Dialectica Machina The Antagonist of Self—Criticism How can we rethink formal design processes in the age of algorithmic generation—? — Ken Rodenwaldt Final Thesis Prof. Dr. Martin Gessmann Hochschule für Gestaltung Offenbach am Main MatrNr 2590 2 March, 2020
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x.x List of abbreviations AI
Artificial Intelligence
ML
Machine Learning
DNN
Deep Neural Network
KBS
Knowledge-Based System
RC
Radical Constructivism
EE
Evolutionary Epistemology
GEB
Gödel, Escher, Bach
x.x Summary In 1952, John Cage performed a musical piece known as 4’33” (Four minutes and thirty-three seconds). It was a piece that essentially questioned our concept of ‘music’ and was refuted by many critics as ‘non-music’, which in fact it was. During the entire duration of the piece, the performer merely stays seated, not playing the piano for four minutes and thirty-three seconds. It challenged our assumptions on what we consider as acceptable in established western music (Austwick, Twenty Thousand Hertz). His composition — as an artefact — thus serves as a philosophical commentary to question our current values. I chose Cage’s expression as one among many musical analogies to mediate the debate on creativity in our contemporary age; this essay serves as an approach to challenge assumptions and conceptions about artifacts and the creative process of designing an artefact. But why should we even rethink formal design processes? A more expanded agenda, such as that proposed by Anthony Dunne, sees design as “relocating the electronic product beyond a culture of relentless innovation for its own sake, based simply on what is technologically possible and semiologically consumable, to a broader context of critical thinking about its role in everyday life” (Dunne, Hertzian Tales). If design is to have such an expanded agenda, it is important to examine what kind of processes might facilitate this. We could attempt to answer this by firstly eliminating all approximations. A design is not defined by its ‘service’ of creating a product. It is also not exclusively defined by his environment in which it operates. What design essentially suggests is a conscious act of applying an imagined idea to the creator’s perceived reality. Creativity may therefore be seen as the ability to use such an idea to create something meaningful, thus a designer is ultimately left to function as the operator of meaning.
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In 1996, the chess computer Deep Blue was the first to bea the world chess champion Garri Kasparow in a game with regular time control.
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To what extent can ‘meaning’ be defined in today's technological age? Using the principles of algorithmic logic as a method to solving a problem or a class of problems whether it be purely mathematical or mechanical, is nothing novel and can be traced back to the ancient Babylonians 2500 BC [1]. Independent of the Babylonian’s method of arithmetic, most Greeks as well as Egyptians and Chinese mathematics in the 6th century BC, developed an approach to solve a problem by applying methods of geometry, such as the established Euclidean principle [2] — yet the principle of logical thinking can be applied and isomorphically mapped onto both arithmetic as well as geometric universes (Boyer, A History of Mathematics). Based on Walter Benjamin’s seminal essay on "The Works of Art in the Age of its Technological Reproducibility“ I decided to describe our current paradigm as the age of algorithmic generation; a catalyst to a fundamental social change — not in its basic concepts but regarding its application in scientific and technologic disciplines. I specifically chose the words algorithmic generation to describe an age where we are able to technologically implement extremely complex algorithmic principles to enhance operations such as the diverse use of artificial neural networks[3] for medical diagnosis, e-mail spam filtering or real-time compositions in various musical styles.[4] Many current problem-solving solutions rely on such ML (machine learning) approaches, relying on real-world data – with great success. However, ML cannot be applied without requiring an extensive amount of data to train it for its tasks, such as the prediction of rare events. And at the very end of the process, it is the human who will have to evaluate the output and make a final decision based on it (Fill, AAAI). As Scott Hamilton once stated: “The computer might give a collage of results, but the human is still responsible for the appropriation of the result”. Thus a machine does not observe itself and question its context in which it operates. This leads to another fundamental ethical challenge: how can we, then, as operators of “meaning”[5], reduce our own bias in collecting meaningful data as well as deciding the meaning of the outcome that it provides us with? This requires an intensive look into one’s self-awareness in his environment by forming critical questions to one’s current set of values in a system of seemingly arbitrary values. It is the mysteriously isomor-
1
The earliest written records indicate the Egyptians and Babylonians used all the elementary arithmetic operations as early as 2000 BC.
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Euclid was the founder of rigor mathematics and wrote of the most enduring mathematical works of all time: the ‘Elements’.
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A deep learning computing system vaguely inspired by the biological neural networks that constitute animal brains.
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Composition in a musical style is referred to a production rather than an intended creative composition
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Meaning in terms of what we value inwardly
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phic connection between the two concepts of creativity[6] and self-awareness that I wish to unravel in order to, first of all, understand myself and secondly to understand my role as someone who enjoys dealing with the subject of creativity, both theoretically and practically. In an attempt to maintain a clear and precise discussion on this topic, I chose among many two of the most profound philosophical approaches on this question of creativity and self-awareness; the radical constructivist (RC) and the evolutionist’s (EE) approach, which I will also attempt to clarify in the main chapters. It is important to note, that throughout this essay I will use "man“ as an androgynous noun, including both sexes, and "he,“ "his,“ and "him“ as androgynous pronouns including women and men equally in their scope. This decision has neither social nor political connotation whatsoever, but rather intends to sustain a flow of reading.
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Creativity as a term to describe the ability to use imagination to create
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Contents Page
Contents Page
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Contents Page
Introduction 12 Background and personal motivation Definition of terms and fundamentals Thesis and goal of this essay
The Associative Mind 22 Objective Reality — EE Frame of Reference — RC
The Formal Mind 36 Design and Automation — EE Paradox and Self-Reference — RC
Conclusion 52 The Conscious Mind
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Chapter 1
Front Side Imagery
Introduction
Data in Record Grooves
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1.1
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Background and personal motivation As a trained designer I am constantly on the search for meaning and purpose in a seemingly vague and complex area of process optimization and automation through application of new technologies. I personally define design as a parallel movement to study the nature of ‘meaning’; to understand how we as operators of meaning can apply our ideas into our physical world, and make it ‘purposeful’. Meaning can be expressed in all kinds of ways and music is such an intimate medium that represents us as humans. Former US President, Jimmy Carter, once inscribed a message on the Voyager Spacecraft for its trip outside the solar system — transporting a golden record:
“This is a present from a small, distant world, a token of our sounds, our science, our images, our music, our thoughts and our feelings. We are attempting to survive our time so we may live into yours.” — Jimmy Carter (June 16, 1977) As a hobby musician, I enjoy dealing with musical composition and the combination of diverse musical methods, ranging from music theoretical approaches to digital sound generation and manipulation. A novel interpretation of musical integration with latest technologies to facilitate interface possibilities is something which has always fascinated me. It is the combination of critical design questions and my interest in music that could help me draw new personal conclusions to our role as ‘creatives’ in this day of age.
1.2
Definition of terms and fundamentals It is important to begin with common terms that will be discussed throughout this dialectic in order to dig deeper into later constellations of meaning and most of all to avoid misunderstandings. The definitions of the following fundamental phenomenon will partially be based on Herbert A. Simon’s statements and ideas in his book “The Sciences of the Artificial” (Simon, p. 1-24, ch. 1).
1.2.1
The Natural The world of biological objects and phenomena which are collectively governed by strings of physical laws within an environment, including all animate and inanimate objects that happen to exist independently of human creation
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. It is important to be careful about equating ‘biological’ within
[7]
“Nature.” Cambridge English Dictionary, 2020. dictionary.cambridge.org/de/worterbuch/englisch/nature.
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‘natural’. To make an analogy taken from Simon’s book: “A forest may be a phenomenon of nature; a farm is certainly not” (Simon, p. 1-24, ch. 1). 1.2.2
The Artificial The word ‘artificial’ has a slightly negative connotation that I must dispel before proceeding, as it will be a central aspect of this essay. The Oxford Dictionary defines artificial as “produced by a human being rather than occurring naturally; not genuine; affected; not pertaining to the essence of the matter.“[8] Furthermore it proposes synonymous words such as fake, manmade, imitation, insincere; as antonyms, it lists: natural, genuine, sincere, real, truthful. Approaching the term in a similar fashion to Simon, I will try using ‘artificial’ in as neutral a sense as possible, as meaning man-made as opposed to natural. There are artificial objects that are based on designs found in nature, either loosely or accurately imitating - though not limited to - everything from design to materials. In some contexts there will be a distinction made between ‘artificial’ and ‘synthetic.’
1.2.3
The Complex The central task of a natural science is for the observer to unveil complexity, if correctly viewed, as a mask for simplicity; to find patterns hidden in apparent chaos. A complex system therefore is a high level system composed of many such components within a constellation where they may interact with each other (Rapaport, Philosophy of Computer Science). Examples of complex systems include the ecosystem, organisms, the human brain as well as economic systems and can extend to the mechanisms of the entire known universe. Systems that are considered as ‘complex’ have specific properties that arise from a behaviour of interwoven dependencies, relationships, competitions and other types of interactions. Some distinct properties include nonlinearity, emergence, spontaneous order, adaption, and feedback loops, among many others (Bar-Yam, General Features of Complex Systems).
1.2.4
The Design When we often speak of phenomena generally concerned with possible man-made objects having intended properties, we tend to connect such creation of artifice with engineering and design, while science is concerned with ‘analysis’. Especially in the English language engineering and design is ambiguously used to describe how things ought to be in order to attain goals, and to function (Simon, p. 1-24, ch. 1). Hence a science of the artificial will be closely akin to a science of engineering and design — but not to Design
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“Artificial.” Oxford English Dictionary, Oxford University Press, 2019.
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or the German idea of Gestaltung. Both words in broader sense describe a creative and conscious intervention in an environment with the goal to construct, change or modify a physical object, a process, a situation or an idea (Dorschel, Gestaltung: Zur Ästhetik des Brauchbaren). A more narrow sense of Design and Gestaltung focuses on the aesthetic awareness and expression in regards to function, form, styling etc. 1.2.5
The Artefact — as an interface Artefact is another word for the concept of a tool that is to be used for a specific purpose. Its purpose can be derived from the intersection of its inner and outer environment (for the definition of environment, see section 1.2.6). In other words, in order for an artefact to fulfill its purpose, the surroundings in which it is to operate (outer environment) and the construction of the object (inner environment) have to be equally considered. This way of viewing artifacts can be equated to many things that are not exclusively man-made. It can apply to all things that can be regarded as adapted to some situations; and in particular it applies to the living systems that have evolved through the forces of organic evolution (Simon, p. 6-7).
1.2.6
The Environment — as a mold The environment in which an artefact functions consists of an inner and outer one. The inner environment is the “substance and organisation” of the object, meaning for example its material or the way it is constructed. The outer environment would be the “surroundings in which it operates”, meaning which external influences it will be exposed to. Simon defines this fulfillment of purpose with three terms that stand in relation to each other: the purpose or goal, the character of the artifact, and the environment in which the artifact performs (Simon, p. 5). He demonstrates the three relationships with a clock and a knife, “[...] whether a clock will in fact tell time depends on its internal construction and where it is placed. Whether a knife will cut depends on the material of the blade and the hardness of the substance to which it is aplied” (Simon, p.6).
1.2.7
The Computer — as a thought The computer program and the environment it operates in are directly linked. The more complex the environment is, the more complex the computer program will become, even if it generally operates along simple general laws (Simon, p.21).
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Machine Learning It is seen as a subset of AI and is a computer operative system to perform a specific task without using explicit instructions[9], relying on patterns and inference instead.
1.2.9
Deep Learning A broader part of the family of machine learning methods are known as deep learning. The family of methods are based on artificial neural networks with representation learning. Learning can be supervised, semi-supervised or unsupervised (Soma, par. 4).
1.3
Thesis and goal of this essay This essay essentially discusses the reception of creativity, consciousness and intelligence in regards to modern computing technology. It raises the question of what intelligence is and if there is a distinction between natural or artificial intelligence (Haugeland, Artifical Intelligence: The Very Idea, p. 255). There are cases, where the term artificial can be applied in a specific way. Such an application would be when something is being changed or created deliberately to fit into a certain environment. This concept can be analogously alluded in Simon’s "The Sciences of the Artificial“ who has stated that "if natural phenomena have an air of necessity about them in their subservience to natural law, artificial phenomena have an air of contingency in their malleability by environment“ (Simon, p. 5). The more complex and intricate a system in an equally intricate and complex environment is, the more interesting artificiality becomes. Neither topic, artificiality nor complexity in an environment, can be discussed without the other. Thus the topics of artificiality and complexity are inextricably interwoven. It is important to emphasise that due to the immense possibilities to approach this topic, I will therefore merely touch on key concepts explained through certain perspectives i.e. the natural sciences, number theory, epistemology, design, music and art. The key concepts of this essay are abstractly based on the principles of Knowledge-Based Systems. It consists of two distinct features, the knowledge base itself (acquisition of explicit knowledge)
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The definition "without being explicitly programmed" is often attributed to Arthur Samuel, who coined the term "machine learning" in 1959, but the phrase is not found verbatim in this publication, and may be a paraphrase that appeared later. Confer "Paraphrasing Arthur Samuel (1959), the question is: How can computers learn to solve problems without being explicitly programmed?" in Koza, John R. et al. Automated Design of Both the Topology and Sizing of Analog Electrical Circuits Using Genetic Programming. Artificial Intelligence in Design '96. Springer, Dordrecht. pp. 151–170. doi:10.1007/978-94-009-0279-4_9, 1996.
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and the inference system (method of reasoning) which will then, ideally, lead to new output (Soma, Knowldege Representation). These two features are the key concepts used to describe the essential mechanisms that constitute reasoning; an approach popularized by Immanuel Kant’s “Critique of Pure Reason” i.e. ‘a priori’ and ‘a posteriori’, which I will not attempt to adequately explain along this discourse as it is a topic by itself. [10] After these introductory thoughts on natural and artificial construction, consciousness, evolution of artefacts or certain artefacts, we want to turn to the key question: what fundamentally characterises us as a species capable of ‘creative’ tasks? This thesis aims to draw the reader's attention to the fundamental differences between traditional creative processes and new integrative processes with technology. Throughout this essay I will always introduce certain topics and principles with analogies to music — as a narrative to convey a sense of parallelism to the constructs of the human mind.
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In this vice versa case of a priori being the inference engine and a posteriori being the knowledge base
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Chapter 2
Woodcut showing Pythagoras with bells, a kind of glass harmonica, a monochord and organ pipes in Pythagorean tuning. From Theorica musicae by Franchino Gaffurio, 1492
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The Associative Mind
Listening and enjoying music is what we particularly as a species are capable of. Even before a human is born it is able to hear and react to music, be
Is the acquisition of information the source of creativity?
it spontaneous kicking or a snooze in the mother’s belly. There seems to be a universal appreciation to music across all cultures and ages; it is what we automatically all do at a young age. This is part because of the way our brain operates. A very distinct human characteristic that has not yet been clearly observed in other animals. If we would purely to define the components that constitute creative consciousness, we could do it by comparatively studying ourselves to other animals and categorize the capability of perceiving complex musical structures as a discrete indication of intelligent behaviour, also seen in brain activities of birds (Earp, Frontiers in Evolutionary Neuroscience). A lot of popular pseudoscientific culture has focused its attention on the way music can help or even increase brain activity, especially in early childhood development (Austwick). While there is proof that learning a musical instrument can increase a young child’s IQ minimally, there is no proof of a toddler becoming smarter just from listening to Mozart or Beethoven. The theory states that listening to classical music will give the babies an intellectual head start (Kaviani et al., Cognitive Processing). Some might be practicing the discipline of musical acquisition while others might be doing other activities to enhance their creative intelligence. The first chapter of this essay will discuss the principles and significance of a KBS (Knowledge Base System). It is a term used in computer and information science focusing on the implementation of ontology [11]. In computer science and information science, an ontology is to limit complexity and organize collected data into comprehensible information and knowledge (Sowa, p. 43). Similar to the philosophical idea of ontology that studies concepts directly related to the being such as existence and reality. What ontologies in both information science and philosophy fundamentally have in common is the attempt to answer the question “what is reality?” — or to state the question with the above example “what is music?”. There have been various publications and debates on the topic of ontology engineering [12] and to what degree normative ontology can be applied. If creativity by definition is the ability to use original ideas to create something, then we must firstly understand what an original idea is and how it is created in the first place. If creative ability is defined by the originality of the creator’s idea, and given that ideas are mental projections based on real constructs; can creativity then 11
Knowledge base focuses on ontology rather than implicitly embedded in procedural code, in the way a conventional computer program does (see SOWA, 1995)
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Ontology engineering: relating to or involving the explanation of phenomena in terms of the purpose they serve rather than of the cause by which they arise
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The Flammarion engraving is a wood engraving by an unknown artist that first appeared in Camille Flammarion’s L’atmosphère: météorologie populaire (1888).
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be understood as the quantity and quality of acquiring external information? I will attempt to assess the significance of information perception, storage and association in regards to creativity from two fundamental, yet opposing philosophies; the perspective of a constructivist and an evolutionist. Constructivism or CE (Constructive Epistemology), believes that the world and humanity’s knowledge of it are two different things. The constructivist believes that the world is and will remain beyond our understanding, with our knowledge of it being an artificial construction (Crotty, Meaning and Perspective in the Research Process). Evolutionary epistemology in animals and humans refers to the assumption that due to biological evolution, cognition is partially genetically predetermined, partially adapted to its environment; a non-teleological process of interaction between the organism and its environment (Bradie, Evolutionary Epistemology).
2.1
Objective Reality — Evolutionary Epistemology From a scientific point of view, we consider the blueprints of nature as inherent, self-organizing construction principles (Richard Dawkins speaks metaphorically of the ‘blind watchmaker’). EE (Evolutionary Epistemology) is based on the ontological assumption of such a subject-independent outside world. This enables the statement that the evolution of structures of knowledge corresponds to an ‘objective being’ — but it also postulates that "the existence of the world out there is not provable" (Vollmer, p.5). Therefore: the EE is not a ‘naive realism’, but a ‘hypothetical realism’, i.e. every access to reality is considered hypothetical. This includes two theses by Gerhard Vollmer in his book “Evolutionäre Erkenntnistheorie”: Postulate of Reality “There is a real world, independent of perception and consciousness.” Postulate of Structure “The real World is structured.” It is important to note that the second postulate cannot be inferred from the first, it is therefore additionally declared. According to Karl R. Popper in regards to EE, we do not have organs for forming hypotheses about reality (the brain), hence all organs are themselves hypotheses (hypothesis organ and organ hypothesis) (Popper, p.64). Organs represent certain mechanisms that are subject to the "trial and error" selection process. In this case, even simple cells perform cognitive work in this sense.
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Equating knowledge acquisition with survivability can therefore be seen as problematic. Eva-Marie Engels suggests replacing the concept of knowledge acquisition of EE with the concept of information acquisition (Engels, Was Leistet die Evolutionäre Erkenntnistheorie?), a shift in focus that Erhard Oeser also postulates (Karger, Semiotik, p.62). What a pure information theory attempts to explain in comparison to epistemology remains to be discussed further on with the following case study: 2.1.1
The Next Rembrandt and the Wealth of Data Computers are now capable of ‘high art’. On April 5, 2016 “The Next Rembrandt” was unveiled in Amsterdam: a new picture by the baroque painter Rembrandt Harmenszoon van Rijn, painted almost 350 years after his death. In order to imitate the deceased artist's style, a team of programmers, advertisers, and experts in AI had analyzed at the university of Delft 346 of Rembrandt’s paintings by specially created deep-learning algorithms. Distances between eyes, mouths, noses, ears, hair and collar folds were measured; the relationship of light and dark emulated; the repertoire of motifs surveys; and typical brush strokes specified. Finally, a suitable motif was developed and transferred in the Rembrandt style to a canvas with up to 13 layers of color via 3D print. The result is an artificial Rembrandt.[13] Is that really creativity? Is “The Next Rembrandt” the invention of a creative machine or just a mere imitation? The question is less whether algorithms can be creative, but rather whether what we generally call ‘creative work’ is really creative i.e. innovative, or whether it is not primarily based on the application of acquired abilities. Against this background, one also has to doubt the creativity of “The Next Rembrandt”. In effect, the motiv has been technically composed from individual, computed average Rembrandt face parts. While still impressive as a complex operation, it is not a genuinely creative achievement of AI. If creativity does not lie in the formalization or application of rules, could the machine be triggered by the wealth of data it receives and learns from?
2.1.2
Creativity through Experience and Theory The examples discussed above essentially describe an artificial (deep learning algorithm to recognize a pattern from data) and biological phenomena (organ to perceive and process a pattern from a specific range of frequencies i.e. musical awareness) of knowledge acquisition respectively. “The Next Rembrandt” is fed by the 346 scanned original works of the artist. What we often encounter in digital technology as creativity, are human ideas ab-
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Further impressions and details of this experiment can be found on www.nextrembrandt.com
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macrocosm
mesocosm
microcosm
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stracted and emulated by machines. Here it can be argued that creativity lies not in the formalization or application, but possibly in the wealth of data. This suggests that our ability to apply information might be a creative component, but in itself does not purely justify creativity. Based on Engel’s postulate, sound in this case can be regarded as natural information and music as the product of expression, which can only be triggered by the wealth of information one receives. An intricate interplay between the concept of reality (what is reality?) and the acquisition of knowledge (how can we know about reality?). Here EE claims a ‘partial isomorphism’, i.e. a partial structural correspondence between reality and knowledge (Karger, p.64). However, since adaptation is always selective — we have no organ to perceive magnetism, only hear in a certain frequency range, etc. Vollmer therefore calls this sensory segment of reality the ‘mesocosm’ — the human ‘cognitive niche’ (Vollmer, p.23). In the context of EE, the mesocosm is “that part of the real world which we master by way of sensation and action, perceptually and motorically [...] The mesocosm is, roughly speaking, a world of medium dimensions” (Lorenz, Die Evolution des Denkens, p.51). However, since our theoretical knowledge also includes microcosm (atomic and subatomic world) and macrocosm, we have to differentiate between perceived experience and theoretical knowledge. Werner Heisenberg once mentioned that every atomic model will always be a priori wrong, as long as a model attempts to mediate atomic principles (Heisenberg, Biologie in unserer Zeit). For him, the elementary particles are nothing but "representations of symmetric patterns", thus the smaller the particles, the more we would find ourselves in a purely mathematical world. We can only address and construct models using such ‘mesocosmic building blocks’ (Karger, p.64); otherwise we would not be able to grasp concepts of quantum mechanics and cosmology due to our sensory niche. In this sense, the phenomena of music can also be seen as a mesocosmic building block to describe the nature of sonic waves. In the following section I will attempt to postulate an alternative conclusion on the same topic — the source of creativity in regards to information acquisition — from the perspective of a RC.
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Frame of Reference — Radical Constructivism The EE was primarily designed by biologists, the RC primarily by system theorists [14], psychologists[15], but also by neurophysiologists[16]. Role models are Kant, Berkeley, Piaget (1896-1980), Vico (1668-1744). Recently there have also been efforts to apply constructivism to sociology and empirical literary studies. The RC essentially rejects any subject-object separation. Nothing is discovered, reality is purely constructed, hence only made by ourselves: “we ‘invent’ the world”, is a common phrase (Karger, p.64). This central thesis of RC is reminiscent of Kant's statement that reality — “the thing in itself” — is unrecognizable. Put simply, constructivism claims that the brain is a self-referential or self-organizing system. I will firstly introduce the idea of RC and explain the principle and paradox of a self-referential system later on in this essay (see section 3.2, “The paradox of Self-Referring and Recursive Systems). Although it is coupled to the outside world via sensory organs, the incoming information does not convey anything from the outside world, but merely creates a change of state in the brain. The nervous system does not receive information, as is often said. Rather, it creates a world by determining which configurations of its environment represent perturbations [17] and which changes trigger them in the organism. The popular metaphor of the brain as a computer is therefore not only misleading, according to RC it is simply wrong (Maturana et al., The Tree of Knowledge, p. 185). Such a system therefore functions autonomously within its framework and thus bears a high degree of responsibility for its own reality constructs — here I must add that the responsibility for its ‘constructs’ can only be discussed provided that they are consciously controllable. In the following section, I would like to briefly give an example of what the constructivists state as evidence to their argument.
2.2.1
The Overjustification Effect The famous ‘Blind-Spot’ can be demonstrated by focusing from a specific distance on only one of two adjacent symbols with the opposite eye respectively, hence the left symbol — right eye and vice versa. This local blindness is due to the fact that there are no light sensory cells (suppositories and
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Systems theorists and key advocates of RC like Ernst von Glasersfeld, Heinz von Förster and Gerhard Roth
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Paul Watzlawick being a main proponent and theoretician in communication theory and radical constructivism
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Examples include Humberto R. Maturana and Francisco Varela
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Perturbation defines the state changes in the structure of a system that are triggered by states in its environment (see MATURANA et al., 1987, p. 185)
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rods) at the location of the retina where the nerve fibers converge from the light-sensitive layer of the eye to the optic nerve. If the black circle is projected onto this exact spot, it is no longer visible. It should be noted that this local blindness is not noticeable by a dark spot in the visual field - seeing a dark spot would presuppose being aware of ‘seeing’ it - though in this case it is not perceptible at all. Only an ‘observation of the observation’ reveals the blind spot, as Watzlawick once stated (Watzlawick, Die Erfundene Wirklichkeit). What this peculiar phenomena suggests is that we can not see, that we can’t see. Experiments from psychology often have an explanatory reference to constructivism. These are the so-called noncontingent reward experiments or overjustification effect (Carlson, Psychology: the Science of Behaviour), in which there is no causal relationship between performance and evaluation, but the test subject is not aware of this (Nehrkorn, 6. Sitzung der Humboldt Gesellschaft). To put this into an experimental context, the participants are shown pairs of numbers (for ex. 31 and 80). They have to decide whether the numbers match with a binary ‘right’ or ‘wrong’ answer, without knowing that the pairs of numbers are randomly put together, and the experimenter solely validates the answers on the basis of a half rising Gaussian bell curve. As the ‘correct’ evaluation increases with the continuation of the experiment the subject naturally starts to develop a hypothesis. In the truest sense of the word, the subject has therefore invented a reality that he rightly believes to have found. For the test situation, this reality is free of contradictions, but it does not remotely recognize the actual experimental setup (Nehrkorn). It is not necessary to delve into constructivist thinking to realize that this view inevitably suggests that the conscious being is solely responsible for his mental constructs, knowledge and actions [18]. 2.2.2
Creativity as the product of approval The above examples show that we have an active part in the construction of reality. There can be a distinction made between the sensory constructions (studies on object resemblance are a crucial aspect here) and agreed realities i.e. conventions that are "constructed" intersubjectively. For this reason it is important to make a distinction between artistic, conventional, and natural, physiological, construction. Self-referential constructions are also commonly observed in the social sciences. Richard L. Henshel, for instance, has studied examples of self-fulfilling prophecies, where the accuracy of earlier predictions, themselves influenced by the overjustification effect, impacts upon the accuracy of the
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Noting in reference of section 2.2 that the responsibility for its ‘constructs’ can only be discussed provided that they are consciously controllable.
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Michelle Obama, Microsoft AI
Oprah Winfrey, Amazon AI
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subsequent predictions (Henshel, p. 511). If creativity were to be defined by the acquisition of information, then the agreed categorisation of such information influences the creative output. But could a machine ever be able to distinguish between different conventions of agreed realities if we as ‘operators of meaning’ even face such difficulties?
As AI technologies become ever more ubiquitous, concern has started around the long-term implications of data bias i.e. its ability to amplify bias found in training datasets, and as a result promote marginalization on a social scale (Lloyd, Bias Amplification in Artificial Intelligence Systems). In a recent online article of Business Insider Google has publicly announced to have removed gender labels to “avoid creating or reinforcing unfair bias” (Ghosh, Business Inside; February 16, 2020). It is striking that in the above examples there always seems to be a relatively "external" frame of reference for a reality construct: e.g. In the "blind spot", this external frame of reference is the eye on which the optic nerve attaches directly. In the case of the psychology experiment on the overjustification effect, the external frame is the set up of the experimenters. Furthermore we as operators of meaning are essentially the external frame on which the pertinent and already existing threat of distorted data representation builts on. The radical constructivist would say that this frame is not the external reality on which we test our constructs, but that we also have to construct this frame of reference first: in this sense, in the blind spot example, the physiology of the eye would not be the frame of reference, the frame of reference would be the description (the theory) of the eye. In reference to Boulding: "Ideas can only be compared with ideas, never with external reality" (Glasersfeld, Sprache und Wirklichkeit). EE postulates that access to an external reality can only be hypothetical, but nevertheless access is presumed. In the RC, access must first be created, constructed and invented, but not arbitrarily as RC assumes restrictive conditions (though nothing can be truthfully said about them). In contrast, the EE attempts to determine such conditions, using observational conditions such as the trial and error principles in natural selection (Karger, p.64). After having explained the two key philosophical principles of EE and RC, I will attempt to introduce the formal and structural principles which set the conditions of EE and RC i.e. the formal logic of evolution (trial and error) and recursion (self-reference). This will take us one step deeper into the mechanisms of our mind and nature — ultimately proposing the question whether creativity can be mechanically defined.
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Principle of fractals visually demonstrated through the Sierpinski Triangle; a tree diagram where each branch has three branches. This principle of recursion can also be exemplified in Mozart’s music, the Adagio of his String Quintet.
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Recursion, simply put, is a formal principle defining the act of repetition. In music, the recursive principle can be observed in fugues. Like a canon,
Can creativity be demonstrated within a formal system?
the fugue consists of multiple scores. The difference between a fugue and a canon is the variety the scores within a fugue can have. While the canon consists of the same melody being performed over and over again, in fugue that melody is altered with each new score that is being produced allowing for more emotional and artistic expression. Given an example of J. S. Bach, "Little Fugue in G Minor”[19], a fugue always starts with a single voice singing its theme. Though fugues have the distinct property that each of their voices is a piece of music in itself; and thus a fugue might be thought of as a collection of several distinct pieces of music, all based on one single theme, and all played simultaneously. As a whole, these altered melodies will create a complicated but in itself harmonized soundscape with the result that the listener can choose between focusing on one individual score or the entirety of it. “The listener can’t quite make himself listen to both ways at once, but it is up to him (or his subconscious) to decide whether it should be perceived as a unit, or as a collection of independent parts[20], all of which harmonize. Nevertheless each of these individually meaningful lines fuses with the other in a highly nonrandom way, to make a graceful totality. The art of writing a beautiful fugues lies precisely in this [creative] ability, to manufacture several different lines, each one of which gives the illusion of having been written for its own beauty, and yet which when taken together form a whole, which a fugue as a whole, and hearing its component voices, is a particular example of a very general dichotomy, which applies to many kinds of structures built up from lower levels.” — Douglas R. Hofstadter (1979, ch. 3, 2. ed. 1999) Principles of recursion is one five fundamental tools of creative thinking according to Hofstadter, the others being the principles of paradox, infinity, isomorphism and rules of inference. I have and will partially allude some of the five concepts but will not delve deeper into them for the sake of maintaining continuity in the discussion of my thesis. Recursion is a particular formal set of instructions that repeats itself until it reaches a final state. Neo-Darwinism or EE teaches this set of instruction as a ground principle for chance and selection - and I emphasize that recursion is one principle in a set of many others that constitute evolutionary processes. In addition, I would just like to also briefly note that many people find it difficult to recognize “coincidence”
19
Link to video visually describing the recursive structure of Bach’s “Little Fugue in G Minor” Smey, Dave, director. J. S. Bach, "Little" Fugue in G Minor, BWV 578. J. S. Bach, "Little" Fugue in G Minor, BWV 578, Youtube, 2015, www.youtube.com/watch?v=MslQU-wwqxc.
20
Independent meaning that each part seems to make sense by itself
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Operating System, Recursive VNC trick, Red Hat 8.0.94, KDE 3.1
M.C. Escher “Swans”, Wood engraving 1956
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as an element of evolution, since it has produced such perfect “optimized” organisms etc. Perhaps the reason for this is that we are used to having maximum control over our designs; Construction then means that in principle we can control or comprehend every operation that we carry out with construction elements or building blocks. Comprehension means that someone with a repertoire of building blocks performs step-by-step operations that another with a similar repertoire of building blocks imitates or simulates. As a rule, man thus proceeds ‘purposefully’ with a construction, i.e. he has a certain “idea" represented as a goal. He then mentally builds a method to realize his goal e.g. if he wants to build a house etc. Can creativity therefore be found within intelligent design of a formal system? Can creativity be mechanized? And if yes, does that kill creativity, making the ‘mechanization of creativity’ an oxymoron? Almost, but not really as according to Hofstadter. He states that creativity is “the essence of that which is not mechanical” (Hofstadter, Gödel, Escher, Bach, p.673). In other words, it is the absence of anything mechanical, yet the pure act of creativity must be to some degree mechanical which I will further allude with examples in this chapter. On the contrary, there is something unmechanical in flexible programs such as in specific neural nets algorithms that can also autonomously abstract design rules from data trove, as with “Chef Watson” or “Jukedeck” (D’Andrea et al., Machines an Robots, p. 201). “[Complex algorithms] may not constitute the essence of creativity, but when programmes cease to be transparent to their creators, then the approach to creativity has begun.” — Douglas R. Hofstadter (1979, 2. ed. 1999)
3.1
Design and Automation — Evolutionary Epistemology A recent thought leadership panel at the Autodesk University on ML has gathered multiple experts
[21]
discussing the implications of ML as a tool
for enhancing productivity. They have come to the conclusion that Machine Learning can act as a tool for a partnership or an opportunity for a dialogue to define a problem. “The tools themselves are becoming the limiting factor for humans. The creativity of people is harmed by the fact that these tools were [originally] designed for very dif-
21
Experts including Bruco Blaho, Francesco Iorio, Scott Hamilton, Scott Ruppert
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AI generated floor plans and styles with machine learning programm developed at Harvard.
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ferent manufacturing methods that have surpassed their capabilities. […] We need to think about methods for people to exploit these materials or technology. There needs to be a leap forward that changes how we interact with these systems. The leap consists mainly in taking these design tools not as ideal ‘drawing boards’ but to have a dialogue, a partnership; not to replace but enhance the capabilities and biases.” — Francesco “Frio” Iorio [22] According to Lorio, the goal should be to create a system that reduces our biases and limitations, to get a deeper understanding of the problems that we have to solve, rather than using “pure” design as the expression of a solution. The design of an AI should be a means to an end, an end where the output is new information (Fill). Generative design could shift one's thinking — from thinking all the way into the solution into thinking his way into the problem. With such a tool, one might therefore not be expressing a solution according to a rigorous plan based on experience or applied theory, but rather use ML to define the problem which needs solving, in a similar fashion that a general computing system can help you. The purpose of those tools is not to present an ideal solution, but potentially provide deeper insights. Thus it represents only a fraction of the thinking, nevertheless it expands creativity as one can focus on the bigger picture rather than the details. Iorio states that ML tools are “in fact not keeping up with the creativity of the mind” (Autodesk University, Depate on Generative Design), though AI and ML technology has its potential to converge. From an EE standpoint that advocates the principles of optimization through adaptation and inheritance, our relationship with such a technology can be regarded as a discussion of a problem between man, his team and his virtual team. 3.1.1
Evolvable Hardware Design Evolutionary hardware development was first established by Adrian Thompson in 1996 with his evolvable circuit board. The specifics of this experiment will be explained in the next chapter 3.2.1 regarding the implications of the outcome. This chapter firstly focuses on the principles of evolvable hardware design. Evolvable hardware combines a number of features such as autonomous systems, evolutionary computation, fault tolerance and reconfigurable hardware. It uses each of the features to adapt its hardware in the same way humans and animals have evolved, through mutation and inheritance (Yao, Evolvable Systems, p. 55). For a particular problem random
22
Francesco Lorio is a research scientist and director of Computational Science Group at Autodesk Research
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designs are developed, tested, and the best results crossed with one another in order to produce new designs, and so forth. This schema is repeated until no improvement can be detected anymore. The distinct function of evolvable hardware is the ability to autonomously adapt and thus optimize itself, and has been the focus point of some researchers since the early 2000s (Edwards, New Electronics, 2015). Evolvable hardware may therefore make more sense at a higher level of abstraction, using reconfiguration of more complex electronic building blocks than transistors, passives or logic gates. In 1999, Howard Abelson, working at MIT, developed the idea of the amorphous computer. This is based on a large array of identical microprocessors connected wirelessly, rather than through dedicated mesh networks, to form a network of parallel processors able to adapt to changes. The idea has been revived in recent years as a possible method for dealing with the higher likelihood of failures in nanometre technologies. Evolutionary algorithms could find alternative networks of processors if some key elements fail (Edwards). 3.1.2
Creativity emerging from automation According to Ge Wang, everything which can be automated should be automated, but it is the ‘should' that postulates a question of meaning. It has long been the consensus of technological utopians that computers and robots would soon free us all from all cumbersome routine chores and take on all formalizable and repetitive tasks. Especially call center employees, tailors, and tax consultants would be replaced by automation and artificial intelligence. Humans would mostly be left with “creative” activities as we build a machine with a set of instructions that repeats until it reaches an end.[23] Could a machine ever take over a ‘creative’ activity and if yes where does creativity start to emerge from? Or could the evolving technology also change the way we define ‘creativity’? In this way “the shaping of technology could also reflect our values as human beings” (Wang, Artful Design); a mirror displaying our reflection. Recent years have indicated that the simulation of the evolutionary principles has often proven to be the more verifiable theory compared to the theory of ‘purposeful’ construction. Ingo Rechenberg from the TU Berlin was able to demonstrate in 1964 that it was intentionally or computationally impossible to find a streamlined body that shows as little wall friction as possible for the largest possible surface. Starting from naturally favorable streamlined bodies (fish, birds, etc.), as in evolution, it gradually applied random changes
23
According to the 2013 Oxford study “Future of Employment”
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Narciss art installation by Christian Mio Loclair, State Studios. An observation of an artificial intelligence whose only purpose is to investigate itself; a synthetic model of self-awareness.
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and selection according to the principle of minimal resistance until it found an ideal form after hundreds of steps “without thinking” (teleology - Teleonomy dispute would be debatable here) (Karger, p.61).
3.2
Paradox and Self-Reference — Radical Constructivism The problem which remains in the principle of any automation is the always failing attempt at observing one’s own observation. Paradoxes, however, cannot be processed by formal digital technology, they lead to a process breakdown. Self-reflection would be a bug (D’Andrea). In light of that, it is interesting to her how Samuel himself feels about the issue of computers and originality. The following extracts are taken from a rebuttal by Samuel, written in 1960, to an article by Norbert Wiener:
“It is my conviction that machines cannot possess [creativity] in the sense implied by Wiener in his thesis “machines can and do transcend some of the limitations of their designers, and that in doing so they may be both effective and dangerous…” … A machine is not a genie, it does not […] possess a will, and, Wiener to the contrary, nothing comes out which has not been put in, barring, of course, an infrequent case of malfunctioning… The intentions which the machine seems to manifest are the intentions of the human programmer, as specified in advance, or they are subsidiary intentions derived from these, following rules specified by the programmer. We can even anticipate higher levels of abstraction […] in which the program [besides modifying subsidiary intentions] will also modify the rules and modify the ways in which it modifies the rules and so on. However, and this is important, the machine will not and cannot do any of these things until it has been instructed as to how to proceed. There is and logically there must always remain a complete [gap] between (i) any ultimate extension and elaboration in this process of carrying out man’s wishes and (ii) the development within the machine of a will of its own. To believe otherwise is either to believe in magic or to believe that the existence of man’s will is an illusion and that man’s actions are as mechanical as the machine’s.” [24] This brings me to the moral of automation: the Samuel argument doesn’t state the differences between people and machines after all. He implies that any automation is essentially some form of simulation, and that behind such mechanisms there has to be either an infinite regress or worse, a closed loop. How then can a simulation ever tell us anything novel? There is
24
Extract mentioned in The Sciences of the Artificial, by Herbert A. Simon, 3rd ed., MIT Press, 1996
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a conceptual parallelism between two assertions about computers and automation that is assessed in Simon’s “The Sciences of the Artificial” (Simon, p.14):
1.
An [automation] is no better than the assumptions built into it.
2.
A computer can do only what it is programmed to do.
If we change the parameters of Simon’s assertions from computers to humans, what would be the result? It is not surprising that a lot of the arguments about the moral of computers and automation are reflected in the way humans justify certain behavioural characteristics in themselves. Examples are plenty, such as someone being stuck in their way of behaviour due to their upbringing (no better than the assumptions built into it) or that someone can only do what he or she has been taught to do (can do only what it is programmed to do). With a computer, it is the programmer who decides the parameters of the automation. With humanity it is the society that dictates its development, be it genealogical or cultural (Hofstadter, p.685). 3.2.1
Adrian Thompson’s Circuit Board Does technology really have to understand the problem in order to solve it? The computer scientist Adrian Thompson tried to disprove this already in 1996 [25]. In an experiment he wanted to test whether a given software would be able to autonomously develop a circuit capable of distinguishing two tones of different frequency. To do so he let the algorithm continuously reconnect a grid field of 100 switch elements, until a functioning diagram — as minimalist as possible — emerged. The experiment succeeded. His result was even more slimmed-down than any human design. Thompson’s computer-generated design required only forty switch elements. What seemed especially paradoxical was that part of the wiring was not connected to the electric circuit. And yet it was vital for the functioning of the switches. Technically that did not make any sense. The computer had found a solution for the problem which was no longer comprehensible to human beings. Only later was it proven that tiny electromagnetic reciprocal effects between the conducting and disconnected components had made the circuit operative in the first place.
25
Thompson, Adrian: An evolved circuit, intrinsic in silicon, entwined with physics. In: Evolvable Systems: From Biology to Hardware. Tsukuba 1996, pp 390-405. http://citeseerx.ist.psu.edu/ viewdoc/download?doi=10.11.50.9691&rep=rep1&type=pdf
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The ancient symbol Ouroboros, a dragon that continually consumes itself, denotes self-reference
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So even without insight creative solutions can be found for real problems. Just as in biological evolution, creativity here is not based on an intelligent analysis of the problem, but on the principle of trial and error.[26] Current research efforts in artificial creativity demonstrate that “intelligent design” must not always be intelligent in the means of being aware of its intelligence. Evolution does not need to know “intelligent design” either in biology or in technology. Sole evolutionary hardware development effectively produces autonomous ideas, which do not, however, emerge from insight, but through trial and error. This form of creativity is more radical and efficient than its human counterpart, but it also has its limits. Technology lacks a reality check. It cannot verify whether a given result is the best feasible solution or simply an evolutionary dead end. Researchers call this the difference between a ‘local’ and a ‘global’ maximum (D’Andrea). Here the problem of validity in the search of true meaning or context is again implied with the accessibility to the external frame of reality. 3.2.2
Paradox of the principle of propositional logic to preserve truth As constructivist Roth says: "The brain is [...] not an information-taking system, but an information-generating system" (Roth, p. 14).. This statement shares a conceptual parallel to solipsism, in spite of its attempt to differentiate itself from the latter. According to RC, the cognitive organ is self-maintaining, self-reproducible, self-referential, and often claimed to behave recursively. Out of its rigid recursive operations emerges a sense of self-confidence — similarly comparable with the self-confidence of programming language.
"We create self-awareness through self-observation. We create descriptions of ourselves (representations), and by interacting with our descriptions, we can describe ourselves as describing ourselves in an endless recursive process." — Humberto R. Maturana (1985) Previous examples of recursive processes include Peirce’s ‘map on the map, on which the map is also marked on the map, etc.’ and Gotthard Günther’s ‘the bottomlessness of the ego’, who introduced the idea that self-referentiality and possible recursion are conditions of self-constitution. If this rigid self-referencing system is self-confident in that it relies on itself, how did this recursive mechanisation develop into some conscious entity that both claims and questions itself?
26
To this day, Charles Darwin’s theory has to be defended against the claim that creation is too creative and innovative to have created itself.
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Returning to Hofstadter’s attempt on explaining the construct of consciousness (Hofstadter, p. 692) — of that which recursion represents merely one of many tools of thinking. The brain can therefore also work in a self-referential manner, yet this does not mean that it does so exclusively and thus is also able to refer to anything else in an implicit manner. Erhard Öser, an Austrian philosopher of science, opposes Roth and Maturana by arguing that the brain is indeed a self-referential and autopoietic system, and yet the brain can still produce whole worlds with almost complete absence of sensorimotor inputs (examples include divers, astronauts, and other situations under extreme conditions). The brain requires at least a smallest fraction of a scanned outside world for this construction. As Öser mentioned in his book “Psychozoikum” (1987): "Despite Maturana's objections, the brain [...] is an information system" (Ösler et al., p.121).
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Despite the many disputes between the RC and the EE regarding true awareness — and there are still a few that need to be discussed, though not in the
Finding meaning within beauty, simplicity and harmony
scope of this dialectic essay — it is exactly their connection which gives rise to the problem of representing true reality. I quote an advocate of RC furthermore: "The logical properties of invariance [27] and change are the properties of representations. If this is ignored, paradoxes arise" (Foerster, Sicht und Einsicht). It is the inextricable interaction — so it seems — between the perception of some outside information and our self-preserving mind to conjure or create meaning out of meaninglessness — despite not being able to define meaning outside our frame of reference. In my attempt to explain a brief summary of some synthesis from this entire discussion: the mind is subject to itself (RC, self-referential and autopoietic system) — yet triggered by unperceivable things that seemingly emerge randomly (EE, undefined outside world evolving without ‘thinking’) — which the mind as a result then creates some meaning out of. Creative actions thus appear to include a component of randomness, giving rise to the assumption that the creative act cannot be done with some kind of randomness involved (Hofstadter, p.641). Even this path of randomness could be programmed, therefore neither pure randomness or pure logic cannot be the distinct form of creativity, but maybe serve as symbiotic components for a dialogue to potentially evoke it. Hence the question is less whether algorithms or mechanisms of our brain can be creative, but rather whether what we generally call “creative work” is really creative, i.e. innovative, or whether it is not primarily based on the application of acquired abilities. Perhaps what differentiates highly creative ideas from ordinary ones is some combined sense of beauty, simplicity, and harmony (Hofstadter, p.641). Whilst beauty and simplicity are a bit more difficult to define with their ambiguity, I will try to explain harmony with a “meta-analogy”. The idea is simple: superficially similar ideas are often not deeply related; and deeply related ideas often seem disparate on a superficial level. The analogy to chords is natural: physical close notes are harmonically distant (e.g. notes E-F-G).; and harmonically close notes are physically distant (e.g. notes G-E-B). Ideas that share a conceptual skeleton resonate in a sort of conceptual analogue to harmony (Hofstadter, p.658).
27
The term “invariant” varies depending on usage in different fields such as mathematics, computer science, linguistics and music, but suggest a similar definition in regards to its function: something that is unaltered under or by a transformation
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Perhaps self-awareness can only occur through the ability to reflect upon yourself among ‘things’ and that such reflection and contemplation is the perception of beauty, simplicity and harmony — which leads to creativity and ultimately defines us as humans. To end this synthesis with a final musical analogy: “When I hear what we call music, it seems to be that someone is talking and talking about his feelings or about his ideas of relationships, but when I hear traffic, the sound of traffic here on Sixth Avenue, I don’t have the feeling that anyone is talking. I have the feeling that sound is acting, and I love the activity of sound. What it does is it gets louder and quieter and it gets higher and lower and it gets longer and shorter. It does all those things, and I’m completely satisfied with that. I don’t need sound to talk to me. We don’t see much difference between time and space. We don’t know where one begins and the other stops, so that most of the arts we think of as being in time and most of the arts we think of as being in space. People expect listening to be more than listening and sometimes they speak of ‘inner-listening’ or the meaning of sound. When I talk about music it finally comes to people’s minds that I’m talking about sound that doesn’t mean anything as it is just outer and not inner, and they say “you mean it’s just sounds?”, thinking that for something to just be a sound is to be useless...whereas I love sounds, just as they are and I have absolutely no need for them to be anything more than what they are. I don’t want them to be psychological. I don’t want a sound to pretend that it’s a bucket...or that it’s a president...or that it’s in love with another sound. I just want it to be a sound. An I’m not so stupid either. There was a German philosopher who is very well known, Immanuel Kant, and he said there are two things that don’t have to mean anything. One is music and the other is laughter.” — John Cage (November 16, 1989)
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Digital Images Baldwin, Eric. “AI Creates Generative Floor Plans and Styles with Machine Learning at Harvard.” ArchDaily, Harvard, 17 Mar. 2020, www.archdaily.com/918471/ ai-creates-generative-floor-plans-and-styles-with-machine-learning-at-harvard. Buolamwini, Joy. “Algorithmic Justice League.” Times, Times, 7 Feb. 2019, time. com/5520558/artificial-intelligence-racial-gender-bias/. Case, John. “Machine Self-Reference.” EECIS, 29 May 2013, www.eecis.udel. edu/~case/self-ref.html. “Deep Blue Supercomputer.” Ibm Research/Science Photo Library, IBM, 16 Sept. 2018, fineartamerica.com/featured/deep-blue-supercomputer-ibm-researchscience-photo-library.html. Escher, MC. “Swan.” Yavneh-Raleigh, Yavneh-Raleigh, 23 May 2015, www. yavneh-raleigh.org/counting-the-omer/today-is-twenty-days-of-the-omertwo-weeks-and-six-days. Fedoryński, Jacek. “Recursion.” Ethan Hein Blog, Ethan Hein, 30 Oct. 2011, www. ethanhein.com/wp/2011/what-are-the-main-ideas-and-highlights-of-godelescher-bach/. Flammarion, Camille. “L’Atmosphère: Météorologie Populaire.” Wikipedia, Digital Library Gallica, 10 Nov. 2010, de.wikipedia.org/wiki/Flammarions_Holzstich#/ media/Datei:Flammarion.jpg. Gaffurio, Franchino. “Theorica Musicae, 1492.” Wikipedia, Digitalen Bibliothek Gallica, 16 Mar. 2016, de.m.wikipedia.org/wiki/Datei:Gaffurio_Pythagoras.png. Harrison, Robert. “The Next Rembrandt.” Medium, J. Walter Thompson Amsterdam, 24 Jan. 2018, medium.com/@DutchDigital/the-next-rembrandt-bringingthe-old-master-back-to-life-35dfb1653597. “The Ouroboros.” Wikipedia, Bridgeman Art Library Ltd. v. Corel Corporation, 28 May 2003, commons.wikimedia.org/wiki/File:Ouroboros.png. Stringer, Avril. “Principle of Recursion.” 3-D Print Works, 4 June 2014, 3d-printworks.com/blogs/news/let-s-do-it-again-and-again. “Visual Description of the Blind-Spot.” CIS.rit.edu, 2006, www.cis.rit.edu/people/ faculty/montag/vandplite/images/chapter_9/dist.gif. “The Voyager Golden Record.” Carl Sagan Tribute Page, NASA, 5 Sept. 1977, codepen.io/SourceHorse/full/mwoGmN.
Ken Rodenwaldt Final Thesis Prof. Dr. Martin Gessmann Hochschule fĂźr Gestaltung Offenbach am Main MatrNr 2590 2 March, 2020
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