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Psychology is the science of behavior and mind, including conscious and unconscious phenomena, as well as feeling and thought. It is an academic discipline of immense scope and diverse interests that, when taken together, seek an understanding of the emergent properties of brains, and all the variety of epiphenomena they manifest. As a social science it aims to understand individuals and groups by establishing general principles and researching specific cases.[1][2]

In this field, a professional practitioner or researcher is called a psychologist and can be classified as a social, behavioral, or cognitive scientist. Psychologists attempt to understand the role of mental functions in individual and social behavior, while also exploring the physiological and biological processes that underlie cognitive functions and behaviors.

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Interdisciplinarity or interdisciplinary studies involves the combining of two or more academic disciplines into one activity (e.g., a research project).[1] It draws knowledge from several other fields like sociology, anthropology, psychology, economics etc. It is about creating something by thinking across boundaries. It is related to an interdiscipline or an interdisciplinary field, which is an organizational unit that crosses traditional boundaries between academic disciplines or schools of thought, as new needs and professions emerge. Large engineering teams are usually interdisciplinary, as a power station or mobile phone or other project requires the melding of several specialties. However, the term “interdisciplinary” is sometimes confined to academic settings.

multidiciplinary.ml

Interdisciplinarity or interdisciplinary studies involves the combining of two or more academic disciplines into one activity (e.g., a research project).[1] It draws knowledge from several other fields like sociology, anthropology, psychology, economics etc. It is about creating something by thinking across boundaries. It is related to an interdiscipline or an interdisciplinary field, which is an organizational unit that crosses traditional boundaries between academic disciplines or schools of thought, as new needs and professions emerge. Large engineering teams are usually interdisciplinary, as a power station or mobile phone or other project requires the melding of several specialties. However, the term “interdisciplinary” is sometimes confined to academic settings.

transdiciplinary-science.tk

Transdisciplinarity connotes a research strategy that crosses many disciplinary boundaries to create a holistic approach. It applies to research efforts focused on problems that cross the boundaries of two or more disciplines, such as research on effective information systems for biomedical research (see bioinformatics), and can refer to concepts or methods that were originally developed by one discipline, but are now used by several others, such as ethnography, a field research method originally developed in anthropology but now widely used by other disciplines. The Belmont Forum [1] elaborated that a transdisciplinary approach is enabling inputs and scoping across scientific and non-scientific stakeholder communities and facilitating a systemic way of addressing a challenge. This includes initiatives that support the capacity building required for the successful transdisciplinary formulation and implementation of research actions.

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Cognitive science is the interdisciplinary, scientific study of the mind and its processes.[2] It examines the nature, the tasks, and the functions of cognition (in a broad sense). Cognitive scientists study intelligence and behavior, with a focus on how nervous systems represent, process, and transform information. Mental faculties of concern to cognitive scientists include language, perception, memory, attention, reasoning, and emotion; to understand these faculties, cognitive scientists borrow from fields such as linguistics, psychology, artificial intelligence, philosophy, neuroscience, and anthropology.[3] The typical analysis of cognitive science spans many levels of organization, from learning and decision to logic and planning; from neural circuitry to modular brain organization. The fundamental concept of cognitive science is that “thinking can best be understood in terms of representational structures in the mind and computational procedures that operate on those structures.”[3]

Simply put: Cognitive Science is the interdisciplinary study of cognition in humans, animals, and machines. It encompasses the traditional disciplines of psychology, computer science, neuroscience, linguistics and philosophy. The goal of cognitive science is to understand the principles of intelligence with the hope that this will lead to better comprehension of the mind and of learning and to develop intelligent devices. The cognitive sciences began as an intellectual movement in the 1950s often referred to as the cognitive revolution.

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1580s, “pertaining to cognition,” with -ive + Latin cognit-, past participle stem of cognoscere “to get to know, recognize,” from assimilated form of com “together” (see co-) + gnoscere “to know,” from PIE root *gno- “to know.”

Taken over by psychologists and sociologists after c. 1940. Cognitive dissonance “psychological distress cause by holding contradictory beliefs or values” (1957) apparently was coined by U.S. social psychologist Leon Festinger, who developed the concept. Related: Cognitively.

Möbius Band

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Created by Christopher B. Germann (PhD, MSc, BSc / Marie Curie Fellow)
Permanent URL: moebius-band.ga

The Möbius Band

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A-non-dual-cognitive-neuroscience-perspective.pdfA non-dual cognitive neuroscience perspective

Figure it out: A non-dual cognitive neuroscience perspective on the Möbius band.


The Möbius band is an extraordinary geometrical figure. The band is eponymously named after the German mathematician August Ferdinand Möbius who described it in 1885, contemporaneously with another German mathematician named Johann Benedict Listing. It is a so called ruled surface with only one side and one boundary and it possesses the mathematical property of non-orientability (viz., a non-orientable manifold). In fact, the Möbius band is the simplest possible non-orientable surface. A Gedankenexperiment is helpful to understand this property intuitively: Imagine walking on the surface of a giant Möbius band. If you would travel long enough you would end up at the very starting point of the journey, only mirror-reversed. This journey can be repeated ad infinitum. Therefore, the Möbius band can also be interpreted as a metaphor for infinity, i.e., the beginningless and the endless. A similar principle can be found in the interpretation of the Ouroboros serpent (which eats its own tail), a gnostic symbol which originated in ancient Egyptian iconography (ἓν τὸ πᾶν – “The all is one”) in the 10th century. A similar symbolism could later also  be found in the western Greek magical tradition (Ancient Greek: οὐροβόρος). The psychoanalytic meaning of the Ouroboros was discussed as an archetype by the depth-psychologist C.G. Jung.
The geometry of the Möbius band (also referred to as “Möbius strip”) has far-reaching interdisciplinary implications. The principles of its peculiar topology have been applied to a broad array of scientific disciplines including mathematics, cosmology, computer science, physics, chemistry, biology, psychology, et cetera. Practical applications include, for instance, superconductors with high transition temperatures, molecular engines, and bandpass filters (see exemplary references below).
In addition to its scientific relevance, the Möbius band can be found as a leitmotif in multifarious artworks across various cultures (for an example see the ancient mosaic depicted below).1 Moreover, the abstract principles derived from its topological structure have been applied to music theory (e.g., the space of all two-note chords, referred to as dyads, resembles the shape of a Möbius band).
The Möbius band is a very interesting visual percept in the context of perceptual cognitive psychology and neuropsychology, as it helps researchers to investigate the cognitive and neuronal mechanism which undergird cognition and perception. (Besides, in the first half of the 20th century magicians used the Möbius band for “magical” tricks.)2 Interestingly, a recent series of fMRI neuroimaging studies focused on the topic of ego-dissolution which is associated with non-dual states of consciousness in which the border between self and other (the dichotomy between inside and outside) temporarily dissolves. The default-mode network3 appears to be an important neuroanatomical correlate in this context.
Next to its neuropsychological aspects, the Möbius band inspires profound philosophical contemplations concerning the relationship between mind & matter (e.g., the “Pauli-Jung conjecture”4 in the context of dual aspect monism)5. In the classical 17th century Cartesian framework (which is still highly influential), mind & matter (psyche & physis – or res extensa & res cogitans)6 are two separate phenomena (this dichotomisation is known as Cartesian dualism or the Cartesian split). However, alternative ontological theories postulate that mind & matter are complementary with respect to each other (in the quantum physical sense of complementarity), i.e., they are different aspects of the same underlying “substance” (hence the term “monism” as opposed to “dualism”).
Currently, a dualistic mind/matter conception is the (mostly implicitly accepted) reigning scientific paradigm (cf. Thomas Kuhn)7, particularly within the neurosciences (e.g., epiphenominalism/emergence theories of consciousness)8. However, this dualistic working hypothesis9 can be challenged on various logical grounds and has not been empirically validated (e.g., correlation ≠ causation; viz., the “cum hoc ergo propter hoc” logical fallacy of implied causality).
Therefore, dual-aspect monism is a viable conceptual alternative worth considering – particularly given recent empirical data obtained in the domain of experimental quantum physics which deeply challenges our intuitive quasi-Newtonian notions of reality which are ubiquitously (prima facie) taken for granted without deeper critical reflection on their logical validity and empirical evidential foundation. The dual-aspect monism perspective is therefore iconoclastic towards the reigning dualistic psychological and neuroscientific status quo paradigm.
It is argued that the Möbius band can be interpreted as a visual metaphor for “chiastic convergence” a coincidentia oppositorum (Latin for “coincidence of opposites”; cf. C.G. Jung), i.e., the non-duality of psyche and physis, internal and external, subject and object, inside and outside, mind and matter, the knower and the known, the “seer and the seen” (Sanskrit: Drg-Drsya; as analyzed in the ancient Advaita Vedānta text “Drg-Drsya-Viveka”). William James eloquently summarized this non-dual view:

“Granted that a definite thought, and a definite molecular action in the brain occur simultaneously, we do not possess the intellectual organ, nor apparently any rudiment of the organ, which would enable us to pass by a process of reasoning from the one phenomenon to the other. They appear together but we do not know why.”

~ William James (1890)

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The instant field of the present is at all times what I call the ‘pure’ experience. It is only virtually or potentially either object or subject as yet. For the time being, it is plain, unqualified actuality, or existence, a simple that. […] Just so, I maintain, does a given undivided portion of experience, taken in one context of associates, play the part of the knower, or a state of mind, or “consciousness”; while in a different context the same undivided bit of experience plays the part of a thing known, of an objective ‘content.’ In a word, in one group it figures as a thought, in another group as a thing. […] Things and thoughts are not fundamentally heterogeneous; they are made of one and the same stuff, stuff which cannot be defined as such but only experienced; and which one can call, if one wishes, the stuff of experience in general. […] ‘Subjects’ knowing ‘things’ known are ‘roles’ played, not ‘ontological” facts’.
~ William James (1904)

The whole duality of mind and matter […] is a mistake; there is only one kind of stuff out of which the world is made, and this stuff is called mental in one arrangement, physical in the other.
~ Bertrand Russell (1913)

There is no such thing as philosophy-free science; there is only science whose philosophical baggage is taken on board without examination.
~ Daniel Dennett (1995)

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Pertinent References

Atmanspacher, H.. (2012). Dual-aspect monism a’ la Pauli and Jung. Journal of Consciousness Studies

Plain numerical DOI: 10.1063/1.4773112
DOI URL
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Atmanspacher, H., & Fach, W.. (2013). A structural-phenomenological typology of mind-matter correlations. Journal of Analytical Psychology

Plain numerical DOI: 10.1111/1468-5922.12005
DOI URL
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Atmanspacher, H.. (2012). Dual-aspect monism à la Pauli and Jung perforates the completeness of physics. In AIP Conference Proceedings

Plain numerical DOI: 10.1063/1.4773112
DOI URL
directSciHub download

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Chapter 4

Formulaic notation specifying a Möbius band in 3-dimensional Euclidean space

\[
{\displaystyle x(u,v)=\left(3+{\frac {v}{2}}\cos {\frac {u}{2}}\right)\cos u}
\] \[
{\displaystyle y(u,v)=\left(3+{\frac {v}{2}}\cos {\frac {u}{2}}\right)\sin u}
\] \[
{\displaystyle z(u,v)={\frac {v}{2}}\sin {\frac {u}{2}}}
\] where \[{\displaystyle 0\leq u<2\pi }\] and \[{\displaystyle -1\leq v\leq 1}\] This parametrization produces a single Möbius band with a width of 1 and a middle circle with a radius of 3. The band is positioned in the xy plane and is centred at coordinates (0, 0, 0). The Möbius band can be plotted in R (an open-source software environment for statistical computing and graphics). The associated code to create the graphic is based on the packages “rgl” (Murdoch, 2001, 2018) and “plot3D” (Soetaert, 2014, 2017) and can be found below. The appended R code creates an interactive plot that allows to scale and rotate the Möbius band in three dimensional space.

R code for plotting a Möbius band

You can plot an interactive Möbius band by using the open-source software “R” which you can download using the URL below. Simply copy & paste the provided code into R and it will produce an interactive scaleable and rotatable 3-dimensional Möbius band. You have to install the “rgl” and “plot3D” package for this to work.
cran.r-project.org/mirrors.html

#Source URL: https://r.prevos.net/plotting-mobius-strip/
library(rgl) #RGL: An R Interface to OpenGL (Murdoch, 2001)
library(plot3D) #plot3D: Plotting multi-dimensional data (Soetaert, 2014)
# Define parameters
R <- 3
u <- seq(0, 2 * pi, length.out = 100)
v <- seq(-1, 1, length.out = 100)
m <- mesh(u, v)
u <- m$x
v <- m$y
# Möbius strip parametric equations
x <- (R + v/2 * cos(u /2)) * cos(u)
y <- (R + v/2 * cos(u /2)) * sin(u)
# Visualise in 3-dimensional Euclidean space
bg3d(color = "white")
surface3d(x, y, z, color= "red")

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Möbius band in Python

import plotly.plotly as py
import plotly.figure_factory as FF
import plotly.graph_objs as go

import numpy as np
from scipy.spatial import Delaunay

u = np.linspace(0, 2*np.pi, 24)
v = np.linspace(-1, 1, 8)
u,v = np.meshgrid(u,v)
u = u.flatten()
v = v.flatten()

tp = 1 + 0.5*v*np.cos(u/2.)
x = tp*np.cos(u)
y = tp*np.sin(u)
z = 0.5*v*np.sin(u/2.)

points2D = np.vstack([u,v]).T
tri = Delaunay(points2D)
simplices = tri.simplices

fig1 = FF.create_trisurf(x=x, y=y, z=z,
                         colormap="Portland",
                         simplices=simplices,
                         title="Mobius Band")
py.iplot(fig1, filename="Mobius-Band")
#Source URL: https://plot.ly/python/trisurf/

How to create a real Möbius band manually

It is easy to create a Möbius band manually from a rectangular strip of paper. One simply needs to twist one end of the strip by 180° and then join the two ends together (see also Starostin & Van Der Heijden, 2007).

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Aion – the Greek God of eternity standing in a celestial Möbius band

Figure 1. The antique mosaic shows a central part of a large floor mosaic, from a Roman villa in Sentinum (now Sassoferrato, in Marche, Italy), ca. 200–250 C.E. The Hellenistic deity named Aion (Greek: Αἰών), the god of time and eternity, is standing inside a celestial sphere (presumably the orb circle encompassing the universe) decorated with zodiac signs, in between a green tree and a bare tree (symbolizing summer and winter, respectively). Sitting in front of him is the mother-earth goddess, Tellus (the Roman counterpart of Gaia) with her four children, who possibly represent the four seasons. Conceptions of “time” play an essential rôle in ancient philosophical schools of thought and consequently in Greek mythology and modern science (subjects which are deeply interwoven).

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Interactive 3-D model of the Möbius band (for closer visual inspection)

You can use the mouse-wheel to zoom within the application.

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Ancient representations of the Möbius band in art across cultures and epochs

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Magician utilising Möbius band on stage

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Art gallery – M.C. Escher

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Further References

Yoon, Z. S., Osuka, A., & Kim, D.. (2009). Möbius aromaticity and antiaromaticity in expanded porphyrins. Nature Chemistry

Plain numerical DOI: 10.1038/nchem.172
DOI URL
directSciHub download

Ajami, D., Oeckler, O., Simon, A., & Herges, R.. (2003). Synthesis of a Möbius aromatic hydrocarbon. Nature

Plain numerical DOI: 10.1038/nature02224
DOI URL
directSciHub download

Chang, C. W., Liu, M., Nam, S., Zhang, S., Liu, Y., Bartal, G., & Zhang, X.. (2010). Optical Möbius symmetry in metamaterials. Physical Review Letters

Plain numerical DOI: 10.1103/PhysRevLett.105.235501
DOI URL
directSciHub download

Fan, Y. Y., Chen, D., Huang, Z. A., Zhu, J., Tung, C. H., Wu, L. Z., & Cong, H.. (2018). An isolable catenane consisting of two Möbius conjugated nanohoops. Nature Communications

Plain numerical DOI: 10.1038/s41467-018-05498-6
DOI URL
directSciHub download

Marchionini, G., Wildemuth, B. M., & Geisler, G.. (2006). The open video digital library: A möbius strip of research and practice. Journal of the American Society for Information Science and Technology

Plain numerical DOI: 10.1002/asi.20336
DOI URL
directSciHub download

Goldstein, R. E., Moffatt, H. K., Pesci, A. I., & Ricca, R. L.. (2010). Soap-film Mobius strip changes topology with a twist singularity. Proceedings of the National Academy of Sciences

Plain numerical DOI: 10.1073/pnas.1015997107
DOI URL
directSciHub download

Walba, D. M., Richards, R. M., & Haltiwanger, R. C.. (1982). Total Synthesis of the First Molecular Möbius Strip. Journal of the American Chemical Society

Plain numerical DOI: 10.1021/ja00375a051
DOI URL
directSciHub download

Cador, O., Gatteschi, D., Sessoli, R., Larsen, F. K., Overgaard, J., Barra, A. L., … Winpenny, R. E. P.. (2004). The magnetic möbius strip: Synthesis, structure, and magnetic studies of odd-numbered antiferromagnetically coupled wheels. Angewandte Chemie – International Edition

Plain numerical DOI: 10.1002/anie.200460211
DOI URL
directSciHub download

Pond, J. M.. (2000). Möbius dual-mode resonators and bandpass filters. IEEE Transactions on Microwave Theory and Techniques

Plain numerical DOI: 10.1109/22.898999
DOI URL
directSciHub download

Leweke, T., Thompson, M. C., & Hourigan, K.. (2009). Motion of a Möbius band in free fall. Journal of Fluids and Structures

Plain numerical DOI: 10.1016/j.jfluidstructs.2009.04.007
DOI URL
directSciHub download

Liu, W. M.. (1997). Is there a Möbius band in closed protein beta-sheets?. Protein Engineering

Cartwright, J. H. E., & González, D. L.. (2016). Möbius Strips Before Möbius: Topological Hints in Ancient Representations. Mathematical Intelligencer

Plain numerical DOI: 10.1007/s00283-016-9631-8
DOI URL
directSciHub download

Todres, R. E.. (2015). Translation of W. Wunderlich’s “On a Developable Möbius Band”. Journal of Elasticity

Plain numerical DOI: 10.1007/s10659-014-9489-y
DOI URL
directSciHub download


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Further Links: https://psilocybin-research.com http://entheogen-science.de