Albrecht von Müller

Working Wonders? Investigating insight with magic tricks

We propose a new approach to differentiate between insight and noninsight problem solving, by introducing magic tricks as problem solving domain. We argue that magic tricks are ideally suited to investigate representational change, the key mechanism that yields sudden insight into the solution of a problem, because in order to gain insight into the magicians secret method, observers must overcome implicit constraints and thus change their problem representation. In Experiment 1, 50 participants were exposed to 34 different magic tricks, asking them to find out how the trick was accomplished. Upon solving a trick, participants indicated if they had reached the solution either with or without insight. Insight was reported in 41.1% of solutions. The new task domain revealed differences in solution accuracy, time course and solution confidence with insight solutions being more likely to be true, reached earlier, and obtaining higher confidence ratings. In Experiment 2, we explored which role self-imposed constraints actually play in magic tricks. 62 participants were presented with 12 magic tricks. One group received verbal cues, providing solution relevant information without giving the solution away. The control group received no informative cue. Experiment 2 showed that participants constraints were suggestible to verbal cues, resulting in higher solution rates. Thus, magic tricks provide more detailed information about the differences between insightful and noninsightful problem solving, and the underlying mechanisms that are necessary to have an insight.

Aha! experiences leave a mark: facilitated recall of insight solutions

The present study investigates a possible memory advantage for solutions that were reached through insightful problem solving. We hypothesized that insight solutions (with Aha! experience) would be remembered better than noninsight solutions (without Aha! experience). 34 video clips of magic tricks were presented to 50 participants as a novel problem-solving task, asking them to find out how the trick was achieved. Upon discovering the solution, participants had to indicate whether they had experienced insight during the solving process. After a delay of 14xa0days, a recall of solutions was conducted. Overall, 55xa0% of previously solved tricks were recalled correctly. Comparing insight and noninsight solutions, 64.4xa0% of all insight solutions were recalled correctly, whereas only 52.4xa0% of all noninsight solutions were recalled correctly. We interpret this finding as a facilitating effect of previous insight experiences on the recall of solutions.

It's a kind of magic—what self-reports can reveal about the phenomenology of insight problem solving

Magic tricks usually remain a mystery to the observer. For the sake of science, we offered participants the opportunity to discover the magicians secret method by repeatedly presenting the same trick and asking them to find out how the trick worked. In the context of insightful problem solving, the present work investigated the emotions that participants experience upon solving a magic trick. We assumed that these emotions form the typical “Aha! experience” that accompanies insightful solutions to difficult problems. We aimed to show that Aha! experiences can be triggered by magic tricks and to systematically explore the phenomenology of the Aha! experience by breaking it down into five previously postulated dimensions. 34 video clips of different magic tricks were presented up to three times to 50 participants who had to find out how the trick was accomplished, and to indicate whether they had experienced an Aha! during the solving process. Participants then performed a comprehensive quantitative and qualitative assessment of their Aha! experiences which was repeated after 14 days to control for its reliability. 41% of all suggested solutions were accompanied by an Aha! experience. The quantitative assessment remained stable across time in all five dimensions. Happiness was rated as the most important dimension. This primacy of positive emotions was also reflected in participants qualitative self-reports which contained more emotional than cognitive aspects. Implementing magic tricks as problem solving task, we could show that strong Aha! experiences can be triggered if a trick is solved. We could at least partially capture the phenomenology of Aha! by identifying one prevailing aspect (positive emotions), a new aspect (release of tension upon gaining insight into a magic trick) and one less important aspect (impasse).

Thought and Reality

Trying to understand how thinking works cannot be separated from trying to understand how reality works. A recent approach to understanding how reality actually “takes place” postulates two complementary aspects. There is a “factual aspect of reality” which is characterized by well-defined predications, causal closure, and local spacetime. But there is a complementary, “statu-nascendi” aspect of reality which addresses how facts, and with them local spacetime, come into being in the first place. This aspect of reality is inherently constellatory, i.e. the constellations of components are the most basic phenomena - somewhat similar to Gestalt phenomena in the visual domain. Human thinking is interpreted as a highly advanced cognitive adaptation to this irreducible Janus-headedness of reality. In parts it can be well defined, in parts it just cannot - because it must leave room for the on-going self-unfolding of meaning. This self-unfolding of meaning is interpreted as the most accurate semantic approximation to the ongoing self-unfolding of reality. It is, thus, not a bug but a crucial feature of complex thinking. Unlike formal languages, which structurally correspond to the factual aspect of reality, natural language is capable of dealing with both aspects of reality: its facticity and its coming into being.

Borromean Link in Algebraic Form Group-Theoretic Encoding: The Borromean Rings as Prime Connectivity Units of All Topological Links

The term “Borromean rings” originates from their display at the coat of arms of the Borromeo family in Northern Italy.

Model of an Autogenetic Universe Constellatory Self-Unfolding: A Novel Syntaxis of Time in the Time-Space of the Present

The philosophical theory of an “autogenetic universe” (von Muller 2011, 2012, 2015) proposes new “categorial foundations” for science aiming to overcome the inherent limitations, incompatibilities, and structural pitfalls of the current scientific paradigm. The basic premise of the proposed new theory is that we live in an autogenetic universe, meaning that we live in a self-unfolding and strongly self-referential universe. In relation to this hypothesis, the theory of an “autogenetic universe” proposes a novel account of time and reality, which aims at a deeper re-conceptualization of these fundamental notions going beyond or underneath the structural reduction of the former to its linear-sequential aspect and the concurrent related reduction of the latter to its factual or event-like aspect. This is of particular significance in relation to the frontier area of theoretical physics aiming at a unification of quantum mechanics and general relativity, where it is argued that a key conceptual element for this purpose requires the relativization of facticity, namely of the event structures pertaining to a local space-time description capturing exclusively the factual portrait of reality. It is instructive to note that the notion of an unfolding universe has also been explored by means of a different approach in the work of (Kafatos and Nadeau 2013).

Borromean Link in Logic A Metaperspective on Algorithmic Information: Logical Conjugation Strategy and the Role of the Borromean Topology

The notion of analogy will be considered in its broadest possible sense, namely as a mode of reasoning or problem-solving in which a phenomenon, or a quantity, or an object, or a class of objects, or even a category of objects, is intentionally compared to another in order to establish similarity of relationship. Moreover, of the two particular instances between which a resemblance (similarity of relationship) is established, one is generally not directly comprehensible, while the other is assumed to be better or more easily tractable. It is important to clarify that according to the above, an analogical relation bears the semantics of a resemblance not between instances, but between the relations of instances. Thus, an analogy is a resemblance relation, involving (at least) two terms, each of which is itself a relation.

Borromean Link in Quantum Theory Loops, Projective Invariants and the Realization of the Borromean Topological Link in Quantum Mechanics

The notion of a topological or geometric phase has been introduced in quantum mechanics by Berry in 1984, and generalized by Aharonov and Anandan 2 years later in 1986. The conceptual precursors of this astonishing discovery, which has been unnoticed in the foundations of quantum theory for more than 60 years, is the work of Pancharatnam in polarization optics and the Aharonov–Bohm effect in electromagnetism. In 1956 Pancharatnam realized that in order to understand interference phenomena it is not required to know the absolute phase, but only the relative phase difference between light beams in different states of polarization. For two light beams this relative phase is given by the phase argument of their complex-valued scalar inner product. Actually all the typical global quantum mechanical observables are relative phases obtained by interference phenomena. These phenomena involve various splitting and recombination processes of beams whose global coherence is measured precisely by some relative phase difference. If we consider an external time parametrization of interference phenomena, then the relative phase global observable can be thought of as the physical attribute measuring the coherence between two histories of events sharing a common initial and final temporal point.

Borromean Link in Relativity Theory What Is the Validity Domain of Einstein’s Field Equations? Sheaf-Theoretic Distributional Solutions over Singularities and Topological Links in Geometrodynamics

One hundred years after Einstein’s initial conception and formulation of the General Theory of Relativity, it still remains a vibrant subject of intense research and formidable depth. In this way, during all these years our understanding of gravitation in differential geometric terms is being continuously refined. We believe that one of the highest priorities of a centennial perspective on General Relativity should be a careful re-examination of the validity domain of Einstein’s field equations. These equations constitute the irreducible kernel of General Relativity and the possibility of retaining the form of Einstein’s equations, while concurrently extending their domain of validity is promising for shedding new light to old problems and guiding toward their effective resolution. These problems are primarily related with the following perennial issues: (a) the smooth manifold background of the theory, (b) the existence of singular loci in spacetime where the metric breaks down or the curvature blows up, and (c) the non-geometric nature of the second part of Einstein’s equations involving the energy-momentum tensor. It turns out that these problems are intrinsically related to each other and require a critical re-thinking of the initial assumptions referring to the domain of validity of Einstein’s equations.

Borromean Link in Quantum Gravity A Topological Approach to the “ER = EPR” Conjecture: Modelling the Correspondence Between GHZ Entanglement and Planck-Scale Wormholes via the Borromean Link

In the absence of an exact quantum gravity theory, the “ER = EPR” conjecture constitutes a recently introduced proposal by Maldacena and Susskind, aiming to shed light on the relations among spacetime geometry, quantum field theory and quantum information theory, which is receiving significant attention currently in relation to its substantiation, proof, and groundbreaking implications. The “ER = EPR” is a short-hand that joins two ideas proposed by Einstein in 1935. One involved the quantum correlations implied by what he called “spooky action at a distance”, referring to the phenomenon of entanglement between quantum particles (EPR entanglement, named after Einstein, Podolsky, and Rosen). The other showed how two black holes could be connected “non-locally” via “topological handles” in space-time, known as “wormholes” (ER, for Einstein-Rosen bridges). If the conjecture “ER = EPR” is correct, then the ideas of quantum entanglement and wormholes are not disjoint, but they are two manifestations of the same essentially topological idea. Effectively, this underlying connectedness would form the foundation of quantum space-time.