appears then as a fragment of a broader system which can be developed by using FOL. (shrink)

We show that we in ways related to the classical Square of Opposition may define a Cube of Opposition for some useful statements, and we as a by-product isolate a distinct directive of being inviolable which deserves attention; a second central purpose is to show that we may extend our construction to isolate hypercubes of opposition of any finite cardinality when given enough independent modalities. The cube of opposition for obligations was first introduced publically in a lecture for (...) the Square of Opposition Conference in the Vatican in May 2014. -/- A COLORFUL ERRATUM: The article Cubes and Hypercubes of Opposition, with Ethical Ruminations on Inviolability, suffered a couple of mishaps when it was published in Logica Universalis, ISSN 1661-8297, 10(2-3), p. 373–376. The worst of them was that the colorful cube was printed in shades of grey, instead of decorating the sides with two transparent sides, and then a red, a yellow, a blue and a green side. The text of the article is not quite understandable because of this mishap, so I avail a colorfully updated version of the original article here. -/- . (shrink)

Various arguments have been put forward to show that Zeno-like paradoxes are still with us. A particularly interesting one involves a cube composed of colored slabs that geometrically decrease in thickness. We first point out that this argument has already been nullified by Paul Benacerraf. Then we show that nevertheless a further problem remains, one that withstands Benacerraf s critique. We explain that the new problem is isomorphic to two other Zeno-like predicaments: a problem described by Alper and Bridger (...) in 1998 and a modified version of the problem that Benardete introduced in 1964. Finally, we present a solution to the three isomorphic problems. (shrink)

In 1929 Tarski showed how to construct points in a region-based first-order logic for space representation. The resulting system, called the geometry of solids, is a cornerstone for region-based geometry and for the comparison of point-based and region-based geometries. We expand this study of the construction of points in region-based systems using different primitives, namely hyper-cubes and regular simplexes, and show that these primitives lead to equivalent systems in dimension n ≥ 2. The result is achieved by adopting a single (...) set of definitions that works for both these classes of figures. The analysis of our logics shows that Tarski’s choice to take sphere as the geometrical primitive might be intuitively justified but is not optimal from a technical viewpoint. (shrink)

Various arguments have been put forward to show that Zeno-like paradoxes are still with us. A particularly interesting one involves a cube composed of colored slabs that geometrically decrease in thickness. We first point out that this argument has already been nullified by Paul Benacerraf. Then we show that nevertheless a further problem remains, one that withstands Benacerraf’s critique. We explain that the new problem is isomorphic to two other Zeno-like predicaments: a problem described by Alper and Bridger in (...) 1998 and a modified version of the problem that Benardete introduced in 1964. Finally, we present a solution to the three isomorphic problems. (shrink)

Should animal advocates be allowed to publicly display graphic footage of how animals live (and die) in industrial animal use facilities? Cube of truth (‘cube’) demonstrations are a form of animal advocacy aimed at informing the public about the realities of animals’ experiences in places such as slaughterhouses, feedlots, and research facilities, by showing footage of mostly lawful practices within these workplaces. Activists engaging in cube-style protests have recently been targeted by law enforcement agencies in two Australian (...) states on the basis that the footage on display was too offensive to be shown in public. In this paper, I argue that these justifications do not stand up to scrutiny. Using an original politics of sight analysis, this paper demonstrates how the democratic costs associated with targeting cube protests outweigh the costs to the public. Cube activists are engaging in public dialogue by drawing attention to sites of potential injustice, and are playing an important role in highlighting the agency of the animals involved in exploitative industries. I further make the case that, where such demonstrations fall foul of the law, they should be regarded as legitimate acts of civil disobedience. (shrink)

The traditional square of opposition is generalized and extended to a cube of opposition covering and conveniently visualizing inter-sentential oppositions in relational syllogistic logic with the usual syllogistic logic sentences obtained as special cases. The cube comes about by considering Frege–Russell’s quantifier predicate logic with one relation comprising categorical syllogistic sentence forms. The relationships to Buridan’s octagon, to Aristotelian modal logic, and to Klein’s 4-group are discussed.GraphicThe photo shows a prototype sculpture for the cube.

Cube Living 221A is the most recent iteration of the Cube Living project, initiated in 2008. It appropriates the language, media and social practices of real estate development campaigns to engage in speculation about spatial ontologies, examining how social, legal and financial conventions determine the creation of space in our cities.This paper describes the staging and production process by which Cube Living 221A performs the creation of a spatial commodity. Drawing on the concepts presented in Žižek’s 2009 (...) talk “Architectural Parallax: Spandrels and Other Phenomena of Class Struggle”, it goes on to speculate that urban real estate development results in an architectural parallax: real estate property must function simultaneously as a financial asset and also as a residence. Similarly, the property owner must play simultaneous but irreconcilable roles as both investor and citizen. The Cube object can be regarded as a spandrel at the hinge of this parallax. (shrink)

Summary In Part 1 Small describes her discovery that an array of depicted cubes produces another and completely different illusion from that of a single cube. When a group of such cubes are viewed at an angle, they turn into rectangular boxes, and as the angle gets more severe, they become narrow ribbons. The illusion works only in one direction. In Part 2, Todorović manipulates the image to demonstrate various transformations and offers an explanation of how and why they (...) work the way they do. (shrink)

"Hungarian Cubes" proposes an aesthetical typology of the ornamentation of cubic houses from the 1960s 70s in Hungary. The book is based on the artistic project Magyar Kocka Hungarian Cube, which German-Hungarian artist Katharina Roters is pursuing since 2005. The origins of the Hungarian Cube, a standardized type of residential house, date back to the 1920s, when the cube as prototype of a radically functional design first appeared in plans for single-family homes in Budapest s suburbs and (...) also in social housing projects. During Hungary s communist era after WW II, many villages were rebuilt on uniform schemes of single-family homes and the "Magyar Kocka "or "Kadar Kocka, " as they were also named after Hungary s communist president Janos Kadar became ubiquitous. A unique characteristic of this housing type is the ornamental decoration of its facades. The facade thereby became an opportunity of both individual and collective expression within uniformity. The ornament is not merely an aesthetic sign. It rather creates meaningful identity and distinguishes the appearance of entire dwellings across the country. Often this individualized ornament can also be read as an act of subversion against the pressure of conformity in the socialist system. Katharina Roters has been investigating and documenting this previously neglected ornamental phenomenon since 2005 from an artistic point of view. The houses are shown in her images cleaned of all surplus information, fences and railings, antennas, road signs, electric power lines. Only by this deletion of additions to each house the project can reach beyond a merely archival nature and the photograph becomes a document of aesthetic typology. The book combines the serial composition of Roters s images with essays on various aspects of this architectural phenomenon. ". (shrink)